A new self-scheduling strategy for integrated operation of wind and pumped-storage power plants in power markets

Applied Energy 88 (2011) 5002–5012

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

A new self-scheduling strategy for integrated operation of wind and pumped-storage power plants in power markets Ali Karimi Varkani a,⇑, Ali Daraeepour b, Hassan Monsef a a b

School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran Iran Grid Management Company (IGMC), Tehran, Iran

a r t i c l e

i n f o

Article history: Received 1 August 2010 Received in revised form 6 April 2011 Accepted 28 June 2011 Available online 23 July 2011 Keywords: Integrated operation Wind farm Uncertainty Power market Pumped-storage plant

a b s t r a c t Competitive structure of power markets causes various challenges for wind resources to participate in these markets. Indeed, production uncertainty is the main cause of their low income. Thus, they are usually supported by system operators, which is in contrast with the competitive paradigm of power markets. In this paper, a new strategy for increasing the profits of wind resources is proposed. In the suggested strategy, a Generation Company (GenCo), who owns both wind and pumped-storage plants, self-schedules the integrated operation of them regarding the uncertainty of wind power generation. For presenting an integrated self-schedule and obtaining a real added value of the strategy, participation of the GenCo in energy and ancillary service markets is modeled. The self-scheduling strategy is based on stochastic programming techniques. Outputs of the problem include generation offers in day-ahead energy market and ancillary service markets, including spinning and regulation reserve markets. A Neural Network (NN) based technique is used for modeling the uncertainty of wind power production. The proposed strategy is tested on a real wind farm in mainland, Spain. Moreover, added value of the strategy is presented in different conditions of the market. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The liberalization of power markets is an ongoing process in various countries around the world. Although the degree of liberalization and rules of different markets differ broadly, participation of renewable resources especially wind farms is encouraged by the regulatory authorities of markets. Wind power generation requires high investment, while they have low operation cost. In spite of various advantages, operation of wind energy resources in the restructured power systems has a lot of problems [1–3]. GenCos, which participate in the market, are expected to present offers and deliver the agreed amount of energy in a given period. So, Due to the uncertain behavior of wind power generation, participation of wind power producers in the market without considering supportive strategies may decrease their profits. Previous researches focus on the single participation of wind generation in electricity markets. In [4], an offering strategy for wind power producers under New Electricity Trading Arrangements (NETA) rules is proposed, allowing participants to offer only a few hours before the operation time. Ref. [5] presents a method ⇑ Corresponding author. Tel./fax: +98 21 88220121. E-mail addresses: [email protected] (A.K. Varkani), modares.ac.ir (A. Daraeepour), [email protected] (H. Monsef).

daraeepour@

0306-2619/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2011.06.043

for optimal offering strategy of wind producers based on minimization of their imbalance costs. This method utilizes stochastic programming to generate optimal wind power generation for a short-term power market. In [6], another strategy for minimization of imbalance costs of wind producers is developed that considers the probabilistic forecasting of wind generation and models the sensitivity of a wind power producer to the regulation costs. A new method for deriving the best offering strategy of a wind power producer in an electricity market including various trading floors is presented in [7]. A strategy for trading option of wind power in the emerging electricity market, based on the effect of wind generation on market clearing price (MCP), is discussed in [8]. It considers an award for wind producers if their participation in the market reduces the MCP. However, this strategy is only effective if there are large-scale wind power producers in the market. The proposed method in [9] models and evaluates the flexibility on switching tariffs as real compound options for wind producers to increase their profits and further reduce their operation risks. The aforementioned papers do not consider any support for participation of wind power producers in the market that can affect their revenues. In contrast, some research works investigate supportive strategies for participation of wind power producers in the market. Presented method in [10] deals with participation of wind resources in daily and hourly energy markets without taking into

A.K. Varkani et al. / Applied Energy 88 (2011) 5002–5012

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Nomenclature A. Indexes i index of scenarios (probabilistic wind production scenarios) t index of hours in a day (t = 1, . . . , 24) B. Parameters and constants C operation cost rate of the pumped-storage plant (€/MW h) ei corresponding error of the ith scenario in the distribution function ; Emin capacity limits of the upper reservoir (MW h) Emax u u E0u ; Eend u

initial and final levels in the upper reservoir in a day (MW h) M a large positive number that exceeds installed capacity of wind farm expected energy price in day-ahead market at hour t MPt (€/kW h) MPdown expected negative imbalance price at hour t (€/kW h) t MPup positive imbalance price at hour t (€/kW h) t expected price in spinning reserve market at hour t MPst (€/kW h) MPrt expected price in regulation reserve market at hour t (€/kW h) MPspot expected energy price in spot market at hour t (€/kW h) t N number of identical pumped-storage units associated in the same pond pi probability of the ith scenario probability of spinning reserve delivery request ps pup probability of regulation-up state r pdown probability of regulation-down state r probable wind production in the ith scenario (kW) PWi,t PW,t real wind production at hour t (kW) b Wt forecasted wind production at hour t (kW) P PWmax installed capacity of wind farm (kW) min generation power limits of each pumped-storage unit Pmax gP ; P gP (MW)

account the imbalance penalty. A new supportive method for pricing and utilizing wind resources in short-term power markets is suggested in [11]. This method derives the best level of contract for wind producers according to their expected power production. The above-mentioned methods increase the operation cost of system, while one of the most fundamental aims of restructuring power markets is eliminating the subsidies of producers to create perfectly competitive power markets. On the other hand, eliminating the subsidies from wind power producers not only reduces their revenues but also diminishes the development of wind energy resources because of their high investment requirements. Thus, some papers consider combinational operation of wind energy resources with other energy resources. Ref. [12] discusses a strategy for offering and operating a combination of wind and hydro-generation resources, which results in an increase in their joint revenues. In [13,14], joint operation of wind and pumped-storage power plants is studied. The studies include energy balance analysis and economic viability. In [15], the combined optimization of a wind farm and a pumped-storage facility from the viewpoint of the GenCo in a market environment is investigated. However, this research only considers participation of the resources in day-ahead energy markets, ignoring the fact that pumped-storage plants can also take part in ancillary service markets. One of the most important strategies for increasing profits of the wind power producers is integrating wind resources with limited

min Pmax pumping power limits of each pumped-storage unit pP ; P pP (MW) g efficiency of the pump-turbine cycle

C. Variables bi,t binary variables used for definition of positive and negative energy imbalances (equals 1 to negative energy imbalance) Eu,t stored energy in the upper reservoir at hour t (MW h) lower limit of stored energy in the upper reservoir at Emin u;t hour t (MW h) mg,t binary variable equals 1 if pumped-storage plant works in generation mode np,t integer variable that indicates the number of units that are running in the pumping mode (0, 1, . . . , N) PPb,t energy offer to the day-ahead market by pumped-storage plant at hour t (kW h) PWb,t energy offer to the day-ahead market by wind farm at hour t (kW h) PWPb,t joint energy offer of the wind farm and pumped-storage plant at hour t (kW h) PgP,t discharge power output of the pumped-storage plant at hour t (kW) PpP,t pumping power input of the pumped-storage plant at hour t (kW) PgsP,t power offer to spinning reserve market by pumpedstorage plant at hour t in the generation mode (kW) PpsP,t power offer to spinning reserve market by pumpedstorage plant at hour t in the pump mode (kW) PgrP,t power offer to regulation reserve market by pumpedstorage plant at hour t in the generation mode (kW) RP expected profit of pumped-storage plant in daily market (€) RW expected profit of wind farm in daily market (€) RWP joint expected profit of both wind farm and pumpedstorage plant in daily market (€)

energy resources such as pumped-storage power plants. Coordinated operation of a wind farm and a pumped-storage plant can provide added value for the wind farm that takes part in the market in comparison with separate participation of them. Pumped-storage plants’ capability of storing energy can significantly reduce the risk of self-scheduling for wind power producers in the market. In other words, as both resources in the integrated operation are owned by a GenCo, its flexibility in operation of them increases. Moreover, the GenCo can lower the uncertainty of its self-scheduling results [15,16]. At the same time, for presenting an integrated self-schedule, a GenCo needs to take part in all markets allowed to participate (i.e. energy market and ancillary service markets). So, self-scheduling the integrated operation of wind resources and pumped-storage plants necessitates participation of pumpedstorage plants in energy and ancillary service markets. Otherwise, the obtained added value of the strategy is not exactly estimated and could be misleading. Another important factor for an integrated self-scheduling is modeling the uncertainty of wind power generation. Without considering this uncertainty, the risk of wind producers for participating in the market increases [3,6]. As the main innovation, a new strategy for self-scheduling the integrated operation of wind generation and a pumped-storage plant is presented in this paper, which takes into account participation of the pumped-storage plant in energy and ancillary service

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markets. Therefore, a joint offer from both wind generation and the pumped-storage plant is presented to the day-ahead energy market. Furthermore, two generation offers for participation of the pumped-storage plant in spinning and regulation reserve markets are calculated. As another contribution, the uncertainty of wind power generation is modeled by a novel probabilistic function which utilizes a Neural Network (NN)-based technique. Considering the uncertainty of wind power generation, the proposed selfscheduling problem is a stochastic programming problem. The resulting problem is solved by a Mixed Integer Non-Linear Programming (MINLP) method. Moreover, the proposed strategy is tested on a real case in mainland, Spain. The remaining parts of the paper are organized as follows. In Section 2, a detailed description of the problem is presented. Section 3 introduces the proposed method for modeling the uncertainty of wind power production. The proposed self-scheduling problem is described in Section 4. A realistic example case is presented in Section 5. Finally, conclusions are stated in Section 6. 2. Problem description 2.1. Wind resources in power market Wind producers, who participate in day-ahead markets, have to submit their offers several hours before the operation. In the Spanish electricity market, offering period is usually 12–36 h ahead [3]. Therefore, wind producers must have a tool for short-term forecasting of their production [17,18]. However, the wind power forecasting tools are not so accurate. Thus, modeling the uncertainty of predicted wind power generation is a serious issue for the wind producers. In this paper, a NN-based technique is employed to forecast wind power generation and model its uncertainty. It is noted that, this paper only investigates the offering of wind power in the day-ahead energy market. 2.2. Pumped-storage plant in the power market A pumped-storage plant is composed of an upper reservoir and a lower reservoir which are connected through a channel called penstock. Typically, a reversible pump-turbine makes possible the storing of energy in off-peak hours so that it could be sold to the market during peak hours, making the operation economically profitable [15]. There are three modes of operation for a pumpedstorage plant: generation mode, pump mode and standby mode. Before the restructuring, pumped-storage plants were usually used for peak-shaving and coordination of hydro-thermal plants. Nowadays, pumped-storage plants can independently participate in energy markets to buy energy in the pump mode and sell it in the generation mode [19–21]. Moreover, they can take part in ancillary service markets. This paper investigates participation of them in a day-ahead energy market and ancillary service markets, including spinning and regulation reserve markets. 2.3. Structure of the markets Based on the considered structure in this paper, a wind farm and a pumped-storage plant can take part in different markets of Table 1, according to their technical characteristics. From Table 1, it is observed that wind resources cannot participate in the ancillary service markets because of the uncertainty in their production. In some energy markets, wind resources can participate in both day-ahead and real time markets. However, presented model in this paper only includes their participation in the day-ahead market. Since pumped-storage plants can take part in both energy and ancillary service markets, the structure of spin-

Table 1 Participation status of wind and pumped-storage plants in power markets. Power plant

Wind farm Pumped-storage plant Generation Pump Standby

Energy market

Ancillary service market Spinning reserve

Regulation reserve

U





U U 

U U U

U  

U: Participation; : no participation.

ning reserve and regulation reserve markets with participation of a pumped-storage plant are explained in the following paragraphs. Two different cases are considered for participation of the GenCo in the spinning reserve market [22]: 1. Energy generation is required: In this case, in addition to the hourly price of spinning reserve market, the GenCo is paid based on spot market price. The occurrence probability of this case depends on the market history, climate conditions, etc. In the proposed strategy, the probability of this case is defined as ps. 2. There is no need to generate energy: In this case, according to the hourly price of spinning reserve market, the GenCo receives a capacity payment. In this paper, the probability of this case is defined as (1  ps). A regulation reserve market is designed to balance the energy generation and consumption instantaneously. Here, three different cases are regarded for participation of the GenCo in the market [22]: 1. Regulation-up state: In this state, besides the hourly price of regulation reserve market, the GenCo is paid based on spot market price and according to its generation increase. The probability of this case is defined as pup r . 2. Regulation-down state: In this state the GenCo is paid hourly price of regulation reserve market as well, but it returns a payment based on spot market price and according to its generation decrease. The probability of this case is defined as pdown . r 3. Non-Regulation state: In this state, the GenCo receives only the hourly price of regulation reserve market. The probability of down this state is defined as 1  pup . r  pr In the generation mode, pumped-storage plant can participate in all three markets, i.e. energy market, spinning reserve market and regulation reserve market. In the pump mode, they can take part in the energy market as a load and in the spinning reserve market as an interruptible load which can reduce its consumption to decrease the total system load. In the standby mode, a pumpedstorage plant can be synchronized to the power grid and it can participate in the spinning reserve market. The other assumed hypotheses of the model are as follows: (a) The modeled markets are the day-ahead energy market and ancillary service markets, including spinning and regulation reserve markets (under Spanish electricity market rules). The other markets of Mainland Spain, e.g. adjustment market, are not modeled. (b) The subsidies for wind power production are not considered in the model. (c) The uncertainty of wind power generation is modeled by probabilistic scenarios.

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18000 Real Forecasting

17000 16000 15000 14000

Wind power (kW)

13000 12000 11000 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0

0

8

16

24

32

40

48

56

64

72

80

88

96

104

112

120

128

136

144

152

160

168

Time interval (hour) Fig. 1. Real and forecasted values of wind power for a test week (September 3–9, 2007).

(d) The uncertainties of energy, spinning reserve and regulation reserve prices are not considered in the model. (e) The risk analysis of the offering strategy for the GenCo is not modeled. 3. Modeling uncertainty of wind power prediction This section seeks to predict the wind power and model its uncertainty for a wind farm that takes part in the energy market. After predicting the wind production and computing error values of production forecasts, probability distribution function of the forecasting error values is obtained. This function and hourly forecasted values of wind production are employed to generate probabilistic production scenarios, which show the uncertainty of prediction. The prediction method and the proposed technique for modeling the uncertainty are introduced in the next subsections. 3.1. Prediction method In this paper, a NN-based method for short-term (next day) wind power prediction is used. The predictor is a Multi-Layer Percepterons (MLP) Neural Network with Levenberg–Marquardt (LM) learning algorithm. The LM algorithm trains a Neural Network 10–100 times faster than the usual gradient descent back propagation method. This algorithm is an approximation of Newton’s method, and it computes the approximate Hessian matrix. Mathematical details of this learning algorithm can be found in [23]. According to Kolmogorov’s theorem, the MLP can solve a problem by using one hidden layer, provided that it has a proper number of neurons [24]. So, one hidden layer has been considered in the MLP structure of the NN to simplify its structure and reduce the number of adjustable parameters (e.g. number of hidden layers and nodes). Wind power production of each hour has strong dependencies on its previous neighboring values. Moreover, wind production signal is usually a nonlinear function of the exogenous variables such as wind speed, wind direction, and temperature. Therefore, the candidate set of inputs for wind power production is including lagged values of wind production and wind speed, so that no effective input is missed [25,26]. However, this candidate set is very

large for using in the NN training. Hence, the candidate set is refined by mutual information (MI) feature selection technique, so that the irrelevant candidate features are removed from it and a small subset of the most effective features is obtained for training the NN. The mathematical details of the MI feature selection technique could be found in [27]. The prediction method is tested on Sotvaneto wind farm in Spain with 17,560 kW nominal capacity. The data of this wind farm can be obtained in [28]. The real and forecasted values of wind power for a test week (September 3–9, 2007) are shown in Fig. 1. 3.2. Modeling the uncertainty In this paper, the forecasting error of the NN-based predictor is used for modeling the uncertainty of wind power production. Modeling the uncertainty is utilized in the offering strategy of wind farm owners in power markets. It is supposed that the wind farm owners use the NN-based predictor as a forecasting tool. Modeling the uncertainty and generating probabilistic production scenarios are performed using the following step by step algorithm: Step 1. Using the historical values of wind production and wind speed, wind production for a 1 month period before offering is predicted. It is noted that considering short run trends of wind production, longer periods may be misleading. Step 2. Hourly values of the prediction error for the respective month are obtained as follows:

errort ð%Þ ¼

b Wt PW;t  P  100 P W max

ð1Þ

b Wt indicate the real and forecasted values of where PW,t and P wind power production at hour t, respectively and PWmax is the installed capacity of wind farm. Step 3. Hourly error values (errort) are categorized in 1% distances and each category is corresponding to a probabilistic scenario. After summing number of error values and computing the density of error in each category (by dividing the number of hourly error values in each category to the whole number of hours in the respective month), probability distribution

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Fig. 2. Probability distribution function of Sotvaneto wind farm.

function of the prediction error is calculated. Therefore, pi, the probability of each scenario (each error range or category) is obtained. In other words, a probabilistic scenario means the probability of having hourly prediction error values in each scenario (respective error distance). Step 4. By predicting wind production of the next 24 h (offering period), probabilistic production scenarios for each hour of the offering period are obtained as follows:

b W;t þ ðei  P b W;t  PW max Þ i ¼ 1; . . . ; I PWi;t ¼ P

ð2Þ

where PWi,t is the likely wind production of hour t in the ith scenario; ei represents the corresponding error of the ith scenario and I is the number of all scenarios (error categories). Obtained distribution function from prediction error of Sotvaneto wind farm is shown in Fig. 2. It is obtained from hourly prediction error of August 2 to September 2, 2007. As seen from Fig. 2, the number of scenarios equals 77 (i.e. I = 77). 4. The proposed self-scheduling strategy In this section, the proposed self-scheduling strategy for integrated operation of wind and pumped-storage plants in the power market is presented. The most important characteristic of the proposed strategy is considering participation of the GenCo in both day-ahead energy market and ancillary service markets. In order to compare performances of the integrated operation with uncoordinated operation of the resources, modeling assumptions of these two different configurations are presented in the following subsections.

the energy offer in each hour of day (PWb,t). In Eq. (3), PWi,t, represents the probable production of hour t in the ith scenario, pi is probability of the ith scenario, MPt indicates the expected energy price in day-ahead market at hour t, MP up t denotes the positive imbalance price at hour t, MPdown is the expected negative t imbalance price at hour t and bi,t is used for definition of positive and negative energy imbalances. Problem constraints are given in (4)–(6). First and second constraints, given in (4) and (5), are considered for calculating the binary variables bi,t. If the wind production is less than energy offer in the market, bi,t = 1, otherwise bi,t = 0. In other words, the phrase [b  MPdown  (Pwb  Pwi)] is a penalty of the wind farm if it does not produce as much as it offers. However, there is no penalty for a positive imbalance, just a different price. The wind farm is still paid for whatever excessive energy is produced beyond what was offered, but it is paid at a different price, MPup (MPup 6 MP 6 MPdown). The last constraint, given in Eq. (6) limits the offer of energy to the installed capacity of wind farm. Operation costs of wind farm are not taken into consideration.

Max : RW ¼

X

( MPt  PWb;t þ

t

ð1  bi;t Þ  MPup t  ðP Wi;t

i

PWb;t Þpi  bi;t  ðPWb;t  PWi;t Þ 6 M  bi;t ;

X

MPdown t

 ðPWb;t  PWi;t Þpi

i ¼ 1; . . . ; I

ðPWi;t  PWb;t Þ 6 M  ð1  bi;t Þ; 0 6 P Wb;t 6 PW max

i ¼ 1; . . . ; I

) i

ð3Þ

ð4Þ ð5Þ ð6Þ

4.1. Modeling the uncoordinated operation

(2) Pumped-storage plant:

In the uncoordinated operation, the wind farm and pumped-storage plant independently take part in the market to maximize their incomes. Each utility derives its offer while satisfying its own technical constraints. In this paper, the wind farm only offers to the day-ahead energy market, while pumped-storage plant offers to the day-ahead energy market and ancillary service markets. Schematic diagram of the uncoordinated operation is illustrated in Fig. 3.

The pumped-storage plant participates in the day-ahead energy market, spinning reserve market and regulation reserve market. The offering strategy of a pumped-storage plant is maximizes the plant’s profits within a daily scope based on Eq. (7). Regarding the integrated operation of the wind farm and the pumpedstorage plant in a daily market, the scheduling time scope of pumped-storage plant is taken one day in the modeling assumptions. Indeed, stored energy level in the upper reservoir in the beginning and at the end of a day are considered equal. It is noted that the corresponding variables of the reservoir volume are expressed in terms of energy.

(1) Wind farm: The offering strategy is a maximizing problem based on stochastic programming, which maximizes Eq. (3), and calculates

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Max : RP ¼ Ic1 þ Ic2  Co1  Co2 Ic1 ¼

24 X

MP t  PgP;t þ

t¼1

Ic2 ¼

24 X

24 X

ð7Þ

MPst  ðPgsP;t þ PpsP;t Þ þ

t¼1

MP spot  ðP gsP;t þ PpsP;t Þ  ps þ t

t¼1

24 X

MPrt  PgrP;t

24 X

MPspot  PgrP;t t

t¼1

down  ðpup Þ r  pr

Co1 ¼

24 X

ð8Þ

t¼1

ð9Þ

MPt  PpP;t

ð10Þ

energy from the day-ahead energy market in the pump mode. In Eq. (10) PpP,t is the Pumping power input of the pumped-storage plant at hour t. finally, Co2 is the operation cost of pumped-storage plant. For computing Co2, the operation cost rate of the plant, C, is multiplied by the sum of generated and consumed energy of the plant, because of working costs in both pumping and generation modes. Constraints of the problem are given in the following equations:

Eu;t ¼ Eu;t1 þ g  PpP;t  PgP;t  g  ps  PpsP;t  ps  PgsP;t  ðpup r

t¼1

Co2 ¼

24 X t¼1



 pdown Þ  PgrP;t r

 C  PgP;t þ PpP;t þ ps  ðPgsP;t  PpsP;t Þ þ PgrP;t

ðpup r



pdown Þ r



ð11Þ

Objective function of this problem consists of four different components, including Ic1, Ic2, Co1 and Co2. First, Ic1 is the income of pumped-storage plant earned from taking part in the day-ahead energy market in the generation mode (the first term of Eq. (8)), in the spinning reserve market in the generation and pump modes (the second term of Eq. (8)) and in the regulation reserve market (the third term of Eq. (8)). In Eq. (8), MPt, MPst and MP rt , respectively, represent expected prices in day-ahead, spinning reserve and regulation reserve markets at hour t, PgsP,t and PpsP,t are, respectively, power offers to the spinning reserve market by the pumped-storage plant at hour t in generation and pump modes, PgrP,t stands for power offer to the regulation reserve market by the pumped-storage plant at hour t in the generation mode and PgP,t indicates discharge power output of the pumped-storage plant at hour t. Second, Ic2 is the income of pumped-storage plant from power delivery request of system operator in the spinning reserve market (the first term of Eq. (9)) and the regulation reserve market (the second term of Eq. (9)). In Eq. (9) MPspot is the expected energy price in spot market at hour t and ps t represents the probability of spinning reserve delivery request. Regarding the increased income of pumped-storage plant in the regulation-up state and its reduced income in the regulation-down state (when it participates in the regulation reserve market), the difference between probabilities of regulation-up and regulation-down down occurrences (i.e. pup ) is taken into account in the second term r  pr of Ic2. Third, Co1 is the cost of pumped-storage plant for buying

ð12Þ

max Emin u;t 6 Eu;t 6 Eu

ð13Þ

Emin u;t

ð14Þ

¼

Emin u

þ PgsP;tþ1 þ P psP;tþ1 þ PgrP;tþ1

max Pmin gP  mg;t 6 P gP;t 6 P gP  N  mg;t

ð15Þ

Pmin pP

ð16Þ

Pmin gP

 np;t 6 PpP;t 6

Pmax pP

 mg;t 6 PgrP;t 6

 np;t

ðPmax gP

 N  mg;t Þ=2

ð17Þ

PgrP;t 6 PgP;t

ð18Þ

max Pmin gP  mg;t 6 P gsP;t 6 P gP  N  mg;t

ð19Þ

Pmin pP

 np;t 6 PpsP;t 6 P pP;t  np;t

PgP;t þ P gsP;t þ PgrP;t 6 P max gP  N  mg;t 1  np;t 6 1 N 1 mg;t1 þ  np;t 6 1 N 1 mg;t þ  np;t1 6 1 N E0u ¼ Eend u mg;t þ

PPb;t ¼ PgP;t  PpP;t

ð20Þ ð21Þ ð22Þ ð23Þ ð24Þ ð25Þ ð26Þ

Eq. (12) models the expected stored energy in the upper reservoir of plant. Upper and lower limits of the storable energy in upper reservoir for each hour ðEmax and Emin u u;t Þ are given in (13) and (14), respectively. The upper limit depends on the reservoir volume and does not vary with time; While, lower limit depends on two factors. A minimum volume of water or energy ðEmin u Þ has to exist in the upper reservoir.

Fig. 3. Schematic diagram of the uncoordinated operation.

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Besides, the plant has to store a minimum level of water for the required production of the next hour (i.e. simultaneously required production for all energy, spinning reserve and regulation reserve markets). It is assumed that the lower reservoir is larger than the upper reservoir of plant and so the limits of storable energy in the lower reservoir are not usually taken into account in the problem. Permissible limits of energy production in generation mode hours min ðPmax gP ; P gP Þ and energy consumption in pump mode hours min ðPmax pP ; P pP Þ are presented in (15) and (16), respectively. The presented constraints in (17) and (18) guarantee the occurrence of regulation down and regulation up states. Permissible limits of the plant for taking part in the spinning reserve market in generation and pump modes are considered in (19) and (20), respectively. Eq. (21) shows the allowable limits for summation of all offered energy in day-ahead, spinning reserve and regulation reserve markets in the generation mode. Eq. (22) guarantees that if a pumped-storage unit is in the pump mode, operation of the other pumped-storage units in the generation mode is not possible. The change-over time is modeled in (23) and (24). Change-over time is a time period (usually about 10– 30 min), which is required for changing the operation mode of the plant, i.e. pump mode to generation mode and vice versa. So, it can restrict participation of the plant in hourly basis energy and ancillary service markets. Therefore, modeling the change-over time is necessary. In order to keep the balance of stored energy level in the upper reservoir in the beginning and at the end of the scheduling time scope, Eq. (25) is used. Energy offer of the plant to day-ahead energy market (PPb,t) is given in (26). Negative values of PPb,t show the pump mode and the positive values show the generation mode.

4.2. Modeling integrated operation

plants is presented to the day-ahead energy market. Moreover, two series of offers from the pumped-storage plant are also given to the spinning and regulation reserve markets. Fig. 4 shows a schematic diagram of the self-scheduling strategy for the integrated operation of a wind farm and pumped-storage units. As seen in Fig. 4, the outputs of problem consists of PWPb,t (joint energy offer of the wind farm and the pumped-storage plant), PgsP,t (offer of the pumped-storage plant to the spinning reserve market in the generation mode), PpsP,t (offer of the pumped-storage plant to the spinning reserve market in the pump mode as an interruptible load) and PgrP,t (offer of the pumped-storage plant to the regulation reserve market in the generation mode). The proposed integrated self-scheduling strategy is a stochastic programming problem, which maximizes an objective function presented in Eq. (27). RWP is daily joint profit of both the wind and pumped-storage plants. The problem constraints are given in (33)–(35) and (12)–(25) from the previous subsection, respectively.

Max : RWP ¼ R1 þ R2 þ R3  R4  R5

ð27Þ

24 X   R1 ¼ MP t  P WPb;t þ MPst  ðP gsP;t þ PpsP;t Þ þ MPrt  PgrP;t

ð28Þ

t¼1

R2 ¼

24 X  spot MP t  ðPgsP;t þ PpsP;t Þ  ps þ MPspot  PgrP;t t t¼1

 down Þ ð29Þ ðpup r  pr " # 24 X X MPup ð1  bi;t Þ  ½ðPWi;t þ PgP;t  PpP;t Þ  P WPb;t   pi ð30Þ R3 ¼ t  t¼1

R4 ¼

24 X

i

" MPdown t



t¼1

R5 ¼

24 X

bi;t  ½PWPb;t  ðPWi;t þ PgP;t  PpP;t Þ  pi

 C  PgP;t þ PpP;t þ ps  ðP gsP;t  PpsP;t Þ þ PgrP;t

t¼1 down Þ ðpup r  pr



ð32Þ

½P WPb;t  ðP Wi;t þ PgP;t  PpP;t Þ 6 M  bi;t ; Pmin pP

6 PWPb;t 6 P W max þ N 

Wind Turbine Generators

Pmax gP

Ancillary Services

PgsP ,t , PpsP ,t Offering Strategy (Stochastic Programming)

Spinning Reserve Market

Regulation Market

Power System

PgrP ,t

Power Power (Pump Mode) (Generation Mode)

Upper Reservoir W

ate

rD

isc

ha rge

N Generators/Motors

...

i ¼ 1; . . . ; I

½ðPWi;t þ PgP;t  PpP;t Þ  PWPb;t  6 M  ð1  bi;t Þ; N

ð31Þ

i

Day Ahead Market

Integrated operation of a wind farm and a pumped-storage plant increases the profits of their owner. The proposed integrated operation takes into account participation of a wind farm and a pumped-storage plant in the day-ahead energy market. Besides, for obtaining the real added value of integrated operation, participation of the pumped-storage plant in the spinning and regulation reserve markets is also considered. Therefore, for integrated selfscheduling, a joint offer from both wind and pumped-storage

#

X

Unit N

Unit 1

Lower Reservoir

Fig. 4. Schematic diagram of the self-schedule strategy for integrated operation.

i ¼ 1; . . . ; I

ð33Þ ð34Þ ð35Þ

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A.K. Varkani et al. / Applied Energy 88 (2011) 5002–5012

Objective function of the problem consists of five main components R1, R2, R3, R4 and R5. First, R1 is the income of both the wind farm and the pumped-storage plant for taking part in the energy, spinning and regulation reserve markets. Second, R2 is the income of pumped-storage plant from power delivery request of system operator in spinning and regulation reserve markets. Third, R3 is the income of both the wind farm and the pumped-storage plant considering the probability of positive energy imbalance and positive energy imbalance price (MPup t ) in the energy market. Next, R4 is the penalty cost of both plants for their negative energy imbalance volume in the energy market. Finally, R5 shows the operation cost of pumped-storage plant. The constraints given in (33) and (34) are considered for determining bi,t, used for definition of positive and negative energy imbalance volumes. If joint production of both wind farm and pumped-storage plant is less than energy offer in the market, bi,t = 1, otherwise bi,t = 0. The third constraint, given in Eq. (35), shows the upper and lower limits of the energy offer regarding the installed capacity of wind and pumped-storage plants. In this case, the energy offer is in the form of generation and consumption. The other constraints were described in the previous subsection. 5. Numerical results To verify the quality of proposed strategy, it is examined on a test case. The proposed model has been implemented in the General Algebraic Modeling System (GAMS) environment to solve the resulted MINLP problem. DICOPT solver is used to solve the problem. The whole running time is less than 17 min on an Intel Core 2 Duo 2 with 2 GB RAM which is reasonable within a day-ahead decision making framework. The linearization technique of paper [7] is utilized to investigate the convexity of the proposed non-linear model. The results of linear and non-linear models show the convexity of the proposed model. 5.1. Test case The following input data are considered in the test case: (1) Wind farm: the generation data of Sotvaneto wind farm, for a test week (September 3–9, 2007) is used [28]. (2) Pumped-storage plant: a small pumped-storage plant with similar units is used and its characteristics are presented in Table 2. Efficiency of pumped-storage plants is generally about 67% [20]. So, the same efficiency is considered for the pumped-storage plant. Operation cost rate of the plant (C) is chosen same as the condition used in [19]. (3) Energy market price: in the time scope of the self-scheduling problem, the real values of hourly day-ahead energy price in the Spanish electricity market are used [29].

Table 2 Parameters of the pumped-storage plant. Capacity limits of the upper reservoir (MW h) Initial energy level in the upper reservoir (MW h) Generation power limit for each pumped-storage unit (MW) Pumping power limits for each pumped-storage unit (MW) Number of identical pumped-storage units Efficiency of the pump-turbine cycle Operation cost rate of the pumped-storage plant (€/MW h)

(4) Spinning and regulation reserve prices: in the time scope of the self-scheduling problem, the real values of ancillary service markets in the Mainland Spain are used instead of forecasted values of spinning and regulating reserve prices [29]. (5) Imbalance energy prices: positive and negative imbalance prices depend on the considered regulation mechanism. In certain cases, they simply equal a certain proportion of the market clearing price [6,30]. For instance in Spain, they are as follows [6]:

(

MPup t ¼ ð1  sÞ  MP t

(6) Spot market prices: Eq. (37) is used to predict the hourly spot market prices [31]. This equation is defined based on peak hours. c1, c2 are two random variables.

MP spot ¼ t



ð1 þ c1 Þ  MPt

0 6 c1 6 0:2 t 2 ½12 ; 23

ð1 þ c2 Þ  MPt

0:1 6 c2 6 0:1 otherwise

5.2. Base case study

N=2

g = 0.67 C = 2.5

ð37Þ

In the base case study certain assumptions are taken: s = 0.5, the probability of spinning reserve delivery request ps = 0.05, and probabilities of being in regulation-up and regulation-down states down are considered pup ¼ 0:35, respectively [32]. r ¼ 0:4 and pr Fig. 5 shows energy offers in the uncoordinated and integrated operations of the resources in the day-ahead energy market. Spinning and regulation reserve offers of the pumped-storage plant in the uncoordinated and integrated operations are shown in Fig. 6. In the curves of spinning reserve offer, negative offer values correspond to the pump mode of pumped-storage plant, which means acting as an interruptible load. Some interesting observations can be seen from Figs. 5 and 6 as follows: 1. The pumped-storage plant always buys energy in off-peak hours. 2. When the pumped-storage plant is in the pump mode, i.e. it buys energy from energy market, spinning reserve offer is presented as an interruptible load. 3. In both uncoordinated and integrated operations, regulation reserve offer and energy offer are equal in several hours. Curves of stored energy in the upper reservoir of pumped-storage plant in both uncoordinated and integrated operations are shown in Fig. 7. As seen, in the third, fifth and seventh days of the test week, operation modes of the plant in the uncoordinated and integrated operations have different conditions, due to the shift of pump mode from the beginning to the end of the day. Expected profits for the uncoordinated and integrated operations of wind and pumped-storage plants in 7 days of the test week are presented in columns 2 to 4 of Table 3. Besides, added value (AV) of the proposed strategy is given in the last column of Table 3 and obtained as follows:

AV ¼ RWP  ðRW þ RP Þ Emax ¼ 125 u ¼ 40 Emin u E0u ¼ 80 P max gP ¼ 6 P min gP ¼ 0 P max pP ¼ 5 P min pP ¼ 5

ð36Þ

MPdown ¼ ð1 þ sÞ  MP t t

ð38Þ

In Eq. (38), RWP is the joint expected profit of both the wind farm and the pumped-storage plant in daily market, RW is the expected profit of wind farm in daily market and RP is the expected profit of pumped-storage plant in daily market. As seen from Table 3, owners earn considerable added value in the integrated operation of both resources with respect to the uncoordinated operation of them. Comparing the weekly profit of integrated operation with the weekly profit of pumped-storage plant in the uncoordinated operation (71736.63–38692.14 = 33044.49) shows 6.23% increase in the weekly profit of wind farm (33044.49/31106.55 = 1.0623).

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20000

Integrated Operation

17500 15000 12500 10000 7500 5000 2500 166

163

160

157

154

151

148

145

142

136

139

133

130

127

124

121

118

109

115

112

106

103

97

94

100

88

91

82

85

76

79

73

67

70

64

58

61

55

52

49

43

46

40

34

31

37

28

19

25

16

22

13

10

1

4

7

0 -2500 -5000 -7500 -10000 -12500 -15000 Fig. 5. Energy offers in the uncoordinated and integrated operations.

Fig. 6. Spinning and regulation reserve offers of the pumped-storage plant in the uncoordinated and integrated operations.

Uncoordinated Operation

Integrated Opration

130 120 110 100 90 80 70 60

40

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106 109 112 115 118 121 124 127 130 133 136 139 142 145 148 151 154 157 160 163 166

50

Fig. 7. Stored energy in the upper reservoir of pumped-storage plant.

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A.K. Varkani et al. / Applied Energy 88 (2011) 5002–5012 Table 3 Expected profits and added values for uncoordinated and integrated operations. Day

Expected profit (€) Uncoordinated operation Wind farm

1 2 3 4 5 6 7 Sum

Added value (€) Integrated operation

Pumped-storage plant

723 996 1447

31106.55

38692.14

71736.63

1937.94

5.4. Effect of modeling ancillary services markets on the added value

Expected profit (€)

Wind farm

Pumped-storage plant

35108.24 31106.55 27104.84

38692.14 38692.14 38692.14

Added value (€) Integrated operation

74277.11 71736.63 70243.93

Expected profit (€)

Wind farm

Pumped-storage plant

31106.55 31106.55 31106.55

38941.71 38692.14 38380.78

476.73 1937.94 4446.95

Added value (€) Integrated operation

71562.32 71736.63 71638.15

Expected profit (€) Uncoordinated operation

0.3 0.35 0.38

11132.28 11141.04 11142.51

in Table 4. Obtained results show that as s increases, corresponding to higher risk for the wind farm, the added value of integrated operation increases. In other words, the added values of integrated operation increase for higher negative imbalance prices.

1514.06 1937.94 2150.82

Table 6 Expected profits and added values of the test week for different values of pdown . r pdown r

26 77 95

535.58 508.23 109.59 188.44 155.27 258.67 182.16

Uncoordinated operation

0.02 0.05 0.1

Computational time (s)

11141.04 13304.31 9853.76 8330.81 10565.23 7995.4 10546.08

Table 5 Expected profits and added values of the test week for different values of ps. ps

Expected profit (€)

5346.84 4762.39 6002.69 5852.11 5606.4 4926.01 6195.7

Uncoordinated Operation

0.1 0.5 0.9

Number of scenarios

5258.62 8033.69 3741.48 2290.26 4803.56 2810.72 4168.22

Table 4 Expected profits and added values of the test week for different values of s.

s

Table 7 Expected profits and computational time for different number of scenarios.

Wind farm

Pumped-storage Plant

31106.55 31106.55 31106.55

38703.65 38692.14 38688.06

Added value (€) Integrated operation

71534.88 71736.63 71882.63

1724.64 1937.94 2088.02

5.3. Effect of imbalance prices on the added value In this subsection, the effect of imbalance prices on the added value of proposed strategy for the integrated operation is investigated. For this purpose, two cases with different imbalance prices are considered. In the first case s = 0.1, which provides a proper condition for wind farm because the price of its positive/negative imbalance energy in operation time is 0.9  MPt/0.1  MPt. In the second case s = 0.9, there is a high-risk condition for the wind farm. Expected profits of the test week for different values of s are given

In this subsection, the effect of participation of the pumpedstorage plant in ancillary services markets (spinning and regulation reserve markets) on obtained added values of the proposed strategy is investigated by changing the values of ps (probability of the spinning reserve delivery request), pup r (probability of the regulation-up state.) and pdown (probability of the regulation-down r state.). The added values and expected profits for different values of ps are presented in Table 5. As seen, slightly increment of ps results in increase of the added values. On the other hand, changing the considered probability for participation of the pumped-storage down plant in the regulation market (pup ) can affect the added r and pr value. In Table 6, the added values and expected profits have been down calculated for different values of pup . Since, the difference r and pr down between pup and p is important in the proposed strategy, the r r presented values in Table 6 are obtained by changing only pdown . r As seen, less difference between pup and pdown results in higher r r added values. 5.5. Effect of number of scenarios on accuracy and tractability of the problem To investigate the trade-off between accuracy and tractability of the considered scenarios, the proposed model is implemented for different number of scenarios based on 4 steps of Section 3.2. In order to have a fair comparison, the proposed model for joint scheduling of the wind and pumped-storage plants is executed for 26, 77 and 95 probabilistic scenarios with the same assumptions (s = 0.5, down ps = 0.05, pup ¼ 0:35) in September 3, 2007. Obtained r ¼ 0:4; pr results are reported in Table 7. Number of scenarios for each experiment is reported in the first column of Table 7. Obtained values of expected profits and computational time for different number of scenarios are shown in the second and third columns of Table 7, respectively. As shown in Table 7, for the case of 95 scenarios the expected profit only increases about 1.5 €, however, the computational burden increases 1447–996 = 451 s. On the other hand, as the number of scenarios decreases to 26, the expected profit decreases to 11141.04–11132.28 = 8.76 €. Though, the computational time decreases 996–723 = 273 s. Comparing the results shows that the problem almost approaches the saturation from this point of view, and increasing the number of scenarios may slightly change the results. 6. Conclusions In this paper a new strategy for self-scheduling the integrated operation of a wind farm and a pumped-storage plant is presented. The proposed strategy takes into account participation of a GenCo, owning both resources, in all markets which is allowed to participate. So, not only participation of the wind farm and the pumpedstorage plant in the day-ahead energy market is modeled, but also

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participation of the pumped-storage plant in spinning and regulation reserve markets is included. A Neural Network (NN) based technique is used for modeling the uncertainty of wind power generation. The proposed strategy is tested on a realistic example case in Spain for different market conditions. Obtained results show that integrated operation of both the wind and pumped-storage plants can significantly increase the added value of the GenCo. Obtained added values of different conditions show that for low/high values of positive/negative imbalance prices, the added value of proposed strategy increases. The results also show that considering participation of the pumped-storage plant in ancillary service markets can affect the obtained added value of the proposed strategy. References [1] Outhred H. Some operation and investment issues for wind farms in a restructured electricity industry, presented at the Solar Harvest, Newcastle, Australian; 2002. [2] Fabbri A, Gómez T, Rivier J, Méndez V. Assessment of the cost associated with wind generation prediction errors in a liberalized electricity market. IEEE Trans Power Syst 2005;20:1440–6. [3] Usaola J, Angarita J. Bidding wind energy under uncertainty. In: Presented at International Conference on In Clean Electrical Power, ICCEP; 2007. p. 754–9. [4] Bathurst GN, Weatherrill J, Strbac G. Trading wind generation in short-term energy markets. IEEE Trans Power Syst 2002;17:782–9. [5] Matevosyan J, Söder L. Minimization of imbalance cost trading wind power on the short-term power market. IEEE Trans Power Syst 2006;21:1396–404. [6] Pinson P, Chevallier C, Kariniotakis G. Trading wind generation from shortterm probabilistic forecasts of wind power. IEEE Trans Power Syst 2007;22:1148–56. [7] Morales JM, Conejo AJ, Perez-Ruiz J. Short-term trading for a wind power producer. IEEE Trans Power Syst 2010;25:554–64. [8] Singh SN, Erlich I. Strategies for wind power trading in competitive electricity markets. IEEE Trans Energy Convers. 2008;23:249–56. [9] Yu W et al. Valuation of switchable tariff for wind energy. Electric Power Syst Res (EPSR) 2006;76:382–8. [10] Piwko R et al. Wind energy delivery issues. IEEE Power Energy Mag 2005;3:47–56. [11] Parsa M, Talebi E, Mohamadian M. A new method for pricing of wind power in short-term power markets. In: Presented at 16th Power Systems Computation Conference (PSCC); 2008. [12] Angarita JM, Usaola JG. Combining hydro-generation and wind energy: biddings and operation on electricity spot markets. Electric Power Syst Res (EPSR) 2007;77:393–400.

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