Aggregation of Distributed Energy Resources under the Concept of Multi-Energy Players in Local Energy Systems

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1 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy 1 Aggregaon of Dsrbued Energy Resources under he Concep of Mul-Energy Players n Local Energy Sysems Mazar Yazdan-Damavand, Member, IEEE, Nlufar Neyesan, Member, IEEE, Ganfranco Chcco, Senor Member, IEEE, Madreza Shafe-khah, Senor Member, IEEE, and João P. S. Caalão, Senor Member, IEEE Absrac In recen years, n addon o he radonal aspecs concernng effcency and profably, he energy secor s facng new challenges gven by envronmenal ssues, secury of supply, and he ncreasng role of he local demand. Therefore, he researchers have developed new decson-makng frameworks enablng hgher local negraon of dsrbued energy resources (DER). In hs conex, new energy players appeared n he real markes, ncreasng he level of compeon on he demand sde. In hs paper, a mul-energy player () s defned, whch behaves as a DER aggregaor beween he wholesale energy marke and a number of local energy sysems (LES). The and he LES have o fnd a long-erm equlbrum n he mulenergy real marke, n whch hey are nerrelaed hrough he prce sgnals. To acheve hs goal, n hs paper he decsonmakng conflc beween he marke players s represened hrough a b-level model, n whch he decson varables of he a he upper level are parameers for he decson-makng problem a he lower level (for he ndvdual LES). The problem s ransformed no a mahemacal program wh equlbrum consrans by mplemenng dualy heory, whch s solved wh he CPLEX 12 solver. The numercal resuls show he dfferen behavor n varous condons ha mpac on he oal flexbly of he energy sysem. Index Terms aggregaon, b-level model, decson-makng, mul-energy, prce sgnal. B. Superscrps AB Auxlary boler CHP Combned hea and power cha Hea sorage chargng dcha Hea sorage dschargng E Equaly consrans EM Elecrcy wholesale marke GM Gas wholesale marke HS Hea sorage IL Inerrupble load n Inpu energy o LES or HS nc The amoun of load nerrupon ncenvzed nj Injeced energy o LES Local energy sysem M EP Mul-energy player M ED Mul-energy demand N Non-equaly consrans ou Oupu energy from LES or HS P V Phoovolac array Sc Scenaro W nd Wnd generaon A. Subscrps e g h n ω Elecrcy Naural gas Hea LES Consran Tme nerval Se of scenaros NOMENCLATURE J.P.S. Caalão acknowledges he suppor of FEDER funds hrough COM- PETE 2020 and Poruguese funds hrough FCT, under Projecs FCOMP FEDER (Ref. PTDC/EEA-EEL/118519/2010), POCI FEDER , POCI FEDER , UID/EEA/50014/ 2013, UID/CEC/50021/2013, and UID/EMS/00151/2013, and also acknowledges fundng from he EU Sevenh Framework Programme FP7/ under gran agreemen no M. Yazdan-Damavand, N. Neyesan, Madreza Shafe-khah, and J. P. S. Caalão are wh INESC TEC and he Faculy of Engneerng of he Unversy of Poro, Poro , Porugal, also wh C-MAST, Unversy of Bera Ineror, Covlhã , Porugal, and also wh INESC-ID, Insuo Superor Tecnco, Unversy of Lsbon, Lsbon , Porugal (e-mal: caalao@ub.p). G. Chcco s wh Polecnco d Torno, Dparmeno Energa Galleo Ferrars, Power and Energy Sysems un, corso Duca degl Abruzz 24, Torno, Ialy (e-mal ganfranco.chcco@polo.). C. Parameers A B I G M p, M d N Q T W γ φ ρ η Π Ω Number of energy sorage uns Number of energy converers Number of LES Amoun of naural gas supply Very bg parameers for he relaxaon of he prmal and dual consrans. Number of consrans Amoun of hea producon Tme perod Amoun of elecrcy generaon Charge/dscharge rae Hea o elecrcy rao of CHP un Scenaro probably Effcency Consan energy prce PV and wnd scenaros D. Varables g Amoun of naural gas supply q Amoun of hea producon (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

2 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy 2 u Bnary varable w Amoun of elecrcy generaon λ Dual varables for equaly consrans µ, µ Dual varables for he lower and upper lms of non-equaly consrans. ξ Dual varables for equaly consrans n specfc me nervals. π Varable energy prce E. Vecors and marces b Vecor of consan rgh hand-sde of consrans. c Vecor of coeffcens for he lnear problem. e Vecor of equaly consrans. n Vecor of non-equaly consrans. Vecor of equaly consrans a specfc me. x Vecor of decson varables. ψ Vecor of decson varables for dual problem. λ Vecor of dual varables for equaly consrans µ Vecor of dual varables for he non-equaly consrans. ξ Vecor of dual varables for equaly consrans n specfc me nervals. H Marx of decson varables coeffcens. Remark I: An underlned (overlned) varable s used o represen he mnmum (maxmum) value of ha varable. Remark II: Ha represens he expeced value of varables. I. INTRODUCTION A. Movaon and Ams THE peneraon of dsrbued energy resources (DER), ncludng dsrbued generaon, demand response and dsrbued sorage, s progressvely ncreasng. Among he man drvers, ogeher wh energy effcency and profably, he curren DER evoluon depends on hgh DER mpacs on envronmenal ssues and secury of supply, as well as economc opporunes for demand sde sakeholders. The generaon mx s changng a he supply sde, o delver he requred energy demand. Meanwhle, he load mx changes, also by ncreasng he number of redundan applances ha delver he same servce beng suppled hrough dfferen energy carrers. The above-menoned pons rase he level of dependency among energy carrers [1] and gve furher opporunes o provde flexbly of usage of dfferen energy carrers dependng on he decsons underaken by he end users n dfferen me perods. Mul-energy sysems and mul-energy arbrage have been nroduced o cope wh such nerdependen envronmen wh ncreased flexbly due o he presence of mul-energy carrers [2]. The ermnology used n hs paper consders Local Energy Sysems (LES) ha conver and sore a se of energy carrers o delver he energy requred o serve he mul-energy demand (MED). Fg. 1 depcs he role of mul-energy players () n he supply chan of he mul-energy sysem. The s an energy player who aggregaes a se of LES o maxmze s operaonal prof and mnmze s rsk of parcpang n he energy markes, e.g., elecrcy and gas markes [3]. Aggregang he small scale LES a he demand sde nroduces a huge amoun of flexble resources o he energy markes. Ths flexbly s helpful o decrease shor and long run operaon coss of he mul-energy sysem [4]. The ransacons wh he LES nvolve more han one energy carrer. Therefore, he behavor s dfferen from he behavor of convenonal energy players ha rade jus one energy carrer. The presence of more han one energy carrer movaes he o explo he nner LES flexbly and become n urn a flexble resource n he wholesale energy marke. B. Leraure Revew The mul-energy conceps and models have been presened n varous references, among whch he energy hub model [5] and he marx modelng for negraed represenaon of mulenergy sysems [6]. These models represen some operaon ceners and her nerconnecors. The operaon ceners delver he requred oupu servces by converng and sorng he npu energy carrers [7]. The nerconnecors are corrdors ha ransm he energy carrers from one operaon cener o oher ones. There are wo man approaches for sudyng he varous ssues regardng he above-menoned models: The frs approach s o sudy a sngle operaon cener wh he specfc equpmen; The second approach consders he managemen of a se of operaon ceners and her nerconnecors. Concernng he frs approach, here s a varey of equpmen ha may be nroduced, and whose presence mpacs on he operaonal framework o be analyzed. In mos of he exsng models, he energy oupus of he operaon ceners are assumed as consan values or me seres. However, n anoher vew, he ulmae servce provded o he end-users can be consdered as he real requremen of he sysem o be provded wh dfferen npu energy carrers. Therefore, nsead of consderng he energy vecors o be he oupu of he model, he requred servces are assumed as he new oupus. The specfc focus on he servces depends on he A se of Prmary Energy Sources Fuel e Fuel h Fuel g Supply Chan of Mul-Energy Sysem Gen. e eg gh Gen. h Trans. e eg Trans. g Ds. h Ds. e egh Ds. g Supply e eg Supply g Supply h Fg. 1: Supply chan of energy sysem from prmary resources o end-user. egh A se of Mul-Energy Demands (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

3 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy M. Y. DAMAVANDI e al.: AGGREGATION OF DERS UNDER THE CONCEPT OF S IN LOCAL ENERGY SYSTEMS 3 consumers avalably of dfferen energy carrers o oban he same servce. Ths ably can be consdered as a parcular ype of provson of demand response resources from he upsream nework pon of vew [8]. Moreover, he demand sde managemen s modeled n [9] as an oupu of he energy hub, and he demand shfng s modeled n [10] o procure reserve servces for elecrcy. The negraon of renewable energy resources changes he neracon n he energy hub, as he renewable energy producon can be njeced no he nework as well as beng used a he local level. Hence, n [11] he energy hub model has been modfed by addng a lnk o show he njecon of he surplus energy from he energy hub oupu o he upsream nework. Furher applcaons have been presened n [12], wh an operaonal framework for resdenal energy hub equpped wh varous end-use applances and phoovolac (PV) arrays, and n [13], where he energy sorage has been modeled and s mpacs n he plannng me horzon have been nvesgaed from boh he uly and he household pons of vew. Wh reference o he second approach, an negraed opmal power flow for gas and elecrcy neworks has been proposed n [14]. The soluon procedure has been developed n [15] and a mul-agen genec algorhm has been used o cope wh he large-scale non-lnear problem, decreasng he compuaon me and ncreasng he accuracy of he resuls. A decenralzed conrol framework for modelng he cooperave envronmen of energy hubs has been presened n [16]. The amoun of energy exchanged and he margnal cos of energy producon are consdered as couplng sgnals among he energy hubs. In oher works such as [17] a framework for real elecrcy marke has been nroduced, proposng a model for negraon of elecrcy prosumers. In addon, also [18] refers o elecrcy as he only energy carrer consdered n he operaon of mulmcrogrds. Alhough n some oher works such as [17] a framework for real energy marke has been nroduced, should be noed ha he sudy n [17] only consders he elecrcy marke and proposes he model for negraon of elecrcy prosumers n he real marke. In he curren work he nroduced benefs from he negraon of dfferen energy carrers (e.g., elecrcy, gas, dsrc heang) and he decson-makng procedure s based on he possbly of energy shfng beween dfferen energy carrers. Consequenly, hs wll make he presen sudy dfferen from oher conrbuons. For example, he man concep n [18] s based on he mcrogrd operaon of he energy sysems, also valdaed n a es bed [20], wh elecrcy as he only energy carrer, whle he framework proposed n he curren sudy can be furher employed n a mul-energy envronmen n dfferen operaon modes. The same reasonng explans he dfferences of he curren work wh respec o wha has been presened n [19]. C. Conrbuons The man conrbuons of hs paper are as follows: The nroducon of he as a mul-commody energy player. Several LES are consdered, and he presence of he ncreases he effcency of negrang dfferen energy carrers (e.g., elecrcy, gas, and hea). The proposal of an aggregaon approach for a he dsrbuon level, couplng he LES on he bass of an equlbrum energy prce sgnal. The proposal of an ndex o assess he effecveness of he aggregaon approach a he energy dsrbuon level. In parcular, wh respec o [16], he proposed model s argeed for an energy marke n whch he couplng sgnals are he energy prces, raher han usng he margnal cos of energy producon. Wh respec o [18], he proposed decsonmakng procedure s based on he possbly of shfng energy beween dfferen carrers, raher han consderng elecrcy as he sole energy carrer. The focus of he proposed approach s se on addressng he neracons of he varous mul-energy sysem componens n a comprehensve marke model hrough he nroducon of. The LES npu and oupu are resrced nsde he capacy lms of he nerconnecors. The dsrbuon nework s no explcly represened, namely, he energy neworks are nroduced wh he sngle-node model, assumng no congeson occurs n he energy neworks. D. Paper Organzaon The res of paper s organzed as follows. Secon II descrbes he problem and nroduces he objecve funcons and consrans for he varous enes operang n he mulenergy sysem. In Secon III he energy and prce exchanges among and LES are represened on he bass of a blevel model. Secon IV nroduces an effecveness ndcaor represenng he LES capably of usng nernal resources raher han akng energy from he supply sysems for each energy carrer, and descrbes dfferen ypes of LES managemen. Secon V llusraes and dscusses he numercal resuls obaned n some case sudy applcaons, quanfyng he resuls of he mul-energy sysem operaon. The las secon conans he concludng remarks. II. DEFINITION AND MATHEMATICAL FORMULATION OF THE INTERACTING WITH THE LES A. Problem Descrpon Ths paper proposes a herarchcal opmzaon ool o model he neracons among he and a se of LES. Fg. 2 shows he comprehensve vew of he decson makng procedure, organzed no four layers, namely, he wholesale energy markes, he, he LES, and he MED [21]. In parcular: In he wholesale energy marke layer, dfferen energy players compee wh each oher, and he man goal of he ndependen marke operaor s o maxmze he socal welfare. The behaves as an energy aggregaor ha faclaes energy and fnancal neracons beween LES and he upsream wholesale energy markes. In hs layer, he goal s he maxmzaon of he prof. The LES conan DER and exchange he energy carrers used o supply he MED ( e.g., elecrcy, gas, and hea) wh oher LES and he. The specfc objecve s he maxmzaon of he LES prof (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

4 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy 4 Maxmze Socal Welfare Subjec o: 1) Energy neracon of marke players 1-1) Convenonal energy players 1-2) Mul-energy players () For he k h Maxmze Prof Subjec o: 1) Energy carrers energy balance n Naural gas Elecrcy Heang 2) Energy neracon of For he h local- energy sysem (LES) Maxmze LES Prof Subjec o: 1) Dsrc heang elemens Combned hea and power (CHP) Auxlary boler (AB) Hea sorage (HS) 2) Local energy resources n dsrbuon sysem Phoovolac array Wnd generaon Plug-n elecrc vehcles parkng lo 3) Energy neracon wh mul-energy demands (MED) For j h MED Mnmze MED energy cos Subjec o: 1) Demand sde energy elemens 1-1) Energy resources 1-2) Energy servces 2) Demand sde managemen Energy Marke Layer Mul-Energy Player Layer Fg. 2: Herarchcal srucure of he decson-makng procedure. In he MED layer, he objecve s he mnmzaon of he MED energy coss. To address hese ssues, a herarchcal b-level model has been nroduced o represen he behavor of and LES n he mul-energy sysem. Ths ype of model s generally adoped when he decsons underaken by a leader a he upper level affec he decsons o be aken by he followers a he lower level, whle he decson of he followers have an mpac on he leaders decsons as well. The relevan aspec s he me sequence, ha s, he leader decdes pror o he followers. However, he leader needs o ge a feedback on how s decsons may change he decsons of he followers. In he b-level model (represenng a Sackelberg game [22]) he decson varables used by he leader a he upper level become parameers for he problem solves a he lower level. In he formulaon presened n hs paper, a he upper Local Energy Sysem Layer Mul-Energy Demand level, he maxmzes s prof whle sasfyng he LES energy exchange. The couplng varables among and LES are he energy prces deermned on he bass of he sraegc behavor a he energy dsrbuon level. Then, a he lower level each LES schedules s energy balance of operaon cener based on he frs level prce sgnal and deermnes he quany of exchanged energy. The problem s ransformed no a mahemacal program wh equlbrum consrans (MPEC), solved wh he CPLEX 12 solver hrough he GAMS sofware. Fg. 3 ndcaes more deals of he neracon wh LES and wholesale energy markes. The rades energy (.e., elecrcy and gas) n he energy marke wh predeermned prce sgnals, and manages he energy exchange (.e., elecrcy, gas, and hea) among s LES. Therefore, he decson makng vecor of conans he enres [πe,, πg,, πh,, w, g ]. On he oher hand, each LES exchanges energy (.e., elecrcy, gas, and hea) o serve he MED wh me of use (TOU) prces, and exchanges energy a he LES level wh a compeve prce. In he proposed b-level model he decson-makng vecor of he LES conans he enres [ŵ LES,n,, ŵ LES,ou,, ˆq LES,n,, ˆq LES,ou,, ĝ, LES ]. As a maer of fac, gas and elecrcy are he man energy carrers raded a all levels, whle hea s a local energy carrer ha s only exchanged a he LES level. B. Mul-Energy Player level 1) Objecve Funcon: The aggregaes he energy rade of LES and manages he energy exchange among hem. The objecve of s maxmzng s prof resulng from he energy exchange wh s LES and he energy marke. I s assumed ha he share of from he wholesale energy marke s neglgble, herefore he operaor s consdered as a prce aker n he energy marke and rades energy (.e., gas and ). On he oher hand, he deermnes he couplng prce among LES. Moreover, he LES conan unceran energy resources and her energy quany s ndcaed based on her nernal elecrcy) a predeermned prces (Π e, n w, Elecrcy Marke (EM) EM e, Upper Level: Mul-Energy Player,, e, g, h, nj w, wˆ Lower Level: Local Energy Sysems and Π g, Gas Marke (GM) g LES LES LES ˆ GM g, LES, n LES, n LES, n,, q,, gˆ, wˆ q LES, nj LES, nj,, ˆ, Fg. 3: Ineracon of wh LES and he wholesale elecrcy marke (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

5 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy M. Y. DAMAVANDI e al.: AGGREGATION OF DERS UNDER THE CONCEPT OF S IN LOCAL ENERGY SYSTEMS 5 uncerany characerzaon. To acheve hs goal a sochasc model s developed o consder he unceran behavor of PV and wnd resources hrough a se of scenaros. The scenaro generaon procedure s presened n Appendx A [23]. On he oher hand, a he level here s no source of uncerany and he LES parcpae wh her expeced values of energy exchange n he aggregaon envronmen. The equaons (1)-(6) represen he operaonal problem for he and are based on references [1] and [21]. The objecve funcon for he s expressed as follows: + { [ max (ŵles, π e,, (w Π EM e, + ĝ, LES πg,, + g Π GM g, ) + ˆq LES, πh,, ) ]} (1) 2) Consrans: The man consrans of deals wh s energy conrac and economcal resrcons ha appear n energy exchange lms. Inpu energy lmaon: he energy exchanged by he wh he energy marke s lmed o predeermned energy exchange lms W w W (2) 0 g G (3) energy balance: In he leraure he energy neracons beween LES are represened by usng lnear and non-lnear models. In he lnear models he volage and pressure drop beween LES are negleced and he model s consdered based on lnear energy balance equaons for each nework node. Reference [24] proposed a nonlnear model for boh gas and elecrcy energy carrers consderng AC load flow for elecrcy and pressure-based model for gas nework. Moreover, Ref. [25] consdered a lnear model for energy neracon beween LES based on he energy balance equaons for each node. In hs paper, he energy nework s consdered as a sngle node and he energy neracons beween LES are based on lnear energy balance equaons for he hree energy carrers. Equaons (4)-(6) ndcae he energy balance n he for elecrcy, gas, and hea, respecvely. The hea s a local energy carrer and s energy balance s based on he energy exchange among LES only, whle he elecrcy and gas energy balance should be deermned based on boh energy exchanges wh he energy marke and he LES. w g ŵ LES, = 0 (4) ĝ LES, = 0 (5) ˆq LES, = 0 (6) C. Local Energy Sysem Level Equaon (7) presens he general form of he opmzaon problem for he LES. Gven he vecor x conanng he decson varables for he h LES, f (x ) s he objecve funcon used for he LES opmzaon based on he LES nernal energy schedule and on he energy exchange a he level, where e (x ) and n (x ) are vecors of equaly and nequaly consrans, respecvely. mn {f (x )} Subjec o : e (x ) = 0 n (x ) 0 (7) x 0 1) Objecve Funcon: The objecve of LES s maxmzng s prof (mplemened as mnmzng he mnus-prof [30]) from sellng energy o he MED and radng energy wh he, whle meeng he operaonal consrans of s nernal energy elemens. Equaons (8)-(11) descrbe he expeced values of LES energy exchange wh he. [( f (x ) = ) ( (W ˆq, LES πh,, MED, wh ŵ, LES πe,, w, IL ) Π MED e,, + ĝ, LES πg,, + )] +Q MED, Π MED h,, w, IL Π IL,nc, ŵ LES, ˆq LES, = ω = ω ĝ LES, ρ ω ( w LES,n,ω, ρ ω ( q LES,n,ω, = ω w LES,nj ),ω, q LES,nj ),ω, + G MED, Π MED g,, (8) (9) (10) ρ ω g LES,ω, (11) 2) Consrans: Equaons (12)-(14) conan he energy balance for gas, hea, and elecrcy, respecvely, n he LES. These balances are based on he nernal energy exchange of he specfc energy componens ncluded n he LES, e.g., combned hea and power (CHP), auxlary boler (AB), hea sorage (HS), and nerrupble load (IL). Moreover, he dual varables of each consran are ndcaed afer he rgh hand sde of he respecve equaon. E LES,1,ω, E LES,2,ω, : W MED, w W nd,ω, : G MED, w LES,n,ω, ηe, T rans + w LES,nj,ω, /ηe, T rans w P V,ω, w IL,ω, w CHP,ω, = 0 : λ MED e,,ω,,,, ω (12) g LES,ω, + g CHP,ω, + g AB,ω, : λ MED g,,ω,,,, ω (13) (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

6 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy 6 E LES,3,ω, : Q MED, +q HS,n,ω, q LES,n,ω, ηh, LES q HS,ou,ω, q CHP,ω, + q LES,ou,ω, /ηh, LES q AB,ω, = 0 : λ MED h,,ω,,,, ω (14) Inpu energy lmaon: The LES npu and oupu energy are resrced by he nerconnecors capacy as follows: N LES,1,ω,, N LES,2,ω, : 0 w LES,n,ω, W LES : µ LES,n, e,,ω, µles,n e,,ω,,,, ω (15) N LES,3,ω,, N LES,4,ω, : 0 w LES,ou,ω, W LES : µ LES,ou, µ LES,ou e,,ω, e,,ω,,,, ω (16) N LES,5,ω,, N LES,6,ω, : 0 q LES,n,ω, Q LES : µ LES,n, h,,ω, µles,n h,,ω,,,, ω (17) N LES,7,ω,, N LES,8,ω, : 0 q LES,ou,ω, Q LES : µ LES,ou, µ LES,ou h,,ω, h,,ω,,,, ω (18) N LES,9,ω,, N LES,10,ω, : 0 g,ω, LES G LES : µ LES, g,,ω, µles g,,ω,,,, ω (19) CHP operaonal consrans: The CHP un consumes gas and generaes elecrcy and hea ((20) and (21)). Moreover, he amoun of he hea and elecrcy producon are resrced based on characerscs ((22)-(24)) of he un, whle s hea o elecrcy rao (Φ CHP ) s a consan value. E LES,4,ω, E LES,5,ω, : w CHP,ω, : q CHP,ω, ηe, CHP g,ω, CHP = 0 : λ CHP e,,ω,,,, ω (20) ηh, CHP g,ω, CHP = 0 : λ CHP h,,ω,,,, ω (21) N LES,11,ω,, N LES,12,ω, : 0 w,ω, CHP W CHP : µ CHP, e,,ω, µchp e,,ω,,,, ω (22) N LES,13,ω,, N LES,14,ω, : 0 q,ω, CHP Q CHP : µ CHP, h,,ω, µchp h,,ω,,,, ω (23) AB operaonal consrans: The oupu hea of he AB s relaed o s effcency and should be lower han s maxmum capacy. E LES,7,ω, : q AB,ω, η AB e, g AB,ω, = 0 : λ AB h,,ω,,,, ω (25) N LES,15,ω,, N LES,16,ω, : 0 q,ω, AB Q AB : µ AB, h,,ω, µab h,,ω,,,, ω (26) HS operaonal consrans: The sored hea a each hour s relaed o he energy exchange of he HS wh he LES and should be lower han he HS lmaons. Moreover, for conssency n he sudy perod, he amoun of he sored energy a he sarng and endng hours of he perod are consdered o be equal and are se o one half of he maxmum capacy. E LES,8,ω, : Q HS,ω, q HS +q HS,n,ω, ηh, HS,ω, 1 0.5Q HS >1,ω, =1 q HS,ou,ω, /ηh, HS = 0 : λ HS h,,ω,,,, ω (27) N LES,17,ω,, N LES,18,ω, : 0 q HS,n,ω, γ HS : µ HS,n, h,,ω, µhs,n h,,ω, N LES,19,ω,, N LES,20,ω, : 0 q HS,ou,ω, γ HS : µ HS,ou, h,,ω, µhs,ou h,,ω,,,, ω (28),,, ω (29) N LES,21,ω,, N LES,22,ω, : 0 q,ω, HS Q HS : µ HS, h,,ω, µhs h,,ω,,,, ω (30) T LES,1,ω, T LES,2,ω, : q,ω,=1 HS = Q HS,ω /2 + q HS,n,ω,=1 ηhs h, q HS,ou,ω,=1 /ηhs h, = 0 : ξh,,ω,=1, HS, = 1, ω (31) : q,ω,=t HS = Q HS,ω /2 + q HS,n,ω,=T ηhs h, q HS,ou,ω,=T /ηhs h, = 0 : ξh,,ω,=t HS,, = T, ω (32) PV arrays operaonal consran: Some scenaros are mplemened o model he unceran naure of he PV array generaon. The generaon n each hour should be based on he scenaro amouns. E LES,6,ω, : w,ω, CHP Φ CHP q,ω, CHP = 0 : λ Rao,ω,,,, ω (24) P V,F orecas N LES,23,ω,, N LES,24,ω, : 0 w,ω, P V W : µ P V, e,,ω, µp e,,ω,, V,, ω (33) (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

7 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy M. Y. DAMAVANDI e al.: AGGREGATION OF DERS UNDER THE CONCEPT OF S IN LOCAL ENERGY SYSTEMS 7 Wnd generaon operaonal consran: Smlar o PV array, for wnd generaon, he oupu energy s based on he wnd scenaros. N LES,25,ω,, N LES,26,ω, : 0 w,ω, W nd W nd,f orecas W : µ W nd nd, µw e,,ω, e,,ω,,,, ω (34) Inerrupble load: The LES operaor gves an ncenve o he MED o reduce s consumpon whle he npu energy prce s hgh and he energy producon s no profable for he LES. In hs paper he IL s only consdered for elecrcy and α, IL s he percenage of elecrcal demand ha can be nerruped. N LES,27,ω,, N LES,28,ω, : 0 w,ω, IL α, IL W, MED : µ IL, e,,ω, µil e,,ω,,,, ω (35) III. MATHEMATICAL FORMULATION OF THE AND LES DECISION MAKING CONFLICT Based on he proposed formulaon, and LES are acve n wo dfferen levels. The model can be consdered as a Sackelberg game n whch a he upper level here s he as a leader, and a he lower level here are LES as followers. The deermnes he energy prce, and he LES schedule her nernal energy resources and propose her energy exchange based on he prce sgnals. Due o he erms ŵ, LES πe,,, ĝ, LES πg,,, and ˆq, LES πh,, n he objecve funcon he lower level problem s non-lnear. To lnearze hese erms, he upper level prce sgnal s consdered as an npu parameer for he lower level problem. Therefore, he lower level problems can be replaced by her Karush- Kuhn-Tucker (KKT) opmaly condons. Afer ha, he srong dualy heorem enforces o he problem o lnearze he non-lnear erms of he upper level objecve funcon (.e. ŵ LES, π e,,, ĝ LES, π g,,, and ˆq LES, π h,, ) [22], [26]. Therefore, he b-level problem s ransformed no a sngle level MILP problem. A. Problem Formulaon a he LES Level As explaned before, he lower level equaons (12)-(35) are lnear and hus convex. For replacng he lower level problem wh s KKT opmaly condons, he Lagrangan expresson of he lower level problem s deermned as n (36), where µ, λ, and ξ are dual varables of LES nequaly consrans, equaly consrans, and equaly consrans n specfc me nervals, respecvely. Equaons (37)-(40) represen he KKT condons of he lower level problem. Equaon (37) s he saonary condon, equaons (38) and (39) are prmal feasbly condons, and (40) s he complemenary condon of he KKT opmaly condons. The superscrp T denoes ransposon. L = f (x ) µ T n (x ) + λ T e (x ) + ξ T (x ) (36) L / x = 0 (37) L / λ = e (x ) = 0 (38) L / ξ = (x ) = 0 (39) 0 µ n (x ) 0 (40) For lnearzng he complemenary condon, a se of bnary varables (u ) are nroduced o ransform he equaon (40) no he equaons (41) and (42) [22]. The parameer M s used o relax he complemenary condon, and should be calculaed on he bass of he range of varaon of he varables appearng n he problem. For he prmal problem, he range of varaon of s varables s based on he energy scale. For he dual problem, he range of varaon of s varables s based on he energy prce scale. I s possble o deermne a specfc M for each equaon, bu for he sake of smplcy wo values are consdered, M p for he prmal problem, and M d for he dual problem; each of hem s based on he maxmum range of varaon ha occurs for he varables of he correspondng problem. 0 n (x ) M p u (41) 0 µ M d u (42) B. Lnearzng he Objecve Funcon Equaon (43) s he prmal opmzaon problem of he lower level problem ha s formed. I s based on he decson varables x, and on he marx H and he column vecor b derved from he equaly and non-equaly consrans, expressed as n Equaon (44). mn {c T x } Subjec o : H x b 0, where c s he vecor of coeffcens e (x ) : H E x = 0 n (x ) : H N x b N 0 H = [ H E H N x 0 ], b = [ ] 0 b N (43) (44) Equaon (45) shows he dual form of he lower level problem nroduced n equaon (43). The vecor ψ conans he dual varables of he LES consrans, ndcaed n he las par of he equaons (12)-(35). max {b ψ } Subjec o : H ψ c 0 (45) ψ 0 Equaon (46) llusraes he srong dualy condon for he lower level problem. Ths condon saes ha, for lnear (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

8 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy 8 (and hus convex) problems, he gap of he dual and prmal objecve funcons can be consdered as zero, so he objecve funcons of he prmal and dual problems become equal [17]. The nonlnear erms of he objecve funcon (ŵ, LES πe,,, ĝ, LES πg,,, and ˆq, LES πh,, ) are he same as he non-lnear erms of he objecve funcon of he LES. Therefore, hey can be replaced based on (46) by her lnear forms, whch are derved from he srong dualy condon. c x = b ψ (46) IV. SYSTEM EFFECTIVENESS IN VARIOUS ENERGY INTERACTION CONDITIONS A. Sysem Effecveness Index The sysem effecveness ndex consdered s relaed o he capably of he LES o ulze her nernal energy resources nsead of mporng energy from he upsream nework. Equaon (47) shows he general formulaon o calculae hs ndex for he generc energy carrer c ha wll be delvered o he MED. The effecveness of he energy sorage un α = 1,..., A o mgae he varaon of he sysem s consdered as he varaon of he normalzed energy level of sorage n consecuve me nervals (he frs addend n equaon (47)). For energy converers, he ndex s based on he share of he oupu energy o he maxmum capacy of he energy converer β = 1,..., B n he sudy me horzon (he second addend n equaon (47)). 1 LRUF c = T (A + B) [ A T E α,c, E α,c, 1 B T + E α,c α=1 =1 B. Energy Ineracon Condons β=1 =1 ] E β,c, E β,c (47) Three energy neracon condons are consdered n hs paper for aggregaon of LES by he. 1) Cenralzed managemen for LES: In hs aggregaon mode, he manages all he energy facles of he LES. Ths mode s relaed o he capably of he o have a leas one-way communcaon wh he LES o send he operaon mode of each elemen. Alhough hs mode needs vas communcaon nfrasrucure, wll reduce he plannng cos for he whole sysem by explong he synergy among LES. Equaon (48) shows he objecve funcon of ha operaes he whole sysem by ulzng LES facles and neracng wh he energy marke. max { (w Π EM e, + g Π GM g, ) } (48) 2) Drec prcng for LES: In hs mode, he sends a specfc prce sgnal o each LES, and he LES send back her energy schedule o he. Therefore, he and each LES have an equlbrum prce for each energy carrer. The dfference beween he LES prces helps he nerac MED #2 IL #2 MED #1 IL #1 MED #3 IL #3 Fg. 4: and LES cooperaon envronmen schemac. energy wh each LES ndependenly. The mahemacal model for he drec prcng scheme s represened by (1)-(35). In hs model he energy prce for each LES has dmensons, as s specfed for each LES (.e. π e,,, π g,,, and π h,, ). 3) Unform prcng for LES: In hs mode, all he LES receve he same equlbrum prce for each energy carrer. Therefore, nsead of havng varous energy prces for each LES (.e. π e,,, π g,, s used for all LES (.e. π e,, and π h,,, π g, V. NUMERICAL RESULTS A. Inpu Daa Characerzaon ) he same energy prce, and πh, ). The numercal sudy s prepared o show he effecveness of he proposed framework n real-lfe cases and rack he behavor of he energy players. Whou loss of generaly, wh he am of provdng a dealed vew on he resuls, nally hree LES are consdered as he mnmum possble amoun of LES ha can suppor he research dea (Fg. 4). In he proposed case sudy, each LES has a ceran specfcaon. LES #1 and #2 are CHP-based and generae boh elecrcy and hea, smulaneously. LES #1 s also equpped wh HS; herefore, can subsue s hea energy consumpon beween me nervals. On he conrary, LES #3 s renewable energy-based and can generae cheap elecrcy, bu he hea producon margnal cos of hs LES wll be hgher han oher LES because s no equpped wh CHP and HS uns. I s assumed ha he s a prce aker n he energy marke. Therefore, s neracon wh oher energy players n he energy marke s based on he predeermned energy carrers prce sgnals (Fg. 5). Daa of elecrcy prces for he npu have been obaned from he hourly daa of he Spansh elecrcy marke n May 2015 [28]. The LES conss of CHP, AB, HS, IL, and renewable energy generaon. The comprehensve daa for elemens of hese hree LES are represened n Table I. The MILP problem has been solved wh he CPLEX12 solver under he lcense of he GAMS sofware, wh an HP Z800 Worksaon (CPU 3.47 GHz, RAM 96GB) (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

9 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy M. Y. DAMAVANDI e al.: AGGREGATION OF DERS UNDER THE CONCEPT OF S IN LOCAL ENERGY SYSTEMS 9 Fg. 5: The hourly prce of elecrcy and gas markes. TABLE I: DATA OF THE LOCAL ENERGY SYSTEM. Fg. 6: Share of each elemen n elecrcy balance of LES n Case I. Elemens LES1 LES2 LES3 Transformer LES Hea Ppelnes Effcency CHP AB Elecrcy Oupu 2.5 MW 1.5 MW Hea Oupu 3 MW 2.2 MW ηe CHP, ηh CHP 0.43, , 0.3 Hea Oupu 2 MW 3 MW 1.5 MW η AB h Fg. 7: Share of each elemen n hea energy balance of LES n Case I. HS Energy Capacy 3 MWh γ HS h 1.5 MW η HS,cha h, η HS,dcha h 0.9, 0.81 Wnd Capacy Renewable 3.3 MW PV Capacy 3.3 MW B. Evaluaon of Players Energy Ineracon Behavor 1) Case I: Cenralzed managemen for LES: Fg. 6 and Fg. 7 show he elecrcy and hea balance for LES whle he manages all facles cenrally. The IL s no used, so he demand s unchanged durng he day. As s shown, he man producon of CHP uns occurs durng hours 9-13 and 17-21, when he elecrcy wholesale prce s maxmum and he MED have smulaneous consumpon of elecrcy and hea. I should be noed ha mos of he me he CHP uns are n hea-followng mode and produce elecrcy based on her hea demand and jus a hours 22 and 23 he CHP uns are n elecrcy-followng mode. In hese hours he elecrcy prce s very hgh, bu LES #1 doesn have enough hea demand, herefore he surplus hea producon of CHP #1 sored n HS #1 and CHP #1 can operae n elecrcy-followng mode. Moreover, a hours 9-12 he can njec s elecrcy generaon o he upsream nework, when he elecrcy prce s almos hgh. A hese hours, he renewable energy generaon s maxmum and he hgh hea demand leads o he mnmum margnal cos for he CHP uns. Therefore, he oal margnal cos for elecrcy producon of he wll be lower han he wholesale elecrcy marke prce. 2) Case II: Drec prcng mode: In hs mode, he deermnes he energy prces o nerac wh each LES. Afer ha, each LES schedules s hea and elecrcy balance. Fg. 8 repors he equlbrum prce for he elecrcy, gas, and hea carrers n each LES. Moreover, Fg. 9 and Fg. 10 show he elecrcy and hea balance for LES, respecvely. As s shown, he deermnes dfferen energy prces for each LES o maxmze s prof by changng he behavor of each LES, ndependenly. The s he only suppler of naural gas n he sysem; herefore, he ncreases he gas prce up o he prce cap o maxmze s prof. Moreover, hgh gas prce leads o ncrease he margnal cos of he CHP uns elecrcy producon. For LES #1 (ha can sasfy s hea demand from HS, AB, and CHP) he manans he hea prce o he lowes amoun, o preven hea njecon of LES #1 o oher LES. Moreover, he equlbrum hea prce s based on he margnal cos of hea producon n LES. The elecrcy prce for each LES s relaed o he flexbly of LES o change s energy neracon wh he. For LES #1 ha has an effcen CHP un, he elecrcy equlbrum prce s almos equal o he margnal cos of he CHP un. Only a hour 11, when he prce of he elecrcy wholesale marke s hgh, he ncreases he equlbrum prce o he prce cap, o movae LES #1 o ncrease s CHP uns (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

10 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy 10 Fg. 8: Elecrcy equlbrum prce beween and LES n Case II. Fg. 10: Share of each elemen n hea energy balance of LES n Case II. Fg. 9: Share of each elemen n elecrcy balance of LES n Case II. Fg. 11: Elecrcy equlbrum prce beween and LES n Case III. producon o s maxmum level. For LES #2, he effcency of he CHP un s lower; herefore, he margnal cos of he CHP un producon s low, whle he LES #2 has maxmum hea demand. Therefore, durng he peak of hea demand n LES #2, he margnal cos of elecrcy producon for LES #2 decreases, and consequenly he elecrcy equlbrum prce s decreased, dramacally. For LES #3 wh hgh peneraon of renewable energy, he margnal cos of elecrcy generaon s very low; herefore, a mos of he hours he elecrcy equlbrum prce s a he lowes amoun for LES #3. Durng hours 4-6, whle he renewable energy generaon s very low and LES #3 has no more opon o generae elecrcy, he ncreases he elecrcy prce up o he prce cap o maxmze s prof from sellng energy o LES #3. I should be noed ha n hs mode he LES ulze her IL resources a he maxmum level. Ths happens because he enforces dfferen prces for each LES, and he average elecrcy prce s hgher han n he oher cases. 3) Case III: Unform prcng for LES: In hs mode all LES schedule her energy balance based on he same equlbrum prce. Fg. 11 shows he equlbrum prce for he elecrcy, hea, and gas carrers. Fg. 12 and Fg. 13 show he elecrcy and hea balances, respecvely. Due o he same prce for all LES n hs case, he equlbrum s formed from all LES and has more varaon. Smlarly o Case II, he s he only suppler of naural gas, and ncreases he gas prce up o he Fg. 12: Share of each elemen n elecrcy energy balance of LES n Case III. prce cap. The ams o maxmze s prof and has hree man sraeges o mpac on he LES behavor: In he frs sraegy (e.g. hours 3, 4, and 13-16) he decreases he energy prce o he margnal cos of CHP uns o ncrease s marke share and oal prof. In he second sraegy (e.g. hours 9-12), he decreases he energy prce and njecs LES surplus energy o he upsream nework o maxmze s prof. In hese hours, due o hgh hea consumpon and hgh renewable energy producon, he margnal cos of elecrcy producon for LES s low. Therefore, he can buy elecrcy a lower prce from LES and sell o he (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

11 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy M. Y. DAMAVANDI e al.: AGGREGATION OF DERS UNDER THE CONCEPT OF S IN LOCAL ENERGY SYSTEMS 11 Fg. 13: Share of each elemen n hea energy balance of LES n Case III. TABLE II: DATA OF LRUF INDEXES. LRUF e LRUF h Cenralzed Drec Prcng Unform Prcng elecrcy marke. In he hrd sraegy (e.g. hours 5-8), he ncreases he equlbrum prce o maxmze s prof hrough sellng he remanng LES energy a he maxmum prce. I should be noed ha he prof of he s relaed o he energy conen ha he neracs wh oher energy players. For nsance, n he case durng hours 9-12, he buys elecrcy from LES a hgher prce han from he elecrcy marke, and sells o he elecrcy marke. The key pon s ha he LES generae elecrcy by ulzng CHP uns, and CHP uns consume naural gas as prmary resources. Therefore, by generang more elecrcy by usng CHP uns means ha he sells more naural gas o he LES. Therefore, he ne energy conen ha he s neracng wh he elecrcy wholesale marke and LES s profable. C. Effecveness Assessmen Based on Decson Makng Framework Table II shows he amoun of each sysem effecveness ndexes for hree energy neracon condons. The LES have wo oupu o he MED, herefore, he LRUF ndex from (47) has been calculaed for boh hea and elecrcy,.e., he carrer c = {e, h}. As s shown, he dfference beween cenralzed managemen mode and drec prcng s neglgble n boh cases. In he cenralzed managemen mode, he can conrol all facles of LES drecly; n he same way as n he drec prcng mode, he sends prce sgnals o each LES, ndvdually and can change he behavor of LES. Alhough he mechansms o shape he behavor of LES n hese wo modes are dfferen, he fnal behavor of LES and especally he energy neracons among LES and are he same. Fg. 14: Comparson of HS un operaon n Case I, II, and III In he unform prcng mode, he sysem effecveness ndex s hgher han n he wo oher modes for each energy carrer. From he drec o he unform prcng mode, he LRUF ndex for hea shows 11% ncrease, and for elecrcy shows 34% ncrease. As a maer of he fac, ncreasng he degree of freedom for decson makng of LES resuls n more flexbly of LES o ulze her nernal energy resources for boh elecrcy and hea. The sharp ncrease n LRUF h s due o more ulzaon of CHP and HS uns n unform prcng, compared wh he drec prcng mode. Fg. 14 shows he operaonal behavor of HS durng 24 hours. In hs fgure he HS has more varaon n case III when he neracs energy n unform prcng mode. I shows more operaonal flexbly of LES n he unform prcng mode. D. Effecveness Assessmen Based on Local Players Characerscs Ths secon shows he resuls of he proposed approach wh a growng number of LES. Whou loss of generaly, he resuls obaned from Case III (unform prcng) wh hree LES are aken as he sarng pon. The number of LES s hen ncreased n order o creae hree energy mx ypes, namely: Type I: only he number of LES #1 s ncreased Type II: only he number of LES #2 s ncreased Type III: only he number of LES #3 s ncreased The added LES for each ype have he same characerscs, bu are ncluded n he model n an ndependen way, hus ncreasng he dmensons of he vecors and marces used. The mpac of he dfferen ypes of energy mx on he flexbly of LES o use he nernal energy resources for elecrcy and hea s expressed hrough he ndexes LRUF e and LRUF h. By ncreasng he amoun of LES #1 n Type I energy mx, hgher producon margnal coss appear. Thereby, he ulzaon facor of CHP uns decreases, he HS capacy n he sysem ncreases, and he sysem experences a reducon n boh ndexes LRUF e (Fg. 15) and LRUF h (Fg. 16). From Fg. 15, he ndex LRUF e ncreases by ncreasng he number of LES of Type II and Type III. In fac, ncreasng he number of LES, he lower producon margnal cos leads o ncreasng he ulzaon of elecrcy-based LES (for Type II) and renewable-based LES (for Type III) (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

12 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy 12 Fg. 15: LRUF e amoun for hree ypes of LES. Fg. 16: LRUF h amoun for hree ypes of LES. From Fg. 16, he ndex LRUF h ncreases by ncreasng he number of LES of Type II. In hs condon, he share of CHP uns n elecrcy generaon ncreases, hea s produced as supplemenary energy carrer from CHP uns, and he HS usage becomes hgher. The rae of LRUF h ncrease s gradually reduced for hgher numbers of LES. On he conrary, by ncreasng he number of LES of Type III, hgher shares of renewable resources mpac on he operaon of he CHP uns and lead o a sgnfcan reducon n he LRUF h ndex. The compuaon me of he soluons ndcaed n Fg. 15 and Fg. 16 ranges from approxmaely one mnue for he sarng pon, up o 15 mnues for he case wh 5 LES of Type I ha s equpped by energy sorage un. For ypes II and III he ncrease of compuaon me versus he number of LES s more lnear and for he case wh 5 LES s approxmaely 5 mnues. The use of parallel processors o run he calculaons on he ndvdual LES would decrease he compuaon me. VI. CONCLUSION Ths paper has developed a model of cooperaon n mul-energy sysems. Frsly, a herarchcal srucure has been proposed o represen he energy exchange wh LES. Afer ha, he and LES have been modeled, ndependenly. The decson-makng conflcs among hese players have been modeled hrough an MINLP b-level approach. A he upper level, he ams o maxmze s prof and he equlbrum prces are deermned by cooperaon of all LES. A he lower level, each LES schedules s energy balance based on he equlbrum prce and he energy exchange for each player wll be concluded. For ransformng he problem no a MILP sngle level problem, frsly he lower level problem has been replaced wh s KKT opmaly condons. Afer ha, based on he srong dualy heorem, he objecve funcon of he upper level problem has been lnearzed. The key fndngs from he numercal resuls are as follows: The resource allocaon of each LES deermnes s operaonal flexbly n he shor erm and explans s behavor o cooperae wh oher LES n a mul-energy sysem. The presence of approprae energy neracon condons n mul-energy sysems affecs he behavor and makes possble o explo synerges among LES. For local energy carrers ha produce and consume locally (.e., hea), he varable margnal prce movaes he o ulze s nernal resources for maxmzng s prof. Man energy carrers ha canno be generaed locally (.e., gas) should be regulaed appropraely o mgae he energy prce spke n he local nework. The proposed approach may be appled o plannng sudes amed a showng he mpac of ncreasng a ceran ype of LES on he effecveness ndexes. Due o lnear mahemacal modelng, he proposed approach guaranees o reach he global opmum. The compuaonal burden can be reduced by ulzng parallel processors o run he ndvdual LES opmzaons. In he fuure works, he role of n energy marke envronmen wll be furher nvesgaed, by evaluang he economc funcons of he energy marke based on he peneraon rae of he. APPENDIX A MODELING OF THE RENEWABLE ENERGY RESOURCE UNCERTAINTY The uncerany n he npus from renewable energy sources (wnd generaon and PV arrays, n hs sudy) s modeled by generang approprae scenaros for he sudy. For hs purpose, me-seres based models such as ARIMA, or arfcal nellgence models (e.g., neural neworks, daa mnng, and evoluonary compuaon) can be used. In hs paper, he same approach s used for PV and wnd. The full descrpon of he procedure s explaned for he case of wnd power. Wnd speed dsrbuons are ofen characerzed by Webull dsrbuons [29]. The Probably Densy Funcon (PDF) of he wnd speed s represened by (49), where c > 0 and k > 0 are he scale facor and he shape facor, respecvely. f v (v) = k c ( ) k 1 v exp[ c ( ) k ] v c (49) The probably dsrbuon funcon s dvded no N s scenaros, and he probably of each sep can be calculaed as follows: prob ω = W Sω+1 W S ω f v (v) dv, ω = 1, 2,..., N s (50) where W S ω s he wnd speed of he ω h scenaro. The power generaed, P GW (ω), correspondng o a specfc wnd (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

13 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy M. Y. DAMAVANDI e al.: AGGREGATION OF DERS UNDER THE CONCEPT OF S IN LOCAL ENERGY SYSTEMS 13 ) +Q MED, Π MED h,, w, IL Π IL,nc, Fg. 17: PV and Wnd Scenaros for LES III n p.u. speed W S ω can be obaned from (50) n whch A, B, and C are consans calculaed accordng wh [29]. 0 0 W S ω V c or W S ω V c0 P GW (ω) = P r (A + B W S ω + C W Sω) 2 V c W S ω V r P r V r W S ω V c0 (51) In (51), V c, V c0, and V cr represen cu-n speed, cu-ou speed, and raed speed, respecvely. Dfferen realzaons of wnd power generaon are modeled hrough a scenaro generaon process based on he Roulee Wheel Mechansm (RWM) [30]. A frs, he dsrbuon funcon s dvded no some class nervals. Moreover, each nerval s assocaed wh a probably. Subsequenly, accordng o dfferen nervals and her probables obaned by PDF, he RWM s appled o generae scenaros for each hour. To hs end, a frs, he probables of dfferen nervals are normalzed n a way ha her summaon becomes equal o uny. Afer ha, random numbers are generaed beween 0 and 1. Each random number falls n he normalzed probably range of a wnd power generaon nerval n he roulee wheel. Tha wnd power generaon nerval s seleced by he roulee wheel mechansm for he respecve scenaro. Of course, hgher numbers of scenaros produce a more accurae model o consder he menoned unceranes. However, yelds an unmanageable opmzaon problem. Hence, a scenaro reducon echnque s consdered, usng he K-means cluserng echnque [31], resulng n a scenaro ree wh en ndependen scenaros, used n case sudes. In hs paper, he Swf Curren wnd daa are used o generae wnd power scenaros [32]. The fnal ulzed scenaros for PV and wnd generaon and he expeced values are depced n Fg. 17. APPENDIX B COMPREHENSIVE MPEC MODELING The MPEC formulaon of problem as follows: Lnear Objecve Funcon: { [ max (w Π EM e, + g Π GM g, ) + ( (W MED, w, IL ) Π MED e,, + G MED, Π MED g,, +λ MED e,, W, MED + λ MED g,, 0.5λ HS h,,ω,q HS,ω, + ξ HS =1 Q HS =T,ω,/2 µ LES,n +ξh,,ω, HS µ LES,n h,,ω, QLES G MED, h,,ω, e,,ω, W LES + λ MED h,, Q HS =1 Q MED,,ω,/2 µ LES,ou e,,ω, W LES µ LES,ou h,,ω, Q LES µ LES g,,ω,g LES µ CHP e,,ω,w CHP µ CHP h,,ω,q CHP µ AB h,,ω,q AB µ HS,n h,,ω, γhs µ HS,ou h,,ω, γhs µ P e,,ω,w V P V,F orecas µ W nd µ IL e,,ω,α, IL W, MED Prmal Opmaly Condons: µ HS h,,ω,q HS W nd,f orecas e,,ω,w ] } (52) W w W (53) 0 g G (54) w g Saonary Condons: / w LES,n,ω, = πe,, ŵ LES, = 0 (55) ĝ LES, = 0 (56) ˆq LES, = 0 (57) λ MED e,, ηe, T rans µ LES,n e,,ω, / w LES,ou,ω, = πe,, / g,ω, LES = πg,, / q LES,n,ω, = πh,, / q LES,ou,ω, = πh,, / w,ω, CHP = λ MED e,, / q,ω, CHP = λ MED h,, / g,ω, CHP = λ MED g,, / q,ω, AB = λ MED h,, µ LES,ou e,,ω, + µ LES,n e,,ω, = 0 (58) + λ MED e,, /ηe, T rans + µ LES,ou e,,ω, = 0 (59) λ MED e,, µ LES g,,ω, + µles g,,ω, = 0 (60) λ MED h,, ηh, LES µ LES,n h,,ω, + λ MED h,, /ηh, LES µ LES,ou h,,ω, + µ LES,n h,,ω, = 0 (61) + µ LES,ou h,,ω, = 0 (62) + λ CHP e,,ω, + λ Rao,ω, Φ CHP µ CHP e,,ω, + µchp e,,ω, = 0 (63) + λ CHP h,,ω, λ Rao,ω, µ CHP + h,,ω, µchp h,,ω, = 0 (64) λ CHP e,,ω,ηe, CHP λ CHP h,,ω,ηh, CHP = 0 (65) + λ AB h,,ω, µ AB h,,ω, µab h,,ω, = 0 (66) / g,ω, AB = λ MED g,, λ AB h,,ω,ηh, AB = 0 (67) / q HS,n,ω, = λ MED h,, + λ HS h,,ω,ηh, HS µ HS,n h,,ω, µhs,n h,,ω, = 0 (68) (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

14 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy 14 / q HS,ou,ω, = λ MED h,, λ HS h,,ω,/ηh, HS µ HS,ou h,,ω, + µhs,ou h,,ω, = 0 (69) / q,ω, HS = λ HS h,,ω, λ HS h,,ω,+1 µ HS + h,,ω, µhs h,,ω, = 0 (70) / w,ω, W nd = λ MED e,, / w,ω, P V = λ MED e,, / w,ω, IL = λ MED e,, Complemenary Condons: 0 µ LES,n e,,ω, 0 µ LES,n e,,ω, 0 µ LES,ou e,,ω, 0 µ LES,ou e,,ω, 0 µ LES,n h,,ω, 0 µ LES,n h,,ω, 0 µ LES,ou h,,ω, 0 µ LES,ou h,,ω, µ W nd e,,ω, + µw nd e,,ω, = 0 (71) µ P V e,,ω, + µp V e,,ω, = 0 (72) µ IL e,,ω, + µil e,,ω, = 0 (73) (w LES,n,ω, ) 0 (74) (W LES w LES,n,ω, ) 0 (75) (w LES,ou,ω, ) 0 (76) (W LES w LES,ou,ω, ) 0 (77) (q LES,n,ω, ) 0 (78) (Q LES q LES,n,ω, ) 0 (79) (q LES,ou,ω, ) 0 (80) q LES,ou,ω, ) 0 (81) 0 µ LES g,,ω, (gles,ω, ) 0 (82) (Q LES 0 µ LES g,,ω, (G LES g,ω, LES ) 0 (83) 0 µ CHP e,,ω, (wchp,ω, ) 0 (84) 0 µ CHP e,,ω, (W CHP w,ω, CHP ) 0 (85) 0 µ CHP h,,ω, (qchp,ω, ) 0 (86) 0 µ CHP h,,ω, (Q CHP q,ω, CHP ) 0 (87) 0 µ AB h,,ω, (qab,ω,) 0 (88) 0 µ AB h,,ω, (Q AB q,ω,) AB 0 (89) 0 µ HS,n h,,ω, (qhs,n,ω, ) 0 (90) 0 µ HS,n h,,ω, (γhs q HS,n,ω, ) 0 (91) 0 µ HS,ou h,,ω, (q HS,ou,ω, ) 0 (92) 0 µ HS,ou h,,ω, (γ HS q HS,ou,ω, ) 0 (93) 0 µ HS h,,ω, (qhs,ω,) 0 (94) 0 µ HS h,,ω, (Q HS q,ω,) HS 0 (95) 0 µ P V e,,ω, (wp,ω,) V 0 (96) 0 µ P e,,ω, V (W 0 µ W nd 0 µ W e,,ω, nd (W P V,F orecas w,ω,) P V 0 (97) nd (ww,ω, ) 0 (98) e,,ω, W nd,f orecas w,ω, W nd ) 0 (99) 0 µ IL e,,ω, (wil,ω,) 0 (100) 0 µ IL e,,ω, (α, IL W, MED REFERENCES w IL,ω,) 0 (101) [1] N. 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Mancarella, Marx modellng of small-scale rgeneraon sysems and applcaon o operaonal opmzaon, Energy, vol. 34, no. 3, pp , [7] T. Krause, G. Andersson, K. Frohlch and A. Vaccaro, Mulple-Energy Carrers: Modelng of Producon, Delvery, and Consumpon, Proceedngs of he IEEE, vol. 99, no. 1, pp , [8] M. Houwng, R. R. Negenborn, and B. De Schuer, Demand Response Wh Mcro-CHP Sysems, Proceedngs of he IEEE, vol. 99, no. 1, pp , [9] F. Kenzle, P. Ahcn, and G. Andersson, Valung Invesmens n Mul- Energy Converson, Sorage, and Demand-Sde Managemen Sysems Under Uncerany, IEEE Transacons on Susanable Energy, vol. 2, no. 2, pp , [10] P. Mancarella and G. Chcco, Real-Tme Demand Response From Energy Shfng n Dsrbued Mul-Generaon, IEEE Transacons on Smar Grd, vol. 4, no. 4, pp , [11] M. Schulze, L. Fredrch, and M. Gausch, Modelng and opmzaon of renewables: applyng he Energy Hub approach. IEEE Inernaonal Conference on Susanable Energy Technologes, Sngapore, 2008, pp [12] M. C. Bozchalu, S. A. Hashm, H. Hassen e al., Opmal Operaon of Resdenal Energy Hubs n Smar Grds, IEEE Transacons on Smar Grd, vol. 3, no. 4, pp , [13] F. Adamek, M. Arnold, and G. Andersson, On Decsve Sorage Parameers for Mnmzng Energy Supply Coss n Mulcarrer Energy Sysems, IEEE Transacons on Susanable Energy, vol. 5, no. 1, pp , [14] M. Gedl, and G. Andersson, Opmal Power Flow of Mulple Energy Carrers, IEEE Transacons on Power Sysems, vol. 22, no. 1, pp , [15] M. Moen-Aghae, A. Abbaspour, M. Fouh-Fruzabad e al., A Decomposed Soluon o Mulple-Energy Carrers Opmal Power Flow, IEEE Transacons on Power Sysems, vol. 29, no. 2, pp , [16] M. Arnold, R. Negenborn, G. Andersson e al., Dsrbued predcve conrol for energy hub coordnaon n coupled elecrcy and gas neworks, Inellgen Infrasrucures, pp : Sprnger, [17] M. Marzband, M. Javad, J. L. Domnguez-Garca and M. Mrhossen Moghaddam, Non-cooperave game heory based energy managemen sysems for energy dsrc n he real marke consderng DER unceranes, IET Generaon, Transmsson & Dsrbuon, vol. 10, no. 12, pp , [18] M. Marzband, N. Parhz, M. Savagheb and J. M. Guerrero, Dsrbued Smar Decson-Makng for a Mulmcrogrd Sysem Based on a Herarchcal Ineracve Archecure, IEEE Transacons on Energy Converson, vol. 31, no. 2, pp , June [19] M. Marzband, F. Azarnejadan, M. Savagheb, and J. M. Guerrero, An Opmal Energy Managemen Sysem for Islanded Mcrogrds Based on Mulperod Arfcal Bee Colony Combned Wh Markov Chan, IEEE Sysems Journal, n press. [20] M. Marzband, A. Sumper, J. L. Domnguez-Garca, and R. Gumara- Ferre, Expermenal valdaon of a real me energy managemen sysem for mcrogrds n slanded mode usng a local day-ahead elecrcy marke and MINLP, Energy Converson and Managemen, vol. 76, pp , December [21] M. Y. Damavand, M. P. Moghaddam, M. R. Haghfam, M. Shafe-Khah, and J.P.S. Caalão, Modelng Operaonal Behavor of Plug-n Elecrc Vehcles Parkng Lo n Mulenergy Sysems, IEEE Transacons on Smar Grd, vol. 7, no. 1, pp , Jan [22] M. Zugno, J. M. Morales, P. Pnson e al., A blevel model for elecrcy realers parcpaon n a demand response marke envronmen, Energy Economcs, vol. 36, pp , [23] N. Neyesan, M. Y. Damavand, M. Shafe-Khah, J. Conreras and J. P. S. Caalão, Allocaon of Plug-In Vehcles Parkng Los n Dsrbuon (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.

15 Ths arcle has been acceped for publcaon n a fuure ssue of hs journal, bu has no been fully eded. Conen may change pror o fnal publcaon. Caon nformaon: DOI /TSTE , IEEE Transacons on Susanable Energy M. Y. DAMAVANDI e al.: AGGREGATION OF DERS UNDER THE CONCEPT OF S IN LOCAL ENERGY SYSTEMS 15 Sysems Consderng Nework-Consraned Objecves, IEEE Transacons on Power Sysems, vol. 30, no. 5, pp , Sep [24] M. La Scala, A. Vaccaro, and A.F. Zobaa, A goal programmng mehodology for mulobjecve opmzaon of dsrbued energy hubs operaon, Appled Thermal Engneerng, vol. 71, no. 2, pp , Ocober [25] T. L, M. Erema, and M. Shahdehpour, Inerdependency of naural gas nework and power sysem secury, IEEE Transacons on Power Sysems, vol. 23, pp , Nov [26] S. J. Kazempour, A. J. Conejo, and C. Ruz, Generaon Invesmen Equlbra Wh Sraegc Producers-Par I: Formulaon, IEEE Transacons on Power Sysems, vol. 28, no. 3, pp , [27] G. Chcco and P. Mancarella, A unfed model for energy and envronmenal performance assessmen of naural gas-fueled poly-generaon sysems, Energy Converson and Managemen, vol. 49, no 8, pp , Augus [28] RED Elecrca de Espana. (Dec. 2014). Energy Prce and Capacy Paymen. [Onlne]. Avalable:hp:// [29] R. Kark, H. Po, and R. Bllnon, A smplfed wnd power generaon model for relably evaluaon, IEEE Transacons on Energy Converson, vol. 21, no. 2, pp , [30] N. Amjady, J. Aghae, and H. A. Shayanfar, Sochasc Mulobjecve Marke Clearng of Jon Energy and Reserves Aucons Ensurng Power Sysem Secury, IEEE Transacons on Power Sysems, vol. 24, no. 4, pp , [31] N. Mahmoud-Kohan, M. Parsa Moghaddam, M. K. Shekh-El-Eslam, An annual framework for cluserng-based prcng for an elecrcy realer, Elecrc Power Sysems Research, vol. 80, no. 9, pp , Sepember [32] Canada s Naonal Clmae Archve, hp:// Madreza Shafe-khah (S 08-M 13-SM 17) receved he M.Sc. and Ph.D. degrees n elecrcal engneerng from Tarba Modares Unversy, Tehran, Iran, n 2008 and 2012, respecvely. He receved hs frs posdoc from he Unversy of Bera Ineror (UBI), Covlha, Porugal n 2015, whle workng on he 5.2-mllon-euro FP7 projec SNGULAR ( Smar and Susanable Insular Elecrcy Grds Under Large-Scale Renewable Inegraon ). He receved hs second posdoc from he Unversy of Salerno, Salerno, Ialy n He s currenly a Vsng Scens (poson only awarded o PhD holders who have scenfc currcula of hgh mer, equvalen o Asssan Professor) and Senor Researcher a CMAST/UBI, where he has a major role of co-coordnang a WP n he 2.1-mllon-euro naonal projec ESGRIDS ( Enhancng Smar GRIDS for Susanably ), whle co-supervsng 4 PhD sudens and 2 pos-docoral fellows. He was consdered one of he Ousandng Revewers of IEEE TSTE, n 2014, and one of he IEEE TSG Bes Revewers n Hs research neress nclude power marke smulaon, marke power monorng, power sysem opmzaon, demand response, elecrc vehcles, prce forecasng and smar grds. Mazar Yazdan Damavand (S 08-M 14) receved he M.Sc. and PhD degrees n elecrcal engneerng from Tarba Modares Unversy, Tehran, Iran, n 2010 and 2015, respecvely. He s currenly a pos-docoral fellow of COMPETE 2020-Porugal projec ESGRIDS (Enhancng Smar GRIDs for Susanably) a C-MAST/UBI, Covlha, Porugal. Hs research neress nclude opmzaon models n power sysem sudes and mul-energy sysem modelng. Nlufar Neyesan (S 09-M 14) receved he M.Sc. degrees n elecrcal engneerng from Iran Unversy of Scence and Technology, Tehran, Iran n 2010 and Ph.D. from Unversy of Bera Ineror (UBI), Covlha, Porugal n She s currenly a posdocoral fellow a INESC TEC, Poro, Porugal. Her research neress nclude elecrc vehcles, smar grds, energy and reserve markes, power sysem opmzaon, mul-energy sysems and energy hub. Ganfranco Chcco (M 98-SM 08) receved he Ph.D. degree n Elecroechncs engneerng from Polecnco d Torno (PdT), Torno, Ialy, n He s currenly a Professor of elecrcal energy sysems wh he PdT, Dparmeno Energa. He s an Edor of he IEEE Transacons on Smar Grd. Hs research neress nclude power sysem and dsrbuon sysem analyss, energy effcency, mulgeneraon, load managemen, arfcal nellgence applcaons, and power qualy. Prof. Chcco s a Member of he Ialan Assocaon of Elecrcal, Elecronc, and Telecommuncaons Engneers. João P. S. Caalão (M 04-SM 12) receved he M.Sc. degree from he Insuo Superor Tcnco (IST), Lsbon, Porugal, n 2003, and he Ph.D. degree and Hablaon for Full Professor ( Agregacão ) from he Unversy of Bera Ineror (UBI), Covlha, Porugal, n 2007 and 2013, respecvely. Currenly, he s a Professor a he Faculy of Engneerng of he Unversy of Poro (FEUP), Poro, Porugal, and Researcher a INESC TEC, INESC- ID/IST-UL, and C-MAST/UBI. He was he Prmary Coordnaor of he EU-funded FP7 projec SNGU- LAR ( Smar and Susanable Insular Elecrcy Grds Under Large-Scale Renewable Inegraon ), a 5.2-mllon-euro projec nvolvng 11 ndusry parners. He has auhored or coauhored more han 490 publcaons, ncludng 168 journal papers, 283 conference proceedngs papers, 23 book chapers, and 14 echncal repors, wh an h-ndex of 29 and over 3395 caons (accordng o Google Scholar), havng supervsed more han 45 pos-docs, Ph.D. and M.Sc. sudens. He s he Edor of he books enled Elecrc Power Sysems: Advanced Forecasng Technques and Opmal Generaon Schedulng and Smar and Susanable Power Sysems: Operaons, Plannng and Economcs of Insular Elecrcy Grds (Boca Raon, FL, USA: CRC Press, 2012 and 2015, respecvely). Hs research neress nclude power sysem operaons and plannng, hydro and hermal schedulng, wnd and prce forecasng, dsrbued renewable generaon, demand response and smar grds. Prof. Caalão s an Edor of he IEEE TRANSACTIONS ON SMART GRID, an Edor of he IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, an Edor of he IEEE TRANSACTIONS ON POWER SYSTEMS, and an Assocae Edor of he IET Renewable Power Generaon. He was he Gues Edor-n-Chef for he Specal Secon on Real-Tme Demand Response of he IEEE TRANSACTIONS ON SMART GRID, publshed n December 2012, and he Gues Edor-n-Chef for he Specal Secon on Reserve and Flexbly for Handlng Varably and Uncerany of Renewable Generaon of he IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, publshed n Aprl He was he recpen of he 2011 Scenfc Mer Award UBI-FE/Sanander Unverses and he 2012 Scenfc Award UTL/Sanander Toa. Also, he has won 4 Bes Paper Awards a IEEE Conferences (c) 2016 IEEE. Personal use s permed, bu republcaon/redsrbuon requres IEEE permsson. See hp:// for more nformaon.