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Bidding strategies for virtual power plants considering CHPs and intermittent renewables
Energy Conversion and Management 103 (2015) 408–418
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Bidding strategies for virtual power plants considering CHPs and intermittent renewables J. Zapata Riveros, K. Bruninx, K. Poncelet, W. D’haeseleer ⇑ University of Leuven (KU Leuven) Energy Institute, TME Branch, Heverlee, Belgium Energyville (joint venture of VITO NV and KU Leuven), Genk, Belgium
a r t i c l e
i n f o
Article history: Received 22 March 2015 Accepted 26 June 2015
Keywords: Virtual power plant Cogeneration Renewable energy Imbalance markets Stochastic programming
a b s t r a c t Energy efficiency and renewable-energy sources (RES) are fundamental parts of the European energy policy. For this reason, efficient distributed generation technologies such as combined heat and power coupled to district heating (CHP–DH) and RES based electricity are largely promoted. Additionally, the flexibility that CHP–DH offers to the power system is seen as an option to balance the intermittent output of RES-based generation. This could be done by aggregating RES based electricity generation and CHP DH in a virtual power plant (VPP). In this framework, the present work presents a methodology to evaluate the optimal bidding strategy of a VPP composed of a CHP–DH and RES based generators. The objective is to investigate the optimal bidding strategy for a VPP that uses CHP DH to compensate for the uncertainties regarding RES-based electricity generation and market prices. The VPP operator nominates its energy to the day ahead market the day before the actual delivery (D-1). In real time, any deviation from the day-ahead schedule is settled in the imbalance market. The uncertainties are modeled using a two stage stochastic programming approach. Three different bidding strategies are studied: ‘static’, ‘flexible DA’ and ‘flexible RT’. The major difference between the studied strategies lies in the dispatch decisions. The ‘static’ strategy does not adjust the scheduled output of the CHP. Whereas, the ‘flexible DA’ and ‘flexible RT’ strategies differ from each other in terms of the information available at the moment of performing the reschedule (second stage decision). The ‘flexible DA’ reschedules the CHP output for the whole day assuming full knowledge of the RES scenario, but under uncertainty regarding the imbalance price. The ‘flexible RT’ strategy allows the VPP to adjust its position at each time step depending on the RES generation and imbalance price scenarios. The results show that in comparison with the ‘static’ strategy, the ‘flexible DA’ operation results in a profit increase during summer (5900 €/week), the intermediate season (2800 €/week) and winter (2700 €/week). This increase is moderate when compared against the total fuel cost in these seasons. Better results are obtained when the ‘flexible RT’ strategy is applied. Using this strategy larger profits are achieved for all seasons. For instance, during winter the difference between the ‘flexible RT’ operation and the ‘static’ case amounts to 22,600 €/week, approximately 5% of the fuel cost. Ó 2015 Published by Elsevier Ltd.
1. Introduction In the fight against climate change, the European Union (EU) has committed itself to reach a set of targets set under the Climate and Energy Package. This package, also known as the ‘‘20-20-20’’ package, sets three main objectives for 2020: a 20% reduction in EU greenhouse gas emissions based on the 1990 level; ⇑ Corresponding author at: University of Leuven (KU Leuven) Energy Institute, TME Branch, Heverlee, Belgium. Tel.: +32 16 322510; fax: +32 16 3 22985. E-mail address: [email protected] (W. D’haeseleer). http://dx.doi.org/10.1016/j.enconman.2015.06.075 0196-8904/Ó 2015 Published by Elsevier Ltd.
raising the share of EU end energy originated from renewable resources to 20% and a 20% improvement in energy efficiency. In this context, it is assumed that combined heat and power (CHP) devices connected with district heating (DH) can play an important role [1]. Furthermore, photovoltaic (PV) facilities and wind farms are seen as a partial replacement of fossil fuel-based electricity generation. The present paper aggregates a hypothetical CHP connected to district heating with a large amount of RES based electricity generators, in a virtual power plant (VPP). In [2] a virtual power plant is defined as an agglomeration of distributed generators, controllable
J. Zapata Riveros et al. / Energy Conversion and Management 103 (2015) 408–418
409
Nomenclature Symbol
ae aq ct;n DE_ IMB t;s;r DE_ RES t;x DQ_ CHP t;s;r DQ_ BOILER t;x Dt
gq gsto ki kr ks
definition units electrical efficiency of the CHP (%) thermal efficiency of the CHP (%) on/off status of the CHP (–) electricity traded in the balancing market (MW) difference between RES electric power scheduled and dispatched (MW) difference between the planned and delivered thermal power of the CHP (MWth) difference between the planned and delivered thermal power of the boiler (MWth) time step of the optimization (15 min) (h) thermal efficiency of the boiler (%) storage tank loss factor (%) probability of the imbalance scenarios (%) probability of the renewable scenarios (%) probability of the day-ahead scenarios (%)
pIMB t;i pDA t;s pFUEL t
imbalance market price (€/MW h)
C DEV t;s;r C OP t;s;r start up C t;n
deviation penalty (€)
dev n
limits of the piecewise deviation function (%)
dxt;s;r
components x of the piecewise deviation function (MW)
EVPP max E_ RT t;s;r E_ CHP
installed capacity of the VPP (MW) electricity generated on real-time (MW)
t
day-ahead market price (€/MW h) gas prices (€/MW h) operational cost of the CHP (€) start-up cost (€)
E_ DA t E_ RES
total electric power traded in the DA market (MW)
n F_ CHP t;n _F BOILER
primary fuel consumption of the CHP plant (MW)
i Q_ CHP
index i, set of imbalance price scenarios (€/MW h)
Q_ BOILER t
thermal power generated by the auxiliary boiler (MWth)
Q SOC t;s;r Q_ CH
state of charge of the storage (MW hth)
RIMB t;s;r
imbalance market profits (€)
RDA t
day-ahead market profits (€)
r s
renewable energy scenarios (MW) day-ahead prices scenario (€/MW h)
t
t
t;n
t;s;r;
RES electric power traded in the DA market (MW) primary fuel consumption of the boiler (MW) thermal power generated by the CHP (MWth)
thermal (dis)charging power to the storage tank (MWth)
Acronyms CHP combined Heat and Power District Heating DA day-ahead DH district heating EU European Union PHSP pumped hydro storage plant PV photovoltaic RES renewable energy sources RT real time SOC state of charge TSO transmission system operator VPP virtual power plant WPP wind power plant
expected electricity generated by the CHP (MW)
loads and storages devices, aggregated in order to operate as a single power plant and being able to participate in the power exchange market. According to [2] the use of a VPP can bring benefits such as increasing the flexibility available in the electric power system without a large investment in infrastructure. It is also mentioned that the VPP operation could help to displace the fossil generation during peak hours and solve grid balance problems [2]. Nevertheless, all the benefits expected from the VPP operation depend largely on the interaction between the VPP and the electric power market. Currently, the largest volume of energy is traded the day before (D-1) on the day-ahead market which consequently has the largest liquidity. The day-ahead market is supervised by the transmission system operator (TSO). The TSO expects that the participants give unbiased bids; this means that the nominations should equal the expected generation. The deviations between demand and generation are settled in the imbalance market which is controlled by the TSO. In order to incentivize the participants to reduce their imbalance, imbalance tariffs are in place. The TSO has the final responsibility to keep the balance between generation and consumption. To achieve this task, a certain amount of capacity has to be kept steady (idle or offline). These reserves are activated in case of positive (generation surplus) or negative (lack of generation) imbalance. The price that the TSO pays to the reserves providers1, is transferred directly as imbalance tariff to penalize those players that caused the imbalance. 1 In Belgium, these prices correspond to the maximum price paid for up regulation (Marginal incremental price) and the minimum received for down regulation (Marginal decremental price).
Trading in the power exchange market brings along several uncertainties, specifically due to errors in the forecast of RES-based electricity generation and the uncertain evolution of the day-ahead and imbalance prices. The objective of this paper is to develop a methodology to coordinate the participation of CHP–DH and RES in the day-ahead market (DA) and to compare different bidding strategies for the VPP, exploiting the flexibility of CHP-DH to compensate for the uncertainty on day-ahead prices, RES-based generation forecast and imbalance tariffs. The uncertainties are explicitly modeled using a two-stage stochastic program. Toward this aim, two different bidding approaches will be considered: ‘static’ and ‘flexible’ VPP operation. In the first ‘static’ strategy, the electric power delivered by the CHP in real-time is equal to the DA schedule. Consequently, the resulting imbalance that stems from renewables forecast errors is settled in the imbalance market. On the other hand, in ‘flexible’ operation the CHP is allowed to reschedule its electric output in order to compensate for the forecast error on RES-based electricity generation. Thus the total imbalance volume might be reduced. Furthermore, it is considered that the rescheduling can be performed at two different moments in time. In the ‘flexible DA’ case it assumed that the CHP schedule is adjusted just once after having a more accurate idea of the realization of the RES generation but not of the imbalance prices. On the other hand, the ‘flexible RT’ case, where RT stands for real time, considers that the rescheduling is done every time step once the actual imbalance price and RES-based generation profile are known. In the literature, several studies about optimal bidding strategies and imbalance cost minimization can be found. For instance,
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the optimal dispatch of industrial cogeneration devices in a liberalized market is studied in [3]. The benefits of using a micro-CHP device to balance the portfolio of a VPP (‘self-balancing’) are assessed in [4,5]. Both studies report little or no incentive for ‘self-balancing’. Nevertheless, these studies are based on deterministic techniques that disregard the uncertainties of the system. Taking uncertainties into account could make the ‘self-balancing’ approach more valuable. Stochastic programming has been extensively used to thoroughly account for uncertainties. The case of optimal wind power integration in the electric power system has been extensively studied [6–9]. In [7] stochastic programming is used to generate an optimal bid for a short-term power market. Results show that using a stochastic approach leads to higher profits compared with a deterministic methodology. Similarly, [8] considers the bidding of a wind power plant (WPP) in the different energy markets (i.e., day-ahead, intraday and balancing market). In addition, [6] includes a risk aversion model to analyze the different optimal offering strategies of a WPP depending on the risk attitude. In [6–9] only wind generators are studied. Joint participation of a WPP and dispatchable generators is an interesting field of study. The case study in [10] consists of a wind farm and a pumped hydro storage plant (PHS). The authors of [10] use two-stage stochastic programming to account for the uncertainties in the day-ahead prices and wind power. However, it does not take into account the available information regarding imbalance prices. The results show that aggregating WPP and PHS can lead to larger profits and reduce the imbalance cost. From the reviewed literature only one model [11] considers simultaneously imbalance price and wind power forecast uncertainties as well as coordinated participation in the day-ahead market. The authors propose a two-stage stochastic optimization of a VPP that aggregates a WPP with a PHS and a conventional electric power plant. The results show substantial profits increase when these power plant operate together. Nevertheless it does not assess the benefits that a VPP can obtain from using its flexibility in real-time to react to the imbalance prices, nor the specific interaction with a heat demand (CHP unit). Compared to the literature, the contributions of this paper are: A stochastic program that coordinates the operation of RES generators with a CHP used for DH including uncertainties in day-ahead prices, imbalance prices and renewable energy generation and the specific constraints characteristics of a DH system (e.g., the heat demand should be met all the time). A comparison between three different bidding strategies: a ‘static’ case in which no rescheduling for balancing the forecast error is implemented, a ‘flexible DA’ that assumes uncertainty regarding imbalance prices when rescheduling the CHP and a ‘flexible RT’ case in which it is assumed that the VPP can react to the imbalance prices. The paper continues as follows: Section 1 provides a detailed description of the optimization model and the characteristics of the case study. The results are presented and discussed in Section 2. Finally, Section 3 presents the conclusions and suggestions for further work.
HEAT BUFFER
BOILER
The present study assesses the optimal dispatch of a hypothetical virtual power plant in Belgium. The VPP system consists of a CHP–DH together with uncontrollable RES based electricity generation (i.e., photovoltaic and wind energy). Fig. 1 gives an overview of the studied system. The CHP–DH plant or CHP system consists of
CHP
Electricity Heat
RES
Fig. 1. Distribution of the electricity and heat connections for the studied case. The CHP system is composed of a prime mover, an auxiliary boiler and a thermal buffer. The electricity generated is traded in the electricity market.
a prime mover, an auxiliary boiler and a thermal storage unit that meet the heat demand of the community. The electricity generated by the VPP is sold in the electric power market. In other words, the DH plant is not responsible for meeting the electrical demand of the community. The VPP controller makes a nomination on the day-ahead market considering the expectations for renewable energy generation in its portfolio, DA and imbalance prices, while the heat demand is assumed to be known. During real time, the deviations between the day-ahead nomination and the actual dispatch have to be settled in the balancing market and/or by changes in the output of the CHP. In order to account for the uncertainties that the VPP faces, a stochastic program is developed. In a stochastic program the uncertainty is represented using a set of scenarios. The stochastic program studied in this work is illustrated in Fig. 2. When bidding electricity in the day-ahead market, the decision process can be split into two different stages. In the first stage, the decisions have to be taken under uncertainty regarding the future RES generation and prices. In this study, the first stage decisions correspond to the day-ahead bidding. The day-ahead bid (i.e., first-stage decision) is obtained using a combination of 10 day-ahead, 10 imbalance and 10 renewables scenarios which result in a total of 1000 scenarios. During the second stage, the day-ahead prices are known. It t is also assumed that at this point the VPP operator has a more accurate forecast regarding the realization of the RES based generation and thus decisions regarding the dispatched volume are taken.
Decision:
DA bid
Known parameter: Uncertain parameter:
2. Methodology
ELECTRICITY GRID
Imbalance volume
Day-ahead prices, RES generation Day-ahead prices, RES generation, Imbalance price
Imbalance prices
FIRST STAGE
SECOND STAGE
Imbalance prices
Fig. 2. Two-stage stochastic programming for the VPP. The first stage decisions correspond to the day-ahead bids, whereas the second stage decisions are related to the actual dispatch.
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Fig. 3. During the first stage decision process the DA bid is obtained. Afterwards the results are evaluated in a larger set of scenarios and the second-stage decisions (or the actual dispatch) are taken.
Table 1 Summary of the different bidding strategies: ‘static’, ‘flexible DA’ and ‘flexible RT’. Case
Dispatch
Information available during dispatch (2nd stage)
Static Flexible DA
Dispatch equals to DA schedule One dispatch per RES scenario
Flexible RT
One dispatch per RES and imbalance price scenario
No
The second stage decisions or actual dispatch decisions are obtained in a ‘re-evaluation’ process. This process is performed once the day-ahead bid is obtained (i.e., after the first-stage decisions are taken) and it makes use of a larger set of scenarios (50 imbalance and 50 renewables scenarios). Fig. 3 visualizes the entire optimization process. Three different bidding strategies are studied: ‘static’, ‘flexible DA’ and ‘flexible RT’ as stated in Table 1. The major difference between the studied strategies lies in the second stage decision process. The ’static’ strategy does not adjust the scheduled output of the CHP. On the other hand, the ‘flexible DA’ and ‘flexible RT’ strategies have the same day-ahead bid. They differ from each other in the information available at the moment of performing the reschedule (second-stage decision). The ‘flexible DA’ reschedules the CHP output for the whole day depending on the RES scenario, but under uncertainty regarding the imbalance price. The ‘flexible RT’ strategy allows the VPP to adjust its position at each time step depending on the RES generation and imbalance price scenarios which are assumed to be known. The ‘flexible RT’ case is performed using a rolling-horizon approach; at each time step once the observed imbalance prices of each scenario are obtained, the dispatch decisions are taken. It is important to remark that both the ‘flexible DA’ and ‘flexible RT’ correspond to two extreme cases. When deciding on the actual dispatch, the ‘flexible DA’ assumes that the VPP operator has no knowledge regarding the imbalance prices. In contrast, the ‘flexible RT’ assumes complete knowledge of the imbalance prices for the current time step. In reality, every 3 min the Belgian TSO provides actualized information on the current imbalance volume. From this information the VPP can obtain a very accurate forecast of the imbalance price in order to perform ‘passive balancing’2. However, the forecast can still deviate from the actual imbalance price as the response of other market participants is unknown and thus the real benefits lie between the economic savings of these two cases ‘flexible DA’ and ‘flexible RT’ operation. This stochastic optimization procedure was formulated as a mixed integer linear program (MILP). The model has been devel2 Passive balancing is a measure implemented by the Belgian TSO to allow the market participants helping to reduce the total system imbalance in real time.
reevaluation Day-ahead price RES-based generation Day-ahead price RES-based generation Actual imbalance price
oped in GAMS, and is solved using the commercial solver CPLEX.
2.1. Stochastic optimization model The objective is to maximize the revenues obtained by the VPP as stated in Eq. (1):
8t; 8s; 8r; 8i : max obj ¼
S R I T X X X X OP IMB ks kr ki RDA t;s þ Rt;s;r;i C t;s;r s¼1
r¼1
i¼1
ð1Þ
t¼1
In this equation, T is the time horizon, in this particular case, two days from which only the first one is implemented (the second day is considered to enforce an optimal behavior in the storage tank). The studied time period is divided in 15 min time steps. Furthermore in Eq. (1), S, R and I represent the sets of scenarios of day-ahead prices, RES-based generation and imbalance prices, respectively. The net profit results from the difference between the revenues obtained in the DA and imbalance (IMB) market RDA and RIMB t t;s;r respectively and the operational cost of the CHP–DH C OP t;s;r . Recall that RIMB t;s;r is the result from settling the deviations between the planned and delivered electricity in the imbalance market; for this reason, this variable can take positive or negative values. The revenues are weighted over all scenarios. The probability of occurrence of each scenario is equal to ks for the day-ahead prices scenarios, kr for the RES generation scenarios and ki for the imbalance price scenarios. The electric power scheduled to be traded on the day-ahead market E_ DA is calculated in Eq. (2): t
_ CHP þ E_ RES 8t : E_ DA t ¼ Et t
ð2Þ
In this equation, E_ CHP corresponds to the scheduled electric power t output of the CHP and E_ RES to the traded RES generation. It is import
tant to remark that the electric power scheduled to be traded on the day-ahead market E_ DA does not depend on the scenarios, as it is a t
first-stage decision.
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On the other hand, the DA RES nomination E_ RES is limited to the t maximum and minimum possible values achieved by the RES scenarios at each time step.
8t : E_ RES ¼0 t
ð3Þ
8t : E_ CHP ¼ t
or
8t :
min r
E_ RES t;r
max _ RES Et;r 6 E_ RES t 6r
ð4Þ
where E_ CHP t;s;r is the actual electricity dispatched by the CHP. The imbalance error DE_ IMB t;s;r represents the difference between the actual electric power generated and the day-ahead schedule. This is expressed in Eq. (5):
_ RT _ DA 8t; 8s; 8r : DE_ IMB t;s;r ¼ Et;s;r Et
ð5Þ
The profits are calculated as the sum of the revenues obtained from trading electricity in the day-ahead market and the imbalance market as stated in Eqs. (6) and (7):
_ DA DA 8t : RDA t;s ¼ Et pt;s Dt
ð6Þ
_ IMB IMB 8t; 8s; 8r; 8i : RIMB t;s;r;i ¼ DEt;s;r pt;i Dt In Eqs. (6) and (7)
p
DA t;s
ð7Þ
corresponds to the day-ahead price and
pIMB t;i to the imbalance price in [€/MW h]. The imbalance revenues can be either negative or positive depending on the nature of the system imbalance (SI) and the imbalance tariff. In addition Dt is the time step of the simulation, in this case 15 min. The heat balance is described in Eq. (8):
_ BOILER ¼ Q_ demand þ Q_ CH þ DQ_ CHP 8t; 8s; 8r : Q_ CHP þ Q_ BOILER t t t;s;r þ DQ t;s;r t t;s;r
According to this equation the optimization must ensure that the heat demand is met during every time step for all the scenarios, using the CHP Q_ CHP , the boiler Q_ BOILER or the heat that is charged to t
or discharged from the thermal storage buffer Q_ CH t;s;r . Additionally, CHP BOILER _ _ the variables DQ t;s;r and DQ t;s;r represent the difference between the actual thermal power delivered by the CHP and backup boiler and their planned thermal power output, respectively. The CHP plant is constituted by three internal combustion gas engines. Eq. (9) states the relationship between the electrical and thermal power output of each unit. Similarly, Eq. (10) links the primary energy use to the thermal and electrical power production. Looking at this equation is clear that once the optimal electrical output is selected, simultaneously the thermal output is settled and vice versa.
_ CHP aE c 8t; 8n : E_ CHP t;n t;n ¼ Q t;n
ð9Þ
aQ
n 8t; 8n : F_ CHP ¼ t;n
E_ CHP t;n
aE
ct;n ¼
Q_ CHP t;n
aQ
ð11Þ
t;n
8t : F_ CHP ¼ t
N chp X n F_ CHP t;n
ð12Þ
n¼1
The start-up cost is calculated using Eq. (13):
8t; 8n : C start t;n
up
P pstart t;n
up
ct;n ct1;n
ð13Þ
up In this Equation pstart is a positive parameter that represents a t;n fixed cost for starting up the machines. In addition, the minimum up and down times of the CHPs are taken into account as follows. For each individual CHP unit, new sets k and l are created:
k ¼ ½1; 2; . . . ; UT n
ð14Þ
l ¼ ½1; 2; . . . ; DT n
ð15Þ
In these equations, UT n and DT n represent, respectively, the minimum up-time and down-time of each CHP unit, being one hour in this particular case (UT n ¼ DT n ¼ 4). The constraints on the minimal up and down time can be written as:
cn;t cn;t1 cn;tþk 6 0
ð16Þ
cn;t1 cn;t cn;tþl 6 1
ð17Þ
The fuel consumption of the boiler in Eq. (18):
F_ BOILER t
is calculated as shown
_ BOILER
Q 8t : F_ BOILER ¼ t t
gboiler
ð8Þ
t
Nchp X E_ CHP n¼1
The actual electricity dispatched E_ RT t;s;r depends on the realization of the scenarios as stated in Eq. (4):
_ CHP _ RES 8t; 8s; 8r : E_ RT t;s;r ¼ Et;s;r þ Et;r
The total electricity generation E_ CHP and primary energy F_ CHP use t t of the CHP plant are estimated as the sum of the total electricity generation and fuel consumption among the individual units, as stated in Eqs. (11) and (12):
ð18Þ
;
It is assumed that the boiler has constant efficiency gboiler . The total operational cost of the system is estimated as the sum of the primary energy cost of the CHP system and the start-up cost; see Eq. (19):
FUEL _ BOILER þ C start 8t : C OP Dt F_ BOILER þ F_ CHP þ DF_ CHP t t t;s;r þ DF t;s;r t;s;r ¼ pt t
up
ð19Þ _ BOILER correspond to the fuel use differIn Eq. (19) DF_ CHP t;s;r and DF t;s;r ence that appears when the CHP system is rescheduled and is the fuel price, which is assumed to be constant.
pFUEL t
The state of charge (SOC) of the storage tank Q SOC t;s;r is calculated using Eq. (20). The efficiency of the storage tank.3 gst is assumed to be constant. Recall that Q_ CH is the average thermal power (kWth) t;S;r
that is charged to/discharged from the storage tank during every time step; consequently, it can take both positive or negative values: SOC _ CH 8t; 8s; 8r : Q SOC t;s;r ¼ gst Q t1;s;r þ Q t;s;r Dt
ð20Þ
Eqs. (21) and (22) ensure that the optimization does not exceed the operational limits of the CHP:
ct;n
ð10Þ
_ CHP _ CHP _ CHP 8t; 8n; 8s; 8r : ct;n Q_ CHP min 6 Q t;n þ DQ t;n;s;r 6 Q max ct;n
ð21Þ
n F_ CHP t;n
In these equations, is the primary fuel consumption of each individual CHP unit n, aQ and aE are, respectively, the thermal and electrical efficiency of the CHP plant. ct;n is a binary variable that indicates the on/off status of each CHP unit. This variable is independent of the scenarios and cannot change during real time generation.
3 The efficiency of the storage tank represents the percentage of thermal energy that is preserved by the storage after it has been stored during one time step of 15 min. For example, a storage tank with an efficiency of 90% is charged with 1 kW hth after 15 min, only 0.9 kW hth remains.
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_ CHP _ CHP _ CHP 8t; 8n; 8s; 8r : ct;n E_ CHP min 6 Et;n þ DEt;n;s;r 6 Emax ct;n
ð22Þ
_ CHP _ CHP _ CHP E_ CHP t;n þ DEt;n;s;r and Q t;n þ DQ t;n;s;r correspond to the actual electric output and the actual thermal output of the CHP, respectively. Consequently, if the CHP is in operation, its output is limited to the minimum electricity E_ CHP and heat capacity Q_ CHP and the maximin
SOC 8t; 8s; 8r : 0 6 Q SOC t;s;r 6 Q max
ð23Þ
_ BOILER 8t; 8n; 8s; 8r : 0 6 Q_ BOILER þ DQ_ BOILER t;n t;n;s;r 6 Q max
ð24Þ
In these equations, Q SOC max is the maximum storage capacity of the thermal buffer. Q_ BOILER corresponds to the maximum thermal power max
þ DQ_ BOILER that can be delivered by the boiler whereas, Q_ BOILER t;n t;n;s;r represent the real output of the auxiliary boiler. 2.2.1. Case specific constraints The previously explained equations apply to the ‘flexible DA’ case; in this subsection, the necessary modifications to these equations for the other cases are described. First, the ‘static’ case is modeled by setting the variables DE_ CHP ; DQ_ CHP ; DQ_ BOILER ; DF_ CHP ; DF_ BOILER to zero. In other words, the t;s;r
t;s;r
t;s;r
t;s;r
CHP is not allowed to deviate from its scheduled output. On the other hand, the ‘flexible DA’ and ‘flexible RT’ have the same day-ahead schedule; thus, it is only necessary to modify the equations that involve RT decisions. This is because in ‘flexible DA’ the imbalance volume decision DE_ IMB is considered indepent;s;r
scenarios. In other words, the dent of the imbalance price pIMB t;i imbalance volume is settled before knowing the imbalance prices but with knowledge of the RES generation and day-ahead prices. In contrast, in the ‘flexible RT’ case, the imbalance volume is estimated depending on the imbalance price scenarios and thus several variables become dependent of these scenarios such as: E_ CHP ; E_ CHP ; Q_ CHP ; E_ RT ; Q SOC ; DE_ CHP ; DQ_ CHP ; DQ_ BOILER ; t;s;r;i
t;s;r;i
t;s;r;i
Heat demand RES-based generation
[MW h/week] [MW h/week]
Summer
Intermediate
Winter
1199 1201
2598 1011
6169 879
min
_ CHP mum electricity E_ CHP max and heat capacity Q max . Eqs. (23) and (24) prevent exceeding the operational limits of the storage tank and boiler:
t;s;r
Table 2 Heat demand and RES-based generation of the studied weeks.
t;s;r;i
t;s;r;i
t;s;r;i
t;s;r;i
t;s;r;i
_ BOILER _ IMB DF_ CHP t;s;r;i ; DF t;s;r;i ; DEt;s;r;i and consequently the equations where these variables appear are also dependent on the imbalance tariffs. 2.2. Application to a case study The developed methodology is applied to a hypothetical case study that assumes a large penetration of renewable energy and the installation of a district heating facility in the city of Leuven (Belgium) which resembles a typical small European city. The heat demand profile is approximated through a bottom-up approach. Data concerning the building stock of Leuven, provided by the municipality [12], is combined with heat demand benchmarks [13] and synthetic load profiles [14] to create the heat demand profile. It is assumed that the thermal energy is sold to the community at a constant retail price. As a consequence, they do not influence the optimization results. For this reason these revenues are not included in the optimization. The optimal size of the CHP is estimated using the maximum rectangle method explained in [15]. It is assumed that the DH system is operated by three parallel internal combustion gas engines (ICGE). Each ICGE has a maximum electrical output equal to 18 MWe. The electrical and thermal efficiency are aE ¼ 44% and aQ ¼ 48% , respectively. Regarding the renewable generation it is assumed that the total installed capacity amounts to 20 MWe, of which 14 MWe corresponds to solar panels and 6 MWe to wind turbines. These numbers
reflect the current (2014) proportion of photovoltaic and wind installation in Belgium. The renewable energy scenarios are based on data provided by the Belgian TSO [16]. The optimization will be performed for three different weeks, each representing the behavior of a season (summer, intermediate and winter). The total heat demand and the RES based generation of each of the studied weeks are summarized in Table 2. Finally, the day-ahead and imbalance price scenarios are also based on historic data of the Belgian electricity market [16,17]; the gas price is assumed to be constant and equal to 39 €/MW hth. The gas price corresponds to the average price that was paid by small and medium sized enterprises in 2014 [18]. 2.4. Scenario generation and reduction As mentioned before, to represent the uncertainty that stems from the renewable energy forecast errors, the day-ahead and imbalance prices, the underlying stochastic processes are approximated using a group of scenarios. A scenario corresponds to a possible realization of the stochastic process, thus a large enough scenario representation should capture the variability and uncertainty of the random variables. The statistical scenario generation technique developed in [19,20] and described in detail in [21], is used in this thesis to generate a large set of scenarios. This technique makes use of historical forecast errors (e.g., difference between the forecasted variable and the measured output of this variable during the previous years) to create different scenarios. Once the ‘error scenarios’ are obtained, they are added to the actual forecasted variable (e.g., wind power forecast of the next day) to obtain the different scenarios for each variable (e.g., wind scenarios). Yet, using a large number of scenarios is computationally expensive. Therefore, a reduction technique is necessary to trim down the number of scenarios. Toward this aim, a modified version of the fast-forward scenario reduction algorithm that includes the inherent characteristics of the optimization problem is implemented, as described in [21,22]. For the purpose of this work, a total of 200 day-ahead, 200 imbalance and 200 renewables scenarios were generated independently. Nonetheless, for computational efficiency, the orginal set was reduced to 10 scenarios for each parameter in the first optimization, resulting in a total number of 1000 combinations of scenarios. Afterwards, as explained before, the reevaluation process has used a larger number of scenarios (50 per set) leading to a total of 25,000 (10 day-ahead, 50 imbalance and 50 renewables scenarios) combinations of scenarios to gain statistical significance. 2.5. Limiting the imbalance volume The results obtained when applying the optimization described in 1.1 during the intermediate season for the ‘flexible DA’ case are illustrated in Fig. 4. In this figure, the black line represents the scheduled CHP electrical power, the shaded area corresponds to the actual electrical power delivered by the CHP.4 It can be 4 Keep in mind that the electric energy traded in the day-ahead market is composed of the electricity generated by the CHP, and the RES-based generation. Nevertheless, for illustration purposes only the electricity nominated by the CHP appears in Fig. 4.
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Fig. 4. Resulting original DA bid (solid line) and actual dispatch of the CHP (gray area). The difference between da schedule and real time dispatch creates large imbalance of the order of 40 MW.
observed that at several moments the CHP was scheduled to operate at maximal output, whilst, it delivers only the minimum capacity (e.g., see Fig. 4 between 14:00 and 16:00). In contrast, when the CHP was scheduled to provide the minimum electrical power, it delivered the maximum power. This behavior creates a very large imbalance volume, of the order of 40 MW. The aim of this large imbalance volume is to profit from the price difference between the day-ahead and balancing markets. This occurs because the VPP operator does not have enough information regarding the reactions of other market players. The imbalance prices are calculated ex-post once the total system imbalance is known. If, for example, the VPP operator expects large imbalance prices at a certain hour (meaning that the system is short) he, as well as other market participants, might decide to create large positive deviations from the DA schedule. This might result in an overcompensation of the system leading to surplus of energy which is generally characterized by very low imbalance prices. As a consequence, the VPP will not only lose profits due to the low imbalance prices, but also forfeit the opportunity to trade larger amounts of energy in the day-ahead market. Similar results are reported in [23] and [24] .The authors of [23] and [24] agree that, though the results are ‘optimal’ from a modeling perspective, a real player will have several reasons to avoid this behavior. One of these reasons, apart from the profit loss, is that, as mentioned before, the TSO expects unbiased bids from the market player. If the TSO realizes that a player is performing arbitrage, he can be penalized. The reason for this is that the imbalance market will be affected if several players behave this way. For these reasons, a penalty function is implemented to limit the imbalance volume caused by the VPP. In the present work, a piecewise linear function is used to limit the imbalance volume, as in [23]. This function emulates the expected behavior of the market by penalizing large deviations from the DA schedule. The penalty function is illustrated in Fig. 5. This function is regarded in [23] as a type of risk model named ‘shortfall cost’. Thus the value of the parameters d1t;s;r , d2t;s;r , d3t;s;r , dev 1 ; dev 2 and dev 3 , shown in Fig. 5, depends completely on the preferences of the user. In this particular case, if the total imbalance is between 0% and 20% of the total installed capacity, the resulting penalization is equal to 3% of the day-ahead price. For deviations between 20% and 30% the penalty is equal to the day-ahead price realization. From 30% and above, the marginal penalty is 10 times the value of the day-ahead price. As such, a player will only deviate from his DA schedule if large profits are to be expected. The following constraints are added to the model in order to include the penalty function. First, the absolute value of the total imbalance is split in the three pieces that comprise the penalty function d1t;s;r , d2t;s;r , d3t;s;r as shown in Eq. (25):
Fig. 5. Shortfall cost function. This piecewise linear function was used to penalize imbalance volumes [23]. Large deviations from the DA schedule are strongly penalized.
8t; 8s; 8r : jDE_ IMB t;s;r j ¼ d1t;s;r þ d2t;s;r þ d3t;s;r
ð25Þ
Splitting the imbalance volume makes it possible to penalize large imbalances more than the small deviations as shown in Eq. (26): DA 8t; 8s; 8r : C DEV t;s;r ¼ ð0:3 d1t;s;r þ d2t;s;r þ 10 d3t;s;r Þ pt;i Dt
ð26Þ
In this equation C DEV t;s;r corresponds to the total imbalance penalty. The variables d1t;s;r ,d2t;s;r andd3t;;r are constrained using Eqs. (27)– (29):
8t; 8s; 8r : d1t;s;r 6 dev 1 E_ VPP max
ð27Þ
8t; 8s; 8r : d2t;s;r 6 ðdev 2 dev 1 Þ E_ VPP max
ð28Þ
8t; 8s; 8r : d3t;s;r 6 ðdev 3 dev 2 Þ E_ VPP max
ð29Þ
where dev 1 ; dev 2 and dev 3 represent the percentage deviation of the schedule with respect to the total installed capacity of the VPP E_ VPP ; in this case 20%, 30% and 100%, respectively. max
Finally, the deviation penalty or shortfall cost is included in the objective function as follows:
8t; 8s; 8r; 8i : max obj ¼
S R I T X X X X OP DEV IMB ks kr ki RDA t þ Rt;s;r;i C t;s;r C t;s;r s¼1
r¼1
i¼1
t¼1
ð30Þ
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J. Zapata Riveros et al. / Energy Conversion and Management 103 (2015) 408–418 Table 3 Day-ahead profit, fuel cost and imbalance profit for the different bidding cases and studied seasons. [k€/week]. Summer
Intermediate
Winter
Static
Flexible DA
Flexible RT
Static
Flexible DA
Flexible RT
Static
Flexible DA
Flexible RT
DA revenues RES DA revenues CHP Fuel cost Imbalance revenues
62.9 82.2 96.3 1.3
64.8 85.2 95.5 1.1
64.8 85.2 91.7 1.3
62.5 146.1 193.9 5.6
62.0 146.4 191.6 4.9
62.0 146.4 180.8 4.3
34.9 305.1 416.8 4.7
34.7 303.9 415.8 1.57
34.7 303.9 398.9 1.3
Total profits
47.5
53.4
59.6
9.1
11.9
23.3
81.5
78.8
58.9
Recall that, when applied to the ‘flexible RT’ case, the previously stated Eqs. (25)–(30) are dependent also on the imbalance price scenarios. The resulting DA schedule and actual dispatch using the designed penalty function are depicted in Fig. 6. The results correspond to the same analyzed scenario in the intermediate season shown in Fig. 4. It can be concluded that using a volume penalty function decreases the deviation between the day-ahead schedule and actual dispatch thus, more realistic day-ahead market bids are obtained. In Section 2, further results using this model are reported.
3. Results and discussion As stated in Eq. (1) the total profits of the studied VPP can be estimated as the profits for trading the electricity in the day-ahead and imbalance market minus the operational cost. These figures are broken down in Table 3 for each of the studied strategies, for each of the weeks considered in the case study. Table 3 shows that the operation of the VPP leads to economic profits during all seasons except for winter. During winter, due to the large heat demand, the total revenues are not enough to offset the fuel cost due to the large heat demand. Nevertheless, it is important to recall that this cost should be reimbursed through sale of heat. Thus, the minimum heat unit cost that should be charged to the consumer, to cover at least the operational cost of the district heating during winter, lies between 9.5 €/MW h and 13.6 €/MW h.5 During the other seasons this heat unit cost is negative. However, it is important to remember that in this work, the investment and maintenance costs are not taken into account. In addition, from Table 3, it can be deduced that in comparison with the ‘static’ operation, the ‘flexible DA’ operation results in a profit increase during summer (5900 €/week) and the intermediate season (2800 €/week).6 Furthermore, during winter the profit increase (2700 €/week) is low when compared to the total fuel cost of this season.7 The largest profits are achieved when the ‘flexible RT’ operation is applied. During winter the difference between the ‘flexible RT’ operation and the ‘static’ case amounts to 22,600 €/week, approximately 5% of the fuel cost. As explained before, the main difference between ‘flexible DA’ and ‘flexible RT’ relies on the information available at the moment of taking the dispatch decisions. Fig. 7 illustrates this further. The first column corresponds, to the ‘static’ case, the second column to the ‘flexible DA’ case and the third column to the ‘flexible RT’ strategy. Results showed were obtained for a specific imbalance price scenario, between 8:00 and 14:00 during the intermediate 5 The heat unit cost was estimated dividing the total operational cost by the heat demand of the season. 6 Recall that the fuel cost in these seasons is of the order of 96,000 €/week in summer and 192,000 €/week in the intermediate season thus, the profit change represent only 6% and 1.5% of this cost. 7 During winter the total fuel cost is of the order of 416,000 €/week, consequently the profit decrease corresponds only to a 0.6% of this cost.
season. The upper panels illustrate both the day-ahead and real time electrical power generation of the CHP.8 The same parameters are depicted in the second panel for the RES based generation. The total remaining imbalance (RES forecast error plus CHP deviation) is shown in the third panel. Finally, in the bottom panels the DA and imbalance prices are shown. Looking at the figures it can be observed that the ‘flexible DA’ strategy uses the cogeneration unit to compensate the lack of generation of the RES. This is done by increasing the output of the CHP on real time. The remaining imbalance is zero. This is done because during the dispatch optimization (re-evaluation) the ‘flexible DA’ strategy does not have information on a specific imbalance price scenario, but on a large set of scenarios that can take positive or negative values and thus, it decides to minimize the total imbalance volume. In contrast, in the ‘flexible RT’, the CHP does not compensate for the lack of generation of the RES but decreases its generation to create a larger negative imbalance. The reason for creating this negative deviation is the low imbalance tariff that appears in this scenario. A low imbalance penalty is an indication that the system is long. Thus when the CHP generates a negative imbalance, it not only increases the profits of the VPP operator by saving fuel cost, as shown in Table 3, but it also helps the grid to alleviate the total system imbalance. The behavior of the different bidding strategies among the three studied seasons is illustrated in Fig. 8. The first figure shows the heat demand (gray area), the thermal power generated by the CHP (blue line) and boiler (red area) and the thermal power charge to (negative values) or discharge from (positive values) the storage tank (blank line) of a characteristic day of each week. The illustrated parameters correspond to the dispatched amounts for a specific scenario combination. During the winter, due to the large heat demand, the CHP is running almost continuously at full load leaving less flexibility available. This explains why implementing the ‘flexible DA’ strategy during this season does not lead to a large profit increase when compared against the ‘static’ strategy. On the other hand, Table 3 also shows that the cost reduction achieved using the ‘flexible RT’ operation is related to a decrease in the fuel cost. This is also visible in Fig. 8, during the intermediate and winter seasons. In comparison with the other strategies, in real time, the ‘flexible RT’ operation uses the CHP less, activating the boiler more often. As the day-ahead schedule of both the ‘flexible DA’ and ‘flexible RT’ is the same, it can be deduced that the ‘flexible RT’ operation decreases its output, generating negative imbalance in order to obtain benefits from the imbalance prices. As explained before, creating an additional imbalance does not necessary aggravate the situation of the electric grid (‘passive balancing’). In fact, in Belgium the imbalance prices are an indication of the status of the system. Thus a low imbalance price suggests
8 Recall that the total bid is the combination of the CHP and RES expectation and the heat demand. Nevertheless, for illustration purposes, Fig. 7 shows the CHP and RES generation separately.
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Fig. 6. Resulting DA bid (solid line) and actual dispatch of the CHP (gray area) when using an imbalance volume penalty. This methodology is effective in limiting the schedule deviations.
Fig. 7. Comparison between ‘static’, ‘flexible DA’ and ‘flexible RT’ cases. The upper panel shows both the CHP electrical power bided DA (solid line) and the actual electrical dispatch (gray area). The second pane depicts the expected RES-based generation (solid line) and the actual RES-based output (gray area). The third panel shows the total remaining imbalance of the VPP and finally, the last panel illustrates the day-ahead (black line) and imbalance prices (gray line).
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Fig. 8. Comparison of the heat flow for the different strategies. The gray area corresponds to the thermal demand. The blue line represents the thermal power output of the CHP. The black line shows the average power charge to (negative values) or discharged from (positive values) the storage tank. Finally, the red area corresponds to the thermal power provided by the auxiliary boiler. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
that there is surplus of generation in the grid. As a result, by slightly decreasing the output of the CHP, the VPP owner is not only saving fuel but also helping the grid and will be remunerated for this via the imbalance mechanism.
4. Conclusions and further work This work was focused on developing a bidding strategy for a VPP composed by a CHP–DH and RES generation. The bidding strategies were estimated using stochastic optimization. This optimization takes into account uncertainty regarding RES electric power generation, day-ahead and imbalance prices. As a consequence, the CHP operation was scheduled not only to maximize the profit and cover the heat demand but also to compensate for the possible forecast errors of the RES based-generation. Three different strategies were assessed: ‘static’, ‘flexible DA’ and ‘flexible RT’ operation. In the first strategy the RES forecast errors are settled in the imbalance market and the CHP flexibility provided by its thermal storage tank is not used. The other
strategies use this flexibility to accommodate the forecast errors. In the ‘flexible DA’ case the CHP is rescheduled only once when accurate information regarding the RES generation is obtained without knowledge on the imbalance prices. On the other hand, the ‘flexible RT’ adjusts the CHP output every time step depending on the actual imbalance price and RES-based generation. These strategies were applied to a hypothetical case study that uses the Belgian city of Leuven as an example. The results of the ‘flexible DA’ case show a profit increase during summer (5900 €/week) and the intermediate season (2800 €/week), to be compared against the total fuel cost in these seasons (96,000 €/week in summer and 192,000 €/week during the intermediate season). In contrast, during winter the difference between the ‘static’ and the ‘flexible DA’ case is low compared with this fuel cost. Better results are obtained when the ‘flexible RT’ strategy is applied. In this case when the VPP is allowed to react to the imbalance prices, thereby changing its position close to real time, the profits increase in all seasons. This indicates that CHP–DH could help not only to reduce the cost due to the forecast errors but may also help the grid to reduce
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the system imbalance. However, this economic advantage should be valued against the additional investment needed to perform the accurate control on real time basis. Further work should assess the investment, maintenance and operational costs needed to perform real time control and the effects of considering other technologies such as heat pumps in the VPP. Additionally, estimating the impact of passive balancing on the remaining imbalance of the system was out of the scope of this work. References [1] Vandevyvere H, Jones PT, Aerts J. Leuven Klimaat neutraal; 2013.
[10] Garcia-Gonzalez J, de la Muela RMR, Santos LM, Gonzalez AM. Stochastic joint optimization of wind generation and pumped-storage units in an electricity market. Power Syst, IEEE Trans 2008;23(2):460–8. [11] Pandzˇic´ H, Morales JM, Conejo AJ, Kuzle I. Offering model for a virtual power plant based on stochastic programming. Appl Energy May 2013;105:282–92. [12] Stad Leuven Directie Data- en Facilitair Beheer, Internal Document; 2013. [13] Woods P, Riley O, Overgaard J, Vrins E, Sipil K, Stobart R, Cooke A. A Comparison of distributed CHP/DH with large-scale CHP/DH. IEA District Heating and Cooling Project Annex VII. [14] Synergrid, Statistieken en gegevens – Synthetic Load Pro les.. [15] Haeseldonckx D, Peeters L, Helsen L, D’haeseleer W. The impact of thermal storage on the operational behaviour of residential CHP facilities and the overall CO2 emissions. Renew Sustain Energy Rev 2007;11:1227–43. [16] Elia, ; 2014. [17] BELPEX Belgian Power Exchange, . [19] Pinson P, Nielsen HA, Møller JK, Madsen H, Kariniotakis GN. Non-parametric probabilistic forecasts of wind power: required properties and evaluation. Wind Energy Nov. 2007;10(6):497–516. [20] Ma X-Y, Sun Y-Z, Fang H-L. Scenario generation of wind power based on statistical uncertainty and variability. Sustain Energy, IEEE Trans 2013;4(4):894–904. [21] Bruninx K, Delarue E, D’haeseleer W. A practical approach on scenario generation & reduction algorithms based on probability distance measures – the case of wind power forecast errors. working paper ; 2014. [22] Conejo AJ, Carrión M, Morales JM. Decision Making Under Uncertainty in Electricity Markets. Int Ser Oper Res Manage Sci, vol. 153. Boston, MA: Springer US; 2010. [23] Fleten S-E, Pettersen E. Constructing bidding curves for a price-taking retailer in the norwegian electricity market. Power Syst, IEEE Trans 2005;20(2):701–8. [24] Vardanyan Y, Soder L, Amelin M. Hydropower Bidding Strategies to Day-Ahead and Real-Time Markets: Different Approaches. Database and Expert Systems Applications (DEXA), 2013 24th International Workshop on; 2013. p. 209–13.
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Bidding strategies for virtual power plants considering CHPs and intermittent renewables J. Zapata Riveros, K. Bruninx, K. Poncelet, W. D’haeseleer ⇑ University of Leuven (KU Leuven) Energy Institute, TME Branch, Heverlee, Belgium Energyville (joint venture of VITO NV and KU Leuven), Genk, Belgium
a r t i c l e
i n f o
Article history: Received 22 March 2015 Accepted 26 June 2015
Keywords: Virtual power plant Cogeneration Renewable energy Imbalance markets Stochastic programming
a b s t r a c t Energy efficiency and renewable-energy sources (RES) are fundamental parts of the European energy policy. For this reason, efficient distributed generation technologies such as combined heat and power coupled to district heating (CHP–DH) and RES based electricity are largely promoted. Additionally, the flexibility that CHP–DH offers to the power system is seen as an option to balance the intermittent output of RES-based generation. This could be done by aggregating RES based electricity generation and CHP DH in a virtual power plant (VPP). In this framework, the present work presents a methodology to evaluate the optimal bidding strategy of a VPP composed of a CHP–DH and RES based generators. The objective is to investigate the optimal bidding strategy for a VPP that uses CHP DH to compensate for the uncertainties regarding RES-based electricity generation and market prices. The VPP operator nominates its energy to the day ahead market the day before the actual delivery (D-1). In real time, any deviation from the day-ahead schedule is settled in the imbalance market. The uncertainties are modeled using a two stage stochastic programming approach. Three different bidding strategies are studied: ‘static’, ‘flexible DA’ and ‘flexible RT’. The major difference between the studied strategies lies in the dispatch decisions. The ‘static’ strategy does not adjust the scheduled output of the CHP. Whereas, the ‘flexible DA’ and ‘flexible RT’ strategies differ from each other in terms of the information available at the moment of performing the reschedule (second stage decision). The ‘flexible DA’ reschedules the CHP output for the whole day assuming full knowledge of the RES scenario, but under uncertainty regarding the imbalance price. The ‘flexible RT’ strategy allows the VPP to adjust its position at each time step depending on the RES generation and imbalance price scenarios. The results show that in comparison with the ‘static’ strategy, the ‘flexible DA’ operation results in a profit increase during summer (5900 €/week), the intermediate season (2800 €/week) and winter (2700 €/week). This increase is moderate when compared against the total fuel cost in these seasons. Better results are obtained when the ‘flexible RT’ strategy is applied. Using this strategy larger profits are achieved for all seasons. For instance, during winter the difference between the ‘flexible RT’ operation and the ‘static’ case amounts to 22,600 €/week, approximately 5% of the fuel cost. Ó 2015 Published by Elsevier Ltd.
1. Introduction In the fight against climate change, the European Union (EU) has committed itself to reach a set of targets set under the Climate and Energy Package. This package, also known as the ‘‘20-20-20’’ package, sets three main objectives for 2020: a 20% reduction in EU greenhouse gas emissions based on the 1990 level; ⇑ Corresponding author at: University of Leuven (KU Leuven) Energy Institute, TME Branch, Heverlee, Belgium. Tel.: +32 16 322510; fax: +32 16 3 22985. E-mail address: [email protected] (W. D’haeseleer). http://dx.doi.org/10.1016/j.enconman.2015.06.075 0196-8904/Ó 2015 Published by Elsevier Ltd.
raising the share of EU end energy originated from renewable resources to 20% and a 20% improvement in energy efficiency. In this context, it is assumed that combined heat and power (CHP) devices connected with district heating (DH) can play an important role [1]. Furthermore, photovoltaic (PV) facilities and wind farms are seen as a partial replacement of fossil fuel-based electricity generation. The present paper aggregates a hypothetical CHP connected to district heating with a large amount of RES based electricity generators, in a virtual power plant (VPP). In [2] a virtual power plant is defined as an agglomeration of distributed generators, controllable
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Nomenclature Symbol
ae aq ct;n DE_ IMB t;s;r DE_ RES t;x DQ_ CHP t;s;r DQ_ BOILER t;x Dt
gq gsto ki kr ks
definition units electrical efficiency of the CHP (%) thermal efficiency of the CHP (%) on/off status of the CHP (–) electricity traded in the balancing market (MW) difference between RES electric power scheduled and dispatched (MW) difference between the planned and delivered thermal power of the CHP (MWth) difference between the planned and delivered thermal power of the boiler (MWth) time step of the optimization (15 min) (h) thermal efficiency of the boiler (%) storage tank loss factor (%) probability of the imbalance scenarios (%) probability of the renewable scenarios (%) probability of the day-ahead scenarios (%)
pIMB t;i pDA t;s pFUEL t
imbalance market price (€/MW h)
C DEV t;s;r C OP t;s;r start up C t;n
deviation penalty (€)
dev n
limits of the piecewise deviation function (%)
dxt;s;r
components x of the piecewise deviation function (MW)
EVPP max E_ RT t;s;r E_ CHP
installed capacity of the VPP (MW) electricity generated on real-time (MW)
t
day-ahead market price (€/MW h) gas prices (€/MW h) operational cost of the CHP (€) start-up cost (€)
E_ DA t E_ RES
total electric power traded in the DA market (MW)
n F_ CHP t;n _F BOILER
primary fuel consumption of the CHP plant (MW)
i Q_ CHP
index i, set of imbalance price scenarios (€/MW h)
Q_ BOILER t
thermal power generated by the auxiliary boiler (MWth)
Q SOC t;s;r Q_ CH
state of charge of the storage (MW hth)
RIMB t;s;r
imbalance market profits (€)
RDA t
day-ahead market profits (€)
r s
renewable energy scenarios (MW) day-ahead prices scenario (€/MW h)
t
t
t;n
t;s;r;
RES electric power traded in the DA market (MW) primary fuel consumption of the boiler (MW) thermal power generated by the CHP (MWth)
thermal (dis)charging power to the storage tank (MWth)
Acronyms CHP combined Heat and Power District Heating DA day-ahead DH district heating EU European Union PHSP pumped hydro storage plant PV photovoltaic RES renewable energy sources RT real time SOC state of charge TSO transmission system operator VPP virtual power plant WPP wind power plant
expected electricity generated by the CHP (MW)
loads and storages devices, aggregated in order to operate as a single power plant and being able to participate in the power exchange market. According to [2] the use of a VPP can bring benefits such as increasing the flexibility available in the electric power system without a large investment in infrastructure. It is also mentioned that the VPP operation could help to displace the fossil generation during peak hours and solve grid balance problems [2]. Nevertheless, all the benefits expected from the VPP operation depend largely on the interaction between the VPP and the electric power market. Currently, the largest volume of energy is traded the day before (D-1) on the day-ahead market which consequently has the largest liquidity. The day-ahead market is supervised by the transmission system operator (TSO). The TSO expects that the participants give unbiased bids; this means that the nominations should equal the expected generation. The deviations between demand and generation are settled in the imbalance market which is controlled by the TSO. In order to incentivize the participants to reduce their imbalance, imbalance tariffs are in place. The TSO has the final responsibility to keep the balance between generation and consumption. To achieve this task, a certain amount of capacity has to be kept steady (idle or offline). These reserves are activated in case of positive (generation surplus) or negative (lack of generation) imbalance. The price that the TSO pays to the reserves providers1, is transferred directly as imbalance tariff to penalize those players that caused the imbalance. 1 In Belgium, these prices correspond to the maximum price paid for up regulation (Marginal incremental price) and the minimum received for down regulation (Marginal decremental price).
Trading in the power exchange market brings along several uncertainties, specifically due to errors in the forecast of RES-based electricity generation and the uncertain evolution of the day-ahead and imbalance prices. The objective of this paper is to develop a methodology to coordinate the participation of CHP–DH and RES in the day-ahead market (DA) and to compare different bidding strategies for the VPP, exploiting the flexibility of CHP-DH to compensate for the uncertainty on day-ahead prices, RES-based generation forecast and imbalance tariffs. The uncertainties are explicitly modeled using a two-stage stochastic program. Toward this aim, two different bidding approaches will be considered: ‘static’ and ‘flexible’ VPP operation. In the first ‘static’ strategy, the electric power delivered by the CHP in real-time is equal to the DA schedule. Consequently, the resulting imbalance that stems from renewables forecast errors is settled in the imbalance market. On the other hand, in ‘flexible’ operation the CHP is allowed to reschedule its electric output in order to compensate for the forecast error on RES-based electricity generation. Thus the total imbalance volume might be reduced. Furthermore, it is considered that the rescheduling can be performed at two different moments in time. In the ‘flexible DA’ case it assumed that the CHP schedule is adjusted just once after having a more accurate idea of the realization of the RES generation but not of the imbalance prices. On the other hand, the ‘flexible RT’ case, where RT stands for real time, considers that the rescheduling is done every time step once the actual imbalance price and RES-based generation profile are known. In the literature, several studies about optimal bidding strategies and imbalance cost minimization can be found. For instance,
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the optimal dispatch of industrial cogeneration devices in a liberalized market is studied in [3]. The benefits of using a micro-CHP device to balance the portfolio of a VPP (‘self-balancing’) are assessed in [4,5]. Both studies report little or no incentive for ‘self-balancing’. Nevertheless, these studies are based on deterministic techniques that disregard the uncertainties of the system. Taking uncertainties into account could make the ‘self-balancing’ approach more valuable. Stochastic programming has been extensively used to thoroughly account for uncertainties. The case of optimal wind power integration in the electric power system has been extensively studied [6–9]. In [7] stochastic programming is used to generate an optimal bid for a short-term power market. Results show that using a stochastic approach leads to higher profits compared with a deterministic methodology. Similarly, [8] considers the bidding of a wind power plant (WPP) in the different energy markets (i.e., day-ahead, intraday and balancing market). In addition, [6] includes a risk aversion model to analyze the different optimal offering strategies of a WPP depending on the risk attitude. In [6–9] only wind generators are studied. Joint participation of a WPP and dispatchable generators is an interesting field of study. The case study in [10] consists of a wind farm and a pumped hydro storage plant (PHS). The authors of [10] use two-stage stochastic programming to account for the uncertainties in the day-ahead prices and wind power. However, it does not take into account the available information regarding imbalance prices. The results show that aggregating WPP and PHS can lead to larger profits and reduce the imbalance cost. From the reviewed literature only one model [11] considers simultaneously imbalance price and wind power forecast uncertainties as well as coordinated participation in the day-ahead market. The authors propose a two-stage stochastic optimization of a VPP that aggregates a WPP with a PHS and a conventional electric power plant. The results show substantial profits increase when these power plant operate together. Nevertheless it does not assess the benefits that a VPP can obtain from using its flexibility in real-time to react to the imbalance prices, nor the specific interaction with a heat demand (CHP unit). Compared to the literature, the contributions of this paper are: A stochastic program that coordinates the operation of RES generators with a CHP used for DH including uncertainties in day-ahead prices, imbalance prices and renewable energy generation and the specific constraints characteristics of a DH system (e.g., the heat demand should be met all the time). A comparison between three different bidding strategies: a ‘static’ case in which no rescheduling for balancing the forecast error is implemented, a ‘flexible DA’ that assumes uncertainty regarding imbalance prices when rescheduling the CHP and a ‘flexible RT’ case in which it is assumed that the VPP can react to the imbalance prices. The paper continues as follows: Section 1 provides a detailed description of the optimization model and the characteristics of the case study. The results are presented and discussed in Section 2. Finally, Section 3 presents the conclusions and suggestions for further work.
HEAT BUFFER
BOILER
The present study assesses the optimal dispatch of a hypothetical virtual power plant in Belgium. The VPP system consists of a CHP–DH together with uncontrollable RES based electricity generation (i.e., photovoltaic and wind energy). Fig. 1 gives an overview of the studied system. The CHP–DH plant or CHP system consists of
CHP
Electricity Heat
RES
Fig. 1. Distribution of the electricity and heat connections for the studied case. The CHP system is composed of a prime mover, an auxiliary boiler and a thermal buffer. The electricity generated is traded in the electricity market.
a prime mover, an auxiliary boiler and a thermal storage unit that meet the heat demand of the community. The electricity generated by the VPP is sold in the electric power market. In other words, the DH plant is not responsible for meeting the electrical demand of the community. The VPP controller makes a nomination on the day-ahead market considering the expectations for renewable energy generation in its portfolio, DA and imbalance prices, while the heat demand is assumed to be known. During real time, the deviations between the day-ahead nomination and the actual dispatch have to be settled in the balancing market and/or by changes in the output of the CHP. In order to account for the uncertainties that the VPP faces, a stochastic program is developed. In a stochastic program the uncertainty is represented using a set of scenarios. The stochastic program studied in this work is illustrated in Fig. 2. When bidding electricity in the day-ahead market, the decision process can be split into two different stages. In the first stage, the decisions have to be taken under uncertainty regarding the future RES generation and prices. In this study, the first stage decisions correspond to the day-ahead bidding. The day-ahead bid (i.e., first-stage decision) is obtained using a combination of 10 day-ahead, 10 imbalance and 10 renewables scenarios which result in a total of 1000 scenarios. During the second stage, the day-ahead prices are known. It t is also assumed that at this point the VPP operator has a more accurate forecast regarding the realization of the RES based generation and thus decisions regarding the dispatched volume are taken.
Decision:
DA bid
Known parameter: Uncertain parameter:
2. Methodology
ELECTRICITY GRID
Imbalance volume
Day-ahead prices, RES generation Day-ahead prices, RES generation, Imbalance price
Imbalance prices
FIRST STAGE
SECOND STAGE
Imbalance prices
Fig. 2. Two-stage stochastic programming for the VPP. The first stage decisions correspond to the day-ahead bids, whereas the second stage decisions are related to the actual dispatch.
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Fig. 3. During the first stage decision process the DA bid is obtained. Afterwards the results are evaluated in a larger set of scenarios and the second-stage decisions (or the actual dispatch) are taken.
Table 1 Summary of the different bidding strategies: ‘static’, ‘flexible DA’ and ‘flexible RT’. Case
Dispatch
Information available during dispatch (2nd stage)
Static Flexible DA
Dispatch equals to DA schedule One dispatch per RES scenario
Flexible RT
One dispatch per RES and imbalance price scenario
No
The second stage decisions or actual dispatch decisions are obtained in a ‘re-evaluation’ process. This process is performed once the day-ahead bid is obtained (i.e., after the first-stage decisions are taken) and it makes use of a larger set of scenarios (50 imbalance and 50 renewables scenarios). Fig. 3 visualizes the entire optimization process. Three different bidding strategies are studied: ‘static’, ‘flexible DA’ and ‘flexible RT’ as stated in Table 1. The major difference between the studied strategies lies in the second stage decision process. The ’static’ strategy does not adjust the scheduled output of the CHP. On the other hand, the ‘flexible DA’ and ‘flexible RT’ strategies have the same day-ahead bid. They differ from each other in the information available at the moment of performing the reschedule (second-stage decision). The ‘flexible DA’ reschedules the CHP output for the whole day depending on the RES scenario, but under uncertainty regarding the imbalance price. The ‘flexible RT’ strategy allows the VPP to adjust its position at each time step depending on the RES generation and imbalance price scenarios which are assumed to be known. The ‘flexible RT’ case is performed using a rolling-horizon approach; at each time step once the observed imbalance prices of each scenario are obtained, the dispatch decisions are taken. It is important to remark that both the ‘flexible DA’ and ‘flexible RT’ correspond to two extreme cases. When deciding on the actual dispatch, the ‘flexible DA’ assumes that the VPP operator has no knowledge regarding the imbalance prices. In contrast, the ‘flexible RT’ assumes complete knowledge of the imbalance prices for the current time step. In reality, every 3 min the Belgian TSO provides actualized information on the current imbalance volume. From this information the VPP can obtain a very accurate forecast of the imbalance price in order to perform ‘passive balancing’2. However, the forecast can still deviate from the actual imbalance price as the response of other market participants is unknown and thus the real benefits lie between the economic savings of these two cases ‘flexible DA’ and ‘flexible RT’ operation. This stochastic optimization procedure was formulated as a mixed integer linear program (MILP). The model has been devel2 Passive balancing is a measure implemented by the Belgian TSO to allow the market participants helping to reduce the total system imbalance in real time.
reevaluation Day-ahead price RES-based generation Day-ahead price RES-based generation Actual imbalance price
oped in GAMS, and is solved using the commercial solver CPLEX.
2.1. Stochastic optimization model The objective is to maximize the revenues obtained by the VPP as stated in Eq. (1):
8t; 8s; 8r; 8i : max obj ¼
S R I T X X X X OP IMB ks kr ki RDA t;s þ Rt;s;r;i C t;s;r s¼1
r¼1
i¼1
ð1Þ
t¼1
In this equation, T is the time horizon, in this particular case, two days from which only the first one is implemented (the second day is considered to enforce an optimal behavior in the storage tank). The studied time period is divided in 15 min time steps. Furthermore in Eq. (1), S, R and I represent the sets of scenarios of day-ahead prices, RES-based generation and imbalance prices, respectively. The net profit results from the difference between the revenues obtained in the DA and imbalance (IMB) market RDA and RIMB t t;s;r respectively and the operational cost of the CHP–DH C OP t;s;r . Recall that RIMB t;s;r is the result from settling the deviations between the planned and delivered electricity in the imbalance market; for this reason, this variable can take positive or negative values. The revenues are weighted over all scenarios. The probability of occurrence of each scenario is equal to ks for the day-ahead prices scenarios, kr for the RES generation scenarios and ki for the imbalance price scenarios. The electric power scheduled to be traded on the day-ahead market E_ DA is calculated in Eq. (2): t
_ CHP þ E_ RES 8t : E_ DA t ¼ Et t
ð2Þ
In this equation, E_ CHP corresponds to the scheduled electric power t output of the CHP and E_ RES to the traded RES generation. It is import
tant to remark that the electric power scheduled to be traded on the day-ahead market E_ DA does not depend on the scenarios, as it is a t
first-stage decision.
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On the other hand, the DA RES nomination E_ RES is limited to the t maximum and minimum possible values achieved by the RES scenarios at each time step.
8t : E_ RES ¼0 t
ð3Þ
8t : E_ CHP ¼ t
or
8t :
min r
E_ RES t;r
max _ RES Et;r 6 E_ RES t 6r
ð4Þ
where E_ CHP t;s;r is the actual electricity dispatched by the CHP. The imbalance error DE_ IMB t;s;r represents the difference between the actual electric power generated and the day-ahead schedule. This is expressed in Eq. (5):
_ RT _ DA 8t; 8s; 8r : DE_ IMB t;s;r ¼ Et;s;r Et
ð5Þ
The profits are calculated as the sum of the revenues obtained from trading electricity in the day-ahead market and the imbalance market as stated in Eqs. (6) and (7):
_ DA DA 8t : RDA t;s ¼ Et pt;s Dt
ð6Þ
_ IMB IMB 8t; 8s; 8r; 8i : RIMB t;s;r;i ¼ DEt;s;r pt;i Dt In Eqs. (6) and (7)
p
DA t;s
ð7Þ
corresponds to the day-ahead price and
pIMB t;i to the imbalance price in [€/MW h]. The imbalance revenues can be either negative or positive depending on the nature of the system imbalance (SI) and the imbalance tariff. In addition Dt is the time step of the simulation, in this case 15 min. The heat balance is described in Eq. (8):
_ BOILER ¼ Q_ demand þ Q_ CH þ DQ_ CHP 8t; 8s; 8r : Q_ CHP þ Q_ BOILER t t t;s;r þ DQ t;s;r t t;s;r
According to this equation the optimization must ensure that the heat demand is met during every time step for all the scenarios, using the CHP Q_ CHP , the boiler Q_ BOILER or the heat that is charged to t
or discharged from the thermal storage buffer Q_ CH t;s;r . Additionally, CHP BOILER _ _ the variables DQ t;s;r and DQ t;s;r represent the difference between the actual thermal power delivered by the CHP and backup boiler and their planned thermal power output, respectively. The CHP plant is constituted by three internal combustion gas engines. Eq. (9) states the relationship between the electrical and thermal power output of each unit. Similarly, Eq. (10) links the primary energy use to the thermal and electrical power production. Looking at this equation is clear that once the optimal electrical output is selected, simultaneously the thermal output is settled and vice versa.
_ CHP aE c 8t; 8n : E_ CHP t;n t;n ¼ Q t;n
ð9Þ
aQ
n 8t; 8n : F_ CHP ¼ t;n
E_ CHP t;n
aE
ct;n ¼
Q_ CHP t;n
aQ
ð11Þ
t;n
8t : F_ CHP ¼ t
N chp X n F_ CHP t;n
ð12Þ
n¼1
The start-up cost is calculated using Eq. (13):
8t; 8n : C start t;n
up
P pstart t;n
up
ct;n ct1;n
ð13Þ
up In this Equation pstart is a positive parameter that represents a t;n fixed cost for starting up the machines. In addition, the minimum up and down times of the CHPs are taken into account as follows. For each individual CHP unit, new sets k and l are created:
k ¼ ½1; 2; . . . ; UT n
ð14Þ
l ¼ ½1; 2; . . . ; DT n
ð15Þ
In these equations, UT n and DT n represent, respectively, the minimum up-time and down-time of each CHP unit, being one hour in this particular case (UT n ¼ DT n ¼ 4). The constraints on the minimal up and down time can be written as:
cn;t cn;t1 cn;tþk 6 0
ð16Þ
cn;t1 cn;t cn;tþl 6 1
ð17Þ
The fuel consumption of the boiler in Eq. (18):
F_ BOILER t
is calculated as shown
_ BOILER
Q 8t : F_ BOILER ¼ t t
gboiler
ð8Þ
t
Nchp X E_ CHP n¼1
The actual electricity dispatched E_ RT t;s;r depends on the realization of the scenarios as stated in Eq. (4):
_ CHP _ RES 8t; 8s; 8r : E_ RT t;s;r ¼ Et;s;r þ Et;r
The total electricity generation E_ CHP and primary energy F_ CHP use t t of the CHP plant are estimated as the sum of the total electricity generation and fuel consumption among the individual units, as stated in Eqs. (11) and (12):
ð18Þ
;
It is assumed that the boiler has constant efficiency gboiler . The total operational cost of the system is estimated as the sum of the primary energy cost of the CHP system and the start-up cost; see Eq. (19):
FUEL _ BOILER þ C start 8t : C OP Dt F_ BOILER þ F_ CHP þ DF_ CHP t t t;s;r þ DF t;s;r t;s;r ¼ pt t
up
ð19Þ _ BOILER correspond to the fuel use differIn Eq. (19) DF_ CHP t;s;r and DF t;s;r ence that appears when the CHP system is rescheduled and is the fuel price, which is assumed to be constant.
pFUEL t
The state of charge (SOC) of the storage tank Q SOC t;s;r is calculated using Eq. (20). The efficiency of the storage tank.3 gst is assumed to be constant. Recall that Q_ CH is the average thermal power (kWth) t;S;r
that is charged to/discharged from the storage tank during every time step; consequently, it can take both positive or negative values: SOC _ CH 8t; 8s; 8r : Q SOC t;s;r ¼ gst Q t1;s;r þ Q t;s;r Dt
ð20Þ
Eqs. (21) and (22) ensure that the optimization does not exceed the operational limits of the CHP:
ct;n
ð10Þ
_ CHP _ CHP _ CHP 8t; 8n; 8s; 8r : ct;n Q_ CHP min 6 Q t;n þ DQ t;n;s;r 6 Q max ct;n
ð21Þ
n F_ CHP t;n
In these equations, is the primary fuel consumption of each individual CHP unit n, aQ and aE are, respectively, the thermal and electrical efficiency of the CHP plant. ct;n is a binary variable that indicates the on/off status of each CHP unit. This variable is independent of the scenarios and cannot change during real time generation.
3 The efficiency of the storage tank represents the percentage of thermal energy that is preserved by the storage after it has been stored during one time step of 15 min. For example, a storage tank with an efficiency of 90% is charged with 1 kW hth after 15 min, only 0.9 kW hth remains.
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_ CHP _ CHP _ CHP 8t; 8n; 8s; 8r : ct;n E_ CHP min 6 Et;n þ DEt;n;s;r 6 Emax ct;n
ð22Þ
_ CHP _ CHP _ CHP E_ CHP t;n þ DEt;n;s;r and Q t;n þ DQ t;n;s;r correspond to the actual electric output and the actual thermal output of the CHP, respectively. Consequently, if the CHP is in operation, its output is limited to the minimum electricity E_ CHP and heat capacity Q_ CHP and the maximin
SOC 8t; 8s; 8r : 0 6 Q SOC t;s;r 6 Q max
ð23Þ
_ BOILER 8t; 8n; 8s; 8r : 0 6 Q_ BOILER þ DQ_ BOILER t;n t;n;s;r 6 Q max
ð24Þ
In these equations, Q SOC max is the maximum storage capacity of the thermal buffer. Q_ BOILER corresponds to the maximum thermal power max
þ DQ_ BOILER that can be delivered by the boiler whereas, Q_ BOILER t;n t;n;s;r represent the real output of the auxiliary boiler. 2.2.1. Case specific constraints The previously explained equations apply to the ‘flexible DA’ case; in this subsection, the necessary modifications to these equations for the other cases are described. First, the ‘static’ case is modeled by setting the variables DE_ CHP ; DQ_ CHP ; DQ_ BOILER ; DF_ CHP ; DF_ BOILER to zero. In other words, the t;s;r
t;s;r
t;s;r
t;s;r
CHP is not allowed to deviate from its scheduled output. On the other hand, the ‘flexible DA’ and ‘flexible RT’ have the same day-ahead schedule; thus, it is only necessary to modify the equations that involve RT decisions. This is because in ‘flexible DA’ the imbalance volume decision DE_ IMB is considered indepent;s;r
scenarios. In other words, the dent of the imbalance price pIMB t;i imbalance volume is settled before knowing the imbalance prices but with knowledge of the RES generation and day-ahead prices. In contrast, in the ‘flexible RT’ case, the imbalance volume is estimated depending on the imbalance price scenarios and thus several variables become dependent of these scenarios such as: E_ CHP ; E_ CHP ; Q_ CHP ; E_ RT ; Q SOC ; DE_ CHP ; DQ_ CHP ; DQ_ BOILER ; t;s;r;i
t;s;r;i
t;s;r;i
Heat demand RES-based generation
[MW h/week] [MW h/week]
Summer
Intermediate
Winter
1199 1201
2598 1011
6169 879
min
_ CHP mum electricity E_ CHP max and heat capacity Q max . Eqs. (23) and (24) prevent exceeding the operational limits of the storage tank and boiler:
t;s;r
Table 2 Heat demand and RES-based generation of the studied weeks.
t;s;r;i
t;s;r;i
t;s;r;i
t;s;r;i
t;s;r;i
_ BOILER _ IMB DF_ CHP t;s;r;i ; DF t;s;r;i ; DEt;s;r;i and consequently the equations where these variables appear are also dependent on the imbalance tariffs. 2.2. Application to a case study The developed methodology is applied to a hypothetical case study that assumes a large penetration of renewable energy and the installation of a district heating facility in the city of Leuven (Belgium) which resembles a typical small European city. The heat demand profile is approximated through a bottom-up approach. Data concerning the building stock of Leuven, provided by the municipality [12], is combined with heat demand benchmarks [13] and synthetic load profiles [14] to create the heat demand profile. It is assumed that the thermal energy is sold to the community at a constant retail price. As a consequence, they do not influence the optimization results. For this reason these revenues are not included in the optimization. The optimal size of the CHP is estimated using the maximum rectangle method explained in [15]. It is assumed that the DH system is operated by three parallel internal combustion gas engines (ICGE). Each ICGE has a maximum electrical output equal to 18 MWe. The electrical and thermal efficiency are aE ¼ 44% and aQ ¼ 48% , respectively. Regarding the renewable generation it is assumed that the total installed capacity amounts to 20 MWe, of which 14 MWe corresponds to solar panels and 6 MWe to wind turbines. These numbers
reflect the current (2014) proportion of photovoltaic and wind installation in Belgium. The renewable energy scenarios are based on data provided by the Belgian TSO [16]. The optimization will be performed for three different weeks, each representing the behavior of a season (summer, intermediate and winter). The total heat demand and the RES based generation of each of the studied weeks are summarized in Table 2. Finally, the day-ahead and imbalance price scenarios are also based on historic data of the Belgian electricity market [16,17]; the gas price is assumed to be constant and equal to 39 €/MW hth. The gas price corresponds to the average price that was paid by small and medium sized enterprises in 2014 [18]. 2.4. Scenario generation and reduction As mentioned before, to represent the uncertainty that stems from the renewable energy forecast errors, the day-ahead and imbalance prices, the underlying stochastic processes are approximated using a group of scenarios. A scenario corresponds to a possible realization of the stochastic process, thus a large enough scenario representation should capture the variability and uncertainty of the random variables. The statistical scenario generation technique developed in [19,20] and described in detail in [21], is used in this thesis to generate a large set of scenarios. This technique makes use of historical forecast errors (e.g., difference between the forecasted variable and the measured output of this variable during the previous years) to create different scenarios. Once the ‘error scenarios’ are obtained, they are added to the actual forecasted variable (e.g., wind power forecast of the next day) to obtain the different scenarios for each variable (e.g., wind scenarios). Yet, using a large number of scenarios is computationally expensive. Therefore, a reduction technique is necessary to trim down the number of scenarios. Toward this aim, a modified version of the fast-forward scenario reduction algorithm that includes the inherent characteristics of the optimization problem is implemented, as described in [21,22]. For the purpose of this work, a total of 200 day-ahead, 200 imbalance and 200 renewables scenarios were generated independently. Nonetheless, for computational efficiency, the orginal set was reduced to 10 scenarios for each parameter in the first optimization, resulting in a total number of 1000 combinations of scenarios. Afterwards, as explained before, the reevaluation process has used a larger number of scenarios (50 per set) leading to a total of 25,000 (10 day-ahead, 50 imbalance and 50 renewables scenarios) combinations of scenarios to gain statistical significance. 2.5. Limiting the imbalance volume The results obtained when applying the optimization described in 1.1 during the intermediate season for the ‘flexible DA’ case are illustrated in Fig. 4. In this figure, the black line represents the scheduled CHP electrical power, the shaded area corresponds to the actual electrical power delivered by the CHP.4 It can be 4 Keep in mind that the electric energy traded in the day-ahead market is composed of the electricity generated by the CHP, and the RES-based generation. Nevertheless, for illustration purposes only the electricity nominated by the CHP appears in Fig. 4.
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Fig. 4. Resulting original DA bid (solid line) and actual dispatch of the CHP (gray area). The difference between da schedule and real time dispatch creates large imbalance of the order of 40 MW.
observed that at several moments the CHP was scheduled to operate at maximal output, whilst, it delivers only the minimum capacity (e.g., see Fig. 4 between 14:00 and 16:00). In contrast, when the CHP was scheduled to provide the minimum electrical power, it delivered the maximum power. This behavior creates a very large imbalance volume, of the order of 40 MW. The aim of this large imbalance volume is to profit from the price difference between the day-ahead and balancing markets. This occurs because the VPP operator does not have enough information regarding the reactions of other market players. The imbalance prices are calculated ex-post once the total system imbalance is known. If, for example, the VPP operator expects large imbalance prices at a certain hour (meaning that the system is short) he, as well as other market participants, might decide to create large positive deviations from the DA schedule. This might result in an overcompensation of the system leading to surplus of energy which is generally characterized by very low imbalance prices. As a consequence, the VPP will not only lose profits due to the low imbalance prices, but also forfeit the opportunity to trade larger amounts of energy in the day-ahead market. Similar results are reported in [23] and [24] .The authors of [23] and [24] agree that, though the results are ‘optimal’ from a modeling perspective, a real player will have several reasons to avoid this behavior. One of these reasons, apart from the profit loss, is that, as mentioned before, the TSO expects unbiased bids from the market player. If the TSO realizes that a player is performing arbitrage, he can be penalized. The reason for this is that the imbalance market will be affected if several players behave this way. For these reasons, a penalty function is implemented to limit the imbalance volume caused by the VPP. In the present work, a piecewise linear function is used to limit the imbalance volume, as in [23]. This function emulates the expected behavior of the market by penalizing large deviations from the DA schedule. The penalty function is illustrated in Fig. 5. This function is regarded in [23] as a type of risk model named ‘shortfall cost’. Thus the value of the parameters d1t;s;r , d2t;s;r , d3t;s;r , dev 1 ; dev 2 and dev 3 , shown in Fig. 5, depends completely on the preferences of the user. In this particular case, if the total imbalance is between 0% and 20% of the total installed capacity, the resulting penalization is equal to 3% of the day-ahead price. For deviations between 20% and 30% the penalty is equal to the day-ahead price realization. From 30% and above, the marginal penalty is 10 times the value of the day-ahead price. As such, a player will only deviate from his DA schedule if large profits are to be expected. The following constraints are added to the model in order to include the penalty function. First, the absolute value of the total imbalance is split in the three pieces that comprise the penalty function d1t;s;r , d2t;s;r , d3t;s;r as shown in Eq. (25):
Fig. 5. Shortfall cost function. This piecewise linear function was used to penalize imbalance volumes [23]. Large deviations from the DA schedule are strongly penalized.
8t; 8s; 8r : jDE_ IMB t;s;r j ¼ d1t;s;r þ d2t;s;r þ d3t;s;r
ð25Þ
Splitting the imbalance volume makes it possible to penalize large imbalances more than the small deviations as shown in Eq. (26): DA 8t; 8s; 8r : C DEV t;s;r ¼ ð0:3 d1t;s;r þ d2t;s;r þ 10 d3t;s;r Þ pt;i Dt
ð26Þ
In this equation C DEV t;s;r corresponds to the total imbalance penalty. The variables d1t;s;r ,d2t;s;r andd3t;;r are constrained using Eqs. (27)– (29):
8t; 8s; 8r : d1t;s;r 6 dev 1 E_ VPP max
ð27Þ
8t; 8s; 8r : d2t;s;r 6 ðdev 2 dev 1 Þ E_ VPP max
ð28Þ
8t; 8s; 8r : d3t;s;r 6 ðdev 3 dev 2 Þ E_ VPP max
ð29Þ
where dev 1 ; dev 2 and dev 3 represent the percentage deviation of the schedule with respect to the total installed capacity of the VPP E_ VPP ; in this case 20%, 30% and 100%, respectively. max
Finally, the deviation penalty or shortfall cost is included in the objective function as follows:
8t; 8s; 8r; 8i : max obj ¼
S R I T X X X X OP DEV IMB ks kr ki RDA t þ Rt;s;r;i C t;s;r C t;s;r s¼1
r¼1
i¼1
t¼1
ð30Þ
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J. Zapata Riveros et al. / Energy Conversion and Management 103 (2015) 408–418 Table 3 Day-ahead profit, fuel cost and imbalance profit for the different bidding cases and studied seasons. [k€/week]. Summer
Intermediate
Winter
Static
Flexible DA
Flexible RT
Static
Flexible DA
Flexible RT
Static
Flexible DA
Flexible RT
DA revenues RES DA revenues CHP Fuel cost Imbalance revenues
62.9 82.2 96.3 1.3
64.8 85.2 95.5 1.1
64.8 85.2 91.7 1.3
62.5 146.1 193.9 5.6
62.0 146.4 191.6 4.9
62.0 146.4 180.8 4.3
34.9 305.1 416.8 4.7
34.7 303.9 415.8 1.57
34.7 303.9 398.9 1.3
Total profits
47.5
53.4
59.6
9.1
11.9
23.3
81.5
78.8
58.9
Recall that, when applied to the ‘flexible RT’ case, the previously stated Eqs. (25)–(30) are dependent also on the imbalance price scenarios. The resulting DA schedule and actual dispatch using the designed penalty function are depicted in Fig. 6. The results correspond to the same analyzed scenario in the intermediate season shown in Fig. 4. It can be concluded that using a volume penalty function decreases the deviation between the day-ahead schedule and actual dispatch thus, more realistic day-ahead market bids are obtained. In Section 2, further results using this model are reported.
3. Results and discussion As stated in Eq. (1) the total profits of the studied VPP can be estimated as the profits for trading the electricity in the day-ahead and imbalance market minus the operational cost. These figures are broken down in Table 3 for each of the studied strategies, for each of the weeks considered in the case study. Table 3 shows that the operation of the VPP leads to economic profits during all seasons except for winter. During winter, due to the large heat demand, the total revenues are not enough to offset the fuel cost due to the large heat demand. Nevertheless, it is important to recall that this cost should be reimbursed through sale of heat. Thus, the minimum heat unit cost that should be charged to the consumer, to cover at least the operational cost of the district heating during winter, lies between 9.5 €/MW h and 13.6 €/MW h.5 During the other seasons this heat unit cost is negative. However, it is important to remember that in this work, the investment and maintenance costs are not taken into account. In addition, from Table 3, it can be deduced that in comparison with the ‘static’ operation, the ‘flexible DA’ operation results in a profit increase during summer (5900 €/week) and the intermediate season (2800 €/week).6 Furthermore, during winter the profit increase (2700 €/week) is low when compared to the total fuel cost of this season.7 The largest profits are achieved when the ‘flexible RT’ operation is applied. During winter the difference between the ‘flexible RT’ operation and the ‘static’ case amounts to 22,600 €/week, approximately 5% of the fuel cost. As explained before, the main difference between ‘flexible DA’ and ‘flexible RT’ relies on the information available at the moment of taking the dispatch decisions. Fig. 7 illustrates this further. The first column corresponds, to the ‘static’ case, the second column to the ‘flexible DA’ case and the third column to the ‘flexible RT’ strategy. Results showed were obtained for a specific imbalance price scenario, between 8:00 and 14:00 during the intermediate 5 The heat unit cost was estimated dividing the total operational cost by the heat demand of the season. 6 Recall that the fuel cost in these seasons is of the order of 96,000 €/week in summer and 192,000 €/week in the intermediate season thus, the profit change represent only 6% and 1.5% of this cost. 7 During winter the total fuel cost is of the order of 416,000 €/week, consequently the profit decrease corresponds only to a 0.6% of this cost.
season. The upper panels illustrate both the day-ahead and real time electrical power generation of the CHP.8 The same parameters are depicted in the second panel for the RES based generation. The total remaining imbalance (RES forecast error plus CHP deviation) is shown in the third panel. Finally, in the bottom panels the DA and imbalance prices are shown. Looking at the figures it can be observed that the ‘flexible DA’ strategy uses the cogeneration unit to compensate the lack of generation of the RES. This is done by increasing the output of the CHP on real time. The remaining imbalance is zero. This is done because during the dispatch optimization (re-evaluation) the ‘flexible DA’ strategy does not have information on a specific imbalance price scenario, but on a large set of scenarios that can take positive or negative values and thus, it decides to minimize the total imbalance volume. In contrast, in the ‘flexible RT’, the CHP does not compensate for the lack of generation of the RES but decreases its generation to create a larger negative imbalance. The reason for creating this negative deviation is the low imbalance tariff that appears in this scenario. A low imbalance penalty is an indication that the system is long. Thus when the CHP generates a negative imbalance, it not only increases the profits of the VPP operator by saving fuel cost, as shown in Table 3, but it also helps the grid to alleviate the total system imbalance. The behavior of the different bidding strategies among the three studied seasons is illustrated in Fig. 8. The first figure shows the heat demand (gray area), the thermal power generated by the CHP (blue line) and boiler (red area) and the thermal power charge to (negative values) or discharge from (positive values) the storage tank (blank line) of a characteristic day of each week. The illustrated parameters correspond to the dispatched amounts for a specific scenario combination. During the winter, due to the large heat demand, the CHP is running almost continuously at full load leaving less flexibility available. This explains why implementing the ‘flexible DA’ strategy during this season does not lead to a large profit increase when compared against the ‘static’ strategy. On the other hand, Table 3 also shows that the cost reduction achieved using the ‘flexible RT’ operation is related to a decrease in the fuel cost. This is also visible in Fig. 8, during the intermediate and winter seasons. In comparison with the other strategies, in real time, the ‘flexible RT’ operation uses the CHP less, activating the boiler more often. As the day-ahead schedule of both the ‘flexible DA’ and ‘flexible RT’ is the same, it can be deduced that the ‘flexible RT’ operation decreases its output, generating negative imbalance in order to obtain benefits from the imbalance prices. As explained before, creating an additional imbalance does not necessary aggravate the situation of the electric grid (‘passive balancing’). In fact, in Belgium the imbalance prices are an indication of the status of the system. Thus a low imbalance price suggests
8 Recall that the total bid is the combination of the CHP and RES expectation and the heat demand. Nevertheless, for illustration purposes, Fig. 7 shows the CHP and RES generation separately.
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Fig. 6. Resulting DA bid (solid line) and actual dispatch of the CHP (gray area) when using an imbalance volume penalty. This methodology is effective in limiting the schedule deviations.
Fig. 7. Comparison between ‘static’, ‘flexible DA’ and ‘flexible RT’ cases. The upper panel shows both the CHP electrical power bided DA (solid line) and the actual electrical dispatch (gray area). The second pane depicts the expected RES-based generation (solid line) and the actual RES-based output (gray area). The third panel shows the total remaining imbalance of the VPP and finally, the last panel illustrates the day-ahead (black line) and imbalance prices (gray line).
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Fig. 8. Comparison of the heat flow for the different strategies. The gray area corresponds to the thermal demand. The blue line represents the thermal power output of the CHP. The black line shows the average power charge to (negative values) or discharged from (positive values) the storage tank. Finally, the red area corresponds to the thermal power provided by the auxiliary boiler. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
that there is surplus of generation in the grid. As a result, by slightly decreasing the output of the CHP, the VPP owner is not only saving fuel but also helping the grid and will be remunerated for this via the imbalance mechanism.
4. Conclusions and further work This work was focused on developing a bidding strategy for a VPP composed by a CHP–DH and RES generation. The bidding strategies were estimated using stochastic optimization. This optimization takes into account uncertainty regarding RES electric power generation, day-ahead and imbalance prices. As a consequence, the CHP operation was scheduled not only to maximize the profit and cover the heat demand but also to compensate for the possible forecast errors of the RES based-generation. Three different strategies were assessed: ‘static’, ‘flexible DA’ and ‘flexible RT’ operation. In the first strategy the RES forecast errors are settled in the imbalance market and the CHP flexibility provided by its thermal storage tank is not used. The other
strategies use this flexibility to accommodate the forecast errors. In the ‘flexible DA’ case the CHP is rescheduled only once when accurate information regarding the RES generation is obtained without knowledge on the imbalance prices. On the other hand, the ‘flexible RT’ adjusts the CHP output every time step depending on the actual imbalance price and RES-based generation. These strategies were applied to a hypothetical case study that uses the Belgian city of Leuven as an example. The results of the ‘flexible DA’ case show a profit increase during summer (5900 €/week) and the intermediate season (2800 €/week), to be compared against the total fuel cost in these seasons (96,000 €/week in summer and 192,000 €/week during the intermediate season). In contrast, during winter the difference between the ‘static’ and the ‘flexible DA’ case is low compared with this fuel cost. Better results are obtained when the ‘flexible RT’ strategy is applied. In this case when the VPP is allowed to react to the imbalance prices, thereby changing its position close to real time, the profits increase in all seasons. This indicates that CHP–DH could help not only to reduce the cost due to the forecast errors but may also help the grid to reduce
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the system imbalance. However, this economic advantage should be valued against the additional investment needed to perform the accurate control on real time basis. Further work should assess the investment, maintenance and operational costs needed to perform real time control and the effects of considering other technologies such as heat pumps in the VPP. Additionally, estimating the impact of passive balancing on the remaining imbalance of the system was out of the scope of this work. References [1] Vandevyvere H, Jones PT, Aerts J. Leuven Klimaat neutraal; 2013.
[10] Garcia-Gonzalez J, de la Muela RMR, Santos LM, Gonzalez AM. Stochastic joint optimization of wind generation and pumped-storage units in an electricity market. Power Syst, IEEE Trans 2008;23(2):460–8. [11] Pandzˇic´ H, Morales JM, Conejo AJ, Kuzle I. Offering model for a virtual power plant based on stochastic programming. Appl Energy May 2013;105:282–92. [12] Stad Leuven Directie Data- en Facilitair Beheer, Internal Document; 2013. [13] Woods P, Riley O, Overgaard J, Vrins E, Sipil K, Stobart R, Cooke A. A Comparison of distributed CHP/DH with large-scale CHP/DH. IEA District Heating and Cooling Project Annex VII. [14] Synergrid, Statistieken en gegevens – Synthetic Load Pro les.