Open Access Impact of Wind Power Generation on System Operation and Costs

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1 Send Orders for Reprns o reprns@benhamscence.ae 580 he Open Elecrcal & Elecronc Engneerng Journal, 2014, 8, Open Access Impac of nd Power eneraon on Sysem Operaon and oss ang Fe 1,2,*, Pan enxa 1 and Quan Ru 1 1 Research ener for Renewable Energy eneraon Engneerng Hoha Unversy, Nanjng , hna 2 School of Elecrcal Engneerng & Auomaon, Jangsu Normal Unversy, Xuzhou , hna Absrac: In hs paper, a deermnsc secury-consraned un commmen (SU) model s deployed n order o opmze generaon oupu and allocaon for spnnng reserve consderng dfferen wnd power dspach modes. In hs model, he schedulng of power plans akes no accoun a smulaneous clearng of power, reserve capacy requremen and O 2 emsson and so on. Spnnng reserve s modelled as an exogenous parameer whch represens load uncerany and wnd power uncerany. Specal aenon n he sudy s gven o deermne he mpac of dfferen dspach modes wh wnd power and dfferen levels of spnnng reserve requremen on sysem operaon and coss. he proposed model can be formulaed as a mxed-neger problem (MIP) and solved n AMS by usng he PLEX opmzer. he model s appled o a wnd-fred nensve power sysem for hree case sudes. he resuls nclude he opmal spnnng reserve and generaor oupu of each generaor, O 2 emsson cos and cos of wnd power for each case sudy. he resuls show ha akng wnd power as a conrol opon can mproves sysem operaon and coss f wnd generaon and radonal sources generaon are coordnaed properly. Keywords: nd power, dspach mode, reserve allocaon, secury-consraned un commmen (SU). 1. INRODUION Power sysem operaors have a number of responsbles ha focus on mananng relably [1, 2]. he relable operaon of a power sysem depends on mananng frequency a or very close o nomnal levels (50 Hz n hna, Europe and many oher areas hroughou he world, 60 Hz n Norh Amerca) [3]. However, many of he properes of he power sysem, ncludng s generaon oupu, load levels, and ransmsson equpmen avalably are boh varable and unpredcable. In parcular, wh he adven of varable renewable generaon echnologes beng nroduced o he elecrc power sysem, he way n whch he sysem s planned and operaed may need sgnfcan changes. For nsance, he characerscs of wnd power echnology are que dfferen from radonal sources of generaon echnology ha has hsorcally me he elecrcy demand [4]. he nheren varably and uncerany of wnd power generaon echnology ncrease he varably and uncerany of he exsng sysem and have sgnfcan effecs on operaon of sysem [5]. A varey of sudes show ha he varyng naure of hese generaon sources affecs he schedulng and operaon of convenonal power plans [6]. herefore, power sysem operaors ofen use schedulng echnques hroughou he day o mach generaon and demand. However, he oal supply of energy s dfferen from he oal demand because of varably and/or uncerany, hus, power sysem operaors mus deploy operang reserves o correc he energy mbalance so ha frequency s mananed [7]. Operang reserves are generally classfed no spnnng reserves and non-spnnng reserves accordng o he Norh Amercan Elecrc Relably orporaon (NER) defnons [8]. Spnnng reserve s he mos mporan resource o compensae energy mbalance. Over he pas decades, much research has been done o evaluae he spnnng reserve requremen. Reference [9] has done he earles work o consder how he spnnng reserve could be opmzed whn un commmen (U) problem whou consderng largescale wnd generaon negraon. In recen years, a large number of enes have been nvesgang he way he sysems wh large peneraon of wnd generaon mpac relably and coss. In [10] and [11] he mpac of wnd power ncreasng sysem mbalances and need for reserve capacy are suded n Nordc counres. Reference [12] bulds a lowcarbon dspach model of wnd-ncorporaed power sysem consderng energy-envronmenal effcency. Moreover, a hybrd algorhm based on parcle swarm opmzaon (PSO) and smulaed annealng s used o oban beer soluons. Reference [13] presens a sochasc mehod for he hourly schedulng of opmal reserves, whch akes he hourly forecas errors of wnd energy and load no accoun. Reference [14] proposes a sochasc programmng model for spnnng reserve opmzaon n he power sysem wh hgh wnd power peneraon, n whch boh load sheddng cos and wnd spllage cos are accouned. A rsk-based reserve allocaon mehod ha accouns mulple conrol sub-area coordnaon s gven n [15], and a PSO mehod s employed o provde a numercal soluon for he problem. he radeoff beween cos and reserves provson has been emphaszed by Reference [16], whch deermnes opmal spnnng reserves usng an approach based on cos-benef analyss. he proposed mehod can be formulaed as a mxed-neger lnear / Benham Open

2 Impac of nd Power eneraon on Sysem Operaon and oss he Open Elecrcal & Elecronc Engneerng Journal, 2014, Volume program (MILP) and solved wh large-scale commercal solvers. In [17] he mpacs of wnd power on sysem operaon coss and O 2 emsson reducon are suded wh respec o he Irsh power sysem. In [18], he sudy nvolves how operang reserve requremens are deermned wh dfferen wnd energy scenaro. Alhough much work has been done on opmal generaon oupu and spnnng reserve deermnaon problem, mos of hese sudes are focused on evaluang he spnnng reserve capacy requremens, and only a lle work pays aenon o he spnnng Reserve allocaon problem, whle he effec of wnd power on sysem fuel savngs and O 2 emsson has no been gven full dscusson n he U modelng process. In hs paper, he spnnng reserve allocaon problem s nvesgaed for acve power generaon dspach. he objecve of power sysem operaors s o mnmze he expeced operang cos from procuremen energy and reserve n he day-ahead marke, assumng a ceran rsk level. he res of hs paper s organzed as follows: Secon 2 provdes a deermnsc secury-consraned un commmen model for opmal generaon oupu and spnnng reserve allocaon based on cos-benef analyss. nd power dspach modes, generaon sysem and demand profle, and he performance ndces used n he model are furher dscussed n Secon 3, whch s appled for hree case sudes of a generaon sysem represenng characerscs of hna s ypcal wnd-fred nensve power sysem, dscussed n Secon 4. he concluson drawn from he analyss s provded n Secon MAHEMAIAL MODEL DESRIPION In hs paper, a deermnsc secury-consraned un commmen model s deployed opmzng he schedulng of power plans whle meeng he elecrcy demand and wnd power negraon. A mahemacal descrpon of he opmzaon model s gven n (1). As represened n [19, 20], he proposed model s formulaed as a cos mnmzaon problem usng mxed neger programmng Objecve Funcon In a resrucured power sysem, s assumed ha he power sysem operaor nends o mnmze he oal power sysem operang cos as follows: * N $ '.,&!!, ( P, )" Z, + SU " Z, "( 1# Z,#1 )), = mn + % =1 =1 (/, SR + E + + L, - + shed 0 here, ( P, ) = BE,! P, N SR =!! BR, " SR, " Z, =1 =1 N E = "" K! E co2! P prce,,! Z, =1 =1 (1) = "! # P = "! # L shed # =! shed "Q shed In he objecve funcon, he oal expeced operaon cos () assocaed wh operang cos (O) of convenonal generang un, oal spnnng reserve cos ( SR!" ), oal O 2 emsson cos ( ), operang cos of wnd power E ( ), wnd almen, and demand sheddng needs o be mnmzed over all problem varables. he operang cos (O) consss of summaon of generaon coss of commed uns and sar-up coss of prevously uncommed uns. In power sysems conanng wnd farms, an addonal par of spnnng reserve capacy s needed o balance wnd power predcon errors and shor-erm flucuaons so ha he sysem can run relably. herefore, spnnng reserve consdered n hs model consss of wo pars: he radonal spnnng reserve deermned from uncerany of load forecas; and he spnnng reserve resulng from varably of wnd power. he radonal spnnng reserve and addonal spnnng reserve consderng wnd power n each hour can be respecvely compued as a fxed percenage of sysem hourly load and wnd power. Based on he premse of he low-carbon economy, he relaon beween generaon and O 2 emsson of varous power plans s formulaed, and he power sysem opmzaon model akes carbon emssons no accoun. As wnd power parcpaes n U wh convenonal uns n model, he objecve funcon s assocaed wh he cos of wnd generaon. he las wo erms of he objecve funcon are compensaon cos of wnd power almen and demand sheddng, as a par of operang reserve. Seng he almen and demand sheddng has an mporan mpac on he feasbly of he model Model onsrans he objecve funcon mus be mnmzed subjec o a number of relably consrans. In hs secon, he consrans for he problem are gven by acve power balance of he sysem, un capacy consran, ramp rae consran for convenonal uns, spnnng reserve requremens consran, mnmum up- and downmes consrans [21, 22]. N P,! " Z, + P = Q (2) Q = q! Q shed P =! (3) (4)

3 582 he Open Elecrcal & Elecronc Engneerng Journal, 2014, Volume 8 Na e al. P mn! Z, " P, " P mn! Z, (5) 0! P! P,! P,!1 " #PR $ # (7) P,! P,!1 "!#PR $ # (8) SR, = mn (!PR "!, P max " Z, # P, ) N SR,! = SR L + SR (6) (9) (10) Z,! Z,!1! Z,+k " 0 (11)!k " $% 1,2,,mu #1& ' Z,!1! Z, + Z,+k " 1 (12)!k " $% 1,2,,mu #1& ' I can be seen from Equaon (1) o Equaon (12) ha he proposed model s a deermnsc secury-consraned un commmen model, ncludng convenonal energy producon, spnnng reserve provson, O 2 emsson, wnd power njecon, wnd almen, and demand sheddng. hs model ams o deermne he opmal schedulng of power plans and reserve allocaon o mee he demand a he lowes coss, and s wdely used for he nvesgaon of he mpac of wnd generaon on he power sysem operaon. he proposed model can be formulaed as a Mxed Ineger Problem (MIP) and solved usng PLEX12.5 under AMS [23]. 3. IND ENERY UILIZAION SUDIES 3.1. nd Power Dspach Modes hs secon consders wnd power dspach modes n day-ahead schedulng wh a focus on he problems proposed by wnd power varably o he overall power sysem operaon. Due o he posve role of wnd power n emsson reducon and fuel savng, polcy ncenves are used n many counres o promoe wnd n power sysems as a prory [24, 25]. hs paper consders wo scenaros for wnd dspach prory: 1) uaraneed wnd power dspach: nd power s fully dspached as long as he operaonal secury and conrollably can be ensured. 2) Prvleged wnd power dspach: nd power s gven prory dspach, bu wnd almen can be used as a conrol opon of wnd generaon n day-ahead un commmen whenever necessary. hree case sudes are presened o sudy he relaonshp beween generaon oupu and spnnng reserve allocae consderng wnd power dspach modes. ase 1: Power plan schedulng whou wnd power negraon. ase 2: Power plan schedulng wh wnd power negraon and guaraneed wnd power dspach. ase 3: Power plan schedulng wh wnd power negraon and prvleged wnd power dspach eneraon Sysem and Demand Profle he generaon model used for hese case sudes represens a concepual power sysem, roughly based on Inner Mongola onglao. However, a few adapaons are done n order o lm complexy and generalze he model. echncal parameers of he dfferen power plans have been obaned from he reference [26, 27] due o a lack of convenonal un daa from hna, whch fnal values used n he model are gven Appendx A. he generaon sysem consss of 21 power plans ncludng sx coal-fred seam urbne power plans, four combned-cycle gas urbnes, fve open-cycle gas urbnes and sx ol-based nernal combuson engne power plans. In hs paper, In order o oban a correc order of procurng, he economc performance of varous power plans s nvesgaed and compared. he daa of hese coss are derved from hose publshed n [28, 29]. he fuel cos s assumed o be 2.63 /J, 8.43 /J, 8.43 /J and /J, whch s respecvely represen SEAM,, and IE power plan. he O 2 conen per fuel s derved from [30] and a forward O 2 emsson prce s se relavely hgh a 38 /on. Accordngly, he varable generaon coss are calculaed by means of he fuel cos and O 2 emsson cos for each power plan. I s assumed ha he spnnng reserve cos of each generaor s 40% of un generaon cos. he hourly spnnng reserve for load and wnd power uncerany respecvely are assumed o be 10% of hourly load and 20% of hourly wnd power. Smulaons are performed wh forecas wnd power and sysem demand profles from Inner Mongola Power roup. hese profles are rescaled akng no accoun unavalably of generaon asses and demand growh owards he forecas wnd power and average demand profles are llusraed n Fg. (1) and Fg. (2). he nsalled wnd power capacy represens 26% of he nsalled capacy. he generaon cos of wnd power s se o be 80 /Mh Sysem Performance Indces he followng sysem performance ndces consdered n hs paper are used o compare dfferen dspach modes. 1) Un Operaon os of he Sysem ( /Mh) c c c c = E sd (13) here!" s gven n Equaons (1) and!!" s gven as E sd =! Q. =1

4 Impac of nd Power eneraon on Sysem Operaon and oss he Open Elecrcal & Elecronc Engneerng Journal, 2014, Volume Fg. (1). Demand profle for he smulaon day. Fg. (2). nd power profle for he smulaon day. 2) oal eneraon os of onvenonal Uns ( )!" P N ( ) P =!!, P, " Z, (14) =1 =1 3) Un eneraon os of onvenonal Uns ( /Mwah) c pg c pg = P E P (15) E P = r u = here!!" s gven by N P,!! =1 =1 4) Un Spnnng Reserve os of he Sysem ( /Mh) r u! SR SR L =1( + SR ) 5) Un O2 Emsson of he Sysem(on/Mh) e u (16) E e u = E sd! K co2 prce 6) nd Energy Average Use Rae (%)! (17)! = E aval " E #100% (18) aval E aval here E =!, E =!. =1 In order o ensure a feasble soluon, demand sheddng s mplemened as a las resor measure,.e. a an elevaed cos. ompensaon cos demand sheddng s assumed o be /Mh. Dfferen compensaon cos of wnd power almen (λ!"#$ ) sengs are used as ndcaors for dfferen wnd power dspach prores. In realy, hs almen cos may depend on he specfc polces appled n a conrol zone. For case 2,! s a very large number,.e. 500 /Mh, so as o dscourage wnd power almen and hus ensure guaraneed wnd power dspach. For case 3, λ!"#$ s 0, so ha wnd power s aled whenever necessary whou havng o worry abou he compensaon. =1

5 584 he Open Elecrcal & Elecronc Engneerng Journal, 2014, Volume 8 Na e al. able 1. Sysem Performance Indces of hree ases. ase!!"!!"!!!!!!"!! % % % As elevaed coss dscourage he use of hese opons n he model, whch are se o keep focus on he flexbly of he convenonal energy generaon sysem. 4. SIMULAION RESULS AND DISUSSIONS In hs secon, he presened deermnsc secury consraned un commmen model s used o deermne he mpac of dfferen dspach modes wh wnd power and dfferen levels of reserve requremen on sysem operaon and coss. hs s an mporan ssue as we have seen ha he generaon oupus and reserve capacy allocaon change when wnd power s added wh dfferen dspach modes Smulaon Resuls1: Impac of he eneraon oss and O 2 Emssons he objecve funcons, he sysem performance ndces of hree cases, are summarzed n able 1. In ase 1, all he loads are suppled by only convenonal generaors wh spnnng reserves from load uncerany. In comparng he sysem ndces n ase 1 and ase 2, can be seen ha!!" and!! followng wnd power negraon n power sysems leads o sgnfcan reducons and addonal ndces,.e.!!",!! and!!" wh ncrease n un cos. hs s explaned ha a and paral peak power plan would be replaced by wnd power leadng o reduce fuel and emsson coss. Furhermore, he ncremen of un cos (!!",!! and!!" ) n ase 2 compared o ase 1 reflecs he mpac of wo facors. One s he reduced effcency of he coal-fred and gas-fred uns n accommodang he varably of wnd power when gvng wnd power guaraneed dspach. he oher s he exra spnnng reserve procuremen o mee he varably of wnd power. omparson of he sysem ndces n ase 2 (guaraneed wnd power dspach) and ase 3 (prvleged wnd power dspach) shows ha, hough he wnd energy use rae (!! ) s smaller n case 3, n whch wnd almen s execued whenever necessary, he sysem performance ndces such as he oal cos of he convenonal uns (!!" ), he un generaon cos of convenonal uns (!!" ), he un reserve cos of sysem (!! ) and un operaon cos of he sysem (!!" ), ouperformed hose wh a slgh ncrease n un O 2 emssons coss (!! ) n case 2. hese ndcae ha n wnd-fred nensve power sysems, wnd almen should be used as a conrol opon o mprove oal sysem operaon f varable renewable generaon and radonal sources generaon are coordnaed properly raher han only when sysem secury s hreaened. As can be seen, all performance ndces of ase 3 are beer han hose of ase 1. he resuls of comparson show ha varable renewable generaon and radonal sources generaon are coordnaed properly, leadng o beer sysem economes and O 2 emssons reducon n ase 3, even wh wnd almen Smulaon Resuls 2: Impac of eneraon and Reserve apacy Schedule he generaon and reserve capacy schedule of commed uns of case sudes 1-3 are shown n Fgs. (3-5), respecvely. e can observe ha he coal-fred power plans are operaed as base load, he combned-cycle gas urbnes as load followng. And he S and IES are manly operaed as peak power plan n he models, bu s dffcul o see due o he low oupu level n Fgs. (3-5) (Lef). Fg. (3). shows he mpac of a varyng spnnng reserve requremen from uncerany of load forecas on sysem operaon n ase 1 whou wnd power, spnnng reserves are manly provded from he and he coal-fred generang uns. hen spnnng reserve requremens exceedng 120M capacy for hgher load and reserve capaces, operaonal flexbly s no longer suffcen and an addonal power plan s scheduled o asss n delverng he requesed amoun of reserves from 10h AM. he hree S are now operaed a paral load, resulng n effcency losses. Also, beween oh-4h and 8h-9h, addonal and IE peak power plans are scheduled a paral load n order o provde addonal reserves. Fnally, somemes, he sxh coal-fred power plan parcpaes n he provson of reserves hough oupu reducons. By comparng ases 1-2 generaons and reserve capacy schedule, n whch he wnd power parcpaes n U wh wnd power forecas. In ase 2, smulaon resuls show ha s replace he whch s scheduled o provde generaon oupu wh wnd power. hs s llusraed n Fg. (4) (Lef) hs represens a smulaon wh guaraneed wnd power dspachng. he oal spnnng reserves are manly provded from he coal-fred generang uns and he. Furhermore, wo gas-fred peak plans and an IE peak plans are scheduled o provde he fnal reserve requremens. Boh coal-fred power plans and S are now operaed a paral load, resulng n effcency losses and ncremen of un generaon coss (!!",!!" ) due o exra spnnng reserve procuremen o mee varably of wnd power. e can see ha he rend of paral load ncreases sgnfcanly beween 10h and 24h due o hgh wnd.

6 Impac of nd Power eneraon on Sysem Operaon and oss he Open Elecrcal & Elecronc Engneerng Journal, 2014, Volume Fg. (3). eneraon and reserve capacy schedule for case 1. Fg. (4). eneraon and reserve capacy schedule for case 2. Fg. (5). eneraon and reserve capacy schedule for case 3. I s llusraed n Fg. (5). for ase 3. Smulaon resuls of ase 3 show ha s wnd power almen can be aken as a conrol opon o mprove sysem economcs and O 2 emsson reducon when wnd power parcpaes n he U and wnd power s gven prvleged dspach. Smulaon resuls show ha s beer o replace he gas-fred peak power plan o provde reserve capacy wh wnd power somemes. he model assesses ha s cheaper o provde hs capacy wh wnd power. In conras, replacng he second gas-fred peak power plan would however be oo expensve as generaor provdes 25 M reserve capacy. ONLUSION In hs conrbuon, a un commmen model s deployed wh spnnng reserve requremens n order o sudy he mpac of a jon demand for generaon and reserve capacy on sysem operaon and coss wh specal aenon o

7 586 he Open Elecrcal & Elecronc Engneerng Journal, 2014, Volume 8 Na e al. dfferen wnd power dspach modes. he demand for reserves s modelled as an exogenous parameer whch s assumed o be decomposed no wo pars,.e., he radonal spnnng reserve assocaed wh uncerany of load forecas and an addonal par of spnnng reserve capacy o respond o he wnd farm power varably. Opmal wnd power dspach and spnnng reserve allocaon were obaned. h dfferen wnd power dspach prores and correspondng U sudes, he mpac of wnd power and he demand for reserves on sysem operaon and coss are presened wh more clary. he sudy s man conclusons are as follows: 1) h wnd power beng nroduced o he convenonal elecrc power sysem, he way whch he sysem s scheduled and operaed may need sgnfcan changes. More focus should be gven o assessng mpac of ncreasng reserve requremens and varably of wnd power on power plan schedulng. hough wnd power self s emsson and fuel free, he negave mpacs has on convenonal generaor fuel consumpon and emsson f varable renewable generaon and radonal sources generaon are no coordnaed properly. One s he reduced effcency of he convenonal generaor n accommodang he varably of wnd power when gvng wnd power guaraneed dspach. he oher s he exra spnnng reserve procuremen o mee he wnd power varably. 2) hen wnd power becomes a relable provder of reserve capacy n wnd-fred nensve power sysems, he use of prvleged wnd power dspach, n whch wnd almen can lead o he achevemen of beer sysem operaon coss han guaraneed wnd power dspach. 3) Alhough no fundamenal echncal objecons are presen o exclude wnd power from parcpang n he reserve marke, when he operaonal flexbly of sysem s no longer suffcen and wnd power should be consdered as a spnnng reserve provder akng wnd power almen as a conrol opon. I can mprove sysem economes and O2 emsson reducon. ONFLIS OF INERES he auhors confrm ha hs arcle conen has no conflcs of neres. AKNOLEDEMENS he auhor grealy hanks he edor and he revewers for her valuable commens and suggesons. hs sudy was suppored by Naonal Naural Scence Foundaon of hna (NO ). APPENDIX A able 2. echncal parameers of convenonal generang uns. Parameer of generaon SEAM IE Uns (#) Fuel ype coal naural gas naural gas heavy ol Max. en. apacy[m] Mn. en. apacy[m] Ramp Rae [M/mn] Mn on me [h.] Mn off me [h.] Fve Mnues Ramp [M] SEAM: seam power plans, : combned-cycle gas urbnes, : open-cycle gas urbnes, IE: nernal combuson engne NOMENLAURE = Index of convenonal uns = Index of me perods (h) N = Number of convenonal uns = he smulaon perods (h) = oal expeced operaon cos ( ), = eneraon cos of convenonal un n perod ( ) Z, P, = Bnary varables, commmen of un n perod (1: on-lne; 0: off-lne) = eneraon oupu of convenonal un n perod (M)

8 Impac of nd Power eneraon on Sysem Operaon and oss he Open Elecrcal & Elecronc Engneerng Journal, 2014, Volume SU = Sar-up cos of convenonal un n perod ( ) BE, = Un generaon cos of convenonal un n perod ( Mh) SR = oal spnnng reserve cos ( )!"!,! = Un spnnng reserve cos of convenonal un n perod ( Mh) SR, = Spnnng reserve of convenonal un n perod (M) E = oal O 2 emsson cos ( ) K co2 prce E, = O 2 emsson prce ( /on) = Average O 2 emsson convenonal un n perod (kg Mh) = oal cos of wnd generaon ( ) = oal compensaon cos of wnd power almen durng he smulaon perod ( ) L shed = oal compensaon cos of demand sheddng durng he smulaon perod ( )! = Un cos of wnd generaon ( Mh) SR L SR = Spnnng reserve capacy demand due o load uncerany n perod (M) = Spnnng reserve capacy demand due o wnd power uncerany n perod (M) md = Mnmum down me of generang un (h) mu = Mnmum up me of generang un E sd c c (h) = he oal off-ake elecrcy demand of he sysem durng he smulaon perod (Mh) = Un operaon cos of he sysem ( /Mh) P = oal generaon cos of convenonal uns durng he smulaon perod ( ) c pg = Un generaon cos of convenonal uns durng he smulaon perod ( /Mh) E P = he oal elecrcy generaed by convenonal un durng he smulaon perod (Mh) r u = Un spnnng reserve cos of he sysem durng e u he smulaon perod ( /Mh) = Un O 2 emsson of he sysem durng he smulaon perod (on/mh) P = Average wnd power njecon n perod (M)! = nd energy average use rae (%) = Average wnd power predced oupu n perod (M)! = ompensaon cos wnd power almen ( Mh) E aval E = oal avalable wnd energy durng he smulaon perod (Mh) = oal aled wnd energy durng he smulaon perod (Mh) = Average wnd power almen n perod (M)! shed = ompensaon cos demand sheddng ( Mh) Q shed Q q = Average demand sheddng n perod (M) = Average off-ake n perod (M) = Average elecrcy demand n perod (M) mn P = Mnmum oupu level generang un (M) max P = Maxmum oupu level generang un (M)!PR = Un ramp rae of convenonal un I (M/mn)! = me duraon, where! s adjused o 5 mn n hs paper accordng o her response me for frequency resoraon reserve REFERENES [1] A.J. ood and B.F. ollenberg, Power eneraon Operaon and onrol, New York: John ley & Sons, [2] P. Kundur, Power sysem sably and conrol, New York: Mcraw-Hll, [3] E Energy. Frequency response sudy fnal draf. Prepared for alforna ISO, November [4] B. Kark, Operang Reserve assessmen of wnd negraed power sysems, PhD hess. Unversy of Saskachewan. Deparmen of Elecrcal Engneerng [5] J. Kng, B. Krby, M. Mllgan, e al. Operang reserve reducons from a proposed energy mbalance marke wh wnd and solar generaon n he wesern nerconnecon. Prepared for he Naonal Renewable Energy Laboraory NREL/P [6] B.. Ummels, M. bescu, E. Pelgrum,. Klng, and A. Brand, Impacs of nd Power on hermal eneraon Un ommmen and Dspach, IEEE ransacons on Energy onverson, vol. 22, no. 1,pp , March [7] E. Ela, M. Mllgan, B. Krby, Operang reserves and varable generaon. Prepared for he Naonal Renewable Energy Laboraory NREL/P [8] Y. Rebours, D. Krschen, M. rognon, e al. Asurvey of frequency and volage conrol ancllary servces Par I: echncal Fea-

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