Cooperative Planning of Renewable Generations for Interconnected Microgrids

Transcription

1 2486 IEEE TRANSACTIONS ON SMART GRID, VOL. 7, NO. 5, SEPTEMBER 2016 Cooperatve Plannng of Renewable Generatons for Interconnected Mcrogrds Hao Wang, Member, IEEE, and Janwe Huang, Fellow, IEEE Abstract We study the renewable energy generatons n Hong Kong based on realstc meteorologcal data, and fnd that dfferent renewable sources exhbt dverse tme-varyng and locaton-dependent profles. To effcently explore and utlze the dverse renewable energy generatons, we propose a theoretcal framework for the cooperatve plannng of renewable generatons n a system of nterconnected mcrogrds. The cooperatve framework consders the self-nterested behavors of mcrogrds, and ncorporates both ther long-term nvestment costs and short-term operatonal costs over the plannng horzon. Specfcally, nterconnected mcrogrds jontly decde where and how much to deploy renewable energy generatons, and how to splt the assocated nvestment cost. We show that the cooperatve framework mnmzes the overall system cost. We also desgn a far cost sharng method based on Nash barganng to ncentvze cooperatve plannng, such that all mcrogrds wll beneft from cooperatve plannng. Usng realstc data obtaned from the Hong Kong observatory, we valdate the cooperatve plannng framework and demonstrate that all mcrogrds beneft through the cooperaton, and the overall system cost s reduced by 35.9% compared wth the noncooperatve plannng benchmark. Index Terms Smart grd, mcrogrd, cooperatve game, Nash barganng, renewable energy, storage, capacty plannng. NOMENCLATURE Abbrevatons CPP Cooperatve plannng problem IOP Investment and operaton problem CSP Cost sharng problem. Indces n t ω Index of nterconnected mcrogrds Index of users Index of tme slots n the operatonal horzon Index of renewable generaton scenaros. Sets M N H T Set of nterconnected mcrogrds Set of users n mcrogrd Plannng horzon Operatonal horzon Set of renewable generaton scenaros. Parameters M Number of mcrogrds D Number of days n the nvestment horzon T Number of tme slots n the operatonal horzon R d Daly dscount rate θ Dscounted coeffcent F Fxed nvestment cost c s Investment cost of solar power n mcrogrd c w Investment cost of wnd power n mcrogrd η s,ω,t Solar power profle of mcrogrd n t and ω η w,ω,t Wnd power profle of mcrogrd n t and ω Q max Maxmum power procurement of mcrogrd S mn Mnmum energy storage level n mcrogrd S max Maxmum energy storage level n mcrogrd E Capacty of energy storage n mcrogrd DoD Maxmum depth-of-dscharge n mcrogrd r max Energy storage charge lmt n mcrogrd d max Energy storage dscharge lmt n mcrogrd η r,ηd Charge, dscharge effcences n mcrogrd η,j Dstrbuton effcency between mcrogrds and j b t Aggregate nelastc load of mcrogrd n t L n Total elastc load of user n ln t,mn Mnmum elastc load of user n n t ln t,max Maxmum elastc load of user n n t y t n Orgnal load of user n n t p t Prce of grd power n tme slot t α Cost coeffcent of storage operaton n mcrogrd β n Dscomfort cost coeffcent of user n π ω Realzaton probablty of renewable scenaro ω. Manuscrpt receved August 31, 2015; revsed January 17, 2016 and March 23, 2016; accepted March 28, Date of publcaton Aprl 11, 2016; date of current verson August 19, Ths work was supported by the Research Grants Councl of the Hong Kong Specal Admnstratve Regon, Chna, through the Theme-Based Research Scheme under Project T23-407/13-N. Paper no. TSG The authors are wth the Network Communcatons and Economcs Laboratory, Department of Informaton Engneerng, Chnese Unversty of Hong Kong, Hong Kong (e-mal: haowang@e.cuhk.edu.hk; jwhuang@e.cuhk.edu.hk). Color versons of one or more of the fgures n ths paper are avalable onlne at Dgtal Object Identfer /TSG Varables z G s G w q ω,t g ω,t e ω,t,j s ω,t r ω,t Renewable generaton nstallaton n mcrogrd Capacty of solar power n mcrogrd Capacty of wnd power n mcrogrd Grd power procurement of mcrogrd n t and ω Renewable power supply of mcrogrd n t and ω Renewable power from mcrogrd j to n t and ω Energy storage level of mcrogrd n t and ω Energy storage charge of mcrogrd n t and ω c 2016 IEEE. Personal use s permtted, but republcaton/redstrbuton requres IEEE permsson. See for more nformaton.

2 WANG AND HUANG: COOPERATIVE PLANNING OF RENEWABLE GENERATIONS FOR INTERCONNECTED MICROGRIDS 2487 d ω,t xn ω,t Energy storage dscharge of mcrogrd n t and ω Elastc load schedule of user n n t and ω v Investment cost shared by mcrogrd. I. INTRODUCTION RECENT years have wtnessed a sgnfcant ncrease of the share of renewable energy n the overall energy generaton profle worldwde. However, the tme-varyng and ntermttent nature of renewable energy makes ts ntegraton nto the man grd very challengng. Mcrogrd [1], as one of the key smart grd technologes, can help wth the ntegraton and management of dstrbuted renewable energy generatons. To prepare for possble ndependent operaton from the man grd, a mcrogrd often needs to have a total generaton capacty that exceeds ts crtcal local load, often n the form of renewable energy nvestment. On the other hand, renewable energy nstallaton can be expensve, hence underutlzaton of the nstalled renewable capacty would be a sgnfcant economc loss. The above observaton motvates the recent studes on power grd plannng and ntegraton of renewable energy. Specfcally, studes n [2] and [3] examned renewable energy nvestment strateges through emprcal (or numercal) approaches, wthout consderng the tradeoff between nvestment and operaton. Ca et al. [4] formulated the generaton capacty optmzaton problem wth nelastc demands, wthout consderng consumers demand responses. Yang and Nehora [5] studed a plannng problem for energy storage and generators n a mcrogrd, and formulated a jont optmzaton problem to mnmze the total nvestment and operatonal cost. Jn et al. [6] studed the mpact of demand response on the thermal generaton nvestment. The studes n [2] [6] all focused on capacty nvestment problems from a sngle mcrogrd operator or socal planner s perspectve. Renewable energy generatons and load profles vary n dfferent geographcal locatons and at dfferent tme perods of a day. Baeyens et al. [7] showed that aggregatng dverse renewable resources from geographcally dstrbuted areas can substantally reduce the generaton varablty. Ths has motvated research towards plannng and operaton of dstrbuted renewable sources n [8] [10]. Plannng of renewable sources n mcrogrds requres comprehensve evaluaton of both the ntal nvestment and ts subsequent mpact on the operaton. Ths requres us to jontly consder the system optmzaton at two dfferent tme scales: the long-term plannng horzon and the short-term operatonal horzon. Moreover, dfferent from the tradtonal power grd operaton, mcrogrds are often desgned to be self-operated, and hence have ther own local nterests. Ths brngs challenges to the cooperatve plannng and operaton of multple mcrogrds. Therefore, an ncentve mechansm s needed to encourage cooperaton among ndependent mcrogrds n generaton capacty plannng. In our prevous work [11], we studed the renewable generaton plannng n a sngle mcrogrd. In [12], we studed the nteracton of multple mcrogrds n a dstrbuton network, assumng that the nvestments are gven n each mcrogrd. In ths paper, we am to study the more challengng plannng problem of multple nterconnected mcrogrds, to explore dverse renewable resources at dfferent locatons. In partcular, nterconnected mcrogrds cooperatvely decde the optmal renewable generaton capactes for long tme perod (say several years), and manage power supples, energy storage unts, demand responses, and energy tradng over many short tme perods (such as on a daly bass). Compared wth our prevous work [11], [12], the cooperatve plannng problem s more challengng n the followng aspects: () each mcrogrd s decsons nvolve two couplng perods: plannng and operaton, and each mcrogrd s decsons on capacty plannng and power schedulng are also coupled wth other mcrogrd s decsons; () renewable generaton profles exhbt dverstes across locatons and technology types. We seek to understand and take advantage of the dversty, and develop a holstc theoretc framework for data analyss and optmal decson. The man contrbutons of ths paper are as follows. Meteorologcal data analytcs: Based on meteorologcal data acqured from the Hong Kong Observatory, we study the potentals of solar and wnd energy generatons and ther correlatons across dfferent locatons of Hong Kong. The results show dverse profles of renewable energy generatons n terms of technologes and locatons, whch motvate us to study the cooperatve plannng of renewable energy generatons. Cooperatve plannng framework: We develop a theoretcal framework that leads the optmal nvestment strateges n deployng dfferent types of renewable generatons across dfferent locatons. We model the plannng problem as a cooperatve game, n whch mcrogrds cooperatvely decde the renewable energy nvestment levels at all mcrogrds and the correspondng cost sharng based on the Nash barganng framework. Numercal case studes based on realstc data: We conduct numercal case studes based on realstc meteorologcal data of Hong Kong, and compute the optmal plannng of renewable generatons and far cost sharng. We show that our proposed cooperatve plannng framework can reduce 35.9% of the overall cost compared wth the noncooperatve approach. The rest of ths paper s organzed as follows. We analyze the renewable energy generatons of Hong Kong n Secton II, and formulate the nterconnected-mcrogrds system n Secton III. We propose the cooperatve plannng problem and desgn the cost sharng scheme n Secton IV. Numercal studes are presented n Secton V, and we conclude n Secton VI. II. RENEWABLE GENERATIONS IN HONG KONG To study the renewable power generatons n Hong Kong, we acqure meteorologcal data from the Hong Kong Observatory. The data nclude the hourly solar radaton data measured at Kng s Park (KP), and hourly wnd speeds measured at seven dfferent locatons of Hong Kong: KP, Ta Me Tuk (TMT), Sha Tn (SHA), Sa Kung (SKG), Tate s Carn (TC), Ta Po Kau (TPK), and Waglan Island (WGL). Snce Hong Kong s a relatvely small area, we assume that the solar

3 2488 IEEE TRANSACTIONS ON SMART GRID, VOL. 7, NO. 5, SEPTEMBER 2016 radaton s the same across the entre Hong Kong and can be represented by the solar radaton at KP. A. Renewable Energy Potental and Correlaton We frst study the renewable generatons from solar and wnd at seven locatons of Hong Kong, and then analyze the potentals and correlatons of dfferent technologes (solar and wnd energy) across dfferent locatons. Solar power and wnd power generatons hghly depend on the solar radaton level and wnd speed, respectvely. We denote the hourly solar radaton as I d,t and hourly wnd speed as V d,t, where t {1, 2,...,T} s the hour ndex, T = 24, and d {1, 2,...,365} s the day ndex wthn an entre year. The hourly solar radaton s measured n Wm 2, correspondng to the solar radaton energy receved on a unt surface area on earth. The hourly wnd speed s measured n m/s, whch corresponds to the dstance traveled per unt of tme. 1 The power generated from a solar module can be calculated usng the followng formula [13]: ps d,t = A m η m P f η c I d,t, (1) where A m s the solar cell array area, η m s the module reference effcency, P f s the packng factor, and η c s the power condtonng effcency. Regardng the wnd speed, we denote V c and V co as the cut-n and cut-out wnd speed. The wnd power wll be zero when the speed s less than V c or above V co. The latter case s due to the protecton of wnd turbne under a very hgh wnd speed. When the wnd speed s between V c and V co, the wnd power output [14] can be modeled as p d,t w = 1 2 ρc pa(v d,t ) 3, (2) where ρ s the densty of the ar, C p s a coeffcent related to the performance of the wnd turbne, and A s the swept area of the turbne blades. To study the potental of renewable generaton, we calculate the average capacty factor of solar power and wnd power at dfferent locatons. Specfcally, the capacty factor s the rato of the output power to the capacty (maxmum possble output power) [15]. We plot the average capacty factor of both solar and wnd power at seven locatons n Fg. 1. We can see that the average capacty factor of solar power s hgher than most of the average capacty factors of wnd power, except for TC and WGL, whch suggests solar power may be a better choce n locaton KP, TMT, SHA, SKG and TPK n terms of the generaton potental. However, average capacty factors of wnd power n TC and WGL are qute hgh, whch suggests hgh nvestment return of wnd power n TC and WGL. Furthermore, we study the statstcal correlaton between the hourly solar and wnd power productons over one year, and calculate the sample correlaton coeffcent [15] as ( X(k) X )( Y(k) Ȳ ) k ρ X,Y = ( k X(k) X ) 2 ( ), 2 k Y(k) Ȳ 1 For presentaton clarty, we omt the locaton ndex for the solar radaton and wnd speed n Secton II. Fg. 1. Average capacty factors at dfferent locatons. Here HK means for the entre Hong Kong. Fg. 2. Solar and wnd power correlaton at dfferent locatons of Hong Kong. where X and Y are data seres wth k = 1,...,K terms, X and Ȳ are the mean values of X and Y, respectvely, and ρ X,Y measures the correlaton coeffcent between X and Y. We substtute the one-year hourly solar power producton nto X, and the one-year hourly wnd power producton nto Y, and calculate the correlaton between solar power and wnd power of each locaton, shown n Fg. 2. We fnd that the wnd powers at four locatons (KP, TPK, SHA, SKG) have postve correlatons wth solar power, whle the correlatons are negatve at the other three locatons (TMT, TC, WGL). Solar power and wnd power complement each other, especally at locatons wth negatve correlatons. We wll show that the optmal plannng mxes negatvely correlated renewable generatons later n Secton V. Smlarly, we calculate the statstcal correlaton of each par of wnd powers across all the locatons, and summarze the results n Table I. We see that all the correlaton coeffcents are postve. Therefore, wnd power at dfferent locatons may substtute each other. The renewable generaton profles exhbt a remarkable dversty, whch motvates us to study the cooperatve plannng of renewable energy across technologes and locatons. For example, the users at those locatons wth low potental of renewable energy have more ncentve to cooperate wth others who have hgh renewable energy output, especally for wnd power. Solar and wnd power generatons also

4 WANG AND HUANG: COOPERATIVE PLANNING OF RENEWABLE GENERATIONS FOR INTERCONNECTED MICROGRIDS 2489 Fg. 3. Renewable energy scenaros (ncludng 10 daly productons of solar and wnd power across seven locatons). TABLE I CORRELATION OF WIND POWER ACROSS DIFFERENT LOCATIONS OF HONG KONG show locatonal patterns. For those locatons wth negatve correlaton between solar and wnd power generatons, t s easer to obtan relatvely stable renewable energy generaton when nvestng both technologes; whle for other locatons one needs to further reply on energy storage and demand response program to acheve relatvely stable renewable energy generaton wth sgnfcant more costs. Wnd power correlatons are postve, and thus a hgh wnd power producton at one locaton can provde supply for several locatons. B. Renewable Energy Scenaros For the purpose of later optmzaton formulatons, we model the renewable generatons as a set of daly realzatons of hourly solar and wnd power productons [16]. Each realzaton of daly power producton s called a scenaro, 2 denoted by ω. Specfcally, each renewable energy scenaro s represented by the jont 24-hour solar and wnd power productons of all seven canddate locatons. Based on one-year data, we have the total number of orgnal scenaros S = 365. The correspondng realzaton probablty of each orgnal scenaro s gven as π ω = 365 1, ω = 1,..., S. 2 The typcal practce of power market s based on hourly power schedulng and bllng, and ths s the reason that we generate 24-hour power producton as one scenaro. Due to the large number of orgnal scenaros, the computaton later on can be ntractable. Thus, t s very useful n practce to approxmate the orgnal large set of scenaros wth a much smaller subset that can well represent the orgnal scenaro set. We use the scenaro reducton algorthms [11], [17] to determne a scenaro subset and assgn new probabltes to the preserved scenaros, such that the correspondng reduced probablty measure s the closest to the orgnal measure n terms of the probablty dstance between the two probablty measures. After reducton, the total number of reserved scenaros s denoted as S, and the scenaro set s ={1,...,S}. The new realzaton probablty of each scenaro s denoted as π ω, and ω π ω = 1. For the purpose of llustraton n ths paper, we set the number of preserved scenaros as 10, and generate selected scenaros for the solar power generaton and wnd power generatons, depcted n Fg. 3. The actual number of scenaros S depends on the tradeoff between performance and complexty n practce. Fg. 3 shows the renewable generatons (both solar power and wnd power) per kw capacty of nvestment, respectvely. We see that the solar power has a peak at noontme, whle wnd power productons show dramatc locatonal dfferences. Wnd power at WGL s often adequate durng nght tme, whle wnd power at TPK reaches a hgher output level durng day tme. In addton, wnd power at TC and WGL has a hgher average output than that at other locatons, whch mples that TC and WGL have hgher potentals for wnd power producton. The dverse renewable generatons motvate us to study the cooperatve plannng of renewable generatons. III. SYSTEM MODEL Consder a dstrbuton network ncludng a set M = {1,...,M} of nterconnected mcrogrds, all of whch are connected to the man power grd as well as wth each other

5 2490 IEEE TRANSACTIONS ON SMART GRID, VOL. 7, NO. 5, SEPTEMBER 2016 nvestment cost covers all expendtures, e.g., nstallaton and mantenance of photovoltac panel for solar energy, turbne for wnd energy, controllers, nverters, and cables. These nvested capactes wll determne the renewable power productons n the future daly operatons. Fg. 4. System archtecture. through the dstrbuton bus, as shown n Fg. 4. Each mcrogrd M owns some energy storage, and has mplemented the demand response program. Each mcrogrd s capable of nvestng both solar and wnd renewable energy generatons, and the actual nvestment amounts are the varables to be optmzed. We further assume that each mcrogrd has space to deploy renewable energy at ts own locaton. To explore the dverstes of renewable energy generaton potentals at dfferent locatons, the nterconnected mcrogrds jontly plan the renewable generatons. Each mcrogrd needs to consder the nteractons wth other nterconnected mcrogrds and the mpact of the long-term nvestment on ts future short-term daly local power schedulng and the operatonal cost. In partcular, renewable generaton nvestment determnes the avalablty of renewable power outputs n the next few years, 3 and thus affects the future daly operatonal cost. On the other hand, the accumulatve operatonal costs can be substantal over a long perod of tme, and should be consdered when plannng renewable generaton nvestment. The nteractons among mcrogrds wll enable the explotaton of dversty across locatons, and hence mprove the overall system effcency through a proper ncentve mechansm. A. Renewable Generaton Investment We consder an nvestment horzon H ={1,...,D} of D days, and let z = {0, 1} denote the long-term nvestment decson of mcrogrd. Usually, renewable generaton facltes (e.g., photovoltac panels and wnd turbnes) occupy large space, whch leads to a sgnfcant fxed cost of nstallaton (besdes the addtonal cost dependng on the capacty). To account for the locatonal dfference, we denote F as the fxed nvestment cost n mcrogrd. We assume that each mcrogrd has two canddate renewable sources: solar and wnd. If mcrogrd decdes to nstall renewable generaton,.e., z = 1, t needs to determne the capactes of solar power G s [0, G s,max ] and wnd power G w [0, G w,max ], both measured n kw, where G s,max and G w,max are the maxmum capactes allowed for solar power and wnd power deployment n mcrogrd. The captal nvestment cost for mcrogrd s C I (z, G s, Gw ) = z (F + c s Gs + cw Gw ), where c s and c w denote the nvestment cost of solar and wnd generaton per kw n mcrogrd. We assume that the 3 We consder 20 years as the plannng horzon n the later case study. B. Daly Operaton Gven the nvested renewable capactes, each mcrogrd s responsble for the power schedulng n the mcrogrd as well as energy exchange wth other nterconnected mcrogrds. The operaton horzon for the mcrogrd s one day, whch s dvded nto T = 24 equal tme slots, denoted as T ={1,...,T}. We assume that the operatons of dfferent days are ndependent, hence we wll focus on the operaton of one day n the rest of ths subsecton. 4 In scenaro ω and an operatonal horzon T, mcrogrd determnes the renewable power supply, man grd power procurement, and energy storage chargng and dschargng to meet ts users aggregate demand, whch conssts of both elastc and nelastc loads. In the followng, we model the operatonal characterstcs of mcrogrds, ncludng supply model, energy storage model, demand model, and energy management of the nterconnceted-mcrogrd system. 1) Supply Model: Mcrogrd has two sources for power supply: renewable power g ω ={g ω,t, t T } and conventonal power procurement q ω ={q ω,t, t T }. The power supples satsfy the followng constrants: 0 g ω,t 0 q ω,t z (G s ηs,ω,t + G w ηw,ω,t ), t T, M, (3) Q max, t T, M, (4) where η s,ω ={η s,ω,t, t T } and η w,ω ={η w,ω,t, t T } denote the solar and wnd generatons n mcrogrd under scenaro ω per each unt of nvested capacty. If z = 0, mcrogrd does not nstall local renewable generaton, and ts local renewable supply s zero. If z = 1, G s ηs,ω,t + G w ηw,ω,t denotes the maxmum avalable renewable power of mcrogrd n tme slot t under scenaro ω. Mcrogrd can curtal renewable power, and thus the actual renewable power supply g ω,t n tme slot t can be less than the avalable renewable power G s ηs,ω,t + G w ηw,ω,t. For the man grd power supply, q ω,t s bounded by Q max, whch denotes mcrogrd s maxmum power procurement from the man grd. The mcrogrds are connected to the man grd through a pont of common couplng (PCC), whch could be dstrbuton feeders, transformers or converters (for DC mcrogrds). The maxmum power procurement of mcrogrd depends on the capactes of PCC and power bus wthn mcrogrd. We assume that net meterng s not allowed, whch means that mcrogrds cannot sell power back to the man grd,.e., q ω,t 0. 2) Energy Storage Model: Energy storage (such as batteres) can smooth out the ntermttent renewable power generaton, and explot tme-varyng operatonal costs for arbtrage. For mcrogrd, we let s ω = {s ω,t, t T }, r ω ={r ω,t, t T }, and d ω ={d ω,t, t T } denote the 4 We assume that the users power consumpton and energy chargng/dschargng behavors are repeated n a daly bass.

6 WANG AND HUANG: COOPERATIVE PLANNING OF RENEWABLE GENERATIONS FOR INTERCONNECTED MICROGRIDS 2491 amount of electrcty stored, charged, and dscharged over the operatonal horzon T n scenaro ω, respectvely. Frst, the energy chargng and dschargng amounts are bounded, and satsfy the followng constrants: 0 r ω,t r max, t T, M, (5) 0 d ω,t d max, t T, M, (6) where r max > 0 and d max > 0 denote the maxmum chargng and dschargng lmts, respectvely. Second, there are power losses when electrcty s charged nto and dscharged from the battery. We denote η r (0, 1] and η d (0, 1] as the converson effcences of chargng and dschargng. The battery s lfetme s heavly affected by the depth-of-dscharge [18], and thus we ntroduce a maxmum allowed depth-of-dscharge DoD to restrct the operaton of battery. Specfcally, the stored energy s ω,t should be bounded between lower and upper bounds. We can set the upper bound S max as the battery capacty E n mcrogrd. The lower bound can be set as S mn = E (1 DoD ), n whch we can choose a low DoD to reduce the mpact of battery degradaton. Therefore, we obtan mcrogrd s battery dynamcs n tme slot t and scenaro ω as { { } } s ω,t = mn max S mn, s ω,t 1 + η r rω,t dω,t η d, S max, t T, M, (7) n whch we further restrct the termnal energy level s ω,t to be equal to the ntal value s ω,0, such that the battery operaton s ndependent across multple operatonal horzons. 3) Demand Model: Let N denote the set of users n mcrogrd M. We classfy the loads of each user n N nto two categores: nelastc loads and elastc loads. The nelastc loads, such as refrgerator and llumnaton demands, cannot be easly shfted over tme. We let b t denote the aggregate nelastc load of all the users n mcrogrd and tme slot t, and denote b ={b t, t T }. The elastc loads, such as HVAC (heatng, ventlaton and ar condtonng) demand, electrc vehcle and washng machne demands, can be flexbly scheduled over tme. For a user n N, we denote the elastc load as x ω n ={xω,t n, t T }, where xω,t n s user n s elastc power consumpton n slot t under renewable generaton scenaro ω. The demand response program can only control the elastc loads, and should be subject to the followng constrants: xn ω,t = L n, n N, M, (8) t T ln t,mn xn ω,t ln t,max, t T, n N, M, (9) where constrant (8) corresponds to the prescrbed total energy requrement L n n each day. Constrant (9) provdes a lower bound ln t,mn and upper bound ln t,max for the power consumpton of user n n each tme slot t. 4) Operatonal Costs: In each operatonal horzon (say a day) under renewable generaton scenaro ω, mcrogrd coordnates ts local power supply and demand by power supply schedulng, energy storage chargng and dschargng, and elastc load shftng through demand response program. Such power schedulng ncurs an operatonal cost, ncludng the costs of purchasng man grd power, energy storage operaton, and demand response. We assume that the cost of renewable power producton s zero [8], as renewable sources are free to utlze when the renewable generaton facltes are nstalled and n operaton. For the power purchased from the man grd, mcrogrd wll be charged by a tme-dependent unt prce p t n tme slot t, and thus the power supply cost of mcrogrd s wrtten as p t q ω,t n tme slot t and scenaro ω. Repeated chargng and dschargng cause degradaton of the energy storage devces. We model the agng cost of energy storage as a functon of chargng and dschargng amounts, and defne the ( cost of energy storage operaton [19] n mcrogrd as α r ω,t + d ω,t ) n tme slot t and scenaro ω, where α s the unt cost of energy storage chargng and dschargng n mcrogrd. Schedulng elastc load may affect user s comfort, as the scheduled power consumpton devates users preferred power consumpton. We let y n ={y t n, t T } denote the most preferred power consumpton of user n, and ( defne the dscomfort cost [20] ofusern n tme slot t as β n x ω,t n y t 2, n) where βn s used to ndcate the senstvty of user n towards the power consumpton devaton. Therefore, we have the followng operatonal cost of mcrogrd over the entre operatonal horzon n scenaro ω: C O (qω, rω, dω, xω n ) = p t q ω,t ( + α r ω,t + d ω,t ) ( + β n x ω,t n y t ) 2 n, t T n N whch ncludes power procurement cost, battery operaton cost and users dscomfort costs. IV. COOPERATIVE PLANNING OF RENEWABLE GENERATIONS As shown n Secton II, mcrogrds n dfferent locatons have dfferent renewable generaton profles and potentals. For example, when renewable generatons n some locatons are n defct (relatve to the demands at those locatons), renewable generatons at other locatons could have sgnfcant surplus. Some locatons have adequate renewable sources (e.g., hgh solar radaton or strong wnd), whle others do not. The costs of renewable generaton plannng are also dfferent. For example, the fxed nvestment costs due to real estate are low n some suburban areas, but hgh n urban areas. All these factors wll affect the economcal plannng and operaton of renewable generatons. Through cooperatve plannng and later utlzaton of renewable generaton, mcrogrds can leverage the dverstes of renewable generaton profles. Those mcrogrds wth larger renewable generaton capactes and excessve local renewable generatons can supply power to other mcrogrds n short of local power supples. However, mcrogrds are often managed by local enttes wth local nterests. They do not have ncentves to over-nvest n ther local renewable generatons and provde power supples to other mcrogrds wthout proper ncentves. To encourage cooperatve plannng among nterconnected mcrogrds,

7 2492 IEEE TRANSACTIONS ON SMART GRID, VOL. 7, NO. 5, SEPTEMBER 2016 we propose a cooperatve plannng and cost sharng scheme based on Nash barganng soluton [21]. Before presentng the cooperatve plannng model, we frst present a non-cooperatve benchmark problem n the followng. A. Non-Cooperatve Benchmark We calculate the best performance (mnmum overall cost) that each mcrogrd can acheve wthout cooperatng wth other mcrogrds. Ths corresponds to the outsde opton n the barganng game, as each mcrogrd needs to decde whether to cooperate or not dependng on whether the cooperaton leads to a performance that s better than ts correspondng outsde opton. In ths noncooperatve plannng benchmark, mcrogrd balances ts local power supply and demand, and mnmzes ts overall cost wthout nteractng wth other mcrogrds. We assume that all the loads and renewable energy generatons are connected to a common power bus wthn each mcrogrd, such that we can restrct the dscusson on the balance between aggregate power supply and aggregate demand. The local power balance constrant for mcrogrd n tme slot t and scenaro ω s g ω,t + q ω,t + d ω,t = r ω,t + b t + xn ω,t, t T, M. n N (10) We denote the expected overall cost (.e., nvestment plus operatonal costs) of mcrogrd over all possble scenaros ω as C Overall (z, G s, Gw, qω, rω, dω, xω n ) C I (z, G s, Gw ) + θ E ω C O (qω, rω, dω, xω n ), whch conssts of the ntal nvestment cost C I(z, G s, Gw ) and the present value of the accumulatve expected operatonal cost θ E ω C O(qω, rω, dω, xω n ) n the entre plannng horzon. The dscounted coeffcent for the operatonal cost θ s calculated by θ = D 1 d=1, where R (1+R d ) d d s the daly dscount rate. The expected daly operatonal cost can be calculated as E ω C O (qω, rω, dω, xω n ) = ω π ω C O (qω, rω, dω, xω n ), where the weght π ω s the probablty obtaned n Secton II. We solve the expected overall cost mnmzaton problem of mcrogrd : mn C Overall (z, G s, Gw, qω, rω, dω, xω n ) subject to (3) (10), varables: z, G s, Gw, gω, qω, rω, dω, sω, xω n, and obtan the optmum denoted as C NonCoop, whch s the mnmum expected overall cost that mcrogrd can acheve wthout cooperatng wth other. In Secton V, we wll compare the performances of the cooperatve plannng and ths noncooperatve benchmark. B. Cooperatve Plannng va Nash Barganng Next we consder the cooperatve renewable generaton plannng of nterconnected mcrogrds. As shown n Secton II, mcrogrds at dfferent locatons have dfferent potentals and patterns of renewable power generatons. Through cooperatve plannng and operaton, nterconnected-mcrogrds system can beneft from the dversty of renewable energy generatons. However, each mcrogrd operator s a ratonal decson maker, and ams to optmze ts own beneft (e.g., cost mnmzaton). Therefore, we need to desgn a proper ncentve mechansm to nduce each mcrogrd to partcpate n the cooperatve plannng. We model the nteractons among mcrogrds n the cooperatve plannng as a Nash barganng game [21]. Frst, n the plannng perod, nterconnected mcrogrds cooperatvely decde the renewable energy plannng, and share the nvestment costs through barganng. Let v ={v, M} be the cost sharng vector of all the mcrogrds. The summaton of all the cost sharng should be equal to the total nvestment expense: v = C I (z, G s, Gw ). (11) M M Such an cost sharng scheme should not only cover the total nvestment expense, but also reflect the beneft ganed by each mcrogrd n the operatonal perod. Second, when the renewable energy facltes are deployed, renewable power generatons are dspatched to mcrogrds at dfferent locatons. Let e ω, t T, j M} denote the power supply vector for mcrogrd, where e ω,t,j 0 denotes the renewable power supply from mcrogrd j to mcrogrd. In practce, the power dspatch can be acheved by algorthm mplemented n the control modules co-located wth supply sde (renewable generatons) and demand sde (mcrogrds). The total renewable power supply should be no greater than the avalable renewable power producton, as shown n the followng constrant: j M e ω,t j, j M z (G s ηs,ω,t ={e ω,t,j + G w ηw,ω,t ), t T, M, (12) where j M eω,t j, represents the total renewable power supply from mcrogrd. Note that the power dstrbuton has loss, and we let η,j denote the dstrbuton effcency between mcrogrd j and mcrogrd. For mcrogrd, we have the new power balance constrant: η,j e ω,t,j + q ω,t + d ω,t = r ω,t + b t + xn ω,t, n N t T, M, (13) where the left-hand sde and rght-hand sde of the equalty constrant represent the net power supply and demand for mcrogrd, respectvely. The total renewable energy servng mcrogrd s represented by j M η,je ω,t,j. To guarantee that each mcrogrd s wllng to partcpate n the cooperatve plannng, ts overall cost should be less

8 WANG AND HUANG: COOPERATIVE PLANNING OF RENEWABLE GENERATIONS FOR INTERCONNECTED MICROGRIDS 2493 than that n the noncooperatve benchmark. Ths leads to the followng ncentve constrant: TABLE II REALIZATION PROBABILITIES FOR RENEWABLE GENERATION SCENARIOS v + θ E ω C O (qω, rω, dω, xω n ) CNonCoop, M, (14) where the overall cost of mcrogrd conssts of ts shared nvestment cost v and the total expected operatonal cost. We formulate the cooperatve plannng problem among M nterconnected mcrogrds as a Nash barganng problem as Cooperatve Plannng Problem (CPP) max [ )] C NonCoop (v + θ E ω C O (qω, rω, dω, xω n ) M subject to (4) (9) and (11) (14), varables: {z, G s, Gw, v, e ω, qω, rω, dω, sω, xω n, M}. To solve Problem CPP, we have the followng Theorem: Theorem 1: We can solve Problem CPP n two steps: Step 1: solve the jont nvestment and operaton problem (IOP) of the system, mn M C Overall (z, G s, Gw, qω, rω, dω, xω n ) subject to (4) (9), (12) and (13), varables: {z, G s, Gw, eω, qω, rω, dω, sω, xω n, M}, where we denote {z, Gs,, G w,, M} as the optmal plannng, {e ω,, q ω,, r ω,, d ω,, s ω,, x ω, n, M} as the optmal power schedule, and C Oper, θ E ω C O (qω,, r ω,, d ω,, x ω, n ) as the optmal mnmum expected operatonal cost of mcrogrd over the entre plannng horzon. Step 2: gven the optmal plannng and operaton decsons n Problem IOP, solve the cost sharng problem (CSP), max M [ C NonCoop subject to (11) and (14), varables: {v, M}. ( )] C Oper, + v Theorem 1 shows that the cooperatve plannng among mcrogrds through barganng acheves the best overall performance for the dstrbuton system. Problem IOP mnmzes the overall cost of the mcrogrds-system, and solves the optmal nvestment n renewable generatons and the optmal power schedulng of all mcrogrds. Gven the optmal plannng of renewable generatons, we solve Problem CSP to derve the optmal cost sharng to ncentvze cooperatve plannng. Problem IOP can be solved by mxed nteger programmng solver and Problem CSP can be solved by standard convex optmzaton technques [22]. Note that the cost sharng scheme not only apples to the scenaro where renewable generaton facltes are planned at the same tme, but also apples to the scenaro where ncremental capacty s bult sequentally. The proof of Theorem 1 can be found n the Appendx. TABLE III PARAMETERS OF SOLAR AND WIND POWER MODELS TABLE IV EFFICIENCY COEFFICIENTS FOR POWER EXCHANGE AMONG MICROGRIDS V. PERFORMANCE EVALUATION In ths secton, we conduct numercal studes usng realstc data of Hong Kong. We consder both noncooperatve and cooperatve cases, n whch nterconnected mcrogrds make renewable generaton plannng by themselves and cooperatvely, respectvely. We am to study the beneft of cooperatve plannng, and to valdate our proposed ncentve mechansm for the nterconnected-mcrogrd system. A. System Setup We consder four nterconnected mcrogrds, whch are assumed to be located at KP, TMT, TC and WGL, respectvely. Renewable generaton scenaros at locatons KP, TMT, TC and WGL llustrated n Fg. 3 are used to mtate the locatonal renewable generatons n the four mcrogrds, respectvely. The assocated realzaton probabltes are summarzed n Table II. Snce our focus s on the renewable generaton plannng, we assume that each mcrogrd has equpped energy storage and demand response program. The users loads are depcted n Fg. 5, and the number of users s set as 800, 900, 1200 and 1100, respectvely. We set the parameters of the solar power model and wnd power model as n Table III. The effcency coeffcents for power exchange among mcrogrds are summarzed n Table IV. We consder 20 years as the plannng horzon, and the dscount rate R d = For nvestment costs, we set fxed costs F 1 = , F 2 = , F 3 = , F 4 = , and varable costs c s = 12, 480 and c w = 7, 800. Other smulaton parameters are summarzed n the followng: α = 0.2, β n = 0.1, η r = η d = 0.98, Q max = 5000, r max = d max = 0.2 S max, DOD = 0.8, E = 1000, G s,max = G w,max = 5000, {1, 2, 3, 4}. B. Plannng Wthout Cooperaton We frst study the noncooperatve benchmark, n whch each mcrogrd tself decdes whether or not to nstall ts own renewable generatons (solar and/or wnd power), wthout nteractng

9 2494 IEEE TRANSACTIONS ON SMART GRID, VOL. 7, NO. 5, SEPTEMBER 2016 TABLE VII COST COMPARISON AT TC (IN MILLION HKD) TABLE VIII COST COMPARISON AT WGL (IN MILLION HKD) Fg. 5. Consumers demands n four mcrogrds. TABLE V COST COMPARISON AT KP (IN MILLION HKD) at TC decreases dramatcally from 303.8M HKD to 46.6M HKD, whch mples that TC s demand can be mostly satsfed by ts local renewable generaton rather than the man grd. Table VIII leads to a smlar observaton for WGL. TABLE VI COST COMPARISON AT TMT (IN MILLION HKD) wth other mcrogrds. Due to locatonal-dversty of renewable generaton, mcrogrds have dfferent condtons n terms of local solar and wnd power profles, and thus make very dfferent decsons on whether to nvest renewable generaton or not. We calculate the optmal mnmum overall cost for each mcrogrd, and derve the optmal strategy toward renewable generaton plannng. For example, Table V and Table VI summarze the mnmzed overall costs of not deployng and deployng local renewable power facltes at KP and TMT, respectvely. In terms of the renewable power profles shown n Fg. 3, both KP and TMT have low wnd power potental. For KP, t s actually optmal not to nstall renewable energy but rely on man grd power. Table V shows that f KP chooses to deploy renewable power, then the best plan s to nvest 78.9M HKD; however, KP only gets 70.5M HKD n cost reducton n the operaton, and the overall cost s 155.5M HKD, whch s stll greater than the overall cost wthout renewable. On the contrary, t s optmal for TMT to nstall renewable energy, as dong so wll reduce the overall cost from 150.6M HKD to 137.1M HKD. Smlarly, we show the mnmzed overall costs of not deployng and deployng local renewable power facltes at TC and WGL n Table VII and Table VIII, respectvely. Both TC and WGL have hgh potental of renewable energy generaton and a complementary relatonshp between wnd power and solar power. It s optmal for both TC and WGL to nstall local renewable energy generatons. Specfcally, by nvestng 61.6M HKD n renewable energy, the operatonal cost C. Cooperatve Plannng From the noncooperatve benchmark analyss above, we can see that dfferent mcrogrds exhbt varous dfferences n renewable generaton plannng behavors. Next we study the cooperatve plannng, n whch mcrogrds coordnate wth each other to determne the socal optmal plannng and far cost sharng. In Fg. 6, we plot the optmal renewable energy plannng (ncludng solar power and wnd power) for the nterconnected-mcrogrds system. The optmal cooperatve plannng does not nstall any renewable energy at KP, as the fxed nvestment cost at KP s hgh, and meanwhle other three locatons can provde adequate renewable energy for the entre system. At TC and WGL, both solar power and wnd power are nvested, and wnd power has a larger nvested capacty than solar power. Ths s because wnd power at TC and WGL has a hgher average power output than solar power. On the contrary, at TMT, only solar power s nvested, because the solar power produces more compared to the wnd power at TMT. Through cooperatve plannng, mcrogrds are able to take full advantage of the dverse renewable resources and mprove the socal welfare. The overall cost of the system (nvestment and operatonal costs) s reduce by 35.9% compared to the overall cost of all the mcrogrds under noncooperatve plannng. In Fg. 7, we compare the operatonal costs under noncooperatve and cooperatve plannngs. The cooperatve plannng sgnfcantly reduces the operatonal cost of each mcrogrd, especally those who do not have hgh potental of local renewable energy generaton (e.g., KP and TMT). For example, t s not economcal for KP to deploy local renewable energy n the noncooperatve case. Instead, KP has a strong ncentve to partcpate n the cooperatve plannng and pay for others n order to get renewable energy supply (also see Fg. 8 later on). As a result, KP reduces ts operatonal cost by more than 4/5 through cooperaton. For TC and WGL, they are able to beneft sgnfcantly from hgh local renewable energy generaton even n the noncooperatve case, and hence the addtonal gans from cooperaton are small.

10 WANG AND HUANG: COOPERATIVE PLANNING OF RENEWABLE GENERATIONS FOR INTERCONNECTED MICROGRIDS 2495 Fg. 6. Optmal plannng of renewable energy. Fg. 8. Optmal cost sharng. Fg. 7. Comparson of operatonal cost. Fg. 9. Comparson of overall cost. In Fg. 8, we plot the optmal cost sharng derved from Nash barganng soluton. Cost sharng reles on the operatonal cost reducton between non-cooperatve and cooperatve scenaros. Fg. 7 shows that KP gans sgnfcant cost reducton (from 147.1M to 22.5M HKD) through cooperatng wth other mcrogrds. Smlarly, TMT also gans sgnfcant cost reducton (from 95.0M to 30.8M HKD) through cooperaton. Therefore, KP and TMT share the largest portons of the total nvestment cost, as they beneft most from the cooperaton (as dscussed n Fg. 7). Relatvely speakng, TC and WGL beneft less from the cooperaton, and hence they share less nvestment costs than KP and TMT. The cost sharng s far as those who beneft more need to share more nvestment cost. The overall costs (shared nvestment cost plus operatonal cost) of all mcrogrds are depcted n Fg. 9. We see that mcrogrds overall costs are reduced by 30% 44% compared wth the noncooperatve benchmark, such that all the mcrogrds are better off n the cooperatve plannng. Ths demonstrates that our proposed cost sharng scheme provdes ncentves to all the nterconnected mcrogrds toward cooperatve plannng. VI. CONCLUSION We proposed a theoretcal framework to study the cooperatve plannng of renewable generatons n a dstrbuton network, consderng varable nature of renewable energy generatons, self-nterested behavors of mcrogrds, and both long-term nvestment and short-term operaton of the system. We analyzed the renewable energy generatons usng realstc meteorologcal data of Hong Kong. We desgned an ncentve mechansm, whch encourages cooperaton among nterconnected mcrogrds towards a socally optmal plannng, and splts the total nvestment cost n a far manner. Smulaton studes based on realstc data characterzed the optmal nvestment decsons, and demonstrated the economc beneft (wth 35.9% overall cost reducton) of the cooperatve plannng method. In our future work, we are nterested n the nteractons not only among mcrogrds but also between the mcrogrds-group and the man grd. APPENDIX A. Proof of Theorem 1 Frst, we dvde the decson varables of mcrogrd nto the jont plannng and operatonal decsons {z, G s, Gw, eω, qω, rω, dω, sω, xω n, n N, ω } and plannng cost sharng decson v. We can characterze the optmal soluton of Problem CPP as follows. Gven the optmal jont plannng and operatonal decsons {z, Gs,, G w,, e ω,, q ω,, r ω,, d ω,, s ω,, x ω, n, n N, ω, M}, we can solve the optmal cost sharng decsons {v, M} through max [ ( )] C NonCoop v + C Oper, M subject to (11) and (14), varables: {v, M}, (15)

11 2496 IEEE TRANSACTIONS ON SMART GRID, VOL. 7, NO. 5, SEPTEMBER 2016 where the mnmum expected operatonal cost of mcrogrd s denoted by C Oper, θ E ω C O (qω,, r ω,, d ω,, x ω, n ). Solvng (15), we obtan the followng relaton between the optmal jont plannng and operatonal decsons and the optmal cost sharng decsons v : ( ) C NonCoop v + COper, [ ( )] M C NonCoop C I(z, Gs,, G w, ) + C Oper, =. M (16) Substtutng (16) nto Problem CPP yelds the optmal objectve of the cooperatve plannng problem: ( ) M C NonCoop C Overall, M, (17) M M where the optmal overall cost of mcrogrd s denoted by C Overall, C I (z, Gs,, G w, ) + C Oper,. From (17), we conclude that Problem CPP maxmzes the socal beneft of all the mcrogrds,.e., ( ) M C NonCoop C Overall,, through cooperatve plannng of renewable generatons. Snce C NonCoop s gven, we prove that Problem CPP mnmzes the socal overall cost of all the mcrogrds,.e., M COverall,. Note that the socal cost of the mcrogrds-system does not contan cost sharng decsons {v, M}. Therefore, we can decompose the orgnal cooperatve plannng problem CPP nto two consecutve problems. Frst, we mnmze the socal cost of the mcrogrds-system by solvng the jont nvestment and operaton problem (IOP). Second, we solve the cost sharng problem (CSP), gven the optmal operatonal cost of each mcrogrd C Oper, and optmal total plannng cost M CI (z, Gs,, G w, ). REFERENCES [1] H. Farhang, The path of the smart grd, IEEE Power Energy Mag., vol. 8, no. 1, pp , Jan./Feb [2] H. Xu, U. Topcu, S. H. Low, C. R. Clarke, and K. M. Chandy, Loadsheddng probabltes wth hybrd renewable power generaton and energy storage, n Proc. Conf. Commun. Control Comput. Allerton, Allerton, IL, USA, 2010, pp [3] Q. Fu et al., Mcrogrd generaton capacty desgn wth renewables and energy storage addressng power qualty and surety, IEEE Trans. Smart Grd, vol. 3, no. 4, pp , Dec [4] D. W. H. Ca, Y. Xu, and S. H. 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Press, Hao Wang (S 10 M 16) s currently pursung the Ph.D. degree wth the Department of Informaton Engneerng, Chnese Unversty of Hong Kong. Hs research nterests are n the control and optmzaton of network systems, wth a recent focus on the bg data analytcs of renewable energy, operatons, and economcs of smart grd. Janwe Huang (S 01 M 06 SM 11 F 16) receved the Ph.D. degree from Northwestern Unversty n He s an Assocate Professor and the Drector of the Network Communcatons and Economcs Laboratory (ncel.e.cuhk.edu.hk) wth the Department of Informaton Engneerng, Chnese Unversty of Hong Kong. He worked as a Post- Doctoral Research Assocate at Prnceton Unversty from 2005 to He has co-authored four books and sx ESI hghly cted papers. He was a co-recpent of eght nternatonal best paper awards, ncludng the IEEE Marcon Prze Paper Award n Wreless Communcatons n He has served as an Assocate Edtor for the IEEE TRANSACTIONS ON COGNITIVE COMMUNICATIONS AND NETWORKING, the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, and the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS COGNITIVE RADIO SERIES. He s the Vce Char of the IEEE ComSoc Cogntve Network Techncal Commttee and the Past Char of the IEEE ComSoc Multmeda Communcatons Techncal Commttee. He s a Dstngushed Lecturer of the IEEE Communcatons Socety.