Offering model for a virtual power plant based on stochastic programming

Applied Energy 105 (2013) 282–292

Contents lists available at SciVerse ScienceDirect

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

Offering model for a virtual power plant based on stochastic programming Hrvoje Pandzˇic´ a,⇑, Juan M. Morales b, Antonio J. Conejo c, Igor Kuzle d a

Department of Electrical Engineering, University of Washington, 185 Stevens Way, 98195 Seattle, WA, USA Department of Electrical Engineering, Technical University of Denmark, Ørsteds Plads, Building 349, 2800 Kgs. Lyngby, Denmark c Department of Electrical Engineering, University of Castilla-La Mancha, Campus Universitario, 13071 Ciudad Real, Spain d Department of Power Systems, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, 10000 Zagreb, Croatia b

h i g h l i g h t s " A two-stage stochastic offering model for a virtual power plant is presented. " The virtual power plant consists of an intermittent source, a dispatchable source and a storage unit. " The virtual power plant trades in the day-ahead and balancing markets. " Characteristic scenarios are thoroughly analyzed and relevant conclusions are drawn.

a r t i c l e

i n f o

Article history: Received 24 August 2012 Received in revised form 30 October 2012 Accepted 29 December 2012 Available online 5 February 2013 Keywords: Virtual power plant Electricity markets Stochastic programming Pumped hydro storage plant Wind power plant

a b s t r a c t A virtual power plant aggregates various local production/consumption units that act in the market as a single entity. This paper considers a virtual power plant consisting of an intermittent source, a storage facility, and a dispatchable power plant. The virtual power plant sells and purchases electricity in both the day-ahead and the balancing markets seeking to maximize its expected profit. Such model is mathematically rigorous, yet computationally efficient. The offering problem is cast as a two-stage stochastic mixed-integer linear programming model which maximizes the virtual power plant expected profit. The uncertain parameters, including the power output of the intermittent source and the market prices, are modeled via scenarios based upon historical data. The proposed model is applied to a realistic case study and conclusions are drawn. Published by Elsevier Ltd.

All these variables are defined in each time period t, each WPP production scenario w and each day-ahead market price scenario p. They do not contain a balancing market price subindex since they are decided before the balancing market prices become known. 1. Introduction 1.1. Virtual power plant concept Growing environmental concerns have started a boom of renewable energy technologies whose task is to both satisfy the ever increasing needs for electricity and to substitute the conventional thermal power plants. On this matter, wind turbines have ⇑ Corresponding author. Tel.: +1 2064273685; fax: +1 2065433842. E-mail addresses: [email protected] (H. Pandzˇic´), juanmi82mg@gmail. com (J.M. Morales), [email protected] (A.J. Conejo), [email protected] (I. Kuzle). 0306-2619/$ - see front matter Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.apenergy.2012.12.077

imposed as the leading renewable technology. The widespread use of wind generators is the result of an economically acceptable technology which can be installed at any windy location worldwide. Due to the intermittency of wind, it is impossible to accurately predict the output of a Wind Power Plant (WPP) in advance. This presents no problem to producers that receive a fixed feed-in tariff for the produced electricity. However, subsidies have a fixed expiry date, mostly 12–15 years, after which WPPs become non-subsidized producers that need to participate in electricity markets. However, energy trading in electricity markets involves high risk to WPP owners due to imbalance costs. In order to lower the risk of the mismatch between the sold and delivered electricity, a WPP can be combined with a dispatchable power plant. One option is the joint operation with a quick response Conventional Power Plant (CPP), able to cover the fluctuations in WPP output. Another option is to use a Pumped Hydro Storage Plant (PHSP) which, besides providing flexibility to WPP

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292

283

Nomenclature Acronyms CPP Conventional Power Plant EPEX European Power EXchange PHSP Pumped Hydro Storage Plant VPP Virtual Power Plant WPP Wind Power Plant Indices j p rdown(t) rup(t) t w

Index of CPP production blocks, running from 1 to nj Index of day-ahead market price scenarios, running from 1 to np Index of down-regulation price scenarios, running from 1 to ndown r Index of up-regulation price scenarios, running from 1 up to nr Index of time periods, running from 1 to T Index of WPP output scenarios, running from 1 to nw

Constants CPP capacity (MW) gc gcj Size of the jth production block of the CPP supply cost function (MW) gc CPP minimum power output (MW) gdown,init Time that the CPP has been down before the beginning of the planning horizon (h) gdown,min CPP minimum down time (h) gonoff CPP on–off status prior to the beginning of the planning horizon (equal to 1 if gup,init > 0, and 0 otherwise) gup,init Time that the CPP has been up before the beginning of the planning horizon (h) gup,min CPP minimum up time (h) Pumping capacity of the PHSP (MW) gp gt Turbine capacity of the PHSP (MW) gw(t) WPP power output in time period t and WPP production scenario w (MW) k0 Fixed cost of the CPP (Euro) kj Marginal cost associated with the jth production block of the CPP supply cost function (Euro/MW h)

operation, also moves electricity delivery from low electricity price hours to high electricity price hours. Results show that including PHSP is an effective way to integrate intermittent renewable energy sources while improving the economic operation of a system [1]. The concept of combining different generation technologies into a single-acting unit in an electricity market is usually referred to as a Virtual Power Plant (VPP). This coordinated cluster of generators performs better in an electricity market than independent generators. Furthermore, the heterogenous generator system increases the overall operation flexibility, often undermined by intermittent sources, such as wind power.

1.2. Sources of uncertainty When considering a VPP optimal market offering problem, there are two sources of uncertainty. The first one is renewable generation, i.e., the WPP, and the second one is market prices. Namely, market prices are known only after all producers and consumers submit their selling and bidding curves, respectively. In order to appropriately address these uncertainties a rigorous stochastic programming framework is used. Uncertain parameters are mod-

Ldown,min Parameter equal to min {T, [gdown,min  gdown,init]  [1  gonoff]}, which is the number of time periods that the CPP has to be down from the beginning of the planning horizon (h) Lup,min Parameter equal to min {T, [gup,min  gup,init]  gonoff}, which is the number of time periods that the CPP has to be up from the beginning of the planning horizon (h) rdc Ramp-down limit of the CPP (MW/h) ruc Ramp-up limit of the CPP (MW/h) storage Equivalent energy capacity of the PHSP upper basin (MW h) SUCc CPP start-up cost (Euro) kp(t) Electricity price in the day-ahead market in time period t and day-ahead market price scenario p (Euro/MW h) g PHSP system efficiency factor pp Probability of the pth day-ahead market price scenario pdown Probability of the rth down-regulation price scenario r pup Probability of the rth up-regulation price scenario r pw Probability of the wth WPP production scenario wrdown ðtÞ Down-regulation price ratio in time period t wrup ðtÞ Up-regulation price ratio in time period t Variables down bmwp ðtÞ Power sold in the balancing market (MW) Power purchased in the balancing market (MW) Total cost of the CPP electricity production (Euro) CPP total power production (MW) CPP power production from block j (MW) PHSP pumping power (MW) PHSP turbine power (MW) Power sold (if positive) or purchased (if negative) in the day-ahead market (MW) storagewp(t) Energy stored in the upper basin of the PHSP at the end of time period t (MW) ucwp ðtÞ Binary variable equal to 1 if the CPP is producing electricity and 0 otherwise v cwp ðtÞ Binary variable equal to 1 if the CPP is started up at the beginning of the time period, and 0 otherwise up

bmwp ðtÞ C cwp ðtÞ g cwp ðtÞ g cwpj ðtÞ g pwp ðtÞ g twp ðtÞ Gwp(t)

eled by a set of finite outcomes, i.e. scenarios, based on historical data.

1.3. Literature review The technical literature is rich in methods and tools to determine the optimal offering strategy of a conventional power producer in an electricity market [2]. As an example, the authors in [3] propose a mixed integer model to compute the optimal response of a thermal CPP to electricity spot prices. Market hourly prices in this model are considered known, and the thermal producer is assumed to be a price taker. Wind producer offering models are, on the one hand, less complex since they do not include generation or start-up costs, ramping constraints, or minimum up/down-time constraints. On the other hand, wind forecast uncertainty, which leads to imbalance penalties, calls for a stochastic offering model. The role of the wind forecast information is examined in [4]. A method for WPP trading in short-term electricity markets using Markov probabilities, which results in reduced imbalance costs, is proposed in [5]. A linear programming technique for WPP producers offering electricity in a market with multiple trading stages is presented in [6]. In [7] the authors conclude that WPP offering strategies derived by

284

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292

stochastic programming generally outperform WPP offering strategies based on forecasts. The risk of failing to comply with the energy schedule settled in the day-ahead market becomes much lower if the WPP is combined with a dispatchable power plant. The problem of the joint market participation of a WPP and a PHSP is addressed in [8]. The optimization model is formulated as a two-stage stochastic programming problem in which the day-ahead market prices and the wind generation are considered as random parameters. The case study shows that the coordinated WPP–PHSP offering strategy provides higher profit compared to the uncoordinated operation mode. Angarita and Usaola [9] also analyzes the economic performance of a WPP–PHSP system. The authors estimate that, depending on the penalty values, the combined operation may avoid up to 50% of the penalties. A method for minimizing the imbalance penalty risks associated with the WPP output uncertainty, in case of a joint WPP–PHSP model, is presented in [10]. A neural network approach is used in [11] to set the self-scheduling strategy of the WPP and PHSP. This model considers day-ahead, spinning and regulation reserve markets. The authors in [12] address the problem of wind–thermal coordinated trading using stochastic mixed-integer programming. The optimal offering strategy is obtained by maximizing total expected profits while controlling trading risks. For risk control, a weighted term of the conditional value at risk is included in the objective function. The offering problem faced by a VPP in a joint market of energy and spinning reserve service is presented in [13]. The proposed model, which is non-linear, is solved using a genetic algorithm. A mixed-integer linear programming model which maximizes the VPP mid-term profit in the day-ahead market, subject to long-term bilateral contracts and technical constraints, is presented in [14]. 1.4. Contributions and paper layout Whilst the papers described in the previous subsection mostly tackle either the WPP–PHSP or the WPP–CPP market offering problem, this paper incorporates all three types of electricity generators: an intermittent energy source, an energy storage and a conventional source into a single model. Additionally, the presented model considers both the day-ahead and the balancing market. In the day-ahead market the VPP is treated as a price-taker, and in the balancing market as a deviator, i.e. as a passive agent. This means that the VPP uses the balancing market to correct its energy deviations with respect to its day-ahead schedule. The proposed stochastic decision-making framework is rigorous yet computationally efficient. Its outputs are hourly offering curves to be submitted to the day-ahead market. A comprehensive real-world case study is presented and its results are analyzed. This paper is laid out as follows. Section 2 provides the model assumptions and description, as well as the mathematical formulation of the model. Application of the presented model to a realistic case study, with appropriate result description and computational burden report, is provided in Section 3. Section 4 summarizes relevant conclusions.

In order to keep the model linear, the CPP fuel cost function is modeled using a piecewise linear approximation. The PHSP is considered to pump water into a lossless upper basin. The lower basin is assumed to always contain enough water to be pumped. Following current practice in European markets, a dual pricing system for the balancing market is considered in such a way that the VPP can only purchase balancing energy at a price higher than in the day-ahead market (up-regulation). Similarly, VPP can only sell electricity in the balancing market at a price lower than in the day-ahead market (down-regulation). 2.2. Model description The proposed model may be understood as a three-stage stochastic programming model in as much as: 1. The VPP owner must submit its offering curve in the day-ahead market before the WPP output and the prices in both the dayahead and balancing markets become known (first stage). 2. The VPP owner must decide on the operation of its CPP and PHSP once the WPP output and the prices in the day-ahead market become known, but before knowing the balancing market prices (second stage). 3. The balancing market prices become known (third stage). However, no decision is made at the third stage and therefore, the stochastic balancing market prices can be replaced by their expectations. As a result, the proposed model boils down to a classical two-stage stochastic programming problem. It is important to notice that the operation of the CPP and PHSP is assumed to be determined once the WPP output becomes known. Therefore, no decision is made in between the disclosure of the day-ahead market prices and the WPP output. Likewise, note that our model guarantees a feasible operation of the CPP and PHSP for every plausible realization of the wind power production. 2.3. Model formulation The VPP profit maximization model is formulated as follows: Maximize np X

down nX r

t¼1 w¼1

p¼1

rdown ¼1

pw

2.1. Assumptions The considered VPP consists of a WPP, a CPP and a PHSP. Since the WPP power output is stochastic, it is modeled using historical scenarios. Historical data is also used to build stochastic trees modeling prices in the day-ahead and balancing markets.

pp

up  bmwp ðtÞ  wup r ðtÞ



pdown r

nr X

h



down pup kp ðtÞ Gwp ðtÞ þ bmwp ðtÞ  wdown ðtÞ r r

r up ¼1

 C cwp ðtÞ  SUCc 

v cwp ðtÞ

i

ð1aÞ

subject to:

ucwp ðtÞ 2 f0; 1g;

8t 6 T; w 6 nw ; p 6 np

v cwp ðtÞ 2 f0; 1g; 8t 6 T;

w 6 nw ; p 6 np

ucwp ðtÞ  ucwp ðt  1Þ 6 v cwp ðtÞ; g cwp ðtÞ ¼

2. Model

up

nw T X X

nj X g cwpj ðtÞ;

8t 6 T; w 6 nw ; p 6 np

8t 6 T; w 6 nw ; p 6 np

ð1bÞ ð1cÞ ð1dÞ

ð1eÞ

j¼1

C cwp ðtÞ ¼ k0  ucwp ðtÞ þ

nj X kj  g cwpj ðtÞ;

8t 6 T; w 6 nw ; p

j¼1

6 np g c  ucwp ðtÞ 6 g cwp ðtÞ 6 gc  ucwp ðtÞ;

ð1fÞ

8t 6 T; w 6 nw ; p 6 np

ð1gÞ

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292 c

rd 6 g cwp ðtÞ  g cwp ðt  1Þ 6 ruc ; Ldown;min X

ucwp ðtÞ ¼ 0;

8t 6 T; w 6 nw ; p 6 np

8w 6 nw ; p 6 np

ð1hÞ

ð1iÞ

t¼1 tþg down;min X 1

   1  ucwp ðttÞ P g down;min  ucwp ðt  1Þ  ucwp ðtÞ ;

tt¼t

8Ldown;min þ 1 6 t 6 T  g down;min þ 1; w 6 nw ; p 6 np

ð1jÞ

T    X 1  ucwp ðttÞ  ucwp ðt  1Þ  ucwp ðtÞ tt¼t

P 0;

8T  g down;min þ 2 6 t 6 T; w 6 nw ; p 6 np

up;min LX 

 1  ucwp ðtÞ ¼ 0;

w 6 nw ; p 6 np

ð1kÞ

ð1lÞ

t¼1 tþg up;min X 1

ucwp ðttÞ P g up;min  v ðtÞcwp ;

8Lup;min þ 1 6 t

tt¼t

6 T  g up;min þ 1; w 6 nw ; p 6 np T   X ucwp ðttÞ  v cwp ðtÞ P 0;

ð1mÞ

8T  g up;min þ 2 6 t 6 T;

tt¼t

w 6 nw ; p 6 np

ð1nÞ

g twp ðtÞ 6 gt ;

8t 6 T; w 6 nw ; p 6 np

ð1oÞ

g pwp ðtÞ 6 gp ;

8t 6 T; w 6 nw ; p 6 np

ð1pÞ

storagewp ðtÞ ¼ storagewp ðt  1Þ þ g pwp ðtÞ  g twp ðtÞ;

8t 6 T;

w 6 nw ; p 6 np

ð1qÞ

8t 6 T; w 6 nw ; p 6 np

0 6 storagewp ðtÞ 6 storage;

ð1rÞ

up

g w ðtÞ þ g cwp ðtÞ þ g twp ðtÞ þ bmwp ðtÞ ¼ Gwp ðtÞ þ

g pwp ðtÞ

g

down

þ bmwp ðtÞ;

wrup ðtÞ P 1;

8r up ðtÞ 6 nup r ðtÞ;

8t 6 T

8rdown ðtÞ 6 ndown ðtÞ; r

8t 6 T

ð2Þ ð3Þ

ð1sÞ 3. Case study

Gw1 p ðtÞ ¼ Gw2 p ðtÞ ¼    ¼ Gwn p ðtÞ; Gwp ðtÞ  Gwp ðtÞ 6 0;

Eqs. (1i)–(1k) enforce the minimum down time constraints [16]. Constraint (1i) forces the CPP to stay off for the appropriate number of hours if in hour 0 it has been off for fewer hours than the minimum down time. This constraint is enforced only if Ldownmin P 1. Constraints (1j) enforce the minimum down time for all combinations of consecutive hours of size gdown,min. Constraints (1k) enforce the minimum down time for the last gdown,min  1 h. Eqs. (1l)–(1n) work in a similar way as Eqs. (1i)–(1k), imposing minimum up time constraints. Constraints (1o) and (1p) are PHSP turbine and pumping capacity limits, respectively. Constraints (1q) are used to define the available energy stored at the end of each time period, while constraints (1r) are upper basin energy storage limits. Constraints (1s) are energy balance equations. They state that the summation of the electricity produced by WPP, CPP, PHSP and the electricity purchased in the up-regulation market has to be equal to the electricity sold in the day-ahead market (negative if purchased), plus the electricity used to pump water in the PHSP upper basin and the electricity sold in the down-regulation market. Variable g pwp ðtÞ is divided by g, which is a PHSP whole efficiency factor. This reflects the fact that it is possible to convert back to electricity only a portion of the electricity used to pump the water to the upper basin. Variable Gwp(t) provides offers to the day-ahead market and is a first-stage variable. Eq. (1t) are non-anticipativity constraints and reflect the fact that information on stochastic parameters cannot be anticipated. In other words, these constraints are necessary to model the fact that only one bidding curve can be submitted to the day-ahead market for each hour, irrespective of the WPP output. Constraints (1u) ensure that the VPP bidding curve is monotonously nondecreasing. Op(t) denotes the order of price scenario p in each hour t. The price scenarios are ordered in each hour from the lowest price value to the highest one. In this model, the VPP can purchase energy in the balancing market at a price higher than the day-ahead market price (up-regulation) and sell energy at a price lower than the day-ahead market price (down-regulation). Thus, the following stands:

wrdown ðtÞ 6 1;

8t 6 T; w 6 nw ; p 6 np

285

8t 6 T;

8t 6 T; p 6 np 8p; p : Op ðtÞ þ 1 ¼ Op ðtÞ

ð1tÞ ð1uÞ

The objective function (1a) to be maximized is an expected profit function that considers the electricity sold/purchased in the day-ahead market, sold in the down-regulation market, and purchased in the up-regulation market, as well as the production and start-up cost of the CPP. Constraints (1b) and (1c) are binary variable declarations. Binary variable ucwp ðtÞ is equal to 1 if CPP is producing electricity in time period t, WPP production scenario w and day-ahead market price scenario p, and 0 otherwise. Binary variable v cwp ðtÞ is equal to 1 if CPP is started-up in time period t, WPP production scenario w and day-ahead market price scenario p, and 0 otherwise. Constraints (1d) are logical expressions used to set the appropriate value to the CPP start-up binary variable v cwp ðtÞ [3,15]. Constraints (1e) state that the CPP total power output is equal to the summation of all production blocks j (the CPP supply cost function is modeled as a piecewise linear approximation), while constraints (1f) define the CPP production costs. Constraints (1g) define the CPP output limits regarding its minimum power output and capacity, and constraints (1h) enforce its ramp limits.

3.1. VPP description The VPP presented in this case study consists of a WPP, a PHSP and a combined cycle gas turbine CPP. The rated capacity of the WPP is 9.6 MW. The equivalent energy capacity of the PHSP upper basin is set to 40 MW h. The turbine and pumping regime capacities are 8 and 6 MW, respectively. The upper basin of PHSP is empty at the beginning of the day under study, and there are no constraints on the water level of the upper basin at the end of the day. The efficiency of the PHSP system is set to 75%. The CPP is based on a TAU5670 turbine [17] with 5.67 MW rated capacity. Its technical minimum is 2.5 MW, and its both up and down ramp limits are 3 MW/h. The CPP cost curve is approximated using a 3-block piecewise linear approximation. Both minimum up and down times are 2 h. It is considered that the CPP has been off for 1 h prior to the beginning of the study horizon. 3.2. Uncertain data Modeling the WPP output, or market prices, is outside the scope of this paper. A review of WPP generation prediction techniques is

286

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292

Fig. 1. WPP output scenarios – winter Wednesdays from March 31, 2010 to January 11, 2012.

available in [18], while market price forecasting techniques are broadly described in [19]. In this case study we compute the optimal offering strategy of the VPP for a winter Wednesday. Offering strategiew for any other day of the week or season, though, can be obtained in a similar manner. Additionally, state-of-the-art forecasting machinery may be used to generate the input scenario set instead of resorting to historical scenarios. The WPP scenarios considered are based on the real-world data collected from a WPP with installed capacity of 9.6 MW operating in coastal Croatia. The gathered data correspond to 25 winter Wednesdays (December–March) ranging from March 31, 2010 to January 11, 2012. All scenarios are assumed equiprobable, i.e., the probability of each scenario is 0.04. These scenarios are provided in Fig. 1, showing the wide range of wind production levels used in the case study. Real-world market price scenarios are collected from the EPEX market historical data [20]. Figs. 2 and 3 show 25 equiprobable day-ahead market and balancing market price scenarios, respectively. These historical data also reflect winter Wednesdays ranging from March 31, 2010 to January 11, 2012. Thus, they are contemporaneous with the WPP output data. It is important to note that it is not possible to distinguish between up and downregulation prices in Fig. 3. This is so because a specific balancing market price can be either up or down-regulation price depending on the realization of the day-ahead market price scenario. 4. Results and discussion The expected hourly profits and cumulative expected profit of the VPP are provided in Fig. 4. The hourly profits in the first 7 h are negative. Since the day-ahead market prices are lowest during these hours in practically all scenarios, the electricity produced by the WPP and CPP (if operating) is used for pumping water to the PHSP upper basin. Since CPP operation increases expenditures, and the produced electricity is generally used for pumping water, the VPP incurs losses amounting to Euro 1159 in the first 7 h of the day. In the 8th hour the expected day-ahead market prices increase and in most scenarios water is no longer pumped to the PHSP upper basin. The highest profit is obtained in hour 19, which exhibits the highest market price in most scenarios. The overall expected profit throughout the day is Euro 4479. The electricity sold in the day-ahead market in average is 130 MW h, which brings the average profit on sold electricity to 34.5 Euro/MW h. Given that the expected profit resulting from implementing the expected-value solution is Euro 4156, the value of the stochastic solution (VSS) is Euro 323, or 7.8 % in relative terms [21].

Fig. 5 shows VPP day-ahead market offering curves for selected hours. In hour 2 the electricity is purchased in the market if the price is lower than 47 Euro/MW h. The highest amount of purchased electricity (7.88 MW h) is obtained at a price of 0.05 Euro/ MW h. In hour 7 the day-ahead market price threshold for selling electricity is around 48.5 Euro/MW h. At prices lower than this, electricity is purchased in the day-ahead market. In hour 10 electricity is solely sold in the day-ahead market, and the corresponding offering curve is similar to that of hour 17. The highest amounts of sold electricity are achieved in hour 19, in which the highest prices occur. Regardless of the low prices, hour 24 is solely used for electricity selling since the storage is emptied at the end of the optimization period. The electricity sold in the day-ahead market for each of the 25 day-ahead market price scenarios is provided in Figs. 6–8. The VPP activity in the market is in direct correlation with the expected market price. Namely, the VPP sells lower amounts of electricity when the price is low, and higher amounts of electricity when the price is high. The largest amount of electricity is sold in hour 19. A sudden drop in sold electricity happening in hours 13 and 14 for one of the market price scenarios in Fig. 7 (black dotted curve) is the result of the distinctive shape of the respective price curve, characterized by relatively low prices during the early afternoon (around 45 Euro/MW h in hours 13 and 14) and high prices in the late hours (prices in hours 21–24 are 73, 63, 65 and 56 Euro/ MW h, respectively). In order to fully understand the behavior of the comprehensive stochastic model presented, the following scenarios are analyzed in detail: 1. 2. 3. 4. 5.

low WPP production, low day-ahead market prices; low WPP production, high day-ahead market prices; medium WPP production, medium day-ahead market prices; high WPP production, low day-ahead market prices; high WPP production, high day-ahead market prices.

For the sake of clarity, we use the following conventions in Figs. 9–13: 1. WPP generation is always positive; 2. PHSP power generation is positive, and its consumption is negative; 3. CPP generation is always positive; 4. a positive value of the balancing market curve displays electricity purchased, and a negative one, electricity sold in the balancing market;

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292

287

Fig. 2. Day-ahead market price scenarios – winter Wednesdays from March 31, 2010 to January 11, 2012.

Fig. 3. Balancing market price scenarios – winter Wednesdays from March 31, 2010 to January 11, 2012.

Fig. 4. Hourly profits and cumulative profit of a VPP.

5. a positive value of the day-ahead market curve displays electricity sold, and a negative one, electricity purchased in the day-ahead market. It is important to note that reverse sign criteria are used for day-ahead and balancing markets. This is so because the day-ahead market offer is equal to the summation of all the other energy variables. Additionally, this sign criteria improves graph clarity.

Fig. 9 shows the electricity produced by the WPP and CPP, the electricity produced/consumed by the PHSP, as well as the electricity purchased/sold in the balancing and day-ahead markets in the case of a low-wind–low-price scenario. In the first 7 h, the PHSP electricity consumption is settled by purchases in the day-ahead market, which is the result of the low day-ahead market price scenario. In these first 7 h, the balancing market activity mimics the WPP production. This means that practically the whole WPP production

288

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292

Fig. 5. VPP day-ahead market offering curves for hours 2, 7, 10, 17, 19, and 24.

Fig. 6. Electricity sold in the day-ahead market for the first eight scenarios.

Fig. 7. Electricity sold in the day-ahead market for the second eight scenarios.

is sold in the balancing market. It is important to note that the electricity sold in the balancing market brings less profit than the electricity sold in the day-ahead market. However, since the offering curve submitted to the day-ahead market is independent of the

WPP production, in some scenarios the electricity is sold in the balancing market instead of in the day-ahead market. Although this has a negative impact on the outcome of the given scenario, the overall performance of the model is optimal.

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292

289

Fig. 8. Electricity sold in the day-ahead market for the last nine scenarios.

Fig. 9. Electricity produced by the WPP and the CPP, electricity produced/consumed by the PHSP and electricity purchased/sold in the balancing market and day-ahead market in a low-wind–low-price scenario.

Fig. 10. Electricity produced by the WPP and the CPP, electricity produced/consumed by the PHSP and electricity purchased/sold in the balancing market and day-ahead market in a low-wind–high-price scenario.

290

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292

Fig. 11. Electricity produced by the WPP and the CPP, electricity produced/consumed by the PHSP and electricity purchased/sold in the balancing market and day-ahead market in a medium-wind–medium-price scenario.

Fig. 12. Electricity produced by the WPP and the CPP, electricity produced/consumed by the PHSP and electricity purchased/sold in the balancing market and day-ahead market in a high-wind–low-price scenario.

The PHSP stops pumping in hour 8 and it produces electricity in hours 12, 13, and 18–20. All the electricity produced in hours 12, 13 and 20 is sold in the balancing market. Electricity produced in hour 18 is mostly sold in the day-ahead market (approximately 6 MW h), while the rest (approximately 4 MW h) is sold in the balancing market. In hour 19 all the electricity produced by the PHSP system is sold in the day-ahead market. The electricity purchased in the day-ahead market in hours 8 and 15 is sold in the balancing market. Since practically all balancing market prices in these hours are higher than the day-ahead market prices, the electricity is sold at the same price as it is purchased, without incurring any economical losses. The largest amount of electricity sold in the day-ahead market is 10.5 MW h in hour 19. Due to low day-ahead market prices the CPP does not operate in this scenario. The case of a low-wind–high-price scenario is illustrated in Fig. 10. The PHSP pumps water during the first 7 h, which is used to produce electricity in hours 13, and 17–20. Due to operation

costs, the CPP is started in hour 7 and stays on-line for the rest of the day. As a result of high day-ahead market prices, large amounts of electricity are sold in the day-ahead market, while the balancing market is only used to purchase electricity. The largest amount of electricity sold in the day-ahead market is 25.4 MW h in hour 21. This electricity is largely obtained from the balancing market. Fig. 11 depicts results in the case of a medium-wind–mediumprice scenario. Again, the PHSP pumps water in the first 7 h. Some of this water is used to produce electricity in hours 9–11. The upper basin is additionally charged during the 17th hour to accommodate the spike in the WPP output. The PHSP is fully discharged during hours 19 and 20. The CPP is not started up in this scenario. The balancing market is used for both selling and purchasing electricity, settling imbalances between produced electricity and electricity traded in the day-ahead market. Due to insufficient wind production, electricity is purchased in the day-ahead market during the first 6 h. The morning selling

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292

291

Fig. 13. Electricity produced by the WPP and the CPP, electricity produced/consumed by the PHSP and electricity purchased/sold in the balancing market and day-ahead market in a high-wind–high-price scenario.

peak occurs in the 9th hour (17.5 MW h), and the evening peak in the 20th hour (19.1 MW h). Fig. 12 depicts the relevant plant generations and the electricity sold/purchased in day-ahead and balancing markets in the case of a high-wind–low-price scenario. Due to the high WPP production and low day-ahead market prices, the CPP stays shut throughout the day. The pumping regime of the PHSP lasts for the first 7 h, which is covered by day-ahead market purchases. On the other hand, the WPP output is sold in the balancing market. The PHSP upper basin is discharged in hours 12, 13, and 18– 20. The balancing market is used solely for selling electricity because balancing market prices are generally higher than day-ahead market prices. Electricity sold in the balancing market reaches 16.8, 18.8, and 19.4 MW h in hours 8, 12, and 20, respectively. Trading in the day-ahead market results in 50 MW h of purchased electricity overall. The profit is made in the balancing market, in which 223.8 MW h are sold. The case of a high-wind–high-price scenario is depicted in Fig. 13. During the first 6 h the day-ahead and balancing market trading focuses on achieving the 8 MW needed to operate the PHSP in its pumping regime. Due to high day-ahead market prices, the CPP is started up in the 7th hour and it runs at its full capacity until hour 24, in which its output is reduced to 3 MW. Only a small portion of PHSP upper basin is discharged in hour 12, while most of it is discharged during the high-price evening hours, i.e. hours 17–20. Electricity is sold in the balancing market only in the 6th hour, while in all the other hours it is purchased in order to fulfill the day-ahead electricity commitment. This results in a large amount of electricity sold in the day-ahead market (329 MW h), while in the balancing market 50 MW h are purchased. Electricity sold in the day-ahead market exceeds 25 MW h in each of the hours 17– 21. The average amount of up-regulation electricity is 1.84 MW h, and down-regulation electricity is 1.42 MW h, which brings the average balancing market traded volume to 3.26 MW h. This makes a mere 1.76% of the average day-ahead market volume which is 185.70 MW h.

4.1. Computational burden The case study is solved using CPLEX 12.1 under GAMS on a 2.93 MHz Quad Core processor with 256 GB of RAM. The required computational time is about 27 min. The high computational time is the result of the large number of scenarios that are used, as each scenario involves two additional binary variables per hour. The overall number of integer variables can be reduced using scenario reduction techniques [22], which would result in a lower computational burden. Another efficient way to cope with uncertain parameters is by means of robust optimization, as described in [23]. This approach requires fine tuning of the robustness of the solution, but reduces the number of integer variables. Tackling market price uncertainty using robust optimization technique is presented in [24]. 5. Conclusions The proposed daily offering model is intended to help a VPP owner to maximize its short-term expected profit. The majority of the trading takes place in the day-ahead market, while the balancing market makes less than 2% of the revenue in the considered case study. The following conclusions are in order: 1. The CPP starting-up decisions depend only on the day-ahead market prices. In case of high day-ahead market prices, the CPP starts operating in the morning and stays on until the late evening. 2. The PHSP operation is fairly independent on the WPP output, CPP output, and even the day-ahead market prices. In most scenarios, the day-ahead market price difference throughout the day is sufficient for the PHSP to make a profit by pumping water during the night hours and producing electricity in the morning and evening peak hours. In case of a high price spread or a volatile WPP output, the PHSP may additionally charge the upper basin in the late afternoon in order to increase the production level during evening peak hours.

292

H. Pandzˇic´ et al. / Applied Energy 105 (2013) 282–292

3. In case of low day-ahead market price scenarios, the balancing market is used mostly for selling electricity. On the other hand, in case of high day-ahead market price scenarios, the balancing market is mostly used for purchasing electricity. This is so because in the case of low day-ahead market price scenarios the expected balancing market prices in this case study are generally higher than the day-ahead market prices, and vice versa. 4. WPP output does not influence significantly the PHSP or the CPP operation. However, higher WPP output reduces the off-peak electricity purchased in the market. 5. Finally, we conclude that the VPP association results in higher expected profits while slightly ‘‘disturbing’’ the individual operation of individual plants integrated in the VPP association. The computational burden of the proposed model is significant, which is the characteristic of most stochastic models. However, using a moderate number of scenarios keeps the computational time in acceptable levels and compatible with the day-ahead market framework. The risk of the actual profit being well below the expected one may be tackled either by employing a robust optimization approach, as described in [23], or the conditional value at risk (CVaR), as described in [25]. Both of these metrics may be linearized and incorporated in the proposed model. The model can be further extended to consider that the VPP producer is able to influence market prices. In that case, the stochastic programming formulation of the offering problem should be upgraded by explicitly modeling the market clearing process as in [26,27]. However, in that case, data for all market participants are needed.

References [1] Brown PD, Paes Lopes JA, Matos MA. Optimization of pumped storage capacity in an isolated power system with large renewable penetration. IEEE Trans Power Syst 2008;23(2):523–31. [2] Li G, Shi J, Qu Xiuli. Modeling methods for GenCo bidding strategy optimization in the liberalized electricity spot markete – a state-of-the-art review. Energy 2011;36(8):; 4686–4700. [3] Arroyo JM, Conejo AJ. Optimal response of a thermal unit to an electricity spot market. IEEE Trans Power Syst 2000;15(3):1098–104. [4] Bitar EY, Rajagopal R, Khargonekar PP, Poolla K, Varaiya P. Bringing wind energy to market. IEEE Trans Power Syst 2012;27(3):1225–35.

[5] Bathurst G, Weatherill J, Štrbac G. Trading wind generation in short term energy markets. IEEE Trans Power Syst 2002;17(3):782–9. [6] Morales JM, Conejo AJ, Perez-Ruiz J. Short-term trading for a wind power producer. IEEE Trans Power Syst 2010;25(1):554–64. [7] Rahimiyan M, Morales JM, Conejo AJ. Evaluating alternative offering strategies for wind producers in a pool. Appl Energy 2011;88(12):4918–26. [8] 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. IEEE Trans Power Syst 2008;23(2):460–8. [9] Angarita JM, Usaola JG. Combining hydro-generation and wind energy: biddings and operation on electricity spot markets. Elect Power Syst Res 2007;77(5–6):393–400. [10] Bourry F, Costa L, Kariniotakis G. Risk-based strategies for wind/pumpedhydro coordination under electricity markets. In: PowerTech 2009. Springer; 2009. p. 1–8. [11] Varkani AK, Daraeepour A, Monsef H. A new self-scheduling strategy for integrated operation of wind and pumped-storage power plants in power markets. Appl Energy 2011;88(12):5002–12. [12] Al-Awami AT, El-Sharkawi MA. Coordinated trading of wind and thermal energy. IEEE Trans Sust Energy 2011;2(3):227–87. [13] Mashhour E, Moghaddas-Tafreshi SM. Bidding strategy of virtual power plant for participating in energy and spinning reserve markets – Part I: Problem formulation. IEEE Trans Power Syst 2011;26(2):949–56. [14] Pandzˇic´ H, Kuzle I, Capuder T. Virtual power plant mid-term dispatch optimization. Appl Energy 2013;101(1):134–41. [15] Ostrowski J, Anjos MF, Vannelli A. Tight mixed integer linear programming formulations for the unit commitment problem. IEEE Trans Power Syst 2012;27(1):39–46. [16] Arroyo JM, Conejo AJ. Optimal response of a thermal unit to an electricity spot market. IEEE Trans Power Syst 2000;15(3):1098–104. [17] Taurus 60 PG Generator Set. [accessed 12.08.12]. [18] Foley AM, Leahy PG, Marvuglia A, McKeogh EJ. Current methods and advances in forecasting of wind power generation. Energy 2012;37(1):1–8. [19] Conejo AJ, Contreras J, Espínola R, Plazas MA. Forecasting electricity prices for a day-ahead pool-based electric energy market. Int J Forecast 2005;21(3): 435–62. [20] European energy exchange: hourly contracts. [accessed 12.05.12]. [21] Birge JR, Louveaux F. Introduction to stochastic programming. York, USA: Springer-Verlag; 1997. [22] Morales JM, Pineda S, Conejo AJ, Carrion M. Scenario reduction for futures market trading in electricity markets. IEEE Trans Power Syst 2009;24(2): 878–88. [23] Bertsimas D, Sim M. The price of robustness. Oper Res 2004;52(1):35–53. [24] Dominguez R, Baringo L, Conejo AJ. Optimal offering strategy for a concentrating solar power plant. Appl Energy 2012;98(10):316–25. [25] Rockafellar RT, Uryasev S. Optimization of conditional value-at-risk. J Risk 2000;2(3):21–41. [26] Pandzˇic´ H, Conejo AJ, Kuzle I, Caro E. Yearly maintenance scheduling of transmission lines within a market environment. IEEE Trans Power Syst 2012;27(1):407–15. [27] Ruiz C, Conejo AJ. Pool strategy of a producer with endogenous formation of locational marginal prices. IEEE Trans Power Syst 2009;24(4):1855–66.