Progress in dynamic simulation of thermal power plants

Progress in Energy and Combustion Science 59 (2016) 79
162

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Progress in Energy and Combustion Science journal homepage: www.elsevier.com/locate/pecs

Progress in dynamic simulation of thermal power plants TagedPD15X XFalah AlobaidD16X X*, D17X XNicolas MertensD18X X, D19X XRalf StarkloffD20X X, D21X XThomas LanzD2X X, D23X XChristian HeinzeD24X X, D25X XBernd EppleD26X X €t Darmstadt, Institute for Energy Systems and Technology, Otto-Berndt-Straße 2, 64287 Darmstadt, Germany TagedPTechnische Universita

TAGEDPA R T I C L E

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Article History: Received 29 March 2016 Accepted 10 November 2016 Available online xxx TagedPKeywords: Dynamic simulation Thermal power generation Flexibility Transient operation Load changes Start-up procedures Flow models Combined-cycle power Coal-fired power Nuclear power Concentrated solar power Geothermal power Municipal waste incineration Thermal desalination

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TAGEDPA B S T R A C T

While the conventional design of thermal power plants is mainly focused on high process efficiency, market requirements increasingly target operating flexibility due to the continuing shift towards renewables. Dynamic simulation is a cost-efficient 0X3D X tool for improving the flexibility of dispatchable power generation in transient operationD1X3 Xsuch as load changes and start-up procedures. Specific applications include the optimisation of control structures, stress assessment for critical components and plant safety analysis in malfunction cases. This work isD2X3 X a comprehensive review of dynamic simulation, its development and application to various thermal power plants. The required mathematical models and various components for description the basic process, automation and electrical systems of thermal power plants are explained with the support of practical example models. The underlying flow models and their fundamental assumptions are discussed, complemented by an overview of commonly used simulation codes. Relevant studies are summarised and placed in context for different thermal power plant technologies: combined-cycle power, coal-fired power, nuclear power, concentrated solar power, geothermal power, municipal waste incineration and thermal desalination. Particular attention is given to those studies that include measurement validation in order to analyse the influence of model simplifications on simulation results. In conclusion, the study highlights current research efforts and future development potential of dynamic simulation in the field of thermal power generation. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Flexible power generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mathematical modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Thermal hydraulic models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1. Mixture flow model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2. Two-fluid model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2.1. Four-equation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2.2. Five-equation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2.3. Six-equation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2.4. Seven-equation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3. Solution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4. Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Process components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1. Connection point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2. Thin-walled tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.1. Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.2. Valve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2.3. Attemperator/desuperheater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Corresponding author:D27X FX alah Alobaid ([email protected]). Tel.: +49 (0) 6151/16 23004; fax: +49 (0) 6151/16 22690.D29X X E-mail address: [email protected] (F. Alobaid), [email protected] (N. Mertens), [email protected] (R. Starkloff), [email protected] (T. Lanz), [email protected] (C. Heinze), [email protected] (B. Epple). http://dx.doi.org/10.1016/j.pecs.2016.11.001 0360-1285/© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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2.3.2.4. Heat exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thick-walled tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3.1. Header. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3.2. Drum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3.3. Separator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3.4. Feedwater storage tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4. Turbomachines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4.1. Compressor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4.2. Fan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4.3. Blower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4.4. Pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4.5. Steam turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4.6. Gas turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5. Additional components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.1. Combustion chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.2. Fluidized bed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.3. Fuel cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.4. Weather. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.5. Mill. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5.6. Flue gas control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Automation system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1. Measurement modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. Analogue modules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2.1. Basic modules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2.2. Static modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2.3. Dynamic modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3. Binary modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3.1. Basic modules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3.2. Advanced modules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4. Signal source modules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.5. Controller modules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.6. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Electrical system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1. Basic modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1.1. Electrical node . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1.2. Electrical line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1.3. Switch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1.4. Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2. Current sources modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2.1. Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2.2. Battery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2.3. Solar photovoltaic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3. DC and AC modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3.1. DC/AC inverter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3.2. AC/DC converter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3.3. AC/AC transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3.4. DC/DC converter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.4. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Combined-cycle power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Load change. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Start-up procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. Optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Additional studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Island operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Compressed-air energy storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3. Integrated gasification combined-cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coal-fired power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Response to disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Start-up procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Flexibility increase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Oxyfuel concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nuclear power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Specific features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1. Basic principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2. Reactor pressure vessel and reactor core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3. Cooling circuits and auxiliary systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3.

3.

4.

5.

19 19 20 20 21 21 21 22 23 23 23 23 24 24 25 25 25 25 26 26 26 27 27 27 27 29 30 31 31 31 32 33 33 34 36 36 36 37 37 37 37 37 38 38 38 38 39 39 40 40 41 44 44 46 48 49 49 50 50 52 53 53 55 56 57 58 58 59

F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79
162

81

Safety analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1. Validation experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2. Statistical accident analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Load cycling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1. Experience with load following . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2. Thermal hydraulic-neutronic instabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concentrated solar power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Specific features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1. Solar field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2. Power block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3. Energy storage and back-up system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Dynamic studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional thermal power technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Geothermal power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Municipal waste incineration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Seawater desalination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion and future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60 60 61 63 63 64 65 66 66 66 69 69 69 70 70 71 77 78 79 79

5.2.

6.

7.

8.

Abbreviation AC AFS AIS BFP BPCV BWR CAES CCPP CHP CCS CFB CFD CP CSP DAEs DBA DC DFGD DNI DSG ECCS ECO EVA FG FEL FTL FVM FW GT HP HPIS HRSG HTF IAEA IAM IGCC IGV IP IS ISCC

alternating current auxiliary feedwater system accumulator injection system boiler feed pump bypass control valve boiling water reactor compressed-air energy storage combined-cycle power plant combined heat and power carbon capture and storage circulating fluidized bed computational fluid dynamics circulation pump concentrated solar power differential-algebraic equation systems design basis accident device control, direct current dry flue gas desulfurization direct normal irradiance direct steam generation emergency core cooling system economiser evaporator flue gas following electric load following thermal load finite volume method feedwater gas turbine high pressure high pressure injection system heat recovery steam generator heat transfer fluid international atomic energy agency incidence angle modifier integrated gasification combined-cycle inlet guide vanes intermediate pressure injection system integrated solar combined-cycle

IT ITF LB-LOCA LCOE LHV LOCA LP LPIS LT MCFC MED MPC MSCV MSF NPP PAFC PEM PI PH PT PV PWR RH RO RP RPV SCR SETF SG SH SNCR SOFC ST TES TIT TOC TOT TVC US NRC WENRA WFGD WS

intermediate temperature integral test facility large break loss-of-coolant accident levelised costs of energy lower heating value loss of coolant accidents low pressure low pressure injection system low temperature molten carbonate fuel cell multiple-effect distillation model-predictive control main steam control valve multi-stage flash desalination nuclear power plant phosphoric acid fuel cell proton exchange membrane proportional-integral controller preheater parabolic trough photovoltaic cell pressurized water reactor reheater reverse osmosis recirculation pump reactor pressure vessel selective catalytic reduction separate effect test facility steam generation superheater selective non-catalytic reduction solid oxide fuel cell steam turbine thermal energy storage turbine inlet temperature total organic carbon turbine outlet temperature thermal vapour compression United States nuclear regulatory commission Western European nuclear regulators association wet flue gas desulfurization water/steam

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1. Introduction TagedPThe expansion of intermittent electricity generation, in particular wind power and photovoltaics, can lead to the seemingly paradox situation of negative electricity prices at times of low power demand and/or high renewable power supply. The main reason is D3X X the relative inflexibility of dispatchable power generation such as coal and nuclear power, which send a negative price signal in order to avoid a cost-intensive unit shutdown. Five major approaches to maintain security of supply and to improve flexibility of the future electricity system can be distinguished in general [1]: (i) expansion of highvoltage transmission infrastructure, (ii) enrollment of demand response, (iii) modification to system operations, (iv) large-scale energy storage and (v) flexibly dispatchable power generation. The authors are convinced that the future electricity system will comprise all of these concepts, to varying degrees and with the possible addition of value-adding processes beyond electricity (e.g. powerto-fuels). However, the conceptsD34X X differ in their potential impact, technological maturity and economic viability. The latter aspect is especially important, considering that there is often no direct reimbursement to a market participant for providing flexibility (with the exception of participation in the limited balancing energy market). iTagedP . The adequate addition of high-voltage transmission infrastructure in combination with smart power electronics is essential to accommodate the growing renewable capacity and ensures security of supply. By increasing the number of interconnections between major load centres, the transmission capacity and robustness of the electricity grid can be greatly improved. For sufficient flexibility of the overall system, the grid expansion must be complemented by additional measures. Environmental and political challenges are common causes for the protractedD35X e X xpansion of grid infrastructure. TagedPii. Demand response is the ability of end users to adjust load demand (could be reduce or increase)D36X Xaccording to price signals or dispatch rules. This measure can be applied to mitigate or counteract short-term grid imbalances. TagedPiii. The average forecast errors of regional wind and solar power generation typically range from 3% to 6% one hour-ahead and 6% to 8% a day-ahead (based on rated capacity) [2]. Improved forecasting decreases the uncertainty in residual load, resulting in reduced utilisation of expensive peaking capacity and a cost-effective modification of system operations. Both (ii) and (iii) are support measures under development with the potential to effectively reduce costs associated with the transformation of the electricityD39X sX ystem. TagedPiv. Large-scale energy storage, also called grid-energy storage, can be charged or discharged flexibly to allow for high shares of renewable electricity feed-in. Grid-energy storage is, in theory, ideally suited to balance intermittent power supply and demand. Pumped hydroelectric storage is commonly used, but it is limited to suitable geographical conditions. Other technologies in various stages of development include battery energy storage, flywheel energy storage, compressed air energy storage, power-to-gas and thermal energy storage. Despite recent advances in battery storage driven by the automotive industry, the specific costs of these storage systems still limit their use to small-scale applications and there is currently no economically viable storage technology available for the required order of capacityD40X (X TWh rather than MWh). TagedPv. The most economic option for increasing system flexibility is to improve the existing infrastructure of electricity supply. In many countries without abundant natural resources suitable for large hydro or geothermal energy, power generation is mainly based on thermal power plants (and will continue to do so in the foreseeable future, considering plant lifetimes of up to

TagedP 0 years). The operating flexibility of thermal power plants is 4 limited by technical constraints such as ramp rates and minimum load limit. Existing power plants can be retrofitted with optimised components and control circuits to mitigate these constraints and to meet enhanced flexibility requirements. Highly dispatchable generating units such as combined-cycle power plants and gas engines are also available to replace outdated plants.D41X X TagedPIn this work, the approach of flexibly dispatchable power generation (v) is reviewed based on the scientific literature dedicated to dynamic simulation of thermal power plants. 1.1. Flexible power generation TagedPA thermal power plant ideally operates at steady state design load, but it is also required to operate on so-called off-design load conditions due to the fluctuations of supply and demand as well as the increased penetration of renewable energy sources. In Europe, these requirements translate into new operating challenges that can be divided in three categories. Firstly, higher load gradients for both positive and negative load changes are required. Furthermore, the dynamic of start-up and shut-down procedures should also be optimised in response to a sudden load change in the grid. Secondly, the technical operating range of thermal power plants has to be extended by re-evaluating the minimum load limit. Lower minimal load potentially reduces the number of shut-down/start-up procedures and thus lifetime consumption of thermally stressed components. A complete shut-down is often not an option for combined heat and power generation unless sufficient thermal storage capacity is installed. Thirdly, high efficiency at part load is relevant since the thermal power plants that were originally operated almost continuously at nominal load should now run in load-following operation. Here, a thermo-economic optimisation at different base loads and off-design load conditions is necessary. A thermal power plant that meets these new requirements will have a competitive advantage in the electricity market. TagedPOperating flexibility of thermal power plants is therefore an essential factor for reliable grid stability as well as for economic operation. Dynamic simulation offers an effective toolD42X Xfor optimising the power plant performance and control structures as well as for assessing capabilities and limitations of the system with regard to process, materials, emissions or economics. This implies strong requirements on both model accuracy and efficiency of the numerical solver. Modern simulation programmes provide user interfacesD,43X X solution algorithms and component libraries for full-scale modelling and simulation of the dynamic processes. These simulation codes are based on different thermal hydraulic models that are described with the governing conservation equations for mass, momentum, energy and empirical correlations for friction and heat transfer. For modelling of thermal power plants, different process components such as pipe, heat exchanger, drum and pump etc. are required. In addition to process components, a thermal power plant includes several automation and electrical systems. The accurate description of automation structures and control devices are essential in order to obtain a realisticD4X X dynamic response. The consideration of electrical components in the dynamic simulation is necessary to compute the electrical power consumption and to study malfunction cases with loss of electricity supply. TagedPMost power plant processes are based on the generation of superheated steam at high pressure, driving a steam turbine coupled with an electrical generator. In water/steam evaporator circuits, two-phase flows are generally present. As this flow type is complicated and shows diverse flow patterns, a number of two-phase models with various levels of complexity were proposed in literature. There are typically two categories of two-phase flow models: In the

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TagedPfirst category, the two-phase flow is considered as mixture and treated as single-phase flow with fairly complex thermodynamic properties. The water and steam phases are assumed to be in thermodynamic equilibrium with equal velocity, pressure and temperature. The second category of two-phase flow models treats each phase as a fluid and accordingly, separate sets of conservation equations for gas and liquid phase are formulated. In addition to the conservation equations, adequate constitutive equations and experimental correlations are required. These can be tables for thermodynamic and transport properties or relations for heat transfer coefficients. The classic six-equation version of the two-fluid model is a single pressure model. Here, both phases are in mechanical equilibrium, but not in chemical and thermal equilibrium. The sevenequation flow model considers separate phases and does not assume, by contrast to the six-equation flow model, pressure equilibrium of phases. The five-equation and four-equation versions of the two-fluid model assume mechanical and thermal equilibrium, but not chemical equilibrium. 1.2. Structure TagedPThis review is divided in two main partsD:5X4 X In the first part (Chapter 2), the mathematical background for modelling of thermal power plants is described, including an overview of simulation programmes that are applied to predict the behaviour of these systems in steady state and during transients. The mixture flow model and the twophase fluid models (four-equation, five-equation, six-equation and seven-equation flow model) are explained. Process, automation and electrical components required for the dynamic simulation of thermal power plants are also described, supported by model examples. TagedPThe second part of this manuscript (chapters 3 to 7) is dedicated to the relevant body of literature, focusing on the application of dynamic simulation to specific energy system technologies: combined-cycle power, coal-fired power, nuclear power, concentrated solar power, geothermal power, municipal waste incineration and thermal desalination. Most of these technologies can also supply useful thermal energy for industrial processes, district heating and other applications, increasing the power plant flexibility and decreasing the total fuel consumption. This approach is known as combined heat and power (CHP) and relevant studies are referenced in the correspondingD46X X chapters. The dynamic studies on CHP frequently address the optimal operating strategy for a given use case, which may be selected among following electric load (FEL), following thermal load (FTL) or a specific mixture thereof. TagedPChapter 3 is a survey of publications on dynamic simulation applied to gas-turbine based power plants, with particular regard to combined-cycle power plants. In the field of power generation, combined-cycle power plants (CCCP) are widely recognized for high efficiency, fast start-up capability and comparatively lowD47X X environmental impact. The technology also supports increasing shares of renewable feed-in due to flexible unit dispatch. After a summary of general CCPP developmentD,48X X Section 3.1 introduces the reader to basic plant dynamics by considering parameter variations and load changes. The D49X X studies on simulation and optimisation of CCPP startup procedures are covered in Section 3.2. The start-up transient has a distinct position among operating transients, which is also reflected in the literature. Finally, Section 3.3 is a brief overview of complementary works on dynamic simulation in the broader context of gas-turbine based technology, including numerical studies of compressed-air energy storage and integrated gasification combined-cycle. TagedPChapter 4 gives an overview of publications that investigate the transient operation of coal-fired power plants. With regard to installed capacity, coal-fired power plants are the most important generating units in many countries. Following a short description of the working principle of the coal-fired plant, the dynamic models

83

TagedP re reviewed. Furthermore, the response of the numerical models to a disturbances is discussed, which is a common approach to verify the model performance when operational data is missing. The relevant investigations of start-up procedures, stress in thick-walled components and power plant optimisation are introduced. The finalD50X sX ection of this chapter focuses on oxyfuel coal-fired power plants for carbon capture and storage (CCS). TagedPChapter 5 offers an overview of dynamic process simulation for nuclear power plants (NPPs). For this purpose, the differences between nuclear power plants and conventional thermal power plants are addressed. The chapter gives a description of the unique and thorough validation process that is used in the field of nuclear safety analysis and refers to further studies in that field. In this context, the statistical approach to safety analysis is presented as well. The topic of load-following operation and its challenges regarding nuclear power plants is discussed, including the special issue of neutronic-thermal hydraulic instability.D51X X TagedPChapter 6 is dedicated to concentrated solar power (CSP) technology. CSP is a renewable technology that is characterized by simple integration of energy storage. It uses mirrors, lenses or a combination of both to concentrate solar rays on a receiver, heating a working fluid that directly or indirectly runs a thermodynamic process to generate electricity. Currently, levelised costs of energy (LCOE) are relatively high. However, recent technical improvement and operating experience show potential for efficiency increase, standardisation and cost reduction. The review lists recent studies that were conducted to analyse dynamic behaviour of whole CSP plants and single sub-systems such as solar field, thermal energy storage and power block. Results and scope of these studies are presented and future areas of investigation are derived. TagedPChapter 7 offersD52X X insight into several technologies that are less frequently considered in dynamic studies, namely geothermal power, municipal waste incineration and seawater desalination. Geothermal power plants use heat released from the earth's crust to drive a Rankine cycle. Until now, a little work has been done to explore the dynamic behaviour of these plants. Municipal solid waste incineration is used to significantly decrease waste volume as well as to produce stable and odourless residue. Although municipal waste incineration has been applied commercially for many decades in industrialised countries, the dynamic behaviour has not yet been investigated in the literature. Calculation results for the start-up procedure of a waste incineration plant are shown in this review for the first time. Industrial thermal desalination processes such as multi-stage flash and multiple-effect desalination are very energy-intensive and cost-intensive processes that ensure a stable and sustainable source of drinking water in arid regions with sea access. The chapter includesD53X X an explanation of the working principle of thermal seawater desalination and an overview of numerical studies. TagedPIn the conclusion of this work, the results of the literature review and current developments are summarised. Furthermore, recommendations for further research effort in the field of dynamic simulation of thermal power plants are given. 2. Mathematical modelling TagedPModern thermal power plants have to be designed for maximum efficiency, low emissions and high flexibility with regard to load changes, start-ups and shutdowns. In complementing the experimental works, mathematical models contribute to a better understanding of the processes, their capabilities and limitations and play an important role for increasing the efficiency and flexibility of thermal power plantsD54X.X Generally, design and optimisation of energy systems start with steady state modelling. Here, it is assumed that the power plant operates continuously at its design base load. The steady state models do not require control

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TagedPstructures and are mathematically based on mass, momentum, species and energy balances. Using steady state simulation tools, analyses of the thermodynamic properties of the working fluid, mass and energy flows as well as process efficiency can be conducted for a series of operating points. However, steady state simulation tools do not allow any information about transient operations. The relevant next step is therefore the process analysis with dynamic models during transients, load changes and malfunction cases. Dynamic simulation is preferred for the proposal stage of a power plant project, e.g. to check whether or not the load changes according to specific customer requirements are feasible without unacceptable lifetime consumption in thick-walled components. However, investigation into the dynamic performance of thermal power plants requires detailed information of the process. The inherent complexity of the governing differential conservation equations and the numerical solution methods make the dynamic simulation codes very sophisticated computer software with long development periods. 2.1. Overview TagedPThe first simulation program for thermal power plants dates back to the 1960s. In the early 1970s, a method was developed, in which a water/steam circuit was solved numerically. Here, the circuit was constructed using individual components connected through lines. The main components of the water/steam circuit as well as the connection lines were systematised in code, so the entire circuit can be defined as a sequence of numbers and interpreted by the computer. This representation (selecting from the library and building component by component) has been widely maintained in most simulation programmes since. Based on this methodology, for example, Stamatelopoulo [3] developed in 1995 an in-house code in the frame of a steady state simulation project of thermal power plants. In line with increasing interest on dynamic simulation, Stamatelopoulo and his successors [4] presented a transient simulation program (known as ENBIPRO) based on the finite volume method (FVM), which was further extended by other researchers. Today, modern simulation programmes combine a graphical user interface with detailed models for flow, thermodynamics and heat transfer. The calculations enable rapid assessment of: TagedP TagedP TagedP  TagedP TagedP

New plant design. Process modifications and retrofitting of existing plants. Plant optimisation. Plant security and safety. Operating behaviour at base loads, off-design loads, start-up and shut-down procedures.  TagedP Operating behaviour during malfunctions.

TagedPThe mathematical background of these programmes is based on the balance equations of mass, momentum, species and energy. The complexity of these equations and the required numerical solution algorithms depends on, firstly whether the flow problem is steady state, quasi-steady or dynamic: TagedP In steady state simulation, the time derivatives are eliminated from the conservation equations.  TagedP In dynamic simulation, the time derivatives must be taken into consideration. TagedP In quasi-steady simulation, the time derivative of certain components is not relevant and it can be consequently neglected in the conservation equations, which in return simplifies the system of equations significantly. and secondly on the dimension of flow problem (zero-dimensional, one-dimensional, two-dimensional or three-dimensional):

TagedP In case of zero-dimensional modelling, the local discretisation is not considered. The modelling of thermal power plant components such as heat exchanger, pump, condenser, turbine, etc., results in an algebraic system of equations with the inputs and output parameters of the components (pressure, enthalpy, mass flow rate and concentration). TagedP In case of one-dimensional modelling, the thermal power plant components are discretised between the inlet and outlet along the flow in finite objects, resulting in so
called numerical grid. The partial differential equations obtained are thus approximated by an algebraic system of equations. Finally, the state variables such as temperature, enthalpy and pressure at each discrete location can be determined. TagedP In case of two-dimensional or three-dimensional modelling, local discretisation of the additional coordinates is required, resulting in more detailed and computationally more expensive calculation of the thermal power plant components. TagedPThe knowledge of the steady state data of process components is sufficient in many practical engineering applications. Design calculations at different loads are also conducted with such steady state simulation models. Dynamic simulation allows investigation into the transient behaviour of the entire thermal power plant with its related control structures. Furthermore, the dynamic behaviour after accidents in case of nuclear power plants is of major relevance for safe operation. Despite the advantages that dynamic simulation offers, the programming effort and computational time is considerably higher compared to steady state calculations. TagedPSeveral in-house developed codes and commercial software programmes for steady state and dynamic process simulation of thermal power plants are available, e.g. EBSILON Professional, APROS and ASPEN Plus DYNAMICS. Some programmes provide specialised component libraries for steady state and time-dependent simulation of energy systems, including combined-cycle, simple cycle plants and many others. Other programmes such as MATLAB/SIMULINK offer the researcher an open interface for modelling of non-standard components. Using the non-proprietary object-oriented, equationbased language (MODELICA), complex physical systems with mechanical and control subcomponents can be modelled. Based on MODELICA, different non-commercial and commercial simulation environments are also available such as DYMOLA, JModelica.org and SimulationX. In nuclear technology, dynamic simulation codes calculate the complex multi-phase phenomena in regular operation and in accident situations. Such programmes were developed in many countries that designed nuclear reactors, e.g. RELAP in the US, CATHARE in France and ATHLET in Germany. TagedPThe above mentioned programmes differ in terms of function and areas of application. Since the development of the programs is ongoing, no details about scope of application can be given. The steady state simulation programmes listed in Table 1 and the dynamic simulation programmes listed in Table 2 are the result of long-term development by companies or universities and are usually not freely accessible. The lists are non-exhaustive and restricted to widely known programmes, which are both used in industrial practice and scientific research. The cited references, among others, are matched with the corresponding simulation code and give the reader an orientation for the application fields of each program. The fact that no study is listed for a certain application does not imply that the simulation code is unable to cover it. 2.2. Thermal hydraulic models TagedPThe state of the art in modelling the thermal hydraulic of thermal power plants differs in the fundamental physical models. Here, various formulations (conservative or non-conservative) have been suggested and different numerical methods for compressible and incompressible

F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79
162 Table 1 In-house codes and commercial software programmes for steady state process simulation. Program

Developer

EBSILON Professional

STEAG Commercial https://www.steag-systemtechnologies.com

GATECYCLE

GE Energy Commercial http://www.ge-energy.com

IPSEpro

SimTech Simulation Commercial www.simtechnology.com

KRAWAL

Siemens In-house code http://www.siemens.com

KPRO

Fichtner IT Consulting AG Commercial http://www.kpro-fichtner.de

NOWA

Vienna University of Technology, Institute for Thermodynamic and Energy Conversion In-house code http://www.tuwien.ac.at/tuwien_home

PEPSE, PMAX, etc.

SCIENTECH, Inc. Commercial http://scientech.cwfc.com

PROATES

POWERGEN, Power Technology In-house code http://www.osti.gov/scitech

PROSIM

Endat Ltd Commercial http://www.endat.fi

Thermoflow (GT PRO, GT MASTER, STEAM PRO, THERMOFLEX, etc.)

Thermoflow Commercial http://www.thermoflow.com

VALI

Belsim S.A. Commercial http://www.belsim.com/vali

TagedPflows were investigated. The complexity of the process is explained by the occurrence of several two-phase flow regimes, heat conduction in solid structures, heat transfer between fluid and solid structures, heat and mass transfer between gas and liquid. TagedPThe thermal hydraulic models describe the steady state and dynamic behaviour of a single phase flow or a two-phase flow. Many approaches can be found in the literature in order to model the twophase flow in a thermal power plant such as mixture flow model or two-fluid models, including four-equation, five-equation, six-equation and even seven-equation flow models. In the two-fluid models, two sets of conservation equations are formulated, governing the mass, momentum and energy balance for each phase. This formulation presents considerable difficulty by reason of mathematical complexity and the uncertainty in modelling the interaction between phases at the interphase boundary. Generally, these relations cannot be derived from fundamental physical laws and in most cases are based on empirical assumptions. Solving the resulting differential equations requires higher computational effort and entails parameters that may cause numerical instability, especially due to improper selection of interfacial terms. The difficulties associated with the two-fluid models can be significantly reduced by formulating the two-phase flow in terms of the mixture flow model. Here, three characteristic fluid variables are computed, including local pressure, total mass flux and temperature or enthalpy, represented by three conservation equations (mass, momentum and energy) of the

85

TagedP ixture. Due to its simplicity and applicability to a wide range of m two-phase flow regimes, this model is of considerable relevance since the response of the total mixture and not of each constituent phase is often sufficient. The two-fluid models become, however, more appropriate for special applications since they offer the possibility to include non-equilibrium thermodynamic situations into the formulation. Furthermore, the two-fluid models allow the treatment of the conservation equations and thus the description of phase boundaries in an easier way. This problem can clearly be observed in the mixture flow model that uses many closure models, resulting in approximate solutions and accordingly accuracy restrictions for certain applications. TagedPThe steady state and dynamic behaviour of thermal power plants can also be described using the lumped parameter model that also known as the lumped element model. Here, the description of the physical system is simplified by mean of discrete control volumes (zones or lumps) that are connected each other by means of thermal resistors and capacitors with the assumption of a small temperature difference inside each lump. The equivalent thermal network consists of thermal resistance, thermal capacitances and power losses inside the system. The lumped parameter model can be applied to electrical and mechanical systems, heat transfer processes and thermal hydraulic analysis of conventional thermal power plants including nuclear reactors. The application of the lumped parameter model is suitable, when a simplified formulation of the transient behaviour of the process is required. The advantage of such an approach lies in the reduced computational cost, but it does not offer the same accuracy of more complex numerical methods such as mixture and two-fluid models. The lumped element model is outside the scope of this review and further information can be found for example in [162]. TagedPIn the following sections, the mixture flow model and the different two-fluid models are explained in detail. TagedP2.2.1. Mixture flow model TagedPThe one-dimensional mixture flow model (also known as homogeneous or three-equation flow model) assumes thermodynamic equilibrium between phases. The mixture flow model is represented by three-partial differential equations for mass, momentum and energy that describe the steady state and dynamic behaviour of the characteristic variables. For single phase flow components (e.g. superheater, reheater, turbine section and economiser), the three characteristic fluid variables are the local pressure, the total mass flux and the fluid temperature or the fluid enthalpy for subcooled water or superheated steam. In case of two-phase flow components (e.g. evaporator and condenser), the three variables are complemented by the void fraction. The void fraction can be computed by adding a fourth additive constitutive equation. The latter is a driftflux correlation that describes an adequate relation between different two-phase parameters, e.g. a relation between the steam quality or steam mass flux and steam void fraction. The drift-flux closure laws that allow a slip relation between phases are based on theoretical, empirical or semi-empirical approaches. Several studies have been carried out, resulting in numerous void fraction experiments and different drift-flux correlations, which show significant deviations. Bhagwat and Ghajar [163] evaluated the correlations available in the literature and observed that the tested correlations, although predicting the void fraction with desired accuracy at a certain point, were inaccurate for a broad range of operating conditions. Furthermore, the correlations that predict the void fraction accurately for vertical pipe orientation fail in case of inclined pipe orientations. According to Bhagwat and Ghajar [164], the recommended correlations by the above mentioned studies lose their accuracy at higher pressure, large pipe diameter and for fluids with higher dynamic viscosity than water. In conclusion, there is no closure relation that reliably predicts the void fraction for a suitable range of flow patterns,

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Table 2 Programmes for the dynamic process simulation of thermal power plants. Program

Developer

Application Combined-cycle power

Coal-fired power

Nuclear power

Concentrated Municipal waste solar power incineration

Thermal desalination, Geothermal power

x

[5
10]

[11]

x

x

ATHLET, ATLAS, COCOSYS, etc.

€ r Anlagen- und Reaktorsi- x Gesellschaft fu cherheit (GRS) In-house code http://www.grs.de/en

Advanced Process Simulation Software (APROS)

Technical Research Center of Finland (VTT) Commercial http://www.apros.fi/en

[12
19]

[20
28]

[29,30]

[31
36]

x

[37]

Advanced System for Process Engineering (ASPEN Plus DYNAMICS, ASPEN HYSYS, etc.)

Aspen Technology, Inc. Commercial https://www.aspentech.com

[15,17,38,39]

[40
44]

x

[45,46]

x

[47]

CATHARE

CATHARE team In-house code http://www-cathare.cea.fr

x

x

[48
51]

x

x

x

ClaRa (based on Modelica language)

Das Projekt Dyncap In-house code http://www.claralib.com

x

[52
54]

x

x

x

x

Dynamic Boiler Simulation (DBS)

Vienna University of Technology, Institute for Thermodynamic and Energy Conversion In-house code http://www.tuwien.ac.at/tuwien_home

[55
57]

x

x

x

x

x

Dynamic Network Analysis (DNA)

Technical University of Denmark Thermal Energy, Department of Mechanical Engineering In-house code http://www.dtu.dk/english

[58
61]

[62
64]

x

x

x

x

DYMOLA (based on Modelica language)

mes Dassault Syste Commercial http://www.3ds.com

[65
70]

[71
73]

[74]

[75
83]

x

x

DYNAPLANT

Siemens In-house code http://www.siemens.com

[84
87]

x

x

x

x

x

ENBIPRO

€t Braunschweig, Technische Universita Institute of Energy and Process Systems Engineering In-house code https://www.tu-braunschweig.de/ines/ research/enbipro

[88,89]

[90
93]

x

x

x

x

gPROMS Platform

Process Systems Enterprise Limited Commercial http://www.psenterprise.com

[94,95]

[64,96
98] x

x

x

[99
101]

JModelica.org (based on Modelica language)

Modelon AB Open-source code http://www.jmodelica.org/

[86,102,103]

[104]

x

[105]

x

x

MATHEMATICA

Wolfram Research Commercial https://www.wolfram.com/ mathematica

x

x

x

[106]

x

x

MISTRAL

€t Darmstadt, Technische Universita Department of Energy Systems and Technology In-house code http://www.tu-darmstadt.de

[87,107
109]

x

x

x

x

x

(continued)

F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79
162

87

Table 2 (Continued) Program

Developer

Application Combined-cycle power

Coal-fired power

Nuclear power

Concentrated Municipal waste solar power incineration

Thermal desalination, Geothermal power

[110
113]

[114
118]

[119
121]

[122,123]

[124]

[125
127]

Power Plant Simula- KED GmbH Commercial tor & Designer http://www.ked.de/index.html?&LD1 (PPSD)

[128
130]

[130]

[130]

[129]

x

x

ProTRAX Software

TRAX Energy Solutions Commercial https://energy.traxintl.com

[131
135]

x

x

x

x

x

EASY5, etc.

MSC Software Commercial http://www.mscsoftware.com

[136,137]

[138]

[139]

x

x

x

EcosimPro, PROOSIS, etc.

Empresarios Agrupados A.I.E Commercial http://www.ecosimpro.com

x

[140]

[141]

x

x

x

SimSci, DYNSIM, etc.

Schneider Electric Software Commercial http://software.schneider-electric.com

x

x

x

x

x

[142]

SimulationX

ITI GmbH Commercial https://www.simulationx.com

x

x

x

x

x

x

RELAP

Idaho National Laboratory Commercial http://energy.gov

x

x

[9,143
146] [147,148]

x

x

Transient System Simulation Tool (TRNSYS)

University of Wisconsin Commercial http://sel.me.wisc.edu/trnsys

x

x

x

[149
153]

x

[154]

UniSim Design (acquired by Aspen)

Honeywell Commercial https://www.honeywellprocess.com

[155,156]

[157,158]

x

x

x

x

3-Key Master

Western Services Corporation Commercial https://www.ws-corp.com

x

x

x

[159
161]

x

x

SIMULINK

The MathWorks, Inc. Commercial https://www.mathworks.com

TagedPvoid fractions, diameters, orientations of pipe and particularly fluid properties. TagedPThe dynamic behaviour of three characteristic fluid variables, including the local pressure, the total mass flux and the temperature or the enthalpy is described by three conservation equations of the mixture. TagedPThe mass conservation is expressed as: @r @ðruÞ DS C @z @t TagedPThe momentum conservation is written as:
 @ðruÞ @ ru2 @p C C Fgra C Fwal C f ðval C form C puÞ D¡ @t @z @z

ð2:1Þ

ð2:2Þ

TagedPThe energy conservation is: @ðrh0 Þ @ðruh0 Þ @p C D C qwal @t @z @t

ð2:3Þ

TagedPIn these equations, Fgra is the gravitational acceleration force per volume, Fwal and qwal represent the friction force per volume and the heat flow through walls per volume. The symbols rD5X X and u refer to the density and longitudinal velocity of fluid, respectively. The function f considers the pressure losses due to valve and form frictions as well as the hydrostatic pressure differences and the pressure force of a pump. The total enthalpy h0 is the static enthalpy including the

TagedP inetic energy of the flow. In the mass equation, the source term can k contain additional mass flows into the system, or vice versa. The pressure derivative term appears in the energy equation due to the fact that the total enthalpy is used instead of the internal energy U. @U @h0 @p D ¡ @t @t @t

ð2:4Þ

TagedPIn thick-walled tubes (e.g. drum and feedwater storage tank), the lower part is pure water and the upper part is pure steam. Here, the composition of the outflowing fluid from the tank is determined by the water level and the connected branch height. Generally, the number of connected branches to the tank is not limited. The branch inlet height must, however, be in the height range of the tank. When the water level is below the branch height, the flow consists of steam, while it consists of water if the water level is above the branch height. In between, there is a transition region, where the composition of the leaving fluid is gradually changing from water to steam. TagedPIn case of two-phase systems, the formulation of the mixture flow model is the fundamental physical laws for the conservation of mass, momentum and energy with the movement between the two phase flow using drift-flux correlations. In this model, the four characteristic fluid variables are the local pressure, the total mass flux, the temperature or enthalpy and the void fraction. The mixture

88

F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79
162

TagedPcontinuity equation is expressed as: @ðrm Þ @ðrm um Þ C D Sm @t @z

ð2:5Þ

TagedPThe symbols rm D56X X , um and Sm represent the density, the fluid velocity and the injection or leakage of the mixture, respectively. The momentum equation of the mixture by neglecting the effect of surface tension is written as:   @ðrm um Þ @ðrm u2m Þ @ xrgas rliq 2 C C ð2:6Þ Vgas;j @t @z @z ð1¡xÞrm @p C Fgra C Fwal C f ðval C form C puÞ D¡ @z TagedPHere, the symbol xD57X X is the void fraction of the gas phase, rD58Xgas X and rliq D59X X denote the density of gas and liquid phase, respectively. The symbol Vgas, j is the drift velocity of the gas phase with respect to the volumetric centre of the mixture. The energy equation of the mixture is defined as: @ðrm h0;m Þ @ðrm um h0;m Þ @ C C @z @t @z






 xrgas rliq @p C qwal Vgas;j h0;gas ¡h0;liq D @t rm

ð2:7Þ

TagedPZuber and Findlay [165] proposed the following relation for Vgas, j: Vgas;j D ugas ¡C0 j

ð2:8Þ

where j is the superficial velocity and C0 represents the distribution parameter: C0 D

〈xj〉 〈x〉〈j〉

ð2:9Þ

TagedPThe expression within the angle brackets (〈 〉) indicate the cross-sectional averaged flow properties. The Eq. (2.9) can be written as: Vgas;j D

jgas

x


 ¡ jgas ¡jliq

ð2:10Þ

TagedPThe superficial velocity of gas or liquid is an artificial velocity, determined by assuming that only a given phase is flowing in a certain cross-sectional area. It can be determined as: jk D

V_ k A

ð2:11Þ

TagedPHere, the subscript k is either gas or liquid, V_ k is the volume flow rate of the phase and A is the cross-sectional area. Using drift-flux correlations, the drift velocity and void fraction can be defined, which in turn can be used to obtain the velocity of gas phase ugas and liquid phase uliq as:

rliq V rm gas;j x rgas uliq D um ¡ V 1¡x rm gas;j ugas D um C

ð2:12Þ

with the mixture density rm D60X X :

rm D xrgas C ð1¡xÞrliq

ð2:13Þ

TagedPIn conclusion, the formulation of the homogenous flow model is based on the mixture balance equations. In two-phase flow regions, the relative motion between phases is taken into account by a kinematic constitutive equation. The constitutive equations are, generally, derived by considering interfacial geometry, body-force field, shear stresses and interfacial momentum transfer. Due to its simplicity and applicability to a wide range of two-phase flow, the mixture flow model with drift-flux correlations is often used when the response of the total mixture and not of each constituent phase is required. Therefore, this flow model can be found in most of simulation programmes such as APROS, ASPEN Plus DYNMICS and PPSD. However, one should distinguish between the drift-flux models, where it is assumed that the two-phase flow can be expressed by

TagedPthe momentum equation of the mixture complemented by a kinematic equation specifying the relative motion between phases and the two-fluid models (see the following section), where the velocity of each phase is solved separately. TagedP2.2.2. Two-fluid model TagedPThe two-fluid models, also known as heterogeneous or Euler
Euler flow model, formulate separate conservation equations of mass, momentum and energy for gas and liquid phase. The two-fluid models describe the two-phase flow more accurately than the mixture flow model, but the definition of the interaction terms between phases is difficult. This is due to the fact that the interaction terms cannot be determined from physical laws and are generally obtained from experiments under several artificial assumptions. Here, careful study of the interfacial constitutive equations is required, since the improper selections of these terms may result in numerical instability. Due to the increased number of differential equations and closure relations, the two-fluid models, in contrast to mixture flow model, are related to higher computational cost and are suitable for thermodynamic non-equilibrium applications. Accordingly, the complex and time-consuming two-fluid models are only implemented in few simulation programmes such as APROS and RELAP. TagedPIn the two-fluid models, the velocities and temperatures of each phase are independent, as opposed to the mixture flow model with drift-flux correlations, where there is only one momentum equation and one energy equation of mixture. The four-equation or five-equation model assumes mechanical and thermal equilibrium, but not chemical equilibrium. In the sixequation version of the two-fluid models, the phases are in mechanical equilibrium (they are at the same pressure), but not in chemical and thermal equilibrium. The seven-equation version of the two-fluid model allows the phases to be completely in non-equilibrium state. In the latter, each phase has its own pressure, own velocity and temperature. According to Stuhmiller [166], the seven-equation flow model avoids the non-hyperbolicity of the six-equation flow model that can lead to ill-posed Cauchy problems. Mathematically, a hyperbolic partial differential equation of order n has a well-posed initial value problem for the first n ¡ 1 derivatives, i.e. the Cauchy problem is solved locally for certain initial data of any non-characteristic hypersurface [167]. In all two-fluid models (excepting the seven-equation model), the void fraction is generally determined by the interfacial drag. The latter is calculated based on drift-flux correlations for the distribution parameter and void-weighted area-averaged drift velocity. TagedPNon-condensable gases may affect the dynamic behaviour of thermal power plants, particularly nuclear power plants. The non-condensable gases can be nitrogen, oxygen, helium or hydrogen that are mixed with steam phase or dissolved in liquid phase. These gases can also be transferred from one phase to another. For example, when the nuclear power plant operates at normal operation for long period, the nitrogen that is used to pressurise the hydro-accumulators and other systems is dissolved into the liquid phase. In case of primary circuit breaks, the accumulator water is injected into the primary circuit, causing lower pressure and accordingly the release of dissolved nitrogen from liquid to gas phase [168]. Furthermore, dissolved oxygen, carbon dioxide and other gases in feedwater leads to serious corrosion damages in the steam generator components and should therefore be removed using a deaerator system. Accordingly, the treatment of non-condensable gases has to be taken into account the simulation programmes that are used in safety analysis work. Generally, the modelling of non-condensable gases can be considered in the formulation of the two-fluid models.

F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79
162

TagedPIn the following sections, the different versions of the two-fluid models, including four-equation, five-equation, six-equation and seven-equation flow model are described in detail. T .2.2.1. Four-equation model. TagedPThe four-equation model assumes agedP2 instantaneous phase change and equilibrium of the two phases. This version of two-fluid model contains one mixture mass equation, one mixture energy equation and two momentum equations for gas and liquid phase. Therefore, the phase velocities are independent from each other, in contrast to the mixture flow model with drift-flux correlations that uses one momentum equation for the mixture. The four conservation equations, describing the physical properties of mixture (pressure and temperature) as well as gas and liquid velocities, are expressed as:     @ xrgas C ð1¡xÞrliq @ xrgas ugas C ð1¡xÞrliq uliq C DS ð2:14Þ @t @z   @ðxrgas ugas Þ @ðxrgas u2gas Þ @p @pext C C D Fgra;gas C Fwal;gas C Fliq;gas ¡x @z @z @t @z

ð2:15Þ

@ð1¡xÞrliq u2liq @ð1¡xÞrliq uliq C @t @z

ð2:16Þ

  @p @pext C D Fgra;liq C Fwal;liq C Fgas;liq ¡ð1¡xÞ @z @z

i @h xrgas h0;gas C ð1¡xÞrliq h0;liq @t i @p @h xrgas ugas h0;gas C ð1¡xÞrliq uliq h0;liq D C qwal C @z @t

ð2:17Þ

TagedPIn these equations, the subscripts gas and liq refer to the gas and liquid phase. The forces Fgra, Fwal and Fik account for gravitation, wall friction and interfacial friction per volume, respectively. The subscript ext refers to an external pressure source/sink such as pump and losses due to valve and component-specific friction. The symbol qwal denotes the wall heat flow per volume.

89

TagedP

Ggas;liq C Gliq;gas D 0

ð2:20Þ

TagedPThe gas momentum balance equation is defined as:   @ðxrgas ugas Þ @ðxrgas u2gas Þ @p @pext C D Fgra;gas C Fwal;gas C Fliq;gas ¡x C @z @t @z @z

ð2:21Þ

TagedPThe liquid momentum balance equation is expressed as:     @ ð1¡xÞrliq uliq @ ð1¡xÞrliq u2liq C @t @z   @p @pext C D Fgra;liq C Fwal;liq C Fgas;liq ¡ð1¡xÞ @z @z

ð2:22Þ

TagedPThe term inside the time derivative expresses the temporal change of gas or liquid flow rate. The term inside the space derivative is equal to the changes of flow momentum along the integration axis z. The last term on the right-hand side of the momentum equation describes the influence of pressure on the momentum conservation due to the axial pressure distribution and external pressure forces such as pump or losses due to valve and form friction. TagedPThe energy balance equation for the gas-liquid mixture is written as: i @h xrgas h0;gas C ð1¡xÞrliq h0;liq ð2:23Þ @t i @p @h C xrgas ugas h0;gas C ð1¡xÞrliq uliq h0;liq D C qwal @z @t TagedPIn the second version of the five-equation model (with draft flux correlation), the phase velocities are coupled by a functional relation. The mass and energy conservation equations are solved for gas and liquid separately, while the momentum equation is only solved for gas-liquid mixture. Here, the summation of gas and liquid momentum (Eqs. (2.21) and (2.22)) results in the mixture momentum conservation equation:   @rm um @r u2 @p @pext C C m m D Fgra C Fwal ¡ ð2:24Þ @z @t @z @z

TagedP2.2.2.2. Five-equation model. TagedPIn the five-equation model, mass balances for each phase are required instead of a mass equation of mixture in the four-equation flow model. The five-equation model can either be formulated with thermal equilibrium or with drift-flux correlation. TagedPThe first version of the five-equation model assumes mechanical and thermal equilibrium between phases (pressure and temperature are kept equal), but the phases will generally not be in chemical equilibrium. Here, mass and momentum conservation equations are solved for gas and liquid separately, while the energy equation is only solved for gas-liquid mixture. The five transient, partial differential equations of two-phase flow can be formulated as below. TagedPThe mass balance in an Eulerian form by neglecting the diffusion term is written for the gas phase as:     @ xrgas @ xrgas ugas C D Sgas C Gliq;gas ð2:18Þ @t @z

where rD61XmX is the mixture density and um is the mixture velocity. The drift-flux model describes the superficial velocity of gas ugas as a function of superficial mixture velocity j, void fraction x, drift-flux velocity Vgas, j and distribution parameter C0. TagedPFor the gas phase, the energy balance equation is expressed as:

and for the liquid phase as:   @ ð1¡xÞrliq uliq @ð1¡xÞrliq D Sliq C Ggas;liq C @z @t

TagedP2.2.2.3. Six-equation model. T TagedP he six-equation flow model, in contrast to the four-equation model and the five-equation model, has attracted more attention in the scientific literature. This flow model allows chemical and thermal non equilibrium (velocity and temperature disequilibrium between phases), but assumes mechanical equilibrium (the phases are at the same pressure at all time). The six-equation flow model is suitable for water/steam mixture with dominating mass and heat transfer between phases. It is characterised by separate conservation equations of mass, momentum and

ð2:19Þ

TagedPThe terms Sgas and Sliq represent the injection and leakage of gas and liquid phase. The interfacial mass transfer of gas Gliq,gas describes the evaporation and the interfacial mass transfer of liquid Ggas,liq considers condensation. The sum of interfacial mass transfer of liquid and gas is zero:

@ðxrgas h0;gas Þ @ðxrgas ugas h0;gas Þ @p C Dx C Gh0;liq;gas C qwal;gas C qliq;gas @t @z @t

and for the liquid phase as: i i @h @h ð1¡xÞðrliq h0;liq Þ C ð1¡xÞðrliq uliq h0;liq Þ @t @z @p D ð1¡xÞ ¡Gh0;gas;liq C qwal;liq C qgas;liq @t

ð2:25Þ

ð2:26Þ

TagedPThe heat flows per volume on the right-hand side of the energy equations are defined separately for the heat transfer from wall to gas qwal,gas, wall to liquid qwal,liq and between phases (qliq,gas and qgas,liq).

90

F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79
162

TagedPenergy for gas and liquid phase. However, the formulation of two complete sets of conservation equations presents considerable difficulty by reason of mathematical complexity and modelling uncertainty of the interaction terms between phases. The six-equation model is therefore more prone to numerical instability, in particular -vis the mixture flow model. vis-a TagedPThis section describes the six-equation flow model, as implemented in the advanced process simulation software (APROS) [169]. The solution of the six-equation flow model is based on the onedimensional six partial differential equations, from which the pressure, the void fractions, the phase velocities and enthalpies are solved. As previously mentioned, the application of the six-equation flow model requires the knowledge of mass, momentum and energy transfer between phases. These interaction terms can be determined using the flow parameters and their derivatives coupled with empirical correlations for various gas/liquid flow regimes. If the two-phase flow also includes non-condensable gases, additional conservation equations, describing the behaviour of the non-condensable gases are required. TagedPThe mass conservation equation for phase k is written as: @ðxk rk Þ @ðxk rk uk Þ C D Gik @t @z

ð2:27Þ

TagedPThe momentum conservation equation for phase k is formulated

TagedPcalculated with the Lee-Ryley correlation, if hgas < hgas,sat (vapour is subcooled, condensation) [170]:   1=2 1=3 6ð1¡xÞλgas 2 C 0:74Redro Prgas ð2:33Þ Ki;gas D d2dro cp;gas with the Reynolds number of droplet flow Redro , the Prandtl number of the gas phase Prgas , the thermal conductivity of the gas phase λgas and the heat capacity of the gas phase cp,gas. The droplet diameter ddro that describes the interface size of the two phases has a considerable influence on the calculation of the interfacial heat transfer coefficient as well as the interfacial friction force. It is determined as: 0 1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u s B 8s u C ddro D min@ ; 1:73t  ð2:34Þ A rgas Du2ik g rliq ¡rgas TagedPThe term Duik represents the relative velocity between phases, s D62X X is the surface tension, rgas D63X X and rliq D64X X denote the density of the gas and the liquid, respectively. The droplet Reynolds number is calculated as follows:

Redro D

as: @ðxk rk uk Þ @ðxk rk u2k Þ @p D ¡xk C C Gik uik C Fgra;k C Fwal;k C Fik @z @t @z

ð2:28Þ

C fk ðval C form C puÞ @ðxk rk h0;k Þ @ðxk rk uk h0;k Þ @p C Gik h0;ik C qik C qwal;k C Fik uik C D xk @t @t @z

ð2:29Þ

TagedPThe subscript k refers to l D liquid or g D gas. The subscript ik refers to the interface between two phases and the subscript wal, k denotes the interface between one phase and the wall. The term G is the mass exchange rate between phases. The function fk considers the effects of valves, pumps and friction on the flow. The terms Fand q represent to the average friction force per volume and the heat flow per volume, respectively. In the energy equation, the symbol h0 is the total enthalpy including the kinetic energy. In the six-equation flow model, the wall friction Fwal,k, the interfacial friction Fik, the interfacial heat flow qik and wall heat flow qwal,k are modelled by means of empirical correlations. TagedPThe gravitation force per volume is determined using the following relation: Fgra;k D xk rk g cosQ

ð2:30Þ

where the symbol Q is the inclination angle and g denotes the standard gravity. TagedPThe mass exchange rate (interfacial mass transfer) G is obtained by forming the energy balance for the phase boundary as follows:

Gik D ¡Gki D ¡

qi;liq C qi;gas ¡qwal;i hgas;sat ¡hliq;sat

ð2:31Þ

TagedPThe symbols hgas,sat and hliq,sat represent the saturation enthalpies of gas and liquid. The interfacial heat flow is calculated separately for the liquid and gas phases as: qi;gas D ¡Ki;gas ðhgas ¡hgas;sat Þ qi;liq D ¡Ki;liq ðhliq ¡hliq;sat Þ

ð2:32Þ

TagedPHere, the terms hgas and hliq are the static enthalpies of gas and liquid, respectively. Separate heat transfer correlations are required for evaporation and condensation. The interfacial heat transfer coefficients Ki,gas and Ki,liq depend strongly on both phase flow velocities and void fraction. The interfacial heat transfer coefficient of gas is

ð2:35Þ

TagedPHere, the symbol hD65Xgas X represents the dynamic gas viscosity. If hgas  hgas,sat (evaporation), the interfacial heat transfer coefficient of gas is reduced by multiplying the Eq. (2.33) by the variable a:

aD

TagedPThe energy conservation equation is expressed as:

rgas Duik ddro hgas

1C

1 ðTgas ¡Tgas;sat Þ

ð2:36Þ

1000

TagedPThe interfacial heat transfer coefficient of the liquid phase Ki,liq is calculated during vaporization (hliq > hliq,sat) as follows: Ki;liq D

1:2 ¢ 10¡8 r2liq u2liq ¢ expð4:5xÞ

hliq Prliq

ð2:37Þ

TagedPHere, the term uliq represents liquid phase velocity, Prliq and hliq D6X X are the Prandtl number and the dynamic viscosity of the liquid phase. During condensation (hliq  hliq,sat), the interfacial heat transfer coefficient of liquid increases and is calculated in droplet flow according to Shah correlation [171]: "  0:38 # 0:8 0:4 0:092Redro Prliq λliq 0:8 0:04 pcri 0:79 Ki;liq D ð 1¡x Þ C 3:8x ð 1¡x Þ ð2:38Þ p D2H cp;liq 6ð1¡xÞλliq CE 2 ddro cp;liq TagedPThe symbol DH is the hydraulic diameter of the flow channel, Prliq , λliq and cp,liq represent the Prandtl number, the thermal conductivity and the heat capacity of the liquid phase, respectively. The terms E and x are the rate of entrainment and the liquid concentration in the flow. The critical pressure of the steam/water mixture pcri is equal to 22.06 MPa. TagedPThe wall heat flow qwal.k is determined depending on the heat transfer zone. Generally, three heat transfer zones can be distinguished: wetted wall, dry wall and a transition zone between wetted wall and dry wall. When the wall temperature is lower than the saturation temperature of the liquid, single phase flow is assumed to be in contact with the wall. During this stage, the heat flux rises with increasing wall temperature. If the heat flux has exceeded the critical heat flux, the wall starts drying out and accordingly the heat transfer decreases sharply. The transition zone ranges from the critical heat flux temperature to the minimum film boiling temperature. Above this temperature, the dry wall zone stars. Here, only the gas phase touches the wall and the heat flux begins to increase again. The critical heat flux and

F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79
162

TagedPthe minimum film boiling temperature are used for the selection of the heat transfer zone. TagedPThe heat flux on a wetted wall can be defined according to several correlations, e.g. the Dittus
Boelter correlation for forced convection and the Thom correlation for nucleate boiling [172]. The nucleate boiling starts when the wall temperature exceeds the saturation temperature of the liquid. The heat flow is expressed as follows [173]: 8   λliq  > 0:8 0:4
> case Twal Tliq;sat > > D2 0:023Reliq Prliq Twal ¡Tliq < H qwal;liq D |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} > A > 
h > 2 i > : A C 1971 ¢ exp 2:3 ¢ 10¡7 p Twal ¡Tliq case Twal > Tliq;sat

ð2:39Þ

TagedPIf the wall temperature is higher than the minimum film boiling temperature, the heat transfer correlations of a dry wall are used. The heat flow between a dry wall and the gas phase is calculated according to Bestion as follows [174]:  
 1 2 3 4 hwal ¡hgas qwal;gas D max Kwal;gas ; Kwal;gas ; Kwal;gas ; Kwal;gas ð2:40Þ 1 with the Berenson coefficient for pool boiling Kwal;gas . The heat trans2 3 fer coefficients Kwal;gas and Kwal;gas denote to laminar and turbulent 4 forced convection, while Kwal;gas is the heat transfer coefficient of natural convection. TagedPIn the transition zone between the wetted wall and the dry wall, the heat flow is interpolated between the heat flow of the dry zone and the critical heat flow. The latter is calculated using the Zuber
Griffith correlation for lower mass flow density and the Biasi correlation for higher mass flow density [172]. TagedPThe friction force between the single phase (gas or liquid) and the wall of the flow channel is computed with the relation:

Fwal;k D

¡2fwal;k rk uk juk j DH

ð2:41Þ

T he phase friction coefficients are calculated employing the BlaagedPT sius correlations and laminar formula. The phase friction coefficients are then determined depending on the void fraction, for the gas phase as:

 16 5 5 fwal;gas D max x ; 0:079Re¡0:25 x ð2:42Þ gas Regas and for the liquid phase as:

 
 16
1¡x5 ; 0:079Re¡0:25 1¡x5 fwal;liq D max liq Reliq

ð2:43Þ

T he interfacial friction force Fik (the friction between liquid and agedPT gas phases) is highly relied on the flow regime. Generally, it can be distinguished between stratified and non-stratified flow, including bubbly, annular and droplet flow regimes. Based on the void fraction xD67X X and the rate of entrainment E, the interfacial friction force is formulated as:

Fik D ð1¡EÞ ð½1¡xÞFik;bub C xFik;ann C EFik;dro ð2:44Þ TagedPThe interfacial friction of bubbly flow Fik,bub is determined according to [174]: ! fd Fh0:25 r 29rgas ;liq liq Fik;bub D C xð1¡xÞ3 Duik jDuik j ð2:45Þ dbub DH where Duik represents the relative velocity between phases. The bubble diameter dD68Xbub X can be estimated using the following

91

rTagedP elation:   1¡0:5 rliq ¡rgas 1 dbub D @ 2 C gA f 2s DH 0

with the variable f that depends on the void fraction: 8 < 1:3 C 15:7x3 ð256¡768xÞ case x < 0:25 fD : 17 case x0:25

ð2:46Þ

ð2:47Þ

and the variable fdD69X X that relies on the bubble diameter and the hydraulic diameter of the flow channel:  5   d 5d 6¡ bub ð2:48Þ fd D 2:81 C 34 bub DH DH TagedPThe viscosity factor Fh,liq of the liquid phase is expressed as folD70X X lows: 30:25 2  g rliq ¡rgas 4 5 Fh;liq D hliq ð2:49Þ 2 3

rliq s

TagedPIn the annular flow regime, the interfacial friction force per volume is determined according to [175] as follows: Fik;ann D

0:01½1 C 75ð1¡xÞrgas Duik jDuik j DH

ð2:50Þ

TagedPIn the droplet flow regime, the interfacial friction force per volume is calculated as a function of the droplet diameter dD71Xdro X [174]: Fik;dro D

0:75ð1¡xÞfdro rgas Duik jDuik j

ddro

ð2:51Þ

with the friction coefficient fdro of the droplet flow: fdro D

24 3:6 0:42 C 0:313 C Redro Redro 1 C 4:25 ¢ 104 ¢ Re¡1:16 dro

ð2:52Þ

TagedPFor specific cases, non-condensable gases can be modelled and therefore additional equations may be required. This can be a noncondensable gas in steam phase or a dissolved component in liquid phase. Assuming that non-condensable gas and steam form a homogeneous mixture, then the steam and the non-condensable gas have the same temperature and velocity. Thus, only one additional partial differential equation for the density of the non-condensable gas is required:
 @ðxrNC Þ @ xrNC ugas C D SNC ð2:53Þ @t @z TagedPThe subscript NC refers to the non-condensable gas. The term SNC describes dissolving/release of non-condensable gas in the steam (positive for formation and negative for reduction). TagedPThe dissolved gas in liquid phase is modelled by a mass transport equation of the dissolved gas as: i i @h @h ð1¡xÞrliq XNC C ð1¡xÞrliq uliq XNC;dis D SNC ð2:54Þ @t @z TagedPHere, the symbol XNC,dis is the molar fraction of the dissolved gas. TagedPIt should be mentioned here that the massive existence of noncondensable gas must also be considered in the conservation equations of the gas phase. The total gas enthalpy is then defined as: h0;gas D ð1¡XNC ÞhNC C XNC h0;gas

ð2:55Þ

TagedPFurthermore, the total gas density is calculated as a sum of steam partial density and non-condensable gas partial density. Similar to gas density, the total pressure is the sum of partial

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TagedPpressures. The heat and mass transfers between wall and gas, wall and liquid, gas and liquid must also include additional terms in order to consider the influence of non-condensable gases. TagedP2.2.2.4. Seven-equation model. T TagedP he two-phase six-equation flow model accounts for significant non-equilibrium of phases, but still assumes pressure equilibrium. The seven-equation model (also known as two-pressure flow model) allows the phases to be totally independent of each other. It solves the fluid dynamic interface problems and the two-phase flow system simultaneously, resulting in separate pressure, velocity, temperature and chemical potential for both phases. The model has two sets of mass, momentum and energy conservation equations as well as one volume fraction evolution equation that describes how the fluid composition changes with time. Although the seven-equation flow model is different from the six-equation flow model, many of the closure models in the six-equation flow model can also be implemented here. The closure laws are determined from the flow parameters and their derivatives, coupled with empirical correlations, describing all regimes of the two-phase flow [176]. TagedPIn the process simulation of thermal power plants and especially nuclear power plant, it is actually more common to apply the two-fluid model with pressure equilibrium. The partial-differential equation system related to the pressure equilibrium suffers, however, from improper mathematical properties. The eigenvalues of the Jacobian matrix are not always real and may assume complex values, which in turn lead to an ill-posed Cauchy problem. The seven-equation model systematically allows seven real eigenvalues and is shown to have a wellposed basis of eigenvectors, particularly in the context of compressible two-phase flows. In comparison to models using a pressure equilibrium assumption, the unconditionally hyperbolic property makes the two-pressure seven-equation model very attractive. Recently, this flow model has gained interest for modelling of a wide range of applications, including non-equilibrium dispersive two-fluid flow, free-surface two-fluid flow under the influence of gravity, boiling and flashing of superheated liquid as well as the bubble collapse in light water reactor. However, the seven-equation model also suffers from several difficulties such as the model complexity and the presence of neoconservative products, i.e. the model cannot be equivalently recast in full conservative form. These neoconservative products naturally disappear, when the void fraction is locally constant in space and the model corresponds to two decoupled gas dynamic systems. TagedPThis section describes the seven-equation model, as implemented in the RELAP software [177]. The seven-equation flow model for one-dimensional two-phase flow presents full mechanical and thermodynamic non-equilibrium and consists of the following conservation equations. TagedPThe volume fraction evolution is expressed as:
 pgas ¡pliq @ðxAÞ @ðxuint AÞ GAint A C D A C ð2:56Þ @t @z pint h |fflfflffl{zfflfflffl} |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} Pressure relaxation rate

Interfacial mass transfer

TagedPThe mass balances for gas and liquid phases are formulated as:     @ xrgas A @ xrgas ugas A GAint A ð2:57Þ C D @t @z |fflfflffl{zfflfflffl} Interfacial mass transfer

  @ ð1¡xÞrliq A @t

C

  @ ð1¡xÞrliq uliq A @z

D ¡GAint A

ð2:58Þ

TagedPThe momentum balances for gas and liquid phases are written:      @ xrgas ugas A @ rgas u2gas C pgas xA C @t @z
 @x @A C xpgas C Ab uliq ¡ugas C GAint Auint D pint A |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} @z @z |fflfflfflfflfflfflfflfflfflffl ffl {zfflfflfflfflfflfflfflfflfflffl ffl } |fflfflfflfflffl{zfflfflfflfflffl} |fflfflfflfflffl{zfflfflfflfflffl} Velocity relaxation rate

Pressure term

Volume fraction term

Interfacial mass

transfer ð2:59Þ
2 0:5 1 ¡fwal;gas rgas x ugas ¡uwal ðpAÞ ¡ fint rgas ugas ¡uint Aint |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 2 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}




2

0:5

Wall drag

C

Interfacial viscous drag

xrgas gA |fflfflfflfflffl{zfflfflfflfflffl} Gravitational term

  @ ð1¡xÞrliq uliq A

@





rliq u2liq C pliq ð1¡xÞA



C @z @t @ð1¡xÞ @A C ð1¡xÞpliq D pint A @z @z

2 C Ab ugas ¡uliq ¡GAint Auint ¡fwal;liq rliq ð1¡xÞ uliq ¡uwal ðpAÞ0:5
2 1 ¡ fint rliq uliq ¡uint A0:5 int C ð1¡xÞrliq gA 2 ð2:60Þ TagedPThe energy equations are:      @ xrgas h0;gas A @ rgas h0;gas C pgas xugas A C @t @z 
 @x pint
D pint uint A ¡ A pgas ¡pliq C uint bA uliq ¡ugas @z h |fflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl {zfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl } |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} Velocity relaxation term Volume fraction term

Pressure relaxation term




 p ¡GAint A int ¡h0;gas;int C Kint;gas Tint ¡Tgas A0:5 int rint |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Interfacial heat transfer

ð2:61Þ

Interfacial mass heat transfer

"  2 #0:5
 @A C xKwal;gas Twal ¡Tgas 4pA C C xrgas gugas A @x |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Gravitational term Wall heat transfer

  @ ð1¡xÞrliq h0;liq A

D pint uint A   
 pint
pint A pliq ¡pgas C uint bA ugas ¡uliq ¡GAint A ¡h0;liq;int @t

h

C

   @ rliq h0;liq C pliq ð1¡xÞuliq A @z

rint

@ð1¡xÞ ¡ @z

"  2 #0:5

 @A C Kint;liq Tint ¡Tliq A0:5 C ð 1¡ x ÞK T ¡T p A C 4 wal;liq wal liq int @x

ð2:62Þ

C ð1¡xÞrliq guliq A

TagedPMost of the two-phase nomenclatures used in these sets of equations have already been mentioned. The interfacial mass transfer G is here has the unit kg/m5s, while it is kg/m3s in other two-fluid models. The symbols A and Aint represent the flow cross-sectional area and the specific interfacial area between phases (gas and liquid) per unit volume. The terms pgas and pliq denote the gas pressure and the liquid pressure. The symbol bD72X X refers to the interphase momentum transfer coefficient (resistance coefficient). The terms pint and uint represent the interfacial pressure and the interfacial velocity that exerted on the surface of a two-phase control volume, where the volume fraction gradients exist. These interfacial variables are expressed as:    pgas ¡pliq @ð1¡xÞ uint D uint C sgn ð2:63Þ @z Zgas C Zliq pint D pint C

   Zgas Zliq @ð1¡xÞ
ugas ¡uliq sgn @z Zgas C Zliq

ð2:64Þ

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TagedPwith the phasic relation: Zk D rk ck

ð2:65Þ

TagedPHere, k denotes liquid or gas and the symbol ck is the phasic sound speed. The average values of interfacial pressure and velocity can be defined as follows: uint D

Zgas ugas C Zliq uliq Zgas C Zliq

ð2:66Þ

pint D

Zgas pliq C Zliq pgas Zgas C Zliq

ð2:67Þ

TagedPSimilar to the six-equation flow model, the non-condensable gases can be included in the framework of the seven-equation flow model. The non-condensable gases can be a part of the gas phase or dissolved in the liquid phase. In this case, additional partial differential equations are expressed for non-condensable gases in the gas phase (e.g. nitrogen, helium and hydrogen in the steam) and for dissolved components in the liquid phase (e.g. nitrogen, helium, hydrogen and even boron dissolved in water). TagedP2.2.3. Solution method TagedPIn order to solve the one-dimensional partial differential equations, the finite difference solution method or the finite volume solution method is, generally, applied. The partial differential equations are discretised with respect to space and time and the non-linear terms are linearised. In the space discretisation (integration over the corresponding element length), several discretisation schemes such as the firstorder upwind scheme, the second-order central differencing scheme and the quadratic upwind interpolation are available. For time discretisation, the implicit method is usually employed. The physical properties such as pressure, velocity and enthalpy in the model can finally be calculated using the discretised conservation equations, the parameters for inlet and outlet flows and the thermodynamic properties. TagedPAccording to the software APROS [169] that uses the finite volume solution method to solve the one-dimensional partial differential equations, the solution method includes: TagedP The conservation equations for mass, momentum and energy are applied to the control volumes.  TagedP Single phase flows, homogeneously mixed two phase flows, nonequilibrium separate phase flows as well as laminar, turbulent or critical flows can be considered. Furthermore, radiation, convection and diffusion as well as relevant heat transfer correlations can be applied. Relevant chemical reactions can be assigned to the control volumes in consideration. TagedP Material property libraries can be called with regard to relevant parameters such as pressure, specific enthalpy and mass fraction.  TagedP For valid application range, empirical correlations are used. TagedP The control system element models such as controllers, logical signals and operations as well as sequential automation blocks can be included functionality in the simulation model. TagedP The electrical components such as generator, electric motors, electrical bus bars, network elements and converters can be included functionality in the simulation model. TagedP The resulting one-dimensional partial differential equations are discretised with respect to space. This can be performed using different interpolation methods such as upwind interpolation, linear interpolation, quadratic upwind interpolation and highD73X X order schemes. TagedP For unsteady flows, the time should be discretised, considering relevant state variables and selected time steps. In order to obtain the time dependent solution, initial conditions and boundary conditions that can also depend on time must be defined. TagedP At the end of each time-step and for each control volume, mass errors are checked and non-linearity errors are iteratively corrected.

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TagedP The physical values of working fluid in a control volume such as mass flow, energy flow and separate substance are determined. TagedP The outputs of automation and electrical components are specified. TagedP2.2.4. Comparison TagedPIn the previous sections, different thermal hydraulic models are presented such as the mixture flow model and the two-fluid models. The selection of the appropriate flow model depends on computational effort and desired level of accuracy. Although the mixture flow model entails a less accurate description of two-phase flow phenomena, in many cases it presents the most efficient approach for the dynamic simulation of thermal power plants. For a more detailed consideration of components such as evaporator or condenser, a two-phase flow model should be selected. In this section, two examples from the scientific literature are presented, showing the mixture flow model and the two-fluid models in direct comparison with measurement data. The first study applied an in-house code, while the second study used two different commercial simulation programmes. TagedPWippel [178] developed a dynamic simulation code (AHKSIM, latter known as MISTRAL) with different thermal hydraulic models, i.e. mixture flow model and six-equation flow model. In order to determine the volumetric void fraction, the driftflow model according to Zuber and Findlay [165] was implemented.

xD

x=rg   C0 rx C 1¡x rl C g

Vgas;j _ m=A

ð2:68Þ

TagedPThe distribution parameter C0 and average drift velocity of the gas phase Vgas,j were computed using Rouhani and Chexal
Lellouche correlations. TagedPTwo heat recovery steam generator (HRSG) models were built based on the mixture flow model and the six-equation flow model. The investigated power plant is a simple single-pressure HRSG without reheat. A breakdown case, in which the live steam valve was suddenly opened, was simulated and the results obtained from both HRSG models were compared to measurement. After opening the live steam valve, the pressure in the system drops sharply and the steam mass flow rate increases considerably. Since the heat input to the HRSG remains constant, the steam temperature decreases by reason of increased mass flow rate. In Fig. 1, the comparison between the measurement values and numerical results of mixture flow model and six-equation flow model is illustrated. It can be observed that the two-fluid model reproduces the system behaviour with better accuracy compared to mixture flow model. Minor differences can be noted between Rouhani correlation and Chexal
Lellouche correlation, where the latter is slightly more favourable. TagedPAlobaid et al.D74X X [15,17] investigated into the capability of different commercial simulation codes to predict the real behaviour of a combined-cycle power plant during part loads, off-design operation and start-up. The combined-cycle power plant with a three-pressure heat recovery steam generator and a single reheat is built with the process simulation software tools ASPEN Plus DYNAMICS using the mixture flow model and APROS using the six-equation flow model. TagedPIn Fig. 2, the dynamic simulation results of the intermediate pressure circuit including feedwater and steam mass flow rates, pressure as well as the superheated steam temperature are presented for off-design operation. The intermediate pressure (IP) feedwater mass flow rate obtained numerically agrees well with measurement. Similar to the IP feedwater mass flow rate, the simulated superheated steam mass flow rate follows accurately

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TagedPthe measured data. However, a slight deviation that lasted for 30 min can be detected between the numerical models and the real power plant in the period of time between t D 90 min and t D 120 min. From t D 120 min on, both models show high accuracy with a maximum relative error of approximately 2%. The superheated steam temperature calculated with the mixture flow model overestimates the measured one, while the simulated temperature in the six-equation model underestimates the measurement. The numerical models reproduce qualitatively the dynamic behaviour of the IP pressure. Compared to the mixture flow model, the six-equation model simulates the dynamic pressure change with higher accuracy, especially in time period between t D 150 min and t D 400 min. Here, the six-equation model and the three-equation model show maximum relative errors of about 3% and 7%, respectively. TagedPThe dynamic behaviour of the low pressure (LP) system during start-up procedure is presented in Fig. 3. The calculated feedwater mass flow rate matches very well with measurement. However, the considerable oscillations in the measured feedwater mass flow rate with average amplitude of 75 kg/s are not predicted by the numerical models. Starting from t D 150 min, the simulated feedwater mass flow rate lies marginally above the measured data with a relative error of 2%. The computed steam mass flow rate exiting from the LP superheater is in good agreement with the real power plant. At t D 36 min, the timing of first steam generation is accurately predicted by the sixequation model, in contrast to the three-equation model. For the latter, the steam production starts about 15 min earlier than measurement. From t D 75 min, qualitative agreement between simulation and experiment can be observed.

TagedPThe steam temperature computed by the mixture flow model shows acceptable agreement. Although the temperature jump preceded the measured data by 20 min, the simulated gradient is close to the real plant with a relative error of approximately 15%. From t D 75 min, the calculation of the steam temperature is close to the measurement. Compared to the three-equation model, the six-equation model shows quantitative agreement with measurement. Prior to start-up, the LP drum level in the six-equation model and experiment is equal to 2.3 m, while it is 2.22 m in the three-equation model. The level of the LP drum obtained numerically by both models agrees very well with experiment. However, the numerical models failed to simulate the oscillations in the drum level in the period of time between t D 20 min and t D 120 min. The three-equation model shows an almost smooth development of the LP drum level, while the six-equation model predicts the level oscillations more accurately. TagedPIn this comparative study between the three-equation flow model and the six-equation flow model, the following conclusions are drawn: TagedP1. In steady state, both three-equation flow model and six-equation flow model can quantitatively reproduce the process parameters of a real power plant. The relative error for mass flow rate, temperature and pressure are all within 5%, while several parameters are captured with a relative error of less than 1%. TagedP2. During off-design operation and start-up procedure, higher discrepancy is observed. Both three-equation and six-equation flow models can qualitatively follow the measurements with a

Fig. 1. Experimental and numerically obtained steam temperature, pressure and steam mass flow rate during a breakdown case (reproduced from reference [178]).

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TagedPmaximum relative error of approximately 12%. Several parameters are captured with a relative error of less than 5%. TagedP . For the given case, the six-equation flow model describes the 3 behaviour of the real power plant during off-design operation and start-up procedure more accurately compared to the threeequation flow model. The correct time prediction of first steam generation and temperature gradients as well as the better reproduction of the measured parameter oscillations are advantages of the six-equation flow model, at the cost of increased computational effort. 2.3. Process components TagedPBasically, a conventional thermal power plant consists of a flue gas side and a water/steam side. In the flue gas side, flows of various reactants are injected into the combustion chamber, where the reactions between oxidiser and hydrocarbon take place. The released heat is transferred through radiation and convection to the water/steam side, converting feedwater into superheated steam. The latter expands in the steam turbine, producing mechanical energy. Using an electrical generator, the mechanical energy is then converted into electrical energy that is transmitted to the grid. The process components required for the modelling of a thermal power plant include points, thinwalled tubes, thick-walled tubes, turbomachines etc. The tubes of the economisers, evaporator and superheater heat exchangers as well as the connecting pipes and valves belong to the thinwalled tubes, while other components such as drum and header belong to thick-walled tubes. The turbo-machines are rotating devices that extract energy from or transfer energy to the working fluid. In this work, the term working fluid refers to water/ steam, flue gas, organic working fluids, etc. TagedP2.3.1. Connection point TagedPThe point or node component is the most basic process component used in process simulation. It has no actual real process component as a counterpart and is used to connect different kinds of process components together. The point may have at least one inlet

95

TagedP ow and one outlet flow. The following mass and energy balances fl can be expressed: iDk X

_ inl;i D m

iD1 iDk X

iDj X

_ out;i m

ð2:69Þ

iD1

_ inl;i hinl;i D m

iD1

iDj X

_ out;i hout;i m

ð2:70Þ

iD1

TagedPThe subscripts k and j represent the number of inlet flows and outlet flows. In case of mixing two fluids with different compositions such as natural gas and air, the materials balances of the individual species must be computed and the mixture enthalpies calculated accordingly. The pressure of all outlet flows involved is assumed to be equal. TagedP2.3.2. Thin-walled tube TagedPThin-walled tubes are used as a representation of several different structures in a power plant like pipes, valves and heat exchangers. The thin-walled tubes incorporate a heat transfer model between wall and fluid, heat storage and a pressure loss of the flow. The wall temperature of thin-walled tubes can be modelled with a constant temperature in the radial direction for simplification. Berndt [179] calculated the wall temperature of thin-walled tubes, formulating the wall energy balance under the assumption of infinite thermal conductivity in the radial direction and negligible thermal conductivity i;n the axial and tangential directions as follows: Awal Dx


 @
r c T D aAin Tfl ¡Twal C Q_ @t wal p;wal wal

ð2:71Þ

TagedPHere, the symbol Awal is the cross-section surface of the wall, rD75Xwal X and cP,wal represent the density and the heat capacity of the wall material, Q_ is the heat flow, a denotes the heat transfer coefficient, Ain is the inner surface area of the wall, Tfl and Twal are the temperature of the working fluid and the wall, respectively. In order to reduce the computational cost, it can be assumed that the physical characteristics of wall material such as density and heat capacity are not subject to major change during the transient.

Fig. 2. Experimental and numerically obtained IP feedwater mass flow rates, IP steam mass flow rate, IP steam temperature and IP pressure during the off-design operation (reproduced from reference [15] with permission of authors and Elsevier).

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Fig. 3. Experimental and numerically obtained LP feedwater mass flow, LP steam mass flow, LP steam temperature and LP drum level during start-up procedure (reproduced from reference [17] with permission of authors and Elsevier).

TagedP2.3.2.1. Pipe. T TagedP he working fluid, other gaseous and liquid fluids can be transported using pipes that entail pressure drop of the flow. Numerically, the pipe component that is defined between two connection points is applied to calculate the fluid flow (e.g. velocity). Here, the shape and dimensions of pipes need to be specified. When it is necessary, the heat storage into the pipe material or the heat flow rate out from the pipe can be taken into account. In some applications (e.g. evaporator with natural circulation operation), the density differences at inlet and outlet have to be considered and are the main driving force for the fluid. TagedPThe pressure drop of the flow in the pipe can be expressed as:

Dppip D fk

L rk u2k D 2

ð2:72Þ

TagedPThe symbol fk represents the friction coefficient, rD76XkX and uk are the density and the velocity of the fluid, L and D denote the length and diameter of the pipe. TagedP2.3.2.2. Valve. TagedPIn a thermal power plant, the main task of a valve is to achieve desired fluid flow rates. In the process simulation, the valve model is considered as flow resistance. The pressure drop over the valve can be computed as a sum of the pressure drop due to friction coefficient fk and the pressure drop due to flow resistance coefficient of the valve fval:   L rk u2k ð2:73Þ Dpval D fval C fk D 2 TagedPThe valve is controlled using automation components and can also be connected to electrical components to simulate its behaviour during the loss of electricity. In thermal power plants, there are different kinds of valves used such as control valve, shut-off valve, check valve and safety valve. TagedP For control valve, the flow resistance is calculated as a function of the valve position that is a non-dimensional value between 0 and 1. The valve is fully closed, when the valve position is 0 and is fully opened, when the valve position is 1. The control valve is specified by a so-called characteristic curve that describes the

TagedPcorrelation between the mass flow rate and the valve position. Typically, the characteristic curves are linear (mass flow increases linearly with valve travel) or equal percentage (mass flow increases exponentially with valve travel). In special cases, different kind of curve types such as parabolic, hyperbolic or square root can also be considered. The position of the control valve is controlled by the automation system. The valve model receives the new setpoint and computes valve movement during the time step, taking into account the driving time of the valve. The driving time of the valve is defined as the time required by the valve actuator to open the valve from the fully closed position to the fully opened position or vice versa. Large valves in thermal power plants use hydraulic pressure or electricity, allowing typical driving times between 10 s and 30 s. Moreover, the process simulation can incorporate loss of electrical energy supply. In this case, there are three possible modes of valve operation: to open, to close or to stay at the same position. agedPT The shut-off valves include different types such as butterfly valve, flap valve and conical seat valve. The characteristic curve of a shut-off valve is usually not known, but the driving time and the flow resistance coefficient of a fully open valve are required. However, there are generic characteristic curves of the flow resistance coefficient as a function of the valve position for each valve type. In contrast to the control valves, the binary signals TRUE or FALSE control the shut-off valve. If the signal is TRUE, the valve starts opening and the valve begins to close, when the signal is FALSE. In break down cases (electrical power is lost), the shut-off valve either stays in its current position, starts closing or opening depending on the valve configuration. agedPT The check valve, also known as non-return valve or one-way valve allows the fluid to flow through it in only one direction. It is either fully open or fully closed. If the pressure difference over the valve is positive, i.e. the pressure at the valve inlet is higher than the pressure at the valve outlet, the valve is open. If the pressure difference over the valve is negative, the check valve is closed. agedPT A safety valve has the function of increasing the safety of thermal power plants by limiting pressure in pressure vessels. Here, the

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TagedPfluid is automatically discharged from a drum or other components when the pressure exceeds the specified limit. In a pressure safety valve, the opening position is linked to the pressure. TagedP2.3.2.3. Attemperator/desuperheater. T TagedP he attemperator (injection cooler) limits the steam temperature to the setpoint value. In thermal power plants, the attemperators are installed at superheater and reheater surfaces to control the temperature at the inlet of the high and intermediate pressure turbines. The attemperators use water directly from the boiler feedwater pumps. The injected mass flow rate is adjusted by a control circuit that controls the valve position. While the attemperator controls the steam temperature, a desuperheater removes the superheating of the steam and reduces the temperature of the steam to a range between 10 °C and 50 °C above saturation temperature. Desuperheaters are found e.g. in the bypass system of the high pressure turbine, which routes the high pressure steam not admitted by the turbine into the cold reheater or condenser. Here, a desuperheater is installed that reduces the steam temperature to approximately 50 °C above the saturated steam temperature. TagedP2.3.2.4. Heat exchanger. TagedPIn thermal power plants, heat exchangers are used, where heat transfer between one or more fluids takes place. Based on the requirements, a variety of different heat exchangers has been developed. Basically, the heat exchangers are designed as regenerator and recuperator. In regenerators, the heat transfer between fluids is carried out in two steps. In the first step, the heat flow is transferred to a storage mass and in the second step the energy stored is emitted to the heat-absorbing fluid after a time delay. The charge/discharge cycle can be discontinuous or continuous. An example of regenerators is the thermal wheel, also known as a rotary air preheater. In recuperators, by contrast, the heat is transferred continuously between fluids through a solid wall. They represent the most commonly-used type of heat exchangers, including double-pipe heat exchangers, plate heat exchangers, shell and tube bundle heat exchangers etc. Depending on the flow configuration of the fluids, it can be distinguished between co-current flow, countercurrent flow, cross-flow or hybrid flow arrangements. If phasechange occurs in any of the fluids, the heat exchanger is referred to as phase-change heat exchanger; otherwise it is a sensible heat exchanger. In thermal power plants, the heat exchangers used are listed as follows: TagedP Shell and tube bundle heat exchangers (economizer, evaporator, superheater and reheater): This type of heat exchanger transfers heat from the flue gas path to the water/steam circuit. It consists of numerous, equally long, heated tubes installed in parallel. The bundle of tubes is connected to one another by a header. The working fluid flows through the tubes, while the flue gas flows over the tubes, transferring heat between the two fluids. TagedP Membrane wall heat exchanger (evaporator): This type of heat exchanger is installed on the combustion chamber walls of coalfired boilers. TagedP Feedwater preheater: This type of heat exchanger heats the feedwater mass flow, before entering the steam generator using steam extractions form the high and low pressure turbines. TagedP Condenser: This type of heat exchanger condensates the turbine exhaust steam by means of cooling water or cooling air, depending on site conditions. TagedP Air and gas preheaters: These types of heat exchangers heat air or natural gas for combustion using the heat of flue gas or process steam. TagedPThe transport equations required to model the heat exchanger used in thermal power plants are mass, momentum and energy balances for flue gas flow and water/steam flow. Only the energy

97

TagedP alance has to be solved for the tube wall, describing the heat b transport from the flue gas to the tube wall and from the tube wall to the water/steam flow. In a tube bundle heat exchanger for example, the heat flows to the tube wall from the flue gas (through convection and thermal radiation) and from an optional flame-radiation zone of a combustion chamber. Then, the heat is transferred from the tube wall to the working fluid. Fig. 4 illustrates the discretised structure of a counter-flow tube bundle heat exchanger as an example. The flue gas path and water/steam tubes are discretised in equally-spaced control volumes with one calculation node in the centre and a calculation branch between two adjacent nodes. Here, each control volume consists of a horizontal pipe pass. To reduce the computational cost, each control volume may consist of many horizontal pipes in parallel. The flue gas path and the water/steam side are coupled by the heat flows through the tube walls. TagedP2.3.3. Thick-walled tube TagedPThe assumption of constant temperature in the radial direction of thin-walled components is acceptable for purposes of simplification. In the case of thick-walled components that are usually not positioned in the flue gas path such as drum and header, this assumption is non-permissible and can lead to errors, especially by calculating the heat storage in the walls. The temperature profile in a thickwalled component can be calculated by solving Fourier's differential equation:    @ @
@T ð2:74Þ rwal cp;wal Twal D λwal wal @t @r @r TagedPHere, the character λwal is the thermal conductivity of the wall. To simplify the problem, the wall can be divided into individual circular ring elements and the differential equation is solved numerically for each segment. This discretisation is valid, if the thermal conduction in the axial direction is negligible and the temperature distribution is radially-symmetric [180]. TagedPDuring start-up procedures of the thermal power plant, especially cold start-ups, the generated steam can condense on the still-cool wall surface of thick-walled components. The heat transfer coefficient of the condensate is much higher than the heat transfer coefficients of the steam and the boiling water in the lower part of the drum, which in turn leads to different heat fluxes along the wall. Accordingly, heat is transported in the tangential direction of the drum wall. In order to consider heat transport in radial and tangential direction, 2D calculation of the heat conduction in the drum wall is required. In contrast, during hot and even warm start-ups no condensation is present and only small temperature differences between the upper and the lower part of the drum occur. Therefore, the heat transfer in thick-walled hollow cylinders can be reduced to heat conduction in the radial direction. TagedPIn thick-walled components, the rate of temperature change is usually required to calculate thermal stresses and thus to prove the safety of operation during start-up and shutdown procedures of boilers. Material stresses are calculated based on the recorded pressure and temperature history. The thermal stresses are proportional the difference between integral average wall temperature and inner wall temperature:

s th D

aT blin Es
1¡v

 T wal ðtÞ¡Twal;in ðr; tÞ

ð2:75Þ

TagedPThe linear thermal expansion coefficient blin D7X X , the modulus of elasticity Es and Poisson's number v are material characteristics. The stress concentration factor aTD78X X takes into account weakening of the cylinder wall due to connected tubes, i.e. this factor is strongly dependent on the geometry and weld joints. The average wall temperature of a thick-walled component with a volume V can be

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Fig. 4. Counter-flow heat exchanger of a low pressure economiser of a HRSG; (a) real geometry (24 rows with 105 tubes per row) and (b) discretisation structure of the investigated heat exchanger.

TagedPcalculated according to the following relation: Z 1 T wal D T dV V V wal TagedPIn case of a hollow cylinder, this relation takes the form: Z rout 2 Twal ðr; tÞrdr T wal ðtÞ D 2 2 rout ¡rin rin

ð2:76Þ

ð2:77Þ

TagedPHere, the symbols rin and rout are the inner and outer radius of the hollow cylinder. From Eq. (2.77), it can be observed that the thermal stresses are a quadratic function of the wall thickness, which in turn increases with the design pressure. TagedPIn the following sections, the thick-walled tubes used in thermal power plants will be explained, including header, drum, separator and feedwater storage tank. TagedP2.3.3.1. Header. T TagedP he header is a thick wall pipe with large diameter connected to a large number of heating surface tubes with relatively small diameter (see Fig. 5). The headers are arranged at the inlet and outlet of tube-bundle heat exchangers. The function of the inlet header is to distribute the working fluid as uniformly as possible in the tubes of the heat exchanger. The outlet header collects and homogenises the working fluid from the tubes and feeds it to interconnecting pipes. As described above, the thick walls of headers can store or release the heat from or to the working fluid during transients. Furthermore, the temperature gradients in the header walls result in material and thermal stresses. Therefore, the headers used in thermal power plants are designed with stringent requirements for strength, corrosion and creep properties. The high mechanical properties of the header are required on the one hand due to the operation under harsh conditions, e.g. high temperature and pressure, high rate of temperature and pressure changes, and on the other hand due to the large number of connected tubes that contribute to cross-sectional weakening. TagedP2.3.3.2. Drum. TagedPThe drum is a horizontal, cylindrical shaped tank with comparatively thick walls. In natural or forced circulation thermal power plants, the drum represents the core of the evaporator system and has a variety of functions. It is used as link between the downcomers and the risers, enabling the circulation of the working fluid through evaporators. Furthermore, the drum separates steam from the water/steam mixture by force of gravity using the density difference between gaseous and liquid phase. The separation of the two-phase mixture can be improved with different types of separators using centrifugal force, e.g. cyclone separators or simply

TagedP eflection boxes. The saturated steam leaves the drum apex through d a steam dryer (demister) that enhances the removal of liquid droplets entrained in the vapour stream. However, the saturated steam flowing into the superheaters may include a small amount of water droplets. The water remains in the drum bottom and flows through the downcomers to the evaporator. Pre-warmed feedwater is fed to the drum through economisers with a certain degree of subcooling and mixed with the saturated water in the drum. The content of salts in the pre-warmed feedwater cannot leave with the saturated steam and remains in the evaporator system. Accordingly, a specific amount of water is constantly discharged from the drum to the blow-down tank, limiting the concentration of salts in the evaporation system. The mathematical model that describes the physical processes in the drum, by contrast to the header model, are extremely complex. This is due to the fact that the separation of the two-phase flow takes place under highly-turbulent flow regime. A schematic of the drum model with all variables is presented in Fig. 6. TagedPIn the drum model, it can be assumed that the momentum transported into the drum with the inlet flows is completely dissipated, but it builds up again at the pipes, when the working fluid leaves the drum. For the definition of the drum, the volume Vdru, the height Hdru and the cross-sectional area Adru are required. The mass of the water and the steam in the drum can be expressed as: mliq;dru D rliq;dru Aliq;dru ldru

ð2:78Þ

mst;dru D rst;dru Adru ðHdru ¡ldru Þ

TagedPHere, the symbol Aliq,dru denotes the cross-sectional area of the drum filled with water, rliq,dru D79X X and rst,dru D80X X are the densities of water and steam in saturation state. A feedwater control valve is used to regulate the level of the water in the drum ldru by adjusting the feedwater mass flow rate entering into the drum (see Fig. 15). According to mass and energy flows at inlet and outlet of the drum, the following unsteady balance equations of mass: iDj iDk iDn X X X dmliq;dru dmst;dru _ fw;i C _ riser;i ¡ _ down;i ¡m _ blow ¡m _ st m m m C D dt dt iD1 iD1 iD1

and energy:

 d mliq;dru h0;liq;dru d mst;dru h0;st;dru C dt dt iDj iDk iDn X X X _ fw;i h0;fw;i C _ riser;i h0;riser;i ¡ m _ down;i h0;down;i m m D iD1

iD1

iD1

_ blow h0;blow ¡m _ st h0;st C Vdru ¡m

dpdru dt

ð2:79Þ

ð2:80Þ

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99

Fig. 5. Header; (a) outlet header and (b) inlet header.

TagedPcan be

applied. In the equations, the subscripts k, j, n represent the number of the feedwater pipes, the number of the risers and the number of downcommers that are connected to the drum, respectively. The inlet mass flows are the feedwater mass flow _ fw and water/steam mixture mass flow from from economisers m _ riser . The outlet mass flows are the water mass flow to the riser m _ down and the water mass flow to blow-down tank downcomers m _ blow as well as the steam mass flow leaving at the drum apex m _ st . m The pressure derivative appears in the energy equation, since the internal energy of the water or the steam is replaced with the corresponding total enthalpy h0. The time derivatives in the mass and energy balance equations can be approximated by using a suitable numerical solution method. TagedP2.3.3.3. Separator. TagedPThe separator (generally called as cyclone) is a vertical, cylindrical shaped tank with a relative small diameter and high wall thickness (see Fig. 7). It is located at the evaporator outlet of once-through boilers with part load recirculation or with superimposed circulation. The once-through boilers can be operated at subcritical and supercritical pressures and offer a higher degree of operational flexibility. In the once-through boiler with superimposed circulation, the circulation number amounts to around 1.3
1.7 and therefore the separator is used to separate the water from the water/steam mixture during operation. In the once-through boiler with part load recirculation, the working fluid is forced to flow through all heat exchangers in a single pass. Here, the separator is used to remove the water droplets within the steam flow and to separate the water from the water/steam mixture only during start-up procedures and at low part loads. If the boiler is operated at supercritical pressure, no phase separation can take place. The working principle of the separator is that the two-phase mixture enters tangentially into the separator, leading to a spiral flow of the gas phase. The water droplets in the stream are centrifuged to the separator wall, where they move downwards and are collected in the separator storage tank. The clean steam leaves through the upper part of the cyclone. Based on the drum model, the following applies for the mass balance: iDk X dmliq;dru dmst;dru _ header;i ¡m _ st ¡m _ liq C D m dt dt iD1

and for energy balance:

 d mliq;dru h0;liq;dru d mst;dru h0;st;dru C dt dt iDk X dp _ header;i h0;header;i ¡m _ st h0;st ¡m _ liq h0;liq C Vdru dru D m dt iD1

ð2:81Þ

ð2:82Þ

TagedPHere, the subscript k denotes to number of the header pipes that are connected to the wall of the separator. TagedP2.3.3.4. Feedwater storage tank. TagedPThe feedwater pumped into the steam generator is typically supplied from a heated container with thick walls known as feedwater storage tank. The feedwater storage

tTagedP ank stores the feedwater in order to decouple the feedwater mass flow rate from the build-up of condensate. Generally, the storage capacity is designed to cover a few minutes of full-load operation of the boiler. This stored energy can be used effectively in order to yield a rapid increase of the electrical power output (condensate throttling method). Here, the steam extraction valves to the low pressure preheaters and the condensate valve to the feedwater tank are temporarily throttled or even closed. Accordingly, the extraction steam passes through the last turbine stages, resulting in a sudden increase in the electrical power output (up to 5% within 30 s) that can lasts for a few minutes depending on the volume of the feedwater storage tank and/or the condenser tank. The condensate throttling method, although it has no impact on the main steam pressure, has complicated dynamic behaviour, since it results in the variations of extraction steam flows as well as the level change of the feedwater storage tank. TagedPIn thermal power plants, the feedwater storage tank is equipped with a deaerator that removes the dissolved oxygen, carbon dioxide and other gases from the feedwater. Dissolved oxygen in feedwater reacts with metallic walls and forms oxides (rust). This in turn leads to serious corrosion damages in the steam generator components. If carbon dioxide is also present, then it combines with water to form carbonic acid that causes additional corrosion. The feedwater storage tank and deaerator are modelled as hydraulic accumulators. In steady state modelling, the mass balance of the storage is simplified to equalisation of the inflow and the outflow. In transient case, the mass balance of the storage can be expressed as:

dmsto _ out _ inl ¡m Dm dt TagedPThe energy balance of the storage is written as:
 d msto h0; sto _ inl h0;inl ¡m _ out h0;out Dm dt

ð2:83Þ

ð2:84Þ

TagedP2.3.4. Turbomachines TagedPTurbomachines are a vital part of every energy system. They transfer energy between a rotor and a fluid (gas or liquid). The energy transfer can take place from rotor to fluid (e.g. compressor, fan and pump) or from fluid to rotor (e.g. steam and gas turbines). Modern turbomachines have smaller gaps between rotor and housing for minimising the leakage loss. In the pump, the pressure of an incompressible fluid is increased to a higher level, while the pressure of a compressible fluid is increased using the compressor. According to ASME, fans differ from blowers and compressors by the pressure ratio that can be achieved (up to 1.1 for fans, from 1.11 to 1.2 for blowers and more than 1.2 for compressors). In a steam turbine, the superheated or reheated steam expands, resulting in mechanical work. The gas turbine with its combustion chamber is a combustion system, converting natural gas or liquid fuels to mechanical energy. In process simulation, turbomachines are integrated into the water/ steam cycle, the electrical system and in the automation system. This allows designer to evaluate their electric power consumption/

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Fig. 6. Drum and the connected tubes (adapted from reference [201] with permission of author).

TagedPgeneration during transients and to assess their behaviour during breakdown cases and when electricity is lost (blackout). Further information regarding the specific turbomachines is presented in the following sections. T .3.4.1. Compressor. T agedP2 TagedP he compressor is a turbomachine that increases the pressure and the enthalpy of compressible, low density fluids. The pressure increase is characterised by the compressor pressure ratio that describes the ratio of the outlet pressure (discharge pressure) to the inlet pressure (suction pressure). Compressors are classified according to two different types, namely intermittent flow (positive displacement) and continuous flow (rotor dynamic). The intermittent flow compressors include rotary compressor and reciprocating compressor, while the continuous flow compressors include centrifugal compressor and axial compressor. Rotary compressors consist of two rotors within a casing. The reciprocating compressors increase the pressure by reducing the volume of the working fluid. This can be carried out by a piston within a cylinder as the compressing and displacing element, achieving high compression ratios. The centrifugal compressors convert angular momentum transferred by a set of rotating impeller blades (dynamic displacement) to the working fluid. The axial compressors use arrays of aerofoils to compress the working fluid. An axial air compressor is one of the main components ofD81X X the combined-cycle power plant. It compresses and supplies the fresh atmospheric air to the combustion chamber of the gas turbine. Relevant input data for the compressor model include the dimensions of components, design point values for pressure and temperature before compressor, pressure ratio, rotation speed, characteristic curve and efficiency. Basically, the compressor model has one inlet flow and one outlet flow and

tTagedP herefore the mass balance is expressed as:

_ out _ inl D m m

ð2:85Þ

TagedPThe energy balance is defined as: _ inl hinl D m _ out hout C P m

ð2:86Þ

TagedPThe following equation can be used to calculate the required performance:

_ p ðT ÞTinl Vcomp P D mc

ð2:87Þ

TagedPHere, cp is the air specific heat capacity at the average temperature. It can be determined simply as:

T D

ðTinl C Tout Þ 2

ð2:88Þ

TagedPThe dimensionless ratio can be expressed as: k

Vcomp D Phpol;comp ¡1

ð2:89Þ

TagedPHere, the term k is the isentropic exponent. The optimum pressure ratio P depends on the selected thermodynamic process and should provide the maximum efficiency of combined gas and steam processes. For the Joule process, the design pressure ratio for modern gas turbines is approximately 18
20 and in case of reheat gas turbines is up to 38. The polytropic compressor efficiency hpol, 2X8D X comp is computed as:

hpol;comp D k

lnP  k  ln hP ¡1 C 1

ð2:90Þ

isen;comp

D83X X : with the isentropic efficiency hisen,comp

hisen;comp D

hout ¡hinl hout;isen ¡hinl

ð2:91Þ

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cTagedP ombustion chamber and the cooler ambient air. Without the induced-draft fan, excess pressure may prevail in the combustion chamber, which should generally be prevented for safety reason due to the flue gas leakage. TagedPIn the fan models, the input data of the fan such as geometry, dimension, characteristic curve, mechanical coupling must be specified. Furthermore, the automation and electrical systems for starting and stopping the motor as well as for controlling the inlet guide vanes can be modeled, if necessary. TagedP2.3.4.3. Blower. T TagedP he blower is used instead of the fan, when higher pressure ratio (approximately 1.11
1.2) is required. In process simulation, the mathematical model of the fan can be used for the blower.

Fig. 7. Separator; (a) side view and (b) front view.

TagedPThe symbol hinl is the state enthalpy at the inlet of the compressor, while hout,isen and hout denote the state enthalpy at the compressor outlet for the isentropic process and for the real process, respectively. The discharge temperature of the compressor is calculated with the following formula:
 Tout D 1 C Vcomp Tinl ð2:92Þ TagedP2.3.4.2. Fan. A TagedP fan generates a pressure difference, allowing for a large mass flow rate of air or gas to overcome a flow resistance. The drive power required is supplied by a rotating shaft (generally an electric motor). Basically, it can be distinguished between centrifugal flow and axial flow fans. In the axial fan, the fluid flows axially along the fan shaft without any change in the flow direction. In the centrifugal fan, the fluid changes its direction relative to the shaft (forward curved, backward curved or radial). TagedPIn thermal power plants, the fans used are forced-draft and induced-draft fans. The forced-draft fan is located at the inlet of the flue gas path, while the induced-draft fan is located at the outlet of the flue gas path. The forced-draft fan supplies fresh air for the combustion chamber via air preheaters. The induced-draft fan creates a certain amount of negative pressure in the combustion chamber (the pressure is below atmospheric pressure) by sucking the flue gas through the stack into the atmosphere. For this purpose, old thermal power plants use only the stack draft, i.e. the density difference between the hot flue gas in the

TagedP2.3.4.4. Pump. W TagedP hile the compressor is designed for compressible low density flow such as air or gas, a pump is designed to increase the pressure of incompressible fluids such as water or oil. In the pump, the mechanical energy of the shaft is transformed into kinetic and potential energy of the flow. At several locations in the thermal power plant, the pumps are used to transport the working fluid from one location to another. For example, the condensate pumps move the condensate water through the low pressure preheaters into the feedwater storage tank. The boiler feedwater pump forces the water from the feedwater tank to flow through high pressure preheaters before entering the steam generator. TagedPThe pump model can include mechanical coupling, motor and busbar. The automation system adjusts the rotation speed of the pump by frequency control or directly by aid of the mechanical coupling. The steady state operation of a pump is computed as a function of the actual volumetric flow rate V_ liq and the rotation speed w as: 0 !2 1 2 V_ liq A w H D @Hmax ¡ðHmax ¡Hnom Þ ð2:93Þ wnom V_ liq;nom TagedPThe initial values required for the pump model are maximum pump head Hmax, nominal pump head Hnom, nominal volumetric flow rate V_ nom and nominal rotation speed wnom. The rotation speed of the pump can be controlled by automation and electrical systems. If electricity is lost, the pump is coast-down according to the following relation:   Dt w D w0 1¡ ð2:94Þ tstop TagedPHere, the symbol w0 represents the rotation speed of the pump at old time step, Dt is the time step and tstop denotes to the coast-down time of the pump. TagedP2.3.4.5. Steam turbine. TagedPThe steam turbine transforms enthalpy of steam to mechanical energy. The model of the steam turbine calculates the enthalpy after the turbine module using the enthalpy before the turbine, the efficiency and the nominal values. The mechanical power produced by the turbine is computed and transferred to the generator model. The steam turbine model may describe the turbine either with a single turbine stage or with many stages in order to consider the steam extractions. TagedPThe pressure and enthalpy drops over the turbine are added as source terms in momentum and energy equations. The pressure change in the turbine stage is specified at nominal load and computed using the Stodola equation at part loads. The pressure drop is _ nom , the nominal pressure at a function of nominal mass flow rate m the turbine inlet pinl,nom and the nominal pressure at the turbine outlet pout,nom:

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TagedP

TagedP

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  n Cn 1 u pout u pinl u 1¡ pinl _ Dm _ nom u  m n Cn 1 pinl;nom t p 1¡ pout;nom inl;nom with: nD



ð2:95Þ



ln ppout   inl   ¡ ln TTout ln ppout inl inl

ð2:96Þ

_ represents the mass flow rate, pinl is the pressure before the where m steam turbine, pout is the pressure after the steam turbine, Tinl and Tout denote the temperatures at inlet and outlet of the steam turbine. TagedPThe enthalpy drop over the steam turbine is determined with the expansion efficiency. Generally, the processes are not purely isentropic or isothermal but a function of the exponent. The expansion equation is obtained from:

hD

1 @h v @p

ð2:97Þ

TagedPIf the specific volume v is solved from Eq. (2.97) and introduced in Johanson‘s equation:

pv D

h

z

ð2:98Þ

the following equation is obtained:

@h h @p D zp h

ð2:99Þ

Where z D g g¡1 and g is the isentropic exponent. By integrating the right side term of Eq. (2.99) from hout to hinl and left side from pout to pinl, the following relation is obatined:

 h hinl pinl z D hout pout

ð2:100Þ

TagedPThe enthalpy is defined with regard to the reference enthalpy href:

 h hinl ¡href pinl z D hout ¡href pout TagedPEq. (2.101) can be written as: "  h #
 pout z hout ¡href D hinl ¡href pinl

ð2:101Þ

ð2:102Þ

TagedPThe specific enthalpy drop over a turbine section is determined using different models. When the fluid is steam, the specific enthalpy drop over a turbine is calculated as:

 Dhturb;st D hinl;st ¡href ¡ hout;st ¡href ð2:103Þ agedPIT f the fluid contains water droplets, the specific enthalpy drop can be computed with the following formula:

 Dhturb;dro D x hinl;st ¡href ¡ hout;st ¡href ð2:104Þ   C ð1¡xÞ hðpÞinl;dro ¡hðpÞout;dro TagedPIntroducing the Eq. (2.102) in Eqs. (2.103) and (2.104), the following Equations:  h

 pout z Dhturb;st D hinl;st ¡href ¡ hinl;st ¡href ð2:105Þ pinl

"







Dhturb;dro D x hinl;st ¡href ¡ hinl;st ¡href

 h #  pout z pinl 

ð2:106Þ

 C ð1¡xÞ hðpÞinl;dro ¡hðpÞout;dro

are obtained. Here, the subscripts st and dro refer to steam and water droplets, inl to the state before the turbine and out to the state after the turbine. The quantities x and hD84X X are the steam mass fraction and the polytropic expansion efficiency, respectively. The notation h(p) refers to the enthalpy in saturation state. TagedPThe mechanical power produced by the steam turbine can be calculated by knowing the mass flow through turbine and the enthalpy drop: Pmech D

iDk X

Dhturb;i m_ i

ð2:107Þ

iD1

_ i is the TagedPHere, the subscript k is number of the turbine stages and m mass flow rate that flows into the turbine stage i. TagedP2.3.4.6. Gas turbine. ITagedP n addition to compressor, combustion chamber and steam generator, the gas turbine represents the core element of a combined-cycle power plant (CCPP). The gas turbine (GT) converts flue gas enthalpy to mechanical energy, driving an electrical generator that produces electrical energy. Using a heat recovery steam generator (HRSG), the waste heat of the gas turbine can be used to generate steam and drive a steam turbine. Typically, gas turbines can be operated with different fuels, including nature gas, crude oil and biogas. They can extend their fuel range to cover biomass and coal through the application of integrated gasification combinedcycle (IGCC). Modern gas turbines can reach their nominal load within 20 min, while 70% of the nominal flue gas temperature and 60% of the nominal flue gas mass flow are already achieved approximately 7 min after the start. TagedPBy contrast to steam turbines, heavy-duty gas turbines with high inlet temperature require cooling of the first blade rows. If the cooling is not required, the mathematical model of the gas turbine is similar to the steam turbine. In case of air cooling, the entire gas turbine has to be divided into many stages. The cooling air of one stage is mixed with the combustion gases and can be considered in the mass balance equation of the turbine stage. Based on empirical data, Wang and Leithner [181] developed an formula to calculate the cooling air mass flow required at nominal load:   _ cool D m _ air 3:1817 ¢ 10¡4 Tinl ¡0:2454 m ð2:108Þ _ air represents the total air mass flow rate and Tinl is TagedPThe symbol m the inlet temperature in degree Celsius. At part loads, the following equation is proposed by Palmer and Erbes [182]: rffiffiffiffiffiffiffiffiffiffi p Tnom _ cool D m _ cool;nom m ð2:109Þ pnom T TagedPThe subscript nom refers to the nominal state. TagedP2.3.5. Additional components TagedPDetailed modelling of conventional thermal power plants requires, besides the above mentioned process components, additional components such as different firing systems, mills and flue gas clearing devices, e.g. electrostatic precipitator and selective catalytic reduction unit. Furthermore, there is an increased attention on hybrid power plants that combine different technologies to produce electrical power. As a result, the dynamic simulation programmes must extend their existing libraries with new models for wind turbines, solar and fuel cells applications. Examples of hybrid systems

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103

TagedPare the integrated solar combined-cycle power plant (ISCC) and the hybrid fuel cell/gas turbine power plant.

TagedPvolume fraction of solid is constant, while the volume fraction of solid in the lean region decreases exponentially with height.

TagedP2.3.5.1. Combustion chamber. TagedPThe combustion of the fossil fuel takes place in the combustion chamber. The combustion chamber model has oxidiser inlet (generally air or oxygen), fuel inlet (such as coal, oil or gas) and flue gas outlet. Compared to combustion process of liquid or gaseous fuels, the combustion of solid fuels (coal, biomass or municipal solid waste) is more complex, including three major mechanisms: drying, pyrolysis and oxidation. The flue gas formed during combustion consists generally of O2, N2, CO2, H2O, SO2 and Ar. The combustion calculation that predicts the composition of the flue gas requires the type of fossil fuel, the fuel mass flow rate, the Air/fuel ratio, temperature etc. Determining the exact composition is of high relevance for defining the material properties of the flue gas. The mass flow balance in the combustion chamber can be expressed as:

TagedP2.3.5.3. Fuel cell. A TagedP fuel cell converts chemical energy into electricity and forms water. The fuel cell has two electrodes, namely anode and cathode. Generally, hydrogen is the basic fuel, but fuel cells can also extend their fuel range to cover methane. There are four different types of fuel cells, including molten carbonate (MCFC), solid oxide (SOFC), phosphoric acid (PAFC) and proton exchange membrane (PEM). The selection of the fuel cell type depends on the specific application; whether large or small scale, stationary or mobile. TagedPThe modelling of a fuel cell requires the consideration of chemical reactions and additional components involved. For example, the simulation model of a solid oxide fuel cell includes a natural gas reformer and a sulphur removal unit. The fuel cell model is connected on the one hand to the process components such as pipe or valve, supplying it with reactants such as air and fuel and discharging products such as water. On the other hand, it is connected to the electrical system (electrical source). The voltage of the fuel cell is used as boundary condition for the electrical system, while the electric current of the electrical network is transferred to the fuel cell calculation and applied as input. Further information regarding the dynamic modelling of fuel cells can be found in the literature, for example in [190,191].

_ out;fg D m _ inl;air C m _ inl;fuel m

ð2:110Þ

and accordingly the energy balance is written as: _ out;fg hout;fg D m _ inl;air hinl;air C m _ inl;fuel LHVfuel m

ð2:111Þ

TagedPHere, the subscript fg refers to flue gas and the term LHV is the lower heating value of the fuel. In addition to the mass and energy balances, a balance equation for each substance is solved. Usually, the combustion chamber is operated under atmospheric pressure like in pulverised coal and incineration power plants. On the contrary, the combustion chamber of a gas turbine is pressurised. TagedP2.3.5.2. Fluidized bed. TagedPThe fluidized bed is a bulk of solid particles located in a vertical vessel and the gas or liquid flows from the bottom via a porous plate or nozzles. The gas-solid fluidized bed is characterised by several advantages such as high heat and mass transfer rates, resulting in uniform temperature gradients in the bed even with highly exothermic or endothermic reactions. Practical applications of fluidized bed reactors include CO2 capture in thermal power plants by chemical or carbonate looping process as well as solid fuels conversion, including gasification and combustion of coal, biomass and even fuel mixtures. Depending on the superficial fluidization velocity, it can basically be distinguished between fixed bed, stationary fluidized bed and circulating fluidized bed. The fluidized bed can, generally, be divided into a dense phase zone and a lean zone. In the dense zone, there is a higher concentration of solids near the air distributor plate. It can be differentiated here between two phases: the emulsion phase (uniform mixing of gas and solids) and the bubble phase (only gas). The dense zone is followed with the lean zone, in which the concentration of solids decreases sharply as the flow moves upwards. TagedPBasically, there are two different numerical approaches for the representation of gas
solid flow in the fluidized bed (Euler
Euler and Euler
Lagrange). In the Euler
Euler method, also known as two
fluid method, each phase is regarded as a continuum and is mathematically calculated by solving the balance equations. The Euler
Lagrange approach combines the continuum descriptions of fluid phase with the Lagrange representation of dispersed phase on the basis of Newton's transport equations. Although these numerical models described here are already implemented in 3D simulation programmes such as ANSYS-FLUENT (among others publications [183,184]), OpenFOAM and CPFD-BARRACUDA (among others publications [185
188]), they are not suitable for 1D process programmes used to simulate the entire thermal power plant system. Therefore, semi-empirical models such as Kunii and Levenspiel [189] are preferred by reason of low computational cost. In this model, the fluidized bed is divided into two regions (dense and lean regions), interacting each other based on several assumptions. The dense region describes the lower part of the rector, where the

TagedP2.3.5.4. Weather. A TagedP mong renewable energy sources, solar energy offers a promising option for electricity generation in the countries with high solar radiation. Solar technologies can be divided into concentrating solar power (CSP) and photovoltaic cells (PV). In the latter, the sunlight is directly converted into electrical energy using semiconducting materials. In CSP, the sunlight of a large area is concentrated using mirrors or lenses onto absorber tubes, through which a heat transfer fluid (generally oil or water) passes. The thermal energy stored in the heat transfer fluid is used as a heat source for a power generation system. This should not be confused with concentrator photovoltaics, a technology that directs concentrated sunlight to photovoltaic cells. Concentrated solar power plants are showing increasing interest in field of research and application, mostly as parabolic trough collectors and solar tower collectors. This is due to the fact that the CSP technology can easily be coupled with thermal energy storage and with fossil fuel combustion system, increasing the plant availability, especially during low radiation periods. However, the daily and monthly variation of the solar radiation is a main drawback. TagedPThe solar radiation module considers the variation of solar radiation at different periods of day. It calculates the solar position and both beam and diffusive irradiation on the horizontal surface according to input parameters such as geometric coordinates of the field, time, elevation from sea level and clear sky index. The data from solar radiation module can be used to determine the total amount of irradiation that is passed to different types of surfaces with different angles of inclination. The direct irradiance received per unit area by a surface normal to the sun is defined as direct normal irradiance (DNI). Using DNI values obtained from weather stations at the location, the absorbed solar energy by an absorber tube can be computed as follows: Sabsorb D ðDNIÞ cosðuÞAaper hopt Etrack fdust fclean frow;shad fend¡loss kIAM

ð2:112Þ

with the mirror aperture area Aaper and the incidence angle u.D85X X The symbol hopt D86X X represents the optical efficiency and Etrack is a tracking error. The reduction in the absorption energy due to several factors can also be considered, including dust on the absorber glass cover fdust, mirror cleanliness fclean, row shadowing frow,shad and end-losses fend ¡ loss caused by spacing between solar collector elements, spacing between solar collector assembly as well as the non-zero incidence angle. When the angle of incidence increases, losses that can arise

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TagedPdue to additional reflection and absorption by the glass envelope are corrected by the incidence angle modifier (IAMD). 87X X TagedP2.3.5.5. Mill. M TagedP ills are mechanical devices used to break different types of solid materials in small pieces by grinding, crushing or cutting. In pulverised coal-fired power plants, a pulveriser coal mill grinds the raw coal into a combustible dust. Here, the coal particles are dried by flue gas or hot air and milled to fine size, so that stable combustion and complete burn-out of pulverised coal can be achieved in the combustion chamber. The coal properties such as volatile components, ash content, hardness, humidity and grinding fineness are the decisive factor for selecting the required mill. Basically, coal pulverisers can be divided into three assembly groups, impact mills, gravity-force mills and external force mills. The impact mills such as hammer and beater wheel mills are classified as high speed mills. While the hammer mill is suitable for lignite and hard coal, the beater wheel mill is preferred for lignite, but can be used conditionally for hard coal. The gravity-force mills are low speed mills and well suited for wet and hard coal. Due to their construction, they are identified as tube mills. When considering the design of external force mills, different constructions are well-known such as bowl mill and roller mill. In such medium speed mills, the grinding bowl is rotated by a gearbox, while the grinding parts are pressed by external force either by springs or hydraulic cylinders against the grinding track. The external force mills are suitable for harder coals, showing different advantages such as high grinding performance, low wear and low power consumption. TagedPAlthough the dynamic of the mill has a significant influence on dynamic behaviour of the entire coal-fired power plant, the mill is, generally, modelled as a mixing point of the coal and the primary air for purposes of simplification. In this mixing point, the water content of the coal is evaporated under the assumption that no combustion will take place. If it is required, complex pulveriser models, e.g. [192
194] can also be applied to achieve accurate dynamic behaviour of pulverised coal-fired power plants. TagedP2.3.5.6. Flue gas control. P TagedP articulate matter, nitrogen oxides (NOx), sulphur oxides (SOx) and carbon dioxide (CO2) emissions emitted by the combustion of fossil fuels contribute to global climate change and might present a hazard for health and environment. The energy system in terms of conversion of fossil fuels as a major emission source is in the focus of attention. Flue gas cleaning systems are therefore considered as an essential part of modern thermal power plants. TagedPFossil fuels, except natural gas, contain non-combustibles that form the majority of the particulate in the flue gas such as ash and some amount of unburned carbon. Particulate control equipment is therefore required to remove particulate, keep the particulate from re-entering the flue gas and discharge the collected material. Different types of particulate control equipment are available, including electrostatic precipitators, fabric filters, mechanical collectors and venturi scrubbers. TagedPThe term NOx denotes cumulative emissions of nitric oxide (NO), nitrogen dioxide (NO2) and other nitrogen-bearing species. In thermal power plants, there are three principal mechanisms of NOx formation, namely thermal NOx, fuel-bound NOx and prompt NOx. A reduction in NOx emissions can be achieved using primary and secondary techniques. The primary measures for NOx aim to reduce both peak temperature and residence time at peak temperature, including fuel/air staging, over fire air, less excess air, flue gas recirculation and combustion optimisation. The secondary techniques are based on chemical reduction of NOx such as selective catalytic reduction (SCR) and selective non-catalytic reduction (SNCR). TagedPMost sulphur emitted to the atmosphere oxidizes slowly to sulphur dioxide (SO2) that is a reactive and acid gas. In the combustion of fossil fuels, large quantities of SO2 are emitted. For SO2 control,

tTagedP wo strategies can be generally applied, either the use of low sulphur coal or installing scrubbers. Commercialised technologies for sulphur scrubbing include wet, semidry and dry processes. For thermal power plants, the technology of choice is the wet flue gas desulfurization (WFGD) scrubber and in case of lower sulphur oxides emissions is the dry flue gas desulfurization (DFGD). TagedPA promising method to reduce CO2 emissions is the carbon capture and storage (CCS). Depending on the manner of CO2 capture and the oxidation of fuel, it is distinguished between three CO2 capture methods, namely pre-combustion, post-combustion and oxyfuel. In the pre-combustion approach, the carbon dioxide is separated before the combustion process. The coal is gasified in a first step at higher pressure levels and the syngas consists essentially of carbon monoxide and hydrogen. In a subsequent water-gas shift reaction, the carbon monoxide reacts under the supply of steam to carbon dioxide and additional hydrogen. The flue gas in the post
combustion process, which is basically consists of nitrogen, oxygen, carbon dioxide and steam, is further treated. Here, different concepts are developed such as the chemical scrubbing of flue gas (among others, Diao et al.D8X X [195]) and the carbonate
loop€ hle et al.D89X [X 196]). In the third method ing process (among others, Stro (the oxyfuel process), the coal is combusted with pure oxygen. After cleaning the flue gas from pollutants and separation of the steam by a condensation process, the flue gas consists of pure CO2 that can be compressed for transport and storage. Due to the provision of the pure oxygen using an air separation unit, there is an enormous loss of overall efficiency of 8
14 percentage points [197]. The combustion of solid fuels by means of the chemical
looping process, a new combustion concept, enables a CO2 capture with low energy input. Here, air and fuel are kept separate, and the oxygen is transferred from the air to the fuel by use of an oxygen
carrier material. Generally, particles containing a suitable metal oxide are used as oxygen
carriers and these particles are moved between two coupled, circulated gas
solid fluidized beds (air reactor and fuel reactor). In an ideal case, the flue gas at the fuel reactor outlet consists of CO2 and H2O. The latter can be easily removed by condensation [198,199]. TagedPFor the modelling of flue gas cleaning devices (dust removal, NOx removal, SOx removal and CO2 capture), the standard library components of dynamic simulation programmes are generally insufficient apart from a few exceptions (e.g. ASPEN Plus DYNAMICS). Therefore, simple numerical models are used, in which the flue gas cleaning systems such as electrostatic precipitator and selective catalytic reduction unit are modelled as pressure drops and thermal masses. Thus, detailed models of flue gas cleaning components should be the subject of further research. TagedP2.3.6. Examples TagedPIn the previous sections, different process components such as thin-walled and thick-walled tubes as well as turbomachines are presented. Base modelling of thermal power plants is carried out by selecting the process components and combining them to generate a model of an existing system and/or a new process for research. Although the building of a model is generally limited by the program libraries, a specific component may be modelled by combining various existing process components. All necessary specifications can be inserted in the components that are linked by flows of either material, energy or heat properties to finish construction. Here, two different examples are selected from the scientific literature, showing detailed dynamic models of a combined-cycle power plant built in ASPEN PLUS DYNAMICS [38] and a pulverised coal-fired power plant built in APROS and in MODELICA [21,53]. TagedPIn Fig. 8, a combined-cycle power plant model that comprises a gas turbine connected to a vertical gas path is illustrated. The heat recovery steam generator that is arranged downstream of the gas turbine is unfired. The water/steam circuit is a three-pressure-stage

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TagedPwith forced circulation in the HP, IP and LP evaporator paths and reheater section after the high pressure turbine. Process components used to build the model are: heat exchangers, drums, pumps, turbines, pipes, valves and attemperator. Furthermore, different controllers and electrical components are used. The LP feedwater directed to the LP economiser is supplied by the condensate pump. A control valve for the LP drum level is located between the LP economiser outlet and the LP drum and the heated water flows into the LP drum. In the LP drum, the water circulates through the LP evaporator tube bundle, where it is heated by the gas turbine exhaust gas and converted into saturated steam. The saturated water in the LP drum is separated and a significant portion of the flow is directed into the HP and IP circuits via high and intermediate boiler feed pumps (HP BFP and IP BFP). The dry steam exits the LP drum and flows through the LP superheater. After leaving the superheater, the superheated steam enters the LP turbine. Process water is extracted from the LP circuit for fuel gas preheating, before it is returned to the condenser. TagedPThe feedwater flows into the HP drum via the HP economisers. The water in the HP drum circulates through the HP evaporator with the help of the forced circulation pump (HP RP). The recirculated water is heated by the flue gas and converted into saturated steam in the HP drum. While the liquid stays in the drum and mixes with water coming from the HP economisers, the steam exits the drum and flows to the HP superheaters. The steam flows through the high pressure superheaters, where it absorbs additional heat from the flue gas. The HP superheated steam exits the HRSG and enters the HP turbine section. A high pressure attemperator is provided at the inlet of the last superheater to control the temperature at the inlet of the HP turbine. The water for the HP attemperator is taken from the high pressure feedwater pump. The high pressure feedwater mass flow is controlled by the HP drum level control valve that is located upstream of the HP economisers. Generally, the analogue structure applies to the IP circuit. TagedPIn Fig. 9, a pulverised coal-fired power plant is modelled using two dynamic simulation programmes APROS and MODELICA. The power plant consists of an air/flue gas system and a water/steam system. In the steam generator, the chemically bond energy of the coal is converted into heat that is transferred from the flue gas side to the water/steam circuit and used to generate steam for a Rankine cycle. TagedPIn the water/steam system, the feedwater enters the economiser (ECO) at the top of the steam generator. The water is then directed to the membrane wall evaporator, where the evaporation takes place. Due the once-through design the evaporation zone is not defined and the two-phase region is load dependent. For low part load operation, during start-up or shut-down, a forced circulation is in operation. A cyclone is installed to separate the water droplets within the steam flow and a separator storage tank is used for phase separation. The circulation is forced by a circulation pump (CP) and the level is controlled by a circulation control valve. The circulated mass flow re-enters the steam generator at the economiser inlet. The produced steam, saturated or partly superheated, enters the steam cooled supporting tube system (superheater 1) of the convective heat exchangers and flows downwards to the superheater 2 (platen superheater). After the platen superheater, the steam flows through superheaters 3 and 4. In between the superheaters, three attemperator stages are arranged for steam temperature control. The reheater is divided into two heat exchangers and has one attemperator. The steam leaves the once-through steam generator and flows through the high pressure turbine before re-entering the steam generator via the reheater. Afterwards the steam fully expands in one intermediate turbine and two low pressure turbines to condenser pressure. The condensed water is fed through seven feedwater preheaters back to the steam generator.

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TagedPIn the air/flue gas system, the primary air is supplied by two speed controlled radial fans and flows through the regenerative air preheater into the mill (pulverizer). The coal dust is entrained with air, fed into the furnace and burned. The secondary air is supplied by two parallel forced draft fans, which are specified as axial fans with variable blade angle. Afterwards the secondary air passes a steam coil air preheater and the regenerative air preheater, before entering the furnace. In order to consider the false air, which is impossible to avoid in a balanced-draft system, ambient air is introduced at the hopper of the steam generator and adjusted for the nominal case. After exiting the steam generator, the now 350
400 °C hot flue gas flows through the selective catalytic reduction, the regenerative air preheater, the electrostatic precipitator and the induced draft fan that keeps the furnace at a slight negative pressure. 2.4. Automation system TagedPIn dynamic simulation, the selection of suitable control structures is essential in order to accurately describe the behaviour of thermal power plants during transients. The automation components, explained below according to Refs. [169,200,201], include measuring devices, analogue and binary modules, signal sources and controllers. TagedP2.4.1. Measurement modules TagedPMeasuring devices collect data on the physical properties and transmit them in analogue signals. The output signal of a measuring device can be used as an input signal for a control structure or for other purposes such as operation monitoring or data recording. Measuring values from thermal power plants include but are not limited to pressures, temperatures, mass flow rates and levels. TagedPThe pressure and temperature measurement modules can be applied to record the pressure and temperature of different process components such as points, tanks, headers, pipes, etc. ypout D ypinp yTout D yTinp

ð2:113Þ

TagedPThe flow measurement module can be used to record the mass flow rate through pipes, channels and valves.

youtm_ D yinpm_

ð2:114Þ

TagedPThe level measurement module can be applied to record the level in different components such as tanks and condensers.

yLout D yLinp

ð2:115Þ

TagedPIt should be mentioned that measurements devices may cause a pressure drop in the flow. This pressure drop is typically not considered in measurement modules and can be considered separately, if required. TagedP2.4.2. Analogue modules TagedPAnalogue modules are used to modify analogue signals. In these modules, the output signal is always analogue, but in addition to the analogue input signal, a binary signal may be found for controlling tasks. The analogue modules can be divided in three groups, namely basic, static and dynamic modules. These are explained in detail in the following sections. TagedP2.4.2.1. Basic modules. TagedPAnalog basic modules are adder, multiplier, divider, mean value, setpoint and signal splitter (see Fig. 10). The adder module is applied to add or subtract the signals yinl,1,yinl,2 and yinl, i. The output signal yout is calculated according to the equation: yout D § yinl;1 § yinl;2 § . . . § yinl;i

ð2:116Þ

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Fig. 8. Combined-cycle power plant modelled in ASPEN PLUS DYNAMICS (adapted from reference [38] with permission of authors and Elsevier).

TagedPThe multiplier module can be used for a multiplication of analogue signals. The output signal is calculated using the following equation: yout D yinl;1  yinl;2  . . .  yinl;i

ð2:117Þ

T n amplifier is a special case of the multiplier module and used to agedPA amplify the input signal yinl by a factor KP. The result is yout:

yout D kP  yinl

ð2:118Þ

TagedPThe divider is a module that can be used for a division of two analogue signals. The value of the output signal is calculated as:

yout D

ynum yden

ð2:119Þ

TagedPThe value of the denominator signal must not be equal to zero. TagedPThe mean value module calculates the average value of analogue input signals. The output signal yout is expressed as:

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Fig. 9. Pulverised coal-fired power plant; (a) modelled in APROS and (b) modelled in MODELICA (reproduced from references [21,53] with permission of authors, Elsevier and Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), License: https://creativecommons.org/licenses/by-nc/4.0/).

TagedP

TagedP yout D

yinl;1 C yinl;2 C . . . C yinl;i N

ð2:120Þ

TagedPThe symbol N represents the number of input signals. TagedPThe term “setpoint” refers to the target value of a variable. The setpoint module may have two operation modes (normal and tracking). In normal operation, the output signal is constant. For example, the control system of the boiler aims to maintain the steam temperature at inlet of the steam turbine at a constant temperature setpoint. In the tracking operation, the output signal is not constant and follows the value of the input signal either immediately or with a given gradient. TagedPThe signal splitter divides the same signal in two information flows. The input signal is yinl and the outlet signals areyout,1 and yout,2.

yout;1 D yout;2 D yinl

ð2:121Þ

TagedP2.4.2.2. Static modules. TagedPAnalogue static modules include delay, memory, switch, dead band, hysteresis, limiter, Max and Min selector, polyline and square root (see Fig. 11). Some of the static modules such as dead band and limiter are a source of discontinuity, which in return may result in numerical instability of the simulation. TagedPA delay module shifts the given value of an input signal yinl by a time constant T. The outlet signal yout is expressed as:

8 case tT <0 yout ðtÞ D : yinl ðt¡T Þ case t > T

ð2:122Þ

TagedPThe memory module is used as memory for an analogue signal value. The module has an analogue input signal, an analogue output signal and a binary input signal. If the binary input signal has the value FALSE, the output signal value is equal to the input signal value. If the binary input value is changed to TRUE, the value of the output signal is fixed and remains independent of the input signal value changes. TagedPThe switch module can be considered as selector between two analogue signals. It has two analogue input signals, a binary input signal and an analogue output signal. The output signal follows the first input signal, if the binary input is TRUE and follows the second input signal, if the binary input is FALSE. This can be described mathematically with the help of the following equation: 8 < yinl;1 case ybin D 0 ð2:123Þ yout D : yinl;2 casey bin D 1 TagedPThe dead band module has an analogue input signal and an analogue output signal. When the absolute value of the input signal is

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Fig. 10. Analogue basic modules; (a) adder, (b) multiplier, (c) divider, (d) mean value and (e) setpoint.

TagedPsmaller than the defined dead band value (DB), the output signal is equal to zero. If the input signal value is bigger than DB, the output signal is the input signal value minus the dead band value. If the input signal value is less than the negative dead band value (¡DB), the output value is then the sum of the input signal value and the dead band value. These relations are expressed by the following equation: 8 0 case jyinl j < DB > > > < ð2:124Þ yout D yinl ¡DB case yinl DB > > > : yinl C DB case yinl < ¡DB TagedPThe hysteresis module is used to form a hysteresis effect to an analogue signal. The value of the output signal will follow the input signal, so long as the value of the input signal is changing to the same direction. If the direction changes, then the value of the output signal is held constant as long as the total change to that new direction is smaller than the defined hysteresis value. TagedPA limiter limits the signal yinl within a predefined range using a highD90X X limit value LDhigh 91X X and a low limit value Llow. If the value of the input signal is between the given limits, the value of the output signal follows the value of the input signal. These can be expressed as: 8 yinl case Llow yinl Lhigh > > > < ð2:125Þ yout ¼ Llow case yinl < Llow > > > :L high case yinl > Lhigh TagedPThe Max and Min modules are signal selectors. The value of the output signal is equal to the highest value of the input signals in case of a Max operator and is the smallest value of the input signals in case of a Min operator. The equation for maximum value selection

fTagedP or two input signal is: 8 < yinl;1 case yinl;1  yinl;2 yout D : yinl;2 case yinl;1 < yinl;2

ð2:126Þ

TagedPThe equation for minimum value selection for two input signal is expressed as: ( yinl;1 case yinl;1  yinl;2 yout D ð2:127Þ yinl;2 case yinl;1 > yinl;2 TagedPThe function module can be used to form a polyline (n-point cross line curve) between two variables. The value of the output signal is a function of the input signal and the given polyline. The polyline will be defined by a set of (x, y) coordinate pairs. If the input signal value is out of the range of the defined x coordinates, the value of the output signal equals the function value of the last x coordinate. TagedPThe square root module returns a square root of an input signal value. The output signal is expressed as: pffiffiffiffiffiffiffiffiffiffi yout D jyinl j ð2:128Þ TagedP2.4.2.3. Dynamic modules. TagedPAnalogue dynamic modules include gradient, integrator, differentiator, derivator and filter. TagedPThe gradient module limits the rate of variation for a variable. The rate of variation can be limited separately for increase and for decrease direction. The value of the output signal follows the changes of the input signal considering the defined gradient limits. The value of the output signal is the same as the input, if the change in the input signal is slower than the defined gradient or the input signal does not change.

Fig. 11. Analogue static modules; (a) delay, (b) memory, (c) switch, (d) dead band, (e) hysteresis, (f) limiter, (g and h) max and min selector, (i) polyline and (j) square root.

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TagedPThe integrator and differentiator modules are simple control components. The output value of an integrator module can be expressed as: yout ðtÞ D

1 Tint

Zt yinl ðt Þdt

ð2:129Þ

0

TagedPThe rate of change of the output value is determined according to the given integration time Tint and the value of the input signal. If the input signal is positive, the output value is increasing. If the value of the input signal is negative, the output value is decreasing. The output value remains constant, when the input value is zero. For example, if the integration time is set to 60 s and the input signal is 1.0, the output value will increase to 1.0 within 1 min. TagedPThe differentiator module can be represented as first-order ordinary differential equation. The rate of change of the output value is calculated according to the given derivation time Tder and the value of the input signal yinl as: yout D Tder

dyinl dt

ð2:130Þ

TagedPThe derivator module defines the rapid changes of a variable. The output signal of the derivator depends on the derivation time and the derivation gain. The latter calculates the height of the impulse, while the derivation time determines the duration of the impulse. Using these parameters, it is possible to define the step response of the derivator module. If the value of the input signal does not change (steady state case), the value of the output signal is zero. TagedPThe filter module performs a filtering operation on an analogue signal. The value of the output signal is determined according to the input signal value and the filter parameters. The simplest filter is a moving average filter. The only parameter in this case is the time constant of the filter Tfil. TagedP2.4.3. Binary modules TagedPBinary modules (Boolean logic elements) are required for selection purposes in many control circuits. In such modules, the input can be binary or/and analogue signals, while the output is always binary. Therefore, when an expression is evaluated by binary modules, the output signal is ether zero or unity (zero means FALSE and unity means TRUE). The most relevant binary modules used in the dynamic simulation of thermal power plants are explained below. TagedP2.4.3.1. Basic modules. ITagedP n Fig. 12, basic binary modules (AND, OR and NOT) are depicted. The logical operator “AND” is applied in order to perform a logical operation AND for binary signals. The output signal is TRUE, when all input signals are in TRUE state. If one of the input signals is in FALSE state, the output signal is FALSE. ( 0 case yinl;1 D 0 or yinl;2 D 0 yout D ð2:131Þ 1 case yinl;1 D 1 and yinl;2 D 1 T he operator “OR” is used to perform a logical operation OR for agedPT binary signals. The output signal is TRUE, if any of the input signals

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iTagedP s in TRUE state. The output signal is only FALSE, if all input signals are in FALSE state. 8 < 0 case yinl;1 D 0 and yinl;2 D 0 ð2:132Þ yout D : 1 case y inl;1 D 1 or yinl;2 D 1 TagedPUsing the logical operator “NOT”, the state of the binary input signal can be inverted. It has only one input signal and one output signal. ( 0 case yinl D 1 ð2:133Þ yout D 1 case yinl D 0 TagedP2.4.3.2. Advanced modules. TagedPThe advanced binary modules include, among others, delay, switch, n/m selector, flip-flop, limit value checker, button, alarm and timer (see Fig. 13). TagedPThe delay module shifts a binary signal in time. It has one binary input signal and one binary output signal. The output signal will follow the input signal after a given delay time, which can be constant or varied by an analogue signal. Mathematically, this relation can be written as follows:

 yout t; DT ðtÞ D yinl t¡DT ðtÞ ð2:134Þ TagedPThe switch module is a selector between two binary signals. It has two input binary signals, an output binary signal and an input binary control signal. The state of the output signal follows the state of either of the two input signals depending on the control signal. ( yinl;1 case ycon D 1 yout D ð2:135Þ yinl;2 case ycon D 0 TagedPThe n/m selector is a logical selector module for binary signals. The symbol m denotes the number of input signals, while the symbol n is a given positive integer. The output signal is TRUE, when at least n number of input signals are in TRUE state. Otherwise, the output signal is in FALSE state. TagedPThe flip-flop is a bistable element, i.e. it has two stable states. The flip-flop module can be used as a memory in logical circuits. The state of the output only can be changed with a TRUE input signal, either SET or RESET signal. The output signal is: TagedP FALSE, if both input signals (SET and RESET) are in FALSE state. TagedP FALSE, if the RESET input only is in TRUE state. TagedP FALSE, if both inputs are in TRUE state and the RESET input is dominating. TagedP TRUE, if the SET input is in TRUE state. TagedP TRUE, if both inputs are in TRUE state and the RESET input is not dominating. TagedPThe limit value checker compares the analogue input value to a given limit value LV, resulting in the following output signal: agedPT FALSE, if the value of the analogue input signal is greater than the given limit value.

Fig. 12. Basic binary modules; (a) AND, (b) OR and (c) NOT.

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Fig. 13. Advanced binary modules; (a) delay, (b) switch, (c) n/m selector, (d) flip-flop, (e) limit value checker, (f) button, (g) alarm and (h) timer.

TagedP TRUE, if the value of the analogue input signal is smaller than the given limit value. TagedPThis relation can be expressed mathematically using the following equation: ( 0 case yinl  LV yout D ð2:136Þ 1 case yinl < LV T he limit value checker module can also form a hysteresis effect agedPT to an analogue signal. In this case, an additional hysteresis value HV has to be given. The output signal is: TagedP FALSE, if the analogue input signal is bigger than the given limit value plus the half of the hysteresis value. TagedP TRUE, if the analogue input signal is smaller than the given limit value minus the half of the hysteresis value. TagedPAccordingly, the following equation can be formulated: 8 0 case yinl  LV C HV=2 > > < yout D constant case LV¡HV=2  yinl < LV C HV=2 > > : 1 case yinl < LV¡HV=2

ð2:137Þ

TagedPA cold junction is a special case of the limit value checker. Here, the analogue signal is compared to another analogue signal, instead of the limit value in case of the conventional module. The output value is then: TagedP FALSE, if the value of the first analogue input signal is bigger than the value of the second analogue input signal.  TagedP TRUE, if the value of the first analogue input signal is smaller than the value of the second analogue input signal. TagedPMathematically, this relation can be written as: ( 0 case yinl;1  yinl;2 yout D 1 case yinl;1 < yinl;2

ð2:138Þ

TagedPThe button module has only an output signal. When the button is pushed, the output is in TRUE state. After a certain period of time defined by user, the output value returns to FALSE. TagedPThe alarm module provides alarms triggered by logical signals. If the input signal shows the desired value (TRUE or FALSE), the module sends an alarm message. TagedPThe timer module has an inlet and an output signal. When the inlet signal is set to TURE, the timer starts counting the time and

cTagedP ompares it to a given max time value. The output signal is in FALSE state, so long as the max time value is not reached. When the max time value is reached, the output signal is in TRUE state. The timer module can also be used as an analogue module. In this case, the time is given as analogue output value. Moreover, the timer can be reset via a RESET signal. TagedP2.4.4. Signal source modules TagedPThe signal source modules can be applied to define transient setpoints or to generate binary or analogue signals. These include pulse, noise, sine or cosine wave, square wave and triangular wav generator (see Fig. 14). The mean value of the output signals for analogue signal generators is zero. In the signal source modules, the output signal is a function of time:

yout D f ðtÞ

ð2:139Þ

TagedPThe pulse generator module generates binary pluses. The module has a binary input signal, an analogue input signal and a binary output signal. When the input signal is FALSE, the output signal is always in FALSE state. If the input signal is changing from FALSE to TRUE, the module will generate pulses. Each pulse lasts for half of the defined period time, which can be constant or varied according to the analogue input signal. TagedPThe noise generator module generates random signal with a constant power spectral density. The module has a binary input signal that is used to switch off the generator, an analogue input signal that is used to define a given variance and an analogue output signal. When the binary input is in FALSE state, the value of the output signal will be zero. If the generator is switched on, the module will generate normally distributed white noise of a given variance. TagedPThe sine wave generator module generates a sine wave. The amplitude and the time period of the sine wave can be constant or varied depending on analogue input signals. A cosine wave has a shape identical to that of a sine wave, with a phase-shift of p/2 radians. TagedPThe square wave generator module generates square waves. It has one binary input, two analogue inputs for amplitude and the time period of the generated wave and one analogue output. The output of the module is zero, if the binary input is in FALSE state. When the generator is switched on, the module will generate square waves according to the given amplitude and the time period that can be constant or varied following the analogue input signals. TagedPThe triangular wave generator module generates triangular waves and can be switched on/off by a binary input signal. The

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Fig. 14. Signal source modules; (a) pulse generator, (b) noise generator, (c) sine and cosine wave generator, (d) square wave generator, and (e) triangular wave generator.

TagedPamplitude and the time period of generated triangular waves can be defined by two analogue inputs. TagedP2.4.5. Controller modules TagedPThe well-known control schemes in process and energy systems are explained briefly below. These include feedback control, feedforward control, feedforward plus feedback control, cascade control and cascade plus feedforward control [202]: TagedP Feedback control scheme: A feedback control system represents the simplest form of closed loop control scheme. The error signal resulting from the comparison between the process output and the setpoint is used as a means for the controller. TagedP Feedforward control scheme: A feedforward control responses to the moment when the disturbance occurs. The process variable adjustment is therefore based on the knowledge of the process using mathematical model and measurement disturbances without having to wait for a deviation in the process variable. Due to modeling errors and unmeasured disturbances, a flawless feedforward control is not possible and is, generally, used in combination with a feedback control. TagedP Feedforward plus feedback control scheme: In this control system, the roll of the feedforward controller is to decrease or eliminate the effect of outer disturbances, while the feedback controller will respond to setpoint variations. Compared to a feedback control system, this combined control technique can significantly give better response to a disturbance that can be measured, before it affects the process output.  TagedP Cascade control with and without feedforward control schemes: The cascade control consists of two loops, namely an inner loop and an outer loop. This control scheme leads to the benefits required, only when the inner loop has faster dynamics as compared to the outer loop [203]. The cascade control is frequently used within the control circuits of thermal power plants. A combination of cascade and feed-forward control is achieved, in which the primary and the secondary processes are controlled by a cascade control, while the disturbance rejection is obtained using a feedforward control.

TagedPTypical variants of controller used in these control schemes are P-controller, I-controller, PI-controller, PD-controller, and PID-controller. The output of the controller yout is determined according to the control deviation of the controller and to possible feedforward input. yout D yPout C yIout C yDout C yFF out

ð2:140Þ

T ere, the term yPout represents the output of the proportional (P) agedPH part of the controller, yIout is output of the integral (I) part of the controller, yDout denotes the output of the derivative (D) part of the

cTagedP ontroller and yFF out is the output of the feedforward (FF) part of the controller. TagedPThe transient equation of a PID controller is expressed as: Z KP dy ð2:141Þ yout D KP yinl C yinl dt C KP TD inl TI dt TagedPThe parameters KP, TI, TD represent gain, integration time and derivation time of the controller, respectively. In order to obtain a PD or a PI controller, TI ! 1 or TD D 0 can be specified. In the control schemes of thermal power plants, the controllers applied are PI and PID controller. For the determination of controller parameters, several tuning methods can be found in the literature, namely stereotypical tuning methods and intelligent methods. The stereotypical tuning methods include Ziegler Nichols, relay auto-tuning, pole placement and internal model control [204]. The intelligent methods use fuzzy logic, genetic algorithms, artificial neutral networks and particle swarm optimization for finding the controller parameters [205]. TagedPWhich control scheme is more appropriate to control a process, it cannot be completely stated. For example, feedforward control may show in some cases better performance than feedback control or cascade control. A detailed understanding of the invistagted process and the control theory are therefore required in order to obtain a physically meaningful operation. Further information can be found for example in [206,207].

TagedP2.4.6. Examples TagedPThe control structures consist of various components such as controllers, analogue and binary components, which are combined in order to satisfy certain control requirements. In this section, different control structures used in thermal power plants, including drum level, steam bypass and feedwater control circuits [14,38] are explained as examples. TagedPThe three-element level controller is used to adjust the water level in different power plant components such as feedwater storage tank, feedwater preheater and drum. In Fig. 15, the three-element level controller of the drum in a heat recovery steam generator is illustrated. The controller adjusts the feedwater mass flow rate by controlling the feedwater valve, which is located between the boiler feedwater pump and the economisers. The operation algorithm of the drum level controller is described as follows: on the one hand, the difference between the feedwater mass flow rate and the steam _ is measured. On the other hand, the difference mass flow rate dm between the drum level setpoint and the actual value dL is measured. _ dL) affects a PI-controller. The The deviation of these two paths (dm, PI-controller commands the continuous device control (DC) that operates the drum level valve. If the pressure in the drum exceeds a certain _ dL) will be replaced by the pressure difference value, the deviation (dm, between the drum and the maximum pressure setpoint in order to prevent further increase of the drum pressure.

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TagedPThe high pressure bypass control circuit used in a combinedcycle power plant is depicted in Fig. 16. It routes the high pressure steam, which is not accepted by the high pressure turbine into the cold reheater. This control circuit is in operation during the power plant start-up, as long as the high pressure steam quality has not matched the high pressure turbine requirements. Furthermore, the high pressure bypass system is used during the steam turbine trip at any load. A desuperheater has been installed, which cools the steam behind the high pressure bypass control valve to 50 °C above the saturated steam temperature, before it enters the cold reheater system. The injection water is delivered from the high pressure feedwater pump. The main tasks of the high pressure bypass controller are to insure a smooth build-up of the high pressure during the start-up, to prevent the high pressure from decreasing during the turbine trip and to prevent the condensation in the high pressure superheater in case of a gas turbine load rejection. The principle of the work is as follows: TagedP During the start-up procedure, both HP bypass valve (HPBPCV) and HP main steam valve (HPMSCV) are initially closed. This procedure enables the pressure in the high pressure circuit to increase rapidly. When the minimum pressure setpoint is met, the HP bypass valve starts opening to counteract further rising of the pressure. Due to the continuous pressure increasing, the HPBPCV is forward opened. TagedP After the HP bypass valve is fully open, the steam pressure rises due to the steam generation increasing. At this stage, the automatic setpoint adjuster is activated. It tracks the bypassed pressure at interval about 1 bar below the high pressure. TagedP When a specified high pressure is reached, the HPBPCV is throttled to intermediate start position (circa 70%). This process ensures the high pressure to reach the fixed pressure setpoint faster. After the fixed pressure is met, the HP bypass valve limitation is switched off to hold the pressure at the fixed value by further opening of the HPBPCV. TagedP When the main steam control valve starts opening, the HP bypass valve starts closing in the same attitude. If the HPMSCV is fully opened, then the HPBPCV is closed. The high pressure bypass valve could be again opened, if the pressure in the high pressure circuit is increased over a defined setpoint (the nominal pressure pulse delta p) in order to discharge the high pressure. TagedP In case of the steam turbine trip, the HP bypass control circuit is put in operation. While the HPMSCV is immediately closed, the

TagedP PBPCV controls the high pressure to reach the pressure level, H which was existent before the steam turbine trip. Holding the pressure at high level has the advantage that the HRSG is already prepared to the hot restart. TagedP In case of gas turbine load rejection, the gas turbine exhaust temperature drops very fast to low level. In order toD92X Xprevent the condensation in the high pressure superheater, the HPBPCV will open to reduce the high pressure to its saturation temperature below the gas turbine exhaust temperature. TagedPA schematic representation of the high pressure feedwater control structure used in a Benson HRSG is illustrated in Fig. 17. This control circuit offers the possibility to operate the high pressure system in level mode (nature circulation) or Benson mode (once-through). Furthermore, it provides a save operation for heat recovery steam generator during GT transients and fast start-up procedures. The idea behind the feedwater mass flow controller is based on the heat of the flue gas that can be absorbed by HP evaporators (DhFG, EVA) as well as the enthalpies of the working fluid at inlet and outlet of HP evaporators (DhWS, EVA). The obtained value is then corrected by the attemperators mass flows as function of the feedwater mass flow, by the derivative element for considering additional heat output of the metal masses of the evaporator (Kmetal,EVA), by the derivative element for considering mass storage process of the working fluid in the economizer (DrWS,ECO), by the degree of sub-cooling at the evaporator inlet (Dsub), by the degree of superheating in case of Benson mode (Dsup) or the steam quality in case of level mode (DxD93X)X at the evaporator outlet. Depending on the operation mode (level or Benson), a further correction is also performed. While in level mode, the water level within the HP separator should be kept at a fixed level independent from the HRSG load, the enthalpy at the outlet of the HP separator in Benson mode should meet the load dependent enthalpy setpoint. 2.5. Electrical system TagedPIn addition to process and automation components, a thermal power plant contains several electrical modules that are vital for the power plant operation. The consideration of electrical components in dynamic simulation of thermal power plants is of high relevance to calculate the electrical power consumption at base loads and make sure that process and automation components get the needed

Fig. 15. Control circuit of the drum water level (extended from reference [38] with permission of authors and Elsevier).

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Fig. 16. High pressure steam bypass control circuit; (a) schematic representation and (b) modelled in APROS (extended from reference [14] with permission of authors and Elsevier).

TagedPelectric power during transients. Furthermore, electrical components are used to evaluate the effect of possible failures in the electrical network on automation and process components and to study the power plant behaviour at severe break down cases such as

TagedP lackout. In the latter, the electricity supply is lost and accordingly b all motor driven components trip. The passive system should direct the power plant to a safe operation point, which can be assessed using dynamic simulation models.

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Fig. 17. Control circuit of the feedwater mass flow rate in a heat recover steam generator (adapted from reference [14] with permission of authors and Elsevier).

TagedPThe electrical components required for the dynamic simulation of thermal power plants consist of node, line, switch, load, generator, transformer, direct current source, battery, inverter, alternating current/direct current converter and direct current/ direct current converter. The node, switch, line and load components can be applied to both alternating current (AC) and direct current (DC) electrical circuits. The battery and DC/DC converter are direct current modules, while the inverter and AC/DC converter connect direct current and alternating current circuits. The generator and transformer can be used only in the alternating current system. The electrical modules described below are explained as implemented in the process simulation software (APROS) [169]. TagedP2.5.1. Basic modules TagedPIn an electrical system model, the basic electrical components are node, line, switch and load. TagedP2.5.1.1. Electrical node. TagedPThe main function of the electrical node is to connect other electrical modules to each other. It can be applied for both alternating current and direct current electrical circuits (for example, see Fig. 18). T .5.1.2. Electrical line. TagedPThe electrical line is a component for agedP2 modelling bulk transfer of electrical energy via the electrical transmission line. The module can be a one phase DC electrical

lTagedP ine represented by a resistance (Fig. 18-(a) and (b)) or an AC electrical line with a pi equivalent circuit (Fig. 18-(c)). Each electrical line has an input and an output connection node, defining the positive direction of line from the input node to the output node. The type of the electrical line is automatically defined according to the type of the connection nodes (both connection nodes must be either DC or AC nodes). The electrical line has a built-in measurement for current, active power and reactive power. Transmission electrical lines become transmission networks, when interconnected with each other. TagedPIn direct current electrical circuits, the power is always active power in steady state. Furthermore, the capacitance or inductance elements are generally not considered. The reactive power only exists considering transient cases. The impedance of a DC electrical line contains only an active part, while the reactive part is zero. The current in a DC electrical line has a homogeneous distribution over the cross-section A. Accordingly, the resistance per length l can be described by the following equation: R D rel

l A

ð2:142Þ

TagedPHere, the character rel D94X X is the electrical resistivity that also known as specific electrical resistance or volume resistivity. The electrical resistivity is an intrinsic property, describing how strongly the material resists the flow of an electric current.

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Fig. 18. Models of a battery and a generator at a defined time during (a) discharging and (b) charging; (c) model of a direct current source followed by a DC/AC inverter.

TagedP2.5.1.3. Switch. TagedPThe switch is located between two electrical nodes and can be applied to direct or alternating current electrical circuits. The order of nodes is insignificant, but they have to be same type, either DC (Fig. 18-(a) and (b)) or AC nodes (Fig. 18-(c)). The switch is controlled by a logical input. If the input signal is in TRUE state, the switch is closed. In this case, the switch is a kind of a transparent module type, i.e. the electrical nodes on both sides of the switch have the same voltage. If the input signal is in FALSE state, the switch is open and there is no connection through this module to another node. TagedP2.5.1.4. Load. TagedPThe load module models the power consumption in alternating current or direct current electrical circuits. The load is connected to one node by either a DC node (Fig. 18-(a) and (b)) or an AC node (Fig. 18-(c)). The load has a built-in measurement for current, active power and reactive power. The reactive power is zero, if the load is connected to a direct current node. TagedP2.5.2. Current sources modules TagedPThe current sources modules are power generation devices. It can be distinguished between alternating current generators such as electrical generator and direct current sources such as battery and solar photovoltaic. TagedP2.5.2.1. Generator. TagedPThe generator module is applied to model the production of electrical power in alternating current electrical

cTagedP ircuits (see Fig. 19). The generator is connected to one node. The electrical power produced by the generator is the mechanical power multiplied by the efficiency. The generator has built-in regulators for frequency, voltage and power. TagedP2.5.2.2. Battery. TagedPA battery is an electric device, converting the stored chemical energy into electrical energy. The battery module can be applied to store the energy of the one-phase direct current or to supply current to the DC electrical circuits. The battery is represented as a direct current source, variable initial resistor and energy charging level counter. The operation modes of the battery include charge, discharge and stand-by. The charge/discharge processes of the battery depend on the voltage level of the direct current system and the remaining capacity of the battery. TagedPThe operating characteristics during the discharge of a battery depend on discharge capacity and voltage. The discharge capacity is a function of discharge current (loading), ambient temperature and long term warehousing, while the voltage is dependent on discharging current and state of energy storage (loading time). The discharge capacity Q can be described by Peukert exponential equation: Q ðIÞ D CI1¡n

ð2:143Þ

T ere, the symbol I is the discharge current, n denotes the Peukert agedPH exponent with default value of 1.4 and C represents a factor that is calculated at the nominal point of the battery:

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Fig. 19. Model of a thermal power plant connected to a power grid.

TagedP C D In t

ð2:144Þ

TagedPThe discharge capacity decrease during a simulation time step Dt is calculated as: 1¡n DQ D In Inom

Dt 3600

ð2:145Þ

TagedPThe symbol Inom is the nominal current. The voltage is determined with the formula: U D K1 K2 Unom

ð2:146Þ

TagedPHere, Unom represents the nominal voltage, the factors K1 and K2 are dependent on discharge current and discharge time. The discharge current is determined by the electricity consumption of the DC system. The discharge capacity of a battery decreases for reduced ambient temperature, during long term warehousing or stand-by without recharging. TagedPThe charging current can be expressed as a function of capacity:

I D Inom e

Q¡0:6Q max 0:5Inom

ð2:147Þ

where Qmax is the maximum capacity of battery and Inom represents the nominal charging current. The internal resistance of the battery can be changed to control the charging current. TagedPThe self-discharge process is simulated by decreasing the capacity of the battery by a small amount during each time step. The self-discharge of a battery can be considered in all operation modes (discharge, charge and stand-by). The self-discharge time of the battery depends mainly on the ambient temperature. For example, at 40 °C, the capacity of the battery is assumed to change from the maximum capacity to zero in 9 months. The self-discharge time is 21 months at 30 °C, while it is 32 months at 20 °C. TagedP2.5.2.3. Solar photovoltaic. TagedPThe solar photovoltaic system, also known as solar panel, is a module type for production of DC electrical power (see Fig. 20). The solar panel module is represented as DC current source with variable internal resistance and is connected to a weather component. The ideal DC source has constant internal resistance, while the internal resistance of the solar panel changes non-linearly with solar radiation. The current and voltage generated

TagedP y the solar panel module are dependent on the consumption of b electricity in the electrical circuit and the I-V curve of the solar panel. TagedP2.5.3. DC and AC modules TagedPThe DC and AC modules required to simulate the electrical network include DC/AC inverter, AC/DC converter, AC/AC transformer and DC/DC converter. TagedP2.5.3.1. DC/AC inverter. T TagedP he inverter is an electrical device, converting the voltage from direct current to alternating current. It can be applied to convert DC electricity from solar panels, batteries or fuel cells to AC for the electrical grid. The DC/AC inverter is usually not suitable for inductive AC and sensitive electronic devices that can be damaged by poor waveforms. TagedPThe inverter module has two connection nodes and simulates the transformation of DC electric power into three-phase AC electric power (see Fig. 18-(c)). The input electrical node is a DC node, while the output node is an AC type. The DC/AC inverter module is represented as one electrical line ending in a node with a high base admittance (nearly zero voltage) to the DC circuit, in addition to an AC three-phase generator for supplying power to the AC circuit. The connection between the DC circuit and AC circuit is arranged in such a way that the AC voltage is dependent on the DC voltage and the AC apparent power is equal to the power losses of the DC side resistance. As a result, the AC load is transferred into the DC supply side. TagedPThe inverter component can either control the voltage of the AC circuit or supply the required power. In the power supply mode, the power of the AC circuit is controlled according to the active power setpoint. In the voltage control mode, the inverter controls the voltage of the second connection node according to the nominal DC voltage and voltage. Generally, the single phase DC voltage UDC of the inverter is higher than the required three-phase (phase to phase) voltage UAC (approximately UDC D 1.634UAc). TagedP2.5.3.2. AC/DC converter. TagedPThe AC/DC converter is an electrical device, converting the voltage from alternating current to direct current. This device can be found in several electrical circuits (e.g. charging

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Fig. 20. Model of a solar panel with a battery and a load; (a) during the day and (b) during the night.

TagedPbatteries), but is characterised by poor current overload capacity and expensive automatic regulators. TagedPThe AC/DC converter module models the transformation of threephase AC electric power into a DC electric power (see Fig. 18-(b)). This is represented as one electrical line ending in a node with a high base admittance (nearly zero voltage) to the AC circuit and a direct current source, supplying the voltage or power to the DC node. The connection between AC and DC circuits is arranged to transfer the DC power loss into the AC supply side. In order to achieve that, the DC voltage should be a function of the AC voltage and the DC apparent power is equal to the power losses of the AC side resistance. TagedPSimilar to DC/AC inverter, the AC/DC converter can either control the voltage of the DC circuit or supply the required power. In voltage control mode, the conversion is based on a model of ideal diode bridge under the assumption that the ratio of AC and DC voltages is constant. The single phase DC voltage of the AC/DC converter is higher than the three-phase AC voltage (approximately UDC D 1.35UAc). If the AC voltage is lower, then the DC voltage shows a reduced amplitude. TagedP2.5.3.3. AC/AC transformer. TagedPThe generated electricity with low level voltage must be transformed to higher voltage for efficient electrical power transmission. In this case, the electrical current decreases, which in turn results in a reduction in the ohmic losses and a reduction in cross-sectional area of the electrical

lTagedP ines. Increasing the voltage by a step-up transformer at the generating side of the power network decreases the capital cost and improves the voltage regulation of the system. With the help of step-down transformer at the receiving end, the high voltage is reduced to the desired level for distribution to the consumers (see Fig. 19). The transformer consists basically of two or more coils that are electrically isolated from each other, but wrapped together around a closed magnetic iron circuit (core), allowing the electrical power to be transferred from one coil to other by induction. TagedPThe transformer is represented as one electrical line ending in a node with a high base admittance to the primary circuit and an alternating current generator for supplying the voltage or power to the secondary circuit (output node). This module has a primary and secondary connection node. Both connection nodes have to be alternating current nodes and the order of the nodes is important. TagedP2.5.3.4. DC/DC converter. S TagedP imilar to the transformer that transforms the voltage level between two AC circuits, the DC/DC converter is a module type for modelling voltage changes in DC electrical circuits (see Fig. 20). The DC/DC converter can either control the voltage of the secondary circuit or supply the required power. In the voltage control mode, the ratio of primary and secondary voltages is assumed to be constant. The converter is represented as one electrical line ending in a node with a high base admittance to the primary

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TagedPcircuit and a direct current source for supplying the voltage or power to the secondary circuit (output node). The connection between the primary and secondary circuits is arranged in such a way that the secondary voltage is dependent on the primary voltage and the secondary apparent power is equal to the power losses of the primary side resistance. Accordingly, the secondary circuit load is transferred to the primary circuit supply side. TagedP2.5.4. Examples TagedPUsing the described electrical components, the impact of possible failures in the electrical network on the energy system can be evaluated. Furthermore, the power consumption of process components can be calculated at steady state and in transient operation cases. The Figures below show different modelling examples of electrical networks. TagedPIn Fig. 18-(a) and (b), the dynamic model of a battery is illustrated during the charge and discharge processes. In addition to the battery, various electrical components, including node, line, AC/DC converter, generator and load are also modelled. In Fig. 18-(c), a DC source (either a battery or a solar panel) with DC/AC inverter, switch and AC load is shown. TagedPThe example of an entire thermal power plant model connected to the power grid is depicted in Fig. 19. The thermal power plant generates superheated steam that enters the steam turbine section. The mechanical power obtained by the steam turbine is transferred to the generator via a shaft. The electric power produced is fed to the power grid in addition to other generating units. Part of the electric power is used to cover the own electricity demand of the power plant. TagedPThe dynamic model of a solar panel with battery and load is presented in Fig. 20. During the day, part of the electricity generated by the solar panel is consumed by the load and the remaining part is used to charge the battery (Fig. 20-(a)). In the night, the direct normal irradiance becomes zero and accordingly the battery starts discharging (Fig. 20-(b)). 3. Combined-cycle power TagedPGas-fired power generation accounted for 22% total share in 2012 worldwide electricity generation according to IEA [208], dominated by combined-cycle power plants (CCPP). The modern concept of the combined-cycle is the result of an evolutionary process in the second half of last century, mainly driven by increasing performance of the gas turbine. As early attempts to combine a gas turbine (GT) and a steam cycle, the GT was installed to enhance the efficiency of existing large-scale steam power plants by using the hot exhaust gas for feedwater preheating instead of steam extractions or as a supply of hot combustion air to the fully-fired steam generator. Korneuburg A power station, commissioned 1960 in Austria, is considered to be the first CCPP according to the modern definition of combined-cycle. The general idea is that the waste heat of a gas turbine is absorbed by a heat recovery steam generator (HRSG) installed downstream in the flue gas path (see Fig. 21). The generated steam is used in a Rankine bottoming cycle, which generates additional power in the steam turbine (ST). Jeffs [209] reports that despite the sound approach, process efficiency of Korneuburg CCPP did not exceed 32.5%. The GT operating temperatures at the time were as low as 620 °C at the turbine inlet (TIT) and 310 °C at the turbine outlet (TOT), so that supplementary firing was still required to support the steam cycle. Major technological developments including high temperature resistant materials and thermal barrier coatings, low-NOx combustion and innovative cooling methods significantly improved GT performance since. Whereas early CCPP configurations only used simple single-pressure HRSGs, additional pressure stages were introduced over time in order to increase steam parameters and to reduce the temperature mismatch between flue gas and water/

sTagedP team side. Today a 1 C 1 arrangement of GT and ST units in combination with a triple-pressure reheat (3PRH) HRSG is state of the art, as shown in Fig. 22. Considering TOTs in the order of 600 °C, supplementary firing is widely omitted and nominal efficiency of the process can reach up to 60%. Also, combined-cycle power plants with efficiency levels greater than 60% are now running, for example Irsching 4 plant that is located in Irsching, Germany. A more detailed introduction to the technical characteristics of the combined-cycle process is offered in Kehlhofer et al.D95X X [210]. Combined-cycle power plants can also supply useful thermal energy for district heating, decreasing the total fuel consumption and reaching high efficiencies [211]. TagedPIn contrast to other thermal power plants, beside higher efficiency combined-cycle power plants are also characterized by flexible unit dispatch, see Lu and Shahidehpour [212]. Fast response capability is a prerequisite for increasing shares of renewable feedin and thus represents a competitive advantage for the operator in a changing market environment. Three criteria are typically considered to assess the practical flexibility of a power plant: start-up time, maximum load gradient (positive and negative) and minimum load. Only 10 min are required for starting a simple-cycle gas turbine, irrespective of its initial temperature. CCPP load transients are, however, limited by thermal stresses in the thick-walled components of the bottoming steam cycle, namely ST rotor, ST casing, high pressure (HP) drum and outlet manifolds of HP superheater and final reheater. A modern CCPP can complete the start-up procedure in less than 30 min after an overnight shutdown and sustain challenging load gradients up to § 60%/min, as e.g. stipulated by the Great Britain Grid Code for primary frequency response. The minimum load of a combined-cycle is mainly determined by the gas turbine, where stable combustion as well as CO and NOx levels in compliance with emission regulations must be preserved. Consequently, the corresponding operating point is dependent on the specific type of gas turbine and possibly country-specific regulation. The operating load can be decreased to 40
50% of nominal load for typical gas turbines. This level may be further reduced to 20% if a sequential-combustion design is used, so that one GT combustor can be shut down entirely. Minimum load is relevant to flexible operation since it defines the lower boundary for negative load changes. If frequent cycling is anticipated, a CCPP capable of operation at low minimum load may also be an economically viable option to reduce the number of startups and shutdowns. TagedPCalculation and optimisation of the transient system behaviour are an integral part of the CCPP design process with particular regard to control design. This ensures that the actual power plant meets the contractual guarantees and regulatory requirements in all states of operation. According to Radin et al.D96X X [213], dynamic

Fig. 21. Schematic of a combined-cycle power plant.

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Fig. 22. Detailed example flow chart of a triple-pressure bottoming cycle with reheat (extended from reference [18] with permission of authors and Elsevier).

TagedPsimulation is also a cost-efficient tool to support unit commissioning and regular operation by estimating component lifetime and directing maintenance. For verification of the overall plant design and control concept, a sophisticated simulation model is required that can be considered a virtual representation of all the essential systems for plant dynamics. The complexity of these simulation models, based on differential equation systems and numerical solution procedures, entails a computational effort that is unsuitable for optimisation purposes. Therefore, a reduced system model must be developed, which captures the dynamic behaviour and makes the problem accessible to mathematical techniques such as optimal control. The results are then verified by applying the optimised solution to the original simulation model and e.g. checking if boundary conditions are violated. TagedPThis chapter gives an overview of the published studies on dynamic simulation applied to gas-turbine based power plants, focusing on combined-cycles. Due to its considerable inertia and delayed system response, the bulk of the studies are dedicated to HRSG modelling and simulation. Section 3.1 introduces the reader to the dynamic behaviour of the CCPP by considering basic parameter variations and load changes. In Section 3.2, the simulation of startup procedures and the numerous investigations dedicated to startup optimisation are covered. Section 3.3 is a brief overview of complementary works on dynamic simulation in the broader context of gas-turbine based power plants, including numerical studies of compressed-air energy storage and integrated gasification combinedcycle.

3.1. Load change TagedPOne of the basic tasks for dynamic simulation in the field of thermal power plants is to calculate the response of the physical system and the control circuits to a change in load demand. While load changes are rather simple procedures both in terms of practical execution and numerical study, they are still useful to gain insight into the transient system behaviour of a combined-cycle power plant. TagedPFor the purpose of describing CCPP dynamics, the gas turbine can typically be treated as quasi-static component since the GT system inertia and characteristic time scale of GT response are negligibly small in comparison to the bottoming cycle. This statement does not hold if there is integration of gas turbine and bottoming cycle that prevents a separate analysis of the two, such as GT steam cooling. Detailed gas turbine modelling is not covered in this chapter: For system-level considerations, describing GT exhaust mass flow (including flue gas composition) and exhaust temperature as simple functions of load is often sufficient. Constant GT exhaust temperature is typically maintained in the range between full load and approximately 50% load whereas the GT exhaust mass flow shows a linear variation due to the changing position of the inlet guide vanes (IGV). Below this load range, the IGV remain at closed position and flue gas temperature is proportional to GT load. Thus a load change directly translates to a corresponding change of GT exhaust mass flow and/or flue gas temperature. TagedPFrom a mathematical point of view, this is a perturbation of the initial system in steady state to which the bottoming cycle responds

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TagedPdynamically. Dechamps [214] suggested four time constants of a single HRSG heat exchanger as measure of the time to reach equilibrium in response to a perturbation: TagedP t1 - governing the enthalpy exchange for the flue gas, TagedP t2 - governing the external heat transfer of the tube wall, TagedP t3 - governing the internal heat transfer of the tube wall, TagedP t4 - governing the enthalpy exchange for water/steam. TagedPPractical calculations show that the time constants for enthalpy exchange processes are comparatively small (t1 » 0.1 s and t4 » 1 s) and that the overall time constant of the single heat exchanger is typically controlled by external gas-side heat transfer (t2 » 100 s): t2 D

mc

a0 A 0

ð3:1Þ

T he time constant is therefore defined as the thermal capacitance agedPT of the heat exchanger mc divided by the rate of convective heat transfer a0D97X X A0. TagedPHowever, the HRSG is a complex arrangement of several heat exchangers positioned in the flue gas channel according to the temperature profile. In order to take into account the thermal capacitance of the components (j D 1. . .i ¡ 1) between the given component € len and Kim [215] state that the time conand the perturbation, Gu stant of a component ti can be approximated with sufficient accuracy by a simple summation of all single time constants: ti D

i X

tj

Fig. 23. Increase of time constants for warm start-up response of selected heat exchangers. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

ð3:2Þ

jD1

TagedPThe heat exchanger closest to GT exhaust, typically the final HP superheater, directly faces the perturbation in gas enthalpy. It is consequently the first to respond and eventually reach steady state. In contrast, the response of the next heat exchanger is delayed since part of the perturbation is absorbed upstream. The time constant of the individual heat exchanger in the HRSG thus increases in proportion to its distance from the source of the perturbation whereas the fraction of the heat input available to the heat exchanger decreases (see Fig. 23). TagedPShin et al.D98X X[216] studied the system response of a simple 2P HRSG to rapid changes and sinusoidal variations of GT load. The HRSG was modelled forming unsteady conservation equations of mass and energy for bulk heat exchangers. Fig. 24 illustrates the characteristic time scales of the gas turbine, high pressure (HP) and low pressure (LP) circuits using 10% load increase as example. The authors assume that GT load is controlled by the fuel mass flow in order to yield a step-like temperature increase, which explains the constant exhaust mass flow. From top to bottom, the figures show the responses of the GT system, HP and LP drum pressures as well as HP steam temperature and flue gas outlet temperature (the latter is closely linked to the temperature variation of the LP economiser). It can be observed that the gas turbine reaches stable operation after (tGT D 4 s), which is negligible in relation to the time constants of the HP and LP circuits (tHP D 200 s and tLP D 2000 s) and confirms that the quasistatic assumption is justified. The delayed response of the LP circuit in comparison to the HP circuit due to the accumulated thermal capacitance of the upstream heat exchangers is also reflected. TagedPPletl [87] conducted transient experiments supported by numerical simulation for a single-pressure once-through HRSG at the combined heat and power plants of TU Munich, where the gas turbine was simulated by a duct burner. Fig. 25 shows the measured and calculated flue gas temperatures as function of time for different tube layers between flue gas inlet and the stack in a rewetting experiment. The system is initially characterised by a deliberate lack of feedwater supply for the given, constant heat input. The steam is completely superheated already when entering the heat exchangers and no additional heat from the flue gas

Fig. 24. Gas turbine load increase and response of the double-pressure HRSG (reproduced from reference [216] with permission of Elsevier).

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TagedPis absorbed. Therefore, the flue gas temperatures for tube layers 36 and 40 are equal at t D 0. For 0  t  70, a linear increase of the feedwater mass flow to the nominal value is conducted. Since the function of heat exchangers in a once-through steam generator is variable, the zone of evaporation is shifted downstream and additional mass is injected in the HRSG. This entails a reduction of the water/steam temperature to saturation temperature for some tube layers that initially contained superheated steam, so that all heat exchangers contribute to heat transfer in steady state. The transient between the two operating points is governed by heat discharge of tube walls and structural material. The simulation results presented in the figure clearly show that neglecting thermal inertia in the HRSG model results in a significant underestimation of time constants and an inaccurate prediction of system response. The author also reports that compared to the consideration of thermal storage masses, replacing the standard homogeneous model with the more sophisticated slip flow model yields only a minor improvement of simulation results. A plausible explanation is that the 180 ° tube baffles between the tube layers allow for momentum exchange between water and steam phase [87]. It should finally be noted that the effect of thermal inertia is -vis a commercial plant more pronounced in this example vis-a due to the relatively large amount of liner and structural material in the scaled down HRSG system. TagedPKim and Edgar [217,218] developed a mixed-integer nonlinear programming approach and applied it to a combined heat and power plant. The power plant completely covers the utility's changing demands of power, heat and cooling throughout the year. The developed model aims to maximise the net income of the power plant by selling surplus power to the grid. The results show that the developed algorithm is an effective methodology with reasonable computation time of few hours to determine the optimal operation in 24 h ahead. TagedPThe dynamic behaviour of uncontrolled HRSG is usually not encountered in practical applications. Commercial CCPP use hierarchical plant control that is structured according to high-level unit control, system control and component control. As the basic control circuit of a transient HRSG model, feedwater control is addressed in the following. However, it must be complemented by several additional control circuits e.g. for live steam attemperation and ST bypass stations in order to describe the transient behaviour of the overall CCPP system.

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TagedPWeiß [219] and Rieger [19] investigated HRSG test configurations at the same plant in order to improve the performance of oncethrough feedwater mass flow control in response to rapid load changes. Weiß distinguishes between load changes with variation of the flue gas mass flow (upper load range) and load changes with variation of the flue gas temperature (lower load range). The former type is controlled with relative ease since all HRSG components are influenced at the same time and the temperature profile along the flue gas path remains largely unchanged. In contrast, for the latter type strong thermal charging and discharging processes of the storage masses are present that dampen load following behaviour of the bottoming cycle. The author therefore suggests a modification of the mass flow controller that introduces a source term for heat storage in the calculation of the mass flow setpoint. Based on measurement data, the current energy content of steel and water/steam inventory is estimated and compared with the fictional energy content in steady state for the current boundary conditions. The difference is used for adjustment of the feedwater mass flow, considering a desired transition time [219]. Rieger studied the capability of different control concepts for once-through HRSG to handle rapid load changes from full load to 38% and vice versa. In level control mode, the separator level is the controlled variable while steam enthalpy at the evaporator outlet is used for once-through control mode. Due to the long distance between control valve and measuring point, both control concepts are initially characterised by a slow response that allows controlling a maximum load gradient of § 7%/min. In an approach similar to Weiß, by considering thermal storage in the HRSG material the permitted load gradients in the test plant could be increased to 30%/min for level mode and 14%/min for once-through mode [19]. TagedPWhile level-based control is typical for drum-type evaporators, this concept is not applicable for once-through evaporators after the initial start-up phase since the separator is run dry. Alobaid et al.D9X X [14] developed a sophisticated mass flow controller for oncethrough HRSGs that covers all states of CCPP operation (see Fig. 17). The controller switches from level control mode to once-through control mode when a sufficient degree of steam superheating is reached at the evaporator outlet. The control principle is derived from the available heat input absorbed from the flue gas, which is corrected by thermal energy storage of the evaporator mass and divided by the desired enthalpy increase in the evaporator. Further corrections account for fluid-side mass storage in the evaporator,

Fig. 25. Boundary conditions for rewetting experiment (left), comparison of calculated and measured flue gas temperatures (right) (reproduced from reference [87]). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

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TagedPthe degree of subcooling at the inlet and the degree of superheating at the outlet to calculate the current mass flow setpoint [14]. 3.2. Start-up procedure TagedPFast start-up capability is the key benchmark for flexibility of a power generation unit and distinguishes CCPP from other conventional power plant technologies. The accurate calculation of combined-cycle start-up procedures and the reduction of start-up time with various optimisation methods therefore receive considerable attention in the literature. Start-up procedures are classified as hot starts after overnight shutdown, warm starts after weekend shutdown and cold starts after a shutdown of several days. However, these categories are too broad for practical purposes. Operating transients are in fact determined as function of initial “cold” metal temperatures of the thick-walled components, in particular ST rotor, ST casing and HP drum. A conventional CCPP start-up sequence, as shown in Fig. 26, is conducted as follows: TagedP Purging: The GT is accelerated to approximately 25% of nominal speed using the generator as motor or with an auxiliary starter. This speed is maintained for some minutes until the gas duct volume has been exchanged with air several times to remove any residual hydrocarbons. Condenser vacuum is established by a vacuum pump or ejector. TagedP Ignition and synchronisation: The burners are ignited, which marks the actual beginning of the start-up (t D 0). The GT quickly accelerates to nominal speed corresponding to the grid frequency, after which it is automatically synchronised. Up to this point, the sequence is independent of the initial metal temperatures. TagedP Steam temperature matching: The GT is loaded to minimum load (IGV in closed position) and held until the required parameters for steam admission to the ST (approximately 50% of nominal pressure and a sufficient degree of superheating) are met. Meanwhile initial steam generation is accommodated by the ST bypass system so that HP pressure is increased in a controlled manner. The hold time increases with the duration of the preceding shutdown. Once steam quality is confirmed, the ST control valve is opened and first steam is admitted to the ST.  TagedP Loading: The GT is loaded to the given load setpoint by gradually shifting the IGV to open position; the permitted load gradient is a function of the selected start-up mode. The switchover of steam

Fig. 26. Warm start-up curve for single-shaft combined-cycle power plant (reproduced from reference [210]).

TagedP dmission from ST bypass valves to the ST control valve is cona ducted in parallel. According to the common OEM definition, the start-up sequence is completed when all bypass valves are fully closed and the total steam generation is admitted to the ST. This point corresponds to approximately 90% of nominal load for a start-up to full load, so that the load may still increase after startup completion. TagedPThis step-by-step start-up sequence is conservative in the sense that the procedure limits thermal stresses due to a gradual increase of metal temperatures in thick-walled components. Kehlhofer et al.D10X X [210] specify conventional start-up times in case of a 400 MW single-shaft CCPP as 155 min for cold start, 105 min for warm start and 47 min for hot start. Recently, dynamic simulation was used to design fast start-up schemes for warm and hot start-ups that shorten or omit steam temperature matching by applying measures such as sophisticated stress control, flexible header design and cascaded HP steam bypass. The start-up time for hot starts can thus be reduced to less than 30 min, see Ruchti et al.D10X [X 220]. The following section is dedicated to publications on start-up simulation and the comparison of simulation results with measurement data. The balance between combined-cycle start-up time and lifetime consumption of the critically stressed components is the determining factor for start-up optimisation, as described in Section 3.2.2. TagedP3.2.1. Simulation TagedPInterest in CCPP dynamic simulation sparked in the early 1990s primarily in Europe and Asian-Pacific countries, owing to the success of combined-cycle in the recently liberalised electricity markets and the rapid progress in digital computing. TagedPIn an early study, Dechamps [214] described an approach to model the complex geometry of HRSG finned-tube bundles with an equivalent one-dimensional heat exchanger. The unsteady energy conservation equations for flue gas, metal and working fluid are discretised by finite-volume method and solved with an explicit integration scheme. The latter uses a constant time step and a density correction for numerical stability and reduced computational effort. Complemented by PID drum level controllers, the method is applied to reproduce the cold start of a 2P HRSG. The comparison with measurement, in particular the timing of first steam generation and the accurate jump of drum level, suggests that the system inertia and swelling effect are well described. Temperature results are not presented in the work, however. TagedPKim et al.D102X X[221] investigated the effect of CCPP cold start-up with a flue gas bypass on thermal stress in the drum of a 1P HRSG. Using the lumped capacitance method, heat exchangers are modeled as bulk heat exchangers and not discretised in space. The drum is assumed to reach thermal equilibrium after each time step, yielding a quasi-static problem formulation. The authors show that operation of the flue gas bypass can be scheduled to mitigate thermal stress peaks at the inner drum surface. Despite the simplifications and although the use of such bypass stacks has been widely omitted since, the study is one of the first to consider thermal stress in combined-cycle operation. TagedPAlobaid et al.D103X X [12] presented the model of a commercial-scale 3PRH HRSG, based on the six-equation flow model of the thermal hydraulic process simulator Apros as well as detailed geometry and heat balance data. The gas turbine is simplified as time-dependent boundary condition of exhaust gas mass flow and temperature. Fig. 27 shows part of the presented results for a warm start-up sequence, which are in close agreement with measurement data. The deviations of initial pressure level as well as steam flow during the switchover from ST bypass valve to ST control valve reflect unavailable information with regard to valve characteristics. TagedPMeinke [65] developed the process model of a 3PRH CCPP with a homogeneous flow model, using DYMOLA/MODELICA. In

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TagedPcontrast to the previously described studies, the model also includes the GT system and the associated control circuits such as exhaust temperature control by IGV and GT power control. This requires proprietary information such as the detailed characteristics of GT compressor mass flow as function of pressure ratio and IGV position. The model is validated with measurement data of a hot start to 54% load and results show generally good agreement, part of which are depicted in Fig. 28. A typical problem is the determination of the exhaust mass flow, which is not measured in the real plant but calculated indirectly via the residual oxygen content. This entails significant uncertainty particularly at low load. Based on the validated model, lifetime consumption of thick-walled components in the natural-circulation HRSG under a future scenario is estimated. This scenario attempts to reflect the German electricity market in 2023, which is characterised by the complete abandonment of nuclear power and a high share of renewable feed-in. Flexibility improvements

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TagedP f the current CCPP that translate into a minimum load of 40% o and a permissible load gradient of 4.8%/min are also considered. The study concludes that the share of lifetime consumption attributed to warm and hot starts of the plant is predominant and that the rate of lifetime consumption is nearly doubled in the future due to the higher frequency of warm starts [65]. TagedPWhile researchers usually close the differential equation system with empirical correlations, Sindareh-Esfahani et al.D104X X [113] used a Genetic Algorithm function of MATLAB/SIMULINK to identify unknown parameters for heat transfer. Two separate sets of experimental data gathered during HRSG cold start-up were required, one for training and one for model validation. TagedPHack et al.D105X X [131] presented a methodology for adaptation of HRSG design to cycling operation. Dynamic simulation of the CCPP system for cold and warm start-up is conducted in a first step, where the natural-circulation HP evaporator loop is considered in particular detail. Secondly, the calculated steam

Fig. 27. Boundary conditions during warm start (a), measured and simulated response of the high pressure circuit (b) (reproduced from reference [12] with permission of authors and Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

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Fig. 28. Calculated and measured parameters during the hot start-up of a gas turbine (reproduced from reference [65]). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

TagedPtemperature and pressure transients as well as the heat transfer coefficients are applied as boundary conditions for detailed finite-element analysis of the drum-riser connection (see Fig. 29). The obtained thermal stresses combined with pressure stresses are used to analyse the material fatigue caused by startup and shutdown cycles. Discontinuities such as weld connections and surface irregularities are accounted for by a conservative reduction factor for fatigue strength. The authors summarize that there is significant potential for start-up time reduction while maintaining acceptable component life. TagedPMertens et al.D106X [X 16] compared the dynamic behaviour of two 3PRH HRSG models - drum-type and once-through
with equal steady state output for cold, warm and hot start-up procedures using Apros. Thermal stress s D107XthX is generally proportional the difference between average wall temperature Tave and inner wall temperature Tin, which is negative for start-up processes:

s th D aT

blin Es 1¡v

ðTave ¡Tin Þ

ð3:3Þ

T ig. 30 shows the temperature responses in the wall of the HP agedPF -vis the wall of the once-through separator bottle, indidrum vis-a cating smaller temperature peaks and comparatively fast temperature adjustment for the separator. The study concludes that the once-through HRSG is favourable for combined-cycle plants with enhanced flexibility requirements, at the cost of slightly increased heat exchanger surface of the HP circuit (approximately 9% in the given case). TagedPRecently, Mertens et al.D108X X [18] studied the dynamic behaviour of a commercial 3PRH CCPP for a start-up and shutdown operating cycle with Apros. The measured and calculated responses for the HP circuit of the bottoming cycle are compared in Fig. 31, showing generally good agreement. However, the premature occurrences of the initial temperature ramp in the HP superheater and of first steam generation indicate that the thermal inertia of the real plant is

TagedP nderestimated in the model. The sudden pressure drop after shutu down, which is not explained by the simulation, is attributed to manual venting of the superheater in order to prevent condensation during extended standstill. € len and Kim [215] developed an independent concept, TagedPGu using the time constant of individual heat exchangers to model transient processes with simplified arithmetic equations rather than differential equations. Experience-based steam admission logic and practical assumptions are presented to complement the approach. For 3PRH HRSGs in combination with F-Class GT, the proposed method is shown to reproduce the published results of sophisticated codes with good qualitative agreement. As most researchers use complex simulation codes, which inherently impairs full transparency of the underlying methods and the possibility of reproducing results, their approach is a notable exception among the cited studies. TagedP3.2.2. Optimisation TagedPConsidering a given simulation model that can successfully reproduce the transient behaviour of the real power plant, it is straightforward to take one further step and investigate the potential for optimisation. For instance, existing CCPPs can generate additional revenue by faster start-up procedures if the additional costs for maintenance and replacement are appropriately taken into account [222]. This increase of lifetime consumption can be mitigated by incorporating rigorous start-up optimisation in the design of the CCPP, more precisely the minimisation of start-up time subject to operating restrictions such as thermal stress. Some recent efforts are dedicated to introducing Model-Predictive Control (MPC) in power plant systems, which offers performance advantages compared to conventional PID control, in particular for highly dynamic systems and systems with delayed response. In MPC the control input is computed by solving an optimisation problem for the

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Fig. 29. FEM analysis of local temperature and stress distribution at the high pressure drum-riser connection during a cold start-up (reproduced from reference [131]).

TagedPdynamic plant model over a receding time horizon. The control is only applied during a small part of the considered time before the calculation is repeated with a new set of states, so that future states of the system are taken into account. TagedPBausa and Tsatsaronis [223] found that numerical solution methods for large-scale dynamic optimisation problems, which assume the general form of differential-algebraic equation systems (DAEs), are available from optimal control problems in chemical engineering. The standard form of an optimal control problem is to minimise the cost functional JD109X X subject to the state equation a, algebraic constraints b and initial condition x0:


  Rt minuðtÞ J D t0f Lðx; u; tÞdt C f x tf ; u tf ; tf s:t: ð3:4Þ x_ D aðx; u; tÞ; 0  bðx; u; tÞ; x0 D xðt0 Þ

TagedPIn this notation xD10X iX s the state vector, uD1X iX s the control vector and tD12X iX s the time. The reader is referred to Bryson and Ho [224] for in-depth discussion on the necessary conditions for optimality. For the purpose of this chapter and the specific application to CCPP start-up, it is sufficient to state that numerical methods are required to solve nonlinear optimal control problems and that direct collocation methods have shown to be an efficient approach for large-size optimisation. The general idea of collocation is to discretise the state and control variables over time and to substitute these variables as well as the cost function with polynomial approximations (see Fig. 32). Polynomial coefficients are treated as variables of the optimisation process that need to satisfy the system equations at discrete points in the time domain, also known as collocation points. The discretised parameter optimisation problem can e.g. be solved by sequential-quadratic programming algorithms. In

Fig. 30. Temperature gradients in the separator wall (left) and in the drum wall (right) during hot, warm and cold start-ups (reproduced from reference [16] permission of authors and Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

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Fig. 31. Boundary conditions for a hot start-up and a shutdown procedure (a), dynamic response of high pressure circuit (b) (solid line: measurement and dashed line: simulation) (reproduced from reference [18] with permission of authors and Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

TagedPthe second part of the study [225], Bausa and Tsatsaronis illustrate the method by comparing unconstrained and constrained optimisation of a load change from 50% to 75% for a simplified single-pressure CCPP model.

TagedPMatsumoto et al.D13X X [226] improved the start-up schedule with a combination of fuzzy reasoning and neural networks in an early work. Expert knowledge is incorporated in fuzzy logic rules, which direct the optimisation qualitatively towards the optimum point.

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Fig.32. Discretisation according to Runge
Kutta method (left) and backward-difference scheme (right) (reproduced from reference [223] with permission of ASME).

TagedPThe neural network is trained in parallel, using start-up schedules and operating parameters as inputs and schedule modification rates obtained by fuzzy logic as outputs. During the optimisation, the actual schedule modification is gradually shifted from fuzzy logic to the neural network for fine adaptation e.g. to ambient temperature and humidity. Constraints such as thermal stress in the ST rotor, temperature gradient in the HP drum and NOx emissions were imposed. The authors report a reduction in start-up time and fuel consumption by 35.6% and 26.3%, respectively. TagedPShirakawa et al.D14X X [227] conducted start-up optimisation of a validated 3PRH HRSG model by sequential quadratic programming. The nonlinear optimisation problem is formulated to reduce start-up time, using control inputs bound by upper and lower boundaries and operational constraints such as ST rotor stress, temperature gradient in the HP drum and NOx emissions. Compared to conventional optimisation based on the practitioner's experience, start-up time is reduced by another 22% while satisfying the specified constraints. TagedPCasella and Pretolani [66] presented the simplified model of a 3PRH CCPP in DYMOLA/MODELICA for optimisation purposes, in which the LP system is largely neglected. The radial temperature distribution in the ST rotor is calculated by Fourier's equation, discretised with finite differences. Results show that the thermal stress

TagedP eak is located at the beginning of ST loading phase and that both p peak stress and start-up time can be significantly reduced with regard to the reference procedure, despite the fact that the optimisation process is described as “trial-and-error” rather than an optimality-based method. TagedPAlbanesi et al.D15X X [228] optimised the cold start-up procedure for different stress constraints of the ST rotor, using the variations of GT load and of valve position for ST admission as control variables. The result shows that the required start-up time is reduced by 20% for a conservative stress constraint and 48% for a standard stress constraint; however, the presented reference procedure is rather lengthy (340 min). TagedPFaille and Davelaar [112] decomposed the start-up transient in four phases and optimised steam temperature matching phase and GT loading phase with MATLAB/SIMULINK. As the resulting start-up sequence satisfies all operating constraints for the reduced model but exceeds one constraint for the detailed simulation model, their study demonstrates that the model to be optimised must accurately capture the original system dynamics despite the reduction in complexity. TagedPTica et al.D16X X [69] derived a reduced model from the simulation model by Casella and Pretolani [66] in DYMOLA/MODELICA in order

Fig.33. Switchover from grid operation to island operation, responses of generating unit (left) and frequency (right) (reproduced from reference [230] with permission of ASME).

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rTagedP esearch is dedicated to state estimation of the energy system required for on-line implementation. 3.3. Additional studies TagedPIn the following a brief overview of complementary works on dynamic simulation in the broader context of combined-cycle power plants is offered, including alternative concepts for GT-based power plants.

Fig. 34. Schematic of a compressed-air energy storage plant (simplified).

TagedP3.3.1. Island operation TagedPA case that rarely occurs in practice is the so-called island operation, i.e. power plant operation disconnected from the grid. Both Ahluwalia and Domenichini [229] and Maderni et al.D19X X [230] studied the transient behaviour of a 60 MW CCPP at Mirafiori, Italy, including the switchover from regular grid operation to island operation. Fig. 33 shows the simulation results for opening of the circuit breaker, yielding a rapid drop from full load to the load level currently demanded by the local manufacturing plant. The authors also report an effort to control high-frequency and high-amplitude load disturbances in island mode, related to welding stations.

TagedPto make it accessible to gradient-based optimisation methods. These methods require continuously differentiable equations so that possible sources of discontinuity in the reference model, such as conditional functions, case distinctions and lookup tables, must be replaced with smooth approximations. Small deviation from the reduced model is reported when the computed solution of the minimum-time optimal control problem is re-applied to the reference model. In conclusion, the authors state that the proposed method is able to convert nonlinear simulation models based on MODELICA into reduced optimisation models suitable for MPC. TagedPIn an effort to close the gap between physical modelling on the one hand and optimisation on the other hand, Larsson et al.D17X X [102] extended the open-source platform JModelica.org as interface to numerical optimisation algorithms. The nonlinear MPC optimisation problem is formulated with the Optimica extension of MODELICA and solved by direct collocation methods and automatic differentiation. A case study of a warm combined-cycle start-up with MPC is presented using the same reference model [66] as Tica et al.D18X IX t is concluded that the proposed framework can be successfully applied to nonlinear MPC in the field of power generation, and that further

TagedP3.3.2. Compressed-air energy storage TagedPThe basic idea of compressed-air energy storage (CAES) is to combine a simple-cycle gas turbine process with storage for pressurised air (see Fig. 34). Operation of the plant is therefore inherently dynamic: In storage mode, the storage cavern is loaded with pressurised air when excess electrical energy is available. In generation mode, the air is used for combustion of natural gas in the GT during peak electricity demand. The gas turbine with compressed air energy storage can be started without additional energy from the power grid and reaches 100% of its nominal load in approximately 6 min. For the purpose of comparison, new gas turbines (without compressed air energy storage) can be run up to full load within 20 min, while the half of the generated power is used to drive the compressor. The fast start-up of CAES power plants is of high relevance as a standby power plant for case of electrical network failure and even to stabilize variances of fluctuating energy sources such as wind energy etc. For CAES a large, well-explored and pressure-tight storage cavern is required, resulting in a limited number of suitable sites. Two plants currently exist in the world: Huntorf in Germany (290 MW, hD120X D X 42%) and McIntosh in the USA (110 MW, hD12X D X 54%). The latter is more efficient since exhaust heat is recovered for preheating

Fig. 35. Simplified flow chart of an integrated gasification combined-cycle process.

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Fig. 36. Overview of a hard-coal fired power plant (reproduced from reference [233] with permission of Springer).

TagedPof the combustion air. Based on dynamic simulation of the cyclic operation, Yoshimoto and Nanahara [231] combined CAES with a water/steam bottoming cycle for increased efficiency. Nielsen and Leithner [88] further improved the concept by means of a thermal storage that absorbs heat from the hot compressed air in storage mode for combustion air preheating in generation mode. In addition the study proposes the use of a brine shuttle pond at the surface connected to the cavern, which in contrast to conventional CAES allows almost isobaric discharging by varying the storage volume (for details, see Nielsen [89]). TagedP3.3.3. Integrated gasification combined-cycle TagedPThe integrated gasification combined-cycle (IGCC) is a promising concept to make the high-efficiency combined-cycle process available to solid fuels such as coal by means of a chemical gasification and syngas treatment plant installed upstream (see Fig. 35). The distinct advantage of IGCC is the possibility to efficiently integrate pre-combustion capture of carbon dioxide. Only a small number of IGCC plants without carbon capture were commissioned hitherto due to the substantial complexity of the process, which drives investment costs and heavily affects practical availability. Operating experience of these plants also shows that dynamic operation is a challenge, motivating several recent publications on the subject. TagedPSeparate component models and their control circuits were presented by Seliger et al.D12X X [111] for the cryogenic air separation unit in MATLAB/SIMULINK and by Robinson and Luyben [39] for H2S absorber unit, water-gas shift reactors and CO2 stripping unit in Aspen Dynamics. Casella and Colonna [67] coupled the MODELICA

TagedPmodel of an entrained-flow gasifier to an existing CCPP model for system-level control studies. Limited validation of the gasifier model is conducted with steady state reference data of an operating IGCC. Bauersfeld [68] developed a modular MODELICA library of IGCC components, focusing on the chemical systems for syngas treatment. Lee et al.D123X X [232] conducted dynamic simulations with the detailed model of a Shell entrained flow gasifier, partially validated by steady state data. Najmi et al.D124X X [95] investigated different control strategies for IGCC load change in gPROMS. A buffer tank between sorptionenhanced water gas shift and GT is used in order to reduce the fluctuations in mass flow and composition of fuel gas. The authors state that smooth operation during load changes can be maintained if the load ramp of the gasifier is initiated ahead of the GT, which follows a sequence of multiple small load changes and intermediate waiting times. 4. Coal-fired power TagedPCoal-fired power plant plays a major role for the global electricity supply at present and in the foreseeable future. The specific contribution varies from country to country and depends on several impact factors such as coal and gas prices, political framework, local resources and access to the world market. In Fig. 36, the flow schematic of a modern hard-coal fired power plant is presented. The main component is the steam generator, where pulverised coal entrained with the primary air flow is burned, releasing the thermal energy stored in chemical bounds. The obtained heat is transferred to the working fluid in economiser, evaporator and superheater in order to generate steam for the Rankine cycle. Modern coal-fired

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TagedPpower plants use single reheat and several low pressure and high pressure feedwater preheaters, resulting in an increase of the thermal process efficiency. The flue gas leaves the steam generator and the remaining heat is applied to preheat the combustion air using an air preheater. The flue gas may pass different cleaning devices like selective catalytic reduction system, a particulate collector and a desulphurisation unit. The size of a coal-fired power plant has a range from small industrial units to large utility power plants with up to 1300 MW per unit [233]. TagedPEven though all coal-fired power plants are working on the same principle, every power plant is individually engineered, which leads to different operation modes and different dynamic behaviour. Criteria that define the specific design are listed in the following points: TagedP Coal composition: The coal composition has the most important influence on pulverisers, burners, furnace, heat exchangers, fouling and size of flue gas cleaning devices. Here, the content ash, sulphur, volatiles, water and fixed carbon lead to specific requirements for each component. The list of fuel categories is long and varies from country to country and reaches from (meta-) anthracite over bituminous and subbituminous coal to lignite [234]. TagedP Fuel handling and firing concepts: Normally, pulverised coalfired plants are equipped with a direct firing system. Here, the raw coal is pulverised in the mill and transported by primary air directly to the burners. Depending on coal composition, different mills like ball tube, ball, roller, beater mills can be used. The respond of the pulverised coal flow to a change of the raw coal feed or the primary air has a significant impact on the dynamic and transient behaviour. In power plants with circulating fluidized bed (CFB) combustion, different dynamic responses are occurring. TagedP Emissions limits: The local emission regulation limits define how large the flue gas cleaning devices have to be designed and weather to be applied at all. TagedP Water/steam cycle: While power plants with supercritical steam parameters are always designed for once-through operation, plants with sub-critical steam parameters may also be equipped with a natural or a forced circulation. Even though one reheater stage is state of the art, some plants are equipped with a second reheater stage. TagedP Reheater temperature control: The usage of water extracted from the feedwater pump in attemperators is the most common way for temperature control of coal-fired power plants. If other reheater control concepts like flue gas recirculation, tilting burners, flue gas dampers or internal heat exchangers in the water/ steam cycle are applied, other controls are necessary and the dynamic behaviour may differ. TagedPDynamic models of coal-fired power plants are developed for different reasons. At early stages, the models were often restricted by the computational time and therefore limited to smaller subsections of the power plant. Here, the models were generally divided into small subsystems like turbine or boiler systems. One of the most detailed model of a fossil-fired plant of the first two decades of dynamic plant simulation was published by Armor et al.D125X X [235] in 1982. The authors used the tool, so-called modular modelling system in order to create a model of the Mystic Unit 7 power plant (550 MW). Although the developed model was very complex, but the used fuel in the steam generator is oil. Apart from the missing pulverisers and the additional flue gas recirculation, the power plant is similar to other coal-fired power plants of the time. The authors described the modelling process and gave an interesting overview of the occurring problems. For a quality check of the power plant model, several simulation tests have been performed, showing a promising match between the measured data and the predicted

sTagedP imulations. The general approach of the model was unconventional for time and gave an idea for whole scope of dynamic power plant simulation. Today, the computational resources are sufficient and the numerical models of coal-fired power plants are becoming more detailed, driven by increasing market pressure for high efficiency, operating flexibility and emissions compliance. Since the response of pulverised coal flow to a change of the raw fuel feed is of great importance for the dynamic behaviour of a coal-fired plant, different mathematical models were developed. For the description of vertical pulveriser, several models are proposed over the last decades (among others: Lee [236], Fan [237], Zhou et al.D126X X [193] or Niemczyk et al.D127X X [238]). Others models developed for tube-balls (Wei D128Xet X al. [239]) or for beater mills used in lignite coal-fired power plant like the model of Debelikovic et al.D129X X presented in their work [240]. In general, the pulveriser models have different parameters that must be adjusted to the specific type of pulveriser, since factors like size or geometry have an influence on the dynamics of the power plant. The pulveriser model of Fan [237] has been validated with operational data of a vertical spindle mill in Australia, but for other pulveriser types the available data is limited. TagedPIn this section, the dynamic models of coal-fired power plants from the literature are categorised in different sections corresponding to the published simulation results. 4.1. Response to disturbances TagedPAt the beginning, researches and engineers tried using dynamic simulation models to understand the response of the coal-fired power plant during a disturbance [241]. The mathematical model of a 200 MW drum-type steam generator was one of the first detailed models published by Kwan and Anderson in 1970 [242]. In order to describe the system, 109 equations have been developed and linearized. In the 1970s, the dynamic process simulation was at the beginning of its development and limited by the computational resources and powerful tools. Nevertheless, the illustrated results show the impact of a step change of the governor valve, fuel, air flow or feedwater supply to the rest of the power plant. With the aid of the dynamic simulation tools, the qualitative and quantitative behaviours after a step disturbance became a well-known scenario. Therefore, the simulation of a step disturbance is often used as an indicator for the model quality of large and complex models when operational data is missing. Lu [117] introduced a model of 677 MW unit located at Castle Peak B power plant in Hong Kong, China using MATLAB/SIMULINK. The model itself has a general purpose reaching from optimisation to personal training. The used equations are described and offer the reader a very good overview of the mathematical structure. However, the numerical results obtained from dynamic simulations lack validation towards experimental data. The model quality is checked via the response to step changes, namely a change in the main pressure step change and a sudden position change of the main steam valve. The given results indicate a reasonable response of modelled physics and control systems. Recently, an entire coal-fired power plant model of one 500 MW unit at the Didcot power station was presented by Oko and Wang [243]. The developed model describes the steam generator and the complete water/steam side without the mills and the gas side. Unlike other transient models, it is validated with steady state plant measurements at 70%, 80%, 94.4% and 100% load. The numerical results obtained from the model shows a good agreement for those four steady state points. Nevertheless, no transient validation has been performed due to the lack of experimental data. The quality of the transient behaviour is uncertain; however the calculated step load changes have reasonable characteristics.

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Fig. 37. Comparison of a classic start-up (left) and an optimised start-up (right) (reproduced from reference [168]).

4.2. Start-up procedures TagedPThe stress in the thick-walled components like headers or drums is induced by the change of pressure and temperature during a transient. These components (see Section 2.3.3) are expensive and damages can lead to crucial economic losses for the operator. In coalfired power plants, the most crucial operation is the start-up when high gradients in the metal structure occur. Since the stresses in the drum or headers limit the absolute start-up time, they are of special interest. In the past, start-up curves of thermal power plants often designed on operational experience and conservative assumptions. The use of dynamic simulations tools offered the possibility of optimisation of the start-up progress by limiting the stresses in the € ger et al.D130X X [244,245] published an optithick-walled components. Kru mised control concept for the start-up procedure of a drum boiler. The model is an extended version of the well-known drum boiler model of Astroem and Bell [246], including economiser, evaporator, drum, superheater, attemperators and bypass system. The main focus was the stress reduction in the thick-walled components. The authors give a very good overview of the start-up procedure as well as the initial conditions and show the results of standard classic start-up and a stress-optimised start-up. In Fig. 37, both start-up procedures are compared. Due an optimised fuel supply and bypass control, it was possible to shorten the start-up time significantly,

TagedP hile keeping the thermal stresses within the required borders. On w the base of this drum steam generator, Franke et al.D13X X [247] extended the generic model for the on-line application in a commercial thermal power plant. TagedPMeinke et al.D132X X [71] developed a detailed model of the 508 MW hard coal-fired plant located in Rostock, Germany, which includes all relevant plant components and control schemes. For the modelling process, the simulation platform MODELICA and the non-commercial library ThermoPower [248] was used. The focuses in this study were the additional developed components like two-phase tanks and the gas side of the steam generator. In order to evaluate the quality of this model, a comparison of a start-up from 0 to 90% after 37 h shut down period between the model and operational data was performed. The given results show a high accuracy of the 240 min long start-up procedure. Fig. 38 illustrates the mass flow rates and temperatures at the inlet and the outlet of the steam generator as well as the pressure and temperature at the outlet of SH1. At the beginning of the simulation, the steam generator operates at part load recirculation mode and a constant mass flow into the high pressure system is maintained. It is visible that the developed model and its corresponding control schemes calculate correctly. Only in the life steam production between 20 and 40 min, larger differences occur. The authors used this model to investigate the stress in the thick-walled components during start-ups and load changes.

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Fig. 38. Experimental and numerically obtained mass flow rates and temperatures at the inlet and the outlet of the steam generator as well as the pressure and temperature at the outlet of SH1 during start-up procedure (reproduced from reference [71], Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), License: https://creati vecommons.org/licenses/by-nc/4.0/). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

Fig. 39. Results of electrical load, main stem pressure, main steam temperature and drum level during transient response for load ramp from 55% to 95% load at 5%/min (top) and transient response for load ramp from 75% to 95% at 20%/min (bottom) (reproduced from reference [249]).

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Fig. 40. Experimental and numerically obtained steam mass flow rate and temperature during a load change (reproduced from reference [118]). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

4.3. Flexibility increase TagedPModifications of existing coal-fired power plants are driven by different reasons and dynamic models can help to investigate new innovations. Here, detailed models are often used for complete system integration of a new control concept or component. A good example is the work of Roth et al.D13X Xin 2005 [23] reported of the waste heat integration into the feedwater preheating system. The authors employed the simulation software APROS for the modelling of the 392 MW coal-fired power plant. The model itself is comprehensive and separates into 500 components. The simulation results show how fast an additional amount of heat could be converted into electricity. Other models are used for the new control concepts like the drum boiler model introduced by Peet and Leung [249]. It takes the boiler, the turbines and the feedwater track into account. The study includes a good overview of the main steam temperature and the unit control. The reheat temperature is controlled by dampers in the second pass of the boiler. With the non-validated model, several simulation have been performed, including load changes (100
95
100%, 55
95% and 75
95%) with different load change rates and a load rejection calculation. The results for a load change from 55% to 95% at 5%/min and 75 to 95% at 20% /min are presented in Fig. 39. The numerical results show that the implemented controls can maintain pressure, steam temperature and drum level after the fast load change. Here, a classic advantage of dynamic simulation tools is visible, i.e. the investigation of the plant response during a load change with 20%/min with a numerical model has much less risks. TagedPIn order to optimise the control strategy of a 600 MW supercritical pulverized coal-fired power plant, Mohmand et al.D134X X [118] used a MATLAB/SIMULINK model with fuel, feedwater and main steam position as input parameters. The focus is on the water/steam side leaving the gas side completely out of the model by converting the fuel flow directly into heat. The reported results, like the main steam mass flow rate and temperature during a load change from 350 to 600 MW in Fig. 40, look promising. The results and the operational data during this specific load change have very little derivations and the implemented control circuits behave like the original ones. Several assumptions for model simplification have been applied, which limit the model for other or more complex purposes. TagedPThe model published by Meinke et al.D135X X[71] was extended in order to evaluate faster load change rates [65]. Here, the regular load change rate (2%/min) was doubled (4%/min) and the corresponding steam temperatures and the induced thermal stresses were analysed. In Ref. [65], it was shown clearly that a load change from 37% to 100% with a doubled change rate results in unfavourable fluctuation in the steam temperatures. With an optimised control strategy

TagedP f the load change, the simulation shows that the steam temperao tures can be kept within reasonable limits. Zehtner et al.D136X X [24] developed a model of the 450 MW hard coal thermal power plant Zolling, Germany in 2008 using the commercial simulation tool APROS. Even though the need for flexibility improvement of existing power plants in Germany was not key motivation for this study, the model was one of the first large detailed models that are used to investigate the dynamic response of the hard coal thermal power plant. The model describes the water/steam side in detail, while the gas side is not modelled in detail as in later published studies [71,21]. The model of Zehtner et al.D137X [X 24] used to evaluate the power plant response for secondary frequency control applying different condensate throttling variants and feedwater oversteering. Here, the standard condensate throttling procedure of the thermal power plant, simulated with the model, shows a good agreement with the operational data (see Fig. 41). The model also includes a stress and fatigue calculation of the thick-walled components. A more detailed description of the numerical model and the corresponding simulation results are given in [25]. TagedPThe recently published study by Starkloff et al.D138X [X 21] of a large hard once-through coal-fired power plant in Germany focused on the model description and the validation of the numerical model with operational data. Therefore, a negative load change from 100% to 27.5% is presented, e.g. live steam pressure during the load change and the O2 content in the flue gas downstream of the regenerative air preheater (see Fig. 42). Unlike most other models in scientific literature, the different firing levels in the steam generator are mod-

Fig. 41. Simulation of a condensate throttling and the comparison with operational data (reproduced from reference [25]). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

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Fig. 42. Measured and simulated steam pressure and O2 content during a load change (reproduced from reference [21] with permission of authors and Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

TagedPelled, which offer the possibility of shutting individual levels off. Since the model was developed for flexibility increase in general, it is modelled with minimal boundary conditions and realistic control schemes. The validated model is prepared to investigate most thinkable flexibility increasing measures. TagedPRichter et al.D139X [X 250] used the simulation tool MODELICA for flexibilisation of coal-fired power plants. By contrast to the study in [71], the ClaRa library is applied. The described unit and the fuel are not specified. The structure of the water/steam side and the steam generator is detailed and comparable to [71] or [21]. However, the different firing levels are not discretised. The dynamic behaviour is validated with operational data during a load change from 60 to 90 to 75% within 100 min of an unknown unit (see Fig. 43). Even though the simulation and the experimental data show a good agreement, some derivations are visible. The authors explained them due to the fact of simplification of the unit control, where the developed model is used to evaluate an energy storage system within the water/steam cycle. The shown concept gives an idea of the future role of thermal energy storage systems in the power plant process. TagedPThe supercritical model developed by Zindler et al.D140X X [251] was generated in order investigate the British grid code. In the non-commercial software Enbipro, a very simplified model of the steam generator and the water/stem side has been generated. Unfortunately, there is no validation of the model performance at all.

4.4. Oxyfuel concept TagedPIn the last decade, the carbon capture and storage (CCS) technology, which has a significant CO2 reduction potential, moved into the focus of scientist and industry [252,253]. One of the CCS technologies is the combustion of a fuel with a nitrogen-free oxidant. Air is therefore separated into nitrogen and 95% pure oxygen, employing an air separation unit. The oxygen enriched air is burned together with recirculated flue gas in order to keep the flame temperature in the range of conventional power plants. A challenge for the design and operation of an oxyfuel coal-fired power plant is the flue gas side with its complex recirculation path, the air separation and the gas processing unit. Unfortunately, the design and operation experiences of large conventional thermal power plants can be only partly applied since whole structure of the gas side is quite different. Furthermore, the experiences of oxyfuel pilot facilities can be only partly adopted for large-scale power plants due to test plants character and inadequate knowledge of the real process. Therefore, onedimensional dynamic process simulation offers the possibilities to evaluate different scenarios and to develop control strategies for the new process. There are different designs for commercial large-scale oxyfuel coal-fired power plants; nevertheless the basic structure of the recirculation path is basically similar. The proposed models are mostly complex and reasonable detailed. Most works concentrate

Fig. 43. Measured and simulated power output and temperatures during an off-design operation (reproduced from reference [250], Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), License: https://creativecommons.org/licenses/by-nc/4.0/). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

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Fig. 44. Flue gas composition and temperatures during a switch over from air to oxygen firing at 100% load (reproduced from reference [256] with permission of Elsevier).

TagedPmore on the model itself than on the results like in [254], where very detailed model of an 800 MW oxyfuel coal-fired power plant was presented. Here, the oxygen boiler is coupled with an air separation unit and the gas processing unit. However, no results of an air to oxygen switch were given. TagedPRecently, Jin et al.D14X X [255,256] described a dynamic model of 600 MW oxyfuel power plant using ASPEN Plus DYNAMICS. The model is very detailed on the gas side and the water/steam side, respectively. A various number of simulations carried out like responses to disturbances in coal feed or oxygen purity. The proposed switch over from air to oxygen and vice versa occurs at the nominal load of 100%. The proposed procedure is capable to switch from air to oxygen firing within 17 min at recycle ratio of 0.7. In their work, the responses of the products SO2, SO3, CO, NO, NO2 are illustrated, which may peak like NOx during the switch over procedureD.D143X2 X Here, the chemical background and the good database of chemical reaction parameters of ASPEN Plus DYNAMICS is very supportive. The results also indicate the changing of the flue gas composition and the higher heat capacity that leads to lower gas temperatures at the end of the switch over (see Fig. 44). However, it is not reported, if the dynamic behaviour of the gas temperatures has an impact on the steam parameters. TagedPApart from oxyfuel coal-fired power plants with pulverised coal furnace, the circulated fluidized bed boiler is another option for a large-scale application of an oxyfuel power plant. Consequently, dynamic models of CFB plants were developed [257,258]. Complex models of air fired CFB models are given in [259,260]. The study of a large CFB power plant published by Lappalainen et al.D14X X [258] gives several CFB specific aspects in an oxyfuel environment. The simulation software APROS is used to model and investigate the air to oxygen switch. In addition to switch over from air to oxygen and from oxygen to air, the sensitivity of the mode switching to disturbances

(TagedP malfunction of the coal feed, low oxygen purity or wrong oxygen measurement) is evaluated. The authors reported relevant observations, showing the model performance. An oxygen content measurement in a power plant with an error of 10% may lead to serious problems since the recirculation of the flue gas amplifies the effect drastically. The oxygen content in the flue gas and the oxidant are of high importance for the safe of operation of such a power plant and a high quality of control is required. Under safety aspects, a wellengineered numerical model is tool with a high potential. Safety aspects are also in the work of Postler et al.D,145X X who discussed in [27] the design of a planned 250 MW plant at Jaenschwalde, Germany. They presented a load change and the impact of a recirculation fan trip followed by a master fuel trip of the power plant. Interactions of the fans, the behaviour furnace pressure and the corresponding mass flow rate are visualized in Fig. 45 (top). Starkloff et al.D146X X [26] extended the Postler et al.D147X Xmodel [27] and simulated a total blackout auf the power plant (see Fig. 45 (bottom)). The dynamic simulations of malfunctions can help to evaluate and design controls and safety mechanisms for this new process. Damper position, driving time or safety sequences can be optimised. Postler [28] described the switch from air to oxygen operation at 50% boiler load using the software APROS. The procedure needs around 30 min, which is comparable to [256] and [258]. TagedPThe air separation unit and the gas processing unit are often modelled as a boundary condition for the oxyfuel power plant, e.g. [27,28,256,258]. The dynamic performance of these air separation units can be the limiting factor of the overall dynamic performance. The integration of air separation unit with its control system in the entire oxyfuel power plant model is of high interest. Pottmann et al.D148X X [158] used the commercial software UniSim and the in-house tool OPTISIM in order to model the gas processing unit and the air separation unit, respectively. The presented results give a good

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cTagedP ompartments around the cooling circuit play a major role and are modelled as well. TagedPAnother typical application of dynamic simulation tools in the context of nuclear power plants is the training of the licensed staff for normal operation as well as unexpected plant transients. These trainings are usually conducted in life-size replicates of the control rooms allowing for a very realistic training environment with the possibility of recreating a broad variety of scenarios. TagedPThis chapter of the review delves into dynamic simulation applied to NPPs, namely the analysis of load changes and the safety analysis. Typical computer codes used for those tasks are presented and exemplary results are shown and discussed. Moreover, this chapter gives an overview of upcoming developments in the field of dynamic simulation of nuclear power plants. 5.1. Specific features TagedPFirstly, a short introduction to the unique aspects of nuclear power plants compared to conventional thermal power plants is offered. This includes the basic principle of nuclear fission as well as the design features of the most common plant types. Fig. 45. Gas dynamics after a trip of the recycle fan (top) and gas dynamics after total blackout of the power plant (bottom) (reproduced from references [26,27] with permission of authors and Elsevier).

TagedPimpression how the numerical models may be used for the development of control and operation strategies. 5. Nuclear power TagedPThe first commercial nuclear power plants (NPPs) came into operation in the 1950s. The two oil crises in 1973 and 1979 led to the demand of an oil-independent and cheap energy source, which spiked the number of newly built NPPs worldwide. Since then NPPs have become a major source of power generation. To date over 430 commercial nuclear power reactors operate in 31 countries with an installed power of about 370 GW, providing more than 2400 TWh of electricity per year. This equals roughly 11% of the annual consumption in electricity worldwide [261]. Today, new plants are still designed, planned and built. Two main driving forces behind those projects can be identified. Firstly, in regard of global warming nuclear power is considered as one of the possible measure to significantly decrease the amount of emitted carbon dioxide. Secondly, nuclear power is a relatively import-independent power source since comparably cheap and little amounts of fuel are needed, which are available in a number of regions all over the world and not used in any competing sector [262]. The second factor is closely linked to the very low marginal cost of nuclear power, which in turn usually puts NPPs to the far left of the merit order. Therefore, NPPs are generally used as base load plants without the need for regular load changes. Only in a few countries, e.g. France and Germany, NPPs are extensively used for load following. This led to a low demand of dynamic process simulation of NPPs during load changes [263,264]. TagedPNevertheless nuclear safety is a main topic during design and operation since the erection of the first commercial plants. The matter became increasingly important over time and first computational analyses of the dynamic behaviour of the plants during accident conditions were conducted very early. Today, several sophisticated program codes for nuclear power plants exist, which can model the transient behaviour of the cooling circuits and the reactor core. Especially for loss of coolant accidents (LOCA) the interactions of

TagedP5.1.1. Basic principle TagedPThe underlying principle for every nuclear power plant is the nuclear fission of heavy elements. In Fig. 46, this is shown for 235U as fuel. The uranium nucleus reacts, in the case of 235U, with a thermal neutron and is split into two smaller nuclei and about 2 to 3 new fast neutrons. At the same time, a considerable amount of energy (about 200 MeV) is released. The fast neurons have to be decelerated by a moderator to be able to initiate the next fission reaction. Other fuels that use thermal neutrons for the reaction are 239Pu and 233Th. Both are artificially produced in so-called breeder reactors. A fuel that uses fast neutrons for the reaction is 238U. In this case no moderator is needed. TagedPSeveral different types of nuclear power plants have been designed and built based on the principle described above. They differ in the type of coolant (e.g. water, helium, CO2, sodium), moderator (e.g. light water, heavy water, graphite and none in case of fast breeder reactors) and the number of cooling circuits. The most common reactor types are light water reactors, namely the boiling water reactor (BWR) with one cooling circuit and the pressurized water reactor (PWR) with two cooling circuits. Furthermore the designs of BWR and PWR concepts vary from one manufacturer to another. TagedPIn addition more uncommon reactor types, like the Canadian heavy water reactor or the French sodium cooled fast breeder reactor Superphenix, exist. The former one uses natural uranium omitting the need for the highly complex enrichment process. The latter one is able to make use of the 238U that which is accounts for 99.3% of the isotopes in natural uranium. Due to the predominance in power generation this review focuses on BWR and PWR power plants. TagedP5.1.2. Reactor pressure vessel and reactor core TagedPThe reactor core is the central part of the power plant. There the nuclear fission takes place and the energy stored in the fuel is released. The layout is similar for PWR and BWR and therefore is described jointly. In light water reactors the core is located in the reactor pressure vessel. It is made up from fuel assemblies which in turn consist of a set of fuel rods filled with sintered UO2 pellets. In between the fuel assemblies control rods, made of neutron absorbers, can be moved in and out in order to control the neutron flux and hence the reactor power. TagedPIn Fig. 47, typical layouts of a PWR reactor pressure vessel (RPV) and a BWR RPV are depicted. The control rod drives are installed on

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Fig. 46. Nuclear fission of Uranium (reproduced from reference [328], Creative Commons Attribution 4.0 International (CC BY 4.0), License: https://creativecommons.org/licenses/ by/4.0/).

Fig. 47. Reactor pressure vessel of a pressurized water reactor (a) and a boiling water reactor (b) (reproduced from reference [329]).

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iTagedP t rises through the core and evaporates. Above the core in the steam separator the liquid is diverted to the downcomer, while the saturated steam leaves the RPV at the top. TagedPThe power of a nuclear reactor is controlled via the neutron flux. In light water reactors an inherent control mechanism exists because of a temperature feedback loop. With higher temperatures, the density and therefore the moderation of water decreases. At the same time, the construction materials and the fuel pellets absorb more neutrons. Both effects reduce the thermal neutron flux and hence reactor power. TagedPBeyond that mechanism the power is controlled by the control rod position and the boron concentration in PWR. In BWR no boron is used in the coolant and the power is controlled mainly with the recirculation pumps. At higher throughputs, the void is reduced, resulting in better moderation and increased reactor power.

Fig. 48. Primary circuit of a pressurized water reactor (reproduced from reference [330]).

TagedPtop of the RPV. The main coolant is injected through inlet nozzles, flows through the downcomer to the bottom of the core and rises through the core. There, the heat from the fuel assemblies is absorbed. The coolant leaves the RPV through the outlet nozzles. In contrast to the PWR, the control rod drives are located below the RPV. The feedwater is injected above the core. With recirculation pumps, the water is pumped down to the lower plenum from, where

TagedP5.1.3. Cooling circuits and auxiliary systems TagedPThe PWR concept is used in most of the nuclear power plants in the world. It is a light water reactor with two cooling circuits. The main components of the primary circuit are the RPV with the reactor core, the main coolant loops, each with their own steam generator and main coolant pump, and a pressurizer (see Fig. 48). The number of loops varies from two to four. Typical pressure levels for the primary circuit are around 16 MPa. TagedPThe steam generators produce saturated steam at about 7 MPa for the secondary circuit. The layout is similar to any other steam power process (see Fig. 49) with a few variations. Firstly, because of the comparably low pressure there are only two turbine stages. Secondly, the superheater is powered by the main steam. This actually lowers the plant efficiency but is necessary to limit the steam moisture to an acceptable level for the low pressure turbine. TagedPSeveral safety and auxiliary systems are integrated in the standard PWR concepts. The actual design, the purposes and the names differ between plant manufacturers. To give an overview only the most important systems are explained in the following. Several safety systems are subsumed under the name Emergency Core Cooling System (ECCS). They are used to remove the decay heat of the

Fig. 49. Secondary circuit of a pressurized water reactor.

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TagedPreactor core both after regular shut down as well as reactor scram under accident conditions. It is therefore designed as a highly reliable and redundant system with emergency power supply. The ECCS is connected to the primary circuit. Typical safety systems of the ECCS are the High Pressure Injection System (HPIS), the Accumulator Injection System (AIS), and the Low Pressure Injection System (LPIS). The HPIS and the LPIS are both pump driven systems, which supply coolant at different pressure levels of the primary reactor. The AIS depends on pressurized accumulators, which release the inventory through a check valve into the primary circuit. TagedPThe emergency feedwater or auxiliary feedwater system (AFS) is connected to the secondary circuit and supplies feedwater to the steam generators if the main feedwater pumps are inoperable. This can be the case during regular start-up and shut-down procedures as well as accident conditions. TagedPThe boiling water reactor is the second most common reactor type. In contrast to the PWR, it consists only of one circuit. Here, the reactor pressure vessel also acts as a steam generator and supplies the main steam directly to the turbine. The layout of the cooling circuit is almost identical to the secondary circuit of a PWR. Also the pressure level of approximately 7 MPa is similar. TagedPIn BWR, the ECCS typically consists of a HPIS and a LPIS. Furthermore, BWR plants contain a pressure control and relief system. It is used to release the pressure form the RPV in accident scenarios to avoid a plant of condition of a high pressure core meltdown at all cost. The steam is lead to a condensation chamber, also called pressure suppression pool, where it is condensed. This system is also used in case of breaks to reduce the pressure in the containment [265]. 5.2. Safety analysis TagedPThe build and operation of NPPs is strongly regulated by the authorities in any country and the safety regulations usually exceed the regulations for conventional thermal power plants by far. Despite the fact that several standards exist basic safety philosophy and requirements are similar. Examples for safety requirements are the German “Sicherheitsanforderungen an Kernkraftwerke” [266], the US NRC Requirements, the IAEA Safety Standards [267] and the yet to be passed European WENRA Reference Levels. TagedPTwo general approaches for safety analyses are differentiated in the safety standards, the probabilistic approach and the deterministic approach. In the probabilistic approach, initiating events are defined and the accident sequences are analysed respecting the fault probability of the plant systems. Hereby, an initiating event is any incident that requires an automatic or operator action to bring the plant into a safe and steady state condition [268]. The final result of the calculation is a core damage frequency. In the deterministic approach, a set of design-basis accidents as well as beyond-designbasis accidents is examined and the event sequence is determined under conservative boundary conditions [269]. Typical scenarios that are investigated in the deterministic approach are loss of coolant accidents (LOCA), loss of offsite power and earthquakes. TagedPIn both cases, probabilistic and deterministic approach, an extensively tested and validated simulation tool is needed for the simulation of the accident sequence in order to convince the surveyors and the regulatory authorities of compliance with the regulations. Therefore, only few dynamic simulation programs, which are specifically validated for these use cases, are used in the supervisory procedures. Common codes are ATHLET [270], CATHARE [271] and RELAP [272,273]. TagedPAll these codes share the twoD-phase 15X X heterogeneous flow model with the addition of non-condensable gases transport equations and 1D-discretisation. Moreover, the application in the field of safety analysis not only requires the simulation of the water/steam process but also the interactions with the neutron kinetics of the nuclear

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rTagedP eactor, in case of reactor transients and the interactions with the surrounding building and compartments (containment codes), in case of loss of coolant accidents. This is achieved either by incorporating additional simulation modules or by linking the software to external simulation programs. TagedPThe simulation of the surrounding building with its compartments is done with very simplified models or with very simplified discretisation, nevertheless validated with numerous experiments. An example of an external program for containment simulation is COCOSYS [274], typically linked to ATHLET. Other examples are GOTHIC and CONTAIN. The thermal hydraulic is usually described with a so-called lumped-parameter model. The containment of the plant is subdivided into control volumes with the thermodynamic state defined only by temperature and mass of the specified components. Typically different zone models are available. For instance, in COCOSYS equilibrium and non-equilibrium (twoD-phase) 156X X zones and special zones for the pressure suppression pool in BWR or the jet vortex condenser in the Russian WWER-440 PWR can be selected. TagedP5.2.1. Validation experiments TagedPThe validation of the nuclear reactor simulation codes is based on separate effect tests, integral system tests and transients in commercial plants. In 1983, a program was initiated by the OECD to compile code validation matrices. Phenomena were identified that are expected to occur during transients in BWR and PWR. The integral test facilities (ITF) and separate effect test facilities (SETF) were built and experiments, useful to characterize the phenomena identified, were conducted. The results of several tens of ITF experiments and about a thousand SETF experiments are compiled in [275,276]. Validation results of containment codes are summarized in [277,278]. TagedPThe reports provide a general overview of accident progression for light water and also heavy water reactors. The main focuses are the phenomena and safety systems employed in these reactor types and to highlight the differences. For example, in the report for the containment code validation approximately 120 phenomena in the categories of containment thermal hydraulic, hydrogen behaviour, aerosol and fission products, iodine chemistry, core melt distribution and system behaviour are identified and a synopsis of more than 200 experiments for those six categories are included. TagedPAn example for a cross reference matrix is shown in Table 3. It allows identifying what phenomena are covered by which test and are suitable for code assessment, in this case for large break LOCAs in PWR. The actual validation is then conducted with pre
test and post
test calculations that are compared to the experiment results. Since the compilation of these reference matrices, more phenomena were marked as important and additional experiments were conducted.  s et al.D157X X [280] illustrated the general approach in code TagedPRevento validation, where some parameters are determined with a parameter study and then the experiments results are compared to the simulation results. Here, the result of one of the OECDSETH experiments is compared to the results of ATHLET and different RELAP versions. The OECD-SETH program is aimed at investigating issues that are relevant to accident prevention and started in 2001. The experiment in question deals with the topic of boron dilution on resumption of natural circulation in the steam generators following a small break LOCA. This scenario constitutes a challenge to analytical methods. The water evaporates within the core and condenses on the primary side of the steam generators. In this so called reflux condenser mode the boron is mainly retained in the liquid phase, so that the vapour phase and the condensate are almost boron free. The boron dilution is an important phenomenon because D158Xrecriticality X can occur if the diluted plug enters the core. TagedPThe experiment was conducted in the integral test facility PKL (see Fig. 50), which is operated at the Technical Center of AREVA and

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162 Table 3 Cross reference matrix for large breaks in PWRs [279].

TagedPis a mock-up of a 1300 MW class PWR [280,281]. The test facility simulates the entire primary side with four loops and the essential parts of the secondary side. The elevations correspond to the elevations in an actual plant and the volumina and power are scaled 1:145. TagedPThe analyses were performed by six working groups from different countries using different codes. The aim of this paper was to both show and compare the results obtained by different working groups in their simulation of the experiment and to analyse the main parameters involved in order to draw conclusions on improvements that can be made in the analytical approach to such tests. All the participants managed to successfully predict the overall thermal hydraulic system behaviour. Vessel fill-up together with slug build-up by reflux-condensation (see Fig. 51) up to 3000 s after start of the transient are phenomena that were correctly predicted, whereas simulation of natural circulation restart and transport of low-borated water slugs (see Fig. 52) were identified as areas for improvement. TagedPIn conclusion, the validation of nuclear system codes is a very broad and well discussed topic. The validation matrices allow for a thorough test of new and changed codes and ongoing researches ensure that newly identified phenomena are considered and experiments are added.

TagedP5.2.2. Statistical accident analyses TagedPThe accident scenarios that need to be analysed in order to receive an operating license are called design basis accidents (DBA). Usually these are divided into two groups, loss of coolant accidents (LOCA) and accidents or transients without loss of coolant. For both it has to be proven, that certain criteria would not be exceeded. TagedPThis is typically done in a deterministic analysis by setting conservative values for the boundary conditions like reactor power, reactor pressure and burn-up of the fuel (higher burn-up yields higher decay heat). The calculations are performed with the validated codes that are best-estimate codes, i.e. the model parameters are not chosen in a way that necessarily yields conservative results but are set to match the validation experiments. Due to the choice of conservative boundary conditions, the calculated result is nevertheless assumed to be a covering or conservative result for the respective performance criteria. TagedPIn a more recent approach that is propagated in the USA Code of Federal Regulation and the German Sicherheitsanforderungen, the boundary conditions are no longer set to values considered conservative but are given as probability distributions. The

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Fig. 50. PKL facility, volume: 1:145, elevations: 1:1, max. pressure: 45 bar, max. power 2.5 MW (reproduced from reference [280,281] with permission of Elsevier and Creative Commons Attribution 3.0 Unported (CC BY 3.0), License: https://creativecommons.org/licenses/by/3.0/).

TagedPsame is done for model parameters like heat transfer coefficients, since these are not known with complete certainty and in some cases even the choice of a conservative value would be non-trivial. This approach yields a result distribution from which the confidence level that the maximum code result will not be exceeded with a certain probability can be obtained [282]. TagedPOn the one hand, the statistical approach requires a much higher calculation effort. The method with conservative

TagedP oundary conditions only uses one calculation whereas for a b result covering 95% of the possible results with a confidence of 95% at least 59 calculations are required according to Wilk's formula. Usually 93 or 124 calculations are performed to be able to omit one or two outliers respectively. On the other hand, the results of the probabilistic method are more realistic and allow for an assessment of result's uncertainties. Additionally the influence of model parameters with a fixed but inaccurately known value is reflected in the result. The difference between the two

Fig. 51. RPV level (left) and mass flow in intact loop 3 (right) (reproduced from reference [280] with permission of Elsevier).

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Fig. 52. Mass flow rate after natural circulation restart (left) and boron concentration in loop 3 (right) (reproduced from reference [280] with permission of Elsevier).

Fig. 53. Consideration of discrete values (left) or of input parameter value distributions instead (right) (reproduced from reference [282], Creative Commons Attribution 3.0 Unported (CC BY 3.0), License: https://creativecommons.org/licenses/by/3.0/).

TagedPapproaches is depicted in Fig. 53 with the conservative boundary conditions on the left and the statistical method on the right [282]. TagedPArkoma et al.D159X X[30] analysed a large break loss-of-coolant accident (LB-LOCA) in EPR-type nuclear power plants using the described statistical method. The best-estimate code used is APROS coupled with the fuel-performance code FRAPTRAN-GENFLO. The goal of the analysis was to show that the maximum number of failing fuel rods in the reactor core in the transient is lower than the performance criterion of 10% of failed rods. The failing of the fuel rods is mainly determined by the cladding temperature of the fuel rod. TagedPThe 59 results for the maximum fuel cladding temperature are plotted in Fig. 54 together with six additional curves: the highest and lowest temperatures in black, the average temperature in blue, and the median in turquoise for each time step as well as the results of two extra calculations with the nominal and conservative values for the model parameters and boundary conditions in green and red respectively. The lowest and highest temperatures at each time step are represented with the black lines. TagedPA clear reason why certain calculations gave high and low extreme values could not be found. More over the conservative case inD160X X which conservative input values were chosen based on engineering judgement did not lead to the absolute highest cladding temperatures. Several other paper on the topic of statistical accident analysis also draw the conclusion, that parameter combinations considered conservative do not necessarily lead to a conservative result.

TagedPThis emphasizes the advantages of the statistical analysis in complex systems, where the interactions between different input parameters are hard to predict. Therefore, the reviewers suggest a transfer of the knowledge in statistical transient analysis from the nuclear energy branch into other fields of study with dynamic simulations.

Fig. 54. Maximum cladding temperatures (reproduced from reference [30] with permission of Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

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5.3. Load cycling TagedPAs briefly described in the introduction, load cycling has not yet played a major role for nuclear power plants since NPPs are generally used as base load plants. The reasons are manifold and include technical as well as economical aspects. Therefore, no dynamical simulations of the power generation process during normal operation are known to the authors. Nevertheless, experience with load following exist.

TagedP5.3.1. Experience with load following TagedPA comprehensive overview on the experience with load following in France, Germany, USA and Sweden as well as on the technical aspects of load changes in BWR and PWR is given by Persson et al.D16X X [283]. The goal of the report was to elicit the capability to complement the fluctuating power supply of renewable energies with the NPPs in Sweden. In order toD162X X achieve this goal, technical aspects that were regarded important for load following, were investigated. These include: TagedP Thermal stress on the components, leading to increased plant wear, TagedP The limit in neutron flux control, usually caused by limited control rod drive speed, TagedP The requirements for the in-core instrumentation,  TagedP Risk of fuel damage caused be different thermal expansion coefficients for the fuel pellets and the surrounding fuel rod, TagedP The so called xenon peak that occurs a few hours after a load reduction and prevents the return to the nominal power, TagedP Increased risk of incidents leaving normal operation, and  TagedP The effect on the fuel economy. TagedPLudwig et al.D163X X [284] conducted a comparable study for German NPPs only. The motivation for this paper was the decision of the German government in favour of a lifetime extension for the German NPPs and the question if those plants can readily react to changes in load demand. The authors identified similar fields of interest to investigate the fast response capabilities. Additionally, the part-load characteristics of German PWR and BWR are explained. TagedPIn Fig. 55, a schematic part load diagram of a PWR is shown. For a reactor power from 0 to 40% of the nominal power, the average coolant temperature rises. Here a load following would yield high thermal stress on the components in the primary circuit. Between 40% and 100% of the nominal reactor power, the average coolant temperature in the reactor is constant. This is therefore the typical range for load following.

Fig. 56. Schematic characteristic curve for recirculation control in a German BWR (reproduced from reference [284] with permission of AREVA NP GmbH).

TagedPIn Fig. 56, the recirculation control curve in a BWR is depicted for constant control rod position. Recirculation control is perfectly suitable for load cycling in the upper power range from about 60% to 100% of the rated electrical output. Hereby the power distribution is not significantly affected minimizing the stress on the reactor components. For lower power output, the control rod manoeuvring sequence has to be optimised. Under these conditions load-following operation between 20% and 100% is expected to be feasible. TagedPBoth studies draw the conclusion that in principle there are no technical obstacles to use the nuclear power plants in Sweden and Germany for flexible power generation in load following with minimum load of 65% and 50% respectively. Both reports also suggest that higher rates and ranges are possible with suitable changes like optimised fuel management, optimised control rod manoeuvring and predictive operating strategies [283,284]. TagedPAn exemplary overview on the maximum load change rate and on the load cycling range for some of the current light water reactor designs is given in Table 4. TagedP5.3.2. Thermal hydraulic-neutronic instabilities TagedPThe aforementioned studies as well as similar works (Pouret et al.D164X X [263], Stein and Griffith [290]) omit the topic of coupled thermal hydraulic-neutronic instabilities that can occur in boiling water reactors. In most power plants, provisions are taken against these by prohibiting certain combinations of control rod position and low recirculation pump speed and thus limit the load cycling range. This

Table 4 Load following capabilities of different reactor designs.

Fig. 55. Schematic part load diagram of a German PWR (reproduced from reference [284] with permission of AREVA NP GmbH).

Design

Reactor type

Maximum load change rate

Load cycling range

ABWR [285] AP1000 [286] EPR [287]

BWR PWR PWR

ESBWR [288] Konvoi [283, 289]

BWR PWR

SWR 69 [283]

BWR

SWR 72 [283]

BWR

Vor-Konvoi [283]

PWR

VVER-1000/1200 (V-392 and V-491) [287]

PWR

60%/min 5%/min 5%/min 2.5%/min N/A 2%/min 5.2%/min 10%/min 3.8%/min 10%/min 4.6%/min 10%/min 4.4%/min 10%/min 5%/min 10%/min

65%
100% 15%
100% 60%
100% 25%
60% 50%
100% 20%
100% 50%
100% 80%
100% 60%
100% 90%
100% 60%
100% 90%
100% 50%
100% 80%
100% 50%
100% §20%

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TagedPAs several in-depth reviews on the topic of thermal hydraulic instabilities exist (e.g. March-Leuba and Rey [291], Prasad et al.D165X X [292], Ruspini et al.D16X [X 293]), no further details are given. Nevertheless, as load following is becoming more relevant with the addition of fluctuating renewable energy sources, thermal hydraulic instabilities during reactor transients should not be neglected. 6. Concentrated solar power

Fig. 57. Instability region in the power-flow map for the Leibstadt NPP (reproduced from reference [331]).

TagedPis shown in Fig. 57 for the NPP Leibstadt in Switzerland. The effect of thermal hydraulic-neutronic instabilities is widely known since the 1980s when such instabilities were observed at the Caorso plant in Italy. TagedPThe basic mechanism causing flow instabilities in BWRs is the density wave. The coolant in BWRs flows in the upward direction through the core. Thus, variations in the density, caused by different steam void fractions, travel upwards with the flow. In two-phase flow regimes, the local pressure drop is very sensitive to the local void fraction and a significant part of a pressure drop is delayed with respect to the original perturbation. If the inlet flow is perturbed at certain frequencies, the pressure drop can decrease with increasing flow and a self-sustained oscillation can occur [291]. TagedPIn addition, in BWRs the power generation is directly linked to the neutron flux which is a function of the reactivity feedback and therefore depends on the void fraction. Thus a density or pressure oscillation respectively is necessarily accompanied by a power or neutron flux oscillation. The feedback paths are illustrated in Fig. 58 [291].

TagedPIn concentrated solar power (CSP) plants, solar rays are concentrated by means of mirrors or lenses or a combination of both to heat a working fluid, which then directly or indirectly drives a thermodynamic process in order to generate electric power. In this chapter, only concentrated solar thermal power is discussed, while concentrated photovoltaics (CPV) and plants with non-concentrating collectors are out of scope. TagedPThe overall efficiency of a CSP plant (see Fig. 59) is determined by the optical efficiency of the reflector, the efficiency of the receiver (absorber tube), the thermal losses during fluid transport, thermal energy storage efficiency (optional) and the efficiency of energy conversion in the power block [294].

hCSP D hopt  hrec  htra  hsto  hcon

ð6:1Þ

T he heat transfer fluid (HTF) is usually a synthetic oil. The size of agedPT the solar field determines the amount of electric output. As the solar field roughly accounts for half of the capital expenditure for a CSP plant, current research efforts are focused on increasing electric conversion efficiency by higher process temperatures in order to downsize the solar field and decrease the levelised cost of electricity (LCOE). This requires application of working fluids that remain stable at high temperatures, such as molten salt or demineralised water, i.e. direct steam generation (DSG). 6.1. Development TagedPIn the beginning of the 20th century, household solar water heaters were commercialised in South West USA and the North-American Frank Shuman successfully completed a parabolic trough plant for powering an irrigation system in Meadi, Egypt, in 1913. The

Fig. 58. Block diagram of the feedback paths for the coupled neutronics-thermal hydraulics instability type (reproduced from reference [291] with permission of Elsevier).

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Fig. 59. Typical setup of a concentrated solar power plant (parabolic through) with thermal storage.

TagedPItalian Giovanni Francia designed and built the first linear Fresnel collector in Genoa, Italy, in 1964 and the first solar tower plant in Sant'Ilario, Italy, in 1965. As of 2011, 29 CSP plants have been in operation worldwide with around 1220 MWel installed capacity [106]. It can be seen in Fig. 60 that the large majority of the solar thermal capacity is installed in Spain and the U.S. Furthermore, parabolic trough CSP plants are the most widely deployed technology, followed by tower, linear Fresnel and Stirling dish CSP plants with huge distance. Growth of installed CSP capacity started in 2009, mainly in Spain (see Fig. 61). At the end of 2013, the total installed CSP capacity amounted to 3.6 GW. About 900 MW were newly

Italy (0.4%)

Australia (0.2%)

Germany (0.1%)

TagedPinstalled in 2013 and a total of 5.5 TWh solar thermal energy were generated. Spain leads the world in solar thermal energy with 2.3 GW of cumulative CSP capacity. Close to 2% of annual electricity in Spain is generated by CSP plants. This is the highest share of all countries in the world. The U.S. ranks second with 900 MW CSP capacity installed at the end of 2013. However, deployment of CSP grows at a high pace in the U.S. with 400 MW being added in 2013 and over 600 MW in early 2014 [295]. The Ivanpah central receiver plant in California, consisting of three distinct towers with each operating its own power block, is the largest CSP plant with respect to installed capacity

Tower (3.0%)

Fresnel (0.7%)

Stirling dish (0.1%)

Iran (1.4%) USA (40.1%) Spain (57.9%)

Parabolic trough (96.3%)

Fig. 60. Solar thermal power plant projects in operation in the world (March 2011). Left: installed power by country. Right: installed power by technology (reproduced from reference [106] with permission of Elsevier).

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Fig. 61. Global cumulative growth of the solar thermal electricity capacity as of 2013 (reproduced from reference [296], (C) D1X X OECD/IEA 2014 Technology Roadmap, Solar Thermal Electricity, IEA Publishing. License: www.iea.org/t&c).

TagedPso far. It was completed in February 2014 and is totalling a net power output of 377 MW [296]. 6.2. Specific features TagedPCSP plants generally consist of a solar field, an energy storage system (optional) and a power block as described in the following sections. TagedP6.2.1. Solar field TagedPThere are different CSP technologies that are mainly distinguished by concentrator and receiver systems, see Fig. 62. Parabolic trough and linear Fresnel reflectors concentrate direct sunlight on a line (line focus), whereas parabolic dish and solar tower technologies concentrate light on a point (point focus) [106]. Furthermore, linear Fresnel and the solar tower technology have in common that the receiver is fixed and does not move together with the concentrator device. This reduces the effort of HTF transport to the power block. In contrast, the receiver of parabolic trough and parabolic dish technology is mobile. In general, a mobile receiver allows collecting more energy compared to a fixed receiver [296]. agedPT Parabolic trough (PT) collectors: This technology focuses solar rays through parabolic trough-shaped mirrors on linear receiver tubes along the parabola's focal line (see Fig. 62-(a)). These receiver tubes are isolated in evacuated glass envelopes. Oil is heated inside the tubes and further transferred to a power block. The parabolic trough technology was used in the first commercial plants built in California and is still most widely deployed [294]. In addition to synthetic oil as heat transfer fluid, more recent projects investigate the deployment of direct steam generation (DSG) collectors to improve performance and reduce costs [297]. One small parabolic trough plant with DSG technology is currently operating in Thailand [296]. The thermal efficiency of parabolic trough collectors is relatively low. Operating temperatures range from 50 °C to 400 °C with concentration ratios between 15 and 45 [298]. Single-axis tracking is common. However, doubleaxes tracking could increase the amount of collected solar energy by up to 46% compared to a fixed surface (experimental investigation by Bakos) [299]. The overall technology maturity can be considered as advanced with relatively low costs [298]. TagedP Heliostat field collector (Central receiver system CRS / solar tower): Multiple heliostat field collectors (large mirrors with double-axes tracking) focus solar rays to a fixed tower mounted

rTagedP eceiver (see Fig. 62-(b)). This technology emerged as major alternative to the parabolic dish technology, since it is characterized by high theoretical efficiency as well as high potential for future cost reduction. The high concentration ratios compared to linear focusing systems allow the receiver to operate at higher temperatures with reduced losses [294]. The capacity is limited by the heat flux that can be absorbed by the receiver surface and transferred to the heat transfer fluid, without overheating receiver walls and heat transfer fluid [299]. As already stated, the thermal efficiency of central receiver systems is relatively high. Operating temperatures range from 300 °C to 2000 °C with concentration ratios between 150 and 1500. Double-axes tracking of the heliostats is common. Overall, the technology is still relatively immature, implying high specific costs [298]. agedPT Linear Fresnel reflector (LFR): Linear Fresnel CSP plants use multiple mirrors moving on one axis. These mirrors focus the solar rays on a downward facing fixed linear receiver (see Fig. 62-(c)). All commercial LFR plants currently in operation use DSG. There is one 30 MW LFR plant operating in Spain since early 2012 and one 125 MW commercial LFR plant operating in India since 2014. The technology is characterized through a simple design but low overall optical and thermal efficiency [294], especially when the sun is low in the sky in early morning and late afternoons and during winter [296]. Operating temperatures range from 50 to 300 °C with concentration ratios between 10 and 40. Single-axis tracking of the reflectors is common. Overall, the technological maturity can be considered as moderate. However, relative costs are the lowest due to its simple design [298]. agedPT Parabolic dish reflector: This technology uses an array of parabolic dish-shaped mirrors to focus solar energy on a receiver located at the common focal point of the dish mirrors [299]. A heat-to-electricity engine, such as a Stirling motor or micro-turbine connected to a generator, is located at the common focal point (see Fig. 62-(d)). Parabolic dish technology is characterized by the highest efficiency potential for solar energy conversion of all CSP technologies (no cosine losses [294]), low start-up losses and favourable modularity, so that the dish can be easily installed in remote areas to meet the local power requirements. The technology requires three-dimensional tracking, rendering systems more complex and reducing tracking accuracy [299]. However, very high costs and risks caused the parabolic dishes to disappear almost completely from the commercial energy landscape [296]. Recently, parabolic dish resurrected as option for future CSP concepts. Operating temperatures range from 150 °C to 1500 °C with

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(a) Parabolic trough

147

(b) Central receiver Solartower

Reflector Absorber tube Solar field piping Heliostats

(c) Linear Fresnel reflector

(d) Parabolic dish

Curved mirrors

Receiver, engine

Absorber tube and reconcentrator

Reflector

Fig. 62. Classification of reflectors (reproduced from reference [296], (C) 2XD X OECD/IEA 2014 Technology Roadmap, Solar Thermal Electricity, IEA Publishing, License: www.iea.org/t&c).

TagedPconcentration ratios between 100 and 1000. Overall, the technology maturity is low [298]. TagedP6.2.2. Power block TagedPDepending on the CSP reflector type with its characteristic operating temperature, the layout and the specific dispatchability requirements, CSP plants are equipped with one of the following power block types: TagedP  TagedP  TagedP  TagedP  TagedP

Rankine cycle (steam cycle). Organic Rankine cycle ORC (low-temperature steam cycle). Stirling engines (heat-to-electricity engine). Brayton (Joule) cycle (gas turbine cycle). Combined-cycle (Brayton combined with Rankine as bottoming cycle) as described in [300,301].

TagedP6.2.3. Energy storage and back-up system TagedPAs solar irradiation is limited to daytime and depending on the clearance of the sky, CSP is generally not dispatchable. However, thermal energy storage (TES) can be integrated in a CSP plant (see Fig. 59), making it highly dispatchable. TES also enables CSP plants to convert the intermittent solar energy source to a constant power output. Round-trip efficiencies above 97% were reported for TES units consisting of two-tanks with hot and cold salt [302]. Furthermore, a storage can increase the solar share (fraction of energy provided by solar) by

TagedP s much as 47% to levels over 70% on a sunny day [303]. The relative a ease of thermal energy storage for high dispatchability is the main -vis photovoltaics. competitive advantage of CSP vis-a TagedPIn most applications, the thermal energy storage medium stores thermal energy in form of sensible heat (heating and cooling a material without change of phase), for instance in synthetic oil and molten salt. However, systems that utilize latent heat (melting and freezing of suitable high-temperature phase-change materials), thermochemical (reversible chemical reactions used to store and discharge energy) and other sensible heat materials are the subject of ongoing research [302]. Furthermore, energy can be stored in steam accumulators. The energy density is low for sensible heat storage, whereas the density increases with latent heat storage, sorption and thermochemical storage. As yet, the maturity level of these storage technologies is in opposite correlation to their prospective power density. TagedPTechnical aspects to be considered when evaluating thermal energy storage technologies are: TagedP High thermal storage capacity, TagedP Good heat transfer rate between heat storage material and heat transfer fluid, TagedP Good stability of heat storage material to avoid chemical and mechanical degradation after a certain number of thermal cycles, TagedP Compatibility between heat transfer fluid, heat exchanger material, and storage material,

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 TagedP Reversibility to achieve large numbers of charging and discharging cycles, TagedP Low level of thermal losses, TagedP Ease of control [299]. TagedPAmong the total installed capacity at the end of 2013, roughly 2.3 GW do not include storage, while approximately 1.3 GW contain a thermal energy storage system. However, among the expected capacity to be added until 2020, about 80% will likely incorporate storage capability [295]. TagedPIn addition to thermal energy storage, back-up systems with fossil fuel or biomass fired auxiliary boilers make CSP plants fully dispatchable, which makes the technology more attractive for utilities. Furthermore, the back-up system can compensate for thermal storage losses during the night, prevent freezing and accelerate the start-up process in the morning. Almost all CSP plants use some fossil fuel as back-up, most commonly natural gas. As the power block already exists, the additional costs for an auxiliary boiler are relatively low and they are outweighed by the operational benefits of a back-up system. TagedPFinally, several full-hybrid setups are conceivable. These hybrid systems routinely use a fuel together with solar energy. For example, small solar fields can be added to a fossil-fired thermal power plant (even as re-powering). These integrated solar combined-cycle (ISCC) plants use solar energy to evaporate steam for the bottoming cycle. Furthermore, solar boosters for coal plants replace the economisers that are heated by extraction flows from the steam turbine. Hence, more steam can be expanded in the turbine so that power output is boosted [296]. Since the conventional part typically plays the major role in these systems and the solar part is the auxiliary support, fullhybrid systems are not further discussed in this work. 6.3. Dynamic studies TagedPDynamic simulation of CSP plants is conducted as the technology relies on direct solar radiation, which in fact is dynamic in nature. Clouding, the angle of irradiation depending on day-time and season as well as the geographic location of a plant influence the amount of energy that can be collected. Dynamic simulation aims to study the performance of CSP plants under different solar irradiance conditions. Furthermore, plant start-up procedures, the capacity and dynamics of TES charge and discharge cycles as well as the annual power output respectively the capacity factor can be analysed. Two different types of studies can be distinguished, which either simulate based on half to one hour time steps and treat most thermal components as quasi-static or which attempt to track short duration cloud and thermal transients using more fundamental approaches. Key inputs for system performance forecasting include direct normal irradiation (DNI) time series data, combined with the local ambient temperature, humidity and wind speed [294]. TagedPCommercial software for energy system modelling used in solar thermal applications includes: IPSEpro, EBSILON Professional, EcoSimPro, TRNSYS, GATECYCLE, DYMOLA, MATHEMATICA and ASPEN. A free, but closed-source package is the System Advisor Model (SAM) from the National Renewable Energy Laboratory (NREL), which is based on the well-known TRNSYS simulation engine. An example for a free open-source system model is SOLERGY (Lovegrove and Stein) [294]. Recent studies also used the APROS simulation code to model and simulate a parabolic trough CSP plant (see [35] and [36]). A detailed overview of codes applicable to CSP technologies is given in Ho [304]. As parabolic trough CSP plants are most widely deployed, this technology offers the most reliable base of operating data and is commonly used to validate dynamic simulation models. Some other studies investigated the dynamics of central receiver and linear Fresnel reflector systems. However, to the authors’ best knowledge there

TagedP re no studies in the field of dynamic simulation for parabolic dish a systems so far. Table 5 provides an overview about recent publications on dynamic simulation of CSP systems. TagedPIn the following, some recent studies that include measurement validation are selected for detailed description. Garcia et al.D17X X [106] were the first researchers to develop a model based on the 50 MWel solar thermal power plant Andasol II in Granada, Spain, where the collected heat is transferred using synthetic oil as heat transfer fluid. Their simulation is conducted using Wolfram's MATHEMATICA 7 software. The model aims to be flexible in order to analyse different characteristics of any trough plant. Hence, it is anticipated to use this model for designing new plants and to optimise operation strategies with respect to maximizing electricity output. Fig. 63 compares validation results with measurement data of the reference plant for partly cloudy days. TagedPThe most recent studies were conducted by Al-Maliki et al.D8X71 X [35,36], in which the 50 MWel Andasol II plant is also modelled, including all required control circuits. However, the authors used the thermal hydraulic simulation code APROS. The model includes a two-tank thermal energy storage operated with molten salt and a detailed dynamic model of the power block. After achieving convincing validation results, it is found that the thermal energy storage enables the plant to deliver an almost constant power output despite small fluctuations in DNI. Furthermore, the plant is capable of sustained power generation for 7.5 h after sunset due to the storage. Comparison between measurement and simulation for a day with strong cloudy periods (see Fig. 64) shows good agreement in the period between 10:00 and 17:00. The discrepancies after this period are related to unknown operator behaviour in particular. With an optimised operation strategy, the time of electrical power output can be increased by about 26% compared to the reference case. TagedPLiu et al.D179X X [122] analysed the dynamic behaviour of a TES system implemented in the 1 MWel central receiver direct steam generation plant Badaling. The thermal energy storage consists of an oil-operated cold and hot tankD180X Xas well as a steam accumulator. The complete plant is modelled in DYMOLA by means of the MODELICA library “ThermoSysPro”. A two-level control loop is designed in MATLAB/ SIMULINK and connected to the simulation model. Fig. 65 shows the results after a dynamic perturbation of DNI. The drum pressure increases instantaneously when DNI rises. At a certain drum pressure, the system switches to storage mode and the storage steam valve opens in order to limit the pressure in the drum. The steam mass flow to the turbine is stabilized with constant drum pressure. The pressure in the steam accumulator increases as steam is injected. Not shown in the diagrams is an increase in feedwater supply to the drum in order to maintain a constant drum level. As the results illustrate, coupling of the two-level control system modelled in MATLAB/SIMULINK with the DYMOLA process model is successful. The authors aim to use the model for prospective studies of further control solutions in the future. TagedPMitterhofer and Orosz [81] modelled a low-cost 3 kWel micro-CSP with a rock-bed TES system in DYMOLA. The solar-thermal loop is represented by a dynamic model, whereas the model of the Organic Rankine Cycle is steady state. The model is validated with experimental data from a test site at Eckerd College in St. Petersburg, Florida. Results show a possible net electricity generation of 4.08 MWh/ annum at an average power output of 2.5 kW and a capacity factor of 18.8%. Operation of the ORC condenser can be optimised by applying a control strategy that allows for a variable pinch point, which results in an increase of annual net electricity generation by 14% in comparison to a constant condensation pinch point (see Fig. 66). 7. Additional thermal power technologies TagedPThere are several further thermal power technologies, in addition to the above-described, that are rarely considered in the dynamic

F. Alobaid et al. / Progress in Energy and Combustion Science 59 (2016) 79
162 Table 5 Recent publications dealing with dynamic simulation of CSP systems. Publication

CSP type

Comments

Al-Maliki et al.D3X [X 35]

Parabolic trough

50 MWel synthetic oil parabolic trough solar thermal power plant; including two-tank TES system and detailed power block; APROS; model validation; clear days and slight cloudy periods.

Al-Maliki et al.D4X [X 36]

Parabolic trough

50 MWel synthetic oil parabolic trough solar thermal power plant; including two-tank TES system and detailed power block; APROS; model validation and optimisation of operation strategy; strong cloudy periods in summer days.

El Hefni and Soler [79]

Central receiver

145 MWel molten salt central receiver power system; including two-tank TES system and power block; DYMOLA; model validation, checking performance and design, and prediction of yearly electricity production; simulation with yearly DNI.

Liu et al. [122] D5X X

Central receiver

1 MWel DSG solar tower power plant; including two-tank oil TES system, steam accumulator, and power block; DYMOLA, coupled with MATLAB/SIMULINK; simulate heat transfer performance and storage charging and releasing procedure, test of two-level control design; artificial DNI transient.

Luo et al.D6X [X 305]

Parabolic trough

Synthetic oil parabolic trough solar field; including hot oil storage tank, w/o power block; own dynamic mathematical collector model; model validation, optimisation of solar field layout; diverse irradiation conditions.

Mitterhofer and Orosz [81]

Parabolic trough

3 kWel micro-CSP plant; including rock bed TES system and ORC (steady state model); DYMOLA and Engineering Equation Solver (EES); model validation, optimisation, and prediction of annual net electricity generation; different DNI profiles during one year.

Diendorfer et al.D7X [X 306]

Parabolic trough

Floating offshore parabolic trough collectors; w/o TES and power block; model validation; analyses of optical performance as a function of time and location; different offshore DNI profiles.

El Hefni [80]

Parabolic trough / linear Fresnel

Synthetic oil parabolic trough solar power plant and DSG linear Fresnel hybrid CCPP; DYMOLA; model validation and prediction of yearly electricity production; simulation with yearly DNI.

Falchetta and Rossi [307]

Parabolic trough

9 MWel molten salt parabolic trough plant; including two-tank TES system; ISAAC Dynamics; analyses of draining operations.

 € Osterholm and Palssonb [82]

Parabolic trough

50 MWel synthetic oil parabolic trough solar thermal power plant; including two-tank TES system and simplified Rankine cycle; DYMOLA; model validation; clear summer day and partly clouded day.

Rodat et al.D8X [X 83]

Linear Fresnel

Synthetic oil and DSG linear Fresnel CSP plant; w/o (oil) and including (DSG) TES, including power block (simplified by a heat sink for oil as HTF and turbine by orifice for DSG); DYMOLA; model validation, investigation of control scheme and response on DNI perturbations; DNI profiles for a sunny and a partly cloudy day.

Russo [147]

Parabolic trough

Molten salt parabolic trough CSP plant; including direct storage system, w/o power block; modified RELAP5 code; model validation, analysing thermal-hydraulic behaviour, filling and draining procedures.

Wagner and Wittmann [308]

Parabolic trough

125 MWel molten salt parabolic trough CSP plant; including direct two-tank TES system, auxiliary heater, and power block (pseudo-transient); EBSILON Professional with add-ons; analyses of different operation strategies; DNI profiles from NREL.

Zhang et al.D9X [X 78]

Central receiver

1 MWel DSG power tower plant; including and w/o two-tank oil TES system and steam accumulator, including power block; DYMOLA; model validation; measured DNI profile from test campaign.

Manenti and Ravaghi-Ardebili [309]

Parabolic trough

4.7 MWel molten salt parabolic trough CSP plant; including direct two-tank TES system; own mathematical model of economiser; dynamic modelling of economiser and whole plant.

Powell and Edgar [303]

Parabolic trough

1 MWth direct parabolic trough CSP plant; including two-tank TES system, boiler, and fossil fuel back-up; analyses of interaction between storage and other components to control power output and collector outlet temperature, comparison between systems with and w/o storage; DNI profile of a clear and a cloudy day.

Xu et al.D10X [X 310]

Central receiver

1 MW DSG solar power tower plant; including two-tank oil TES system and steam accumulator, w/o power block; own mathematical model; analyses of recharge and discharge process of TES system, response of dynamic steam flow disturbances.

Garcia et al.D1X [X 106]

Parabolic trough

50 MWel synthetic oil parabolic trough solar thermal power plant; including two-tank TES system; Wolfram's Mathematica 7; model validation; different DNI profiles.

Larrain et al.D12X [X 311]

Parabolic trough

100 MW DSG parabolic trough plant with fossil-fueld auxiliary heater; w/o TES; Engineering Equation Solver (EES); estimate required back-up fraction for different plant locations; different DNI profiles during one month.

Eck and Hirch [76]

Parabolic trough

DSG parabolic trough collector loop; w/o TES and power block; MODELICA; model validation, investigation of different feed water control systems; overall and local shadings of collector loop.

Stuetzle et al.D13X [X 312]

Parabolic trough

30 MWel synthetic oil parabolic trough solar electric generating system; w/o TES, including simplified Rankine cycle (steady state model); model validation and development of a linear model predictive controller; summer and winter day.

Jones et al.D14X [X 149]

Parabolic trough

30 MWel synthetic oil parabolic trough solar electric generating system; w/o TES, including power block (steady state); TRNSYS; model validation; simulations on daily basis with DNI profiles for sunny and cloudy days.

149

150

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Fig. 63. Comparison of measured data and simulated results. Left: mostly clear and sunny days. Right: days with slight cloudy periods (reproduced from reference [106] with permission of Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

TagedPsimulation studies. These technologies include geothermal power, municipal waste incineration and seawater desalination. The general lack of in-depth studies for those technologies is mainly linked to the economics that strongly favour steady state operation or to the comparatively small market penetration. In this chapter, the available research on these technologies in the literature is reviewed.

7.1. Geothermal power TagedPThe geothermal power plants use heat generated by radioactive decay in the earth, which is removed by accessing natural hot water reservoirs or by the so called hot-dry-rock process, where an artificial circulation system between the heat source and the plant is generated by injecting water into the ground.

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800

400

2

HTF temperature [°C]

500

DNI [W/m ]

1000

600

400

200

0

0

5

10

15

Sim. 300

200 Exp. 100

0

20

151

0

5

Time [h]

10

15

20

Time [h] 150

Thermal power [MWth]

Total HTF mass flow rate [kg/s]

1200 1000 800 600 400

100

50

200 0

0

5

10

15

0

20

0

5

Time [h]

Electrical power [MWel]

Storage energy [MWth]

20

60

150

100

50

0

15

Time [h]

200

0

10

5

10

15

20

Time [h]

50 40 30 20 10 0

0

5

10

15

20

Time [h]

Fig. 64. Comparison of measured data and simulated results for a day with strong cloudy periods (reproduced from reference [36] with permission of authors and Elsevier). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

TagedPThe retrieved hot water than can either be flashed directly to drive a Rankine process or the heat is transferred to a secondary circuit using a working fluid with more favourable evaporation characteristics. Generally, high temperature geothermal resources above 150 °C are applied to D18Xpower X generation. Moderate

tTagedP emperature geothermal resources in the range between 90 °C and 150 °C and low temperature geothermal resources (below 90 °C) are preferably applied to direct uses. Several novel designs are proposed recently to generate electricity from moderate or low temperature resources geothermal resources economically,

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Fig. 65. Dynamic response of thermal storage system on DNI perturbation (reproduced from reference [122], Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0), License: https://creativecommons.org/licenses/by-nc/4.0/). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

TagedPbut these are not efficient like power generation from high temperature geothermal resources [313]. TagedPDue to the near-zero marginal cost for geothermal power, the power plants are mostly used for base-load demand and there is little motivation to investigate transient operation. On the other hand, a number of studies on the dynamic storage behaviour of the wells/reservoirs exist, which are typically the limiting factor for those types of power plants. For example, Casella [314] conducted a study on the modelling, control and optimization of a double-flash geothermal plant using ProcSim, an in-house code from Laboratory of the Politecnico di Milano. Within this study, modelling approaches for components unique to geothermal power plants, e.g. the stripper columns, are presented and a

TagedP ynamic model of the plant is generated. Other recent studies d can be found in [47,154]. 7.2. Municipal waste incineration TagedPIn the last few decades and due to the rapid development of national economies, continued urbanisation and improvement of living standard, the solid waste output is constantly increasing. In order to effectively dispose of solid waste, different solutions have been suggested such as recycling, reduction of waste generation and landfills. A proven approach for the large-scale disposal of municipal solid waste is the thermal treatment in grate systems. Municipal waste incineration is characterised by several advantages such as

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153

Fig. 66. Net electricity generation and comparison of the accumulated power output for two different control strategies (reproduced from reference [81] with permission of ASME).

TagedPthe cost reduction of residual landfill due to the lower volume of end products (10% of the original volume) and decreasing the total organic carbon (TOC) of waste, resulting in inert residues unable to produce landfill gas. The heat released in waste combustion can be recovered by a water/steam circuit for the supply of electricity and district heating. Accordingly, the residual waste can be used as substitute fuel for the conventional fossil fuels. TagedPA municipal waste incineration power plant, shown in Fig. 67, consists basically of water/steam side, flue gas path and flue gas cleaning devices. In a waste bunker, the delivered raw waste is classified and treated. Here, bulky components are crushed and incombustible materials are discharged. Using a crane, the waste is transported to the firing system. The combustion system is composed of a primary

cTagedP ombustion on the grate, a post-combustion zone, in which the secondary air is injected and a zone with auxiliary burners. The auxiliary burners are required on the one hand for plant start-up and on the other hand for supporting the combustion temperature, when the calorific value of waste is insufficient. On the grate, the incineration of waste takes place in different zones using primary air (air/fuel ratio between 0.4 and 1.3). The thermal process steps are drying, pyrolysis, combustion of volatile matters and burn out of char. During the pyrolysis, the products of char, tar, gases (e.g. carbon monoxide, carbon dioxide and nitrogen) and volatile organic compounds are basically formed, which are released in different proportions. The char is the remaining solid that almost consists of pure carbon. In the post-

Fig. 67. Schematic of a municipal waste incineration (TREA Leuna) (reproduced from reference [332]).

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To horizontal pass

HTS_09

+32 m

Water/steam HTS_14 HTS_10 HTS_08 HTS_13 HTS_11 HTS_07

HTS_06

HTS_05 HTS_12 HTS_04

Air +18.4 m

Light fuel

HTS_03

Auxiliary burners secondary air

HTS_02

Flue gas

+15 m

Heat exchanger

Flue gas pipe

Control valve

Point

Heat flow

Boundary condition

HTS_01

Water +13 m

Primary combustion zone Fig. 68. Municipal waste incineration modelled in APROS.

TagedPcombustion zone, the remaining combustible species are burned with excess secondary air (approximately 1.5 air/fuel ratio). The exhaust gas flows into the flue gas path that is composed of vertical radiation passes and a horizontal pass, in which shell and tube heat exchangers are installed. Although most pollutants are

TagedP estroyed by the combustion, the waste incinerators can emit d high quantities of solid residues (particulate matter), heavy metals, acid gases and nitrogen oxides. Therefore, complex flue gas treatment is required, see Section 2.3.5.6. The thermal energy released from waste combustion (heating value: approximately

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155

Fig. 69. Temperature profile within the vertical passes at full load operation.

TagedP10 MJ/kg) is transferred to the water/steam circuit via membrane wall evaporators, superheaters and economisers. TagedPMunicipal waste incinerations can also be used to remove the sewage sludge, which denote the residual by-product of industrial and municipal wastewater treatment. The dry sewage sludge contains up to 70% organic components and the remaining 30% are composed of, among others, silicates, phosphates, phosphor and heavy metals. With a heating value of 9 to 12 MJ /kg (dried), more than half of the sewage sludge in Germany was incinerated in 2010 with the aim of full thermal treatment in the current decade. TagedPThe availability and operation efficiency of a municipal waste incineration can be improved using numerical simulations that can be divided in one-dimensional process simulation and three-dimensional computational fluid dynamics (CFD). While 3D simulations are often used for individual components to visualize flow patterns, 1D process simulations can model the entire power plant. In the scientific literature, numerical studies of waste incinerator using CFD and steady state process simulation were frequently reported. In contrast, no publication on 1D dynamic simulation of a municipal waste incineration exists to the authors’ knowledge. For the first time, dynamic simulation results for a 60 MWth municipal waste incineration built in Tampere, Finland, are presented in the following. The plant burns 5.7 kg/s of waste with an ideal LHV of 10.5 MJ/ kg and discharges 36.3 kg/s of flue gas at 160 °C as well as 0.7 kg/s of slag at 450 °C. The primary air is fed to the grate through 5 zones at 150 °C, while the secondary air that equates to about 30% of the total air mass flow rate is then supplied through a series of jets on the sidewalls of the post-combustion zone at 225 °C. The water/steam circuit consists of 4 economisers, 7 superheaters and 5 evaporators with natural circulation. At full load, the superheated steam mass flow rate at turbine inlet amounts to 20.5 kg/s at 400 °C and 45 bar. The gross electrical output of the steam turbine is approximately 16 MWel, which yields an electrical gross efficiency of 26.5%. The dynamic model of the municipal waste incineration was generated using APROS. The influence of waste heating value variations on the plant efficiency as well as the dynamic behaviour for both part loads and start-up procedures were investigated. In Fig. 68, the flue gas vertical passes including post-combustion zone, auxiliary burners and membrane wall heat exchangers are displayed. TagedPFig. 69 shows the temperature profile within the vertical passes of the municipal waste incineration at full load operation. The y-axis refers to the height above ground and the x-axis represents the temperature. At the outlet of the primary combustion zone (h D 14 m), the flue gas temperature is around 1200 °C. In the height range between h D 14 m and h D 15 m, the temperature of the flue gas decreases due to the heat transfer to the water-cooled combustion chamber walls. In the post-combustion zone, the combustion

Fig. 70. Dynamic behaviour of a waste incineration power plant during start-up procedure: (top) pressure, (bottom) steam mass flow rate (red line, first axis) and gross electrical output of the steam turbine (blue line, second axis). (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)

TagedPtemperature decreases sharply due to secondary air supply. The flue gas enters the second vertical pass at h D 32 m and the third vertical pass at h D 18 m. Along the flow path, the flue gas temperature decreases to approximately 700 °C, before the horizontal pass. The comparison between numerical results and design data shows high consistency. TagedPPressure, steam mass flow rate and the gross electrical output of the steam turbine during start-up procedure of the municipal waste incineration are depicted in Fig. 70. Approximately 20 min after ignition, the steam pressure reaches a fixed holding point at 15 bar. The bypass valve to condenser opens in order to counteract any further pressure rise. Subsequently, the steam mass flow increases sharply within minutes to 15 kg/s. Between t D 120 min and t D 180 min, the heat input starts increasing, resulting in higher steam production rate and thus pressure increase. At t D 145 min, the main steam control valve to steam turbine starts opening and the bypass valve to condenser closes in reverse. As a result, the electrical output of the steam turbine increases to its nominal value of about 16 MWel. The LHV variation of the solid waste is reflected by fluctuations of the steam mass flow. 7.3. Seawater desalination TagedPIn emerging economies especially, the growing population together with improved living standard is accompanied by a rapid increase in clean water demand. Recent studies unanimously expect that in the future, stress on water availability will rise even more due to global warming and agricultural irrigation. Desalination of seawater is an essential part in providing drinking water in arid regions around the world. In the Gulf Arab states for example, where drinking water has always been a scarce and precious resource, most of the fresh water is produced with seawater desalination plants. Generally, desalination processes can be divided into thermal processes and membrane processes. TagedPThe separation technology using membrane is a purely physical process without heating. For practical application, reverse

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TagedPosmosis (RO) that uses a semipermeable membrane is especially relevant. In reverse osmosis, an external pressure considerably higher than the osmotic pressure (seawater: 23 bar) is applied on the side of seawater with high salt concentration. While the membrane allows the solvent to pass to the other side, it keeps the solute on the pressurized side. Reverse osmosis desalination process utilizes electrical power generated by thermal power plants, e.g. combined-cycle, nuclear power plant and recently renewable energy sources [315]. Since the large-scale electricity storage is now related to technical challenges, modern operation concept of RO desalination offers the ability to use the excess generation capacity at times of reduced grid demand and/or increased renawable generation to produce clean water that can be easily stored in containers [316,317]. TagedPIn thermal processes or distillation processes, part of the seawater is evaporated, so that brine with high salt concentration remains. After condensing the vapour and adding calcium bicarbonate and other mineral nutrients to the pure distillate, drinking water is obtained. The thermal processes include multi-stage flash, multiple-effect evaporation possibly combined with thermal vapour compression. In multi-stage flash desalination (MSF), the seawater is heated to a maximum temperature of about 115 °C and then passes through a series of pressure stages. In each chamber a lower pressure than in the previous one prevails, so that part of the salty seawater is spontaneously flashed to steam in order to reach the local saturation state. The multipleeffect distillation (MED) consists of multiple stages. In each stage, the seawater flows on horizontal pipes in the direction of gravity, forming seawater films on the surface of pipes. The horizontal pipes are internally heated by a steam flow. Accordingly, part of the seawater is vaporized, collected and directed into the horizontal pipes of the next stage. There, the vapour condenses; releasing its condensation heat to another seawater film and the process is repeated. For large applications, multi-effect distillation is often used together with vapour compression in order to recover low temperature heat, resulting in an efficiency increase of the MED process. The thermal desalination processes (based on enthalpy of evaporation) are, in contrast to membrane processes, an energy-intensive. However, the membranes are sensitive to chlorine or organic components, so that an additional pre-treatment of the seawater is essential. TagedPThe thermal desalination processes require heating steam that is, generally, produced by a combined heat and power plant or a nuclear reactor. The thermal desalinations are operated at their nominal base loads (stable regimes) and therefore steady state simulation models are adequate. However, a few studies on the dynamic simulations of desalination plants can be found in the literature. For example, Agha et al.D182X X [37] developed the dynamic simulation model of a thermal desalination process (MSF-TVC) using APROS. The model was evaluated towards the design data of an industrial desalination plant in Tripoli-Libya with 1200 m3/day production capacity. Furthermore, detailed models of thermal desalination units (MED and MSF) coupled with nuclear reactors are presented. Al-Fulaij et al.D183X X[99,100] developed lumped parameter dynamic models for oncethrough MSF and brine circulation MSF using gPROMS. The generated models were in good agreement with measurement data obtained from existing MSF plants with relative error below 1.5% in steady state and dynamic conditions. Among others, further publications on the dynamic simulation of desalination plants are [126,142,318
324]. Recently, new technologies are developed to desalinate seawater using renewable energy sources [325], especially solar energy [326] or even municipal solid waste [327]. These intermittent energy sources (e.g. cloudy day in case of solar energy and variation in heating value of municipal solid waste) require an understanding of the transient process behaviour, which in turn can be evaluated using dynamic simulation.

8. Conclusion and future prospects TagedPOperating flexibility of thermal power plants is essential in order to compensate the intermittency of renewable energy sources such as wind or photovoltaics. Enhanced flexibility requirements for power plants translate, among others, into high load gradients, reducing the minimum load limit and minimising start-up duration. D184X X This study is a review of dynamic simulation for design, optimisation and the development of novel thermal power plants, including hybrid concepts that integrate renewables in conventional power plants. TagedPAn overview of dynamic simulation programmes widely used for scientific and industrial application is presented, supported by example models for different simulation codes such as ASPEN PLUS DYNAMICS, DYMOLA and APROS. The simulation codes are generally based on the governing conservation equations of mass, momentum, species and energy. The specific mathematical formulation of the balance equations depends on the underlying flow model. Many approaches can be found in the literature such as mixture flow model or two-fluid models, which in turn can be divided into fourequation, five-equation, six-equation and seven-equation flow models. Due to its relative simplicity and suitability for a range of practical applications, the mixture flow model is of considerable relevance since the calculation of average mixture properties is often sufficiently accurate for system-level analysis. The two-fluid model offers the possibility to consider thermodynamic non-equilibrium phenomena. It is thus more suitable for detailed analysis of specific components and application cases characterised by intense mass and heat transfer between phases. The resulting partial differential equation system is discretised and typically closed with empirical correlations, which are selected according to the prevailing flow regime. Basic process components required for modelling thermal power plants such as tubes, flow valves, heat exchangers, turbomachines etc. are discussed, complemented by automation and electrical modules vital for power plant control. The latter include analogue and binary modules, signal sources, controllers, generator, transformer, inverter and others. TagedPRelevant publications on dynamic simulation are discussed for the different technologies of combined-cycle power, coal-fired power, nuclear power, concentrated solar power, geothermal power, municipal waste incineration and thermal desalination in the individual chapters. The results can be summarised as follows: TagedP ombined-cycle power: Since the gas turbine is an inherently flexiC ble component, studies in the literature are largely focused on the dynamic response of the water/steam bottoming cycle, in particular the heat recovery steam generator. Detailed modelling and calculation of CCPP start-up transients are conducted rather frequently, as well as dynamic optimisation under thermal stress restraints. In contrast, system-level dynamics of the IGCC process and the interaction of syngas path components are not well understood and should be the subject of further study. By deriving reduced models for realtime computation from the detailed simulation models, the prospective use of model-predictive control in power engineering applications can be envisaged. Some recent studies are dedicated to shift the field of dynamic simulation and optimisation away from commercial codes towards more openly accessible models and software tools, a promising approach that the authors would encourage other researchers to follow in the interest of scientific progress. PTagedP ulverised coal power: In many countries, coal-fired power generation remains indispensable in the foreseeable future in order to cover base load demand. While all coal-fired power plants have the same working principle, each power plant is unique engineered, leading to individual dynamic behaviour. Here, the load change and start-up behaviour by increasing flexibility requirements are in the focus of

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TagedPinterest. The lack of available data for validation of the developed models is a major problem. Although the technology of coal-fired power is well known, there is still potential for further improvement regarding load gradients, minimal load limit and start-up procedure, which can be explored using dynamic simulation. Furthermore, the combustion of coal with a nitrogen-free oxidant (oxyfuel concept) has recently received attention. Dynamic simulation can contribute to this field of research, since design and operation experiences from conventional coal power plants can only be applied to a limited degree.D185X X N TagedP uclear power: The topic of dynamic simulation for nuclear power plants is broadly discussed and thorough work has already been done, in the field of accident analyses in particular. The amount of research on NPP load-following capability is limited but not a likely focus for further study due to both economic and technical reasons. The statistical analysis of transient system behaviour is an approach only used for NPPs as yet. The existing body of literature shows that the classic approach of selecting conservative boundary conditions has its downsides for complex systems. Therefore, statistical analysis should be considered as option for other applications where operating safety is paramount.D.186X X C TagedP oncentrated solar power: Due to the inherently dynamic nature of CSP operation, a significant number of studies are available in the literature. Most studies focus on system-level plant dynamics considering transient solar radiation. Some other studies investigate the dynamic behaviour of sub-systems such as thermal energy storage, considering stable power output and improvement of capacity factor. In case of molten salt as heat transfer fluid, detailed analyses of filling and draining procedures are conducted. Optimised operation strategies are frequently reported. The considered time horizons vary from operating transients of several minutes up to the prediction of annual performance data. A certain emphasis lies on mathematical models for the solar field. Most studies use a simplified steady state model rather than a detailed dynamic model of the power block. Thus, more attention should be dedicated to detailed modelling of the whole plant in order to analyse the dynamic interaction of sub-systems (solar field, thermal energy storage, power block) with D187X X higherD18X a X ccuracy.

sTagedP tudies regarding the dynamic behaviour of thermal desalination plants (e.g. MSF and MED). The absence of detailed analysis of desalination process dynamics, in addition to the missing validation with plant data should be covered with future studies. Furthermore, there is an interest in developing new desalination technologies using renewable energy sources, which increases the need for dynamic simulation.

TagedPD19X X The desirable expansion of renewable energy sources in many countries around the world is drastically altering the traditional landscape of power generation, which is required to ensure security of supply. Intermittent energy sources such as wind and solar lead to increasing market demand for control energy in order to maintain grid stability. However, this does not compensate for the decline in wholesale electricity prices that impairs the economic viability of thermal power plants. A number of measures are introduced by power plant operators in response to the new market environment such as retrofitting existing power plants for higher load gradients and reduced minimum load. Thus, the accurate prediction of dynamic system behaviour becomes an integral part of design and operation of thermal power plants. Furthermore, process optimisation, which is not always feasible in the real plant due to economic D192X X and safety reasons, is numerically possible. Dynamic simulation is a valuable tool for both the researcher and the practitioner in order to gain valuable insight and understanding of the system. TagedPIn closing: “Static is simple, but the universe is dynamic”. Acknowledgments TagedPThe authors would like to thank both Institute for Energy Systems & Technology and TU Darmstadt Energy Center for financial support, enabling open-access publication of this review. Mr. D193X X Mertens and Mr. Lanz gratefully acknowledge funding by Deutsche Forschungsgemeinschaft (DFG) within the framework of the Darmstadt Graduate School of Energy Science and Engineering (GSC 1070).

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References

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M TagedP unicipal waste incineration: In many industrialized countries, municipal waste incinerations are the preferred choice for the largescale disposal of municipal solid waste. The variation of waste heating value has a considerable influence on the water/steam circuit and accordingly on the plant operation and efficiency. There are no studies in the literature on dynamic simulation of a municipal waste incarnation plant hitherto. For the first time, selected calculation results are presented in this review. Additional dynamic studies have to be provided to the scientific literature, with particular attention to validation at the real plant.D190X X Thermal TagedP desalination: In order to expand the available water resources in arid countries, large-scale seawater desalination is a mature, but energy-intensive technology. In the literature, there are only few

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