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Renewable Energy 55 (2013) 252e259

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Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Risk-averse profit-based optimal operation strategy of a combinedwind farmecascade hydro system in an electricity market

Iman Gerami Moghaddama, Mostafa Nick b,*, Farhad Fallahi b, Mohsen Sanei a, Saeid Mortazavi a

aDepartment of Electrical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, IranbDepartment of Energy and Environment, Niroo Research Institute, 1015 Tehran, Iran

a r t i c l e i n f o

Article history:Received 31 July 2012Accepted 4 December 2012Available online 24 January 2013

Keywords:Electricity marketVirtual power plantWind powerCascade hydro systemRisk aversion

* Corresponding author. Tel.: þ41 216934819; fax:E-mail addresses: i-gerami@phdstu.scu.ac.ir (I.G.

epfl.ch (M. Nick), ffallahi@nri.ac.ir (F. Fallahi), mmortazavi_s@scu.ac.ir (S. Mortazavi).

0960-1481/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.renene.2012.12.023

a b s t r a c t

There is a trend toward direct participation of wind farms in electricity markets. However, wind power isinherently intermittent and cannot be accurately predicted even in short time; thus increasing theimbalance costs paid by wind farm owners. To cope with these problems, some techniques have beenproposed in literature including wind farm coupling to hydro units, energy storage facilities, and con-structing a virtual power plant (VPP). This paper presents a stochastic profit-based model for day-aheadoperational planning of a combined wind farmecascade hydro system. The generation company (GenCo)that owns the VPP considers a portion of its hydro plants capacity to compensate the wind powerforecast errors. The proposed optimization problem is a mixed integer linear programming (MILP),formulated as a two-stage stochastic programming model. The day-ahead scheduling is a here and nowdecision and the optimal operations of facilities are resources variables. In order to protect the GenCoagainst low price scenarios and wind power variation, the conditional value at risk (CVaR) is used as therisk aversion criterion. The proposed model is successfully applied to a real case study and the results arepresented and discussed. The results are illustrated varying in the risk aversion level and the penaltycoefficients for negative/positive imbalances. It is shown that the bidding strategy of the GenCo variessignificantly depending on the chosen penalty market mechanism.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Due to increasing concerns related to environment, depletingresources of fossil fuels and security of supply along with techno-logical advances, renewable energy is receiving more attentionthan ever [1]. Wind energy is one of the cheapest availablerenewable energy and is experiencing a rapid growth around theworld especially in the USA and Europe. The wind turbine hasachieved a technological maturity; however its power production isintermittent and intrinsically dependent on the variability of windspeed [2,3]. Thus large-scale integration of wind power brings newchallenges and difficulties to the operation of power systems.

In addition, the electricity industries are evolving towardderegulation and competition around the world. In this contextthe generation companies are more exposed to higher risk thanmonopolistic context [4]. Most electricity markets consist of a day-ahead market with a real-time or balancing market. The generation

þ41 (0)21 69 34662.Moghaddam), mostafa.nick@saniei@scu.ac.ir (M. Sanei),

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ownersmust submit their bid 10e14 h prior to the time of operationfor day-ahead market [5]. When the penetration of wind energyincreases in a power system, wind farm owners should participatein the day-ahead electricity market and submit their bids (as is inSpain) [5]. Their bid is subject to high uncertainties due to the windspeed forecast errors. These uncertainties would cause imbalancecost to system operators and this cost should be compensated bypenalizing those who produce it [6]. This would incur more cost onwind farm owners and may hinder investments in wind energydevelopment.

Several methods are proposed to deal with variability andintermittency of wind power and decrease its imbalance costs. InRef. [7] two methods are compared for hedging wind power,purchasing option and using pumped-hydro storage (PHS). Jointbidding strategy for wind farm together with hydro units or PHSs isinvestigated in many research papers [2e11]. In Ref. [8], it is shownthat a hybrid model of a wind farm and PHS can decrease theimbalance cost and smoothen the wind farm output. The operationpolicies for a combined wind farm and PHS in an island grid arestudied in Ref. [9]. Two different strategies for a wind farm owner,using short-term wind power prediction tools and using a hydrounit for participating in a spot market, is presented in Ref. [10] and

Nomenclature:

Parameters:l(scp,t) energy price in hour t in scenario price scpWV(i) marginal value of water of hydro plant iPenaltyPI positive imbalance penalty coefficientPenaltyNInegative imbalance penalty coefficientP1max, P2max upper limit of operation zones for hydro plant i

P1min, P2minlower limit of operation zones for hydro plant i

PW(scw,t) total amount of wind power available in hour t inwind scenario scw

b1(i), b2(i) slopes of input/output function of hydro plant iEmax(i), Emin(i) maximum and minimum reservoir capacity of

hydro plant is(i,t) the amount of water spillage of hydro plant i in hour tsi,j time constant of water flow between hydro reservoir i

and jsi,j the amount of water flow spillage between hydro

plants i and jinflow(t) the amount of water inflow into hydro plant 1 in hour t

Variables:Qscp,scw(i,t) the amount of water discharged from hydro plant i in

hour t in price scenario scp and wind scenario scwPh(i,t) the amount of power scheduled of hydro plant i in hour

tPscp,scwdn (i,t) the amount of down-regulation used from hydro

plant i in hour t in price scenario scp and windscenario scw

Pscp,scwup (i,t) the amount of up-regulation used from hydro plant i

in hour t in price scenario scp and wind scenario scwPscw(t) wind farm power production in hour t inwind scenario

scwCSD(i,t) shut-down cost of hydro unit i in hour tCSU(i,t) start-up cost of hydro unit i in hour tOC(i) operation cost of hydro plant i in hour tPI(scp,scw,t) the amount of positive imbalance in hour t in price

scenario scp and wind scenario scwNI(scp,scw,t) the amount of negative imbalance in hour t in price

scenario scp and wind scenario scwP1h(i,t), P2h(i,t) the amount of power scheduled of hydro plant i in

each operation zone in hour tP1up(i,t), P2up(i,t) the amount of up-regulation capacity of hydro

plant i in each operation zone in hour tP1down(i,t), P2down(i,t) the amount of down-regulation capacity of

hydro plant i in each operation zone in hour tv(i), w(i) binary variables associated with each operation zone

of hydro plant iu(i) binary variable associated with on/off sate of hydro

plant iBid(t) the total amount of GenCo bid for hour tEscp,scw(i,t) the amount of water stored in hydro reservoir i in

hour t

Sets:i index of hydro plantsscp index of energy price scenariosscw index of wind scenariost index of hours

I.G. Moghaddam et al. / Renewable Energy 55 (2013) 252e259 253

their benefits are investigated under various assumptions. A two-stage stochastic programming approach with two random param-eters, wind output and market price, is proposed in Ref. [5] foroptimal participating of a joint wind farm/PHS in a spot market. Infirst stage, a decision is made about the amount of bid for each hourof the day-ahead market. Second stage decision deals with theoperation of wind farm and PHS in real-time. A method for intra-day management of an energy storage facility to reduce theimbalances of awind farm is presented in Ref. [2]. The results in Ref.[2] show the impacts of a combined scheduling on the risks asso-ciated with the imbalance costs. In Ref. [11] a methodology toevaluate the profit of an energy storage facility for wind powertrading in a market environment, taking into account the forecasterrors of wind speed is presented. The results in Ref. [11] show thatthe profit increases with the use of an energy storage device.However, it is shown that the profit will be decreased with theincrease of its level of confidence. In mentioned studies variousmethods are proposed, however, a risk aversion criterion has notbeen yet incorporated into the optimization problems for a com-bined bidding strategy of a wind farmecascade hydro system,which is the subject of this work.

In this paper we propose a model for the optimal biddingstrategy of a combined wind farmecascade hydro system intoa day-ahead energy market considering the risks associated withimbalance costs. The Conditional Value at Risk (CVaR) method isused here as the risk aversion criterion. The CVaR method is analternative method for value at risk (VaR), which is a populartechnique for risk evaluation. It is a coherent risk measure [12] andcan protect the portfolio for very severe but less probable scenariosand it has consistency with VaR. The most important feature ofCVaR method that we use here is its versatility for incorporationinto an optimization model [13,14]. In our model the Generation

Company (GenCo) is allowed to consider a part of its hydro unit’scapacity for up-regulation (increasing output power) and down-regulation (decreasing output power) in order to compensate itsimbalances related to wind power variability. The technical con-straints of hydro units, such as forbidden zone, are preciselymodeled. The rest of the paper is organized as follows: in Section 2the problem is described and the energy market, the cascade hydrosystem, and the wind farm models are presented. The mathemat-ical formulation of the proposed model is presented in Section 3.The simulation results and conclusion are presented in Sections 4,and 5 respectively.

2. Problem description

2.1. Day-ahead energy market model

In this paper a day-ahead market, where the consumers andsuppliers submit their bids into the market before the gate closure,is considered. The Independent System Operator (ISO) or Trans-mission System Operator (TSO) [15] performs the clearing processin order to determine the share of each supplier and producer forthe next 24 h. The system marginal price is considered for theremuneration of the suppliers. Energy imbalances are penalized inrelation to the market price. The electricity market studied in thispaper has enough number of participants so that it can be treated asa competitive market. The wind farm together with hydro powerplants, form a VPP which is owned by the GenCo. The size of theGenCo is small enough compare to the whole electricity market;therefore, the GenCo is price-taker in the market. It means that itcannot determine or impact the market price since it holds a smallshare of it.

Fig. 1. Input/output model of a hydro unit.

Fig. 2. Scenario tree.

I.G. Moghaddam et al. / Renewable Energy 55 (2013) 252e259254

2.2. The virtual power plant model

The VPP considered in this paper contains a cascade hydrosystem and a wind farm. The objective of the GenCo that owns theVPP is to maximize its profit in the day-ahead energy market. TheGenCo submits its bid for each hour of the following day. In themarket there is no difference between the power producers,whether it is the wind farm or one of the cascade hydro plants.The GenCo does the scheduling of the resources and the hydroplants can be used for compensating the wind farm forecast errors.The GenCo can reserve a portion of its hydro plants capacity forup-regulation and down-regulation for managing its powerproduction in order to minimize its imbalance costs.

2.2.1. Wind farmThe power output of a wind turbine has a non-linear relation-

ship with the wind speed, so the output power characteristic ofa wind farm is quite different from those of conventional genera-tion units. The relationship between power output and wind speedcan be represented by using operational parameters of windturbine. These operational parameters are cut-in, cut-out and ratedwind speeds [16]. The model proposed in Ref. [17] which definesthe relationship between the wind speed and wind farm poweroutput is used in this paper. The hourly power output of a windfarm is a function of the wind farm capacity Ckw, and the nominal1-MWwind power output function. The total wind power output ofa wind farm is as follows [17]:

PðvÞ ¼ Cw �

8>><>>:

0 0 � v � viaþ bv3 vi � v � vr

1 vr � v � vo0 v � vo

9>>=>>; (1)

where parameters a, and b are given as follows [17].

a ¼ v3iv3i � v3r

(2)

b ¼ 1v3r � v3i

(3)

2.2.2. Cascade hydro plantsThe production function of a hydro unit is more complicated than

a wind farm and depends on the turbine-generator efficiency, waterhead level, andwater discharge [18]. The inputeoutput characteristicof a hydro unit is non-linear. However, it can be represented viaa piecewise-linear model. The model introduced in Ref. [19] is usedhere. The inputeoutput model of a hydro unit is shown in Fig. 1.

In this paper, the inputeoutput function is represented by apiecewise-linear approximation with two blocks and one forbiddenzone. The forbidden zone is between P1

max, the upper bound of theoperation zone in the first interval, and P2

min, the lower bound of theoperation zone in the second interval. The inputeoutput function canbe represented as follows:

Q ¼ v� Qmin1 þw� Qmin

2 þ b1P1 þ b2P2 (4)

P ¼ v� Pmin1 þw� Pmin

2 þ P1 þ P2 (5)

0 � P1 ��Pmax1 � Pmin

1

�� v (6)

0 � P2 ��Pmax2 � Pmin

2

��w (7)

vþw � 1 v; w binary variables (8)

Eq. (4) represents the amount of water discharged from hydrounit and Eq. (5) shows the amount of power generated by hydrounit. The constraint Eqs. (6) and (7) represent the length of eachoperation region within its lower and upper limits. The constraintEq. (8) is added to ensure the unit operates in just one of the tworegions.

2.3. Sources of uncertainties

The day-aheadmarkets normally are closed 10e14 h prior the dayof operation. Therefore, the wind speed is required to be estimatedfor 10 (14)e34 (38) h ahead. Even with the best prediction tools,there would be some prediction errors between 30% and 50% [5].This amount of error could cause a significant loss to wind farmowners. In addition, there is an uncertainty related to the marketprices. To deal with these two sources of uncertainty, different sce-narios are considered for market price and wind speed. By usingthese scenarios a stochastic scenario tree [20] as shown in Fig. 2 iscreated and a stochastic optimization is used to find the optimalscheduling. The most famous stochastic programming model is the

I.G. Moghaddam et al. / Renewable Energy 55 (2013) 252e259 255

two stages programming where the set of decisions is divided intotwo stages. First, the decision must be made with uncertainty beforethe time that random variables occur and it is called “here and now”

decision [5]. Second, the decision that must be taken when therandom variables are revealed [5]. In this paper the “here and now”

decision is the amount of bid which is submitted to day-aheadmarket for each hour and the amount of up-regulation and down-regulation which are considered to compensate the day-aheadforecast errors. The second decision is related to operation of thecascade hydro system and thewind farm in real-time. A risk aversioncriterion is used to hedge the GenCo against uncertainties. It will bedescribed in the next section.

2.4. Risk aversion criterion

One of the most famous techniques for evaluating the risk is theVaR method. Based on the definition, the b-VaR value of a portfoliois the lowest amount z such that, with probability b, the loss willnot exceed z. On the other hand, the b-CVaR is the conditionalexpectation of losses above that amount z [13]. The VaR cannot beeasily applied to non-normal distribution and may become unsta-ble. It also provides a lower bound for losses and is biased towardoptimism rather than conservatism [13,14]. The CVaR methoddoes not have these problems and it can be easily formulated asa minimization problem. The b-CVaR will never be greater thanb-VaR, hence, the low b-CVaR value ensures the low b-VaR value.Therefore, we use the b-CVaR method in this paper. The mathe-matical formulation of CVaR is as follows [13]:

CVarbðxÞ ¼ ð1� bÞ�1Z

f ðx;yÞ�VaRbðxÞf ðx; yÞpðyÞdy (9)

The f(x,y) is the loss function with decision variable x anduncertainty vector y with p(y) probability distribution and b is theconfidence level ranging between 0 and 1.

The b-CVaR value in an optimization problem can be formulatedas follows [14]:

minx CVaRbðxÞ ¼minx;z

zþ ð1� bÞ�1 XN

k¼1

p�yk�$

�max

�hf�x; yk

�� zi;0��! (10)

in which z is value at risk at confidence level b. More informationabout CVaR and VaR methods and the proof of the above equationscan be found in Refs. [13,14].

3. Problem formulation

The objective of the model is to maximize the GenCo profit inthe day-ahead market. The GenCo will receive the energy price foreach MWh that produces. However, it will be penalized for theamount of mismatch between its real-time production and its day-ahead bid. There are different scenarios both for market prices andwind speeds, thus a stochastic formulation is used here. The GenCoconsiders up-regulation and down-regulation to compensate windpower forecast errors and also regulates its output with respect tomarket prices. It is assumed here that the operation cost of thehydro plants would be increased by 1 percent for the amount ofcapacities, which are not scheduled from day-ahead and are used inreal-time. The objective function of the model is formulated asfollows:

Maximize ZXX( X24 X3 h �

Z �

scw scpProbscw�Probscp

t¼1 i¼1

lðscp; tÞ� Phði; tÞ

�CSUði; tÞ�CSDði; tÞ�OCðiÞ��Phði; tÞ�0:99

�Pdnscp;scwði; tÞþ1:01�Pupscp;scwði; tÞ�

�Qscp;scwði; tÞ�WVðiÞi

�X24t¼1

½PenaltyPI:lðscp; tÞ� PIðscp; scw; tÞ

þPenaltyNI:lðscp; tÞ�NIðscp; scw; tÞ�)

� d�Risk

ð11Þ

Risk ¼ zþ 1

1� b

Xscw

Xscp

Probscw � Probscp � mscw;scp

!(12)

mscp;scw �(X24

t¼1

X3i¼1

hlðscp; tÞ �

�Phði; tÞ � Pdnscp;scwði; tÞ

þ Pupscp;scwði; tÞ�þ lðscp; tÞ � PscwðtÞ � CSUði; tÞÞ

� CSDði; tÞ � OCðiÞ ��Phði; tÞ � 0:99� Pdnscp;scwði; tÞ

þ 1:01� Pupscp;scwði; tÞ�� Qscp;scwði; tÞ �WVðiÞ

i

�X24t¼1

½PenaltyPI:lðscp; tÞ � PIðscp; scw; tÞ

þ PenaltyNI:lðscp; tÞ � NIðscp; scw; tÞ�)

� z c : scp; scw ð13Þ

mscp;scw � 0 (14)

The first term of objective function in (11). defines the revenuesand the costs of energy production. The second term is associatedwith the positive imbalance (power production more than day-ahead bid) and the negative imbalance (power production lessthan day-ahead bid) costs, and the third term is related to the riskminimization criterion. The coefficient of risk, d, defines theimportance of risk minimization in the objective function. Thebigger the d, the more risk-averse the GenCo will be in the day-ahead scheduling. The GenCo will receive the energy price ofeach scenario for each MWh that it produces. However, if theamount of real production is different from its day-ahead bid, it willbe penalized for the amount of mismatch. For the positive andnegative imbalances the GenCo will be penalized proportional toenergy market price. The wind farm energy is considered to becurtailable. The up-regulation and down-regulation are consideredfor compensating the wind farm forecasting errors and regulatehydro plants output. The constraints of the problem are as follows:

Ph1ði; tÞ þ Pup1 ði; tÞ ��Pmax1 � Pmin

1

�� vðiÞ (15)

Ph2ði; tÞ þ Pup2 ði; tÞ ��Pmax2 � Pmin

2

��wðiÞ (16)

Ph1ði; tÞ � Pdn1 ði; tÞ (17)

Table 1Hydro plants characteristics.

Plant 1 Plant 2 Plant 3 Plant 1 Plant 2 Plant 3

P1min (MW) 20 14 14 Q1

min (m3) 28 20 19P1max (MW) 80 20 20 Q2

min (m3) 209 75 75P2min (MW) 170 60 70 Shut-down cost ($) 200 150 150

P2max (MW) 250 120 120 Start-up cost ($) 400 300 300

b1 (m3/MWh) 1.11 1.21 1.15 Marginal benefit of water ($/m3) 10 13 15b2 (m3/MWh) 1.18 1.25 1.20 Operation cost ($/MWh) 4 4 4

I.G. Moghaddam et al. / Renewable Energy 55 (2013) 252e259256

Ph2ði; tÞ � Pdn2 ði; tÞ (18)

vðiÞ þwðiÞ � uðiÞ (19)

Phði; tÞ ¼ Ph1ði; tÞ þ Ph2ði; tÞ þ v� Pmin1 þw� Pmin

2 (20)

Pdnði; tÞ ¼ Pdn1 ði; tÞ þ Pdn2 ði; tÞ (21)

Pupði; tÞ ¼ Pup1 ði; tÞ þ Pup2 ði; tÞ (22)

CSUði; tÞ � ðuði; tÞ � uði; t � 1ÞÞ � StartUpCost t � 2 (23)

CSDði; tÞ � ðuði; tÞ � uði; t þ 1ÞÞ � ShutDownCost t � 23 (24)

CSUði; tÞ � 0 (25)

CSDði; tÞ � 0 (26)

PIðtÞ � 0 (27)

NIðtÞ � 0 (28)

PIðscp; scw; tÞ � X3

i¼1

�Phði; tÞ � Pdnscp;scwði; tÞ þ Pupscp;scwði; tÞ

�

þ PscwðtÞ � BidðtÞ!

ð29Þ

Fig. 3. Energy pri

NIðscp; scw; tÞ � X3

i¼1

�BidðtÞ�

�Phði; tÞ þ Pupscp;scwði; tÞ

� Pdnscp;scwði; tÞ��

þ PscwðtÞ!

(30)

PscwðtÞ � PWðscw; tÞ (31)

Pdnscp;scwði; tÞ � Pdnði; tÞ (32)

Pupscp;scwði; tÞ � Pupði; tÞ (33)

Qscp;scwði; tÞ ¼ vði; tÞ � Qmin1 ði; tÞ þwði; tÞ � Qmin

2 ði; tÞþ b1ðiÞ

�Ph1ði; tÞ þ Pup1;scp;scwði; tÞ � Pdn1;scp;scwði; tÞ

�þ b2ðiÞ

�Ph2ði; tÞ þ Pup2;scp;scwði; tÞ � Pdn2;scp;scwði; tÞ

�(34)

EminðiÞ � Escp;scwði; tÞ � EmaxðiÞ (35)

Escp;scwð1;tþ1Þ ¼ Eð1;tÞ�Qscp;scwð1;tÞ�sð1;tÞþ inf lowðtÞ (36)

Escp;scwð2;tþ1Þ ¼ Eð2;tÞ�Qscp;scwð2;tÞ�sð2;tÞþQ�1;t�s1;3

�s1;3

(37)

Escp;scwð3;tþ1Þ ¼ Eð3;tÞ�Qscp;scwð3;tÞ�sð3;tÞþQ�2;t�s2;3

�s2;3

(38)

ce scenarios.

Fig. 4. Mean and standard deviation of wind farm power output.

I.G. Moghaddam et al. / Renewable Energy 55 (2013) 252e259 257

The constraints Eqs. (15)e(18) define the length of the operatingzones for the hydro plants. The binary variables v and w representthe two operation regions of the hydro plants that are divided bythe forbidden region, and u shows the on/off state of the hydroplants. The constraints Eqs. (20)e(22) represent the total amount ofpower scheduled, up-regulation, and down-regulation of the hydroplants. The constraints Eqs. (23)e(26) define the start-up and shut-down cost of the hydro plants. The constraints Eqs. (27)e(30)determine the amount of positive and negative imbalances that

Fig. 5. GenCo schedule for the day-ahead energy market fo

the GenCo has in each hour. The constraints Eq. (31) represents themaximum amount of wind energy that can be produced in eachhour. The constraints Eqs. (32) and (33) represent the maximumamount of up-regulation and down-regulation with respect today-ahead schedule. The amount of water discharged in each houris defined by constraint Eq. (34). The constraint Eq. (35) defines themaximum and minimum storage capacity of the hydro plants. Theenergy stored in the hydro reservoirs in each hour is represented byconstraints Eqs. (36)e(38).

r different positive and negative imbalance penalties.

Table 2GenCo profit and imbalances for different penalty mechanisms.

Positiveimbalance penalty(% energy price)

Negativeimbalance penalty(% energy price)

Profit ($) Negativeimbalance(MWh)

Positiveimbalance(MWh)

0 0 1.2638 � 105 0 1.2019 � 104

50 50 1.0786 � 105 601.77 58680 50 1.0637 � 105 893.46 23550 80 1.0444 � 105 261.72 853

I.G. Moghaddam et al. / Renewable Energy 55 (2013) 252e259258

4. Simulation and results

The methodology proposed here is applied to a 300 MW windfarm and a cascade hydro system consisting of three hydro plants.The characteristics of three hydro plants are shown in Table 1. Total400 scenarios are considered for the day-ahead (20 scenarios forday-ahead prices and 20 scenarios for wind profiles.). The waterspillage in the reservoirs and between hydro plants is consideredto be zero and the time constant of water flow between hydroreservoirs is considered to be 1 h. The price scenarios, and windpower mean and standard deviation are shown in Figs. 3 and 4respectively.

The proposed methodology is implemented in the GeneralAlgebraicModeling System (GAMS) and CPLEX 9 [21] is used to solvethe Mixed Integer Linear Program (MILP) problem. GAMS/CPLEX isa powerful MILP, solver based on the CPLEX Callable Library fromIBM ILOG CPLEX [22]. It includes state-of-the-art implementationsof simplex and barrier algorithms and runs on many differentplatforms. The solution of the optimizationmodel contains the set ofoptimal bid for the day-ahead market and the set of up-regulationand down-regulation capacity for daily operation. The model isperformed for various imbalance penalties and risk levels and theresults are presented and discussed in the following.

4.1. The effect of imbalance penalties on the bidding strategy

The GenCo would face imbalance costs in real-time if itsday-ahead schedule does not match its real-time production. Theamount of penalties for positive and negative imbalances wouldimpact the GenCo bidding strategy for the day-ahead market. If theGenCo has negative imbalance, not only it will be penalized but alsoit will not receive the energy price for the amount of mismatchbetween its bid and its real-time production. In case of positiveimbalance, the GenCo will receive the energy price for the amount

Fig. 6. Total bid for the

of its mismatch however it will be penalized. Fig. 5 shows theGenCo day-ahead plan for the different amount of positive andnegative imbalance penalties.

In Fig. 5a, the penalties are considered to be zero. It is clear thatthe GenCo will not bid in day-ahead and in real-time produces asmuch as wind energy that is available. A portion of the hydro plantscapacity is considered for up-regulation and down-regulation toregulate hydro plants output with respect to price variation in real-time. It is clear from Fig. 5a, that it is essential to penalize the GenCofor its energy imbalances; otherwise it would not care about itsday-ahead operation planning. In Fig. 5b, the amounts of penaltyfor the both positive and negative imbalances are 50% of themarketprice. It shows that the imbalance penalties would force the GenCoto accurately bid in day-ahead. The amount of up-regulation anddown-regulation capacities in time of high energy prices aregreater because the penalties are proportional to energy prices andhigh energy price means high imbalance cost.

In Fig. 5c and d the impact of positive and negative imbalancepenalties are shown on the GenCo day-ahead scheduling. In Fig. 5c,the positive imbalance penalty is 50% of the market price and thenegative imbalance penalty is 80%. In this case, the GenCo is moreconservative about bidding into the day-ahead electricity market. Itdecreases its amount of bid comparing to previous case. It considersmore capacities for up-regulation to compensate its wind speedforecast errors. However, in some scenarios the GenCo in real-timeuses the up-regulation capacity to benefit from high energy pricesalthough it would be penalized for its positive imbalance. The sit-uation is vice versa in Fig. 5d. The positive imbalance penalty is 80%of the market price and the negative imbalance penalty is 50%. TheGenCo prefers to have negative imbalance rather than to bepenalized because of positive imbalance. Therefore, the GenCo in-creases its bid in day-ahead in compare with other cases. It alsoincreases its down-regulation capacity to hedge itself from the riskof being penalized from positive imbalance.

In Table 2, the total profit, which is the sum of each scenarioprofit, multiplied by its probability, and total positive imbalanceand negative imbalance are shown for four case studies. It is shownthat when the positive and negative imbalance penalties are thesame the GenCo positive and negative imbalances are almost equaland the GenCo does not have the tendency to neither of them.Therefore, it does its best effort to accurately plan its day-aheadoperation and bidding into the market.

The above discussion shows that the bidding strategy of a GenCowith stochastic resources is highly dependent on the market penaltymechanism. Therefore, in order to maximize the penetration of wind

different risk levels.

Fig. 7. Profit histogram for the different risk levels (a) d ¼ 0, (b) d ¼ 1.

I.G. Moghaddam et al. / Renewable Energy 55 (2013) 252e259 259

energy a proper penalty mechanism should be used. This penaltymechanism should force the wind farm owners to do their best forday-ahead bidding and, besides, it should not penalize them in awaythat they underestimate their resources for energy production.

4.2. The effect of risk aversion on bidding strategy

The GenCo should consider the stochastic nature of energy priceand wind power in the day-ahead scheduling. In Fig. 6, the GenCototal bid is shown for three value of d. The positive and negativeimbalance penalties are considered to be 40% of energymarket price.It is clear from Fig. 6 that when the d is increased the total bid isdecreased because the GenCo becomes more conservative and doesnot have the tendency to experience high and low profit scenarios.The total profit for the case with d¼ 0 is 1.0808� 105 which is 2.03%greater than the case with d ¼ 1, however, its risk is not minimizedand the GenCo is subject tomore losses in the day-aheadmarket. Thehistogram of profit for two cases, d ¼ 0 and 1, is shown in Fig. 7. It isobvious that when d is increased, the profits of scenarios are moreconcentrated and GenCo would not experience high profit and lowprofit scenarios and it will be more confident about its profit.However, its total profit will be decreased. When d is set to zero, theCVaR is not minimized, the profits of scenarios have more variationand GenCo is subject to more risk, although its total profit, which isthe sum of all scenario profits multiplied by their probability, isgreater.

5. Conclusion

In this paper a model for the optimal scheduling of a combinedwind farmecascade hydro system for day-ahead market is intro-duced. The objective function is to maximize the expected GenCoprofit. Different wind speed and energy price scenarios are used tobuild a scenario tree for a two-stage stochastic programmingapproach, which is used to obtain the optimal day-ahead operationplanning. The objective function determines a portion of hydro

plant’s capacity for compensating the wind power forecast errors.The CVaR method is used as risk-averse criterion to hedge theGenCo against low price scenarios and wind farm power outputvariations. The model is applied to a real case study system. Theresults show that a combined bidding from a wind farm and cas-cade hydro plants would decrease the wind farm imbalance costsand consequently its cost of participation in an energy market. It isalso shown that the amount of positive and negative imbalancepenalties would affect the GenCo bidding strategy in day-aheadmarket. The results show that an ineffective imbalance mecha-nism would bring losses to both market operator and GenCo. Theyalso indicate that the GenCo profit is decreased when its risk isminimized and it would not experience high and low profitscenarios.

References

[1] Dorn JG. Global wind power capacity reaches 100,000 MW. Earth PolicyInstitute; March 4, 2008.

[2] Bourry F, Costa LM, Kariniotakis G. Risk-based strategies for wind/pumped-hydro coordination under electricity markets. Bucharest, Romania: IEEE PowerTech.; 2009.

[3] Castronuovo ED, Lopes JAP. On the optimization of the daily operation ofa wind-hydro power plant. IEEE Transactions on Power Systems 2004;19:159e1606.

[4] Vespucci MT, Maggioni F, Bertocchi M, Innorta M. A stochastic model for thedaily coordination of pumped storage hydro plants and wind power plants.Annals of Operations Research 2010:1e15.

[5] Javier GG, Rocio MRM, Luz MS, Alicia MG. joint optimization of wind gener-ation and pumped-storage units in an electricity market. IEEE Transactions onPower Systems 2008;23:460e8.

[6] Angarita JL, Usaola J, Martínez-Crespo J. Combined hydro-wind generationbids in a pool-based electricity market. Electric Power Systems Research 2009;79:1038e46.

[7] Hedman KW, Sheble GB. Comparing hedging methods for wind power: usingpumped storage hydro units vs. options purchasing. In: Probabilistic methodsapplied to power systems, Stockholm, Sweden; 2006.

[8] Bathurst G, Strbac G. Value of combining energy storage and wind in short-term energy and balancing markets. Electric Power Systems Research 2003;67:1e8.

[9] Papaefthimiou S, Karamanou E, Papathanassiou S, Papadopoulos M. Operatingpolicies for wind-pumped storage hybrid power stations in island grids. IETRenewable Power Generation 2009;3:293e307.

[10] Angaritam JM, Usaola JG. Combining hydro-generation and wind energy:biddings and operation on electricity spot markets. Electric Power SystemsResearch 2007;77:393e400.

[11] Yuan Y, Li Q, Wang W. Optimal operation strategy of energy storage unit inwind power integration based on stochastic programming. IET RenewablePower Generation 2011;5:194e201.

[12] Artzner P, Delbaen F, Eber JM, Heath D. Coherentmeasures of risk. MathematicalFinance 1999;9:203e28.

[13] Rockafellar RT, Uryasev S. Optimization of conditional value-at-risk. Journal ofRisk 2000;2:21e42.

[14] Rockafellar RT, Uryasev S. Conditional value-at-risk for general loss distributions.Journal of Banking & Finance 2002;26:1443e71.

[15] Shahidehpour M, Yamin H, Li Z. Market operations in electric power systems:forecasting, scheduling, and risk management. 1st ed. New York: JohnWiley &Sons; 2002.

[16] Billinton R, Wangdee W. Reliability-based transmission reinforcement planningassociated with large-scale wind farms. IEEE Transactions on Power Systems2007;22:34e41.

[17] Zhao M, Chen Z, Blaabjerg F. Probabilistic capacity of a grid connected windfarm based on optimization method. Renewable Energy 2006;31:2171e87.

[18] García-González J, Parrilla E, Mateo A. Risk-averse profit-based optimalscheduling of a hydro-chain in the day-ahead electricity market. EuropeanJournal of Operational Research 2007;181:1354e69.

[19] Daneshi H, Choobbari AL, Shahidehpour M, Li Z. Mixed integer programmingmethod to solve security constrained unit commitment with restrictedoperating zone limits. In: Int. conf. Electro/Information Technology, Chicago,US; 2008.

[20] Gülpınar N, Rustem B, Settergren R. Simulation and optimization approachesto scenario tree generation. Journal of Economic Dynamics and Control 2004;28:1291e315.

[21] Rosenthal RE. Gams e a user’s guide. Technical report, Washington, DC: GAMSDevelopment Corp, 2010.

[22] Lougee-Heimer R. The CommonOptimization INterface for Operations Research:promoting open-source software in the operations research community. IBMJournal of Research and Development 2003;47(1):57e66.