Optimal ESS Allocation for Load Management Application

Transcription

1 1 Optmal ESS Allocaton for Load Management Applcaton Ahmed S. A. Awad, Graduate Student Member, IEEE; Tarek H. M. EL-Fouly, Member, IEEE; and Magdy M. A. Salama, Fellow, IEEE Abstract The recent deployment of dstrbuted generaton has led to a revoluton n the use of dstrbuton systems and the emergence of smart grd concepts. Smart grds are ntended prmarly as a means of facltatng the ntegraton of renewable energy sources and of aevng greater system relablty and effcency. Energy storage systems (ESSs) offer a number of benefts that can help utltes move toward those goals. One of those benefts s the capacty to mprove the utlzaton of network nfrastructure by means of proper load management. Ths paper proposes a methodology for allocatng ESSs n dstrbuton systems n order to defer system upgrades, mnmze system losses, and take advantage of the arbtrage beneft. The cost and arbtrage beneft of energy storage nstallaton are optmzed wth respect to system upgrade and energy losses costs. The prmary goal of ths resear s to determne the optmal sze and locaton of storage unts to be nstalled, n addton to ther optmal operaton, so that total system costs are mnmzed, whle system benefts are maxmzed. In ths paper, a probablstc load model s adopted nstead of utlzng tme-seres based models, wh provde an optmal soluton that s vald only for the tme-seres pattern that s appled. Index Terms smart grd; energy storage system; load management Sets and ndces I. OMECLATURE B Set of canddate buses for nstallaton Scrpt referrng to argng ds Scrpt referrng to dsargng hr Hour ndex, j System bus ndces k Renforcement ndex l Load state ndex Set of load states mn Scrpt referrng to mnmum values max Scrpt referrng to maxmum values off-peak Scrpt referrng to off-peak demand peak Scrpt referrng to peak demand The authors would lke to thank the Government of Canada for fnancally supportng ths resear through the Program on Energy Resear and Development. A. S. A. Awad and M. M. A. Salama are wth Electrcal and Computer Engneerng Department, Unversty of Waterloo, Ontaro, Canada (e-mals: asamr@uwaterloo.ca; msalama@uwaterloo.ca) T. H. M. EL-Fouly s wth CanmetEERGY, atural Resources Canada, Varennes, Quebec, Canada (e-mal: telfouly@nrcan.gc.ca) s Combned load-dg state ndex Set of combned load-dg states v Constrant ndex y Index of the year by wh renforcement k s k requred yr Year ndex Varables Cost of energy losses C R et present value of the replacement cost of the E Energy stored at the PV AR et present value of the arbtrage beneft PV LO et present value of the energy losses costs PV UP et present value of the system upgrade costs P Output argng/dsargng power of the CE loss P Total power losses n the dstrbuton network loss r Replacement perod of the R Cost of renforcement k k V Bus voltage magntude x Integer decson varable controllng the power sze of to be nstalled at bus y Integer decson varable controllng the energy capacty (sze) of to be nstalled at bus z Bnary varable assocated wth constrant v, v wh equals to zero f the correspondng constrant s satsfed, or otherwse equals to one Bus voltage phase angle Parameters c C P C C E E M F FR IR IR' M c Electrcty prce Captal power cost of the Captal energy cost of the Annual operaton and mantenance cost of the capacty Inflaton rate Future value of replacement cost Interest rate Effectve nterest rate Total number of requred upgrades Total number of system buses Total number of constrants

2 2 yr P D P P G PVF umber of years n the plannng perod Demand actve power argng/dsargng power Gene actve power Present value functon Q D Demand reactve power Q G Gene reactve power Y Magntude of bus admttance matrx element Angle of bus admttance matrx element Probablty of state round-trp effcency of the P II. ITRODUCTIO OWER systems are now evolvng from the conventonal regulated system, wth centralzed generaton connected to the transmsson networks, to a deregulated structure that allows small generators to be connected drectly to the dstrbuton networks. Su networks thus become actve and are usually referred to as actve dstrbuton networks, n wh new tenologes should facltate adaptaton to su actve envronments and enable the use of smart grd concepts. Energy storage systems (ESSs) are one promsng tenology that can support the ncorporaton of smart grds because of ther capacty to mprove the system relablty and to facltate the ntegraton of hgh penetraton levels of renewable energy sources (RESs). ESSs can also provde addtonal benefts for dstrbuton utltes, su as an effcent expanson alternatve through peak load shavng and methods of mtgatng power qualty ssues [1]. Peak load shavng mples power exange between base generaton unts and storage devces n order to store some power durng off-peak perods and dsarge them durng peak load perods. Ths practce enhances the utlzaton of network nfrastructure. Furthermore, that off-peak power can be stored or bought wth a low prce, and then dsarged or sold wth a hgh prce. Ths prce dfference, usually termed as arbtrage beneft, s benefcal for ESS owner, e.g. utlty or customer drven ESS [2]. In Canada, the frst battery-energy storage projects have been recently mplemented by Brtsh Columba (BC) Hydro and Toronto Hydro wth ratngs of 2 MW and 500 kw-250 kwh, respectvely [3], [4]. Several resear works have addressed the problem of szng ESS n order to reduce the uncertanty assocated wth RESs, e.g. wnd energy, as n [5], or to accommodate hgh penetraton levels of RESs as n [6]. Moreover, the authors n [7] have nvestgated determnng the optmal ESS operaton n order to ncrease the value of wnd-power generaton. In [8], the authors presented a probablstc approa for szng and stng energy storage n dstrbuton systems n order to mprove the relablty of dstrbuton systems. Other resear works have focused on szng ESS for solated mcro-grd applcatons as n [9], [10]. In [7] and [10], tme-seres models have been appled n order to forecast the stoastc nature of system components and determne the optmal ESS operaton durng a certan perod, based on wh the sze of the ESS s optmzed. Despte the dffcultes assocated wth forecastng hghly stoastc components, su as wnd speed and solar rradance, the applcaton of tme seres models provdes an optmal soluton that s vald only for the tme-seres pattern that s appled. Consequently, the soluton obtaned s not guaranteed to be the global optmal for other possble patterns [9]. A preferable soluton would therefore be to derve probablstc models that take nto account all possble system states, as proposed n ths paper. Moreover, few resear works have dscussed the economc feasblty of dstrbuted storage () 1 ntegraton wth dstrbuton substatons n order to aeve several benefts, su as upgrade deferral, arbtrage beneft maxmzaton, etc., n [11] and [12]; however, the dstrbuton network model has not been represented, thus the upgrade deferral has been evaluated by means of emprcal formulas that consder the nvestment cost of dstrbuton substaton only. As n [7] and [10], a typcal one-day demand profle has been further utlzed n determnng the optmal operaton and the correspondng sze. It s worth mentonng that when batteres are used as storage tenology, they may be replaced once or more durng the plannng perod; however, the replacement cost of batteres was not consdered n these works. From another perspectve, the authors n [13] presented a systematc approa for clusterng dstrbuton systems nto vrtual mcrogrds based on mnmzng energy flows between them. The mpact of allocatng pre-specfed amount of unts and dstrbuted reactve sources on maxmzng the selfadequacy of formed mcrogrds was further studed n that paper. Based on the above survey, t can be concluded that suffcent work has been conducted wth respect to szng and sedulng ESS operaton for promotng large penetraton levels of RESs. On the other hand, few studes have nvestgated other benefts of ESS mplementaton n dstrbuton networks, su as peak load shavng and upgrade deferral, wthout modelng the dstrbuton network. Therefore, ths paper ams to develop a plannng framework for determnng the sze and locaton of unts to be nstalled n dstrbuton networks n order to defer system upgrades usng load management strateges. In ths paper, models for dstrbuton feeders and substaton s transformers are consdered. Moreover, ths paper provdes an operatonal plannng gude that helps dstrbuton utltes manage the operaton at ea load state n order to maxmze the arbtrage beneft. Ths operatonal gude s smply to control the operaton based on the measurement of system load magntude only,.e., wthout any further utlzaton of advanced forecastng modules and controllers. To the best of the author s knowledge, ths problem has not been addressed yet n the lterature. Evolutonary optmzaton algorthms, e.g. genetc algorthm (GA), partcle swarm optmzaton, Tabu sear, etc., are emergng as effcent optmzaton tenques to solve complcated problems su as dstrbuted generaton (DG) 1 The terms ESS and are used nterangeably n ths paper.

3 3 plannng [14], and unt commtment [15]. GA has been extensvely used n the lterature as n [16], [17], and t has showed superor performance compared to other metaheurstc tenques n terms of the soluton error and the executon tme [18]. In ths work, we propose a methodology based on GA and a lnear-programmng (LP) solver as wll be dscussed later on. The man contrbutons of ths paper can be summarzed as follows: The paper presents a plannng framework that takes nto account the dstrbuton network model n ascertanng the most cost-effectve stng and szng of unts n order to defer system upgrades by means of load management. Unlke prevous work that appled tme seres patterns for optmzng the sze of unts, a probablstc approa s proposed n ths paper n order to consder the uncertanty of system components. The approa proposed further ncludes determnng the optmzed operaton of unts at ea load state. The rest of ths paper s organzed n fve sectons. Secton III descrbes the problem under study. The methodology and the mathematcal formulaton are further dscussed n secton IV. Secton V ntroduces a sample case study. The results and conclusons are fnally provded n sectons VI and VII, respectvely. III. PROBLEM DESCRIPTIO The applcaton of energy storage to shave peak load s smlar to demand sde management programs that shft demand use of energy from peak to off-peak perods. In ths applcaton, energy s stored wthn durng off-peak tmes and s released when the load s hgh (.e., peak). However, the economc feasblty of ths usage of energy storage should be justfed snce unts are expensve n nstallaton and mantenance costs. To aeve ths task, the benefts from ntegratng to attan demand sde management need to be frstly enume as follows: Arbtrage beneft ths s the drect beneft from buyng and storng energy wth an nexpensve prce durng off-peak perods, and sellng the energy stored back, after accountng of the losses n the ESS, wth a hgh prce at peak tmes. System upgrade deferral system upgrades are usually requred n order to account for the annual load growth n a gven dstrbuton system. Through peak load shavng, system upgrades can be deferred to later years, and the net present value (PV) of system upgrades can be then reduced. Energy losses reducton ths s the secondary beneft from ntegratng unts nto dstrbuton systems. By means of proper placement of energy storage unts, the cost of energy losses n dstrbuton systems can be mnmzed. From the aforementoned dscusson, the proposed work focuses on fndng the optmal allocaton n dstrbuton systems that mnmzes the PV of system costs.e., system upgrades, energy losses, and nstallaton and mantenance costs and maxmzes the PV of arbtrage beneft. Allocatng energy storage for ths applcaton nvolves determnng the sze and the locaton of unts to be nstalled (plannng decsons) as well as the control strategy of those allocated unts (operatonal decsons). Controllng operaton s the key for maxmzng arbtrage beneft regardless of where the unts are located. On the other hand, mnmzng system upgrade and energy losses costs depends on both the plannng and operatonal decsons. IV. METHODOLOGY Ths secton presents the general methodology adopted n ths paper. The nput to the methodology proposed s the dfferent probablstc models of load and DG unts, whle the output of ths methodology s the optmal sze and locaton of unts as well as the optmzed operaton of unts. The ratonale behnd the work presented n ths paper s the optmzaton of the nvestment costs by dstrbuton companes through deployment and control of unts. Due to the complexty of handlng plannng and operatonal plannng decsons, GA combned wth LP solver s utlzed for mnmzng the objectve functon under study. In the followng paragraphs, an overvew of the methodology proposed s descrbed, and the detals are dscussed n the next subsectons. The proposed methodology s based on the followng assumptons: The dstrbuton companes (utltes) are the canddate owners of unts, and thus they would make beneft from the work presented n ths paper. Controllng the operaton of unts s assumed to be the responsblty of the dstrbuton company. The control of unts s based on maxmzng the arbtrage beneft and mnmzng the cost of system upgrades. Dscrete load and DG models are utlzed n ths work n order to take nto account the stoastc nature of system components. The sze of dscrete models should be carefully selected so that the smplcty and accuracy of the analyss are not compromsed: a large number of states ncreases accuracy but at the expense of also addng to the complexty, and a small number of states has the opposte effect. The man step of the methodology proposed s the romosome encodng of GA. In the presented work, ea soluton (romosome) conssts of nteger varables that control the sze (n kw and kwh) to be nstalled at every canddate system bus, as shown n Fg. 1. For every populaton gene by GA, three man steps are requred to evaluate the objectve (ftness) functon of ea ndvdual, as shown n Fg. 2. Mult-year plannng approa s further proposed n ths work n order to evaluate the PV of both system expenses and benefts. The frst step adopts a dscrete load model, wh mples certan load states wth ther magntudes and the assocated probabltes, n optmzng the argng/dsargng operaton at ea state through a LP solver. The next step s to smulate the energy storage operaton, utlzng the optmzed operaton from the prevous step as an nput, n order to estmate the annual arbtrage

4 4 beneft and the number of argng-dsargng cycles per year. Fnally, load flow analyss s performed at ea state n order to determne the requred system upgrades and the correspondng energy losses. These man steps are detaled n the next subsectons and the assocated mathematcal formulatons are presented. A. Load modelng The load demand s assumed to follow the hourly load shape of the IEEE-relablty test system (RTS) as n [19]. The hourly load data has been clustered nto 10 load states that have proved a good trade-off between complexty and accuracy of the analyss, as shown n Table I [20] Integer decsons for power szes of unts Integer decsons for energy szes of unts Fg. 1. A sample structure of the romosome encodng Start Genetc Algorthm (GA) generates an ntal populaton {locaton and sze of unts} Year =1 Update load demand wth certan load growth % Generate new populaton o End Dsplay results Yes Stoppng crtera? B. DG modelng Intermttent based DGs are modeled through utlzng proper probablty dstrbuton functons (PDFs). Generally, PDFs can be obtaned from the avalable hstorcal data of dfferent DG types. For example, a Raylegh PDF s assumed sutable for modelng wnd speeds, as presented n [20]. In ths work, contnuous PDFs are further dvded nto several states wth assocated probabltes, thus creatng a probablstc model for every DG. Moreover, dspatable DGs are represented wth constant output power generaton, wh equals to the ratng of the DG nstalled, and constant power factor (.e., unty accordng to Hydro One regulatons [21]). C. Optmze the operaton of unts Ths step nvolves determnng the optmal argng/dsargng power at ea load state. Frst of all, the load states are dvded nto canddate states for argng and dsargng based on the magntude of ea load state. In partcular, the frst four states (.e., up to 51% of the peak load) are assumed to be off-peak states, and thus canddate states for argng, whle the last sx states (.e., greater than 51% of the peak load) are consdered to be canddate states for dsargng. Furthermore, the electrcty prces are assumed to follow the averaged off-peak and peak prces wh are calculated from the hourly prces provded by the ndependent electrcty system operator (IESO) [22]. Ths sub problem s formulated as a LP optmzaton problem that has an objectve functon of maxmzng the expected arbtrage beneft as follows: Optmze argng/dsargng operaton at ea load state n order to maxmze the expected arbtrage beneft Smulate the system n order to determne the annual arbtrage beneft and the number of argng-dsargng cycles per year Conduct load flow analyss n order to determne the requred upgrades and the correspondng energy losses Fg. 2. Flowart of the proposed methodology Evaluate the populaton gene by GA o TABLE I PROBABILISTIC LOAD MODEL Yes Year > number of years n the plannng perod? Year = Year +1 Load state no. Load magntude (% of peak load) Probablty P l ds l l peak l l off-peak (1) l ds l Maxmze P c P c From the above objectve functon, t s clear that ths sub problem depends only on the electrcty prces and the load states probabltes as parameters. Although the load states magntudes (n MW) ncrease at every year over the plannng perod, ea load state s probablty can be assumed to reman constant. If we further assumed that off-peak and peak electrcty prces may ncrease, or probably decrease, wth the same percentage over the plannng perod, then the above problem needs to be solved only once, thus leadng to the same optmal operaton at every year. evertheless, the above objectve s maxmzed subject to the followng constrants. The frst constrant mples that the expected stored energy n a certan perod equals to the expected dsarged energy n the same perod. Moreover, the energy stored n a typcal day s lmted to the energy sze n (3). The last constrant further enforces the dsargng power at the most peak load state (.e., state 10) to be equal to the power sze n order to reduce the cost of system upgrades snce the upgrades requred are usually determned at ths state as wll be dscussed later on.

5 Subject to: ds P l l l P ds ds 10 l l P l l 24 P E P ds l 0 P, P P l l l l (2) (3) (4) (5) Afterwards, the PV of the arbtrage beneft can be calculated as n (9) usng the PVF, wh s expressed n terms of IR, F, and yr as n (10-11) [23] PV AR Annual arbtrage beneft PVF (9) yr 1IR 1 PV F yr IR 1 IR IR F IR 1 F 5 (10) (11) D. Determne the annual arbtrage beneft and the number of operaton cycles In ths step, a sequental Monte Carlo smulaton (MCS) s performed n order to estmate the annual arbtrage beneft and the number of argng-dsargng cycles per year. Ths smulaton takes nto account the optmzed operaton from the foregong stage. It s worth mentonng that the arbtrage beneft obtaned from smulaton s dfferent from the expected value determned n the prevous step. Ths dfference s attrbuted to the fact that unts mght fal to operate as preplanned f they are fully arged or dsarged. The procedure for performng MCS s descrbed as follows: 1- For ea study perod (.e., one year), the load state at every hour (hr) s gene through the generaton of a unformly dstrbuted random number between 0 and 1, and roundng t to the nearest value n the cumulatve dstrbuton functon (CDF) that corresponds to the load probablstc model n Table I. 2- Based on the load state at every hour, recall the output power at ea state from the foregong stage. Then, calculate the energy stored at the (E ), takng nto consderaton the physcal constrants of the at any tme nterval, va the followng relatons: ds E E P P hr (6) hr 1 hr hr hr mn E E E hr (7) hr 3- Determne the annual arbtrage beneft as n (8) n wh, at a certan hour, only one term has a value whle the other term equals to zero. The frst term, wth negatve sgn, represents the energy purased at off-peak perods, whle the second term, wth a postve sgn, corresponds to the energy sold at peak tmes. The effcency s used to accurately account for the energy purased at energy storage termnals c off-peak max 0, E E / hr 1 hr (8) hr 1 c max 0, E E peak hr hr 1 4- Calculate the number of annual operatng (arge/dsarge) cycles for ea. 5- Stop f the rato of the standard devaton of the sample mean of the ndex of nterest (.e., the arbtrage value) to the sample mean of the same ndex becomes less than a predetermned tolerance, otherwse go to step 1. E. Evaluate system upgrade and energy losses costs In ths step, a combned load-dg model s gene va convolvng the dscrete probablstc models of the load and exstng ntermttent based DGs, assumng that these ndvdual models are ndependent (uncorrelated) as n [20], [13]. Su a model combnes all possble operatng states for the avalable DG unts and the dfferent load levels. The total number of states s therefore equal to the product of the number of states for ea component. Ths step further apples mult-year probablstc load flow analyss n order to evaluate system upgrade and energy losses costs. The energy losses only account for the losses n the lnes of the prmary dstrbuton system. Moreover, system upgrade nvolves the renforcement of feeders (lnes) and substaton n order to account for the annual load growth. In ths work, the dstrbuton network s confguraton s presumed fxed; therefore, upgradng network s equpment to larger szes s consdered to be the unque alternatve for satsfyng the growng demand. For radal dstrbuton systems, system upgrades are usually evaluated at the condton of extreme power flow n the lnes,.e., the most peak load state. Wth the ntegraton of unts, however, the extreme power flow n the lnes may not occur at the peak load state due to peak load shavng. Consequently, system upgrades should be determned based on the maxmum upgrade requred over all load states. The procedure for evaluatng system upgrade and energy losses costs s explaned as follows: 1- For ea year (yr), update load demand wth a certan load growth percentage. 2- For ea combned load-dg state (s), solve load flow equatons as n (12-14), and calculate the correspondng upgrades for all equpment and the total power losses (P loss ) G, s, yr D, s, yr s, s, yr j, s, yr j j 1 P P P V V Y (12) cos, s, yr j j, s, yr, s, yr

6 6 ds G, s, yr D, s, yr s, s, yr j, s, yr j j 1 P P P V V Y (13) cos, s, yr j j, s, yr, s, yr ds Q Q V V Y (14) G, s, yr D, s, yr, s, yr j, s, yr j j 1 sn, s, yr j j, s, yr, s, yr 3- For ea pece of equpment, determne the maxmum upgrade requred. 4- For ea year, determne the expected energy losses costs as follows: CE 8760 loss yr s ds P c P c s losss peak s losss s off-peak (15) 5- At the end of the plannng perod, determne the PV of system upgrade and energy losses costs as n (16-17), respectvely. M R (16) k PV UP y k (1 IR ') PV LO k 1 yr yr 1 CE loss yr (1 IR ') F. Evaluate the objectve functon yr (17) In ths step, the objectve (ftness) functon s presented that mnmzes the aforementoned costs and maxmzes the arbtrage beneft. The problem constrants are further added to the objectve functon usng penalty terms, as presented n the last term of (18). Bascally, there are several tenques mentoned n the lterature to handle constrants n evolutonary algorthms, e.g., elmnatng or reparng nfeasble romosomes, and penalty terms appled to the objectve functon. Elmnatng or reparng nfeasble romosomes are neffcent and problem dependent. On the other hand, the approa of penalty terms s smple and generally works well wth all problems [24]. x, y 1 8 c v 1 P M Mnmze C C PV F P C C E PV PV PV E R UP LO AR 10 z v (18) If batteres are used as the energy storage tenology, then they may need to be replaced once or more durng the plannng perod; therefore, C R s calculated as n (19) [6] 1 ' r 1 ' 2 r C R FR IR IR (19) where r s the replacement perod n years that can be calculated by dvdng the battery s lfe tme,.e. the maxmum number of arge/dsarge cycles, by the number of operatng cycles per year. Subject to: Voltage lmts constrants: V mn V, s, yr V max, s, yr (20) sze constrants: P x dscrete step B (21) E y dscrete step B (22) max P P B (23) max E E B (24) nstallaton constrants: x and y 0 B (25) V. CASE STUDY The system used for the case study s a 33-bus radal dstrbuton system, as shown n Fg. 3. The actve and reactve power levels of the load ponts as well as the feeder data are taken from [25]. The system peak demand s 3715 kw at base year, and t grows wth a constant annual rate of 5 %. For ths case study, the plannng perod s consdered to be 20 years. The followng fnancal parameters are further assumed: 5% nterest rate and 1% nflaton rate. The captal fxed and varable upgrade costs of the system equpment are gven n Table II [26]. Moreover, Table III lsts the average off-peak and peak electrcty prces calculated from the hourly prces provded by the IESO [22]. Substaton Fg. 3. System under study TABLE II CAPITAL FIXED AD VARIABLE UPGRADE COSTS [26] Fxed cost Varable cost Feeder $150,000 per km $1000 per MW Substaton $200,000 $50,000 per MW TABLE III AVERAGE ELECTRICITY PRICES [22] Peak Off-peak Energy prce ($/MWh) 27 18

7 7 Two dfferent DG types are used n the system under study: dspatable DG (DG1) based on desel and ntermttent DG (DG2) based on wnd. DG1 and DG2 are placed at buses 33 and 18, respectvely. DG1 s a 500 kva synronous generator that operates at 500 kw (unty power factor). DG2 s a 1 MW wnd turbne wth power curve parameters as shown n Table IV. The sum of the DG power levels s confrmed as meetng the Hydro One capacty requrement that lmts nstalled DG ratngs to 60 % of the substaton capacty plus the mnmum staton load [21]. The wnd speed data for the ste under study are assumed to reveal a mean wnd speed of 6 m/s. Both wnd speed and wnd turbne data are utlzed n the development of the probablstc wnd-based DG model, wh s based on the adopton of a Raylegh PDF for modelng wnd speeds, as presented n [20]. Moreover, 12 states were consdered for modelng the wnd-based DG, as shown n Table V. In ths paper, the GA and lnprog solvers n MATLAB optmzaton toolbox are used for solvng the methodology proposed. The settng parameters and termnaton crtera of GA are further gven n Table VI. nstallaton costs are sub-dvded nto four man parts: the captal power cost of converter nterface, the captal energy cost of storage capacty, the captal replacement cost, and the annual fxed operaton and mantenance (O&M) cost. Leadacd (LA), sodum-sulfur (a/s), and vanadum-redox (VR) batteres are selected as canddate storage tenologes because ther power and dsarge tme capactes are sutable for the applcaton under study. It s assumed that the canddate storage tenologes are avalable n dscrete szes n steps of 100 kw/kwh. Table VII lsts the captal and mantenance costs for the three canddate tenologes. Dependng on land avalablty and/or utlty regulatons, the canddate buses for nstallaton are assumed to be ncluded n set B: (16, 17, 21, 22, 25, 32). TABLE IV WID TURBIE PARAMETERS Cut-n speed (m/s) 4 Rated speed (m/s) 14 Cut-out speed (m/s) 25 TABLE V PROBABILISTIC WID-BASED DG MODEL Wnd state no. Output power (% of power) Probablty TABLE VI GA PARAMETERS AD STOPPIG CRITERIA Populaton sze 20 Selecton crtera Roulette wheel Crossover algorthm and probablty Scattered 0.6 Mutaton probablty 0.01 Termnaton crtera and value Stall generatons 50 TABLE VII CAPITAL AD MAITEACE COSTS OF TECHOLOGIES [27], [28] LA a/s VR Rated output power (kw) Round-trp effcency (%) Captal and mantenance costs Captal power cost ($/kw) See note below Captal energy cost ($/kwh) Captal replacement cost ($/kwh) Annual O&M cost ($/kw) umber of arge/dsarge cycles ote: Captal power cost for VR battery s ncluded n captal energy cost. VI. RESULTS Ths secton summarzes the fndngs of ths resear, n wh unts are optmally allocated n order to aeve load management, and thus defer system upgrades and mnmze system losses. The mpact of pre-allocated DG types s studed n ths secton through three dfferent cases: the system wthout any DG, the system wth ntermttent DG type only (.e., DG 2 ), and the system wth both ntermttent and dspatable DG types (.e., DG 1 and DG 2 ). In ea case, several scenaros representng the base case (.e., wthout unts) and the three dfferent storage tenologes, as shown n Table VIII, are compared. The PV of total costs are summarzed for ea scenaro n Fg. 4, and the detals are shown n Table IX. ote that the percentage of savngs n ea scenaro s calculated wth respect to the correspondng base case. As an example, the graphcal representaton of GA convergence s presented n Fg. 5, wh shows the superor performance of GA n terms of the number of teratons before stoppng. Moreover, t s worth mentonng that GA, as one of the heurstc algorthms, does not guarantee the same soluton even after runnng the same problem several tmes. Therefore, the GA run was repeated ten tmes wth dfferent ntal populatons that were randomly gene. The maxmum dfference between the optmal solutons obtaned was then recorded and found to be less than 5%. Su statstcal results also prove the effectveness of the GA.

8 Installed unts (kw, kwh) PV of costs 8 TABLE VIII DIFFERET SCEARIOS Case DG type DG locaton Scenaro Base case (A.0) A o DG -- LA a/s (A.1) (A.2) VR (A.3) Base case (B.0) B Wnd based 18 LA a/s (B.1) (B.2) VR (B.3) C Wnd based 18 Desel 33 Base case LA a/s VR (C.0) (C.1) (C.2) (C.3) Fg. 4. Results of the dfferent scenaros Fg. 5. Graphcal representaton of the GA convergence (case C.1) TABLE IX DETAILED RESULTS OF THE DIFFERET SCEARIOS Case A B C Scenaro A.0 A.1 A.2 A.3 B.0 B.1 B.2 B.3 C.0 C.1 C.2 C.3 Captal costs ($) Mantenanc e costs ($) Replacement costs ($) 0 48, ,000 74, , ,000 74, , , ,457 27,276 27, ,457 27,276 27, , , ,720 41, ,720 41, , Total ($) 0 82, , , , , , , ,660 PV of arbtrage value ($) PV of system upgrade costs ($) 0 1,142 1, ,142 1, , ,038 3,395,200 3,076,500 3,076,500 3,076,500 3,395,200 3,076,500 3,076,500 3,076,500 2,929,100 2,275,200 2,929,100 2,275,200 % Savngs 0.00% 9.39% 9.39% 9.39% 0.00% 9.39% 9.39% 9.39% 0.00% 22.32% 0.00% 22.32% PV of energy losses cost ($) 311, , , , , , , , , , , ,910 % Savngs 0.00% 0.45% 0.46% 0.43% 0.00% 0.42% 0.43% 0.43% 0.00% 1.83% 0.00% 1.89% Total cost 3,706,360 3,467,305 3,603,654 3,487,130 3,669,630 3,430,805 3,567,184 3,450,580 3,117,570 2,946,061 3,117,570 3,064,732 % Total savngs 0.00% 6.45% 2.77% 5.91% 0.00% 6.51% 2.79% 5.97% 0.00% 5.50% 0.00% 1.69% Bus , , 100 Bus , , , , , , , , 500 Bus Bus Bus Bus

9 9 A. o DG In ths case, the system s assumed to have no pre-allocated DGs. Scenaro A.0 represents the base case n wh the total cost s only comprsed of the costs assocated wth the system upgrades and energy losses. The next three scenaros present the allocaton of dfferent storage tenologes. The results of allocatng unts are the same for the three dfferent tenologes. Therefore, the cost of system upgrades s found smlar; t s notably reduced from $3.40 mllon (base case) to $3.10 mllon, thus resultng n 9.39% savng. Ths reducton s due to deferrng system upgrades to later years. However, the cost of the system losses s slghtly decreased (.e., ~0.45% savng) due to the demand management aeved. It s worthy to note that the costs of energy losses are dfferent n ea scenaro based on the correspondng optmzed operaton, as gven n Table X. Ths table shows the optmal argng/dsargng output powers at ea load state for ea storage tenology. Ths table would be very useful for utltes operators n controllng the operaton, n order to aeve the maxmum arbtrage beneft, based on the measurement of system load magntude only,.e. wthout any further utlzaton of advanced forecastng modules and controllers. ote that the dfference n the operaton of the varous tenologes s attrbuted to the dfferent correspondng effcences. Wth respect to the total cost n Table IX, LA batteres are revealed to provde the least expensve soluton: total costs are decreased from $3.71 mllon (base case) to $3.47 mllon, thus resultng n 6.45% total savngs. It s worthwhle to menton that these costs are system dependent. More savngs can be further aeved f other benefts of are taken nto consderaton, su as the enhancement of relablty and the mtgaton of power qualty problems. As can be seen, the a/s batteres represent an expensve opton due to ther hgh captal costs and low lfe tme. On the other hand, although VR batteres have hgher captal costs compared to LA ones, VR batteres have long lfe tme and they do not need to be replaced durng the plannng perod, thus reducng the PV of costs to almost those of LA batteres. TABLE X OPTIMAL OUTPUT POWER (I KW) AT EACH LOAD STATE Load state no. status LA a/s VR 1 Chargng Chargng Chargng Chargng Dsargng Dsargng Dsargng Dsargng Dsargng Dsargng Wth respect to the arbtrage beneft, t s clear that the more effcent the energy storage tenology s, the hgher the arbtrage beneft wll be. evertheless, the hghest arbtrage beneft s sgnfcantly less than the nstallaton and mantenance costs. Therefore, accordng to the current costs of energy storage tenologes, no prvate nvestors would nstall energy storage unts n order to aeve ths arbtrage beneft only. B. Wnd based DG only Only the wnd based DG (.e., DG 2 ) s assumed exstng n the system under study n order to study the mpact of ntermttent based DGs on the allocaton of unts. As can be seen n the base case (B.0), the cost of system upgrades s the same of scenaro (A.0) snce the requred upgrades are determned at the extreme power flow condton as mentoned earler, wh mples mnmum output power from DG 2 (.e., zero n ths case) and maxmum (peak) load. Consequently, the same allocaton of unts s depcted n ths case. However, the cost of system losses s sgnfcantly reduced by 11% compared to scenaro (A.0) due to the ntegraton of wnd based DG. C. Wnd and desel based DGs In ths case, the system s assumed equpped wth both dspatable and ntermttent DGs,.e., DG 1 and DG 2, respectvely. The results of the base case (C.0) show that the total cost, ncludng the costs of system upgrades and energy losses, s sgnfcantly reduced by $0.59 mllon compared to scenaro (A.0). Ths reducton s due to the two DGs nstalled n ths case. The next three scenaros present the allocaton of unts for the three storage tenologes. As can be seen, the number and szes of unts allocated are the same for LA and VR batteres, whle a/s batteres are found not economc for ths case study. Moreover, the number and szes of unts allocated n scenaros (C.1) and (C.3) are hgher than those of cases A and B. These results are attrbuted to the fact that the system costs are already decreased wth the ntegraton of the two DGs. Therefore, more energy storage unts are needed n order to reduce the total cost. Furthermore, the cost of system upgrades s sgnfcantly reduced from $2.93 mllon (C.0) to $2.28 mllon n scenaros (C.1) and (C.3), thus resultng n 22.32% savng. Moreover, the losses are decreased by almost 1.8%. The LA batteres are also shown to be the least expensve soluton n ths case. VII. COCLUSIOS In ths paper, a mult-year plannng framework was proposed for the allocaton of unts n dstrbuton systems n order to defer system upgrades, reduce energy losses, and take advantage of the arbtrage beneft. The PV of nstallaton and mantenance costs as well as system upgrade and energy losses costs were then mnmzed n order to determne the optmal sze and locaton of unts to be nstalled. Furthermore, a probablstc approa, rather than tme-seres models used n the lterature, was adopted n order to optmze the operaton at ea load state, and thus to aeve the maxmum arbtrage beneft. The optmzed

10 10 operaton allows utltes operators smply control the unts based on the measurement of system load magntude only,.e. wthout any further utlzaton of advanced forecastng modules and controllers. A sample case study was presented, and three dfferent cases are dscussed. Moreover, three storage tenologes were compared and measured aganst a base case wth no nstallaton. The results were shown to be dependent on the system under study, e.g., type and sze of exstng DGs. evertheless, the results showed that ntegratng unts wth dstrbuton systems reduces the total costs of utltes because of ther capacty to shave peak load. However, the results mght be more promsng f storage costs become less n the future, or other benefts of ESS are consdered, su as the mprovement of dstrbuton system relablty and the mtgaton of power qualty problems. VIII. REFERECES [1] C. Chen, S. Duan, T. Ca, B. Lu, and G. Hu, "Optmal allocaton and economc analyss of energy storage system n mcrogrds," IEEE Transactons on Power Electroncs, vol. 26, no. 10, pp , Oct [2] R. B. Sanker, "Executve overvew: energy storage optons for a sustanable energy future," n IEEE Power Engneerng Socety General Meetng, pp Vol.2, 6-10 Jun [3] (2011). BC Hydro breaks ground on nnovatve clean energy project, Avalable: project_golden_feld.html [4] (2013). Introducng the frst urban communty energy storage project, Avalable: untyenergystorage.aspx [5] H. Bludszuwet and J. A. Domnguez-avarro, "A Probablstc Method for Energy Storage Szng Based on Wnd Power Forecast Uncertanty," IEEE Transactons on Power Systems, vol. 26, no. 3, pp , Aug [6] Y. M. Atwa and E. F. El-Saadany, "Optmal Allocaton of ESS n Dstrbuton Systems Wth a Hgh Penetraton of Wnd Energy," IEEE Transactons on Power Systems, vol. 25, no. 4, pp , ov [7] M. Korpaas, A. T. Holen, and R. Hldrum, "Operaton and szng of energy storage for wnd power plants n a market system," Internatonal Journal of Electrcal Power & Energy Systems, vol. 25, no. 8, pp , Oct [8] A. S. A. Awad, T. H. M. El-Fouly, and M. M. A. Salama, "Optmal ESS Allocaton and Load Sheddng for Improvng Dstrbuton System Relablty," to appear at IEEE Transactons on Smart Grd. [9] C. Abbey and G. Joos, "A Stoastc Optmzaton Approa to Ratng of Energy Storage Systems n Wnd-Desel Isolated Grds," IEEE Transactons on Power Systems, vol. 24, no. 1, pp , Feb [10] S. X. Chen, H. B. Goo, and M. Q. Wang, "Szng of Energy Storage for Mcrogrds," IEEE Transactons on Smart Grd, vol. 3, no. 1, pp , Mar [11] F. A. Chacra, P. Bastard, G. Fleury, and R. Clavreul, "Impact of energy storage costs on economcal performance n a dstrbuton substaton," IEEE Transactons on Power Systems, vol. 20, no. 2, pp , May [12] R.-C. 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Rohatg, "Recloser allocaton for mproved relablty of DG-enhanced dstrbuton networks," IEEE Transactons on Power Systems, vol. 21, no. 3, pp , Aug [18] S. Kannan, S. M. R. Sloanal, and. P. Padhy, "Applcaton and comparson of metaheurstc tenques to generaton expanson plannng problem," IEEE Transactons on Power Systems, vol. 20, no. 1, pp , Feb [19] C. Grgg, P. Wong, P. Albret, R. Allan, M. Bhavaraju, R. Bllnton, Q. Chen, C. Fong, S. Haddad, S. Kuruganty, W. L, R. Mukerj, D. Patton,. Rau, D. Reppen, A. Sneder, M. Shahdehpour, and C. Sngh, "The IEEE Relablty Test System A report prepared by the Relablty Test System Task Force of the Applcaton of Probablty Methods Subcommttee," IEEE Transactons on Power Systems, vol. 14, no. 3, pp , Aug [20] Y. M. Atwa and E. F. El-Saadany, "Probablstc approa for optmal allocaton of wnd-based dstrbuted generaton n dstrbuton systems," IET Renewable Power Generaton, vol. 5, no. 1, pp , Jan [21] HydroOne. Dstrbuted generaton tencal nterconnecton requrements, Avalable: [22] Market Summares, Avalable: [23] G. M. Masters, Renewable and Effcent Electrc Power Systems: Y: IEEE/Wley Interscence, [24] B. Craenen, A. Eben, and E. Maror, "How to handle constrants wth evolutonary algorthms," Practcal Handbook of Genetc Algorthms: Applcatons, pp , [25] B. Venkatesh, R. Ranjan, and H. B. Goo, "Optmal reconfguraton of radal dstrbuton systems to maxmze loadablty," IEEE Transactons on Power Systems, vol. 19, no. 1, pp , Feb [26] S. Wong, K. Bhattaarya, and J. D. Fuller, "Electrc power dstrbuton system desgn and plannng n a deregulated envronment," IET Generaton, Transmsson & Dstrbuton, vol. 3, no. 12, pp , Dec [27] S. Soenung and C. Burns, "Utlty energy storage applcatons studes," IEEE Transactons on Energy Converson, vol. 11, no. 3, pp , Sep [28] P. Poonpun and W. T. Jewell, "Analyss of the Cost per Klowatt Hour to Store Electrcty," IEEE Transactons on Energy Converson, vol. 23, no. 2, pp , Jun Ahmed S. A. Awad (S 11) receved the B.Sc. and the M.Sc. degrees n electrcal engneerng from An Shams Unversty, Caro, Egypt, n 2007 and 2010, respectvely. He s currently pursung the Ph.D. degree n the Department of Electrcal and Computer Engneerng, Unversty of Waterloo, Waterloo, O, Canada. In between September 2007 and 2009, he worked as an electrcal desgn engneer wth Dar El-Handasah (Shar and partners) and Alled Consultants Co. n Egypt. Snce 2008, he has been workng wth the Department of Electrcal Power and Manes Engneerng, An Shams Unversty, Caro, Egypt, where he s currently on a study leave untl he receves the Ph.D. degree. Hs resear nterests nclude applcaton of energy storage n smart grds, ntegraton of renewable energy resources, electrcty market equlbrum, as well as operaton and control of dstrbuton systems.

11 11 Tarek H. M. EL-Fouly (M 02) receved the B.Sc. and M.Sc. degrees n electrcal engneerng from An Shams Unversty, Caro, Egypt, n 1996 and 2002, respectvely, and the Ph.D. degree n electrcal engneerng from the Unversty Of Waterloo, Waterloo, O, Canada, n He joned CanmetEERGY, atural Resources Canada, n 2008, as a Transmsson and Dstrbuton Resear Engneer, where he s conductng and managng resear actvtes related to actve dstrbuton networks, mcrogrds and remote communtes. In 2010, he was apponted as Adjunct Assstant Professor at the Electrcal and Computer Engneerng Department, Unversty of Waterloo. Hs resear nterests nclude protecton and coordnaton studes, ntegraton of renewable energy resources, smart mcrogrds, smart remote communty applcatons, demand sde management, and forecastng. M. M. A. Salama (F 02) receved the B.Sc. and M.Sc. degrees n electrcal engneerng from Caro Unversty, Caro, Egypt, n 1971 and 1973, respectvely, and the Ph.D. degree n electrcal engneerng from the Unversty of Waterloo, Waterloo, O, Canada, n Currently, he s a Professor n the Department of Electrcal and Computer Engneerng, Unversty of Waterloo, Waterloo, O, Canada. He has consulted wdely wth government agences and the electrcal ndustry. He s a regstered Professonal Engneer n the Provnce of Ontaro. Hs resear nterests nclude the operaton and control of dstrbuton systems, power-qualty montorng and mtgaton, asset management, and electromagnetcs.