Optimal DR and ESS Scheduling for Distribution Losses Payments Minimization Under Electricity Price Uncertainty

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1 1 Opmal DR and ESS Schedulng for Dsrbuon Losses Paymens Mnmzaon Under Elecrcy Prce Uncerany Alreza Soroud, Member, IEEE, Perlug Sano, Senor Member, IEEE Andrew Keane, Senor Member, IEEE Absrac The dsrbuon nework operaor s usually responsble for ncreasng he effcency and relably of nework operaon. The arge of acve loss mnmzaon s n lne wh effcency mprovemen. However, hs approach may no be he bes way o decrease he losses paymens n an unbundled marke envronmen. Ths paper nvesgaes he dfferences beween loss mnmzaon and loss paymen mnmzaon sraeges. I proposes an effecve approach for decreasng he losses paymen consderng he unceranes of elecrcy prces n a day ahead energy marke usng energy sorage sysems and demand response. In order o quanfy he benefs of he proposed mehod, he evaluaon of he proposed echnque s carred ou by applyng on a -bus dsrbuon nework. Index Terms Acve losses, demand response, energy sorage sysem, robus opmzaon, uncerany. NOMENCLATURE For quck reference, he man noaon used hroughou he paper s saed n hs secon. A. Ses and Indces l Ω L Ω ESS Ω DR Ω n Ω T B. Parameers Index for nework buses. Index for nework feeders. Index for operaon nervals. Se of lnes n dsrbuon nework Se of nodes conanng ESS Se of nodes parcpang n demand response Se of all nework nodes Se of me perods θ j Angle of j h elemen of admance marx. Conservaveness degree of decson maker regardng he prce uncerany. ǫ Cural-able percen of energy of demand n node. η ch/dch Effcency of chargng and dschargng of ESS (%). λ f/a Forecas/acual value of elecrcy prce a me ($/MWh). (P/Q) D, Inal acve/reacve demand of nodea me perod whou demand response (MW). Alreza Soroud and Andrew Keane are wh he School of Elecrcal, Elecronc and Communcaons Engneerng, Unversy College Dubln, (emal: alreza.soroud@ucd.e, andrew.keane@ucd.e) The work of A. Soroud was conduced n he Elecrcy Research Cenre, Unversy College Dubln, Ireland, whch s suppored by he Commsson for Energy Regulaon, Bord Gás Energy, Bord na Móna Energy, Cylon Conrols, ErGrd, Elecrc Ireland, EPRI, ESB Inernaonal, ESB Neworks, Gaelecrc, Inel, SSE Renewables, UTRC and Vrdan Power & Energy. A. Soroud s funded hrough Scence Foundaon Ireland (SFI) SEES Cluser under gran number SFI/9/SRC/E178. P. Sano s wh he Deparmen of Indusral Engneerng, Unversy of Salerno, 8484 Fscano, Ialy (e-mal: psano@unsa.) Λ Maxmum number of nodes allowed o parcpae n demand response. V mn/max Maxmum/mnmum volage magnude (pu). I l Maxmum feeder capacy (A). γ max/mn Maxmum/mnmum demand flexbly a node. ES max/mn Maxmum/mnmum energy sored a node (MWh). P ch,max/mn Maxmum/mnmum power charge of ESS a node (MW). P dch,max/mn Maxmum/mnmum power dscharge of ESS a node (MW). λ max/mn Maxmum/mnmum bounds of elecrcy prce a me ($/MWh). Y j Magnude ofj h elemen of admance marx (pu). ± Posve/negave devaon of acual prce from he forcased prce ($/MWh). λ Unceran elecrcy prce a me ($/MWh). C. Varables (P/Q) D/G, Acve/reacve demand of node a me perod wh demand response (MW). ω,ζ,υ Auxlary varables. Λ Bnary decson varable ndcang wheher node parcpaes n demand response or no. P ch/dch, Charge/dscharge power of ESS a node a me perod. I l, Curren flowng n feeder l a me (A) γ, Demand response decson varable of node a me perod. ES, Energy sored n ESS a node a me perod. (P/Q) ne, Ne acve/reacve power njecon o node a me perod wh demand response (MW). L ESS Power losses n ESS a me (MW). ψ Toal acve power losses a me (MW). V, Volage magnude a node a me perod. δ j, Volage angle a node a me perod. I. INTRODUCTION A. Background and Am THE goal of he dsrbuon nework operaor (DNO) s o maxmze he effcency of he nework n s errory as well as monorng and mprovng he echncal condon of he nework. The cos of elecrcy s drecly lnked o he effcency of he ransmsson and parcularly he dsrbuon sysem. The fnancal reamen of losses s crucal n hs regard. The role of DNO for dealng wh acve losses (as a measure of nework effcency) s dfferen n each regulaory framework. In some counres lke Denmark, France, Belgum, Ausra and Germany he acve losses are procured n wholesale marke whle n Ireland, Ialy, UK and Porugal some ncenve effcency measure ndcaors are used [1]. There are dfferen

2 2 sraeges o effcency mprovemen of dsrbuon neworks such as schedulng he dsrbued energy resources (DER) [2], [], capacor swchng, nework reconfguraon [4], energy sorage sysems (ESS) [5], demand response (DR) [], ec. The radonal sraegy for DNO s o decrease acve losses usng he avalable opons. In hs paper, whou loss of generaly, among he wde range of performance mprovng acons, he focus s placed on ESS schedulng and DR. Demand response s referred o all acons (ncludng energy sorage devces managemen, energy reducon and demand shfng) o change he nomnal demand paern of he end-use consumers []. Ths paper proposes a mehod for opmal ESS and DR schedulng o mnmze he acve losses paymens. Ths opmzaon has one mporan uncerany source namely, elecrcy prces. There are dfferen echnques o handle he unceranes n decson makng frameworks such as nformaon gap decson heory (IGDT) [7], sochasc programmng, fuzzy mahemacs and robus opmzaon. These echnques are nherenly dfferen n naure and can be easly compared wh each oher. Choosng he bes echnque among hem depends on he uncerany naure and avalable daa abou he unceran parameers of he model. Usng fuzzy echnques requres knowng membershp funcons. The sochasc models need o know he probably dsrbuon funcon (PDF) of unceran parameers and usually hese echnques are compuaonally neffcen [8]. The IGDT framework s very conservave and may lead o over-esmaed acons [8]. I s more suable n severe uncerany cases [9]. In hs paper, robus opmzaon s used for handlng hs uncerany. The gap ha hs paper res o fll s o answer wo quesons: 1) Loss mnmzaon or loss paymen mnmzaon?. Whch s he bes sraegy for effcency maxmzaon under prce uncerany? 2) How should be done usng DR and ESS? B. Leraure Revew Dfferen references referred o ESS and DR for ncreasng he effcency and flexbly n dsrbuon neworks. The ESS are used o ncrease he nework capacy for accepng new wnd urbnes [1], volage regulaon [11], maxmzng revenue for non-frm dsrbued wnd generaon [12], energy managemen and power qualy mprovemen [1] and loss reducon [1]. DR acons can also brng ancllary servces o he grd [14], volage conrol [15], acve loss reducon [1] and beer exploaon of renewable energy sources as well as a reducon of he cusomers energy consumpon coss wh boh economc and envronmenal benefs [17]. In [18], a heursc algorhm s proposed o reduce he acve losses coss reconfguraon of dsrbuon neworks. A dsrbuon sysem expanson plannng model whch consders he consrucon/renforcemen of subsaons/feeders/capacors banks and he radal opology modfcaon was nroduced n [19]. The opmal allocaon of capacor banks and DG uns s found usng he dfferenal evoluon algorhm n [2]. I s mul-objecve and res o opmze he cos of energy no suppled, relably ndex, coss of energy losses and nvesmen. The shorcomng of hese models ( [18] [2]) s assumng he consan cos of energy losses as well as gnorng he unceranes assocaed wh marke prces. ESS and DR are no consdered n hem. C. Conrbuons To he bes knowledge of he auhors of hs paper, here s no reference addressng he mpac of hourly elecrcy prces as well as her uncerany on loss paymen mnmzaon acons. Gven he dscussed conex, he conrbuons of hs work are fourfold: 1) To provde a framework for economc effcency ncrease for DNO. 2) To consder he unceran elecrcy prces usng robus opmzaon echnque and converng he b-level opmzaon no a sngle opmzaon problem. ) To model he opmal schedulng of ESSs. 4) To quanfy he benefs of DR for effcency maxmzaon. D. Paper Organzaon The remander of he paper s organzed as follows. Secon II descrbes he problem formulaon. Secon III presens he modellng feaures and assumpons made n he proposed decson makng framework. Smulaon resuls and dscussons are presened n Secon IV. Secon VI concludes he paper. A. Assumpons II. PROBLEM FORMULATION The DNO s responsble for acve loss procuremen from day ahead elecrcy marke [1]. The day ahead marke mechansm s followed n many counres such as Ireland, Greece and Poland [21]. In hs framework, he elecrcy prces are se based on marke clearng mechansm one day n advance of acual operang pon. The DNO s assumed o be prce aker. However, n some regulaory frameworks lke Nordc counres he real me and nraday balancng marke [22] s used. The elecrcy prces of he day ahead marke are subjec o uncerany. I s due o many dfferen reasons lke: compeon beween prce maker generang uns, conngences of ransmsson nework and generang uns, volale and unceran renewable energy sources and demand uncerany [2]. I s assumed ha only lmed nformaon s avalable regardng he elecrcy prces (nerval based modelng [24]). I s more explaned n secon III-A. The DNO s he owner of ESS and herefore responsble for conrollng he operang schedules of ESS. The DNO has he auhory for conrollng demands n some specfc nodes. Ths can happen usng muual agreemen/conrac [25] beween he consumers and he DNO. The ganed benefs of hs agreemen wll be shared beween he DNO and he consumers.

3 B. Objecve funcons and consrans In a generc acve power losses mnmzaon sraegy, he followng opmzaon problem s solved: mn z = ψ (1) DV Ω T F(DV,Π) (2) G(DV,Π) = () ψ n (1) s he hourly acve loss. DV and Π represen he decson varables and npu parameers (prce values and echncal daa), respecvely. T denoes he operang horzon. F and G represen he nequaly and equaly consrans of he opmzaon framework as descrbed n (5) o (22), respecvely. In hs paper, a new sraegy s proposed ha res o mnmze oal paymens relaed o he acve power losses. Obvously, he opmal acons DV drecly depend on he npu parameers (Π) ncludng prce values for he day ahead marke. The ssue s ha usually here s lmed nformaon abou he elecrcy prces of he nex day. The opmzaon problem can herefore be formulaed as follows: mn z = (ψ λ ) (4) DV Ω T F(DV,Π) G(DV,Π) = λ s he unceran elecrcy prce a me n day ahead marke. The power flow equaons o be sasfed Ω n, Ω T, l Ω L are: ψ =, +L ESS (5) Ω n P ne P, ne = P, G P, D P, ch +P, dch () Q ne, = Q G, Q D, (7) P, ne = V, j Ω n Y j V j, cos(δ, δ j, θ j ) (8) Q ne, = V, Y j V j, sn(δ, δ j, θ j ) j Ω n (9) V mn V, V max (1) I l, = Y l=j ( V, δ, V j, δ j, ) I l (11) where L ESS s he power losses n ESS a me. P ne,,qne, n () and (7) are he ne njeced acve and reacve power o bus, respecvely. Y j,θ j are he magnude and angle of he jh elemen of admance marx, respecvely. V,,V mn,v max n (1) are he volage magnude, mn/max operang lms of each bus, respecvely. I l n (11) s he curren passng hrough feeder l and I l n (11) s he maxmum allowable curren n feeder l. P, G,QG, n () and (7) are he acve and reacve power njeced o he nework by he DG uns or grd connecon. Ω n,ω T,Ω L are he se of sysem nodes, operang hours, feeders, respecvely. P ch/dch, s he charged/dscharged power of ESS n (). The ESS echncal operang consrans o be sasfed Ω ESS & Ω T [2] are: ES, = ES, 1 + ( η ch P, ch P, dch ) /η dch (12) ES mn P ch,mn P dch,mn L ESS ES, ES max (1) P ch, P ch,max (14) P, dch P dch,max (15) = (1 η ch )P, ch +P, dch (1/η dch 1) (1) where Ω ESS s he se of nodes whch have ESS. The energy sored n ESS n me and bus, ES, depends on he energy sored n ESS n me 1 and he chargng and dschargng of he ESS (P, ch/pdch, ) whch s descrbed n (12). η ch and η dch are he chargng and dschargng effcency of ESS, respecvely. s he duraon of me nerval. The sored energy n ESS should be kep beween specfc lms (ES max/mn ) as enforced by (1). ES, s he nal value of sored energy n ESS. The chargng and dschargng lms of ESS are gven n (14) and (15). Demand response consrans for Ω DR are: P, D = P, D γ, (17) Q D, = Q D, γ, (18) (1 γ mn Λ ) γ, (1+γ max Λ ) (19) Λ Λ (2) Ω DR P, D (1 ǫ ) Ω T Q D, (1 ǫ ) Ω T Ω T P D, (21) Ω T Q D, (22) The se of demands parcpang n DR program s represened by Ω DR. (P/Q) D,,(P/Q)D, specfy he orgnal/modfed demand paern whou/wh DR perurbaon n (17), (18). γ, denoes he decson varable for changng he demand paern n (17),(18). The consran (19) models he flexbly degree of he demands. γ max and γ mn specfy he maxmum possble ncrease and decrease of demand n node. Λ s a bnary varable. If Λ = hen he node does no parcpae n a DR program and vce versa. The oal number of nodes whch can parcpae n a DR program are specfed n (2) as Λ. Alhough he demand paern changes, he oal energy consumpon of he demand n node s kep more han 1 (1 ǫ ) percen of s nal energy value (whou DR) as mposed by (21) and (22). In oher words, ǫ s he cural-able percen of energy of demand n node. Whou hese equaons ((21) and (22)), he DR decson varables (γ, ) as defned n ((17) and (18)) would ake her leas possble values (γ mn ) for all me perods. I should be noed ha hese equaons are vald for each node Ω DR. Ths means ha he energy of node s redsrbued n dfferen me perods (no ransferred o oher nodes). In he curren formulaon, f Λ are gven as consan npu parameers hen he model s a non-lnear problem (NLP). Ths means he nodes parcpang n demand response are known n advance. I s also possble o fnd he opmal locaons of nodes o parcpae n DR program. In hs case, he resulng problem s a mxed neger non-lnear problem (MINLP).

4 4 I s neresng o know how o deermne he order of DR nodes wh respec o her mpac on energy losses paymens. A echnque o denfy he mers of nodes for parcpang n DR s enumerang he oal number of nodes ( Λ) permed o parcpae n DR (Λ) from 1 o he number of load pons. Then for he gven number of permed nodes (Λ) he DR parcpang nodes are found usng bnary varables Λ. In each case, he opmal nodes (wh Λ = 1) are denfed. The frequency of selecon n each scheme specfes he mer of each node. III. PROPOSED STRATEGY The opmzaon sraegy s o fnd he opmal decson varables n such a way ha he wors case cos s conrolled for a gven degree of conservaveness (). In hs secon, frs he uncerany modelng s nroduced and fnally he robus opmzaon based soluon sraegy s gven. A. Uncerany modelng There are several echnques avalable for modelng he uncerany of elecrcy prce n (4). These echnques nclude sochasc scenaro modelng (Fg.1a ) [8], fuzzy modelng (Fg.1b ) [27] and robus opmzaon (Fg.1c) [28]. Usng each echnque requres ceran nformaon regardng he unceran parameer. In sochasc scenaro based modelng, he decson maker should be aware of probably densy funcon of unceran parameer. In fuzzy modelng he membershp funcon of unceran parameers should be known. The compuaonal burden of hese echnques are hgh and he obaned resuls are subjec o rsk. For example he acual realzaon of he unceran parameer may devae drascally from he expeced value of he objecve funcon. The robus opmzaon uses he a) b) S λ ( ) M α λ c) ( ) U λ Scenaro 1 1. T Scenaro 2 1. T Scenaro 1. T. 1. T Scenaro N 1. T 1 α mn λ f λ max λ Fg. 1. a) Scenaro based sochasc uncerany modelng, b) Fuzzy based uncerany modelng, c) Robus opmzaon based uncerany modelng. uncerany ses for handlng he unceranes. One of he mos frequenly used uncerany se s nerval se. The uncerany nervals can be found usng dfferen mehods as follows: Usng me seres models (ARIMA) [29] Usng Neural Neworks λ λ Usng exper opnon and hsorc daa The same echnque has been used n he leraure such as n [] []. I s formulaed as follows: λ U( λ ) = { λ : λ mn λ } λ max (2) λ mn,λ max are he lower and upper bounds of λ, respecvely. I s assumed ha no nformaon s avalable from day ahead marke prces oher han hese bounds. B. Robus opmzaon formulaon The dea of robus opmzaon s o mnmze z n eq. (4) whou knowng he exac values of λ. Addonally, he opmal decson makng s done n a way ha hese acons sll reman good (no opmal) even hough he acual values (λ a ) of unceran parameers devae (o some degree ) from he forecased values λ f. Two cases may happen: frs, he acual prce λ a s more han he forecased prce λ f. The consran for uncerany modellng of he prce can be expressed as: λ a = λ f + + ω (24a) + = λ max λ f (24b) ω 1 (24c) where, ω s he predcon error. The second case happens when he acual prce λ a s less han λ f as: λ a = λ f + ω (25a) = λ mn λ f (25b) As he decson maker seeks he robusness agans he undesred evens, he equaons gven n (25a), (25b) do no cause rouble. Acually he man concern of he decson maker s on he equaons gven n (24a), (24b) where he acual prces may be more han he forecased values. Thus, he formulaon expressed n equaons (4), (2) can be replaced by he followng one: mn z = ψ λ f +ψ + ω (2a) DV T ω 1 (2b) ω (2c) T Subjec o : (5)o(22) n (2c) s a parameer specfed by he decson maker whch s also called he conservaveness degree. I denoes he maxmum oal devaon (robusness degree [28]) ha can be oleraed. Ths parameer can ake a value from o 24 (ncreases wh he conservaveness of he decson maker). For example, f = 2 hs means ha he algorhm wll reman robus even hough he maxmum oal predcon error s 1% n 2 hours or 5% n 4 hours of he day ahead marke. The robus couner

5 5 par of (2) would become [24]: mn z = max ω ψ + ψ λ f ω + Subjec o : DV T (2b),(2c) Subjec o : (5)o(22) (27) The formulaon descrbed n (27), requres o solve a blevel opmzaon snce he nner maxmzaon res o smulae he wors case realzaon of unceran prce (by changng ω ) whle he ouer mnmzaon aemps o decrease he undesred mpacs of unceran prces by conrollng DV. The decson varables n nner maxmzaon s w and he consrans are he (2b), (2c). Ths s done n order o fnd he wors case condon of uncerany n elecrcy prces ha would cause he maxmum ncrease n oal paymens. Once he opmal values of w are found, hese values are passed o he ouer mnmzaon. The decson varables of hs level are he nework power flow, demand response and energy sorage sysem consrans. max ω ψ + ω The complexy of he opmzaon block, Subjec o : (2b),(2c) n (27), s lnear wh respec o ω snce he erms ψ + are deermned n he upper level of opmzaon. Accordng o he dualy gap heory [9], s concluded ha : max w T [ ψ1 + 1 ψ T + ] T s equvalen o : w 1. w T w 1. w T (28) [ ][ mn 1 1 ζ1 ζ T Υ ] Υ,ζ T T 1 ζ 1 ψ ζ 2 ψ ζ T 1. 1 ζ T Υ ψ T + T (29) () (1) where ζ,υ are dual varables. Usng (28) o (1), he b-level opmzaon descrbed n (27) would ransform no (2): mn λ f ψ + ζ +Υ DV T T (2a) Υ+ζ (λ max λ f )ψ (2b) Υ,ζ (2c) Subjec o : (5)o(22) The obaned sngle level opmzaon n (2) can be solved usng decomposon echnque [4] or Lagrange Relaxaon approach [5]. I s obvous ha he resuled sngle level opmzaon s easer o solve han he orgnal b-level opmzaon srucure. The decson varables (U), parameers (Π) and he ses are as follows: ψ,γ,,λ,ω,ζ,υ DV = (P/Q) D/G,,I l,,v,,δ j, (),,(P/Q) ne P ch/dch,,es, (P/Q) D,,γmn/max,,ES mn/max η Π = ch/dch,p ch,mn/max,p dch,mn/max λ max/mn,λ f/a (4), λ,θ j,y j ±,, Λ,V mn/max,i l Ses = {Ω DR,Ω T,Ω n,ω L,Ω ESS } (5) Indeed he DNOs would raher mnmze he maxmum coss ha he hey may experence. Ths maxmum cos occurs when he acual prce s more han he forecas prce. The reformulaed sngle level opmzaon mnmzed he maxmum regre (paymens) of DNO by usng dualy gap heory [] and robus opmzaon. Ths s because n deregulaed envronmen he DNO s concern s he paymens oward he losses (no he losses as n radonal dsrbuons nework managemen sysems). I s shown ha mnmzng he z 1 = DV ψ does no resul n mnmum z 2 = DV λ ψ. Especally when λ s unceran. A. Daa IV. SIMULATION RESULTS The proposed algorhm s mplemened n GAMS [7] envronmen runnng on an Inel R Xeon TM CPU E5-12. GHz PC wh 8 GB RAM. As far as he demand response node/nodes s/are known, he proposed framework s a NLP model whch can be easly solved by commercal solvers such as Modular In-core Nonlnear Opmzaon (MINOS) [8]. However, f he opmal DR allocaon s o be nvesgaed he model would become MINLP and he Dscree and Connuous OPTmzer (DICOPT) [9] solver s used. In large scale neworks, usng he bender decomposon echnque [4] would be benefcal. The non-convexy of he AC-OPF problem makes dffcul o fnd he global opmal soluon. Some novel echnques have been proposed n he leraure o address he dualy gap n OPF and make convex [41], [42]. The proposed model s appled o a -bus dsrbuon nework [4]. The peak demand values used n hs sudy are hgher han wha s repored n [4] n order o ncrease he acve losses n he nework and can be accessed n [44]. T s consdered o be 24h. The predced prce values as well as prce bounds are depced n Fg. 2. These values can be found usng me seres models lke ARIMA [45] based on hsorc daa. The daly load curve shown n (Fg. 2) s obaned from ErGrd whch s he Irsh TSO (accessed 28/12/214) [4]. The daly load curve s shown n Fg. 2 [4]. Whou loss of generaly s assumed ha no load curalmen can be done e.g. ǫ =, Ω n. The echncal characerscs of he consdered ESS are descrbed n Table I.

6 Percen of peak load (%) Elecrcy prce ($/MWh) Fg P ch,max, P ch,mn, λ max λ f λ mn Hour () Day ahead demand and prce characerscs TABLE I THE TECHNICAL CHARACTERISTICS OF ESS Parameer Value Un ES, max 4 (8 5KW REDOX baeres [47]) MWh ES, mn 1 MWh ES, 2 MWh = P dch,max, 1 MW = P dch,mn, MW η ch = η dch 95 % B. Consdered cases In hs sudy, hree dfferen cases are suded: Case A) Ths case s added for he purpose of provdng a bass for comparson. In hs case, neher ESS nor DR s scheduled. No opmzaon s performed n hs case. The consrans o be sasfed are (5) o (11). The decson varables of hs case are lmed o load flow varables and no opmzaon s performed. Ths means ha DV a = { V,,δ,,P G,,QG,}. In hs case, s red o sasfy he consrans (5) o (22). Ths s bascally because here s no ndependen DV (DR or ESS) so he objecve funcon can be chosen as (1) or (4). Case B) The acve loss mnmzaon (objecve funcon s (1) ) s acheved whou consderng he prce unceranes and usng opmal schedulng of: B 1 : The loss mnmzaon s performed by opmzng he ESS schedule. The consrans o be sasfed are (5) o (1). Ths mples ha DV b1 = DV a { ES,,P ch,,pdch, }. I s supposed ha only one ESS exss n he nework. B 2 : The loss mnmzaon s performed by opmzng he DR schedule. The consrans o be sasfed are (5) o (11) and (17) o (22). Ths mples ha DV b2 = DV a {γ,,λ }. In hs case, s assumed ha load demand a only one node parcpaes o a DR program. The flexbly degree can be adjused by changng he γ mn/max, γ max, =.. n (19). I s assumed ha γ mn, =. and B : The loss mnmzaon s performed by opmzng he ESS and DR schedule. The consrans o be sasfed are (5) o (22). Ths mples ha DV b = DV b1 DV b2. I should be noed ha he elecrcy prce unceranes have an mpac on he fnal paymens of case A, B and C. I s assumed ha he DNO s a prce aker eny and s operang decsons do no nfluence he marke prce values. The dfference beween hese cases s ha case A does no have he ools (DR & ESS) o reduce he undesred prce unceranes. In case B, he ools (DR &/OR ESS) are avalable bu no an approprae operang sraegy s chosen for reducng he paymens. In fac, n case B s red o mnmze he losses whou consderng he prce values and her unceranes. In conrary o case A & B, he decson maker n case C ncorporaes he prce unceranes n decson makng process. Tha s why n all of hese cases he mpac of values (he degree of conservaveness regardng he fuure prces) on fnal paymens are assessed. Case C) Loss paymen mnmzaon (objecve funcon s (2a) ) s acheved by consderng he prce unceranes and usng opmal schedulng of correspondng decson varables whch are as follows: C 1 : The decson varables are he same as case B 1. Therefore U c1 = U b1. The consrans o be sasfed are (5) o (11). C 2 : The decson varables are he same as case B 2. Therefore U c2 = U b2. The consrans o be sasfed are (5) o (11) and (17) o (22). C : The decson varables are he same as case B. Therefore U c = U b. The consrans o be sasfed are (5) o (22). The value of shows he conservaveness degree of he decson maker. I s a parameer whch s se by he decson maker. I can vary from (meanng no uncerany may happen) o 24 (all unceran parameers may ake her wors value). The smulaons have been done for all values of = 24. C. Resuls 1) Case A: The oal paymens are $ ( = ) and he oal daly acve energy losses are 8.9 MWh. The hourly acve losses are shown n Fg.. The possble reducon n loss paymens vs he degree of conservaveness () are depced n Fg. 4. The numercal values of possble loss paymens for dfferen degrees of uncerany () are gven n Table II. I s observed ha as he uncerany degree ncreases, he possble paymens would ncrease from $ ( = ) o $8.452 ( = 24). 2) Case B: Case B 1 : The connecon node of he ESS can have an nfluence on he effcency of he acve managemen sraegy. Ths s nvesgaed by changng he connecon node of ESS n he nework. Based on he plos shown n Fg. 5, s evden ha he bes locaon for ESS connecon s bus #15. In hs case, he acve losses do no change wh he change of values. However, he possble paymens

7 B1 B2 Acve energy losses (MWh) Energy losses paymens ($) DR or ESS Connecon node Hour () Fg.. The energy losses paymens n loss mnmzaon sraegy vs he ESS node (case B 1 ) and DR node (case B 2 ). Fg.. The hourly acve energy losses n case A, where neher ESS nor DR exss n problem formulaon. Losses paymens reducon compared o case A (%) 12 A B 1 B 2 B C 1 C 2 C Fg. 4. The energy losses paymen reducons (%) vs n dfferen cases. A:base case, B: loss mnmzaon (usng ESS B 1, usng DR B 2, usng boh DR & ESS B ), C: loss paymens mnmzaon (usng ESS C 1, usng DR C 2, usng boh DR & ESS C ). Acve energy losses (MWh) B2 B DR or ESS Node Fg. 5. a) The mpac of ESS connecon node on acve losses (case B 1, loss mnmzaon usng ESS). b) The mpac of DR connecon node on acve losses (case B 2, loss mnmzaon usng DR) wll change wh ESS connecon node as shown n Fg.. If he ESS s conneced o node #15 hen n case B 1 he sored, charged and dscharged energy paern of ESS are depced n Fg. 7. As shown n Fg. 4, hs sraegy can reduce he loss paymens up o 2.8% compared o case A. The mnmum oal acve losses are kwh. Case B 2 : Fg. 5 shows he energy losses vs he node where a load wh a demand response capably s assumed n case B 2. Node # s he bes node for demand response Energy Sored, chareged or dscharged (MWh) Hour () Fg. 7. The sored, charged and dscharged energy schedule of he ESS conneced o node 15 (case B 1, loss mnmzaon usng ESS). ES P, ch P, dch parcpaon regardng he energy losses mnmzaon. Fg. shows he energy losses paymen vs he node where a load wh a demand response capably s assumed. As shown n Fg. 4, hs sraegy can reduce he loss paymens up o 4.98 % compared o case A. The mnmum oal acve losses are KWh. In he case ha bus s seleced as he node wh DR capably, he new demand paern of bus s depced n Fg. 8. Ths new paern s deermned based on he echncal characerscs of he nework ncludng he admance marx as well as he demand paern of oher nodes (whch do no parcpae n DR program). Rao of demand o peak load (%) B 2 A C Hour () Fg. 8. The hourly demand paern n dfferen cases. A: no ESS/DR, loss mnmzaon usng DR (B 2 ), loss paymens mnmzaon usng DR (C 2 ).

8 8 Case B : I s assumed ha he DR node s node # and he ESS s conneced o node 15. Table II and Fg. 4 show he energy losses paymen as well as oal losses vs n case B, respecvely. As shown n Fg. 4, hs sraegy can reduce he loss paymens up o 7. % compared o case A. The mnmum oal acve losses are kwh. ) Case C: In hs case, he proposed algorhm res o mnmze he oal daly paymens due o acve losses n he nework usng dfferen combnaons of acons as prevously descrbed: Case C 1 : Agan, he mpac of ESS connecon node on acve losses paymens n case C 1 s shown n Fg. 9. Ths clearly shows ha mnmum acve losses does no necessarly occur a mnmum acve losses paymens. Node 15 s opmal for loss mnmzaon no loss paymen mnmzaon. Fg. 1 depcs he mpac of ESS connecon ES (MWh) (case C 1 ) Hour () Fg. 11. The hourly energy sored n ESS vs n case C 1 (loss paymens mnmzaon usng ESS) vs n case C 2. Ths mples ha he node # s he bes node for demand response parcpaon regardng he losses paymens mnmzaon. Fg. 9 shows he energy losses DR(C 2 ) ESS(C 1 ) 4 Acve energy losses paymens ($) = =12 = DR/ESS connecon node Fg. 9. The energy losses paymens n losses paymens mnmzaon sraegy vs he ESS node (case C 1 ) and DR node (case C 2 ) for hree dfferen values of. Acve energy losses (MWh) node on acve losses n case C 1. The varaons of acve energy losses n Fg. 1 shows ha ESS operaon changes he lne flows and hs would ncrease he oal acve losses for dfferen () and connecon nodes Fg. 1. The mpac of ESS connecon node on acve energy losses (wh loss paymens mnmzaon sraegy usng ESS (C 1 )). Fg. 11 shows he hourly energy sored n ESS vs n case C 1 f s conneced o node 11. As shown n Fg. 4, hs sraegy can reduce he loss paymens by up o 5.2 % compared o case A. In hs case, he mnmum oal acve losses vary from 87.8 kwh o kwh (based on values). CaseC 2 : Fg. 12 shows he energy losses vs he node where a load wh a demand response capably s assumed and Acve energy losses (MWh) Connecon node Fg. 12. The energy losses vs he DR node vs (n loss paymens mnmzaon sraegy usng DR (C 2 )). Toal energy losses (Kw) paymen vs he DR node and vs (case C 2 ). In hs case, he mnmum oal acve losses vary from kwh o 8.97 kwh (based on he varaon of values). The new demand paern of bus s depced n Fg. 8. Ths new paern s deermned based on he echncal characerscs of he nework (lke case B 2 ) as well as he elecrcy prce varaons. As shown n Fg. 4, hs sraegy can reduce he loss paymens up o.4% compared o case A. Case C : I s assumed ha he DR node s node # and he ESS s conneced o node 15. Fg. 4 shows he energy losses paymen vs n case C. The energy losses vs n case C are shown n Fg. 1. In hs case, he mnmum oal acve losses vary from kwh o kwh (based on ). As shown n Fg. 4, hs sraegy can reduce he loss paymens up o 11.44% compared o case A. 875 A B 1 B 2 B C 1 C 2 C Fg. 1. The acve energy losses vs n dfferen cases. A: no ESS/DR, B: loss mnmzaon (usng ESS B 1, usng DR B 2, usng boh DR & ESS B ), C: loss paymens mnmzaon (usng ESS C 1, usng DR C 2, usng boh DR & ESS C )

9 9 D. Comparson The wors possble realzaon of elecrcy prces (based on he gven budge of uncerany ()) s calculaed by solvng he max ω ψ + ω followng opmzaon problem: Subjec o :. Then (2b),(2c) s used for loss paymen calculaon n all cases. Ths s why alhough he opmal decson varables n case B do no depend on prce uncerany, he paymens are dependen on unceran prces. In oher words, he prce uncerany wll be presen n he fnal paymens wheher consdered n decson varables (case C) or no (case B). The maxmum reducon occurs n C where boh ESS and DR are used o reduce he acve loss paymens. The operang sraegy of ESS n case C 1 and C depends on prce uncerany so he oal round rp losses wll be dependen on. The round rp losses of ESS vs me n cases C 1 and C are shown n Fg. 14. Snce he operaon of ESS s no Energy losses n ESS (Kw) Fg. 14. The round rp losses of ESS vs n case C: Acve power losses paymens mnmzaon (usng ESS C 1, usng boh DR & ESS C ). dependen on elecrcy prce n case B, hen he OC ESS s consan n hs case. The round rp losses of ESS n B 1 and B are 44.2 KWh, 4.8 KWh, respecvely. However, he operang schedule of ESS changes wh conservaveness degree () for case C. The comparson beween dfferen cases regardng acve losses and losses paymens are depced n Fg. 1 and Fg. 4, respecvely. Accordng o Fg. 1, he bes sraegy for loss mnmzaon s B snce focuses on loss mnmzaon and ulzes boh DR and ESS opons. In Cases A, B 1 he oal losses do no change wh values snce hese sraeges are nsensve o prce varaons. The oal losses n C 1 change wh. However, hese changes n C 2 are less han C because ESS s a more powerful ool compared o DR (wh only one parcpang node n DR). Usng he echnque descrbed n secon II-B, he mers of nodes for parcpang n DR program are calculaed and shown n Fg. 15. The oal numercal values of losses paymens n dfferen cases vs () are descrbed n Table II. I s found ha he oal losses paymens are reduced when boh DR and ESS are ulzed compared o base case (A) whle hs value ncreases wh he ncrease of conservaveness level (). The smulaon resuls showed ha he loss mnmzaon and loss paymen mnmzaon sraeges do no necessarly converge o he same C 1 C Percen of cases ha node parcpaes n DR Fg Load node The mers of nodes for parcpang n DR program TABLE II TOTAL ACTIVE LOSSES PAYMENTS ($) VS () IN DIFFERENT CASES. A: NO ESS/DR, B: LOSS MINIMIZATION (USING ESS B 1, USING DR B 2, USING BOTH DR & ESS B ), C: LOSS PAYMENTS MINIMIZATION (USING ESS C 1, USING DR C 2, USING BOTH DR & ESS C ). ESS & DR DR ESS Base C B C 2 B 2 C 1 B 1 A soluon. Ths has several reasons as follows: The elecrcy prces are no he same n all operang perods (hese values ac as he weghng facors n opmzaon problem). If a consan cos (prce) s consdered for all me perods, hen hese sraeges wll converge o he same answer. The acve losses n me perod depend on acve losses values n prevous and upcomng me perods. Ths means ha he opmal decsons may ncrease he losses n me (whch has low prce values) o decrease he losses n me ( > or < ). Ths may ncrease he oal acve losses bu wll decrease he paymens. I s mpossble o mnmze he losses n all me perods because of he

10 1 dynamc operang consrans of DR (21) o (22) and ESS (12) o (1). In order o check he robusness of he proposed algorhm a Mone carlo smulaon has been conduced. I nends o verfy he robusness of he obaned soluons. Case C s used for robusness verfcaon. For hs purpose, he opmal schedule of DR and ESS are obaned for a gven conservaveness degree (e.g. = 12) and as ndcaed n Table II (case C ) he oal paymens are $8.7. Nex, 1 samples of prce values λ 1 24 are generaed n a way ha w sasfy equaons (2b) and (2c). The value of oal losses paymens are calculaed usng (2a). The Mone carlo smulaon resuls are shown n Fg. 1. The mnmum, average, maxmum and he sandard devaon of smulaed coss are $19., $49.5, $78.1 and $8., respecvely. From Fg.1, s nferred ha usng he decson varables found by he algorhm guaranees ha he losses paymens wll no exceed he value specfed by he algorhm (vercal lne ndcaed n Fg.1 whch s $8.7). The Mone carlo smulaon shows ha applyng he decson varables can ensure he DNO ha he paymens wll no exceed he obaned resuls n Table II f he oal elecrcy prce unceranes reman less han = 12 ((2b) and (2c)). Frequency of cos occurrence Fg. 1. Smulaed Fed Dsance o average Dsance o mnmum Dsance o maxmum Cos n case C Cos values ($) The Mone carlo smulaon resuls for robusness esng I s assumed ha he marke s he only energy procuremen opon for DNO. In case, any renewable energy source exss n he nework, he uncerany of s generaon paern should be aken no accoun. On he oher hand, he self owned DG uns are no allowed n many regulaory frameworks. The maxmum annual cos savng for usng he sraegy of case C s $45.7. The proposed framework s focused on operang sraegy of DNO (usng DR and ESS). Ths means ha ESS s already nsalled (so nvesmen cos are already pad). The obaned annual cos savng can be shared beween he DNO and demand nodes whch parcpae n DR program as an ncenve. The man dea of he proposed framework s o demonsrae and quanfy he effecveness of he developed model n mnmzng he losses paymens. There are dfferen frameworks for modelng he demand response such as welfare maxmzaon on consumer sde [48], [49], prce elasc demand curve [5], moneary ncenves [51]. The consumer welfare maxmzaon s negleced as s ousde he scope of hs paper and he DR s lmed o demand shfng. The proposed model receves some npus and provdes some nsghs regardng he DR and ESS operaon o deal wh elecrcy prce unceranes as shown n Fg. 17. I can be used o generae he rade-off curve beween consumer welfare maxmzaon and DNO paymens mnmzaon. Fg. 17. DR ncenves DR se/sze Acve losses ESS operaon Model DR locaons Nework opology DR flexbles Elecrcy prces ESS uns The npu-oupu neracons n he proposed model V. DISCUSSION If he exac values of unceran elecrcy prces values λ are known (λ f ) hen solvng he (4) would be an easy ask. The decson maker s no able o fnd he opmal decson varables (because he can be sure abou he unceran prces). The only remanng opon s avodng he hgh values of he prce. In oher words, opmal decson makng s no oward mnmzng he mnmum coss ha he decson maker may experence. I should be noed ha he model s fed by some prce values whch some of hem are he same as forecased and some of hem are more han forecased values (wors case s calculaed based on he gven value of ). Sll he ESS res o sore he energy n perods where he prces are low and release hem when he prces are hgh. VI. CONCLUSION In hs paper, a general framework s presened n whch he unceran prce s consdered for losses paymens mnmzaon. Ths framework can accommodae dfferen sraeges for effcency maxmzaon of cusomers. Smulaon resuls answered he prevously posed quesons regardng loss and losses paymens mnmzaon. I was demonsraed ha he losses paymens mnmzaon sraegy domnaes he radonal losses mnmzaon approaches n an unbundled power sysem envronmen. The ESS and DR are used as flexbly provder ools o enable he decson maker handle he unceranes n a more effcen way. Consderng he fac ha robus opmzaon framework does no need he probably dsrbuon of unceran parameers, can be used n praccal cases. As evdenced by he smulaon resuls, he proposed mehod offers some neresng feaures over radonal mehods as follows:

11 11 Modelng he uncerany of elecrcy prces whou knowng he probably densy funcon usng uncerany se (wh lmed hsorc daa) and robus opmzaon mehod. I s racable and capable of conrollng he conservaveness degree of decson maker. I can be ulzed o assess he mers of nodes for parcpang n demand response programs based on her conrbuons o effcency maxmzaon of he nework. Provdng he opmal schedule of DR and ESS usng a holsc approach mmunzed agans he nheren operang unceranes. Increasng he benefs of consumers compared o he radonal loss mnmzaon approaches. Ths mehod by mnmzng he DNO loss paymens, reduces he coss of he DNO and hus provdes a clear benef o he cusomer. 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