Energy efficiency analysis of steam ejector and electric vacuum pump for a turbine condenser air extraction system based on supervised machine learning modelling

Applied Energy 173 (2016) 386–405

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Energy efficiency analysis of steam ejector and electric vacuum pump for a turbine condenser air extraction system based on supervised machine learning modelling Dušan Strušnik a,⇑, Milan Marcˇicˇ b, Marjan Golob c, Aleš Hribernik b, Marija Zˇivic´ d, Jurij Avsec a a

University of Maribor, Faculty of Energa Technology, Hocˇevarjev trg 1, SI-8270 Krško, Slovenia University of Maribor, Faculty of Mechanical Engineering, Smetanova ulica 17, SI-2000 Maribor, Slovenia University of Maribor, Faculty of Electrical Engineering and Computer Science, Smetanova ulica 17, SI-2000 Maribor, Slovenia d J.J. Strossmayer University of Osijek, Mechanical Engineering Faculty in Slavonski Brod, Trg Ivane Brlic´-Mazˇuranic´ 2, HR-35000 Slavonski Brod, Croatia b c

h i g h l i g h t s
Steam ejector pump and electric liquid ring vacuum pump are analysed and modelled.
A supervised machine learning models by using real process data are applied.
The equation of ejector pumped mass flow from steam turbine condenser was solved.
The loss of specific energy capable of work in a SEPS or LRVP component was analysed.
The economic efficiency analysis per different coal heating values was made.

a r t i c l e

i n f o

Article history: Received 26 December 2015 Received in revised form 21 March 2016 Accepted 10 April 2016 Available online 16 April 2016 Keywords: Ejector Machine learning Mixing section Operating principle Thermodynamic analysis Vacuum pump

a b s t r a c t This paper compares the vapour ejector and electric vacuum pump power consumptions with machine learning algorithms by using real process data and presents some novelty guideline for the selection of an appropriate condenser vacuum pump system of a steam turbine power plant. The machine learning algorithms are made by using the supervised machine learning methods such as artificial neural network model and local linear neuro-fuzzy models. The proposed non-linear models are designed by using a wide range of real process operation data sets from the CHP system in the thermal power plant. The novelty guideline for the selection of an appropriate condenser vacuum pumps system is expressed in the comparative analysis of the energy consumption and use of specific energy capable of work. Furthermore, the novelty is expressed in the economic efficiency analysis of the investment taking into consideration the operating costs of the vacuum pump systems and may serve as basic guidelines for the selection of an appropriate condenser vacuum pump system of a steam turbine. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction A steam condenser is an important subset of a condensing steam turbine. Its main purpose is to maintain the prescribed vacuum condition of around 0.01 MPa by evacuating exhaust gases from the steam turbine [1]. Exhaust gases are multiphase gases, comprising a condensable and a non-condensable gas phase. The condensable gas phase includes dry and wet vapour. Water vapour is removed from the turbine condenser through its condensation and by pumping the condensate into the boiler feeding system ⇑ Corresponding author. E-mail address: [email protected] (D. Strušnik). http://dx.doi.org/10.1016/j.apenergy.2016.04.047 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

[1]. Non-condensable gases are evacuated by means of a vacuum pump system. Two steam vacuum pump systems are most frequently used in practice, namely the steam ejector pump system (SEPS) and the liquid ring vacuum pump system (LRVP) [1]. Some other authors have analysed in their research the operation of vacuum pump systems. Dennis et al. [2] have analysed the SEPS by mathematical methods. The LRVP for Tokamak have analysed and designed by Khan et al. [3]. Zhu et al. [4] and Chong et al. [5] proposed a 2D exponential model to predict the velocity distribution in ejector, however the pressure is still assumed to be uniform in the radial direction. Sözen et al. [6] explored the exergy analysis of an ejector-absorption heat transformer using artificial neural network approach. We didn’t find the article that compare the SEPS

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Nomenclature Abbreviations ANN artificial neural networking ANFIS adaptive network-based fuzzy inference algorithm CHP combine heat and power LRVP liquid ring vacuum pump MAE mean absolute error MF membership functions MSE mean square error PID proportional-integral-derivative R2 correlation coefficient RMSE root mean square SCADA supervisory control and data acquisition SEPS steam ejector pump system

system

Parameters narrowest Laval nozzle cross section area, m2 AL A2 inlet diffuser cross sectional area, m2 c1 steam speed at the exit from the Laval nozzle, m/s c2 inlet diffuser mixed gas speed, m/s ein,LRVP amount of specific energy capable of work in the LRVP, kJ/kg eloss,p loss of specific energy capable of work in a specific part, kJ/kg h gas enthalpy, J/kg or kJ/kg hb boiler steam specific enthalpy, kJ/kg hin,p specific enthalpy of a gas mixture to a specific part, kJ/kg hout,p specific enthalpy of a gas mixture from a specific part, kJ/kg 00 hout turbine exhaust steam specific enthalpy, kJ/kg h0 specific enthalpy of motive steam, J/kg h1 specific enthalpy of steam Laval nozzle expansion, J/kg specific enthalpy of steam isentropic Laval nozzle h1s expansion, J/kg h3 diffuser outlet mixed gas specific enthalpy, J/kg isentropic specific enthalpy of diffuser outlet mixed gas, h30 J/kg h4 specific enthalpy of pumped gas, J/kg Ic investment cost, EUR mnon-in mass of the non-condensable gas entering the turbine condenser, kg mnon-out mass of non-condensable gas pumped form the turbine condenser, kg mtot-c total mass of the non-condensable gas of the turbine condenser, kg n LRVP impeller speed, rpm pc pressure in the turbine condenser, Pa or MPa pin pressure on the suction side of the LRVP, Pa pout pressure of the pumped gas on the pressure side of the LRVP, Pa p1, p4, px pressure in the mixing section, Pa p0 inlet motive steam pressure, Pa p2 diffuser inlet mixed gas pressure, Pa p3 exhaust ejector mixed gas pressure, Pa generated power in the case of SEPS motive steam Pgen expansion in the turbine, kW

and LRVP power consumptions in the CHP system in thermal power plant with machine learning algorithms by using real process data. Simulations models copying the functioning and behaviour of a real vacuum pumping system was designed using the supervised machine learning algorithms and real process data. The real

PLRVP LRVP power consumption, kW qmnon-in mass flow of non-condensable gas penetrating into the turbine condenser, kg/s qmnon-out mass flow of the pumped non-condensable gas from the turbine condenser, kg/s qmH2 O mass flow of the pumped condensable gas, kg/s motive steam mass flow through the Laval nozzle, kg/s qmO qmLRVP masni pretok cˇrpane plinaste zmesi LRVP, kg/s qm4 pumped gas mass flow, kg/s qV volumetric flow rate of the pumped out gas, m3/h qVnon-gas volumetric flow rate of the pumped non-condensable gas, m3/h qV H2 O volumetric flow rate of the pumped condensable gas, m3/h motive steam gas constant, J/(kg K) R0 Rmix2 gas constant of the gas mixture in the mixing section, J/(kg K) Rn gas constant of the non-condensable gas, J/(kg K) sin,p specific entropy of a gas mixture to a specific part, J/(kg K) sout,p specific entropy of a gas mixture from a specific part, J/(kg K) t time, minute, second T temperature, K Ta ambient temperature, K temperature in the turbine condenser, K Tc T0 inlet motive steam temperature, K T2 diffuser inlet mixed gas temperature, K v2 inlet diffuser specific volume of the mixed gas, m3/kg Vc turbine condenser volume, m3 Vcell LRVP impeller blade cell volume, m3 qc density of non-condensable gas in the turbine condenser, kg/m3 qnon-out density of the pumped non-condensable gas, kg/m3 qH2 O density of the pumped condensable gas, kg/m3 Subscripts and superscripts B, C article d differential HP high pressure j, k iterations LP low pressure M Mach number MP middle pressure M2 Mach number in the mixing section oj output value p, s pattern tj target value gdif-is diffuser isentropic efficiency gem LRVP electromechanical efficiency gLaval-is Laval nozzle isentropic efficiency motive steam specific heat ratio x0 xmix2 specific heat ratio of the gas mixture in the mixing section P Eelectric consumed or additionally generated energy at an annual level in case of 6000-h yearly operation

process data was obtained from the supervisory control and data acquisition system (SCADA) [7], comprising the information on the operation of a CHP system in thermal power plant in Slovenia. SCADA [7] contains more than 850 data groups on the operation of a CHP system in thermal power plant and are constantly recorded on an hourly basis 365 days a year. The data on the 2013/2014

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heating season is used in the paper. Some other authors also used the SCADA in their research [8–12]. The SEPS and LRVP simulation models were created using two different non-linear models and learning algorithms falling within the supervised machine learning scope. A multilayer perceptron network is the most widely applied neural network architecture (ANN). The ANN and ANFIS based non-linear models were developed and applied for the SEPS and LRVP simulation. The models were validated on the independent data set. Comparing simulation results to process monitoring results is a common validation method of estimating the accuracy and a quality of modelling and simulation applications. The learning algorithms often slow down and converge to the solutions in local optimums. The results of learning depend on initialisation parameters. The local linear neuro-fuzzy models, also known as Takagi–Sugeno fuzzy models, are popular because of their ability to use heuristic knowledge in the learning process, allowing us to avoid non-linear optimisation. As a result, the learning algorithm becomes simpler and faster. Moreover, the Takagi–Sugeno fuzzy system is also used in nonlinear modelling through an adaptive neuro-fuzzy inference system (ANFIS), where we optimise the fuzzy rule premise parameters by non-linear local optimization and the fuzzy rule consequent parameters by global least squares. The ANFIS typically yields very accurate process modelling performances but it is a computationally expensive approach. [13]. The ANN and ANFIS modelling of various energy systems has been studied by numerous researchers [14–19]. In study [14], an ANN model was developed to predict the behaviour of the commercial 100 kW micro gas turbine fed with a mixture of natural gas and biogas. The predictability of the model was validated and the results showed that the model can predict the performance parameters of the MGT with high accuracy. Adaptive Neuro-Fuzzy Inference System (ANFIS) technique was applied in study [15] to predict the performance of a hybrid furnace microgeneration system in a residential application. The validation results show that all developed ANFIS are able to predict system operating temperatures over a range of operational conditions with a high degree of accuracy. In our model presented in paper [16], three ANNs were used, computing the position of a the steam turbine control valve and the quality of the turbine extracted steam. Our other paper [17] describes a computation model using an artificial neural network (ANN) for a thermoeconomic analysis of district heating money flows. The model computes the results of the money flows in accordance with an energy method or a caloric method and an exergy method at various district heating substations. The paper [19] has presented an ANN based maximum power point tracking method that provides an accurate and fast estimation of the global maximum power point in a photovoltaic system subjected to continuous and rapidly changing shadowing patterns. The ANN and ANFIS based non-linear models were developed and applied for the SEPS and LRVP simulation. The models were validated on the independent data set. Comparing simulation results to process monitoring results is a common validation method of estimating the accuracy and a quality of modelling and simulation applications. The results of the models were analysed and used for the energy efficiency analysis of the SEPS and LRVP performance. The simulation models are designed by means of the Matlab software. The proposed supervised machine learning algorithms, on the other hand, are created by means of a set of subprograms (functions), provided by the Matlab software to design non-linear models such as ANNs and ANFIS. The new body of knowledge is presented by solving the unique equation for the calculation of the SEPS pumped mass flow rate from the steam turbine condenser. The unique equation is created by taking into consideration the mass and energy balances. In the energy balance, the potential energy of gases moving through the

SEPS was neglected, as it is negligibly low due to small differences in height. The inlet kinetic energy of gases entering the system was neglected. The analysed systems were treated as adiabatic, having no heat exchange with the environment. The novelty and originality are presented by uniquely created simulation models, verified by the real data. The uniquely created simulation models provide the results with almost zero error tolerance in comparison with the real process. Therefore, the unique simulation models are capable of providing the results for situations that cannot be analysed in a real process. The new body of knowledge in this paper is also presented with a diagram of dynamics of a comparative analysis of a thermodynamic state in the turbine condenser from putting the steam turbine into operation to the synchronisation of the generator with electricity grid. The turbine condenser pressure was analysed and compared to the results provided by the simulation models and the compared to the results of the real process from the SCADA system [7]. The novelty and originality are expressed in the comparative energy analysis of losses of energy capable of work in specific components of the SEPS and LRVP system. The novelty and originality are also presented by the SEPS–LRVP comparative economic efficiency analysis of the investment taking consideration the operating costs of the SEPS and LRVP and may serve as basic guidelines for the selection of an appropriate condenser vacuum pumps system of a steam turbine. The investment comparative economic efficiency analysis contributes to the decisionmaking criterion concerning a more rational use of vacuum pump systems and investments in such vacuum systems. The LRVP operate specification is expressed with installation pumped gas condenser. The pumped gas condenser serves for removal of water vapour from the pumped gas, thus reducing the pumped gas volume and quantity.

2. Description of SEPS and LRVP of a condensing steam turbine Steam ejector pump systems (SEPS) are devices designed to use the pressure energy of a working fluid for the transport of another working fluid, whereby no mechanical work is supplied or recovered. SEPS can be operated with incompressible fluids (liquids), and in this application they are normally referred to as jet pumps or educators. They are used as vacuum compressors or vacuum pumps in order to produce vacuum in steam turbine systems, in refrigeration systems, for bulk material transport etc. The actual efficiency is low, ranging from 0.1 to 0.35. The process is nonreversible due to mixing of two flows. Some other authors also analysed the SEPS in the following papers [20–24]. The SEPS operating principle is shown in Fig. 1. Water vapour from the turbine steam extraction 1, previously expanded in the steam turbine, thus emitting part of its energy, is used for the operation of the SEPS. The quality of water vapour, travelling to steam extraction 1 of the steam turbine is regulated with pressure amounting to approx. 0.9 Mpa and temperature to approx. 570 K. The suction pipe of an SEPS is connected to the coldest spot of the turbine condenser, where there is remarkably little steam due to sub-cooling, and therefore almost non-condensed gas is pumped. In our case, a SEPS is a two-stage flow-type compressor of a primary and secondary stage. In the primary stage, i.e. the condensation stage, the pumped gas from the turbine condenser is compressed at a pressure of approximately 0.01 Mpa. A mixture of the pumped gas from the turbine condenser and motive steam from the primary ejector stage is led to the primary cooler. Most of the water steam is condensed here and returned to the condenser through a special barometer loop. The mixture remaining in the primary cooler after the condensation is pumped at the steam pressure of the secondary (atmospheric) stage and compressed to the pressure slightly higher than the atmospheric

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Fig. 1. SEPS of a condensing steam turbine.

pressure, then led, together with the motive steam from the second stage, to the secondary cooler. The water steam is also condensed in this cooler. The condensate passes through the condensate pot to the turbine condenser and the residual non-condensed gas to the atmosphere. The LRVP is used in contemporary turbine systems to maintain the vacuum condition in the turbine condenser. The advantage of the LRVP is its improved adjustment to operating conditions, as by means of the impeller speed controller the operation is fully adjusted to the operating needs. The main components of the LRVP are: a pumped gas condenser, a liquid ring vacuum pump, a cooler and a separator [25]. Fig. 2 shows the working principle of the LRVP.

The pumped gas condenser serves for removal of water vapour from the pumped gas, thus reducing the pumped gas volume and quantity. The liquid ring vacuum pump consists of a cylindrical casing partly filled with liquid and an eccentrically positioned impeller with blades [26,27]. The impeller blades create impeller blade cell, causing a change in volume due to the eccentric shape so that at the inlet side of the pump they create vacuum and overpressure at the outlet side [26,27]. The liquid and gas phases are constantly interacting in the pump. If a two-phase, liquid and gas mixture is pumped the centrifugal force of the impeller separates the gas and liquid phases [26,27]. The liquid phase is used as a sealing agent of the pump casing and contributes to the compression of

Fig. 2. LRVP of a condensing steam turbine [25].

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the pumped gas phase that is compressed in the impeller blade cells [26,27]. To maintain the temperature of the pump sealing agent the liquid from the separator is used, previously cooled down in the cooler to appropriate temperature. The separator is designed to separate the liquid and gas phases from the pumped gases. The liquid phase is gravitationally discharged to the bottom of the separator and the gas phase, on the other hand, is discharged to the atmosphere. The principle and operation of the LRVP were also described by the authors of the papers indicated under [28–30].

3. Selection of appropriate advanced machine learning algorithm structure The selection of an appropriate structure of a non-linear model for supervised machine learning is carried out depending on the complexity of the non-linear system and the data set used for supervised learning. This is followed by the selection of the machine learning method, i.e. a linear or a non-linear optimisation algorithm to optimise the parameters of the model on the basis of the input output data set for learning. The non-linear model structure and parameters are chosen for the final model to make sure that after the validation of the model using a test input output data set the results have the lowest possible error [31]. Fig. 3 shows the process of selecting the structure and optimisation of non-linear parameters by means of machine learning. The process of selecting a non-linear model of machine learning comprises processing and selecting a training data set, selecting an

Fig. 3. Process of selecting appropriate non-linear structure of a non-linear model and optimisation of parameters by means of supervised machine learning methods.

appropriate non-linear model structure, selecting and using a learning algorithm (training algorithm), and model validation with a test data set in order to choose the best model. Processing and selecting training data set is obtained from the SCADA [7], which supplies the information about the plant’s operation. Parameters include those related to turbine inlet steam quality and quantity, extracted steam quality and quantity, turbine power, turbine condenser condition, turbine stretching and vibration, etc. However, before using data for the training, some preprocessing is required. This is necessary as there will always be some erroneous data in an extensive data set. This may either be due to faulty sensors, human errors, errors in the data capturing system, etc. Moreover, any data for the off-nominal operation of the plant must be removed from the training data set as it may confuse the algorithm. In our case, filtering was chosen for processing and selecting training data set. Fig. 4 shows the plot of whole input and output unfiltered real training data set for the algorithm. In our case the input data set was the temperature, pressure and quantity of steam entering the turbine. The variation of the unfiltered steam temperature was approximately between 750 K and 800 K, the variation of the unfiltered steam pressure approximately between 7 MPa and 9.5 MPa and the variation of the unfiltered steam quantity approximately between 0 kg/s and 60 kg/s (Fig. 4). The output data set was the steam temperature and pressure in extract 1 or SEPS motive steam temperature and pressure (Fig. 1). The variation of the unfiltered steam temperature was approximately between 280 K and 680 K and the variation of the unfiltered steam pressure approximately between 0.7 Mpa and 0.96 Mpa. Fig. 5 shows the plot of input and output filtered real training data set. The variation of the filtered steam temperature was approximately between 780 K and 800 K, the variation of the filtered steam pressure approximately between 8.8 MPa and 9.5 MPa and the variation of the filtered steam quantity approximately between 26 kg/s and 50 kg/s. The variation of the filtered steam temperature in extract 1 or SEPS motive steam temperature was approximately between 490 K and 680 K and the variation of the filtered steam pressure in extract 1 or SEPS motive steam pressure approximately between 0.88 MPa and 0.96 MPa. The above procedure of processing and selecting training data set by means of data filtering was also used by the authors in [32–35]. The structures of non-linear models may vary and depend on the complexity of the non-linear problem, on the quantity of the used real input–output process data and last but not least, on the restrictions of the computer-designed model, e.g. on the overload of the computer memory in the learning process implementation. The number of hidden layers and the number of neurons in each hidden layer were changed in the application of the non-linear ANN models. In the application of the non-linear ANFIS models, however, a grid partition and sub cluster learning methods were used, whereby the type and number of membership functions (MF) were changed. Several other authors also chose an appropriate structure of non-linear models in a similar manner in their research [36–41]. Selecting training algorithm is carried out so as to choose the simplest algorithm generating results within a reasonable time in accordance with the required model performances. In practice, linear training algorithms are most frequently used, such as the least mean square method or non-linear optimisation algorithms, i.e. backpropagation algorithm, genetic algorithms, differential evolution method and their various improvements [31]. In our case, non-linear processes were modelled with ANN and ANFIS nonlinear models and the structure was used in the simulation model with the least erroneous results. The quality of the selected and trained non-linear models was tested using the validation with test data set (Fig. 3).

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Fig. 4. Input and output unfiltered real data set.

Fig. 5. Input and output filtered real data set.

The SEPS simulation model (Fig. 6) consists of three auxiliary algorithm structures, namely a non-linear ANN unit, a calculation unit and a turbine condenser calculation unit.

turbines, two output data items, namely temperature and pressure of water vapour travelling to the steam turbine steam extraction 1 or is used for the SEPS drive. In the non-linear ANN unit design, 3 groups of input data expressed in a matrix form [3  4793] were used from the SCADA system [7] and 2 groups of output data expressed in a matrix form [2  4793]. As a result, each group contains 4793 data items. The non-linear ANN unit algorithm structure comprises an input layer, two hidden layers and an output layer. The input layer contains 3 neurons, the first hidden layer contains 35 neurons, the second hidden layer 5 neurons and the output layer 2 neurons. The non-linear ANN unit algorithm structure (Fig. 6) was selected through validation and it has minimum errors between the results provided by the non-linear ANN algorithm structure in the real process results.

4.1.1. Non-linear ANN unit algorithm structure A non-linear ANN unit (Fig. 6) constitutes a non-linear ANN system that calculates by means of 3 input data items, i.e. temperature, pressure and mass flow of water vapour entering the

4.1.2. Calculation unit algorithm structure The calculation unit algorithm structure comprises the Matlab x-steam calculator functions to calculate the enthalpy and entropy value of water vapour travelling into steam extraction 1 or steam

4. SEPS and LRVP simulation models The structure and functioning of the SEPS and LRVP simulation models providing the desired energy efficiency results are presented below. The energy efficiency results of the SEPS and LRVP simulation model will be analysed and compared with each other to identify the most appropriate system in terms of energy efficiency. 4.1. SEPS simulation model

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Fig. 6. SEPS simulation model.

used for the SEPS operation. Once the thermodynamic properties of water vapour used for the SEPS operation are known, the primary and secondary ejector calculation units compute the mass flow of water vapour used for the SEPS operation, water vapour speed in the narrowest Laval diameter, speed of water vapour from the Laval nozzle and quantity of removed non-condensable gases from the turbine condenser. The algorithm structure of the primary and secondary ejector calculation units are identical and only differ in geometrical dimensions of the primary and secondary SEPS. The calculations recorded in the primary and secondary calculation units are based on the thermodynamic transformation of the SEPS shown in Fig. 7. Several other authors described the thermodynamic transformation of the SEPS in a similar way [22,5,42]. The motive steam enters the ejector at point 0 and flows through the Laval nozzle, where the steam expands at supersonic speed. In the mixing section x, the expanded motive steam pumps gases from the turbine condenser 4, where they mix with each other from point 1 to point 2. The mixture of gases enters a diffuser, where kinetic energy of gas transforms into pressure energy and at point 3, the gases exit at a higher pressure and a lower speed. The analysis is based on the facts of conservation of momentum, mass and energy balances in each part of the ejector (Laval nozzle, mixing section and diffuser). The following facts are taken into consideration in the calculation: there is no heat transfer in the transformations in the Laval nozzle, the motive steam expands in the Laval nozzle from the initial state of p0 up to pressure in mixing section, px (Fig. 7), we assume that pressure px in the mixing section equals the gas pumping pressure p4 (Fig. 7), the gases in the mixing section mix with each other, potential energy is

negligibly low and is not taken into consideration and outlet speed from the diffuser is extremely low and is therefore neglected. The motive steam mass flow through the Laval nozzle is calculated using the equation. [2,43]:

AL  p qm0 ¼ pffiffiffiffiffi0  T0

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x0 þ1 x0 1 x0 2 ð  gLaval-is Þ R0 x0 þ 1

ð1Þ

where qm0 is motive steam mass flow through the Laval nozzle, AL is narrowest Laval nozzle cross section area, p0 is inlet motive steam pressure, T0 is inlet motive steam temperature, x0 is motive steam specific heat ratio, R0 is motive steam gas constant and gLaval-is. Laval nozzle isentropic efficiency. The Laval nozzle isentropic efficiency is defined as [2,43,44]:

gLaval-is ¼

h0  h1  0:97 h0  h1s

ð2Þ

where h0 is specific enthalpy of motive steam, h1 is specific enthalpy of steam Laval nozzle expansion and h1s specific enthalpy of steam isentropic Laval nozzle expansion. Steam speed at the exit from the Laval nozzle is calculated as [2,43,44]:

c1 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  gLaval-is  ðh0  h1s Þ

ð3Þ

where c1 is steam speed at the exit from the Laval nozzle. The motive steam expanded in the Laval nozzle and gases pumped from the turbine condenser are mixed in the mixing section. The thermodynamic analysis is described by means of

Fig. 7. Thermodynamic transformation of the SEPS.

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the mass, momentum and energy balance equations. Mass balance equation [2,43–45]:

qm0 þ qm4 ¼

A2  c 2

ð4Þ

v2

where qm4 is pumped gas mass flow, A2 is inlet diffuser cross sectional area, c2 is inlet diffuser mixed gas speed and v2 is inlet diffuser specific volume of the mixed gas. Geometrical data of the existing SEPS is indicated in Table 1 [46]. Momentum balance equation [2,43,44]:

qm0  c1 þ p4  A2 ¼ ðqm0 þ qm4 Þ  c2 þ p2  A2

ð5Þ

By inserting Eq. (11) into Eq. (9) we obtain: 1  xmix2   p3 xmix2 gd  ðxmix2  1Þ qm0  c1 þ p4  A2   1 1¼0 2  xmix2 p2 p2  A2

If p3 is known, Eq. (12) is solved, and p2 is obtained and then M2 is calculated from Eq. (11). It is necessary to determine c2, T2 and qm4. Taking into account Eq. (4), the energy Eq. (6) can be written as follows:

  xmix2  R  T 2 c22 þ Rmix2  T 2 xmix2  1 2   xmix2 xmix2 þ  M22 ¼ A2  c2  p2 xmix2  1 2

qm0  h0 þ qm4  h4 ¼ A2  c2 

where p4 is pumped gas pressure and p2 is diffuser inlet mixed gas pressure. Energy balance equation [2]:

qm0  h0 þ qm4  h4 ¼ ðqm0 þ qm4 Þ  ðh2 þ

c22 Þ 2

ð6Þ

where h4 is specific enthalpy of the pumped gas. Pressure in the mixing section px = p1 = p4 is taken into consideration in the calculation. The diffuser conditions are calculated using the energy balance equation [2,43,44]:

h2 þ

c32 ¼ h3 2

ð7Þ

where h3 is diffuser outlet mixed gas specific enthalpy. By introducing isentropic efficiency of a diffuser we obtain [2,43,44]:

h30  h2 ¼ gd  ðh3  h2 Þ

ð8Þ

where h30 is isentropic specific enthalpy of diffuser outlet mixed gas and gd is diffuser isentropic efficiency. Gas pumped mass flow qm4 is calculated using a derived equation where thermodynamic properties of the mixed gas are taken into consideration, Mach number in the mixing section and geometrical properties of the diffuser. The Mach number in the mixing section is calculated [2,43]:

c2 M 2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xmix2  Rmix2  T 2

ð9Þ

where M2 is Mach number in the mixing section, xmix2 is specific heat ratio of the gas mixture in the mixing section, Rmix2 is gas constant of the gas mixture in the mixing section and T2 is diffuser inlet mixed gas temperature. Using Eqs. (4), (5) and (9) the necessary diameter A2 is expressed and calculated [2]:

A2 ¼

qm0  c1

ð10Þ

p2  ½xmix2  M 22 þ 1  p4

Eqs. (7)–(9) are used to obtain the equation:

 xxmix2 1 p3 mix2 g  M22  ½xmix2  1 ¼1  d 2 p2

ð11Þ

where p3 is exhaust ejector mixed gas pressure. If the inlet diffuser cross-section area A2 is known, it is possible to express M2 as a function of p2 from Eq. (10) to obtain [2]:

qm0  c1 p  p2 M 22 ¼ þ 4 p2  A2  xmix2 p2  xmix2

ð12Þ

Table 1 Geometrical data of the existing SEPS [46]. Parameter

Primary ejector

Secondary ejector

Narrowest Laval nozzle diameter (m) Laval nozzle outlet diameter (m) Diffuser inlet diameter (m) Final diameter of a diffuser (m) Diffuser expansion angle (°) Nozzle efficiency (%) Diffuser efficiently (%)

0.0098 0.0396 0.0496 0.1025 10 0.97 0.75

0.0121 0.0264 0.0323 0.0872 10 0.97 0.75

ð13Þ

p2

ð14Þ

From Eq. (14) we express c2 and insert it into Eq. (5) to obtain a unique quadratic equation for the calculation of the mass flow rate of pumped gas from the steam turbine condenser, whose solution is:

qm4 ¼

B 

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 B2  4  h4 fqm20  h0  C  xxmix21  A2  p2  ½1 þ xmix2  M 22 g 2 mix2

2  h4 ð15Þ

Article B in Eq. (15) is calculated:

B ¼ qm0  ðh0 þ h4 Þ

ð16Þ

Article C in Eq. (15) is calculated:

C ¼ qm0  c1 þ p4  A2  p2  A2

ð17Þ

The solution of quadratic equation for the calculation of the mass flow rate of pumped gas from steam turbine condenser was unique and it not yet been published. The unique equation is created by means of the mass and energy balances of the SEPS. The pumped gas mass (qm4) is a two-phase mixture comprising condensable steam and non-condensable gas. The analyses of the existing SEPS showed that the ratio of the pumped two-phase mixture is 1:4 on average. The mass flow of the non-condensable gas is calculated using the equation:

qmnon-out ¼ qm4  0:75

ð18Þ

where qmnon-out is mass flow of the pumped non-condensable gas from the turbine condenser. 4.1.3. Turbine condenser calculation unit algorithm structure The turbine condenser calculation unit algorithm structure calculates the generated power of the steam turbine if the steam used for the SEPS expands in the steam turbine, namely from the thermodynamic state of steam from the boiler to the thermodynamic state of exhaust steam from the turbine or thermodynamic state of steam in the turbine condenser. The generated power in the case of SEPS motive steam expansion in the turbine is calculated [44,47] using: 00

Pgen ¼ qm0  ðhb  hout Þ

ð19Þ

where Pgen is generated power in the case of SEPS motive steam expansion in the turbine, hb is boiler steam specific enthalpy and 00 hout is turbine exhaust steam specific enthalpy. In the calculation of pressure in the turbine condenser, ((q – const., V = const.) were taken into consideration [45].

mnon-in  mnon-out ¼

dmtot-c dðV c  qc Þ dq ¼ Vc  c ¼ dt dt dt

ð20Þ

where mnon-in is the mass of the non-condensable gas entering the turbine condenser, mnon-out is mass of non-condensable gas pumped form the turbine condenser, d differential, mtot-c total mass of the non-condensable gas of the turbine condenser, t time, Vc turbine condenser volume in qc density of non-condensable gas in the

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turbine condenser. The density of the non-condensable gas in the turbine condenser qc is a function of pressure and temperature and can be written as [48]:

dqc dqc dpc dqc dT c   ¼ þ dt dpc dt dT c dt

ð21Þ

where pc is pressure in the turbine condenser and Tc is temperature in the turbine condenser. As condensation in the turbine condenser occurs at a constant temperature (T = constant) it is assumed that the derivative of temperature with respect to time equals zero and the equation is written as [48]:

dqc dT c ¼0  dT c dt

ð22Þ

and we take into consideration [48]:

dqc 1 ¼ dpc Rn  T c

ð23Þ

where Rn is a gas constant of the non-condensable gas. If Eq. (23) is integrated into Eq. (20) the final equation is obtained written in the turbine condenser calculation unit algorithm structure for the pressure calculation in the turbine condenser [48]:

qmnon-in ðpc ; tÞ  qmnon-out ¼

Vc dp  c Rn  T c dt

ð24Þ

where qmnon-in is the mass flow of non-condensable gas penetrating into the turbine condenser. The measurements of the existing CHP system in thermal power plant showed that the mass flow of non-condensable gas penetrating into the turbine condenser due to the vacuum condition depends on the pressure in the turbine condenser. At the condenser pressure of pc = 0.01 MPa (90% vacuum) the mass flow of non-condensable gases penetrating the condenser amounts to qmnon-in = 0.0336495 kg/s. As the vacuum condition in the condenser changes, qmnon-in also changes so that at the atmospheric pressure of 0.1 MPa in the condenser noncondensable gases no longer enter the condenser. The mass flow of non-condensable gas as a function of pressure in the condenser is calculated using the interpolation equation:

qmnon-in ðpc Þ ¼ 0:0336495 

  ðpc  0:01Þ  0:0336495 0:09

The speed unit algorithm structure comprises a proportional-i ntegral-derivative (PID) controller, regulating the LRPV impeller speed according to the pressure difference between the required and actual pressure in the turbine condenser. Some other authors used the PID controller for the regulation purpose in similar cases [49–51]. The non-linear ANN unit and the condenser pressure unit algorithm structure will be presented in detail below. 4.2.1. Non-linear ANN unit algorithm structure The non-linear ANN unit algorithm structure (Fig. 8) represents a non-linear ANN system, calculating by means of two input data items, i.e. pressure in the turbine condenser and the LRVP impeller speed, one output data item, i.e. mass flow of the pumped noncondensable gas. When designing the non-linear ANN unit structure two groups of input data were used from the SCADA system expressed in the [2  1242] matrix form and in one group of output data expressed in the [1  1242] matrix form. Each group contains 1242 data items. The non-linear ANN unit structure comprises an input layer, two hidden layers and an output layer. The input layer contains 2 neurons, the first hidden layer contains 9 neurons, the second hidden layer contains 3 neurons and the output layer contains 1 neuron. The non-linear structure used in the non-linear ANN unit structure (Fig. 8) was chosen using the validation and has the least deviations between the results provided by the non-linear ANN structure and the real process. 4.2.2. Condenser pressure unit algorithm structure The condenser pressure unit algorithm structure computes the pressure in the turbine condenser and the power needed by the LRVP for operation. The turbine condenser pressure is computed using the mass balance, the non-condensable gas pumped by means of the LRVP and the non-condensable gas entering the turbine condenser as a result of the vacuum condition in the turbine condenser. The calculation of pressure in the condenser was already presented in Section 4.1.3, so that only the LRVP power consumption calculation unit (Fig. 8) will be described below. The power consumed by the LRVP for its operation is calculated using the equation. [25]:

ð25Þ PLRVP ¼

4.2. LRVP simulation model The LRVP simulation model (Fig. 8) comprises three auxiliary algorithm structures, namely a speed unit, a non-linear ANN unit and a condenser pressure unit algorithm structure.

pin  qV  ln ppout in 3; 6  106  gem

ð26Þ

where PLRVP is power consumed by the LRVP, pin is pressure on the suction side of the LRVP, qV is volumetric flow rate of the pumped out gas, pout is pressure of the pumped gas on the pressure side of the LRVP and gem is electromechanical efficiency of the LRVP. The

Fig. 8. LRVP simulation model.

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volumetric flow rate of the pumped gas is calculated using the equation [25]:

qV ¼ ðqV non-gas þ qV H2 O Þ ¼

qmnon-out

qnon-out

þ

qmH2 O

qH2 O

!

 3600

¼ 60  V cell  n

ð27Þ

where qmnon-gas is the volumetric flow rate of the pumped noncondensable gas, qV H2 O is the volumetric flow rate of the pumped condensable gas, qmH2 O is mass flow of the pumped condensable gas, qnon-out is density of the pumped non-condensable gas, qH2 O is density of the pumped condensable gas, Vcell is the LRVP impeller blade cell volume and n is the LRVP impeller speed. 5. Validation of non-linear models The validation of non-linear algorithm structures is carried out using the calculations of errors between the results provided by the non-linear structure and the real process data. The winning or non-linear structure with the lowest errors was used in the simulation model. Errors can be calculated in several ways. The most suitable error calculation method, the mean square error (MSE), is defined as [15,16]:

1X ðt j  oj Þ2 p j¼1 p

MSE ¼

ð28Þ

and the root mean square (RMS) is defined as follows

$

p X RMS ¼ ð1=pÞ ½tj  oj 2

%1=2 ð29Þ

j¼1

In addition, the correlation coefficient (R2) and mean absolute error (MAE) are respectively defined as [15,16]

"Pp

j¼1 ðt j  oj Þ P2 2 j¼1 ðoj Þ

2

R ¼1

2

#

ð30Þ

1X jt j  oj j p j¼1 p

MAE ¼

ð31Þ

where tj is the target value, oj is the output value, and p is the pattern. The correlation coefficient ranges between 0 and 1. A very good fit yields an R2 value of 1, whereas a poor fit results in a value near 0 [15,16]. The same error calculation method was also used by the authors of the following papers [52–54]. The non-linear ANN and ANFIS structures of various architectures were validated using Eqs. (28)–(31). When validating the non-linear ANN structure the architecture was changed by varying

the number of hidden layers and the number of neurons in each hidden layer. When validating the non-linear ANFIS structure, however, the architecture was changed by varying the learning method using the grid partition and sub clustering methods. Within the grid partition method, various types of MFs (Gauss, Gbell and Trap) and numbers were used. Considering that the non-linear structure employed in the SEPS simulation model (Fig. 6) has two output data items, two parallel non-linear ANFIS structures were designed, integrated and validated as a single non-linear ANFIS structure. The results of the validations of nonlinear ANN and ANFIS structures of various architectures, used for the selection of the winning non-linear structure in the SEPS simulation model, are shown in Table 2. Table 2 shows that the winning non-linear ANN structure used in the SEPS simulation model has the 35-5 architecture (in bold), as this architecture has the lowest errors. The architecture of the winning ANN structure was presented in detail in Section 4.1.1 and shown in Fig. 6. The process of design and regression of the winning non-linear ANN structure, used in the SEPS simulation model, is shown in Fig. 9. It is evident from Fig. 9 that the creation of the non-linear ANN structure, used in the SEPS simulation model, was carried out in 700 epochs. The best validation performance in terms of MSE is 41.063 at epoch 54. Regression R2 is 0.99995. Fig. 10 shows a comparison of the results provided by the winning non-linear ANN structure, employed in the SEPS simulation model and the real process results. The results of the validations of non-linear ANN and ANFIS structures of various architectures to select the winning nonlinear algorithm structure used in the LRVP simulation model are shown in Table 3. Table 3 shows that the winning non-linear ANN structure used in the LRVP simulation model is of 9-3 architecture (in bold), as the above architecture has the lowest errors. The architecture of the winning ANN structure was presented in more detail in Section 4.2.1 and shown in Fig. 8. The design process and regression of the winning non-linear ANN structure, used in the LRVP simulation model, is shown in Fig. 11. It is evident from Fig. 11 that the creation of the non-linear ANN algorithm structure, used in the LRVP simulation model, was carried out in 700 epochs. The best validation performance in terms of MSE is 0.000002 at epoch 700. Regression R2 is 0.98941. Furthermore, pressure oscillation was validated in the turbine condenser during the steam turbine cold start from the atmospheric pressure (0.1 MPa) to the operating pressure in the turbine condenser. The validation was carried out by comparing pressure dynamics in the real process turbine condenser and the results provided by the SEPS and LRVP simulation models presented in Fig. 12.

Table 2 Results of validations of non-linear ANN and ANFIS structures of various architectures to select the winning non-linear algorithm structure used in the SEPS simulation model. Algorithm architecture

Layers

Epochs

Data set size

MSE

RMSE

R2

MAE

ANN 10-8-5 ANN 60-10 ANN 35-5 ANN 10-5 ANN 9-3 ANN 120 ANN 80 ANN 40 ANFIS-Grid Gauss MF 2-2-2 ANFIS-Grid Gauss MF 3-3-3 ANFIS-Grid Gbell MF 4-4-4 ANFIS-Grid Trap MF 4-4-4 ANFIS-sub. clustering

5 4 4 4 4 3 3 3 6 6 6 6 6

700 700 700 700 700 700 700 700 700 700 700 700 700

4793 4793 4793 4793 4793 4793 4793 4793 4793 4793 4793 4793 4793

43.7962 50.1995 41.0635 45.7717 55.2172 52.2107 52.5508 45.6821 91.3053 67.5520 58.0144 75.8338 76.8797

6.6178 7.0852 6.4081 6.7655 7.4308 7.2257 7.2492 6.7588 9.5554 8.2190 7.6167 8.8083 8.7681

0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9999 0.9997 0.9998 0.9998 0.9998 0.9998

3.0765 3.2408 2.8508 3.1879 3.6369 2.8141 2.7487 3.0329 4.8939 4.0837 3.6797 4.2395 4.3344

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Fig. 9. Process of design and regression of the winning ANN non-linear structure used in the SEPS simulation model.

Fig. 10. Comparison of the results of the non-linear ANN structure used in the SEPS simulation model and real process results.

The unique diagram in Fig. 12 shows the real process turbine speed rotation during the steam turbine cold start, namely from the moment when non-condensable gases start to be pumped from the turbine condenser or when the pump system is switched on until the generator synchronisation with the electric grid. The middle diagram shows the movement of the temperature in the real process turbine condenser and the bottom diagram the pressure oscillations of the real process turbine condenser and the pressure oscillations of the turbine condenser provided by the SEPS and LRVP simulation models. It is found that the differences of pressure dynamics between the real process and results provided by the SEPS and LRVP simulation models are minimal. In all cases, the required pressure (operating manual) is achieved after 20 min in the turbine condenser as a condition for the beginning of the steam turbine impeller rotation providing further confirmation of the reliability of the results obtained by the SEPS and LRVP simulation models. The presented based SEPS and LRVP models could not be implemented directly on the SCADA system because this system does not have the capacity to deal with complex mathematical

operations requested by this type of models. But, for the purpose of the real-time analysis, it is possible to develop a communication channel between the SCADA [7] and the Matlab software, where the ANN’s and ANFIS model was implemented. The used communication channel is the OPC protocol (Object Linking and Embedding – OLE – for process control). This standard specifies the communication of real-time data among control devices from different manufacturers. This protocol provides the exchange of data between two independent software programs, for example the Matlab software initiates the communication, as it is the Client and the SCADA [7] software responds to Client’s requests.

6. Results and energy efficiency comparative analysis of the SEPS and LRVP simulation models The results of the SEPS and LRVP simulation models describe and compare the most important thermal energy states of the systems in question to define the most efficient operation and provide an analysis of the said systems in terms of energy efficiency. The

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Table 3 Results of the validations of non-linear ANN and ANFIS structures of various architectures to select the winning non-linear algorithm structure used in the LRVP simulation model. Algorithm structure

Layers

Epochs

Data Set Size

MSE

RMSE

R2

MAE

ANN 10-8-5 ANN 60-10 ANN 35-5 ANN 10-5 ANN 9-3 ANN 120 ANN 80 ANN 40 ANFIS-Grid Gauss MF 2-2 ANFIS-Grid Gauss MF 3-3 ANFIS-Grid Gbell MF 4-4 ANFIS-Grid Trap MF 4-4 ANFIS-sub. clustering

5 4 4 4 4 3 3 3 6 6 6 6 6

700 700 700 700 700 700 700 700 700 700 700 700 700

1242 1242 1242 1242 1242 1242 1242 1242 1242 1242 1242 1242 1242

0.000028 0.000063 0.000009 0.000008 0.000002 0.000023 0.000032 0.000004 0.000023 0.000016 0.000013 0.000019 0.000025

0.0054 0.0081 0.0030 0.0029 0.0015 0.0048 0.0057 0.0020 0.0048 0.004 0.0036 0.0044 0.0051

0.8510 0.7818 0.9571 0.9585 0.989 0.9103 0.8551 0.9824 0.8736 0.9175 0.9339 0.8961 0.8563

0.0018 0.0017 0.0016 0.015 0.0010 0.0018 0.0035 0.0011 0.0023 0.0022 0.002 0.0024 0.0025

Fig. 11. Process of design and regression of the winning ANN non-linear structure used in the LRVP simulation model.

Fig. 12. Validation of pressure dynamics in turbine condenser.

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energy efficiency analysis of the systems in questions is based on the calculated mean values of any event of the analysed period.

6.1. Results of the SEPS simulation model The results of the SEPS simulation model were obtained using the real process data set from the SCADA system [7] of the 2013/2014 heating system. The input data used in the SEPS simulation model are shown in Fig. 13. Three groups of input data were used in the matrix of size [3  1000], representing the steam turbine inlet steam quality variations. The quality of steam travelling to the turbine steam extraction 1 or the SEPS motive steam quality was calculated using the non-linear ANN structure in the SEPS simulation model. The relevant results are shown in Fig. 14. The mean SEPS motive steam temperature in the analysed period is 590.59 K and the mean pressure is 0.907 MPa. The SEPS motive steam enters the primary and secondary steam ejector Laval nozzle where steam expands and the thermal energy of the steam transforms to kinetic energy. The results of the SEPS simulation model, steam speeds in the narrowest Laval crosssection and speeds of the steam from the primary and secondary ejector are shown in Fig. 15. The mean steam speed at the narrowest Laval cross-section of the analysed period is 555 m/s, the mean speed of steam from the Laval nozzle of the primary ejector is 1276 m/s and the mean speed of steam from the Laval nozzle of the secondary ejector is 1140 m/s. The consumption of steam for the SEPS drive is essential for carrying out the energy efficiency analysis. Steam consumption constitutes the highest cost of the SEPS’s operation. The results of the SEPS simulation model referring to the consumption of steam for the SEPS drive are shown in Fig. 16. The mean mass flow of steam expanded in the Laval nozzle of primary ejector or steam used for the primary ejector drive is 0.0874 kg/s. The mean mass flow of steam needed for the secondary ejector drive is 0.1332 kg/s and the total mean mass flow of steam for the SEPS drive in the analysed period is 0.2206 kg/s. The results of the SEPS simulation model of the mass flow of the

pumped non-condensable gas from the turbine condenser and the turbine condenser pressure are shown in Fig. 17. The mean mass flow of non-condensable gas in the analysed period, pumped by the SEPS from the turbine condenser is 0.0347 kg/s, whereby the mean pressure in the turbine condenser amounts to 0.01012 MPa. By means of the mass flow of steam used for the SEPS operation (Fig. 16) and Eq. (19), the SEPS simulation model also calculates the acquired turbine power if the steam consumed for the SEPS operation expands in the steam turbine. The results of the SEPS simulation model of the acquired steam turbine power in the case of expansion of the steam used for the SEPS operation in the steam turbine are shown in Fig. 18. The mean acquired steam turbine power in the case of expansion of the steam used for the primary ejector operation in the analysed period amounts to 49.62 kW and of the secondary ejector to 75.65 kW. The total acquired steam turbine power in the analysed period in the case of expansion of the whole quantity of steam used for the SEPS operation is 125.3 kW. This means that in terms of energy efficiency the SEPS is a low cost-efficient system as it consumes steam which in the case of expansion of the said steam quantity in the steam turbine would additionally generate 123.5 kW of power on average. 6.2. Results of the LRVP simulation model In order to obtain the appropriate results to provide an assessment of the energy efficiency analysis of the LRVP simulation model a simulation was carried out for monitoring the response and operation of the LRVP under normal operating conditions of the turbine condenser during the period in which the steam turbine operates. In doing so, 890 real process data items (SCADA) of the turbine condenser pressure condition were used, constituting the input data of the LRVP simulation model. The simulation results of the LRVP simulation model are shown in Fig. 19. The top diagram 1 in Fig. 19 shows the data of the LRVP simulation model or the real process data of the turbine condenser pressure oscillation. Diagram 2 in Fig. 19 shows the mass flow rate of the pumped non-condensable gas from the turbine condenser amounting to 0.0349 kg/s on average in the analysed period OK.

Fig. 13. Input data of the SEPS simulation model referring to steam turbine inlet steam quality.

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399

Fig. 14. Results of the non-linear ANN structure of the SEPS simulation model referring to the ejector motive steam quality.

Fig. 15. Results of the SEPS simulation model referring to the steam speed from the primary and secondary Laval nozzle.

Diagram 3 in Fig. 19 shows the LRVP impeller speed, regulated by the PID controller according to the required condenser pressure. The average LRVP impeller speed in the analysed period amounts to 1599.7 rpm. The bottom diagram 4 in Fig. 19 shows the power required by the LRVP for its operation, amounting to 26.99 kW on average during the analysed period. 6.3. Comparative analysis of SEPS and LRVP energy efficiency The SEPS and LRVP energy efficiency comparative analysis was made by comparing the results of the simulation models and investment costs. The average values of results of the SEPS and LRVP simulation models in the analysed period include: additional generated power in the case of expansion of steam used for the operation of the SEPS in the steam turbine (Pgen), power consumed for the LRVP operation (PLRVPS), mass flow of steam used for the SEPS operation (qm0), mass flow of the pumped non-condensable gas from the turbine condenser (qmout-non), turbine condenser pressure (pc), consumed or additionally generated energy at an

P annual level in case of 6000-h yearly operation ( Eelectric) and cost of investment of an individual pumping system (Ic). The investment costs include the cost of purchase, installation, construction works and design of an individual vacuum system. Fig. 4 shows the results of energy efficiency comparative analysis. Table 4 shows that SEPS is less energy efficient. If the average amount of steam used for the operation of the SEPS expanded in a steam turbine, the steam turbine would generate 751,800 kW h more electricity annually in the analysed period. The LRVP, on the other hand, consumes for its operation on average 161,400 kW h of electricity annually. This means that LRVP consumes 4.66 times less electricity annually than additionally generated by a steam turbine in case of expansion of the steam in the steam turbine required for the SEPS operation. The fact that the SEPS consumes more energy was also established by means of a comparative analysis of losses of specific energy capable of work in specific components of the SEPS or LRVP (Figs. 1 and 2). The loss of specific energy capable of work in a specific component of the SEPS or LRVP was calculated using the equation [16]:

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Fig. 16. Result of the SEPS simulation model referring to the ejector motive steam mass flow.

Fig. 17. Results of the SEPS simulation model referring to the pumped non-condensable gas and turbine condenser pressure.

Fig. 18. Results of the SEPS simulation model of the acquired steam turbine power in the case of expansion of steam used for the SEPS operation in the steam turbine.

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Fig. 19. Results of the LRVP simulation model referring to the operating characteristics of the LRVP.

Table 4 Energy efficiency SEPS and LRVP comparative analysis (6000 h per year). System

P_ gen (kW)

P_ LRVP (kW)

_ con (kg/s) m

_ out-non (kg/s) m

pc (Mpa)

P Eelectric (kWh vs year)

Ic (Eur)

SEPS LRVP

125.3 /

/ 26.9

0.2206 /

0.0347 0.0349

0.0101 0.0089

751,800 161,400

54,580 129,620

Fig. 20. Losses of energy capable of work in specific components of the SEPS and LRVP from Figs. 1 and 2

eloss;p ¼ ðhin;p  hout;p Þ  T a  ðsin;p  sout;p Þ

ð32Þ

where eloss,p is loss of specific energy capable of work in a specific component, hin,p is specific enthalpy of a gas mixture to a specific

part, hout,p is specific enthalpy of a gas mixture from a specific part, Ta is ambient temperature, sin,p is specific entropy of a gas mixture to a specific part and sout,p is specific entropy of a gas mixture from a specific part of the SEPS or LRVP. The amount of specific energy

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Fig. 21. Annual consumption of coal for the SEPS motive steam production.

capable of work, entering the LRVP system, is calculated using the equation:

ein;LRVP ¼

PLRVP qmLRVP

ð33Þ

where ein,LRVP is the amount of specific energy capable of work in the LRVP system and qmLRVP is the mass flow rate of the pumped gas mixture. Fig. 20 shows the results of the losses of energy capable of work in specific components of the SEPS and LRVP.

Fig. 20 shows that the SEPS uses 1854 kJ/kg for its operation and the LRVP only 423 kJ/kg of specific energy capable of work. The SEPS consumes as much as 4.4 times more specific energy capable of work for its operation than the LRVP. To pump gases from the turbine condenser, both systems consume almost the same amount of specific energy capable of work. The SEPS consumes a total amount of 206 kJ/kg to pump the gases, and the LRVP 248 kJ/kg of specific energy capable of work. The highest losses of specific energy capable of work of the SEPS occur in the constant section, followed by losses in the mixing section and those in the diffuser. The above losses cannot be avoided; nevertheless, they can be reduced by reshaping the geometrical form of the SEPS and choosing the Laval nozzle of appropriate dimensions. The actual energy efficiency comparative analysis of the systems is expressed in the amount of coal saved for the production of steam in the boiler for the SEPS drive. Fig. 21 shows the result of the annual consumption of coal of the simulation model in the boiler for the generation of steam consumed by the SEPS at various heating values of coal and dynamic hourly annual operation. The average consumption of steam for the SEPS operation, amounting to 0.2206 kg/s, was taken into consideration in the calculations, whereby steam pressure was 0.907 MPa and its temperature 590.59 K, whereas the boiler efficiency was 90%. It is evident from Fig. 21 that the annual consumption of coal for steam production in a boiler used by the SEPS for operation depends on the duration of the SEPS operation and heating value of coal. If the SEPS operates 6 000 h annually, the coal heating value is 18 GJ/ton and boiler efficiency 90%, the annual consumption of coal for the generation of steam used for the SEPS drive is

Fig. 22. SEPS and LRVP operating costs at 18 GJ/ton coal calorific value.

D. Strušnik et al. / Applied Energy 173 (2016) 386–405

403

Fig. 23. Economic viability of investment at coal calorific values of 15 GJ/ton and 18 GJ/ton.

Fig. 24. Economic viability of investment at coal calorific value of 21 GJ/ton.

792.2 tons. The SEPS and LRVP operating costs were calculated for the fifteen-year period and the costs include cost of investment, cost of energy consumption for system operation and cost of maintenance using the linear increments method. As regards the costs of energy consumption for the SEPS operation, the amount of coal burned in the boiler generating the ejector motive steam was taken into consideration. The costs of consumption of energy for the LRVP operation referred to the quantity and price of electricity consumed by the system for its operation. The costs of maintenance amount to 5% of the investment costs according to the linear

increments method. Fig. 22 shows the SEPS and LRVP operating costs taking account of different prices of fuels, various annual operating times and the heating value of coal of 18 GJ/ton. It is evident from Fig. 22 that operating costs depend on operating time and electricity price as regards the LRVP and on coal price as regards the SEPS. The SEPS’s overall operating costs amount to 43,370 euros during its 15-year period of operation of 2000 h/year, at the heating value of coal of 18 GJ/ton and the coal price of EUR 90/ton. The operating costs of the LRVP, however, amount to only 23,970 euros with the same operating hours per year and

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electricity price of EUR 90/MWh. In this case, the cost savings would total as much as 201,780 euro in the LRVP’s 15-year operating period. The SEPS’s overall operating costs during a 15-year operating cycle of 8000 h/year, at the heating value of coal of 18 GJ/ton and the coal price of EUR 90/ton amount to as much as 1,493,900 euro. The operating cost of the LRVP, on the other hand, with the same annual hourly operation and the electricity price of EUR 90/MWh is only 449,860 euro. In this case, the cost savings during a 15-year operating period of the LRVP would total as much as 1,044,040 euro. The economic efficiency analysis of the investment was made by calculating its discounted cash flow. The discounted cash flow of the investment is the difference between the operating costs of the SEPS and LRVP from Fig. 22 reduced by the discount rate. Some other authors used a similar approach to the discount cash flow calculation [55–58]. A discount rate of 7%, decreasing each year, was taken into account in the calculations. The discount rate is taken into consideration due to the inflationary impacts and other unforeseen operating costs. Figs. 23 and 24 show the economic efficiency of the investment at various operating hours per year and annual heating values of coal varying from 15 GJ/ton, 18 GJ/ton to 21 GJ/ton. Figs. 23 and 24 show the discounted cash flows at the 0.25–1 ratio between the coal and electricity prices. At the ratio of prices of 0.25, the coal price of EUR 140/ton was taken into account and electricity price of EUR 35/kWh, whereas at the price ratio of 1, the coal price taken into account was EUR 80/ton and electricity price EUR 80/kWh. The investment is economically viable when the discounted cash flow is positive or higher than the investment cost difference between the LRVP and SEPS. The charts on the l.h. side of Figs. 23 and 24 show the discounted cash flows during a 15-year period of operation, whereas those on the r.h. side, the zoom charts on the l.h. side, where the economic viability of investment is evident from the cross-sections of zero planes of the discounted cash flow. The economic viability of the investment depends on fuel prices, operating hours per year, depreciation, discount rate and heating value of coal burned in the boiler to produce steam used for the ejector drive. The assessment made from the discounted cash flows (charts on the r.h. side of Figs. 23 and 24) is that the investment in the LRVP is worthwhile as the payback period of the more expensive investment in the LRVP is approx. 2.5 years of operation. The comparative analyses of energy consumption, losses of specific energy capable of work and comparatives economic efficiency analysis of the investment by calculating its discounted cash flow at various operating hours per different coal calorific values vacuum pump system provide guidelines for more rational use of vacuum pump systems and decisive criteria for an investor to choose an appropriate vacuum system.

7. Conclusion This paper describes basic guidelines for the selection of an appropriate condenser vacuum pumps system of a steam turbine. The SEPS consumes 4.6 times more energy for an equivalent flow rate than the LRVP. The SEPS is characterised by high energy consumption, favourable price, reliability (no motive parts) and no maintenance. The LRVP is energy efficient and unfavourable in terms of price (purchase price, maintenance cost, etc.). Even though the installation costs of the LRVP are higher since for safety reasons two systems operating in parallel need to be installed (one in operation and the other in reserve) the investment in the LRVP is more viable in terms of energy efficiency given that its payback period is after no more than 2.5 years of operation. The advantages of the SEPS, however, are its more reliable operation, as the system

has no motive parts and requires almost no maintenance, contrary to the LRVP, where exposure to cavitation is high.

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