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Cost Trading in Wind Power

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1396 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 21, NO. 3, AUGUST 2006
Minimization of Imbalance Cost Trading Wind Poweron the Short-Term Power Market
Julija Matevosyan and Lennart Söder
, Member, IEEE
Abstract—
Present power markets are designed for tradingconventional generation. For wind generation to participate in ashort-term energy market, lengthy wind power production fore-casts are required. Although wind speed forecasting techniquesare constantly improving, wind speed forecasts are never perfect,andresultingwindpowerforecasterrorsimplyimbalancecostsforwind farm owners. In this paper, a new method for minimizationof imbalance costs is developed. Stochastic programming is usedto generate optimal wind power production bids for a short-termpower market. A Wind power forecast error is represented as astochasticprocess.Theimbalancecostsresultingfromthisstrategyare then compared to the case when wind power production bidson a short-term power market are based directly on a wind speedforecast.
Index Terms—
Forecasting, optimization, power market, sto-chastic process, stochastic programming, wind power generation.
I. I
NTRODUCTION
T
HE PRESENT short-term power markets are designed fortrading conventional (dispatchable) generation. The timespan after the market clearing until the delivery hour can be upto 36 h (Scandinavia) and up to 38 h (Spain); any deviationsfrom the submitted production plan are penalized. In order toavoid high imbalance penalties, many different techniques areused to forecast wind energy generation (see [1] for a review).Theforecastingtechniqueshaveconsiderablyimprovedoverthelast decade but never will give perfect results. Furthermore, theforecasterrorincreaseswithincreasingpredictionhorizon.Withforecast being needed 36 or 38 h ahead of time, wind generatorsmay be subjected to substantial imbalance costs.In the Nordic countries, all bulk electricity production mustbe traded through a balance responsible player. For a windpower owner, there are, thus, three options available. Oneoption is to become a balance responsible player, second isto trade wind power and have a contract with the balanceresponsible for balancing any mismatches, and third is to sellall wind power to the balance responsible player [4]. In theﬁrst case, the wind power owner is paying a market imbalanceprice for its imbalances. In the other two cases, the wind powerowner is paying a contracted imbalance price, which is lowerthan the market imbalance price, due to the fact that the balanceresponsible player has other energy sources in its portfolio andcan balance wind power mismatches internally.
ManuscriptreceivedAugust25,2005;revisedDecember28,2005.Thisworkwas supported by the Swedish Energy Agency. Paper no. TPWRS-00544-2005.The authors are with the Royal Institute of Technology, Stockholm, Sweden(e-mail: julija@ets.kth.se; lennart.soder@ets.kth.se).Digital Object Identiﬁer 10.1109/TPWRS.2006.879276
When trading wind power on the short-term power market,the balance responsible player may choose the followingstrategies.1) Assume wind power forecast as certain and bid it on themarket.2) Bid the amount that minimizes expected costs for imbal-ances considering possible scenarios of wind power pro-duction and imbalance costs.The latter strategy has been previously studied in [2]. In [2],
power production scenarios are generated using statisticalmethods based upon historically observed power production.The energy output of the wind farm (WF) is divided into severalenergy bands and, given the band, where the WF productionresidesinitially, theprobabilitiesthattheWFproductionresidesin each of energy bands are calculated for each forecastingdelay and form probability tables. There is, however, a dif-ﬁculty with generating these probabilities as they require asigniﬁcant quantity of historical data. The drawbacks of thismethod, reported in [2], are as follows: one year of data is notenough to produce smooth probability tables, and, since windexhibits seasonal behavior, probability tables are likely to differbetween seasons and years.In this paper, bidding strategy 2 is studied further. Here windpower production scenarios are generated based on day-aheadwind speed forecast and statistical data about the forecast error.Any forecasting method can be used. The statistical forecasterror data are required. The advantage of this method is thatthe forecast error is modeled and added on top of actual day-ahead wind power production forecast that already accounts forseasonal winds. One year of the forecast error data proved to besufﬁcient to calibrate the forecast error model.The imbalance prices are assumed deterministic in [2],whereas in this paper, the imbalance prices are representedby several equally probable scenarios in the planning stage,and, in the imbalance cost calculation stage, actual imbalanceprices are used. This allows more realistic evaluation of biddingstrategy 2.The method for minimization of imbalance costs suggestedin [2] is applicable only for a small amount of scenarios. In thispaper, bidding strategy 2 is formulated as a stochastic optimiza-tionproblem.Mixedintegerprogrammingisusedheretoobtainthe solution for large number scenarios for wind power produc-tion and imbalance price. The proposed method can be used toã determine the energy level to bid on the day-ahead market,to minimize the imbalance costs of the WF;ã estimate the value of using better forecasting techniques.The imbalance cost minimizing strategy is explained with anexample of the Nordic power market, but with some minor ad- justments, it can be applied in any market.
0885-8950/$20.00 © 2006 IEEE
MATEVOSYAN AND S
Ö
DER: MINIMIZATION OF IMBALANCE COST TRADING WIND POWER 1397
This paper is organized as follows. A short overview of theNordic power market is provided in Section II. Section III pro-
videsmodelingdetails:windfarmmodelforconversionofwindspeed forecast into power production forecast; brief descriptionof the forecast error model; and stochastic optimization pro-gram for bidding strategy 2 together with some helpful hintsfor problem solution and applicationof theoptimization results.The detailed derivation and analysis of the solution to the opti-mization problem is provided in Section IV. Bidding strategy2 is compared to strategy 1 in a case study; the results are pre-sented in Section V. Section VI summarizes the main conclu-
sions and plans for future work.II. O
VERVIEW OF THE
N
ORDIC
P
OWER
M
ARKET
A. Spot Market
On the Nordic power market, Norwegian, Finnish, Swedish,and Danish actors trade in hourly contracts for the 24 h of thecoming day. The spot market is closing at 12:00 the precedingday.Purchasingandsellingcurvesareconstructed,andthepointwhere they cross determines the spot market price and the vol-umes being traded during each hour the coming day [3]. Withsuch market structure, wind power forecast length should be12
–
36 h to bid on the spot market.
B. Elbas
Elbasisanadjustmentmarketforthepowerexchangeplayersin Sweden, Finland, and East Denmark. The market opens fortradefor thecoming powerexchangeday at 15:00eachday, i.e.,after the spot market has closed. Trading in hourly contracts isconducted electronically and can take place up until one hourprior to delivery.Trading on Elbas is more bene
ﬁ
cial for wind power becausemoreaccurateforecastscanbemadefortheshortertimehorizon[4]. However, currently, Elbas is not very active, and only smallamounts of energy are traded there. Nevertheless, the biddingstrategy described in this paper may be easily used also fortrading on the Elbas market.
C. Regulating Market
The transmission system operator (TSO) is responsible forphysical balance between production and consumption. Priordeliveryhouractorswithpowerreservesareplacingbidsforfast(up to 10 min) production increase or decrease to the so-calledregulating market. The bids are arranged in order of price andform a staircase for each delivery hour. At the end of eachhour, the regulation price is determined in accordance with themostexpensiveupwardregulationmeasurethatwastakenbytheTSO, or the cheapest down regulation measure that was takenby the TSO [3].Wind power could also be bidden for upward regulation if a certain production margin is kept on the WF for this pur-pose (see, e.g., [5]), but for simplicity, this possibility is dis-regarded in this paper, as participation in downwards regulationmeans power spillage for the wind power owner (power cannotbe stored to the next hour). This option is, thus, not economi-cally ef
ﬁ
cient.
Fig. 1. Flowchart for the bidding strategy and its evaluation.
D. Balance Settlement
Via balance settlement, the TSO distributes the costs of reg-ulation among balance responsible actors on the power market.All balance responsible actors pay or are getting paid for theirunplanned deviations from the balance.If upward regulation alone was activated, the upward regu-lation price is paid by players with negative imbalance (i.e.,actualproduction purchase actual load sold power),whileplayers with positive imbalance are getting paid according to aspot price.If downward regulation alone was activated, the downwardregulationpriceispaidtoplayerswithpositiveimbalance,whileplayerswith negativeimbalance pay according tothespot price.If no regulation took place, all actors are settled at spot price.If both upward and downward regulation have been ordereddepending on which regulation had higher volume, upward ordownwardregulationpriceisapplied.Ifvolumesfororderedup-ward and downward regulation are equal, the spot market priceis used [3].The balance responsible player further distributes imbal-ance costs among power producers/consumers in his area of responsibility.III. B
IDDING
S
TRATEGY
The
ﬂ
owchart for the presented bidding strategy is given inFig. 1 and is discussed step by step in this section.
A. ARMA Forecast Error Scenarios
A wind speed forecast for the next day is obtained from, e.g.,numerical meteorological programs (box A1). A wind speedforecast is never perfect, and the forecast error should be con-sidered when placing a bid to the spot market.A model for wind speed forecast error (box A2) is developedin [6]. It is assumed that data concerning accuracy of the fore-cast are known. Wind speed forecast is assumed available for
1398 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 21, NO. 3, AUGUST 2006
the studied site. The model then simulates possible outcomes(scenarios) of the wind speed forecast errors that have the cor-rect statistical behavior. The model is based on autoregressivemoving average series (ARMA), [7], de
ﬁ
ned as(1)where is a wind speed forecast error in -hour forecast,is a random Gaussian variable with standard deviation ,and and are parameters.The wind speed scenario for each hour can then be cal-culatedasthesumofthewindspeedforecast andthewindspeedforecasterrorscenario ,i.e.,theoutcomeof (2)where is number of forecast error scenarios.The parameters , , and are identi
ﬁ
ed using the least-square
ﬁ
tting, minimizing a difference between sample forecasterrorvariance,basedondatafromthesite,andmodeledforecasterror variance (see [6] for details).Obtained wind speed scenarios should, thus, be converted topower (box B; see Fig. 1).
B. Wind Speed to Ower Conversion
Power production of the wind farm depends on wind speed,wind direction, wind farm layout, and availability of the windturbines within a wind farm.
1) WakeEffectModel:
Astheairpassesthroughthewindtur-bine rotor disc, the speed of the air
ﬂ
ow downstream is reduced.As a result, not all wind turbines within a wind farm meet thesame undisturbed wind speed. The wind turbine wake model onthe
ﬂ
at terrain is assumed as follows [8]:(3)where is wind speed in the wake, is undisturbed windspeed at the upwind turbine with rotor radius , is a hori-zontaldistancebetweenwindturbines, iswakedecayconstant( onshore, offshore [9]), and is a thrustcoef
ﬁ
cient that depends on wind turbine (WT) type and can beobtained from the respective WT manufacturer.
2) Wind Farm Model:
The expression for power productionof the wind turbine depending on wind speed is [10](4)where issweptareaoftheWTrotor, isairdensity,andis overall ef
ﬁ
ciency of the WT, expressed here as a function of the wind speed.In practice, the relation between WT power production anda wind speed for each WT type is given by a so-called powercurve,whichisasetofexperimentallyobtainedvaluesavailable
Fig. 2. Power curve of 2000-kW wind turbine
and its continuous approxi-mation (solid line).Fig. 3. Example of power curve of the 160-MW wind farm (80
2
2-MW windturbines) with (solid line) and without (dashed line) consideration of the wakeeffect according to equation (3). Note that here, all wind directions were as-sumed equally probable.
from WT manufacturer (see Fig. 2, stars). It is convenient to ap-proximate the power curve with continuous function, to be ableto calculate power output at any wind speed. This is achievedas follows. First, is expressed from (4); then, substitutingwith discrete, experimental values, is calculated forcorresponding wind speeds. Approximating obtained discretevalues by continuous piecewise linear function [11], andsubstituting it back to (4), an experimental power curve can beapproximated by a continuous function that will allow us to de-termine the power production at any wind speed. As shown inFig. 2 (solid line), the approximation is quite good.Given a wind speed forecast for undisturbed wind
ﬂ
ow forhour , ,windspeedscenarios forundisturbedwind
ﬂ
ow are calculated using (2). Then, given the wind direction,wind speed scenarios at each wind turbine within a windfarm are calculated by (3) (see Fig. 3). Power production sce-
nariosofeachWTcanbeobtainedusingcontinuousapproxima-tion of the WT power curve described above. Power productionscenarios of individual wind turbines are summed to represent
MATEVOSYAN AND S
Ö
DER: MINIMIZATION OF IMBALANCE COST TRADING WIND POWER 1399
the power production scenario of the wind farm, , ,where is the set of all considered scenarios.
C. Scenario Reduction
The computational effort for solving scenario-based op-timization models depends on the number of scenarios.Therefore, it is necessary to obtain the subset of wind powerproduction scenarios that has a smaller number of scenariosbut still is reasonably close to the srcinal set. The scenarioreduction approach that is used here (box C) is described indetail in [12]. The scenario reduction algorithm determines asubset of preserved scenarios that is the
“
closest
”
to the srcinalset of scenarios using the Kantorovich metric. The
“
distance
”
trades off scenario probabilities and the distances betweenscenario values.
D. Optimization Problem
As discussed in Section II, the imbalance price can be dif-ferent depending on if the balance responsible actor is in posi-tive or negative imbalance and if upward or downward regula-tion was undertaken by the system operator during the hour inquestion.As an illustration,in this paper, theimbalance prices from theprevious days are used as price scenarios for the day in question(see Fig. 1, box D1). The price model does not effect the opti-mization methodpresented inthis paper.The analysisof theop-timization problem, provided in Section IV, is general and doesnot depend on the chosen price model. In the real application of this bidding strategy, the stochastic model (see, e.g., [15]) of theregulating prices can be used to achieve better results.The following imbalance price model is used:
ã
, where is a spot price at hour, if the actor is in positive imbalance in hour and nodownward regulation is undertaken;
ã
, where is a price for downwardregulation at hour , if the actor is in positive imbalance inhour anddownwardregulationisundertakenwith;
ã
, where is a price for upwardregulation at hour , if the actor is in negative imbalance inhour and no upward regulation is undertaken or;
ã
, if the actor is in negative imbal-ance in hour and upward regulation is undertaken with.The negative sign means that the balance responsible playeris paying the price for imbalance, and the positive sign meansthat the balance responsible player is getting paid.Note that the wind power producer is assumed to be a
“
pricetaker
”
here; it means its bidding strategy does not affect powerprices.Incountrieswithsmallamountsofwindpower(lessthan5%oftotalpowerproductionaccordingtothestudyin[16]),thisis a reasonable assumption.The stochastic optimization problem is formulated for eachhourtomaximizeWFownersexpectedpro
ﬁ
tand,consequently,minimize the imbalance costs(5)where is a variable, and the rest are parameters. is a bid of theWFoperatortothespotmarket, iswindpowerproductionaccording to scenario , is probability of wind speed scenario, is probability of the imbalance price scenario , andis spot price forecast. The terms are equivalent tomean imbalance price of the given set of price scenarios .There is no coupling between subsequent hours of operationof WF; the optimization problem can be solved separately foreach hour. This also minimizes computational efforts.For the small number of the production scenarios, the opti-mization problem (5) can be solved analytically, as in [2]. With
ARMAseries, thousandsofscenarioscanbe generated; thisim-provesthesolutionbutmakes itimpossible tosolve(5) byhand.Inthispaper,mixedintegerprogrammingisappliedtosolve(5);thus, the hourly optimization problem is expressed as follows(box D):(6)where is the total installed capacity of the WF, is a bi-nary variable, is a large positive number that exceeds anymaximum feasible value of , and is a set of preserved sce-narios after scenario reduction (see Section III-C). , if it is optimal to keep (underproduction), and the thirdterm of the objective function would disappear; , if it isoptimal to keep (overproduction), and the second partof the objective function would vanish.The detailed derivation and analysis of the solution to theoptimization problem (6) is provided in the next section. Also,several special cases are analyzed.
E. Evaluation of Bidding Strategy
The suggested bidding strategy can be tested against actualdata for the same period, for which forecast error statistics andimbalance prices are available. Real wind speed measurements(box E1) should be converted to power following the same pro-cedure as wind speed scenarios above (box B, see Fig. 1). If actual power production measurements are available, no con-version is needed. The actual power production data and bids,obtained from the optimization, are then used to calculate im-balance costs (box E)(7)where and are actual imbalance prices,known
ex-post
for the studied hour for the balance settlement(see Section II-D). As it will be shown in the case study, thedifference between the expected imbalance prices and actual

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