Simulation Of Energy Storage In A System With Integrated Wind Resources

Transcription

1 Simulation Of Enery Storae In A System Wit Interate Win Resoures Yannik Deeil, Justine Desloux, Geore Gross University of Illinois at Urbana-Campain, USA Abstrat Utility-sale storae is key to proviin te means of better arnessin win enery potential. Tis paper proposes a probabilisti simulation approa apable of assessin - over loner time perios - te impats of a utility sale storae unit on te eonomis an reliability of power systems wit interate win resoures. We eploy a snapsot-base simulation approa to aount for te time epenenies of te loa, win power outputs an storae operation as well as teir impats on te utilization of te transmission resoures as presribe by te learin meanism of te ourly transmission-onstraine ayaea markets. We run Monte Carlo simulations in orer to apture te unertainty in termal unit availabilities, te loa an te win power outputs. Te metooloy is able to represent te seasonal effets in loas an win spees, te impats of maintenane seulin an te ramifiations of new poliy initiatives. We illustrate te benefits of storae exploitation wit several appliation stuies run on te IEEE 118 test system. Results sow tat storae an effetively elp reue te overall buyer payments an improve system reliability by storin enery in te low loa ours an isarin at peak ours, tereby isplain more expensive units. Keywors Utility-Sale Storae Interation, Win Resoures Interation, Transmission-onstraine Day Aea Markets, Probabilisti Simulations, Loational Marinal Pries, Reliability. I. Introution Win is a lean an renewable soure of enery wit zero fuel osts. However, win eneration outputs are ily variable, intermittent an not fully ontrollable/ ispatable by te operator. Te win spee pattern presents a key allene to interation of win resoures [1] sine te win may not blow urin te peak loa ours wen te system most nees it. Te lak of ontrollability over su win spee patterns implies tat te interation of win resoures into te ri may be unable to realize te full potential of win resoures. Moreover, tere are onerns about spillin of win enery at nit ue to te insuffiieny of te loa eman, not proviin to te system, in su ases, te benefits from tis enery to meet te eman. Te basi tool operators use to manae te win variability is te raisin of te reserve levels [2], wi, typially, results in inreasin te overall proution osts, notwitstanin te zero fuel osts of te win resoures. Su situations reate exellent appliations for utility-sale storae [3],[4] to failitate te improve arnessin of te win resoures by storin win enery for release urin peak-loa ours so as to isplae te ostly enery from pollutin eneratin units. We ave worke on te evelopment of a probabilisti simulation approa of systems wit interate win an storae resoures over loner-term perios. Te approa is able to evaluate te impats of storae interation into a ri wit win resoures, takin expliitly into aount various soures of unertainty, win variability an intermitteny as well as te impats of te time varyin utilization of transmission resoures on te eliverability of te eletriity to te loas. Te metooloy may be use to quantify te variable effets of lare-sale power systems wit storae an intermittent win resoures operatin in a market environment over loner-term perios. Te approa uses an our as te smallest ineomposable unit of time an eploys a snapsot representation of te resoures an te ri. We inorporate into te snapsot-base framework probabilisti reimes [5] for moelin te timeepenent win resoures at various sites an te moelin of te storae operations takin into aount arbitrae an storae yle effiieny an te impats of transmission onstraints. Te simulation metooloy makes effetive use of te wiely-use onepts in probabilisti simulation an eploys Monte Carlo Simulation [6] wit systemati samplin teniques to represent te various soures of unertainty onsiere. Te emulation aptures effetively te syneries between win an storae to allow te assessment over te loner term of te impats on reliability an eonomis of storae interation into power systems wit multi-site win farms. We represent te eonomi effets by learin te 24 ourly transmissiononstraine ay-aea markets (DAMs) by eterminin te solution of an OPF problem. From te samplin performe in te framework of te Monte Carlo simulation, we obtain te approximations to te various eonomi an reliability metris, inluin loational marinal pries (LMPs), te total buyer payments, arbon emissions an te LOLP an te EUE. We note tat tese metris impliitly aount for te effets in te eliverability of te eletriity. Te metooloy is able to apture te seasonal effets in loas an win spees, te impats of maintenane seulin an te ramifiations of new poliy initiatives. We ensure te simulation seme omputational tratability for appliation in lare sale systems an/or over lon stuy perios by makin use of te Latin Hyperube samplin tenique [6] to improve Monte Carlo simulation tratability an by reuin te number of weeks to be simulate to a smaller number of representative weeks. Tere are numerous appliations of te approa to a broa rane of plannin, investment, transmission

2 utilization an poliy formulation an analysis stuies for systems wit eepenin penetration of win an storae resoures. We illustrate te apabilities of te simulation approa usin a moifie version of te IEEE 118-bus system moel wit istorial win ata. Our extensive testin iniates tat storae effetively isplaes peakin units an auses a marke reution in total buyer payments wereas system reliability is improve. As storae apaity is inrease, te synereti benefits of win an storae beome more pronoune in terms of te better utilization of te win resoures eneration, wit favorable impats on system eonomis an reliability. Te paper ontains five aitional setions. In setion II, we aress te moelin of win resoures as well as te proess trou wi we establis an averae storae operatin poliy for use in te simulations. Setion III esribes te snapsot-base probabilisti simulation approa an te obtainin of realizations of market outomes of interest an ontributions to te reliability metris. In setion IV, we fous on te steps taken to ensure te omputational tratability of te simulation approa in pratial ases. Setion V emonstrates te apabilities of te approa wit ase stuies run on te IEEE 118 bus test system. We onlue wit a summary in setion VI alon wit iretions for future work. II. Inorporation of time-epenent resoures in probabilisti simulations We evote tis setion to te moelin of win an storae resoures in te probabilisti simulation an teir interation in te framework of te ourly market learin meanism. Loa an enerator availabilities are moele aorinly to onventional approaes [7]. As su, te loa is moele as a ranom variable for wi we use te ourly foreaste ata to estimate te umulative istribution funtion (..f.), wereas termal enerator availabilities are moele as multistatemultiblok units. Note tat our moels make te assumption tat te win resoures, te termal eneratin unit availabilities are statistially inepenent from ea oter. A. Win Resoures Te basi moelin of win resoures at S eorapially isperse win farms is torouly esribe in [5]. System win spee patterns are essentially moele by a multivariate ranom variable for te purpose of apturin win aily patterns as well as te ross-orrelation existin between tem. Note tat su ross-orrelations wi epen on te eorapial sprea of te win farms [8] are of importane sine tey etermine te pattern of win power injetions to te network an terefore impat te utilization of te transmission resoures. We enote te aforementione multivariate r.v. by system win spee aily pattern an empirially buil its probability istribution base on istorial ata. Realizations of su a r.v. are none oter tan supervetors of imension 24S tat apture te simultaneous win farm win spees for ea our of te ay. We o furter in te struturation of te probability spae by reprisin te notion of win reimes evelope in [5]. Te basi iea of reimes onsists in roupin supervetors of aily win spee patterns into lasses of look-alike. Te result is an effetive partition of te state spae of te r.v. system win spee aily pattern into mutually exlusive subsets for wi we an efine speifi ranom variables esriptive of our so-alle reimes. Also, for te nee of te Monte Carlo simulations as presente in setion III, te joint probability ensity funtion of system win spee aily pattern is smoote out an mae ontinuous tanks to te appliation of kernel smootin teniques [9]. Gaussian kernels are osen for tis purpose an te joint probability ensity funtion is effetively turne into a Gaussian mixture from wi realizations an easily be sample. Note tat ea sample of te win spee pattern ranom variable is a 24S vetor tat ontains te ourly realizations of ea win farm. As su, a partiular sample for te win is rawn only one for 24 ours of simulation. Win spees are onverte into orresponin power outputs usin well known win farm arateristi power urves [1]. Te latter are non-linear mappins wose arateristis learly epen on te win turbine moels an number witin a iven win farm. It is important to note tat win turbines witin te same win farm are all assume to experiene te same win spee, i.e. win turbines o not annibalize ea oter. Tis means tat two turbines of te same lass an witin te same site are assume to yiel te exat same power output at all time. Win power outputs are terefore obtaine by feein win spees as inputs to te appropriate win farm power urve. B. Storae In view of arryin out te propose snapsot-base simulations, we nee to ain insit in ow a utility sale storae unit may effetively be use eonomially in a power system wit interate win resoures. To tis en, we make use of an aloritm relyin on probabilisti proution ostin metos to erive a near optimal way of eployin te storae unit eonomially in atual operations [11] tat is, operatin te storae unit in su a way tat eletriity pries are reue an system reliability improve. Te aloritm inores transmission onstraints as it represents te loa wit its uration urve (LDC). Te termal units are loae aorinly to a merit (ost-base) orer tat also aounts for te osts assoiate wit te unit ommitment. Te aloritm is apable of assessin te expete proution osts an elivere enery of ea termal unit base on teir respetive marinal osts of enery an availabilities. Te oal is to provie a list of te termal units tat may be use to are te storae unit, as well as te eonomial positionin of te storae

3 unit in te merit orer. We aount for te timeepenent win resoures by moifyin te loa aorinly to te win power output patterns. Su moifiation is aieve by oneptually subtratin te areate win power output r.v. from te ourly loa r.v. for ea iven our of te stuy perio. Su operation results in te ontrollable loa, tat is te loa left to be serve by ontrollable termal units after eutin te areate win power output. In pratie, sine te win an loa patterns are assume to be statistially inepenent from ea oter, te operation may easily be performe by onvolvin te ourly loa wit te ourly areate win power output. Ten, te..f. of te ontrollable loa r.v. an be reonstitute by applyin te law of total probability over te set of te ours of te stuy perio. Te use of te ontrollable loa allows for te representation of te win as a timeepenent resoure espite te time-abstrate framework. However, su use learly makes te assumption tat win is te eapest soure of enery available an omes first in te merit orer. In su a framework, te storae unit is to be eploye as a limite enery plant wit te followin speifis: first, te storae unit must aomplis a full yle over te stuy perio, tat is, all store enery must be isare before te en of te perio. Takin into aount te effiieny η s of te overall proess of storin an isarin enery, we obtain te followin formulation ξ ηξ = ηηξ = ξ ηsξ = ξ, η witη te effiieny of te storae unit wen arin, η te effiieny of te storae unit wen isarin, ξ te exess enery taken from te termal units to are te storae unit, ξ te enery effetively provie by te storae unit upon isarin. Seon, te storae must be use eonomially, tat is, te ost of storin one MW must never exee te ost of prouin one MW wit te termal unit(s) te storae is suppose to isplae. Terefore, te storae unit is usually are by absorbin te exessive enery of oterwise-spille win enery or base loae termal units tat are not ispate at full apaity to meet te ontrollable loa urin low peak ours. As su, te ost of arin te storae unit is always assoiate wit te atual prie of eletriity (notwitstanin te transmission onstraints), i.e. te marinal ost of te last termal unit ispate to meet te loa. Matematially, we write su eonomi riterion as follows: ω η ω Tat is, te marinal ost ω of te most expensive termal unit use to are te storae must be less tan s (1) (2) te marinal ost of te eapest unit isplae by te storae, takin into aount te effiieny ηs of te storae yle. It is important to note tat no unit is ispate for te speifi purpose of arin te storae unit; in oter wors, te arin of te storae must not inrease te marinal ost of enery. Tir, te storae unit must be operate witin its own pysial limits, i.e. apaity onstraint an reservoir onstraint. Given tose onstraints, te aloritm etermines exatly te list I of termal units tat soul be use for arin te storae unit, te amount of total enery te storae is to store urin a full yle an te position of te storae unit in te merit orer list so tat as mu expensive enery as possible is isplae. For future referene, we enote by I te set of termal units ier in te merit orer tan te storae unit. Su seme terefore provies a oo iea of te way te storae unit soul be operate espite its nonrepresentation of te transmission onstraints an ronoloy of events. We use su solution as an averae operatin poliy in te emulation of te storae unit in te snapsot-base simulations. However, te onsieration of te transmission onstraints in ea installment of te ourly ay-aea markets may entail te moifiation of su a seule so as to ensure tat (1) ols in te MCS. We next introue te market learin proess an esribe ow storae is interate into su a framework. C. Te ourly market learin meanism We aopt te ispat meanism use in omoenous transmission-onstraine ay-aea markets [12] for te purpose of emulatin system operation in a iven our of te simulation perio. Te ourly DAM learin meanism is moele by a DC Optimal Power Flow (DCOPF) wose oal onsists in imizin te soial welfare (or minimizin te soial osts wen te entire loa is eeme to be fixe) uner a set of DC power flow onstraints tat moel te transmission network. Te followin moel takes into aount te win power injetions. We enote byb te set of enery buyers an G te set of ontrollable enerators sellin enery in te market. b β is te prie at wi buyer b is willin to buy enery; γ is efine as te prie offer of seller (enerator). Matries A, B an B respetively esinate te reue bran to noe iniene matrix, te bran suseptane matrix an te reue noal suseptane matrix wereas b is te olumn vetor of te aumente suseptane matrix orresponin to te slak noe. p esinates a vetor of power injetion. Supersript s iniates seller (supply sie players), b buyers (eman sie players), onventional eneration (termal units) an w win power.

4 θ is te vetor of power anles ( at te slak bus) an f is te vetor of transmission line termal ratin. λ te vetor of ual variables assoiate wit te noal power balane onstraints. λ is te ual variable of te power balane onstraint of te slak noe. Ten te DC OPF formulation for our (wit no referene to for more larity) is te followin linear proram M ( G,S ) : subjet to b s p, p b B β ( p ) γ ( p ) b b s s s S s w p = p + p w b p + p p = Bθ λ w b T + = p p p b θ λ B Aθ f min p p p b b b p p p min Note tat te first equality onstraint ilits te fat tat sellers in te market are entities su as termal eneratin units or win farms (plus storae unit in te relevant onitions as esribe in te followin pararap). Te storae is operate base on te knowlee of te resoure ispat provie by te solution to M ( G,S ). If te most expensive termal unit ispate to serve te loa belons to I, ten exess apaities from units belonin to I are use to are te storae witin its pysial limits. On te oter an, if expensive termal units belonin to I are ispate, ten te storae unit must ome in an isplae, witin its pysial ratins, as mu enery as possible from te more expensive termal units. In a oneste network, te storae unit may be bie/offere bot as a loa an enerator in view of ivin more erees of freeom to te ispat proess. It an be sown tat an optimal solution to te DCOPF etermines witout ambiuity storae operation in su a moe. Te DCOPF formulation is ten run a seon time to take storae operation into aount. For tis purpose, storae is bie/offere at a prie onsistent wit te eonomi riterion (2). Te next setion is evote to te use we make of tose moels in te atual simulation proess an te obtainin of realizations of market outomes of interest as well as reliability inies. III. Te propose simulation approa (3) Te oal of te propose simulation approa is to emulate power systems wit win an storae resoures over loner term perios. We ivie te stuy perio into non-overlappin simulation perios typially weeks to apture seasonal effets, anes in te resoure mix an te transmission ri, maintenane seules as well as te introution of new poliies. Any system ane must terefore entails switin to anoter simulation perio for wi system arateristis are require to remain onstant. Insie ea simulation time perio, we employ a snapsotbase approa to aommoate te time varyin nature of te loa, win an storae yle wit a time ranularity of one our. Terefore, we view te system to be in steay-state in ea our of te simulation perio. Te resolution osen oes not allow for te representation of any penomenon of uration sorter tan an our an, onsequently, su penomena are entirely inore. Te basi simulation proess onsists in learin te ourly transmission-onstraine markets M ( G,S ) for ea our of te simulation perio, so as to obtain te loa an eneration ispat from wi we erive te eonomi an reliability effets. However, most inputs to te market are soures of unertainty; te loa, win power outputs an enerator availabilities beave in unpreitable ways we nee to aount for. We run Monte Carlo simulations for ea simulation perios in orer to aount for te multiple possible (an likely) realizations of te input spae - ranom variables assoiate wit te loa, te win power outputs an te enerator availabilities - an obtain, via te solution of te orresponin ourly market learin proesses, representative realizations of te market outomes. Wit su realizations, it is possible to approximate te..f. s of market outomes of interest as well as some reliability metris, wi provie us wit a oo piture of power system eonomis an reliability over loner term perios wen eep penetrations of win power an a utility sale storae unit are interate to te ri. In pratie, for ea our of te simulation perio, te DAM learin proess is fe wit eterministi inputs tat are partiular realizations (samples) of te ranom variables assoiate wit te win power outputs, te loa an te ontrollable eneratin unit availabilities. Oter inputs are moele eterministially from te onset an terefore an be seen as avin a unique realization wit probability 1. In tis rear, note tat we assume tat sellers (enerators) always offer at ost (win is assume to be offere at $/MW) an eletriity buyers bi in a eterministi (an terefore known) fasion. Te solution to M ( G,S ) (or rater its solution after onsieration of te storae unit as esribe in te en of setion II) yiels orresponin realizations of te loa an eneration ispat from wi we erive te realizations of market outomes of interest. Failure to solve M ( G,S ), tat is infeasibility of te linear proram, is an ourrene of loss of loa tat ounts towars te evaluation of te reliability metris LOLP an EUE. Su event is likely to our wen most of te loa is fixe (prie insensitive), a

5 situation leain to potential sortfall in te total eneration apaity or inability of te transmission network to eliver enery at ertain noes of te network. We ompute te eonomi outomes of a partiular realization of te market for our, iven te realizations of win power outputs, loa an ontrollable enerator availabilities fe as inputs to M ( G,S ). We provie te formulas for evaluatin some market outomes an reliability metris of interest. Te LMPs are iven by te ual variables λ assoiate wit te power balanes at ea noe. Terefore, te LMP at noe i is iven by λ i. Te total buyer payments are ompute as N 1 b { λ p } B ϖ = i i i= were, N is te total number of buses in te network. Te total payments to te supply sie are iven by ϖ w {[ λ ] ( p p p )} N S 1 s = i i + i + i i= p s i were is te storae power output wen use as a enerator. Te ourly arbon emissions ε rents are evaluate by ε = χ p, G wit χ te emission fator of unit (k/mw) an G te set of termal units. We assess te unserve loa ui at ea noe i of te network an te total unserve enery ue to loss of loa in our as in U U N 1 = ui. i= is a realization of te unserve enery r.v. U ɶ, for > = LOLP. ɶ ɶ Note tat all aforementione outomes are merely one realization of te assoiate ranom variables onitione on our. Monte Carlo simulations require a reasonable amount of su realizations to approximate te assoiate ranom variables. We terefore lear te market for ea our of a simulation perio multiple times in orer to obtain a suffiient number of realizations. In te en, we quantify te variable effets of te system by evaluatin te expete values of te market outomes r.v. s an te reliability metris LOLP an EUE. We next isuss some metos for ensurin te omputational tratability of our simulation approaes wen emulatin lare sale systems over lon term perios. wi we ave Pr ( U ) IV. Implementational aspets, an EUE = E ( U ) In tis setion, we isuss implementational aspets of te propose approa an te steps taken to ensure its omputational tratability an appliability to lare sale (4) (5) (6) (7) power systems over lon stuy perios. Te main onern lies in te omputational buren assoiate wit te Monte Carlo simulations of stuy perios spannin many years. We onsier simulation perios efine as 168 weeks an notie te fat tat bot win an loa patterns ave a seasonal nature; te onsequene is tat weeks witin a same season experiene omparable win an loa patterns. We effetively take avantae of tis fat by simulatin only representative weeks of a season in orer to reue te omputational buren. However, seule maintenane may still iffer aross weeks wit similar patterns, rivin us to inrease te number of representative weeks to well aount for tis feature. Eventually, ea roup of similar weeks effetively ens up bein represente by a ertain number of representative weeks. Te ontribution of tose representative weeks to te metris we evaluate over te wole stuy perio is ten weite by te number of weeks tey represent. In pratie, su seme an reue te omputational buren by a fator 3, as exemplifie in our appliation stuies in wi te 52 weeks of te year are reue to a mere 16 representative weeks. We an furter enane te overall omputational tratability by improvin on te MCS samplin seme use in te emulation of ea our of a iven simulation perio. We make use of te Latin Hyperube Samplin (LHS) tenique to reue te number of samples neessary to obtain a representative overae of te input probability spae (i.e. representative samples/realizations). LHS is essentially a variane reution tenique tat uses stratifie samplin [5] to effiiently over te probability spae of r.v.s wit known istributions iven te user speifie number of samples (realizations). Consier te one ranom variable ase: te LHS metooloy ivies te probability omain of te ranom variable..f. into a number of intervals also alle strata equal to te esire number of samples. Ten te next step onsists in extratin a sample from ea stratum by use of semes su as te inverse transform meto. Tis simple seme is easily extene to te samplin of multiple r.v.s tat are statistially inepenent from one anoter, as tis is te ase - or at least we assume it is in our moelin wit te r.v.s tat moel te win, te loa an te enerator availabilities. Unlike ranom samplin, LHS ensures tat te entire rane of a istribution is sample, tus makin te most out of te user speifie number of samples wen it omes to proviin a representative overae of te r.v. probability spae. We perform a suffiient number of Monte Carlo runs to asertain onverene. We use a onverene riterion base on te stanar error of te sample mean (similar to oeffiient of variation/relative stanar error as seen in [12]). For te partiular ase stuies presente in Setion V, extensive testin sows tat 2 unre runs allow te Monte Carlo simulation to onvere for all ranom variables of interest. Te implementation of bot representative week seme an Latin Hyperube samplin allows for substantial reution in te omputational time require by te

6 simulation approa. We next introue appliation stuies to illustrate our approa on a number of sensitivity stuies of interest. V. Appliation stuies We illustrate te appliation of te propose simulation approa wit some representative results for a lare test system. We limit our analysis to a sinle year in orer to ain insits into te nature of te results obtaine. We buil a base ase wit interate win resoures an stuy te system beavior wen a utility-sale storae is inorporate into te ri. We run sensitivity stuies to assess te impats of te storae nominal apaity on various metris of interest. Simulations are run on te IEEE 118 bus test system [14] wit a loa sape base on te 1996 IEEE RTS [15] an sale so tat te annual peak loa is 821MW. Te base system sports 99 ontrollable enerators wit an areate total nameplate apaity of 9914MW. Takin into aount te seasonality effets, win an loa patterns as well as maintenane seules, we selet 16 representative weeks out of te 52 weeks of te year in orer to improve omputational tratability. Te unit ommitment is performe for every one of te 16 representative weeks so as to maintain a reserve marin of 2%. Te win resoures are moele after 4 win farms wose win spee ata an win turbine arateristis (inluin power urves) are ollete from NREL win interation stuies [16]. Te areate nameplate apaity of win power amounts to 2584MW (about 3% of te peak loa) an is equally istribute between win farms. Storae nominal apaity is respetively taken as, 2, 3 an 4 MW in ea ase stuy. Storae reservoir (enery apability) is limite to 5 MW, wile are an isare effiienies are set to.89 in orer to simulate ier-en effiient utility-sale storae. We examine storae beavior uner various storae nominal apaities. Fi.1 isplays te averae areisare yles of te storae unit for various nominal apaities (2, 3 an 4MW) as well as te loa pattern urin te so-alle averae week of te year. Storae are an isare (MW) Hourly averae storae utilization ase 3: storae 4MW ase 2: storae 3MW ase 1: storae 2MW ours Fi. 1 Averae are-isare yles of te storae unit urin te averae week of te year Loa (MW) Note tat we onstrut te averae week of te year for a speifi metri usin te results of te representative weeks in te simulation. For ea of te 168 ours of a week, we etermine te weite averae of te metri wit te weit iven by te fration of te number of weeks in te year tat orrespon to tat representative week. In tis way, for ea our of te week, we obtain an estimate of te averae value of te metri. Bak to Fi.1, it an easily be seen tat enery is store urin te low loa ours an release at peakin times. Interestinly, week-ens are bein use for te sole purpose of arin an in orer to meet te i eman of te seon ay onwars. Also, storae utilization is obviously amplifie as te nominal apaity inreases. We next look at te expete total buyer payments to etermine weter inrease storae apaity (tat is inrease storae utilization as seen in Fi. 1) yiel benefits for te buyers. We plot in Fi.2 te uration urves of su expete buyer payments for te averae week of te year an observe tat te interation of te utility-sale storae unit elps reue te total buyer payments urin ours wen payments are enerally iest. Su ours an be sown to be te peak ours by lookin at te same ata but keepin te ronoloial format. total buyer payment (in $) 18 x 15 Total buyer payment uration urve base ase: no storae ase 1: storae 2MW ase 2: storae 3MW ase 3: storae 4MW fration of ours in te "averae week" (in %) Fi. 2 Total buyer payments uration urve for te averae week of te year. Te plot isplays all ases. Te reutions in total buyer payments are sinifiant in rear to te yearly-averae perentae of enery serve (an terefore are) by a 4MW storae unit wit respet to te supplie loa tat amounts to.81%. Tis iretly results from te fat tat storae is primarily use to isplae expensive termal units, tereby rivin own LMPs. Also note tat buyers never ave to pay more at any time, inluin for ours urin wi te storae ares. Tis is ue to te fat tat storae is only are wit te exess apaities of te marinal units (tose tat set te market prie). No more expensive unit is ispate for tat sole purpose. Lookin more losely, we also notie tat as storae apaity inreases, so o te reution in payments, altou te effet beomes less an less pronoune as reater apaities are selete. Su saturation effet

7 may be explaine by te fat tat te storae isplaes more units an terefore omes lower in te ost merit orer as storae apaity is inrease. However, eonomi riterion (2) limits te number of base loae units tat an effetively are te storae, terefore resultin in te impossibility to fully take avantae of its lare apaity. We now present in Table 1 te impats of storae apaity on te averae total buyer payment, averae onestion rents, arbon emissions as well as te reliability metris LOLP an EUE for te all ases of te sensitivity stuy. ase base ase - no storae ase 1-2MW ase 2-3MW ase 3-4MW averae buyer payment ($) averae onestion rents ($) averae arbon ioxie emissions (k) LOLP EUE (MW) 425,83 32,977 89, ,19 3,565 9, ,63 28,956 9, ,1 29,37 9, Table 1. Impats of storae on various metri of interest Havin isusse te averae total buyer payments wit Fi. 2, we now examine te impat of te utility-sale storae unit apaity on te averae total onestion rents. Total onestion rents are ompute as te ifferene between te total buyer payments an te total seller earnins an may be interprete as te ost of network onestion. From Table 1, we notie tat te interation of a storae unit onsistently reues te total onestion rents. As su, storae tens to relieve network onestion. However it is not exatly lear wat role storae apaity plays in tis reution, espeially sine tose results also eavily epen on te storae loation in te network. Carbon ioxie emissions larely epen upon te eneration mix of te onsiere power system. Tere is always a trae-off between te emission fators of te units use for arin an tose of te units isplae by te storae. In te partiular ase of our stuy, te arin of te storae unit involves onventional units tat turn out to be more pollutin tan te peakin units te storae isplaes urin peak ours. Te LOLP an EUE results from Table 1 sow tat storae also ontributes to system reliability. Te latter an be seen to improve as storae apaity inreases. VI. Conlusion In tis paper, we propose a probabilisti simulation approa apable of quantifyin over loner term perios te variable effets of win an storae resoures on power system eonomis, reliability an environmental impats. Te metooloy eploys a snapsot-base simulation approa in orer to aount for te time varyin natures of te win, loa an utilization of te transmission network, an make use of Monte Carlo simulation teniques to represent te various soures of unertainty. As su, te propose approa allows te omparison of multiple resoure mixes an network onfiurations an is terefore useful in a variety of plannin stuies or poliy analysis. We present results tat sow tat win an storae resoures bot ontribute to effetively rive buyer s eletriity payments an onestion rents sinifiantly, wereas system reliability is improve. Carbon ioxie emissions o not vary sinifiantly ue to te partiular setup of our eneration mix tat sports base-loae units enerally more pollutin tan peakin units. Future work inlues te onsieration of multiple storae units, an te interation of win, storae, eman response resoures an solar power altoeter. VII. Aknowleement Tis resear was supporte by te NSF Awar # , Global Climate an Enery Projet aministere by Stanfor University an PSERC projet S-4. VIII. Referenes [1] G. Sinen, Carateristis of te UK win resoure: lon-term patterns an relationsip to eletriity eman, Enery Poliy 35 (27), pp [2] R. Doerty an M. O Malley, A New Approa to Quantify Reserve Deman in Systems Wit Sinifiant Installe Win Capaity, IEEE Transations on Power Systems, Vol. 2, No. 2, May 25 [3] A Report by te Eletriity Avisory Committee, Bottlin Eletriity: Storae as a Stratei Tool for Manain Variability an Capaity Conerns in te Moern Gri, Deember 28 [4] Oualov, A.; Bueler, T.; Cartouni, D.; "Utility Sale Appliations of Enery Storae," Enery 23 Conferene, 28. ENERGY 28. IEEE, vol., no., pp.1-7, Nov. 28 [5] N. Maisonneuve, A proution simulation tool for systems wit win enery resoures Master s tesis, Department of Eletrial an Computer Enineerin, University of Illinois at Urbana- Campain, 29. [Online]. Available: ttp://enery.ee.uiu.eu/ross/papers/dissertations/maisonneuv e.pf [6] G. S. Fisman, A first ourse in Monte Carlo, Duxbury, 26 [7] A. Kowli an G. Gross, Simulation-Base Plannin Approa for Systems wit Time-Depenent Resoures, Proeeins of te 21 IREP Symposium - Bulk Power System Dynamis an Control - VIII, Buzios,Rio e Janeiro, Brazil, Auust 1-6, 21 [8] J. Carlin an J. Haslett, Te Probability Distribution of Win Power From a Disperse Array of Win Turbine Generators, Journal of Applie Meteoroloy, Vol. 21, Issue 3, pp , Mar 1982 [9] A. W. Bowman, A. Azzalini, Applie smootin teniques for ata analysis. Oxfor, Clarenon Press, 1997,. 1 [1] G. Masters, Renewable an Effiient Eletri Power Systems, New York, NY: Jon Wiley & Sons, 27 [11] Class notes for ECE 588, Eletriity Resoure Plannin, Proution Costin, Storae Analysis, G. Gross, 21. [12] C. Sin, P. Jirutitijaroen, Monte Carlo Simulation Teniques for Transmission Systems Reliability Analysis, Tutorial presentation at te IEEE PES General Meetin 27. [13] S. Stoft, Power System Eonomis: Desinin Markets for Eletriity. New York, NY: Wiley-IEEE Press, 22. [14] 118 bus power flow test ase [Online] Available: ttp:// s.tm [15] RTS task fore of te appliation of probability metos subommittee, Te IEEE reliability test system 1996, IEEE Trans Power Syst 14 (3) (1999), pp [16] Eastern Win Interation an Transmission Stuy NREL ata. [Online]. Available: ttp://win.nrel.ov/publi/ewits/