Optimal Offering Strategies for Wind Power in Energy and Primary Reserve Markets

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1 Downloaded fom obit.dtu.dk on: Nov 21, 218 Optimal Offeing Stategies fo Wind Powe in Enegy and Pimay Reseve Makets Soaes, Tiago; Pinson, Piee; Jensen, Tue Vissing; Moais, Hugo Published in: IEEE Tansactions on Sustainable Enegy Link to aticle, DOI: 1.119/TSTE Publication date: 216 Document Vesion Pee eviewed vesion Link back to DTU Obit Citation (APA): Soaes, T., Pinson, P., Jensen, T. V., & Moais, H. (216). Optimal Offeing Stategies fo Wind Powe in Enegy and Pimay Reseve Makets. IEEE Tansactions on Sustainable Enegy, 7(3), DOI: 1.119/TSTE Geneal ights Copyight and moal ights fo the publications made accessible in the public potal ae etained by the authos and/o othe copyight ownes and it is a condition of accessing publications that uses ecognise and abide by the legal equiements associated with these ights. Uses may download and pint one copy of any publication fom the public potal fo the pupose of pivate study o eseach. You may not futhe distibute the mateial o use it fo any pofit-making activity o commecial gain You may feely distibute the URL identifying the publication in the public potal If you believe that this document beaches copyight please contact us poviding details, and we will emove access to the wok immediately and investigate you claim.

2 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 1 Optimal Offeing Stategies fo Wind Powe in Enegy and Pimay Reseve Makets Tiago Soaes, Piee Pinson, Senio Membe, IEEE, Tue V. Jensen, and Hugo Moais, Membe, IEEE Abstact Wind powe geneation is to play an impotant ole in supplying electic powe demand, and will cetainly impact the design of futue enegy and eseve makets. Opeatos of wind powe plants will consequently develop adequate offeing stategies, accounting fo the maket ules and the opeational capabilities of the tubines, e.g., to paticipate in pimay eseve makets. We conside two diffeent offeing stategies fo joint paticipation of wind powe in enegy and pimay eseve makets, based on the idea of popotional and constant splitting of potentially available powe geneation fom the tubines. These offeing stategies aim at maximizing expected evenues fom both maket floos using pobabilistic foecasts fo wind powe geneation, complemented with estimated egulation costs and penalties fo failing to povide pimay eseve. A set of numeical examples, as well as a case-study based on eal-wold data, allows illustating and discussing the popeties of these offeing stategies. An impotant conclusion is that, even though technically possible, it may not always make sense fo wind powe to aim at poviding system sevices in a maket envionment. Index Tems Ancillay sevices, decision-making unde uncetainty, electicity makets, offeing stategies, wind powe. NOMENCLATURE The main notation used thoughout the pape is stated next fo quick efeence. Othe symbols ae defined as equied. A. Vaiables α Popotional stategy split fo enegy and eseve λ Pices and costs in the electicity maket E Enegy P Powe (eseve) Total amount bid into day-ahead stage MW] R Total evenue T Regulation enegy maket evenue W Potential penalty fo pimay eseve maket B. Indices + Positive imbalance (downwad egulation) Negative imbalance (upwad egulation) Available enegy/powe at eal-time stage bpt Penalty cost fo eseve imbalance C/MW] Manuscipt eceived July 28, 215; evised Novembe 7, 215 and Decembe 17, 215; accepted Januay 1, 216. This wok was suppoted by the Danish Council fo Stategic Reseach (DSF) though the poject 5 s Futue Electicity Makets. Pape no. TSTE Tiago Soaes, Piee Pinson, and Tue V. Jensen ae with the Depatment of Electical Engineeing, Technical Univesity of Denmak, Kgs. Lyngby 28, Denmak ( tiasoa@elekto.dtu.dk). Hugo Moais is with Dépatement MIRE, EDF Lab Clamat, Clamat, Fance. Colo vesions of one o moe of the figues in this pape ae available online at Digital Object Identifie 1.119/TSTE c cap obs pt sp Contacted enegy/powe at day-ahead stage Reseve pice at day-ahead stage C/MW] Total eventually obseved powe MWh] Penalty fo eseve imbalance C/MW] Fixed eseve MW] Spot maket I. INTRODUCTION T HE continuous deployment of wind powe geneation capacities in seveal counties, and especially in counties like Denmak, has an inceasing impact on powe system opeation and electicity makets. Fo instance accoding to Eneginet.dk (the Danish Tansmission System Opeato TSO), Decembe 213 was an exceptional month whee, on aveage, 54.8% of the electical enegy consumption was supplied by wind powe 1]. Accoding the same epot, on Decembe 1 st, an exteme scenaio with wind geneation equal to 136% of the Danish powe consumption was obseved. In the futue, situations with vey high wind (and most cetainly also sola) geneation will be moe and moe common, esulting in new challenges in powe system opeation 2]. The vaiability and limited pedictability of wind powe geneation foce the system opeato to pocue additional eseves to ensue adequate eliability of the electic powe system 3]. Howeve, accoding to 4] among othes, wind powe plants ae able to povide eseves themselves, theeby educing the additional pocuement of eseves fom othe taditional esouces. Thus, new mechanisms fo eseve pocuement, as well as fo the paticipation of wind geneation in poviding eseves should be developed and implemented 5], 6]. Cuently, wind tubine technology and wind fam contol allow poviding distinct ancillay sevices such as fequency and voltage contol. Thus wind fams ae able (i) to povide and contol active powe injection in a few seconds, (ii) to espond to eactive powe demands in less than 1 second, (iii) to suppot and maintain voltage levels, and (iv) to povide kinetic enegy (vitual inetia) 4], 7] 9]. Taditionally, pimay eseve makets ae designed to assist in dampening deviations fom nominal fequency. Geneatos supply the sevice based on thei inetia chaacteistics. Depending on the county ules, this sevice can eithe be supplied and piced though maket mechanisms 4] o made mandatoy without payment. With high penetation of vaiable geneation, the sevice design tends to change, since eseve equiements may dynamically vay on an houly o even minute basis 1], while the system may have lowe inetia. Wind powe plants and othe emeging geneating technologies IEEE. Pesonal use is pemitted, but epublication/edistibution equies IEEE pemission. See fo moe infomation.

3 2 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY may then be asked to contibute to this new sevice design 11], 12]. Fo optimal integation of wind powe in enegy and pimay eseve makets, new business models and emuneation mechanisms should be thought of. The liteatue on optimal offeing stategies fo wind powe poduces in the day-ahead maket while accounting fo potential balancing costs has been flouishing ove the last few yeas. This includes a numbe of studies (assuming that wind powe poduce act as a pice-take) on expected utility maximization stategies 13], 14], additional consideation on isk-avesion and tempoal dependencies 15], extension to LMP makets 16] and multi-peiod setting to adjust contacted offeings 17], appaisal of uncetainties on both wind and maket quantities 18], bidding unde one-pice and two-pice system 19], genealized oppotunity cost bidding 2], as well as minimizing imbalance costs accounting fo wind powe pedictions and imbalance pices 21], among othes. Although it is not the goal of the pesent pape to wok on optimal stategies assuming that the wind powe poduce acts as a pice-make, eades ae encouaged to consult these ecent woks 22] 27] fo detailed infomation. In contast, little attention has been paid to the joint offeing unde uncetainty of wind powe geneation in both enegy and eseve makets 12], 28]. Liang et al. 12] poposes an analytical appoach (based on the so called multi-newsvendo poblem with budget constaint) fo wind powe paticipating in enegy and eseve, assuming that offes fo enegy and eseve can be feely detemined (i.e., independently of any contol paadigm), since only subject to this budget constaint. Such joint offeing stategies ae expected to bing additional evenue steams to wind powe plant opeatos. Howeve, wind powe plants face the challenge to guaantee that powe scheduled as pimay eseve is available at any time without failue. The eseve maket is designed to ensue the opeation of electic powe systems with appopiate levels of stability, safety, quality, eliability and competitiveness. In this way, intemittent enegy esouces, such as wind powe, have difficulties to ensue and fulfil powe scheduled as pimay eseve. Thus, a futue eseve maket must be designed to account fo the possibility of wind failing to povide eseve, e.g. though penalties, if wind (o demand-esponse) is to paticipate in these makets. This pape poposes an analytical appoach fo wind powe paticipating in both enegy and pimay eseve makets taking into account the maket penalties. The aim is to maximize the expected evenue fom optimal offeing on both enegy and pimay eseve makets. Ou appoach takes a diffeent stating point is compaed to pevious wok in the liteatue, e.g. 12], as instead of consideing a budget constaint fo the joint offeing of enegy and eseves, we fist stat fom the vaious contol paadigms descibed in the liteatue fo wind to offe system sevices in pactice. A majo contibution of this wok is the implementation, evaluation and compaison of two diffeent offeing stategies, namely the popotional and the constant wind stategies poposed in 29], 3], fo the splitting of potentially available wind powe consideing the same wind distibution pobability fo the two sevices. In pactice, they ae easy to implement since uses simple contolles due to the locking of enegy and eseve quantities 3], while stategies that utilize all opeational degees of feedom would equie advanced contolles that ae unlikely to admit analytical teatment, and may be highly susceptible of misestimate due to foecast eos. An advantage of ou appoach is then to show how offeing behavio and maket evenues can be highly affected by the contol paadigm oiginally adopted. Both stategies ae intoduced with the motivation of allowing the split of the available wind powe fo enegy and eseve. Futhemoe, an economical evaluation of both stategies illustating thei advantages and inconveniences is undetaken. Optimal offes ae detemined unde uncetainty based on pobabilistic foecasts of potential powe geneation fo the maket time unit consideed. Additional input vaiables include expected maket pices (fo enegy and eseve) as well as expected penalties on balancing and eseve mechanisms. The methodology is applied and demonstated on numeical examples. Wind powe plants incease thei pofit by using these stategies fo optimally offeing in enegy and eseve makets, theeby educing the deviation penalties fom the balancing maket. Additionally, these stategies seek to motivate wind powe penetation on powe system, theeby, inceasing the competition in both makets, as well as ensuing a cheap esouce in the system opeato standpoint. Besides that, futue wind powe plants will be able to povide fast eseve sevices that will be cucial in the opeation of futue powe systems with high penetation of enewable esouces 12]. Thus, system opeatos have inteest in wind powe paticipating in both enegy and eseve makets. The pape is stuctued as follows. Section II descibes electicity makets chaacteistics with a pespective on futue enegy and eseve maket tends. Section III pesents the detailed fomulation of joint offeing stategies (fo popotional and constant stategies) in enegy and pimay eseve makets. Section IV descibes ou empiical investigation based on a set of numeical examples. Section V assembles the most impotant conclusions. II. WIND POWER IN ELECTRICITY MARKETS A. Cuent Day-Ahead and Balancing Maket The inceasing penetation of wind powe geneation in electic powe systems has been changing wholesale maket chaacteistics. In Denmak, wind powe poduces tade in the wholesale maket and ae emuneated though a combination of maket pice and pemium 28]. This emuneation mechanism allows wind powe ownes to submit bids into the day-ahead maket with zeo o negative pices 29]. The balancing maket is used to compensate fo enegy deviations in eal time fom the day-ahead and inta-day schedules. In a Euopean context these ae un by the local TSO 3]. Fo the example of Denmak, this maket is cleaed just befoe the opeating hou and is divided into a egulating powe maket (whee the system opeato puchases the equied egulating powe to balance the system) and a balancing powe maket (whee coection of the system and maket paticipant imbalances is pefomed) 31]. Fo the case of wind powe, the balancing maket is the final mechanism pemitting to mitigate foecast eos, and it can be highly penalizing.

4 SOARES et al.: OPTIMAL OFFERING STRATEGIES FOR WIND POWER 3 is expessed as R = λ sp E + λ cap P T W (1) Fig. 1. Schematic epesentation of the maket stuctue fo the wind offeing stategies. B. Joint Offeing in Enegy and Pimay Reseve Makets Cuently and even moe in the futue, wind powe plants will be able to povide some type of ancillay sevices, such as fequency and voltage contol 4]. Wind powe plants ae willing to paticipate in enegy and pimay eseve maket only in the case whee wind powe poduces may eceive inceased benefits fom joint maket paticipation, instead of paticipating in the enegy maket only. With that objective in mind, we will examine an analytical model fo obtaining the optimal quantile bid of wind powe paticipating in multiple makets with diffeent expected pices and penalties fo deviation fom schedule. The enegy and eseve makets have diffeent chaacteistics. On the one hand, wind enegy bids submitted in the day-ahead maket should account fo potential imbalance situations and thei asymmetic penalties. On the othe hand, bids submitted in the pimay eseve maket ae to accommodate the possibility to fail in poviding the sevice, cetainly associated with a much highe penalty. Fig. 1 pesents the stuctue of the maket fo the offeing stategies detemination. The bids submitted at the day-ahead maket conside the expected costs in the balancing stage. In the fomulation outlined hee, the effect which the day-ahead bid has on the penalties of the balancing maket, known as the time coupling effect, is not captued. We assume that any diffeences aising fom this effect cancel out ove time. The fomulation consides the impotant assumption of the split between enegy and pimay eseve emain the same in both day-ahead (α c ) and balancing stages (α ). This allows us to develop an analytical fomulation to solve the poblem. Futue wok may involve stochastic pogamming 32] allowing diffeent enegy and eseve shae between day-ahead and balancing stages, theeby, educing the time coupling effect. III. METHODOLOGY A. Geneal Fomulation of Maket Revenues The objective function to be optimized diectly elates to the maximization of the combined evenue fom day-ahead and eseve makets consideing the penalties fom the balancing maket. Time indices ae not used, since all vaiables and paametes ae fo the same maket time unit. This combined evenue R in eal-time fo a given wind powe poduce whee λ sp is the spot pice, E is the amount of deliveed enegy, λ cap is the capacity pice fo pimay eseve allocation, P is the deployed level of pimay eseve in eal-time, T is the egulation costs fom the egulation maket and W is the penalty cost fo wind powe plant failing to povide the scheduled pimay eseve. In addition, we assume that the wind powe poduce acts as a pice-take. This means that the poduction of the wind powe poduce is independent of maket pices and penalties. Because of this independence, and the fact that all pices ente linealy in the expessions below, all calculations depend only on the expected mean pices, athe than thei full distibution. This eduction follows fom cetainty equivalent theoy 36], and emoves the need fo a full stochastic desciption of pices using, e.g., scenaios 18]. In the following, we will efe to the sum of λ sp E and λ cap P as the expected inflow. In paallel, the sum of T and W is efeed to as expected costs. Subtacting the expected costs fom the expected inflow yields the expected evenue of the wind powe poduce. In (1), the egulation costs ae defined as { λ,+ T (E E c ), E E c = λ, (E E c ), E E c (2) < whee (E E c ) is the enegy imbalance between the enegy deliveed E and the enegy contacted (offeed) E c.thevaiables λ,+ and λ, ae the egulation unit costs fo positive and negative deviations, i.e., λ,+ = λ sp λ c,+ λ, = λ c, λ sp (3) whee λ c,+ is the unit down-egulation pice fo being long, while λ c, is the up-egulation pice fo being shot. We place ouselves hee in unde two-pice settlement ule, as in the NodPool 13]. In cases whee the system imbalance is negative (enegy suplus need fo downwad egulation), it holds that λ c,+ λ sp λ c, = λ sp (4) In contast, when system imbalance is positive (enegy deficit need of upwad egulation), one has λ c,+ = λ sp λ c, λ sp (5) While finally duing hous of pefect balance both λ c,+ and λ c, ae equal to the spot pice λ sp. In paallel, the penalty costs fo eseve imbalance can be witten as { λ bpt,+ W (P P c ), P P c = (6) λ bpt, (P P c ), P P c <

5 4 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY Fig. 2. Popotional wind offeing stategy (epoduced with authoization fom 29], 3]). Fig. 3. Constant wind offeing stategy (epoduced with authoization fom 29], 3]). whee (P P c ) is the pimay eseve powe imbalance between the ealized level of eseve P and the eseve contacted (offeed) P c. λ bpt,+ is a unit penalty when wind poduce geneato moe powe than the contacted (suplus), and λ bpt, is the unit penalty cost when wind powe poduce geneate less than contacted. These ae given by λ bpt,+ = λ cap λ pt,+ (7) λ bpt, = λ pt, λ cap hence λ pt,+ =since (exta) positive eseve is not detimental to the system s eliability. λ pt, is the penalty fo negative eseve imbalance, weighted by the pobability that eseve is needed. In pinciple, a wind powe poduce can bid any E c,p c into the day-ahead maket, and choose to delive any amount E,P in eal time, bounded by E +P E obs, the obseved enegy. To make the poblem analytically tactable, we poceed by constaining the choice of E and P based on E c and P c. This estiction is pefomed though the use of two known stategies, which have been peviously shown to be opeationally feasible 26], 27]. The following subsections define these stategies, while the analytical optimal bids ae finally given. B. Popotional Wind Offeing Stategy The popotional wind offeing stategy (illustated in Fig. 2) consists in a popotional cutailment of available powe geneation to yield an enegy offe E c and a pimay eseve offe P c 29], whee E c = α c P c =(1 α c ) In the above, denotes the total powe bid in MW fo that maket time unit and α c is the stategy paamete contolling the popotional split between enegy and pimay eseve bids. This last paamete natually vaies between (fo full eseve allocation) and 1 (fo full enegy allocation). (8) On the othe hand, the eventually obseved wind powe poduction E obs is similaly composed of an enegy potion E and P the amount of pimay eseve actually available, E = α E obs (9) P =(1 α )E obs whee α is the stategy paamete used when eaching ealtime opeation. It is assumed that stategy paamete in dayahead and eal-time ae the same α =α c. C. Constant Wind Offeing Stategy The constant wind offeing stategy (Fig. 3) is based on a constant cutailment of enegy when the expected enegy poduced is ove a cetain expected level of wind powe 26], whee E c = P c (1) P c = P R P R is the amount of fixed eseve to be submitted in the pimay eseve maket, and X% is the pecentage of installed wind powe. Simila to the popotional stategy, the obseved wind poduction E obs is elated to E. The eseve amount is assumed to be constant and fixed in day-ahead decision. That is, pioity delivey of the eseve is assumed. The deliveed amount of enegy and pimay eseve may be witten as E = E obs P P = P (11) IV. ANALYTICAL DERIVATION OF OPTIMAL BIDS A. Popotional Stategy Optimization Poblem Assuming that the wind powe plant acts as a pice-take, the maximization of its expected evenues is equivalent to the minimization of the expectation of egulation and penalty costs.

6 SOARES et al.: OPTIMAL OFFERING STRATEGIES FOR WIND POWER 5 Optimal offes ae then the solution of (, α c )=agmin E {T + W λ sp E λ cap P } (12),α c The loss function in the above compises an extended vesion of that used in 13], whee hee, the available wind powe is split into two diffeent maket poducts. The shae of the available expected powe α c and obseved powe α fo enegy and eseve paticipation is the same (α = α c ). Consequently, the total expected costs O ae given by λ, α c ( x)+ O (, α c )= λ bpt, (1 α c )( x) f (x) dx + λ sp α c x λ cap (1 α c ) x λ,+ α c (x ) λ sp α c x λ cap (1 α c ) ] f (x) dx (13) whee f(x) is the foecast pobability density function of the wind powe plant poduction. To analytically solve the poblem the Leibniz ule is used. The Leibniz ule, fo an abitay function f, paametes θ, and integation bounds a and b, tells that θ ( ) b(θ) f (x, θ) = a(θ) θ f (x, θ) dx + f (b (θ),θ).b (θ) f (a (θ),θ).a (θ) (14) Fig. 4. Illustative behaviou of Eq. (13) unde diffeent elations fo enegy and eseve penalties. Note, that evenues ae maximized fo α c =o 1, i.e. the wind powe poduce paticipates fully in one maket o the othe. depending on. This means that Eq. (13) will be maximized fo one of α c =o α c =1. Bids fom this popotional stategy will take place in eithe the enegy o the eseve maket, but neve in both (see Fig. 4). In this way, the enegy bid is equal to the total expected enegy when the eseve penalty is highe than the enegy penalty (λ bpt, >λ, ), so total availability is submitted to the enegy maket. On the contay, when the enegy penalty is highe than the eseve penalty (λ, >λ bpt, ), the total expected powe is submitted to the pimay eseve maket. Thus, the deivative of (13) with espect to is given by (, αc )= λ, α c + λ bpt, (1 α c ) ] f (x) dx λ sp α c + λ cap (1 α c ) ] f () + λ,+ α c λ cap (1 α c ) ] f (x) dx +λ sp α c + λ cap (1 α c ) ] f () (15) The optimal bid is obtained by equating the deivative in (15) to, then yielding an optimal quantile of the pedictive cumulative distibution function F fo wind powe geneation at that lead time = F 1 λ,+ α c + λ cap (1 α c ] ) (λ, + λ,+ ) α c +(λ bpt, + λ cap )(1 α c ) (16) Similaly, the deivative of (13) with espect to α c wites ] α c (, λ αc )=, ( x) λ bpt, ( x) λ sp x+λ cap f (x) dx x + λ,+ (x ) λ bpt,+ (x ) λ sp x + λ cap x ] f (x) dx (17) Equation (17) is a nonlinea equation in. Its solutions detemine the possible values that may be used. Note that Eq. (13) is affine in α c, with the sign of the coefficient of α c B. Constant Stategy Optimization Poblem The constant stategy assumes that a cetain amount of the available powe is fixed to paticipate in the pimay eseve maket, while the emaining available powe is submitted in the enegy maket 26]. The stategy splits into thee distinct domains accoding to the elationship between the pices on day-ahead makets, and the penalties fo enegy and eseve deviations. 1) Nomal Opeation: Unde cuent electicity makets egulatoy famewok it is moe advantageous fo wind powe plants to povide enegy than to povide eseve, since the enegy pice is usually highe than the eseve pice 37]. If enewable enegy poduces ae able to povide in eseve makets, maket opeatos should ensue appopiate pice signals to povide incentive fo wind powe plants to offe thei flexibility 4]. I.e. the eseve pice must be highe than the enegy pice (λ cap λ sp ). The nomal opeational hieachy of electic powe systems implies that not meeting a call fo eseve is wose than not poducing the enegy pomised, such that the eseve penalty should be highe than the enegy egulation penalty (λ bpt, λ, ). The deivation below assumes that these elations hold. The deivation is also valid fo the invese case λ, λ bpt, and λ sp λ cap, but fo the above easons, we expect that the invese case is unlikely to occu in pactice. Again assuming the wind powe plant is a pice-take, the expected available powe, and the pimay eseve offe

7 6 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY This finally yields the optimal bid fo eseve paticipation P = F 1 λ cap λ sp ] λ bpt, λ, + λ cap λ sp (23) Fig. 5. Regions of opeation of constant stategy. P R, ae detemined fom a minimization of the expectation of egulation and penalties costs. This wites (, P R )=agmin E {T + W λ sp E λ cap P } (18),P R This poblem contains thee diffeent egions of opeation (Fig. 5): (i) obseved wind enegy lowe than fixed eseve offe P R E obs, (ii) obseved wind powe between fixed eseve offe and expected wind powe E obs P R, and (iii) obseved powe highe than expected wind powe E obs E exp. The mathematical fomulation which minimizes the total expected costs (O) isasfollows O (, P )= + P λ, ( P )+ λ bpt, (P x) λ cap x ] f (x) dx λ, ( x) λ sp (x P ) λ cap P ] f (x) dx P 1 + λ,+ (x ) λ sp (x P ) λ cap P ] f (x) dx (19) The integals coespond espectively to the opeation egions 1, 2, and 3 in Fig. 5. We poceed to minimize this function by diffeentiation. The deivative of (19) with espect to is given by P (, P )= λ, f (x) dx + λ, f (x) dx P R λ sp ( P )+λ cap P ] f ()+ λ,+ f (x) dx +λ sp ( P )+λ cap P ] f () (2) which leads to = F 1 λ,+ ] λ, + λ,+ The deivative of (18) with espect to P is P P (, P )= λ bpt, λ, ] f (x) dx (21) + λ, ( P ) λ cap P ] f (P )+ λ sp λ cap ] f (x) dx P λ, ( P ) λ cap P ] f (P )+ λ sp λ cap ] f (x) dx (22) 2) Special Opeation Reseve Only Maket:: Thee ae a few cases whee the stategy should be decoupled to paticipate in a single eseve maket: when the enegy bid is negative only eseve maket paticipation; and when λ bpt, <λ, and λ cap λ sp, the full availability of the wind poduce should be submitted to the eseve maket. In that case, the objective function is a special case of that in Eq. (19), i.e., O (P )= P + P λ bpt, (P x) λ cap x ] f (x) dx ] λ,+ (x P ) λ sp (x P ) λ cap P f (x) dx (24) The deivative with espect to P R is obtained as P (P )= P λ bpt, f (x) dx λ cap P ] f (P ) + λ sp λ,+ λ cap] f (x) dx +λ cap P ] f (P ) P (25) esulting in the optimal quantile bid fo eseve paticipation, ( P = F 1 λ,+ + λ cap λ sp ) λ bpt, + λ,+ + λ cap λ sp (26) 3) Special Opeation Enegy Only Maket: In cases whee λ bpt, λ, and λ cap <λ sp, it is intuitive that the wind powe poduce will opt to paticipate in the enegy maket only. The objective function fo this case is a paticula case of Eq. (19), given by O () = + λ, ( x) λ sp x ] f (x) dx λ,+ (x ) λ sp x ] f (x) dx The deivative of (27) with espect to E exp becomes () = λ, f (x) dx + (27) λ,+ f (x) dx (28) which esults in the well-known quantile fo enegy-only paticipation ( = F 1 λ,+ ) λ, + λ,+ (29) C. Stategies Summay A geneal oveview of the analytical fomulas to obtain optimal offes in both makets and fo both stategies is given in Table I.

8 SOARES et al.: OPTIMAL OFFERING STRATEGIES FOR WIND POWER 7 TABLE I SUMMARY OF OPTIMAL BIDS TABLE II PRICES AND PENALTIES IN ENERGY AND RESERVE MARKET TABLE III SIMULATION RESULTS FOR STRATEGIES BASED ON PROPORTIONAL, CONSTANT, AND ENERGY-ONLY MARKET STRATEGY Fig. 6. Objective function behavio fo constant stategy, based on base case data. TABLE IV SIMULATION RESULTS FOR λ cap LARGER THAN λ sp FOR PROPORTIONAL, CONSTANT, AND ENERGY-ONLY MARKET STRATEGIES Fig. 7. Expected evenue fo constant stategy unde vaiation of day-ahead enegy and pimay eseve maket pices. A. Test Cases V. EVALUATION OF OFFERING STRATEGY 1) Base Case:: The base case is based on the following paametes and assumptions. The wind powe plant has a 3 MW installed capacity. An example pobabilistic wind powe foecasts takes the fom of a beta distibution with shape paametes α =2and β =4. The expected evenue is evaluated using 1 samples fo wind poduction dawn fom this distibution. Besides, Table II gathes the pices fo enegy and eseve in ou numeical example, as well as the unit penalty fo up and down deviations fom contact. The evaluation of the popotional stategy is pefomed by an iteative pocess. α c is assumed to vay between and 1 with steps of.3. is detemined based on Eq. (16) fo each α c. The total evenue fo each given α c is detemined. The constant stategy is fist analyzed based on the most ealistic assumption on the elation between penalties and maket pices, i.e., such that λ bpt, λ, and λ cap λ sp.inthis case, Eqs. (21) and (23) ae used to detemine the enegy and the eseve bid, espectively. Fig. 8. Expected shae of enegy and eseve fo constant stategy unde vaiation of day-ahead enegy and pimay eseve maket pices. Dashed lines epesents the pimay eseve shae fo each case of pimay eseve pice (case 1 eseve pice of 25 C/MW; case 2 eseve pice of 35 C/MW;andcase3 eseve pice of 5 C/MW). Table III shows a compaison between thee diffeent stategies fo paticipation in electicity makets (popotional, constant and enegy-only). The expected evenue is the diffeence

9 8 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY TABLE V CUMULATIVE SIMULATION RESULTS OF TWO YEARS DATA FOR PROPORTIONAL, CONSTANT, AND ENERGY-ONLY MARKET STRATEGIES Fig. 9. Constant and popotional stategies behavio ove the time, unde eal data adapted fom 13]. between the expected inflow and expected costs (defined in Sect. IV). The enegy-only stategy is based on the common newsvendo poblem 13]. Thus, the quantile fo this stategy is given by Eq. (29). Obseving the behavio of the stategies in Table III, one can veify that constant stategy has highe expected etun than the othe stategies. 2) Full Reseve Case: Assuming that λ cap is much lage than λ sp, fo instance λ cap =4 C/MW, the stategies may split the enegy and eseve bids diffeently. Table IV compae the stategies paticipation in both enegy and pimay eseve maket fo this capacity pice. One can veify that thee is a change in the behavio of both poposed stategies. Both stategies allocate all the available enegy to the pimay eseve maket. This is since the evenue fom the pimay eseve maket is much highe than the evenue fom the enegy maket. Both poposed stategies get bette esults than the enegy-only stategy. B. Constant Stategy Behavio 1) Objective Function Behavio: The objective function fo the base case is depicted in Fig. 6. One can veify that this function is convex, allowing to obtain a unique optimal solution. The expected eseve bid can neve be highe than the total expected enegy, hence the tiangula cutoff fo highe expected eseve. 2) Constant Stategy Pefomance Unde Diffeent Spot and Pimay Reseve Maket Pices: The behavio of the constant stategy stongly depends on the diffeence between day-ahead enegy and pimay eseve maket pices. Fig. 7 depicts the behavio of the stategy unde diffeent spot and eseve maket pices. The simulation is pefomed unde the base case data with vaiation in spot and pimay eseve pices. The spot pices vaies between 17 and 32 C/MWh, while the pimay eseve maket pice is epesented by thee cases, 25, 35 and 5 C/MW, espectively. The simulation shows that inceasing pimay eseve pice leads to highe evenue, as expected. As long as the spot pice inceases, the expected evenue inceases too, since the stategy splits its available powe fo enegy and eseve. Thus, as long as one of the day-ahead enegy spot o capacity pice impoves, the evenue tends to incease. Fig. 8 illustates the dependency of the shae of the offes into the enegy and eseve makets as a function of day-ahead enegy and eseve capacity pices. The eseve shae tends to educe with the incease of the spot pice, as expected. Howeve, at a cetain point, the eseve maket no longe geneates highe pofit than the enegy maket, making that full availability is submitted to the enegy maket. This occus when the spot pice is highe than 25 C/MWh. In case 1 (eseve pice of 25 C/MW) this occus because the pimay eseve penalty is highe than the enegy penalty, so thee is no incentive to paticipate in the pimay eseve maket. The intesection between enegy and eseve cuve fo case 1, gives pecisely the esult of the base case fo the constant stategy. C. Stategies Behavio Ove Time Real Data The data and assumptions used fo simulation of both stategies ove time ae the same used in 13]. We conside a wind fam of 15 MW paticipating in the Nod Pool, whee the wind

10 SOARES et al.: OPTIMAL OFFERING STRATEGIES FOR WIND POWER 9 fam data is based on powe measuements and a seies of 48 h- ahead point pedictions between Mach 21 and Apil 23 13]. Nod Pool pices and penalties between 21 and 23 ae used. Reseve penalty is assumed to be 5% highe than the capacity pice in the pimay eseve maket. The cumulative data esults fo enegy and evenue ove the two yeas fo each stategy ae shown in Table V. In oveall, one can see that the popotional stategy submits moe powe to the enegy and eseve makets than the constant stategy. In the same pespective, the popotional stategy gets moe expected evenue than constant stategy. Futhemoe, popotional and constant stategies impove the evenue of wind powe poduces elative to the enegy-only stategy by about 12% and 3%, espectively. In addition, Table V povides a compaison fo each stategy between the expected esults unde foecast scenaios and unde deployed wind powe. Fig. 9 illustates the diffeent behavio of both popotional and constant stategies ove time. It can be seen that in most of the peiods, the constant stategy splits the available powe fo paticipation in both makets. On contay, the popotional stategy tends to submit all the available powe to one maket only. Fom the economic point of view, both stategies ae balanced. I.e., in some peiods, the constant stategy may get moe evenue than the popotional one, howeve, the opposite also occu. This is because of the diffeent assumptions on the fomulation of each stategy, yielding diffeent behavio in the maket. VI. CONCLUSION The inceasing flexibility of wind powe plants will allow them to povide moe maket sevices, such as pimay eseve, in the futue. This wok fomulates and deives optimal offeing stategies fo wind powe plants paticipation in enegy and pimay eseve makets. Two stategies (popotional and constant eseve offeing stategies) wee consideed. Both stategies have diffeent behavio and flexibility, howeve, they incease wind powe ownes expected pofits as compaed to an enegyonly bid. The esults show that such stategies povide additional pofits in expectation. The popotional stategy leads to a binay behavio whee all the available enegy is submitted in eithe the enegy o the eseve maket. In contast, the constant stategy enables a joint paticipation of wind powe plants in both enegy and pimay eseve makets. In addition, esults show that these offeing stategies stongly depend on the maket pices and penalties fo enegy and pimay eseve. An impotant conclusion fom this wok is that, even though tubines may have the technical ability to povide eseves, they may not always do so in the cuent maket famewok, since the elative pofitability and penalties in both enegy and eseve makets will dive the behavio of wind powe poduces. Futue wok will focus on impovements of the stategies consideing that the shae fo enegy and eseve submitted in the day-ahead maket can change in the balancing maket. ACKNOWLEDGMENT The authos would like to thank thee eviewes whose comments allowed to impove the contents and pesentation of this wok. REFERENCES 1] Eneginet.dk. (214). Annual epot 213, pp , 214, Online]. Available: %2dokumente/Om%2os/Annual%2Repot%2213.pdf 2] Danish Govenment, Enegy stategy 25 Fom coal, oil and gas to geen enegy, Danish Enegy Agency, pp. 1 66, 211 Online]. downloads/enegy_stategy_25.pdf 3] M. A. Otega-Vazquez and D. S. Kischen, Estimating the spinning eseve equiements in systems with significant wind powe geneation penetation, IEEE Tans. Powe Syst., vol. 24, no. 1, pp , Feb ] E. Ela, B. Kiby, N. Navid, and J. C. Smith, Effective ancillay sevices maket designs on high wind powe penetation systems, in Poc. IEEE Powe Enegy Soc. Gen. Meeting, 212, pp ] H. 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11 1 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 22] M. Zugno, J. M. Moales, P. Pinson, H. Madsen, and A. Sets, Pool stategy of a pice-make wind powe poduce, IEEE Tans. Powe Syst., vol. 28, no. 3, pp , Aug ] L. Baingo and A. J. Conejo, Stategic offeing fo a wind powe poduce, IEEE Tans. Powe Syst., vol. 28, no. 4, pp , Nov ] S. J. Kazempou and H. Zaeipou, Equilibia in an oligopolistic maket with wind powe poduction, IEEE Tans. Powe Syst., vol. 29, no. 2, pp , Ma ] K. C. Shama, R. Bhaka, and H. P. Tiwai, Stategic bidding fo wind powe poduces in electicity makets, Enegy Conves. Manage., vol. 86, pp , ] L. Baingo and A. J. Conejo, Offeing stategy of wind-powe poduce: A multi-stage isk-constained appoach, IEEE Tans. Powe Syst., 215, pp. 1 1, doi: 1.119/TPWRS ] T. Dai, S. Membe, W. iao, and S. Membe, Optimal bidding stategy of a stategic wind powe poduce in the shot-tem maket, IEEE Tans. Sustain. Enegy, vol. 6, no. 3, pp , Jul ] M. Shafie-khah, A. A. S. de la Nieta, J. P. S. Catalão, and E. Heydaian- Foushani, Optimal self-scheduling of a wind powe poduce in enegy and ancillay sevices makets using a multi-stage stochastic pogamming, in Poc. Smat Gid Conf. (SGC), 214, pp ] Y. Wang, Evaluation de la pefomance des églages de féquence des eoliennes à l echelle du système electique: Application à un cas insulaie, (in Fench), Ph.D. dissetation, L2EP, Ecole Centale de Lille, Villeneuve-d Ascq, Fance, ] Y. Wang, H. Bayem, M. Gialt-Devant, V. Silva, X. Guillaud, and B. Fancois, Methods fo assessing available wind pimay powe eseve, IEEE Tans. Sustain. Enegy, vol. 6, no. 1, pp , Jan ] S. Kohn, P. E. Mothost, and S. Awebuch, The economics of wind enegy, EWEA Eu. Wind Enegy Assoc., pp , 29 Online]. Available: publications/epots/economics_of_wind_enegy.pdf 32] Eneginet.dk, Wind powe to combat climate change How to integate wind enegy into the powe system, pp. 1 56, 29 Online]. Available: Klimaogmiljo/Wind%2powe%2magazine.pdf 33] K. Skytte, The egulating powe maket on the Nodic powe exchange nod pool: An econometic analysis, Enegy Econ., vol. 21, no. 4, pp , ] Eneginet.dk, Regulation C2: The balancing maket and balance settlement, Doc. no, , pp. 1 2, 28 Online]. Available: dokumente/el/regulation%2c2%2the%2balancing%2maket%2 and%2balance%2settlement.pdf 35] A. J. Conejo, M. Caión, and J. M. Moales, Decision Making Unde Uncetainty in Electicity Makets. New Yok, NY, USA: Spinge, ] H. Raiffa and R. Schlaife, Applied Statistical Decision Theoy. Boston, MA, USA: Division of Reseach, Havad Business School, ] B. Kiby and A. Tuohy, Pofitability of wind plants poviding ancillay sevices Regulation and spinning eseve, 213 Online]. Available: 24kiby.pdf Tiago Soaes eceived the B.Sc. and M.Sc. degees in electical engineeing fom the School of Engineeing, Polytechnic Institute of Poto, Poto, Potugal, in 21 and 213, espectively. He is cuently pusuing the Ph.D. degee at the Technical Univesity of Denmak, Kgs. Lyngby, Denmak. His eseach inteests include electicity makets, distibuted geneation, enegy esouces management and optimization, optimization unde uncetainty, and futue powe systems. Piee Pinson (M 11 SM 13) eceived the M.Sc. degee in applied mathematics fom the National Institute fo Applied Sciences (INSA), Toulouse, Fance, and the Ph.D. degee in enegetics fom Ecole des Mines de Pais, Pais, Fance. He is a Pofesso with the Depatment of Electical Engineeing, Cente fo Electic Powe and Enegy, Technical Univesity of Denmak, Kgs. Lyngby, Denmak, also heading a goup focusing on Enegy Analytics and Makets. His eseach inteests include foecasting, uncetainty estimation, optimization unde uncetainty, decision sciences, and enewable enegies. He is an Edito fo the IEEE TRANSACTIONS ON POWER SYSTEMS and the Intenational Jounal of Foecasting and fo Wind Enegy. Tue V. Jensen eceived the M.Sc. degee in physics fom Aahus Univesity, Aahus, Denmak, in 213. He is cuently pusuing the Ph.D. degee at the Technical Univesity of Denmak, Kgs. Lyngby, Denmak. His eseach inteests include enewable enegy makets, complex netwoks, and gaming aspects of enegy makets. Hugo Moais (S 8 M 11) eceived the Ph.D. degee in electical engineeing fom the Univesity of Tás-os-Montes e Alto Douo, Vila Real, Potugal. He is a Reseache with the Mesues et système d Infomation des Réseaux Electiques Goup, Électicité de Fance, Clamat, Fance. His eseach inteests include distibuted enegy esouces management, vitual powe playes, smat gids, futue powe systems, agents technology, and powe systems visualization.