Ragne Hildrum Statkraft SF Oslo, Norway

Transcription

1 23(5$7,21$1'6,=,1*2)(1(5*<6725$*()25:,1'32:(5 3/$176,1$$5.(76<67( Magnus Korpås NTNU Trondhim, Norway Ragn Hildrum Statkraft SF Oslo, Norway Arn T. Holn NTNU Trondhim, Norway $EVWUDFW±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± ZLQG SRZHU HQHUJ\ VWRUDJH RSHUDWLRQ VFKHGXOLQJGLVWULEXWHGJHQHUDWLRQ,1752'8&7,21 Wind nrgy is a valuabl supplmnt to convntional nrgy sourcs, as wind powr tchnology has bcom matur. Howvr, th maximum pntration of wind powr in lctricity ntworks is limitd by th intrmittnt natur of wind nrgy. Fluctuations in wind powr production also maks it difficult for ownrs of wind powr plants to compt in th mrging lctricity markts. Enrgy storag dvics with th ability to stor larg amounts of nrgy for svral hours or mor, such as flow clls and ful cll systms [1], could provid th ncssary flxibility for smoothing of wind powr, and thus incras th possibilitis for markt opration. Morovr, for potntial wind farm sits rmot from a strong lctrical connction point, nrgy storag could provid an altrnativ to grid rinforcmnts. Thr is a growing rsarch intrst in using nrgy storag to incras th valu of intrmittnt nrgy sourcs in lctricity markts [2,3,4]. Howvr, important issus such as th impact of markt mchanisms, transmission lin constraints and forcasting accuracy of wind powr must b furthr xplord to fully dtrmin th advantags and limitations of nrgy storag for this purpos. Thrfor, a mthod for th schduling and opration of such a distributd rsourc in a markt systm has bn dvlopd and implmntd in a computr modl. This papr aims to dscrib th proposd mthod, and to show an application of th mthod on a casstudy, whr th impact of nrgy storag sizing and wind forcasting accuracy on systm opration and conomics ar mphasizd. A list of symbols is providd in th appndix. 6<67('(6&5,37,21 Th distributd rsourc is prsntd in Figur 1, and consists of a wind powr plant and an nrgy storag dvic. Th ownr of th rsourc is assumd ithr to hav a dmand for lctricity, 3 O, or to hav contracts with th local lctricity consumrs rprsntd by an aggrgatd load dmand. Th systm is connctd to th main lctricity ntwork by a transmission lin with limitd capacity. Ractiv powr flow is nglctd in th simulations prformd hr, in ordr to kp th focus on th schduling and flow of ral powr. Th systm componnts and th lctricity markt modl ar prsntd blow. wind powr plant xtrnal grid nrgy storag P l local load transmission lin )LJXUH Wind powr plant with local nrgy storag connctd to a scarcly populatd grid. Th dirction of th arrows rfrs to positiv valus of th variabls. :LQGSRZHUSODQW Th powr output of th wind powr plant is calculatd from th powr curv in Figur 2. It is assumd that th wind powr plant consists of idntical wind turbins, P P cl controllabl load

2 and that th wind conditions ar th sam for all turbins. [MW] PD[ wind vlocity, v [m/s] )LJXUHTh wind gnrator input/output charactristics usd in th modl. (QHUJ\VWRUDJH Th nrgy storag dvic is dfind by its nrgy capacity, charging fficincy, discharging fficincy, charging powr capacity and discharging powr capacity. Th storag quations ar as follows: S( t + 1) min S min 1 St () -----P η s () t t ( > ) = d St () η c () t t ( < ) () t P max s St () S max whr η F and η G ar th fficincis of charging and discharging rspctivly. Charging and discharging occurs for ngativ and positiv valus of 3 V W, rspctivly. Th round-trip fficincy of th storag dvic is η s = η c η d. 7UDQVPLVVLRQOLQH Th transmission lin will act as a powr sourc or sink, dpnding on th balanc btwn local load and gnration. Th powr transportd on th lin is th powr xchangd with th markd systm, and is calculatd from th powr balanc: P = + P l P cl Pmin P Pmax (1) (2) (3) (4) (5) Powr xport corrsponds to positiv valus for 3 H which is masurd at th load sid of th transmission lin. Th xprssion for activ powr losss is: P, loss = c t P 2 (6) Th maximum allowabl powr xchang is qual to th transmission lin capacity, whil th minimum valu is givn by. P min = ( ) 2 Pmax + c t Pmax (7) If th nt powr production xcds th lin capacity, th xcss powr is consumd by a controllabl load, 3 FO, which is usd only for this purpos. 7KHHOHFWULFLW\PDUNHW In th Nordic spot markt, daily bids for sal and purchas of nrgy in th spot markt ar providd to th powr pool 12 hours bfor th actual day. Aftr th spot pric has bn sttld, th final schdul is workd out. During th opration, if a participant dos not dlivr th spcifid amount at th spot markt, thn th discrpancy must b sttld on th rgulating powr markt, which normally rsults in a rducd incom [6]. Markt opration is simplifid considrably in th modl. Sinc th marginal cost of powr producd from a wind powr plant is zro, it is prsumd that wind nrgy always can b sold on th markt. Each day at 12., th ownr of th distributd rsourc prforms th schduling of th hourly powr xchang with th markt, Pˆ. Th hourly incom from th spot markt participation is: f = spot SP Pˆ t (8) Powr flow in th transmission lin causs losss which ar bought for spot pric: f loss = SP c P 2 t t Th rgulating markt is simplifid by using avrag valus. Th prics for sal and purchas of lctricity tradd on th rgulating markt ar assumd to b proportional to th spot pric: ( 1 c rs ) SP P dv t ( P dv > ) f rg = (1) ( 1 + c rp ) SP P dv t ( P dv < ) whr th dviation btwn actual and schduld powr xchang, P dv = P Pˆ, is tradd on th rgulating markt. In th Norwgian rgulating markt, a discrpancy btwn th actual and plannd production could in fact lad to highr rvnu, dpnding on th ovrall powr balanc in th markt. This could for instanc happn in th cass whn th actual powr xchang is highr than schduld at th sam tim as thr is a powr dficit in th markt. Howvr, it is prsumd that in avrag, dviations from th production plan ar disadvantagous, sinc thy incras th uncrtainty of th ovrall powr balanc. 23(5$7,21675$7(*< (9) Th opration stratgy consists of thr sparat parts: 1) forcasting of wind vlocity 2) schduling of th powr xchang with th markt and 3) on-lin opration of th storag. In th prsnt modl, th forcasts of load and spot pric ar assumd to hav 1% accuracy. A flowchart of th mthod is shown in Figur 3,

3 and th various stps of th algorithm ar dscribd blow.,1,7,$/,6( Rad systm info i = 1, t = 1 t = t sch? Y N )25(&$676 Rad v i+1 (t), P i+1 l (t), SP i+1 (t) for t = 1..t nd rgulating markt, on should considr all possibl combinations of wind vlocitis in th complt optimization problm. Howvr, at this stag of th modlling work, th forcastd valus ar tratd as dtrministic variabls in ordr to rduc th computational ffort to a rasonabl siz. Trading losss du to dviations btwn actual and schduld gnration ar consquntly omittd in th optimization problm. Givn th spot pric, load dmand and short trm forcast of wind vlocity, th optimization task is to dtrmin th hourly trading of lctricity in th spot markt which maximizs th xpctd profit ovr th schduling priod. Mathmatically, th schduling of th distributd rsourc can b formulatd as: OPERATION SCHEDULING Estimat S i+1 (). Find optimal P i+1 (t) for t = 1..t nd max F = f( Pˆ () t ) t = 1 whr t nd (11) ON-LINE OPERATION Masur v(t), P l (t) Oprat storag such that P (t)=p (t) Updat i, t N i = i nd? Y TERMINATE )LJXUHFlowchart of th opration stratgy for a wind powr plant with nrgy storag. Th indxs for day and hour ar L and W. )RUHFDVWV A simpl algorithm for computr-gnratd wind vlocity forcasts has bn dvlopd. Th forcastd avrag wind vlocity for a spcifid tim priod is calculatd, basd on th actual wind data for th sam priod. Th algorithm includs th following stps: Rad wind data YW for t=1..t nd and th cofficint of variation 9 for man wind vlocity prdiction Calculat v Draw a random numbr [ from th normal distribution with man v and standard dviation v V Rturn th prdictd wind vlocity vˆ () t = x for t=1..t nd As an xampl, for a wind sris with man valu 8.1 m/s and standard dviation of 4.4 m/s, th RMSE valu of prdiction rror is found to b 2.57 m/s using th proposd mthod with V =. 2SHUDWLRQVFKHGXOLQJ Th opration schduling of th systm is prformd at th spcifid hour W VFK ach day. Th objctiv is to find th schduling plan for th nxt day which maximizs th xpctd profit. Sinc th wind vlocity forcast is uncrtain, and a pnalty is givn for trading in th f( Pˆ () t ) = f spot ( Pˆ () t ) + f loss ( Pˆ () t ) (12) subjct to th systm oprating constraints (1)-(7) and th initial storag lvl. Th trms I VSRW and I ORVV ar dfind in quations (8) and (9). Sinc thr ar normally larg uncrtaintis both in th short-trm and longtrm prdiction of wind vlocity, th optimization horizon W HQG is chosn to b 24 hours. It is thrfor bnficial from an conomic point of viw to discharg th storag compltly at th nd of ach day. If thr wr ngligibl rrors in wind vlocity prdictions, th optimization horizon should b incrasd. Thn, it could b favorabl to stor nrgy at th nd of th day, for instanc if thr wr a risk for long priods with no wind. Th optimization problm is solvd using a dynamic programming algorithm, which rquirs discrtisation of th storag lvl. Th optimization routin rturns th xpctd path Ŝ() t for t = 1..t nd, which givs th optimal schduling of powr xchang Pˆ () t from quations (1) and (4). Th controllabl load 3 FO is usd as dump load, and thrfor its valu diffrs from zro only whn th storag is compltly filld at th sam tim as th nt local production xcds th transmission lin capacity. Altrnativly, on or mor wind turbins could b shut down or downrgulatd in ordr to not ovrload th transmission lin. Th nrgy loss du to downrgulation of wind powr output will b qual to 3 FO. Th opration schduling is prformd 12 hours in advanc, which mans that th storag lvl is unknown at th start of th optimization priod. If th wind forcasts wr 1% corrct, th stimatd valu Ŝ( t nd ) from th prvious optimization should b usd. Howvr, bcaus of uncrtaintis in th wind forcasts, th hourly storag lvls will dviat from th stimatd valus. To gt a nw stimat of th initial storag lvl of day Lth following quation is mployd:

4 S ˆi ( ) = Ŝ i 1 ( t nd ) + S (13) whr 6 is th storag lvl corrction basd on th masurd lvl at th schduling hour W VFK and an improvd forcast of th wind forcast for th rmaining hours of th day. 2QOLQHRSHUDWLRQ A straightforward opration stratgy is usd. Th nrgy storag is opratd in ordr to follow th hourly schduling plan for powr xchang with th markt. Consquntly, it is prsumd that th amount of lctricity producd by th wind powr plant and consumd by th load ar continuously masurd. 6<67(6,8/$7,21 A cas-study is usd to tst th proposd opration stratgy of th distributd rsourc. Th systm data for th bas cas ar listd in Tabl I. Tim sris for wind vlocity ar computd using a synthsis algorithm dscribd in [5], and tim sris for load dmand ar computd using th daily load curv in Figur 4. Th man load for a crtain day is obtaind from a normal distribution N( P l, σ l ) whr P l is th daily man load and σ l is standard dviation of th daily man load. Th hourly valus is obtaind by multiplying with th corrsponding valu of th curv in Figur 4. load [pu] tim [hours] )LJXUHTypical daily load curv for Norwgian housholds. Elctricity prics ar shown in Figur 5, and ar assumd to b th qual for all days. Th typ of nrgy storag is not spcifid, but could for instanc b a rgnrativ ful cll or a rdox flow cll. Such storag systms ar still undr dvlopmnt, and th futur spcific costs ar uncrtain. Thrfor, th spot prics usd in th simulations ar chosn to b highr than prsnt valus obsrvd in th nordic powr markt. As a comparison, th actual avrag spot pric in yar 1996 and yar 2 wr 254 NOK/MWh and 13 NOK/MWh rspctivly [7] (1$ = 9 NOK in novmbr 21). Also, th variations in simulatd spot pric during th day ar chosn to b highr than th rlativly low variations obsrvd in th markt today. Th simulatd avrag pric for purchas of lctricity in th rgulating markt is 17% highr than th spot pric, and th avrag pric for sals is 12% lowr than th spot pric. Ths valus ar partly basd on [6], assuming a rlativly high pntration of wind powr in th markt. P max c t max η s max S max [MW] [MW -1 ] [MW] [MW] [MWh] P l σ l v RMSE [MW] [MW] [m/s] [m/s] DEOH,Systm data for th bas cas. lctricity pric [$/MWh] )LJXUHSimulatd hourly spot pric (middl) and pric for purchas (uppr) and sal (lowr) of lctricity in th rgulating markt. 'HPRQVWUDWLRQRIGDLO\RSHUDWLRQ In ordr to study th hourly systm opration, a 48 hour simulation run of th bas cas is prsntd. Forcastd and actual valus of hourly wind powr production ar shown in Figur 6. ral powr [MW] )LJXUH Actual, 3 Z, and forcastd, Pˆ w, valus of wind powr production. Figur 7 displays th schduld and actual powr xchang with th markt. Th systm manags to follow th production plan most of th tim xcpt for som hours at th start and at th nd of th simulation priod. This discrpancy can b xplaind from Figur 8, whr th stimatd and actual storag lvl ar plottd. At th start and th nd of th priod, th actual storag lvl is mpty for a longr priod than xpctd. For thos hours, th storag cannot compnsat if th wind powr production is lowr than prdictd. This undsirabl situation can b avoidd by stting th minimum N Z tim [hours] tim [hours]

5 allowabl storag lvl, 6 PLQ, largr than zro in th optimization routin. Morovr, th actual powr xchang also dviats from th schduling plan for W. Th rason for this discrpancy is that th powr capacity of th storag is too low compard to th wind powr production in that hour. ral powr [MW] P P tim [hours] )LJXUHActual, 3 H, and schduld, Pˆ, powr xchang with th markt. Positiv valus man xport of powr. storag lvl [MWh] S S tim [hours] )LJXUH Actual, 6 and stimatd, Ŝ, storag lvl for a storag dvic with 75% round-trip fficincy. It is important to obtain a good stimat of th initial storag lvl usd in th optimization routin. If th actual storag lvl is highr than th stimat, th storag can rach its maximum valu too arly by following th schduling plan. Likwis, if th storag lvl is lowr than th stimat, th storag can b dischargd too arly. Th lattr is obsrvd in Figur 8, whr th stimatd storag lvl at th start of day two (W ) is highr than th actual valu. This causs a full discharg of th storag at th nd of th priod on hour arlir than stimatd, and th systm bcoms lss flxibl. RQWHFDUORVLPXODWLRQV A simpl Mont-Carlo simulation tchniqu has bn mployd in ordr to study th impact of storag dsign and wind forcasting rror on th prformanc and conomics of th systm. Th paramtr valus in Tabl I ar usd in th bas cas, and Pmax, 6 PD[ s and th RMSE of wind spd prdiction ar varid in th simulations. Th stochastic variabls ar wind vlocity Y and load dmand 3 O. It should b notd that th modlling mthod of wind spd and load dscribd abov dos not tak into account sasonal variations. Howvr, th rror causd by this simplification is considrd to b small for Norwgian conditions, sinc thr is a clos match btwn th sasonal lctricity dmand and wind nrgy in Norway [8]. max [MW] 6 PD[ [MWh] P dv Pˆ yarly rvnu [1 $] DEOH,,Th impact of storag sizing on th prformanc and conomics of th systm. Th bas cas paramtrs ar usd, max xcpt for and 6 PD[. Rsults from simulation runs with diffrnt storag paramtrs Pmax and 6 PD[ s ar prsntd in Tabl II. Th rlativ dviation P dv Pˆ from schduld powr varis from 3% for th largst storag systm to 11% for th smallst storag systm. Thus, unprdictabl variations in wind powr production ar smoothd by th storag most of th tim. Th ratio P cl is a masur of th probability of lin ovrload, sinc th controllabl load is only usd whn th nt local production xcds th lin capacity. Th rlativ usag of th controllabl load is low for all storag dsigns, although thr is a clar corrlation with 6 PD[. A two-fold incras in nrgy capacity rsults in a four-fold rduction in th lctricity consumd by th controllabl load. Morovr, an intrsting ffct is obsrvd whn comparing P cl for storag configurations with diffrnt powr capacitis, but qual nrgy capacity. Th usag of th controllabl load actually incrass slightly for incrasing powr capacity, although th opposit could b xpctd, bcaus th ability of th storag to consum xcss powr also incrass. Howvr, with a highr powr capacity, it is possibl to stor mor nrgy during offpak priods. Consquntly, th storag will b compltly filld mor oftn. This is undsirabl, but can b avoidd by adding a limitation on th powr capacity usd in th optimization routin. Furthrmor, Tabl II shows that th rvnu incrass with incrasing powr and nrgy capacity of P cl

6 th storag, as xpctd. On th othr hand, th storag dvic is thn likly to b mor xpnsiv, which is particularly tru for ful cll systms. Thus, finding an appropriat siz of th storag is not only critical for th systm opration but is also of grat conomic importanc, du to potntial high invstmnt costs. Figur 9 displays th duration curvs of charging, discharging and th nrgy rsrv, which provids information about th utilization of th storag dvic. It is vidnt from th charging and discharging curvs that an nrgy storag with sparat charging and discharging dvics (for instanc an lctrolysr and a ful cll) will hav an undsirabl low utilization of th total installd capacity. Howvr, th diffrnc btwn th curvs implis that storag dsigns with diffrnt charging and discharging capacitis should b invstigatd furthr. Th usag of th total nrgy capacity is also rlativly low, as can b sn from th duration curv for storag lvl in Figur 9. This is bnficial from a opration point of viw, sinc a full storag incrass th risk for transmission lin ovrload. In th cas of no transmission constraints, th nrgy capacity could b considrably lowr. Morovr, th duration curv also shows that th storag is mpty for som tims. As this rducs th flxibility of th storag, on should considr to st th minimum allowabl storag lvl in th schduling routin highr than zro. % of maximum valu charg discharg nrgy rsrv % of total tim )LJXUH Duration curvs for charg (circls), discharg (crosss) and th nrgy rsrv (solid) of th storag dvic. Th bas cas paramtrs ar usd for th simulation. Th conomic valu of accurat wind forcasts is illustratd in Figur 1. As xpctd, th rvnu is highst for prfct forcasting, sinc in that cas all th nrgy can b tradd in th spot markt. As th forcasting rror incrass, it bcoms mor difficult to follow th schduld production plan. Hnc, mor nrgy must b tradd in th balancing markt, and th rvnu is rducd, according to th pric curvs in Figur 5. This is particularly tru for th prsistnc mthod, with RMSE qual to 4.84 m/s. Th bnfit of accurat wind forcasts dpnds strongly on th pric diffrnc btwn spot pric and rgulating powr prics. In this study, th diffrnc is rlativly larg, which mans that th ffct of forcasting accuracy can b smallr in practic. rvnu [1 $] RMSE of wind vlocity prdiction [m/s] )LJXUH Yarly rvnu as a function of forcast rror of wind vlocity. Th bas cas paramtrs ar usd, xcpt for RMSE. ',6&866,21 Th simulation rsults show that with a proprly sizd nrgy storag, it is possibl for ownrs of wind powr plants to tak advantag of hourly pric variations in th spot markt. Furthrmor, rsults obtaind from th simulations should ultimatly b usd as a part of an conomic assssmnt whr also invstmnt costs ar considrd. It is also intrsting to compar nrgy storag with grid rinforcmnts in cass whr th wind powr potntial xcds th capacity of th xisting transmission lin. Taking into account th rducd costs for providing th load with lctricity from th distributd rsourc, th yarly rvnu for th bas cas is 1.1 Mill.$. For comparison, simulations of th systm with a nw paralll transmission lin instad of nrgy storag givs a rvnu of 1. Mill.$. Consquntly, with a priod of analysis of 2 yars and 7% intrst rat, th diffrnc in invstmnt costs of th nrgy storag and th nw lin cannot b highr than about 1 Mill.$, if th storag should b an conomic viabl altrnativ. With prsnt cost stimats [4], it is likly that lctrochmical nrgy storag such as th hydrogn-bromin ful cll systm will b an xpnsiv altrnativ to grid rinforcmnts. On th othr hand, for aras whr grid xpansions lad to unwantd intrfrnc with th local nvironmnt, nrgy storag should b considrd as a rasonabl way to incras th pntration of wind powr. Anothr altrnativ is to rduc th powr output from th wind powr plant in priods with high wind and low load by ithr shutting down units or downrgulating th output. For th systm studid hr, such a stratgy would giv a yarly rvnu of.9 Mill.$. Th nrgy loss du to th downrgulation is 16%. Th chosn opration stratgy of th nrgy storag is simpl, namly to follow th spcifid production plan. Othr, mor sophisticatd mthods could b mployd if th spot pric and rgulating prics wr rprsntd as stochastic variabls, and if a mor dtaild modl of th lctricity markt wr usd. Th optimal powr xchang with th markt could thn b updatd ach

7 hour, by using principls of stochastic programming. Morovr, in som cass it will b valuabl to hav an nrgy rsrv in th storag at th nd of th day, for instanc if high spot prics and low wind spds ar prdictd for th nxt days. This approach is analogous to th so-calld watr valu mthod usd in hydro powr planning [9], and will b invstigatd furthr. It should also b noticd that th proposd mthod is not limitd to wind powr, but could also b usful for th analysis of othr intrmittnt nrgy rsourcs such as solar, wav and small-scal hydro. &21&/86,216 A mthod for th schduling and opration of a wind powr plant with nrgy storag in a markt systm has bn prsntd. Th mthod is suitabl for any typ of lctrical nrgy storag and is also usful for othr intrmittnt nrgy rsourcs than wind. By implmnting th mthod in a computr simulation modl, valuabl information about th impact of nrgy storag sizing on systm opration and conomics can b obtaind. Simulation rsults of a cas study show that with a proprly sizd nrgy storag, ownrs of wind powr plants can tak advantag of variations in th spot pric of lctricity, by thus incrasing th valu of wind powr in lctricity markts. Howvr, with availabl tchnology and xisting pric stimats, nrgy storag dvics such as rvrsibl ful clls ar likly to b an mor xpnsiv altrnativ than grid xpansions for th siting of wind farms in wak ntworks, although rducing th nvironmntal impact. A simplifid rprsntation of th lctricity markt is usd in th modl. In ordr to xplor furthr possibilitis for nrgy storag in connction with stochastic gnration, furthr work with a dtaild markt dscription will b carrid out. List of symbols: $33(1',; 3 O : load dmand [MW] 3 Z : output of wind powr plant [MW] 3 H : powr xchang with markt [MW] 3 V : powr output of nrgy storag [MW] 3 FO : controllabl load [MW] 3 GHY : Dviation btwn actual and schduld powr xchang [MW] 6 : nrgy storag lvl [MWh] η s : round-trip fficincy of nrgy storag η c : charging fficincy of nrgy storag η d : discharging fficincy of nrgy storag Y : wind vlocity [m/s] xˆ : stimatd valu of variabl [ x : man valu of variabl [ I : hourly rvnu [$/h] ) : Expctd rvnu ovr th schduling priod [$] F W : transmission losss cofficint [MW -1 ] 63 : spot pric of lctricity [$/MWh] F UV : rlativ diffrnc btwn spot pric and sals pric in th rgulating markt F US : rlativ diffrnc btwn spot pric and purchas pric in th rgulating markt σ : standard dviation of random variabls 9 : cofficint of variation of random variabls N Z : Wibull shap paramtr RMSE : Root-man-squard rror of wind forcast [m/s] W : indx for tim W : tim stp [hours] L : indx for day 5()(5(1&(6 [1] J. N. Bakr and A. Collinson, Elctrical nrgy storag at th turn of th millnnium, Powr Enginring Journal, vol 13, no.3, pp , Jun 1999 [2] A. Crudn and G. J. W. Dudgon, Opportunitis for Enrgy Storag oprating with Rnwabl Enrgy Systms, Proc. EESAT 98, Elctric Enrgy Storag Applications & Tchnologis, Sptmbr 2 [3] W. A. Amos, Economic Assssmnt of Wind Enrgy Coupld with a Rvrsibl Hydrogn Ful Cll, National Rnwabl Enrgy Laboratory, Goldn, CO, Milston Typ P rport, Fbruary 2. [4] M. Korpås, R. Hildrum and A. T. Holn, Hydrogn nrgy storag for grid-connctd wind farms, 6th IASTED Intrnational Confrnc, Powr and Enrgy Systms, pp , July 21, ISBN [5] D. Infild t al, Enginring tools for wind disl systms - Volum 6, EFI Tchnical Rport No. A433, Trondhim, Sptmbr 1995 [6] L. H. Nilsn and P. E. Morthorst, Systm intgration of wind powr on libralisd lctricity markt conditions. Mdium trm aspcts (in Danish), Risø- R-155(DA), april 1998, ISBN [7] Hompags of Nordpool - Th Nordic Powr Exchang, [8] J. O. G. Tand and K-O. Vogstad, Opration implications of wind powr in a hydro basd powr systm, EWEC99, 1999 Europan Wind Enrgy confrnc, pp , August 1999 [9] O. B. Fosso t al, "Gnration Schduling in a drgulatd systm. Th Norwgian cas", IEEE Transactions on powr systms, Vol. 14, No.1, 1999