720 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 6, NO. 3, JULY k 1,k 2. p min. i p max. t m. u it. e c t g it s t

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1 720 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 6, NO. 3, JULY 2015 Generaton Dspatch Technques for Remote Communtes Wth Flexble Demand Juan Claver, Franços Bouffard, Senor Member, IEEE, Dmtry Rmorov, Student Member, IEEE, and Géza Joós, Fellow, IEEE Abstract Remote communtes are typcally solated from the man electrcty grd and requre local generaton, most often relyng on expensve resources (especally desel) to supply ther load. The economc and logstcal aspects are such that there s value n explorng dfferent approaches to reduce the consumpton of desel and to ncrease the energy nput from local renewables. In ths paper, we focus on usng the vrtual storage capabltes of the demand sde to perform desel generaton optmzaton. Specfcally, we revst the economc dspatch (ED) problem by adaptng t to the presence of flexble demand. We compare three dfferent formulaton approaches: 1) where demand s reallocated heurstcally to shave the peak; 2) where the reallocaton s tself optmzed; and 3) that attempts to optmze the overall effcency of the desel unts. A case study based upon a remote mcrogrd shows that flexble demand can decrease desel fuel consumpton n an economcally meanngful manner, whch s stll sgnfcant gven the costs assocated wth the purchase and haulage of desel to these small communtes. Index Terms Demand response (DR), dstrbuted generaton, economc dspatch (ED), mcrogrds, power generaton economcs, remote communtes. NOMENCLATURE The man symbols used n ths paper are defned below. Others wll be defned as requred n the text. A. Indces Index of desel generatng unts runnng from 1 to I. t Index of tme perods runnng from 1 to T. B. Parameters d t Forecasted electrcty demand n perod t (kw). ˆd Yearly peak electrcal load (kw). Maxmum effcency output of desel unt (kw). g Manuscrpt receved June 12, 2014; revsed October 14, 2014 and January 28, 2015; accepted February 25, Date of publcaton Aprl 03, 2015; date of current verson June 17, Ths work was supported by the Natural Scences and Engneerng Research Councl of Canada, Ottawa, ON, Canada through fundng from the NSERC Smart Mcrogrd Network. Paper no. TSTE J. Claver s wth GE Dgtal Energy, Montreal, QC H4S 2A1, Canada (e-mal: juan.claver@ge.com). F. Bouffard s wth the Department of Electrcal and Computer Engneerng, McGll Unversty, Montreal, QC H3A 0E9, Canada, and also wth the Groupe d études et de recherche en analyse des décsons (GERAD), Montreal, QC H3T 1J4, Canada (e-mal: francos.bouffard@mcgll.ca). D. Rmorov and G. Joós are wth the Department of Electrcal and Computer Engneerng, McGll Unversty, Montreal, QC H3A 0E9, Canada (e-mal: dmtry.rmorov@mal.mcgll.ca; geza.joos@mcgll.ca). Color versons of one or more of the fgures n ths paper are avalable onlne at Dgtal Object Identfer /TSTE k 1,k 2 p mn p max t 0 t m u t Factors lmtng the rate of load curtalment or reallocaton (p.u.). Mnmum output power of desel unt (kw). Maxmum output power of desel unt (kw). Frst perod of demand curtalment avalablty (h). Maxmum number of perods curtaled demand can be wthheld for (h). Commtment status of desel unt n perod t (u t =0f OFF, u t =1f ON). γ Porton of curtallable demand at the peak (%). Δ Duraton of one tme perod (h). C. Varables d t Effectve load suppled by desel unt n perod t (kw). e a t Demand avalable for curtalment n perod t (kwh). Demand actually curtaled n perod t (kwh). e c t g t s t Power output of desel unt n perod t (kw). Demand curtalment/reallocaton n perod t (kw); s t < 0 when demand s curtaled and s t > 0 when demand s reallocated. D. Functons B ( d t ) Vrtual beneft assocated wth desel unt n perod t f generatng d t (l). C (g t ) Actual fuel consumpton of desel unt n perod t (l). C (g t ) Average fuel consumpton of desel unt n perod t (l/kwh). C (g t) Margnal fuel consumpton of desel unt n perod t (l/kwh). I. INTRODUCTION R EMOTE communtes are characterzed by solaton from the man electrcty grd and mostly use desel plants for ther energy provson [1]. Thus, remote locaton from the man transport hubs and major utltes makes those communtes dependent on volatle and hgh fuel prces and assocated transportaton costs. The economc and logstcal aspects are such that there s value n explorng dfferent approaches to reduce the consumpton of desel and potentally to ncrease the energy nput from local renewables. Numerous technologes are avalable to help remote grd operators and planners to reduce desel fuel dependency and costs. Demand response (DR), understood to be an ntegral part IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

2 CLAVIER et al.: GENERATION DISPATCH TECHNIQUES FOR REMOTE COMMUNITIES WITH FLEXIBLE DEMAND 721 Fg. 1. Example solated power system [5]. of the smart grd paradgm [2], s one of those technologes. It provdes an addtonal degree of flexblty to grd operatons whch can be leveraged nto fuel savngs. It s usually defned as a process of voluntary [3] or automatc [4] adjustment of electrcty consumpton that results n a devaton from expected consumpton patterns. DR can be trggered n response to varous sgnals, such as changes n electrcty prces, relablty alerts, etc. Automatc DR s mplemented through drect load control [5], whereas voluntary DR requres customer decsonmakng and acton n ts mplementaton. The purpose of ths paper s to compare dfferent economc dspatch (ED) technques ntegratng drect load control to mprove solated system performance. We consder three dfferent formulatons of the optmzaton problem: 1) daly producton cost mnmzaton wth DR as an addtonal decson varable; 2) producton cost mnmzaton wth targeted DR actons for daly peak shavng; and 3) a control polcy ncorporatng DR whose role s to maxmze the effcency of fuel usage. An exstng solated DR-desel power system [5], [6] was selected as the benchmark of the study as t fts the scenaro of nterest here, and t reflects ssues of typcal Canadan rural communtes. Fg. 1 llustrates ths system. A. Lterature Revew Several technques have been proposed for schedulng DR systems n solated networks [7] [15]. Although models used n those references vary n ther level of sophstcaton (e.g., wth respect to system dynamcs or the stochastc nature of loads and renewable sources), we dentfy three man groups of methods for schedulng flexble demand. Publcatons [7] through [10] address the problem of schedulng controllable loads by performng a producton cost mnmzaton. References [11] and [12] mplement evolutonary and genetc algorthms to fnd the approprate allocaton of resources. Authors from [13] [15] solve the storage optmzaton problem by mportng the prncples of game theory nto a flexble load supply problem. In contrast, for our formulaton, the ntroducton of flexble demand s ntended solely for the purpose of mprovng the effcency of one or multple thermal generators by seekng for ther nherent mnmum short-run average cost, a topc yet to be explored for an solated system. B. Contrbutons The man contrbuton of ths paper s the desgn and mplementaton of a new polcy-based approach for schedulng controllable loads n a desel-powered solated grd. The proposed algorthm does not rely on the forecasted varables of the network, but utlzes predefned rules to allocate the avalable resources wth the objectve of optmzng desel generaton effcency based on the observed demand and avalable DR resources. Valdaton evdence s provded to demonstrate the mert of our proposal. We compare our approach to the classc daly cost mnmzaton problem of [8] as adapted to the context and ssues of a desel-dr case. Another comparson s performed aganst the more practcal method found n [6]. C. Paper Organzaton The structure of the paper s as follows. Secton II dscusses the scope and lmtatons of the current study as t formulates the problem to be solved. Secton III descrbes optmzaton methods mplemented n the paper. Secton IV proposes a case study for the comparson, whle Secton V contans the results analyss and dscusson. Secton VI concludes and summarzes fndngs of the paper. II. PROBLEM FORMULATION The representaton of an solated generaton-responsve load system (such as what s found n Fg. 1) s assembled n ths secton. A. Assumptons Frst, the objectve of ths paper s for the operator of the solated power system to mnmze the consumpton of fuel (.e., desel here.) We do not consder the cost of producton but rather the correspondng fuel consumpton. Costs can be obtaned through multplcaton of the consumpton wth the prce of desel fuel. Ths practce s often used when dealng wth fuel-based generaton systems. Second, we assume that the system s lossless as the types of network n queston here have small geographcal footprnts. Fnally, voltage and reactve power set pont ssues are neglected as we focus our attenton on actve power optmzaton. B. Generaton As just mentoned, the goal of the solated power system operator s to mnmze the system s fuel consumpton (n lters) of all ts generatng unts ( =1,...,I) over a tme wndow of several perods (t =1,...,T) T T mn C (u t,g t )= c 0 u t + a g t b gt 2 t=1 t=1 where the generatng unt commtment status values u t are assumed known and where the parameters c 0 (l/h), (1)

3 722 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 6, NO. 3, JULY 2015 a (l/kwh) and b (l/kw 2 h) are nferred from generatng unts performance measurements or ther manufacturer data sheets. The generatng unts outputs g t (for =1,...,I)have restrctons on ther range of operaton u t p mn g t u t p max (2) n each of the tme perods t =1,...,T, where p mn and p max are, respectvely, the mnmum and maxmum output levels for the system s generatng unts. C. Load The system load here has two components: a fxed one and another wth lmted flexblty allowng t to change n response to external sgnals. The modelng of ths flexblty s ntroduced through constrants and extra decson varables n generaton dspatch problem formulatons. The specfc assumptons regardng the nature of the flexble demand here nclude the followng. 1) Flexble demand conssts of loads that can be curtaled at some specfc tme, but whch must be redspatched n a later perod [16]. Such curtalment/recovery cycles may be restrcted to happen over prescrbed tme wndows (e.g., startng at t 0 and fnshng t m perods later). 2) Demand s flexble over a contnuous range whose maxmum s equal to a porton of the system s yearly peak,.e., γ ˆd. 3) Effcency losses assocated wth energy consumpton tme shftng are neglected whle response fatgue s not consdered. These assumptons are made to smplfy the presentaton so to focus on the dfferent dspatch approaches rather than on specfc flexble load features. Of course, the tghtenng of any of those constrants would lead to hgher operatng costs. Flexble load s often seen as vrtual storage because t can delay or advance energy consumpton [17]. However, unlke storage systems, flexble load generally requres tmng constrants on the potental demand advance or delay. Here the type of load most capable of provdng ths type of flexblty are thermostatcally controlled loads, e.g., electrc water heaters, space heatng, ar condtonng, etc. Those applances can be nterrupted automatcally wthout drect acton of consumers. Flexble demand s thus constraned by energy lmts over curtalment recovery tme wndows of length t m, where for all t (t 0,t 0 + t m ] the runnng curtaled energy tally (e c t) must be below the maxmum curtalable energy e c t = t 1 τ=t 0 s τ Δ γ ˆdΔ (3) where varables s τ represent demand curtaled (f negatve) or reallocated (f postve) durng perod τ, and symbols Δ, ˆd and γ represent, respectvely, the duraton of one dspatch tme step, the yearly peak electrcty demand and the porton of the peak demand that can be curtaled. Note that f t 0 =1and t m = T demand s avalable for curtalment/recovery at any tme durng the plannng horzon. Over tme wndows of t m perods, however, the runnng energy tally has to balance out t 0+t m τ=t 0 s τ Δ=0. (4) Ths constrant of operaton requres that at the end of a cycle of operaton of the DR system, any curtaled demand has to be dspatched completely n order to mantan the mnmum comfort/productvty level of the flexble demand usage [16]. In addton, we defne the resdual (avalable) curtalable load e a t for all t (t 0,t 0 + t m ] as e a t = γ ˆdΔ e c t. (5) The quantty e a t s used to track how much load s avalable for curtalment and wll be used n later stages of the paper as a new generaton dspatch problem varable. Fnally, we establsh bounds on how much demand can be curtaled or reallocated n any tme perod t ( ) mn k 1 γ ˆd, ea t Δ s t mn ( ) k 2 γ ˆd, ec t Δ where the lower bound s the smallest value between k 1 γ ˆd and the load s resdual flexble power e a t /Δ, and the upper bound s the largest among k 2 γ ˆd and the current value of the energy curtalment tally e c t/δ. Here, constants k 1 and k 2 are n the range [0, 1] and are ted to power consumpton lmtatons of the flexble demand assets. It s mportant to underlne that decreasng the operatonal costs n remote communty electrcty supply systems does not necessarly need to be ncentvzed through real-tme prcng. The ncentve here les essentally wth the utlty that has to decrease ts fuel supply costs. The ncentve on the sde of the consumers s not as tangble, however. Generally, n solated systems, nonetheless, consumers are well aware of the partcular stuaton of ther electrcty supply system, and they are ready to accept more readly modulatons of ther consumpton. Ths s especally the case when generatng capacty s lmted and when envronmental concerns motvate the need for flexblty on the sde of the consumers. D. Economc Dspatch Classcally, ED reles on an observaton or a short-term forecast of the load d t over the full duraton a generaton plannng horzon. It nvolves fndng g t for all generatng unts and all tme perods t mplementng the objectve of (1) whle satsfyng generaton lmts (2) and the system power balance (6) g t = d t, t =1,...,T. (7) If no generatng unts tme couplngs are consdered, e.g., ramp and energy constrants, ths problem can be separated and solved at every tme step t ndependently. Ths s generally how ED s conducted n practcal contexts where an observaton of the system load or a short-term predcton of the load s used

4 CLAVIER et al.: GENERATION DISPATCH TECHNIQUES FOR REMOTE COMMUNITIES WITH FLEXIBLE DEMAND 723 to drve ths process. Otherwse, f the unts tme couplngs are explct, the ED has to adopt a dynamc or recedng horzon approach, such as n [18], whereby the dspatch decsons at the current tme are constraned by the expected realzaton of the load movng forward n tme (e.g., up to 24 h n the future). Ths s the case when DR and energy storage mechansms are consdered, snce those have tme dynamcs whch need to be properly represented and constraned as part of the ED process. It s mportant also to acknowledge here the mportance of unt commtment n allowng solated system dspatchers to take approprate decsons durng real-tme operaton. Unt commtment solutons are obtaned pror to dspatch wth the objectve of guaranteeng that there s a very low probablty of a generatng capacty shortage or oversupply for some antcpated demand level. In the case of small solated systems, unt commtment algorthms are often rule-based, and may not be optmal from a dspatch operatons perspectve, as seen later n Secton IV. An extensve dscusson of unt commtment remans nonetheless out of the scope of ths paper whose focus s prmarly on ED. Currently, dynamc/recedng horzon ED problem formulatons are what we shall call offlne approaches. These problem formulatons are all solved ahead of tme as operatonal plannng steps. They rely on the avalablty of accurate load forecasts, and they need the support of approprate optmzaton software and computng hardware. On the other hand, onlne heurstc/operatng polcy soluton approaches, whch rely only on a lmted tme look ahead, allow for an approxmate soluton wthout the need to solve the dspatch problem over the entre (uncertan) horzon n a sngle problem. The latter approach s attractve n cases where there s sgnfcant uncertanty over the future load (and potentally varable and ntermttent renewable sources operatng alongsde the fossl-fuel generatng unts), whch warrants more onlne redspatch. Ths s also the case when some mnor loss of optmalty may be tolerable and n small systems where more rule-based approaches may be acceptable. The former s usually more sutable for large systems where there s a wder set of generaton resources, smoother load uncertanty, and where sgnfcant optmalty losses are not justfable. III. FLEXIBLE LOAD IN ED FOR ISOLATED SYSTEMS In the context of an solated network, desel fuel consumpton mnmzaton s a prmary objectve of the system operator. In the followng sectons, we present three specfc approaches for achevng ths whle takng nto account the potental contrbuton of flexble load toward that goal. 1) As a benchmark, we frst present the classc (offlne) mnmum producton cost dspatch that entals perfect foresght over the values of the load throughout the plannng horzon. 2) We contrast the above approach to a smplfed offlne peak shavng dspatch. 3) We ntroduce a new onlne dspatch approach that leverages the propertes of average cost curves of desel generators. A. Producton Cost Optmzaton (PCO) The man feature of ths problem formulaton (adapted from [8] and [19]) s to mnmze the total cost of operatng the system for the entre plannng horzon. In addton to the objectve functon (1) and the constrants descrbed n Secton II, (2) (6), ths problem formulaton requres the modfcaton of the power balance (7) g t s t = d t, t =1,...,T. (8) Ths problem formulaton consders all the features of generaton and of the flexble demand n an ntegrated fashon wth all the explct tme couplngs arsng from the consderaton of flexble demand. The PCO problem formulaton s a convex quadratc optmzaton problem because all ts constrants [(2) (6) and (8)] are lnear and ts objectve functon (1) s a quadratc n the generaton outputs wth a 0 and b 0 for all. Therefore, computatonal cost should not be an ssue for most solated systems. In addton, f a perfect load forecast s avalable, ths formulaton would lead to the least fuel consumpton over the plannng horzon. It remans, however, that obtanng good load forecasts for small solated systems s a challenge. Frst, load forecastng n small systems can be challengng because the cost of obtanng a forecast may be prohbtve. Moreover, the accuracy of load forecasts n small solated power systems (wth N 10 2 customers) cannot be as good as n typcal large power systems where the number of consumers s much larger (e.g., wth N>10 4 customers.) Ths s smply due to the fact that sample varance s nversely proportonal to N 1. Thus, as PCO reles on load forecasts, ts results may, n fact, be far from optmal n the event where ts load forecast s off. Gven that forecast errors are more sgnfcant n small solated systems, the PCO dspatch approach s more senstve to those errors when compared to forecast-free dspatch strateges. B. Peak Shavng Optmzaton (PSO) The DR system mplemented n [5] and [6] s based on predctng the tmng of the peak load durng a gven day and shavng t off (and reallocatng t for later) usng flexble demand. A smlar approach s adopted n ths secton, but wth dfferent tmeframes for peak duraton and redspatchng perods. Ths approach s computatonally smpler than the full PCO formulaton because the demand reductons and reallocatons can only happen n a restrcted subset of perods that are determned for each day of the year. As a result, the cost savng potental of ths formulaton s not as hgh as wth PCO. Assumng that the peak demand s predcted to happen over the subset of hours T p {1,...,T} that s determned for each day and that consumpton recovery has to be performed over a subsequent subset of hours T r {1,...,T} followng the peak so that T p T r =, we mpose s t γ ˆd (9) t T p s t γ ˆd (10) t T r s t =0 (11) t T p T r

5 724 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 6, NO. 3, JULY 2015 and s t =0, t / T p T r. (12) Here, constrants (9) and (10) put an upper bound on the flexble demand that can be curtaled and re-allocated, respectvely. Constrant (11) ensures energy neutralty of the curtalment/reallocaton process, whle (12) ensures that flexble demand s not used outsde of the allowed tme range. As wth the PCO approach, the goal s to mnmze desel consumpton (1) whle meetng the power balance constrant (8) along wth the relevant restrctons on the operaton of flexble demand, namely (6) and (9) (12). Moreover, the qualty of the soluton here depends on the qualty of the load forecast over the plannng horzon. C. Average Cost Optmzaton (ACO) As mentoned before, the above two ED problem formulatons are essentally offlne operatonal plannng approaches whch requre a good predcton of load and the tmng of ts peak. As mentoned earler, obtanng good load predctons for small solated systems may be too expensve or smply not possble consderng the low number of ndvdual consumers n the system. Moreover, but to a lesser extent, these feedforward approaches requre suffcently good soluton codes and supportng computng hardware. The approach we develop next moves away from those needs and formulates the ED soluton as an ntegrated DR-generaton onlne heurstc control polcy based on real-tme observatons of system load. The premse of ths new approach s rooted n the prncples of the Theory of the Frm from mcroeconomcs [20]. One feature of the Theory of the Frm s that producton assets operate at maxmal effcency when mnmum average producton costs are attaned (.e., when the ratos of nputs to outputs are the lowest). Ths condton s also satsfed when margnal costs of producton are equal to the average costs see Fg. 2. Hence, what we propose here s to make use of the avalable flexble demand n a coordnated way to favor the applcaton of ths prncple to the system s desel generatng unts. In the context of an optmal DR-generaton dspatch scheme, ths problem s cast as the followng optmzaton problem: max T t=1 subject to, for all t =1,...,T B ( d t ) C (g t ) (13) g t = d t (14) d t = d t + s t (15) e c t = e c t 1 s t Δ (16) 0 e c t γ ˆdΔ (17) n addton to generatng unt lmts (2), the relatonshp between e c t and e a t (5), and the bounds on s t (6). Specfcally, Fg. 2. Illustraton of maxmal effcency operaton for generatng unt. C (g t ) represents the average producton cost of the unt, whle C (g t) s ts margnal generaton cost. Maxmum effcency operaton happens at g. ths problem attempts to maxmze the beneft for the generatng unts of carryng a vrtual porton d t of the system load B ( d t ) less the cost of actually operatng at g t, C (g t ).The amounts d t have to sum up to the total generaton n (14), whle n (15) t s requred that these vrtual generator load allocatons sum up to the current demand d t and the flexble demand curtalment/reallocaton decson s t. In (16), the curtaled load tally e c t s updated from ts value n the prevous perod e c t 1 through the current value of the s t decson. Fnally, e c t s bounded from above and below n (17). As t s cast, the above problem can be solved just lke PCO and PSO. However, our goal here s to establsh a heurstc polcy for settng the generaton and flexble load dspatch as a functon of the observed load. As a frst step toward ths, we can clam that f the followng property holds: db ( d t ) = db ( d t ) dg t d d d d t = t dg C (g t )= C (g t ) (18) t g t then the frst-order optmalty condton of the problem wth respect to g t can be wrtten as C (g t ) C (g t )+λ t μ t + μ t =0 (19) where C (g t ) and C (g t) are, respectvely, the average cost and margnal generaton cost functons of unt, and λ t, μ t and μ t are, respectvely, the Lagrange multplers assocated to the power balance (14) and to the upper and lower bounds on s t. From (19), f there are no actve lmts on s t [(6) or because of the bounds on e c t and e a t we can nfer the followng flexble demand curtalment/reallocaton rule for any perod t: s t = g d t (20) where g s defned as the generaton level of unt at whch maxmum unt effcency s acheved. If ths rule apples, ths entals also that generaton unt dspatches are gven by gt = g for each =1,...,I. That s, the flexble demand should be

6 CLAVIER et al.: GENERATION DISPATCH TECHNIQUES FOR REMOTE COMMUNITIES WITH FLEXIBLE DEMAND 725 used to balance generaton and load so that maxmum effcency operaton (.e., C (g t ) C (g t) =0) s ensured. In cases where s t s constraned by ether a lack of remanng curtalable capacty or a defct of load to reallocate, generatng unts have to be dspatched over the resdual demand of d t + s t usng the classc λ-teraton approach for sngle-perod ED descrbed n [25]. We expect, n general, that the avalable flexble demand capacty wll be large enough and that constrants on flexble demand capacty rarely become actve. Moreover, the relatve regularty n the cyclcalty of the demand should allow for the averagng out of the curtalment/reallocaton cycles of flexble demand. The man beneft of ths approach, asde from the fact that t does not need accurate load forecasts, s the maxmzaton of the operaton tme of the generatng unts at ther maxmum effcency ponts. An added beneft of ths approach should be the assocated reducton n the unts mechancal wear and tear as set pont changes should no longer be the norm. Fnally, we have here a smple decson rule whch only depends on the current state of the system. It s clear, however, that because the tme dynamcs assocated wth the use of DR are gnored, solutons should be myopc by httng capacty constrants more often, and DR use wll be suboptmal. Ths approach renforces the mportance on commttng approprate generaton capacty whch can match qute closely the forecasted demand when runnng at g for each. D. Dscusson: ACO Versus PCO and PSO In comparson, the dspatch solutons comng out of PCO and PSO may also be as suboptmal as those comng out of ACO. What ACO does s to optmally use the avalable DR and generaton capacty based on the avalable nformaton at run tme. Obvously, ts outcomes could be grossly optmstc or conservatve n lght of the future realzatons of demand. On the other hand, f the demand forecast nputs to PCO and PSO are erroneous, ther outcome may also be suboptmal movng forward n addton to that at the current tme. Ths s so because bad forecasts could contrbute to overly constran dspatch and DR use decsons taken at the current tme. The only way to properly address poor forecasts nto PCO and PSO s to consder stochastc optmzaton or stochastc dynamc programmng approaches n jontly dspatchng DR and generaton. These approaches are sure nonstarters for small systems especally because of ther much greater computatonal complexty and ther contnued relance on an expensve forecast and on the need to have an estmaton of the forecast naccuracy. ACO represents a good compromse between the need to have foresght when managng DR capacty whle stll adoptng a dspatch approach whch provdes an optmal decson at every step. Approaches smlar to ACO are used n other areas where there s a great deal of uncertanty over the future demands on a system. For example, ACO-lke approaches are used n battery management schemes for parallel hybrd vehcles whereby the nternal combuston engne s operated at optmal effcency, whle the battery buffers the drvng TABLE I FUEL CONSUMPTION DATA OF DIESEL GENERATING UNITS demands of the vehcle. In theory, f the complete drvng pattern (speed and torque aganst tme) for a gven trp s known ahead of tme, the jont operaton of the battery and nternal combuston engne could be optmzed exactly. Obvously, ths s not somethng whch s achevable n practce because of the great uncertanty over the true speed torque pattern assocated wth any trp. Ths s exactly what we argue here for the case of small solated power systems. As seen n the next secton, the loss of optmalty of ACO over PCO or PSO s mnute whle we use perfect forecasts for PCO and PSO. In our opnon, the ACO heurstc approach s as justfed as PCO and PSO because t grossly acheves the same savngs as the exact approaches usng much smpler setups. IV. CASE STUDY In ths secton, we present a case study based on a remote communty mcrogrd whch s fed by desel generatng unts. We compare fuel savngs assocated wth each of the three dspatch approaches ntroduced n the prevous secton and a DR-free benchmark. A. Test System Descrpton We consder the solated power system llustrated n Fg. 1 wth ts three desel generaton unts (G1, G2, and G3), an annual peak load of 420 kw. Table I provdes pont-wse average and margnal fuel consumpton nformaton about the three unts. Here, unts G1 and G3 are dentcal (wth p mn = 126 kw and p max = 420 kw for = G1, G3), wth the smaller unt G2 beng more expensve to operate and p mn G2 =63kW and p max G2 = 210 kw. The hourly varaton of the demand follows the pattern found n [23] whch s scaled to the system peak of 420 kw. In the case where the DR resource s avalable, ts capacty s equal to γ = 20% of the peak load. The unt commtment here s conducted heurstcally. G1 s assumed to be always on wth G3 on standby (whle not producng any energy) ready to swtch over n case of a falure of G1. G2 s turned ON whenever the demand exceeds 340 kw, as descrbed n [6]. If DR s avalable and enough load curtalment capacty s avalable, G2 does not need to be turned ON at such a low load level. In ths case, G2 s turned ON when the load d t less the avalable curtalable demand e a t s greater than 340 kw. As a result, G2 gets to operate less n the presence of DR.

7 726 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 6, NO. 3, JULY 2015 TABLE II ENERGY PRODUCED BY GENERATING UNITS AND FUEL CONSUMED IN YEAR 1 TABLE III ENERGY PRODUCED BY GENERATING UNITS AND FUEL CONSUMED IN YEAR 20 B. Smulaton Setup We smulate the operaton of the generaton system over ts assumed 20-year lfetme [24], takng an hourly tme step. Moreover, as years advance, we assume a 1% peak load growth. Four dstnct smulatons are carred out. Frst, we obtan fuel consumpton nformaton for runnng the system wthout any DR [base case (BC)]. The generators here are dspatched usng a classc λ-teraton n each of the hours. The next case consders the addton of DR and performs a dspatch for each day (24 consecutve hours) usng PCO where t s assumed that curtaled demand has to be reallocated wthn t m =3hours. The thrd case uses PSO wth the set T p preset for each day n such a way that t carres the three consecutve hours wth the hghest load. The correspondng load recovery nterval T r conssts of 3 h mmedately followng curtalment ntervals. Fnally, we smulate the use of ACO. In all cases, we assume perfect load forecasts. C. Results and Dscusson In Tables II and III, we present the total fuel consumpton of the system and of the peakng unt (G2) n the frst and last year of the system s lfetme. Also, n Fg. 3, we present a sample of three consecutve days durng week 30 of the frst year of operaton as decded by the three dspatch approaches of Secton III and for the BC. The traces n the upper part of the plot correspond to the output of G1 and those n the lower part to G2 s. The data here suggest that addtonal flexblty on the demand sde brngs benefts n terms of fuel cost savngs. Yet, for the frst year of the system lfetme, the mprovements are not sgnfcant as a consequence of the over-szng of the unts wth respect to the average annual electrc demand. Nonetheless, as load ncreases over the years, the system ends up operatng n a much effcent way as capacty s better utlzed (.e., generaton operates much closer to ts optmal effcency) The results allow for a comparson on the relatve performance between onlne (PCO and PSO) and offlne (ACO) methods. As expected, PCO yelds the best results snce t models well the tme dynamcs of the vrtual storage capacty offered by the flexble demand. Stll, n spte of ts much cruder representaton of the DR dynamcs, ACO s capable of provdng nterestng savngs through the applcaton of a smple heurstc. The unts dspatch can also dffer sgnfcantly for each type of the optmzaton method (see Fg. 3). It s mportant to menton that whle the offlne technques (PCO, PSO) tend to flatten the demand profle, ACO may create addtonal small demand peaks to force operaton of the system near to ts optmal pont. These happen because ACO does not have the fore vson that the other two approaches have. In the context here, where there s plenty of generaton capacty avalable, those extra peaks are nconsequental from a capacty pont of vew. What matters s that they contrbute toward maxmzng the effcency of the desel power generaton. The relatvely poor performance of the PSO approach can be explaned by the tme constrants put on the curtalment and reallocaton perods. As seen n the case study setup, the PSO approach consders only three consecutve peak hours (t m =3). Therefore, t cannot contrbute to shftng demand at all tmes of the day (lke PCO and ACO). Ths means that n cases where there are two or more daly peaks, the PSO approach remans qute lmted and cannot acheve better fuel savngs. As can be seen from Fg. 3, an ncrease n the energy dspatched by G1 was acheved for all three generaton-dr optmzaton approaches. In the case of the frst year, the PCO method yelds no energy dspatched by G2 as a consequence of the vrtual capacty enabled by the flexble demand. One observaton s that the unt commtment rule for G2 could be tuned better n lght of the vrtual capacty offered by the DR resource. As t stands, G2 s meant to start generatng when the net demand d t e a t reaches 80% of G1 s capacty. When comparng the average and margnal fuel consumptons of G1 and G2 n Table I, we can see that G2 s much more expensve than G1 per kwh. In fact, one should consder brngng n G2 when G1 s much closer to ts full capacty. Wth the same smulaton parameters as before, but ths tme wth G2 beng brought n when G1 operates at 95% of ts capacty (400 kw), smlar fuel savngs are acheved for each of the generaton-dr dspatch approaches even n year 1 see Table IV. More sgnfcant savngs obvously arse when loadng ncreases over the lfetme of the system. For sure, a more

8 CLAVIER et al.: GENERATION DISPATCH TECHNIQUES FOR REMOTE COMMUNITIES WITH FLEXIBLE DEMAND 727 Fg. 3. G1 dspatches n three consecutve days of operaton of week 30 (year 1): BC wthout use of flexble demand (BC), PCO, PSO, and ACO. TABLE IV ENERGY PRODUCED BY GENERATING UNITS AND FUEL CONSUMED IN YEAR 1 WITH UPDATED UNIT COMMITMENT LOGIC systematc unt commtment would help mprovng the performance of all three dspatch technques. It remans, however, that the heurstc unt commtment approach used here s frst and foremost targeted at provdng supply securty n the event of one unt falng. Therefore, unless a larger number of smaller unts are nstalled nstead of a few lumper unts, such neffcences wll happen and a more systematc unt commtment would not brng much more mprovement. Snce the results obtaned are hghly dependent on the load profle, the relatvely small value n acheved savngs s not fully representatve of the capabltes of flexble load. For example, a more pronounced dfference between daly peaks and valleys s lkely to result n greater savngs. Asde from pure economc benefts, DR can be seen as an effectve tool to enhance the operatonal effcency of remote communty networks, e.g., as a substtuton for dump loads. Addtonal vrtual capacty as a consequence of the ntegraton of a DR system accounts for most of the savngs observed n the case studes. Moreover, t was observed that the unt commtment rules affect the overall system performance sgnfcantly. Therefore, t s also mportant to sze generatng unts approprately so they are operated as close as possble to ther optmal effcency pont for the most part of the system lfetme. V. CONCLUSION Ths paper explored three dspatch technques for the schedulng of desel-powered solated systems wth DR. It was shown that a technque that targets solely peak perods s not able to acheve savngs n the same extent that technques that are specfcally desgned to mnmze the cost of operatng the system. Thus, these technques can be seen as a more approprate alternatve for the schedulng of solated networks. Among the technques proposed, the onlne ACO approach s able to acheve sgnfcant savngs even n comparson to the best possble approach (PCO) whch optmzes generaton and DR together over tme n a completely ntegrated fashon. The ACO approach, unlke the other offlne approaches, s a smple polcy heurstc whch does not requre sophstcated load predcton and optmzaton software and hardware. Ths feature should be of clear nterest to solated system planners and ther operators. Some suggestons regardng the future work nclude more realstc models of DR. Also, research n [5] and [7] suggests that often DR system s experence payback effects and load spkes durng the recovery perods. The ncluson of ths feature would provde a better valuaton of the potental of DR n solated systems. Fnally, we are consderng extensons of the dspatch approaches to solated systems where desel generaton s coupled to renewable generaton. In such cases, nondspatchable renewable generaton would merely be subtracted from the demand (.e., to obtan the system s net load), requrng no sgnfcant change to the dspatch technques presented. As the renewable generaton s essentally free, the desel generaton would be dspatched to cover the net load, along wth flexble load playng the same role n attemptng to reduce fuel consumpton.the ncluson of nondspatchable generaton would renforce the practcal value of the ACO approach, as t does not have to rely on fne predcton of both load and renewable generaton. ACKNOWLEDGMENT J. Claver would lke to thank M. Momen from McGll Unversty and S. Wong from Natural Resources Canada for ther useful suggestons and contrbutons to the paper.

9 728 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 6, NO. 3, JULY 2015 REFERENCES [1] C. Abbey, W. L, and G. Joós, An onlne control algorthm for applcaton of a hybrd ESS to a wnd-system, IEEE Trans. Ind. Electron., vol. 57, no. 12, pp , Dec [2] P. Palensky and D. Detrch, Demand-sde management: Demand response, ntellgent energy systems, and smart loads, IEEE Trans. Ind. Informat., vol. 7, no. 3, pp , Aug [3] H. Saele and O. S. Grande, Demand response from household customers: Experences from a plot study n Norway, IEEE Trans. Smart Grd, vol. 2, no. 1, pp , Mar [4] K. Detrch, J. M. Latorre, L. Olmos, and A. Ramos, Demand response n an solated system wth hgh wnd ntegraton, IEEE Trans. Power Syst., vol. 27, no. 1, pp , Feb [5] M. Wrnch, G. Denns, T. H. M. El-Fouly, and S. Wong, Demand response mplementaton for mproved system effcency n remote communtes, n Proc. 12th Elect. Power Energy Conf.,London,ON,Canada, Oct. 2012, pp [6] M. Wrnch, G. Denns, T. H. M. El-Fouly, and S. Wong, Demand response mplementaton for remote communtes, n Proc. 11th Elect. Power Energy Conf., Wnnpeg, MB, Canada, Oct. 2011, pp [7] S. J. Ahn, S. R. Nam, J. H. Cho, and S. I. Moon, Power schedulng of dstrbuted generators for economc and stable operaton of a mcrogrd, IEEE Trans. Smart Grd, vol. 4, no. 1, pp , Jan [8] P. Brown, J. Lopes, and M. Matos, Optmzaton of pumped storage capacty n an solated power system wth large renewable penetraton, IEEE Trans. Power Syst., vol. 23, no. 2, pp , May [9] E. Mayhorn et al., Optmal control of dstrbuted energy resources usng model predctve control, n Proc. IEEE Power Energy Soc. Gen. Meetng, San Dego, CA, USA, Jul. 2012, pp 1 8. [10] H. S. Oh, Optmal plannng to nclude storage devces n power systems, IEEE Trans. Power Syst., vol. 26, no. 3, pp , Aug [11] S. Cont, R. Ncolos, S. A. Rzzo, and H. H. Zeneldn, Optmal dspatchng of dstrbuted generators and storage systems for MV slanded mcrogrds, IEEE Trans. Power Del., vol. 27, no. 3, pp , Jul [12] T. Logenthran, D. Srnvasan, and T. Z. Shun, Demand sde management n smart grd usng heurstc optmzaton, IEEE Trans. Smart Grd, vol. 3, no. 3, pp , Sep [13] A. Pantoja and N. Qujano, A populaton dynamcs approach for the dspatch of dstrbuted generators, IEEE Trans. Ind. Electron., vol. 58, no. 10, pp , Oct [14] A. Mohsenan-Rad, V. Wong, J. Jatskevch, R. Schober, and A. Leon- Garca, Autonomous demand-sde management based on game-theoretc energy consumpton schedulng for the future smart grd, IEEE Trans. Smart Grd, vol. 1, no. 3, pp , Sep [15] I. Atzen, L. G. Ordonez, G. Scutar, D. P. Palomar, and J. R. Fonollosa, Demand-sde management va dstrbuted energy generaton and storage optmzaton, IEEE Trans. Smart Grd, vol. 4, no. 2, pp , Jun [16] E. Karangelos and F. Bouffard, Towards full ntegraton of demandsde resources n jont forward energy/reserve electrcty markets, IEEE Trans. Power Syst., vol. 27, no. 1, pp , Feb [17] G. Strbac, Demand sde management: Benefts and challenges, Energy Polcy, vol. 36, no. 12, pp , Dec [18] L. Xe and M. D. Ilć, Model predctve economc/envronmental dspatch of power systems wth ntermttent resources, n Proc. IEEE Power Energy Soc. Gen. Meetng, Calgary, AB, Canada, Jul. 2009, pp [19] E. D. Castronuovo and J. A. Peças Lopes, On the optmzaton of the daly operaton of a wnd-hydro power plant, IEEE Trans. Power Syst., vol. 19, no. 3, pp , Aug [20] D. S. Krschen and G. Strbac, Fundamentals of Power System Economcs. Hoboken, NJ, USA: Wley, [21] A. Gómez-Expósto, A. J. Conejo, and C. Cañzares, Electrc Energy Systems: Analyss and Operaton. Boca Raton, FL, USA: CRC Press, [22] J. Claver, M. Ross, and G. Joós, Dspatch technques for Canadan remote communtes wth renewable sources, n Proc. 13th Elect. Power Energy Conf., Halfax, NS, Canada, Aug. 2013, pp [23] Relablty Test System Task Force, The IEEE relablty test system 1996, IEEE Trans. Power Syst., vol. 14, no. 3, pp , Aug [24] G. Y. Morrs, C. Abbey, S. Wong, and G. Joós, Evaluaton of the costs and benefts of mcrogrds wth consderaton of servces beyond energy supply, nproc. IEEE Power Energy Soc. Gen. Meetng, San Dego, CA, USA, Jul. 2012, pp [25] A. J. Wood and B. F. Wollenberg, Power Generaton, Operaton and Control, 2nd ed. New York, NY, USA: Wley, Juan Claver receved the B.Eng. degree n electrcal engneerng from the Smon Bolvar Unversty (USB), Caracas, Venezuela, n 2008, and the M.Eng. degree n electrcal engneerng from McGll Unversty, Montreal, QC, Canada, n He s currently enrolled n the Edson Engneerng Development Program (EEDP) at GE Dgtal Energy, Montreal, QC, Canada. Franços Bouffard (S 99 M 06 SM 15) receved the B.Eng. (Hon.) and Ph.D. degrees n electrcal engneerng from McGll Unversty, Montreal, QC, Canada, n 2000 and 2006, respectvely. In 2006, he took up a Lectureshp wth the School of Electrcal and Electronc Engneerng, Unversty of Manchester, Manchester, U.K. In 2010, he joned McGll Unversty as an Assstant Professor. Hs research nterests nclude the felds of power system modelng, economcs, relablty, control, and optmzaton. Dr. Bouffard s a Lcensed Engneer n the provnce of Québec, Canada. He s an Edtor of the IEEE TRANSACTIONS ON POWER SYSTEMS, and he chars the System Economcs Subcommttee of IEEE PES. Dmtry Rmorov (S 14) receved the B.Eng. (Hon.) and M.Eng. (Hon.) degrees n electrcal engneerng from Moscow Power Engneerng Insttute (MPEI), Moscow, Russa, n 2010 and 2012, respectvely. He s currently workng toward the Ph.D. degree n electrcal engneerng at McGll Unversty, Montreal, QC, Canada. Hs research nterests nclude power system analyss, and power system stablty and control. Géza Joós (M 82 SM 89 F 06) receved the M.Eng. and Ph.D. degrees n electrcal engneerng from McGll Unversty, Montreal, QC, Canada. He has been wth McGll Unversty as a Professor snce He s nvolved n fundamental and appled research related to the applcaton of hgh-power electroncs to power converson, ncludng dstrbuted generaton and power systems. He was also wth ABB, the Unversty of Quebec, Sante-Foy, QC, and wth Concorda Unversty, Montreal, Canada. He has been nvolved n consultng actvtes n Power Electroncs and Power Systems, and wth CEA Technologes as the Technology Coordnator of the Power Systems Plannng and Operatons Interest Group. He has authored extensvely and presented numerous papers and tutorals on these topcs. Dr. Joós s a Fellow of the Canadan Academy of Engneerng. He s actve n a number of IEEE Industry Applcatons Socety commttees and n IEEE Power Engneerng & Energy Socety and Internatonal Councl on Large Electrc Systems (CIGRE) actvtes and workng groups that deal wth power electroncs and applcatons to dstrbuted resources.