Impact of electricity price fluctuations on the operation of district heating systems: A case study of district heating in Göteborg, Sweden

Applied Energy 204 (2017) 16–30

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Impact of electricity price fluctuations on the operation of district heating systems: A case study of district heating in Göteborg, Sweden Dmytro Romanchenko ⇑, Mikael Odenberger, Lisa Göransson, Filip Johnsson Department of Space, Earth and Environment, Chalmers University of Technology, Göteborg 412 96, Sweden

h i g h l i g h t s
Techno-economic optimisation model is developed to study operation of DH systems.
Operation of the DH system is investigated under 5 future electricity price profiles.
Flexibility of heat pumps and CHP plants provides extra benefits to the DH system.
The value of CHP plants with variable power-to-heat ratio will increase in future.

a r t i c l e

i n f o

Article history: Received 26 February 2017 Received in revised form 20 June 2017 Accepted 28 June 2017

Keywords: District heating (DH) Combined heat and power (CHP) Heat pumps (HP) Modelling Optimisation Flexibility

a b s t r a c t This paper investigates the characteristics of interaction between district heating (DH) systems and the electricity system, induced by present and future price curves of the electricity system. A mixed integer linear programming unit commitment model has been developed with the objective of studying optimal operating strategies for DH systems. The model minimises the total operating cost of heat generation for a given DH system, which in this work is exemplified by the DH system of Göteborg, Sweden. The results should have important implications for operating strategies for DH systems as a response to future electricity price development. The results indicate significant changes in the operation of heat generation units in DH systems as a response to future electricity price profile with a, relative to today, high yearly average electricity price and more frequent high-electricity-price periods. The observed changes include a 20% decrease in heat generation from heat pumps (HP) and an increase of up to 25% in heat generation from combined heat and power (CHP) plants, owing to a switch in the merit order of these two technologies. We show that large fluctuations in the electricity price lead to an increased value being placed on CHP plants with variable power-to-heat ratio. The results indicate that with reoccurring high-electricity-price periods the value of sold electricity alone can become high enough to motivate investment in CHP plants, i.e. indicating that the generation and selling of heat from CHP plants may not be the core business in the future. Furthermore, there are additional opportunities for increased value of both CHP plants and HPs for time periods of less than 48 h, given that such short duration periods can be identified in a reasonable time in advance, i.e. dependent on, for instance, wind power forecasts. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction According to the International Energy Agency (IEA), around 46% of the total global energy demand in Year 2012 was from heating and cooling [1]. In Europe, heating and cooling constitute approximately 50% of the total final energy consumption [2]. According to the Energy Roadmap 2050 [3] the EU goal to decrease greenhouse gas emissions by 80% by 2050 compared to 1990 levels will have a ⇑ Corresponding author. E-mail address: [email protected] (D. Romanchenko). http://dx.doi.org/10.1016/j.apenergy.2017.06.092 0306-2619/Ó 2017 Elsevier Ltd. All rights reserved.

substantial influence on the energy system, and, obviously, on the energy use for heating and cooling. Currently, the major part of the European building stock is supplied with heat from fossil-fuel fired onsite boilers that are required to, at least, change fuel to comply with future goals. The share of district heating (DH) in heat supply to residential and service sector buildings in Europe is only 13% [4]. Despite the number of benefits that DH can provide to the energy system (e.g. high fuel conversion efficiencies, ability to convert variety of fuels, high level of operational flexibility) its widespread development is not included in the energy system development scenarios highlighted in the Energy Roadmap 2050. Yet, there

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are studies that claim that DH has an important role to play in a future non-fossil sustainable energy system. Connolly et al. [4] claims that with DH added to the European energy system the EU goals in decreasing primary energy supply and reducing carbon dioxide emissions can be achieved at lower cost (heating and cooling costs can be reduced by 15%) as compared to the reference scenarios outlined in the Energy Roadmap 2050. This is further strengthened by the study of Hansen et al. [5], who claim that DH and heat pumps (HP) are the least cost alternatives in Year 2050 in terms of cost of heat. The studies of Lund et al. [6] and Persson et al. [7] suggest that DH and district cooling (DC) should be recognised as important energy system components, needed to reduce primary energy consumption and increase energy efficiency and integration of renewable energy sources (RES). Scandinavian countries constitute a good base for case studies when investigating the future performance of DH systems, since DH has higher market share than the average value in Europe. In Sweden, which is used as a case study in this work, DH covers about 55% of the heat demand of all buildings and up to 92% of the heat demand of multi-family residential dwellings [8]. Swedish DH systems are characterised by a rather diverse mix of fuels and technologies used for heat generation, with local waste heat resources being typically harvested. In Year 2013, around 40% of the total DH heat generation was generated by combined heat and power (CHP) plants and around 8% was generated by HPs [9], using waste heat as a heating source. The utilisation of CHP plants and HPs in DH systems creates a strong linkage between the heat and electricity systems. While electricity prices affect the operational strategies of CHP plants and HPs in DH systems, DH systems have generally been operating with heat as the main product and electricity as a by-product that, at best, can offset some of the operating costs of the CHP plants. However, in the future energy system with large penetration levels of RES (nondispatchable), electricity generation within DH systems can be increasingly profitable. Moreover, HPs can benefit from low electricity price periods induced by, for example, diurnal price variations. Thus, there is a need to achieve a better understanding of how DH systems can respond to changes in the price of electricity, in terms of both price level and price variability, due to the increased level of variable RES (VRES) in the electricity system. To study operation of energy systems, including DH systems, unit commitment (UC) models are widely used. UC models provide the possibility to identify the optimal combination of fuels and energy generation units (along with their corresponding dispatches) that fulfils a required energy demand at each time-step over the modelled period, while complying with the objective of the optimisation, e.g. lowest cost of energy generation. A few UC techno-economic models, which are able to generate costoptimal commitment and dispatch of units in DH systems, have been developed. Wang et al. [10] and Carpaneto et al. [11] developed UC models to determine the optimal configurations and operating strategies of CHP based DH systems with solar thermal plants and thermal energy storage systems in Finland and Italy, respectively. Bachmaier et al. [12] used techno-economic optimisation tool to find the location, size and operation of thermal energy storage systems, connected to a DH system, with the aim to increase flexibility of CHP plants and provide balancing services to the electricity grid. A number of studies have developed techno-economic models to co-optimise supply of heat, electricity and, in some cases, cooling in district energy systems. In the studies of Mehleri et al. [13,14] a techno-economic model is developed to satisfy both heating and electricity demands at the level of a small neighbourhood. The modelling minimises yearly annualised investment and operating costs and defines optimal district energy system components and heating pipeline network. Chen et al. [15], Yang et al. [16] and Fang et al. [17] provided studies in which heat and

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electricity supplies are co-optimised with the focus to maximise the wind power integration rate within the district energy system using the flexibility provided by CHP plants and energy storage systems to balance electricity and heat generation. The studies of Ameri et al. [18] and Buoro et al. [19] applied optimisation models to district energy systems, which include solar fields and thermal energy storage systems, with the objective to co-optimise heating, electricity and cooling supplies to a residential and an industrial area, respectively. Some studies have developed multi-objective optimisation, i.e., simultaneous optimisation of e.g., costs and CO2 emissions, models to research district energy systems. Fazlollahi et al. [20] presented a multi-objective optimisation model with the aim to optimise size and operation of DH systems with thermal energy storage tanks. Morvaj et al. [21] developed a multi-objective optimisation model to study the effect of different shares of RES in the electricity grid on the optimal design and operation of distributed energy systems, including the design of a DH network. The study of Falke et al. [22] applied multi-objective modelling for the investment planning and operation of district energy systems and investigated the impact of different energysaving renovation measures in buildings on the model results. Using optimisation modelling to co-optimise heat and electricity generation within a district energy system can be beneficial for a specific local system, but will not provide enough insights on how DH systems interplay with the national electricity system and its possible different electricity price areas. This interplay with the national system, which in turn is linked to the surrounding countries (or price areas), will be increasingly important with rising share of electricity from VRES, resulting in increased volatility in electricity prices. Using a linear techno-economic optimisation model Åberg et al. [23] investigated the impact of different electricity price profiles, constructed to reflect Swedish price variations, on the operation of a DH system (exemplified by Uppsala, Sweden). Yet, the time resolution of the price profiles used in that study (four price levels throughout the year) will not be able to reflect price fluctuations induced by VRES, which typically require an hourly resolution to reflect aggregated wind and solar generation. The study of Hast et al. [24] applied the energyPRO software to identify economically optimal dimensioning of the heat storage in a DH system in Finland based on three future electricity price profiles with high shares of VRES. The modelling has an hourly time resolution. Yet, the optimisation span is limited to three weeks. Moreover, the study focuses on the role of potential investments, i.e., heat storage, heat pumps and solar collectors, on the operation of the DH system and does not evaluate flexibility potential of the heat generation technologies already available in the system, i.e. how the operation pattern of certain facilities can change due to forthcoming dynamics in the electricity price. There is a lack of studies in literature that investigate how changes in the surrounding electricity system can affect the operation of existing DH systems, and thus, there are few estimations on the possible flexibility1 offered by contemporary DH systems back to the electricity sector. The UC models developed in the above works use either linear programming (LP) or mixed integer linear programming (MILP) approach and each contain some – but not all – of the following unit specific constraints: minimum and maximum output level constraints, ramp-up and ramp-down limits, start-up and shut down characteristics, minimum up- and down-time constraints and constraints, regulating power-to-heat ratio of CHP plants

1 In this paper we refer to ‘‘flexibility” as an ability of a system/unit, here the DH system or a heat generation unit, to adapt in response to a steering signal. In this work the signal is the electricity price, which is given exogenously to the modelling in this work. The flexibility stems from the dynamics from changes in the state of operation as a direct response to the signal.

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(constraints are explained further in Appendix A). Further, all of the above-mentioned modelling approaches either have hourly resolution and cover a short time-span (from 1 day to 1 month) or they adopt the strategy of discretisation of an entire year into specific time-bands. In the present work, we develop and apply a UC model that covers a modelling period of up to 1 year, with a time-step resolution of 1 h. This enables investigation of the impacts from both short-term (hourly) and long-term (seasonal) variations in electricity prices, induced by VRES, on the operation of a chosen DH system. Thus, one of the novelties in this work is that it combines the application of a high time resolution with long term modelling. Moreover, the UC model in the present work includes the whole set of the unit-specific constraints listed above, as well as the possibility to operate CHP plants with a variable power-to-heat ratio. With respect to estimating the value of flexibility and the DH systems’ ability to harmonise fluctuations in the electricity supply, the inclusion of all these modelling features is necessary, and thus, a novelty of this work. Finally, we analyse the effect of future fluctuating electricity prices on the operation of a DH system at a time resolution sufficiently high to evaluate the DH systems’ flexibility, which in the future is believed to gain in value as the employment levels of VRES increase. In summary, using the DH system with integrated CHP plants and HPs in a large city in Sweden as a case study, this work addresses the following research questions:
In what way and to what extent will the operating strategy of a DH system change in response to changes in electricity price profiles?
What benefits can the presently unused flexibility of heat generation units bring to a DH system in the future with fluctuating electricity prices? The paper is organised as follows. Section 2 outlines the modelling method and the main characteristics of the DH system investigated, Section 3 presents and discusses the results obtained from the modelling, and Section 4 summarises the conclusions from the study. 2. Methodology To evaluate changes in the operating strategies of the DH system of Göteborg that are caused by varying electricity prices, six scenarios are investigated using the UC optimisation model. The scenarios are defined by different electricity price profiles, derived from the other modelling work, which are influenced by an increased wind power penetration level and, in one scenario, the potential phasing out of nuclear power plants from the Swedish national electricity system. 2.1. The model The optimisation model developed in this work generates a cost-optimal UC and heat generation dispatch of units available in a chosen DH system. The model accounts for specific unit parameters, such as the minimum and maximum heat and electricity output constraints, ramp-up and ramp-down limits, minimum up- and down-time constraints, and start-up and shut-down characteristics in terms of time and cost. Some of these parameters are given by discontinuous relationships, thereby requiring a MILP approach. In the model, the reduction in efficiency that occurs when operating a unit at part load is omitted. The model is deterministic, i.e., the hourly heat load, electricity prices, and the technical and economical characteristics of all units available in a DH system are assumed to be known prior to the optimisation and are exogenously provided to the model. The mathematical

formulation and detailed explanation of the developed computer model are presented in Appendix A. The objective function value and, subsequently, the target variable of the model represents the total system operating cost, i.e., the total yearly operating cost for heat and electricity generation, while accounting for the profits generated from sold electricity. Since the model has perfect foresight and considers the system operating cost, its output is to be used for the analysis of the operating strategies of a DH system under the different scenarios, rather than for real-life operational planning. While the model is applicable to any DH system, it does not include the possibility to import and/or export heat to other DH systems. Although most DH systems are limited to a specific city, import and export heat flows might be of greater interest in the future if smaller DH networks from neighbouring municipalities will be connected to the DH system of a larger city. The time-steps in the model are discrete, and the length of a time-step (here, at hourly resolution) and the duration of a modelling period (total length of all timesteps, here up to a year) are inputs. The model is developed using the high-level modelling language GAMS [25]. The model defines two groups of heat generation technologies: (i) units that generate only heat, such as heat-only boilers (HOB), HPs, and waste heat utilisation technologies; and (ii) CHP units. The output from any unit in the first group is characterised by a single variable that describes output, which is the heat generation level. The operation of CHP plants is characterised by levels of both heat and electricity (power) generation. Theoretically, CHP plants can be operated with some flexibility regarding the power-toheat ratio. The theoretical feasibility region of operation, O, of a CHP plant is schematically shown in Fig. 1. The operation of a CHP plant along the line formed by Points 2–3 in Fig. 1 is characterised by a constant power-to-heat ratio and is called the ‘backpressure mode’. In this mode, steam is first led via the turbine for electricity generation and then through a heat exchanger, where the DH water is heated. If a fraction or all of the steam is expanded further and led through a condenser, instead of into the DH heat exchanger, then the CHP plant is operated in the socalled ‘extraction mode’. In this case, higher electricity generation is achieved, albeit at the expense of decreased heat generation and lowered total plant efficiency (from Point 2 to Point 1 in Fig. 1). The line formed by Points 3–4 in Fig. 1 arises from the practical limitations imposed on the minimum electricity output. By varying the ratio of steam extraction and amount of fuel fed, the operational mode of a CHP plant can be theoretically achieved within the area that lies inside the lines connecting Points 1–4 in Fig. 1. In reality, some CHP plants are run exclusively with a constant power-to-heat ratio, due to either construction specifications or operational practice. The model applied in this work allows for the operation of CHP plants with both constant and variable power-to-heat ratios, and the representative DH system in this study includes both types of ratios.

2.2. The DH system of Göteborg The model is applied and validated using the DH system of Göteborg, Sweden, as an example. This DH system can be seen as principally representative of many DH systems, since the generation portfolio mainly comprises a mix of CHP plants, HPs and HOBs. Thus, the size of the DH system, the diverse mix of heat generation technologies, and the availability of statistical data regarding the system’s real-life operation were the main reasons for choosing the DH system of Göteborg as a case study. This work assumes that the existing fleet of plants is unchanged, and the focus is on investigating the flexibility of operation of these units with respect to their electricity price sensitivity. In reality, in a future system a

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Fig. 1. The theoretical feasibility region of a CHP plant operation with different levels of electricity, p, and heat, q, outputs.

certain proportion of the generation units may have been replaced with new and more-flexible units. The DH system of Göteborg is the second largest DH system in Sweden, having a piping network with total length of around 1000 km. The DH network covers more than 90% of all multifamily dwellings and 9000 single-family houses in the city and is connected to two smaller DH networks in neighbouring municipalities. In Year 2001, total yearly heat deliveries peaked at around 4200 GWh [26]. Thereafter, there was a gradual reduction in heat deliveries, reaching 3300 GWh in Year 2015 [27], mainly due to energy efficiency measures in the building stock. Assumptions regarding the technical and economical characteristics of the heat-only and CHP units present in the DH system of Göteborg are listed in Tables 1 and 2, respectively. Three suppliers of industrial waste heat are present in the investigated DH system, which in the modelling are considered as ‘‘must-run” units (for contractual reasons). Since the modelling of these suppliers is not explicit and is limited to heat deliveries

into the DH system, hereinafter they are aggregated and referred to as ‘waste heat technologies’. The HPs in the DH system, which are fed with electricity from the grid and use heat from the municipal sewage sludge plant, are, due to technical similarities, grouped into the two modelled units: RYA HPs 1–2 and RYA HPs 3–4. Due to its composition (three gas turbines, heat recovery steam generator with supplementary firing and a steam turbine), the gas-fired RYA CHP plant can run in different operational modes. Therefore, it is modelled such that its heat and electricity outputs create the feasibility region of operation, O (similar to the one shown in Fig. 1). However, due to technical features, the electricity generation from the RYA CHP plant cannot exceed 245 MW. This means that the upper line of the feasibility region of the RYA CHP (from Point 2 to Point 1 in Fig. 1) is strictly horizontal, limiting the electricity generation to 245 MW. The efficiency and COP values in Table 1 are derived from real-life operational records for Year 2014 [28]. The assumed data regarding the economic parameters (Table 2) are representative of Year 2012. The fuel prices are taken from the statistics published by the Swedish Energy Agency [29,30], except for the prices of natural gas and bio oil, which are assumed based on contractual information. All the CHP plants are connected to the national electricity grid and, thus, all the generated electricity is assumed to be sold on the wholesale electricity market. Furthermore, all the electricity generated in CHP plants is part of the Swedish-Norwegian Electricity Certificate Scheme, which supports renewable electricity generation. Hence, all sold or purchased electricity must meet the quota obligation. In the modelling, this quota is embodied by the total DH system certificate balance, i.e., the purchasing and selling of electricity certificates is calculated based on the total electricity generation from biofuel-fired (receive certificates) and fossil fuel-fired (must-buy certificates) CHP plants. Any electricity consumed by the HPs must also comply with the quota obligation. This is also included in the modelling, albeit separately from the CHP plants. In Year 2012, the quota obligation in Sweden was 18% [31] (applied in all the investigated scenarios).

Table 1 Technical parameters of the heat-only and combined heat and power generation units available in the DH system of Göteborg. The efficiencies of the Sävenäs CHP and the Sävenäs HOB1 units have values higher than ‘‘1” because the calculations are performed based on the lower heating value of fuel (a flue gas condensation technology is used in these units). Unit name

Unit type

Fuel type

Total efficiency /COP

Max/min output, MWh/h

Ramp-up/ramp-down limits, MWh/h

Minimum up-time/ down-time, h

Heat generation capacity ST1 – Preem – Renova – Sävenäs CHP CHP RYA CHP CHP Högsbo CHP CHP RYA HPs 1–2 HP RYA HPs 3–4 HP RYA HOB1 HOB RYA HOB2 HOB Sävenäs HOB1 HOB Sävenäs HOB2 HOB Rosenlund HOB4 HOB Angered HOB1 HOB Angered HOB2 HOB Angered HOB3 HOB Rosenlund HOB1 HOB Rosenlund HOB2 HOB Rosenlund HOB3 HOB Tunnered HOB HOB

Waste heat Waste heat Waste heat Wood chips Natural gas Natural gas Electricity Electricity Wood pellets Wood pellets Natural gas Natural gas Natural gas Bio oil Bio oil Bio oil Fuel oil Fuel oil Fuel oil Fuel oil

1 1 1 1.11 0.91 0.79 3.60 3.15 0.92 0.92 1.01 0.90 0.97 0.90 0.90 0.90 0.98 0.98 0.98 0.89

85/35 60/15 185 (130)/0 110/25 295/50 14/3 60/0 100/0 50/25 50/25 90/20 60/20 140/30 35/15 35/15 35/15 140/20 140/20 140/20 20/8

25 7.5 92.5 42.5 245 11 60 100 25 25 70 40 110 20 20 20 120 120 120 12

8760 8760 8760 24 (down-time) – – – – 6 (up-time) 6 (up-time) – – – – – – – – – –

Electricity generation capacity Sävenäs CHP CHP RYA CHP CHP Högsbo CHP CHP

Wood chips Natural gas Natural gas

– – –

13/3 245/41.5 13/2.8

5 203.5 10

– – –

Power-to-heat ratio

0.12 Variable 0.93

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Table 2 Assumed costs and taxes for the heat-only and combined heat and power generation units available in the DH system of Göteborg. Unit name

Fuel cost, SEK/MWh [29,30]

Variable O&M cost, SEK/MWh [33]

Energy tax, SEK/MWh [32]

Carbon dioxide tax, SEK/tCO2 [32]

Electricity certificate, SEK/MWh [31]

Start-up cost, SEK

ST1 Preem Renova Sävenäs CHP RYA CHP Högsbo CHP RYA HPs 1–2 RYA HPs 3–4 RYA HOB1 RYA HOB2 Sävenäs HOB1 Sävenäs HOB2 Rosenlund HOB4 Angered HOB1 Angered HOB2 Angered HOB3 Rosenlund HOB1 Rosenlund HOB2 Rosenlund HOB3 Tunnered HOB

– – – 209 230 230 Price profile Price profile 292 292 230 230 230 600 600 600 542 542 542 542

10 10 10 87 22 22 20 20 28 28 15 15 15 15 15 15 15 15 15 15

– – – – 25 25 290 290 – – 82 82 82 – – – 82 82 82 82

– – – – – – – – – – 950 950 950 – – – 950 950 950 950

– – – 168 – – 168 168 – – – – – – – – – – – –

– – – 200,000 400,000 – – – – – – – – – – – – – – –

only. Nevertheless, the prices reflect the integrated electricity market in Europe, including the effect from import and export from neighbouring regions. The ELIN model provides the overall development of the European (EU27 + Switzerland and Norway) electricity system from Year 2010 to Year 2050, taking into consideration both the commissioning and decommissioning of power generation units. The modelling is divided into 50 price areas, defined by major European transmission bottlenecks, and considers the import and export electricity flows between these areas. The ELIN model then puts forward the ELIN scenario results to the EPOD model, where the power plant structure from certain years (in this study, Years 2012 and 2030 are extracted and used) can be analysed at higher time-resolution (dispatch model). Thus, different scenario assumptions regarding, for example, wind power penetration levels can be studied. The main characteristics of the scenarios investigated in this work are listed in Table 3. The scenarios include different penetration levels of wind power, as well as one scenario in which it is assumed that the Swedish nuclear power fleet is phased out completely (by Year 2030) and the Swedish electricity system, as a result, mainly consists of hydro and wind power. This work applies the price profiles for the price area of the south of Sweden, corresponding to the real system price area of Stockholm (and Göteborg), as derived from the EPOD model. The electricity price profiles are obtained from the ELIN-EPOD modelling in 3-h time resolution. In order to be used in the model developed for this work the price profiles are converted to hourly resolution by assigning the same price for every group of 3 h. Appendix B gives the hourly electricity price profiles used in the scenarios investigated. It should be noted that the electricity prices from the ELIN-EPOD modelling, which in this work are used as a proxy for future electricity prices, reflect marginal costs of electricity

In Sweden, the usage of fossil fuels is levied for energy and carbon dioxide taxes. The energy tax is applied in full to fossil fuel-fired HOBs, whereas heat generation from CHP plants is subject to 30% of the tax (as included in the model). The carbon tax in the modelling is only applied to fossil-fired HOBs, since from Year 2013 both electricity and heat generation from CHP plants within the EU ETS scheme are 100%-exempt from the carbon dioxide tax [32]. The start-up cost for the Sävenäs CHP plant is linked to the operational specifics of wood chip-fired CHP plants. Natural gas or oil is used in this type of CHP plants, to achieve the required temperature inside of the boiler before the wood chips can be used. The start-up cost of the RYA CHP plant, as applied in the modelling, is the sum of the individual start-up costs of its three constituent gas turbines. Start-up costs for the waste heat technologies are not applied, since they must run every time-step in the modelling period. No start-up costs are applied for HPs and HOBs due to their low start-up times (less than 1 h) and the fact that the start-up costs are in the range of the hourly operating costs. 2.3. Scenarios The scenarios investigated are defined by the six different electricity price profiles. The profiles correspond to Year 2012 (reference year) and five different futures projected for Year 2030, assuming different penetration levels of wind and nuclear power in the national electricity system of Sweden. The electricity price profiles are generated by the ELIN-EPOD modelling package [34], i.e. they are obtained from modelling not within the present study, and thus taken as input to the present work. The ELIN-EPOD model covers the EU-27 countries plus Norway and Switzerland, yet, here we apply the price profiles for Sweden

Table 3 Six scenarios for development of the Swedish electricity system, which correspond to different wind power penetration levels and nuclear power availability and, respectively, different electricity price levels and profiles, obtained from the ELIN-EPOD modelling, as applied in this study. Note that the wind power penetration level is presented in energy terms (TWh), whereas the nuclear power penetration is in capacity units (GW). Scenario name

Year

Wind power penetration level, TWh (%)

Nuclear power penetration level, GW [35]

Average electricity price, SEK/MWh

5% wind 10% wind 20% wind 35% wind 50% wind 50% wind no NUC

2012 2030 2030 2030 2030 2030

7 TWh  (5%) 16 TWh  (10%) 25 TWh  (20%) 50 TWh  (35%) 70 TWh  (50%) 70 TWh  (50%)

9.5 9.5 9.5 9.5 9.5 0

243 381 351 253 229 503

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Electricity price [SEK/MWh]

5% wind

10

10

10

10% wind

20% wind

35% wind

50% wind

50% wind no NUC

3

2

1

0

1000

2000

3000

4000

5000

6000

7000

8000

Time [h] Fig. 2. The electricity price duration curves, as obtained from the ELIN-EPOD modelling for the price area in the south of Sweden (including Göteborg), for the reference Year 2012 and for Year 2030 with varying penetration levels of wind power and availability of nuclear power in the Swedish national electricity system. Note the logarithmic scale of the y-axis.

generation and not the price formation on the market (for more details, see [36]). Fig. 2 shows the electricity price duration curves, as obtained from the ELIN-EPOD modelling. Despite a significant capacity of Nordic hydro power, which can be used to moderate the fluctuations created by VRES, with an increased penetration level of wind power in the Swedish electricity system, both the high- and lowelectricity-price periods can be expected to increase in number and duration. However, the duration of the low-electricity-price periods is expected to be longer than that of the high-electricityprice periods. The increasing number of high-electricity-price periods is a combined effect of increased part-load operation and more frequent starts and stops of power plants, limitations in import/export of electricity to surrounding regions (congestion in the grid) and the need for running costly, peaking electricity generation units during the periods of low electricity output from the wind power. The increase in low-electricity-price periods is obviously a result of increased amount of wind generation (in the ‘‘10% wind” – ‘‘50% wind” scenarios the generation mix is constant but the energy from wind is increasing), which has very low running cost. In the scenario where all the Swedish nuclear power fleet is assumed to be decommissioned (substituted mainly by wind power), the number of hours with high electricity prices increases significantly. The price level of the high-electricity-price periods is determined in the EPOD modelling by the cycling costs of the marginal thermal generation in the electricity system. The number of low-electricity-price periods in the scenario with no nuclear power is lower than in the scenario with nuclear being still available (‘‘50% wind no NUC” and ‘‘50% wind” scenarios respectively), while the wind power penetration level is constant. This is an effect of a surplus capacity in the system, which is the case when adding the wind energy while keeping the nuclear capacity fixed. In addition, it should be kept in mind that the total installed European (including Swedish) electricity generation capacity differs between the reference Year 2012 scenario and the remainder of the scenarios considering Year 2030. Again, due to the current capacity surplus average electricity price in Year 2012 is lower than in Year 2030. The heat demand curve applied in this work is taken from the records of actual heat generation in the DH system of Göteborg

in Year 2012. Thus, the actual heat consumption was lower due to distribution losses. Moreover, it should also be noted that the actual demand profile could be slightly different, as the DH network can buffer some heat energy, thereby smoothing heat demand fluctuations. The heat demand is assumed to be the same for scenarios that consider Year 2030 as for the scenario for Year 2012. This is to evaluate only the influence of future electricity prices on the DH system operating strategies and operating cost while keeping other parameters constant. Heat exchange with the neighbouring municipalities is not included in the modelling, i.e., the above-mentioned possibilities for import/export of heat to the two smaller DH networks in neighbouring municipalities is not included in the model. The UC model developed within this work was validated by comparing the model results to the data records for hourly heat generation from each heat generation facility in the DH system of Göteborg from Year 2012 (the influence of export/import heat flows to neighbouring DH systems was taken in the account). For the model validation, the actual historical wholesale electricity prices from the Scandinavian wholesale electricity market Nordpool from Year 2012 were used as input to the model. 3. Results and discussion 3.1. Model validation In Year 2012, the total heat generation in the DH system of Göteborg was 4125 GWh, whereas the result from the optimisation is 20 GWh higher, i.e., a difference of less than 0.5%. This difference can be explained by the fact that the export/import possibilities with neighbouring municipalities are not included in the model. The individual generation patterns (the variations over the year) of the modelled generation units agree well with the corresponding operational data registered in Year 2012. However, some differences are seen for the CHP units and HPs due to their dependencies on the electricity price and the fact that the model has perfect foresight, which is not the case in reality. Differences between the modelled and the real-life data (Year 2012) are also evident when comparing the supplies of waste heat; while the real-life records indicate some fluctuations, in the modelling, the waste heat technologies are assumed to run at steady-state (except for during

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the summer, when the waste heat technologies are on the margin and meet fluctuating demand, which can result in the spill of heat when supply is higher than demand). Furthermore, there are other factors that contribute to the observed differences between the modelling and real-life records. For example, the limited forecast in reality for the heat demand and electricity prices, availability of biomass, and uneven fuel quality or unpredictable start-ups and shut-downs due to unplanned maintenance or repairs. Despite these differences between the modelled and real-life generation data for the CHP plants and HPs, we consider that the modelled results mirror well the real-life operation of the DH system of Göteborg. 3.2. New operational strategies

Heat generation [MWh/h]

Fig. 3, a and b shows the cost-optimal dispatch and the corresponding merit order for the heat generation technologies in the DH system of Göteborg for two winter weeks in the ‘‘5% wind” scenario in reference Year 2012 and in the ‘‘50% wind no NUC” scenario in Year 2030, respectively. The electricity price profile with a high number of high-electricity-price periods changes the operational strategies of the electricity price-sensitive technologies, i.e.,

HPs and CHP plants, followed by the shifting of their positions in the merit order. The decrease in heat generation from HPs during the hours with high electricity prices is observed already in the reference scenario in Year 2012 (Fig. 3a). However, for Year 2030, when the electricity price fluctuates to a greater extent, frequent changes in the outputs from HPs and CHP plants are seen. During the high-electricity-price periods HPs stop operation and CHP plants maximise heat generation. Such frequent shifts in the merit order create new challenges for the operation of DH systems that include HPs and CHP plants. However, it should be noted that the change in the merit order does not only reflect the electricity price but also the heat demand, the start-up and shut-down characteristics, and the minimum up-/down-time constraints of the units. Furthermore, the results indicate that the occurrence of highprice periods can lead to the curtailment of nearly zero-cost heat generation technologies in favour of CHP plants. The results of the modelling show that high-electricity-price periods during the summer season, being more common in the scenarios with higher wind power penetration levels, can lead to the reduced heat output from waste heat technologies with respective increase in generation from CHP plants. This, in turn, can lead to a heat generation

Heat generation [MWh/h]

22

Fig. 3. The cost-optimal hourly dispatch of the heat generation technologies in the DH system of Göteborg for the period of two winter weeks for: (a) the ‘‘5% wind” scenario in Year 2012; and (b) the ‘‘50% wind no NUC” scenario in Year 2030. The heat generation duration curves for: (c) the Sävenäs CHP plant; and (d) the RYA HPs 1–2, as obtained from the modelling for Year 2030 (compared to reference Year 2012) in the six scenarios investigated (cf. Table 3). Note that plots (c) and (d) only show the time-span between Hours 3000 and 6000 (during the time-spans from Hour 1 to Hour 3000 and from Hour 6000 to Hour 8760, the lines on the plots, representing the scenarios investigated, follow the same path and overlap).

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high-electricity-price periods on the merit order of HPs and CHP plants should hold for other DH systems that include those technologies and are subject to fluctuating electricity prices. 3.3. Variable power-to-heat ratio In this section, we focus on the value of flexibility in terms of variable power-to-heat ratio of CHP plants, here exemplified by the results from the RYA CHP plant, i.e., opportunities for increased interplay between the electricity and DH heating systems. Fig. 4 shows the total yearly heat and electricity generation and the total number of operational hours of the RYA CHP plant for all the scenarios investigated (Fig. 4a), together with the operational modes in the ‘‘5% wind” scenario (Fig. 4b), in terms of electricity and heat outputs. The results indicate that in a future with more fluctuating electricity prices (compared to today’s price fluctuations), CHP plants with variable power-to-heat ratio can benefit from operating in an ‘‘electricity price-following” mode, in which electricity generation is prioritised over heat during most of the operational time. This is due to the high value of electricity generation during the high-electricity-price periods. The greatest effect of the CHP plant operating in an ‘‘electricity price-following” mode is observed in the ‘‘50% wind no NUC” scenario, for which there is a substantial increase in both the average electricity price level and the number of high-electricity-price periods. In this scenario, the number of hours when the CHP plant prioritises electricity generation over heat generation and operates with the maximum possible electricity output (with electricity generation along the horizontal line in Fig. 4b) is double the number of hours during which the heat output is maximised. The heat output from the CHP plant in this scenario increases by approximately 25%, whereas the electricity output is doubled compared to the other scenarios investigated. The number of total operational hours and the share of electricity generated compared to the heat output from the CHP plant also increases in the ‘‘20 wind” – ‘‘50% wind” scenarios (cf. Fig. 4a), even though the average electricity price is decreasing. This is, again, due to higher number of high-electricity-price periods. An additional model run was performed under the assumption that all three CHP plants available in the investigated DH system have the possibility to vary their power-to-heat ratios (i.e., not only the RYA CHP plant). Under this assumption, the operational mode

Electricity generation [MWh/h]

Total yearly output [GWh]

surplus. The prioritised use of CHP plants is explained by the fact that the profit generated from the electricity sales during the high-electricity-price periods is sufficiently high to motivate using CHP plants merely for electricity generation. Yet, it should be noted that at the same time the generation of heat (both from waste heat technologies and CHP units) exceeds the heat demand. The excess generation of heat is only true if there is a technical possibility of heat spillage at zero price, which in reality is the case for the investigated DH system. The possibility to spill extra heat and prioritise operation of CHP plants can benefit the power system by generating electricity during the high-electricity-price periods, i.e. periods of low VRES generation. The heat generation duration curves of the CHP plant with constant power-to-heat ratio and the two HPs lumped together, as obtained from the modelling, are shown in Fig. 3, c and d, respectively. The results indicate that the heat outputs from the two technologies depend on both the average electricity price level and the electricity price profile. Moreover, high-electricity-price periods noticeably influence the heat generation, whereas low-electricityprice periods have little effect. As expected, in the ‘‘50% wind no NUC” scenario, which has the highest average electricity price level and highest number of high-electricity-price periods, the heat output from the CHP plant is higher than in all the other investigated scenarios. Comparing the reference ‘‘5% wind” scenario with the ‘‘50% wind” scenario, which have similar average electricity prices (cf. Table 3) but with the latter having more both low- and highelectricity-price periods (cf. Fig. 2), shows that the heat generation from the CHP plant is increased in the ‘‘50% wind” scenario (cf. Fig. 3c). An increased number of low-electricity-price periods has little effect on the output from the CHP plant, since already today CHP plants do not run during low-electricity-price periods (the capacity of waste heat technologies and HPs is sufficient to cover basic heating needs, such as the supply of hot tap-water in summer time). This indicates that in a future with increased frequency of high-electricity-price periods, the heat generation by CHP plants will increase. Similarly, HPs, which act as base-load units already in the reference ‘‘5% wind” scenario, experience only a moderate increase in the heat output in the scenarios that have an increased number of low-electricity-price hours. However, the ‘‘50% wind no NUC” scenario, which has a larger proportion of hours with high electricity prices, results in an approximately 20% lower heat output from HPs. Those effects of low- and

Heat generation [MWh/h] Fig. 4. The relationship between heat generation and electricity generation in the RYA CHP plant: (a) the total yearly heat and electricity generation together with the total number of operational hours, as obtained from the modelling for reference Year 2012 and for the five different scenarios for Year 2030; and (b) the operational modes in the ‘‘5% wind” scenario, representing the heat generation and respective electricity generation levels (the corresponding distributions for the other scenarios give a similar pattern). All the operational modes are aligned along the lines, which limit the feasibility region. Therefore, to enhance readability, the operational modes are shown only for every 10th time-step (hour).

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of the biomass-fired CHP plant is affected the most. This is explained by the fact that the biomass-fired CHP plant receives an Electricity Certificate for each unit of generated electricity and thereby, reduces total operating cost. Applying the same price profile as was used in the ‘‘10% wind” scenario, it was found that the biomass-fired CHP plant would be operated with the maximum power-to-heat ratio (maximised electricity generation) during all the operational hours. However, applying the price profiles with the higher number of low-electricity-price periods causes the unit to run more in back-pressure mode (along the line connecting Points 2–3 in Fig. 1) and to prioritise heat generation over electricity generation. These results suggest that future CHP plants in DH systems, which have a high flexibility to adjust their output, will generate higher profits from electricity sales and deliver electricity to the electricity sector during periods of no VRES generation. It should also be noted that the model does not limit the operational modes of CHP plants simply to align along the edges of the feasibility region (as shown in Fig. 4b). The units can be operated at

5% wind

10% wind

any point within the feasibility region. The reason why the operational modes are aligned along the limiting lines is the cost minimisation function used in the model. This means that if the electricity price is sufficiently high, the model will always choose to maximise electricity generation and thereby, maximise the profit from electricity sales. This is under the condition that excess heat can be dumped at zero cost (as is assumed in the model). This is true for all the operational modes along the horizontal line in Fig. 4b). The picture might be different if the part-load operation of CHP plants was implemented in the model. 3.4. Operational flexibility Fig. 5 shows the number of start-ups for the heat generation units in the investigated DH system (Fig. 5a), as well as the number of occasions when the CHP plant with variable power-to-heat ratio (Fig. 5b) and the two HPs lumped together (Fig. 5c) are running continuously within different duration segments, as obtained from

20% wind

35% wind

50% wind

50% wind no NUC

Number of start-ups

200

160

120

80

40

0

Sävenäs CHP

a

RYA CHP

Högsbo CHP

RYA HPs 3-4

RYA HPs 1-2

RYA HOB1

RYA HOB2

Sävenäs HOB1

Sävenäs Rosenlund HOB2 HOB4

Heat generation units 70 12

Number of occasions

Number of occasions

60 10

8 6 4 2

40 30 20 10

0 5

b

50

0-

h

0

1 5-

h 1

2 0-

0

h 2

5 0-

0

h 50

0 -1

0

h 1

00

0 20

h 2

Duration segments RYA CHP

00

0 -5

0

h >

0 50

0

h

5

c

0-

h

10

5-

h 10

20

h 20

50

h 50

10

0

h 10

2 0-

00

h 20

5 0-

00

h

00

h

>5

Duration segments RYA HPs 1-2

Fig. 5. The numbers of: (a) start-ups for the heat generation units in the DH system of Göteborg; and (b) occasions when the RYA CHP plant and (c) the RYA HPs 1–2 were operated continuously within different duration segments, as obtained from the modelling for Year 2030 (compared to reference Year 2012) in the six scenarios investigated (cf. Table 3).

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D. Romanchenko et al. / Applied Energy 204 (2017) 16–30

the modelling of the six investigated scenarios. The results indicate that electricity price profiles with a high level of volatility, i.e., with high levels of wind power, yield more frequent utilisation of CHP plants with variable power-to-heat ratio (exemplified by the RYA CHP plant in Fig. 5, a and b), as compared to the scenarios with less-fluctuating prices. The number of start-ups of the CHP plant with variable power-to-heat ratio increases significantly in the scenarios which correspond to wind power penetration levels of 35% and higher. This is due to the growth in the number of highelectricity-price periods, which are sufficient to cover a significant start-up cost. Note that the periods of high electricity prices can be shorter than 24 h and still justify start-up and short-term operation of the CHP plant (cf. Fig. 5b). From a scheduling point of view, this should not be too risky, since – in a real-world case – both wind power and electricity price prognoses should be relatively reliable in that time perspective. It should also be noted that in the ‘‘50% wind no NUC” scenario, which has longer periods of high electricity prices, the CHP plant with variable power-to-heat ratio also starts to run for longer periods of time (up to 2 days). The results also show that the number of start-ups of the biomassfired CHP plant does not vary with more-fluctuating electricity prices, which is due to the fact that it is a base-load unit and has a low and non-variable power-to-heat ratio (cf. Fig. 5a). Six additional model runs were performed with the same input data as for the six default scenarios, except that the start-up cost of the CHP plant with variable power-to-heat ratio was 30% of the reference value (the start-up cost of the plant corresponds to the start-up cost for one turbine). The results indicate that with a lower start-up cost, the CHP plant can be started-up and operated for short periods of time twice as often in all the scenarios with lowered cost than in the case for the default scenarios. Higher numbers of starts and stops and operations within short-duration segments (less than 24 h) reveal a stronger linkage and higher value to the electricity sector of the CHP plants with variable power-to-heat ratio. Although this might entail additional challenges for the UC of units, as well as increased operational and maintenance costs. In the absence of a minimum heat output level requirement and a start-up cost, the HPs can be considered as the most flexible heat generation technology in the investigated DH system. It is found that the number of start-ups and duration of segments with continuous operation of HPs (exemplified by the RYA HPs 1–2 in Fig. 5a and c) correlate to both the degree of volatility/fluctuations in the electricity price and the general price level of electricity. If one considers only the scenarios for Year 2030 with nuclear capacity being available and a rising penetration level of wind power capacity (scenarios ‘‘10% wind” to ‘‘50% wind”), the modelling shows that the number of start-ups of HPs decreases due to a decreasing average electricity price and an increasing number of low-electricity-price periods (cf. Table 3 and Fig. 2). However, in the ‘‘50% wind” scenario, the increased number of highelectricity-price periods causes the HPs to start-up and to operate for short periods more often (cf. Fig. 5c). In the ‘‘50% wind no NUC” scenario with the highest number of high-electricity-price periods, HPs start-up and run for short periods of time twice as often as in the other scenarios investigated. Note that the results for the RYA HPs 3–4 are slightly different and do not follow the trend of the

RYA HPs 1–2, i.e., regarding the number of start-ups. Yet, the RYA HPs 1–2 have a higher COP value and are, therefore, believed to represent the future generation of HPs. In Fig. 5 it should also be noted that the peaking heat generation units available in the studied DH system are not greatly affected (in terms of the number of commitments) by the increasing volatility of the electricity price profiles caused by the increasing penetration level of wind power. It is clear from the results that only in the ‘‘50% wind no NUC” scenario with the highest number of price fluctuations, the number of start-ups of the gas-fired peaking units decreases. This indicates that the CHP plants and the HPs are able to moderate electricity price fluctuations, with few consequences for the operation of other heat generation units in the investigated DH system. 3.5. Economics Table 4 lists the total system cost, the total electricity generation, and the spot market value of electricity sales for the five scenarios for Year 2030, normalised to the ‘‘5% wind” scenario and presented in percentages, as obtained from the modelling of the investigated system. It should be kept in mind that the total system cost is the sum of all operating costs minus the income from electricity sales, with no capital costs taken in account. During high-electricity-price periods, the electricity generation from CHP plants in DH systems becomes as valuable as the heat deliveries. In the ‘‘50% wind no NUC” scenario, where the average price level and the number of high-electricity-price periods are the highest among all the scenarios, the profit from selling electricity increases to such an extent that it exceeds the total operating cost of heat and electricity generation. This can result in a situation in which delivering heat to DH consumers becomes profitable even at a zero heat price. Thus, in a future Swedish power system that is more or less entirely dependent upon renewables (hydro and VRES), the value of electricity generated might, to a large extent, motivate and cover the cost of installing CHP plants in DH systems. This is different from the present situation where low electricity prices make investments in new CHP generation capacity risky. The results indicate that there is no obvious correlation between the amount of generated electricity and the profit received from electricity sales in the investigated scenarios. In the scenarios where the price profiles correspond to 20% and 35% wind power penetration levels, the total amount of generated electricity is the same but the profit from electricity sales is lower in the latter case (cf. Table 4). This is due to the higher frequency of low-electricity-price periods in the ‘‘35% wind” scenario. An increased number of high-electricity-price periods has the opposite effect. Comparing the ‘‘50% wind” and ‘‘50% wind no NUC” scenarios, it is evident that the amount of electricity generated in the latter scenario is almost twice as high as in the former one. Yet, the profit from sold electricity is almost four times higher in the ‘‘50% wind no NUC” scenario (note that in the ‘‘50% wind no NUC” scenario, the yearly average electricity price is twice than that in the ‘‘50% wind” scenario). When interpreting the results obtained in this work it should be kept in mind that the cost-optimal heat generation dispatch is based on a case study, i.e. the existing composition of the DH

Table 4 The total system cost, the total electricity generation, and the total profit from electricity sales normalised to the ‘‘5% wind” scenario and presented in percentages, as obtained from the modelling of the DH system of Göteborg.

Total system cost, % Electricity generation, % Profit from selling electricity, %

5% wind

10% wind

20% wind

35% wind

50% wind

50% wind no NUC

100 100 100

75 90 120

85 70 100

95 70 90

90 85 100

80 155 390

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system of Göteborg applying the heat demand curve for Year 2012. In existing DH system, the future heat demand may decrease or remain on the same level depending on the development of existing and new buildings. Energy efficiency measures in the building stock and likely increase in the average outdoor temperature (due to expected climate change) will act to reduce heat demand, whereas development of new buildings will increase the heat demand (in the City of Göteborg and many other large cities in Europe, there are significant building activities, from development of new settlements). The linkage between the DH systems and power sector in this work is shown through the increased electricity generation from the CHP plants during the high-electricity-price periods and increased output from the HPs when the electricity price is low. A tailored operational strategy could help to mitigate electricity price fluctuations and facilitate even greater adoption of VRES. As noted from the electricity price profiles used in this study (Appendix B), the hourly electricity prices can be as high as 5500 SEK/ MWh, which is due to the assumptions made regarding the cycling costs for technologies included in the ELIN-EPOD modelling package. Meanwhile, the highest hourly electricity spot price on the Nordpool during Years 2013–2015 has peaked at 1392 SEK/MWh [37]. Additional model runs for the modelling periods of 2 months (January-February) having the same input data as the ‘‘20% wind”, ‘‘50% wind”, and ‘‘50% wind no NUC” scenarios, but with the electricity price peaking at 1392 SEK/MWh (all hourly prices higher than 1392 SEK/MWh were substituted with the value of 1392 SEK/MWh) were performed to validate our results. The conclusion regarding the shift in merit order of CHP plants and HPs holds even if the electricity price peaks at 1392 SEK/MWh. Nevertheless, the total system cost in this case increases due to the lower profits derived from the sales of electricity. In addition, fuel prices are considered to be constant in the present study, whereas these will most likely differ over the coming 15 years. Overall, more thorough and continuously updated modelling is required to cover a wider span of probable future scenarios.

4. Conclusions The impact of the future fluctuating electricity prices on an individual DH system was investigated with a unit commitment (UC) optimisation model, using the DH system of the City of Göteborg as a case study. The results indicate a clear increase in value of heat generation units in DH systems that can offer flexibility in a future with increased volatility of electricity prices. We show that the dispatch and the individual operational strategies of CHP plants and HPs are affected by both the average electricity price and the price fluctuations. In a future with a higher average electricity price and increased frequency of high-electricity-price periods, as compared to current prices, the modelling results indicate up to 25% higher total yearly heat generation from CHP plants and up to 20% lower generation from HPs. Furthermore, the results indicate that dips in electricity price strengthen the current merit order of the HPs and the CHP plants, while high-electricity-price periods change the merit order. The results also show an increasing value of CHP plants with variable power-to-heat ratio. With increasing number of high-electricity-price periods the CHP plant with a variable powerto-heat ratio starts to operate more often maximising electricity generation instead of the heat output. In the scenario with the highest number of high-electricity-price periods and the highest average price level, the CHP plant with flexible power-to-heat ratio

is in operation for almost twice as many hours as in all the other investigated scenarios. Furthermore, the total electricity output of that CHP plant is more than 50% higher than the heat output in that scenario. Thus, CHP plants with variable power-to-heat ratio can be beneficial for both the DH owner (higher profits from electricity sales) and as well as to provide system benefits with dispatchable electricity generation. The results show that the increased number of high-electricityprice periods with a duration of less than 48 h, caused by increased employment of VRES, potentially lead to more frequent short-term operation of HPs and CHP plants with a variable power-to-heat ratio. Yet, in reality this will depend on the accuracy of forecasts of RES electricity generation in comparison to start-up time. On the contrary, little effect is seen from the increased number of low-electricity-price periods, i.e., the scheduling of HPs and CHP plants is unaffected by low cost periods. Finally, the results indicate that, with electricity prices high enough during the high-electricity-price periods, the revenue from electricity sales has the potential to bear the full variable costs of the DH system, i.e. profitable even at zero heat price. Acknowledgements This work was carried out under the auspices of E2B2 Research Programme, which is financed by the Swedish Energy Agency. Lennart Hjalmarsson, Per Gustafsson, and Jon Angelbratt at Göteborg Energi AB are acknowledged for providing information about the DH system of Göteborg and for valuable discussions. Appendix A. The model Nomenclature Indices chp chp_bio chp_const chp_var k N n T t Parameters Alpha Cel Cfuel CO2tax Energytax

g

heatdemand K1, K2

subset of CHP plants subset of biomass-fired CHP plants subset of CHP plants with constant power-to-heat ratio subset of CHP plants with variable power-to-heat ratio subset of time-steps, t, corresponding to the minimum up- or down-time total number of heat generation units in the system set of heat generation units in the system total number of time-steps (hours) in the modelling period set of time-steps (hours) in the modelling period power-to-heat ratio of a CHP plant with constant power-to-heat ratio electricity price [SEK/MWh] fuel price [SEK/MWh] CO2 tax [SEK/MWh] energy tax [SEK/MWh] efficiency of unit n (total efficiency of CHP plant, COP for heat pumps) heat demand in any given time-step t [MWh/h] slopes of the lines, which limit the feasibility region of CHP plant operation

D. Romanchenko et al. / Applied Energy 204 (2017) 16–30

min_el/max_el min_heat/max_heat min_off_time min_on_time R1, R2

RDpar REC RUpar Shutdown Startup Variablecost Variables E

minimum/maximum electricity generation of CHP plant n [MWh/h] minimum/maximum heat generation of unit n [MWh/h] minimum down-time of unit n [hours] minimum up-time of unit n [hours] y-axis intercepts of the lines, which limit the feasibility region of CHP plant operation ramp-down limit of unit n [MWh/h] price of renewable electricity certificate [SEK/MWh] ramp-up limit of unit n [MWh/h] shut down cost of unit n [SEK] start-up cost of unit n [SEK] variable operation and maintenance cost of unit n [SEK/MWh] total output (heat and power) of unit n in any given time-step t [MWh/h] objective function [SEK] 1/0 binary variable, 1 if unit n is turned off in any given time-step t 1/0 binary variable, 1 if unit n is turned on in any given time-step t electricity generated by CHP plant n in any given time-step t [MWh/h] heat generated by unit n in any given time-step t [MWh/h] ramp-down limit of unit n depending on the time-step of operation [MWh/h] ramp-up limit of unit n depending on the time-step of operation [MWh/h] 1/0 variable, 1 if unit n is in operation in any given time-step t 1/0 variable, 1 if unit n is not in operation in any given time-step t

obj off_trans on_trans P Q RD RU u y

A.1. The objective function The overall objective of the model is to create an optimal dispatch of the heat generation units available in the DH system while satisfying system- and technology-specific constraints and ensuring a minimum system operating cost. Taking into account the amounts of heat and electricity generated/consumed, the total system operating cost is calculated using the equation:

obj ¼

T X N X Eðt;nÞ  CfuelðnÞ t¼1 n¼1

gðnÞ

þ

T X N X Q ðt;nÞ  ½VariablecostðnÞ t¼1 n¼1

þ EnergytaxðnÞ þ CO2taxðnÞ  þ StartupðnÞ þ ShutdownðnÞ 

T X N T X N X X Pðt;chpÞ  CelðtÞ  Pðt;chp t¼1 n¼1

bioÞ

 REC

ðA:1Þ

t¼1 n¼1

A.2. Demand-supply constraints

n¼1

This equation ensures that at every time-step the sum of the heat generated by all the generation units in the DH system is equal to or larger (spillage of heat is technically available) than the heat demand in this time-step. In addition, there are constraints that limit the minimum and maximum heat outputs from each generation unit, as well as constraints that keep the electricity generation levels in CHP plants within the predefined boundaries. Technology-specific constrains can be represented as follows:

min heatðt;nÞ 6 Q ðt;nÞ 6 max heatðt;nÞ

ðA:3Þ

min elðt;chpÞ 6 Pðt;chpÞ 6 max elðt;chpÞ

ðA:4Þ

A.3. Ramp-up and ramp-down constraints Ramping limits control the magnitude of the change in heat or electricity output between adjacent time-steps. Ramping limits are applied for both increases and decreases in the heat/electricity output and are specific for each generation unit. The ramp-up limit for heat generation is the maximum difference between the amount of heat generated at time-step t and time-step t  1 if the level of heat generation increases. The same logic is valid for the ramp-down limit if the level of heat generation decreases. Ramping limits are also applied for electricity generation in CHP units. Ramp-up and ramp-down constraints for heat generation can be described as follows:

Q ðt;nÞ 6 Q ðt1;nÞ þ RUðt;nÞ

ðA:5Þ

Q ðt;nÞ P Q ðt1;nÞ þ RDðt;nÞ

ðA:6Þ

Due to technical limitations, heat generation units cannot generate the maximum possible amount of heat in the first time-step of operation after being started. Similarly, a generation unit cannot operate at the maximum allowed capacity during a given time-step and be shut down in the very next time-step. Thus, constraints described in Eqs. (A.7) and (A.8) ensure that in the case of an ‘‘on transition” (unit is started) for a generation unit, the model sets the heat output in that time-step as equal to the minimum generation limit of that unit. Similarly, in the case of an ‘‘off transition” (unit is shut down) for one unit, the model assures that the heat output in the previous time-step is equal to the minimum generation limit of that unit. The respective constraints are:

RUðt;nÞ ¼ min heatðnÞ  on transðt;nÞ þ uðt1;nÞ  RUparðnÞ

ðA:7Þ

RDðt;nÞ ¼ min heatðnÞ  off transðt;nÞ þ uðt;nÞ  RDparðnÞ

ðA:8Þ

A.4. Minimum up-time and minimum down-time constraints ‘‘Minimum up-time” constraints are applied to prevent a unit from being shut down before it has been in operation for at least the required minimum number of time-steps. In the same manner, ‘‘minimum down-time” constraints ensure that the limit regarding the minimum required time that a unit should be out of operation is fulfilled. Limitations as to the ‘‘minimum up-time” and ‘‘minimum down-time” are unit-specific and exogenously provided to the model. The respective constraints are written as: tþmin on timeðnÞ 1

X

The objective function is subject to a number of constraints. The main task of any DH system is to satisfy the heat demand at every time-step (hour), so the overall heat balance is expressed as: N X Q ðt;nÞ P heatdemandðtÞ

27

ðA:2Þ

uðk;nÞ P on transðt;nÞ  min on timeðnÞ

ðA:9Þ

k¼t tþmin off timeðnÞ 1

X k¼t

yðk;nÞ P off transðt;nÞ  min off timeðnÞ

ðA:10Þ

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D. Romanchenko et al. / Applied Energy 204 (2017) 16–30

Pðt;chp

A.5. Power-to-heat ratio constraints As stated in Section 2, the operational mode of a CHP plant with variable power-to-heat ratio must lie within the feasibility region defined by the heat and electricity generation boundaries. The developed optimisation model is designed to identify the optimal power-to-heat ratio for each CHP plant with variable power-toheat ratio in the most flexible way. This means that there are no other boundaries to the relationship between the heat and electricity outputs from CHP plants, except for the feasibility region of operation, which is defined by linear functions. Thus, the constraints that regulate the power-to-heat ratios in CHP plants with variable power-to-heat ratio can be written as:

K 1  Q ðt;chp

varÞ

þ R1 P Pðt;chp

K 2  Q ðt;chp

varÞ

þ R2 6 P ðt;chp

varÞ Þ varÞ Þ

ðA:11Þ ðA:12Þ

The coefficients K1, K2, R1, R2 are pre-defined and exogenously provided to the model. Power generation from CHP plants with constant power-to-heat ratio is calculated using the equation:

constÞ

¼ Q ðt;chp

constÞ

 Alphaðchp

constÞ

ðA:13Þ

A.6. Logical constraints In addition to the constraints described above, several logical constraints are defined in the model. For instance, every generation unit must be either in operation or in shut-off mode but never in both states simultaneously. Similarly, the model ensures that the heat generation unit is not started up and shut down in the same time-step. These conditions are regulated by Eqs. (A.14) and (A.15):

uðt;nÞ þ yðt;nÞ ¼ 1

ðA:14Þ

on transðt;nÞ þ off transðt;nÞ 6 1

ðA:15Þ

There are also constraints related to the operating state of the heat generation unit and the transition between states of the same generation unit. This relationship ensures that the generation unit is considered to be in operation when started up and to be out of operation when is shut down. The equation is written as:

on transðt;nÞ  on transðt;nÞ ¼ uðt;nÞ  uðt1;nÞ

Appendix B. Electricity price profiles

(a)

(b)

ðA:16Þ

D. Romanchenko et al. / Applied Energy 204 (2017) 16–30

(c)

(d)

(e)

29

30

D. Romanchenko et al. / Applied Energy 204 (2017) 16–30

(f)

Fig. B1. Electricity price profiles derived from the ELIN-EPOD modelling package and applied in the present study (first hour of the profiles corresponds to the first hour on January 1st in Years 2012 and 2030, respectively): (a) 5% wind power penetration level, current nuclear power fleet; (b) 10% wind power penetration level, current nuclear power fleet; (c) 20% wind power penetration level, current nuclear power fleet; (d) 35% wind power penetration level, current nuclear power fleet; (e) 50% wind power penetration level, current nuclear power fleet; (f) 50% wind power penetration level, nuclear power fleet is decommissioned.

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