Hybrid Renewable Energy Investment in Microgrid

Transcription

1 Hybrd Renewable Energy Investment n Mcrogrd Hao Wang, Janwe Huang Network Communcatons and Economcs Lab (NCEL) Department of Informaton Engneerng, The Chnese Unversty of Hong Kong Emal: {haowang, jwhuang}@e.cuhk.edu.hk Abstract Both solar energy and wnd energy are promsng renewable sources to meet the world s problem of energy shortage n the near future. In ths paper, we dentfy the complementary relaton between solar power and wnd power at certan locatons of Hong Kong, and am at studyng the hybrd renewable energy nvestment n the mcrogrd. We jontly consder the nvestment and operaton problem, and present a two-perod stochastc programmng model from the mcrogrd operator s perspectve. In the frst perod, the operator makes optmal nvestment decsons on solar and wnd power capactes. In the second perod, the operator coordnates the power supply and demand n the mcrogrd to mnmze the socal operatonal cost. We desgn a decentralzed algorthm for computng the optmal prcng and power consumpton n the second perod, and based on ths solve the optmal nvestment problem n the frst perod. Wth realstc meteorologcal data obtaned from Hong Kong observatory, we numercally demonstrate that the demand response saves 18% of the captal nvestment, and hybrd renewable energy nvestment reduces the generaton capacty by up to 6.3% compared to a sngle renewable energy nvestment. I. INTRODUCTION Amng at reducng greenhouse gas emssons and enhancng the power grd relablty, many countres are buldng new power nfrastructures known as the smart grd [1]. The major features of the smart grd nclude more dstrbuted power generatons (especally from renewable energy sources), two-way communcatons between the utlty company and consumers for a better demand sde management, and decentralzed operatons of power grd n the form of mcrogrds [1]. It s essental to understand the mpact of these new features, and how to make optmal economc and technology decsons on the plannng and operaton of the smart grd. Recently, there are many studes on power grd plannng, ntegraton of renewable energy, and demand response. Specfcally, studes n [2] and [3] examned nvestment strateges on renewable energy generaton through emprcal (or numercal) approaches, wthout consderng the power schedulng operaton. Studes n [4] and [5] formulated the renewable generaton nvestment optmzaton problems to meet nelastc demands, wthout consderng consumers demand responses. Another body of lterature focused on the study of optmal demand response for resdental consumers [6] [8], data centers [9], and electrc vehcles [10] n smart grd, by dervng the proper ncentve schemes through ether game theoretc models [6], [10] or optmzaton models [7] [9]. The key dea of these studes s to desgn ncentve mechansms usually n the form of prcng schemes to users, and let cost-aware users schedule ther elastc demands as response to the prcng over tme. The study n [11] consdered the mpact of demand response Ths work s supported by a grant from the Research Grants Councl of the Hong Kong Specal Admnstratve Regon, Chna, under Theme-based Research Scheme through Project No. T23-407/13-N. on the thermal capacty nvestment, and showed that demand response reduces the thermal capacty nvestment. To summarze, the exstng lterature focused on ether renewable energy nvestment at a large tme scale (years), or demand response optmzaton under gven energy capacty at a small tme scale (hours and days). However, the decsons at these two dfferent tme scales are actually tghtly coupled. The renewable energy nvestment determnes the (tme varyng) power supply avalablty, and thus affects the flexblty of users demand response at a smaller tme scale. Meanwhle, demand response can try to match the demand wth the tme varyng renewable energy supply, and hence can maxmze the beneft of renewable energy and even reduce unnecessary nvestment expendture at a large tme scale. In ths paper, we wll jontly consder the optmal renewable energy nvestment and demand response optmzaton n the smart grd. In partcular, ths paper wll focus on the hybrd renewable energy nvestment that nvolves both solar energy and wnd energy, whch are expected to be the most popular sources n the near future [12]. The optmal mx of solar and wnd energy nvestment wll hghly depend on the stochastc nature of these two sources, whch s hghly locaton dependent. Hence we wll rely on the meteorologcal data n Hong Kong to valdate the practcal relevance of our study, and examne the mpacts of key system parameters and constrants on the optmal nvestment n renewable energy capacty. Our goal s to develop a theoretcal framework that captures the economc mpact of renewable energy and demand response n the smart grd, and derve the optmal nvestment strategy and optmal demand response scheme based on realstc data. The man contrbutons of ths paper are as follows. Hybrd renewables modelng: In Secton II, based on meteorologcal data acqured from the Hong Kong Observatory, we dentfy the complementary relatonshp between solar power and wnd power at certan locatons of Hong Kong, and suggest hybrd renewable nvestment n both solar power and wnd power. Framework development: In Secton III, we develop a theoretcal framework that enables us to derve the optmal hybrd renewable energy nvestment and operaton n a demand responsve mcrogrd. The problem s challengng due to the couplng of decsons at dfferent tme scales. Modelng and soluton methods: In Secton IV, we formulate the jont nvestment and operaton problems as a two-perod stochastc program, desgn a dstrbuted algorthm to acheve the optmal power schedulng n the second perod, and derve a sngle level optmzaton formulaton to solve the optmal nvestment n the renewable energy portfolo n the frst perod.

2 Smulatons and mplcatons: In Secton V, numercal studes based on realstc meteorologcal data llustrate the optmal portfolo nvestment decsons, and demonstrate the benefts of jontly consderng demand response and hybrd renewable energy technologes, n terms of reduced renewable energy nvestment. II. SOLAR POWER AND WIND POWER IN HONG KONG Both solar power and wnd power are ntermttent power sources, and ther stochastc features are hghly locaton dependent. Amng at studyng the renewable power patterns n Hong Kong, we acqure meteorologcal data from the Hong Kong Observatory. The data nclude the hourly solar radaton n Kng s Park (KP) of Hong Kong, and hourly wnd speed at seven dfferent locatons of Hong Kong, as shown n Fg. 1. Snce Hong Kong s relatvely small, we assume that the solar radaton s the same across Hong Kong and s represented by the data measured n Kng s Park. The wnd power, however, has clearly dfferent patterns at dfferent locatons. In ths paper, we wll focus on one year meteorologcal data (from Sep to Aug ) to study the daly solar power and wnd power productons. We fnd that the wnd powers n fve locatons (KP, TMT, TPK, SHA, SKG) of Hong Kong have postve correlatons 1 wth solar power, whle the correlaton s negatve n two locatons (TC, WGL). As an example, n ths paper we wll focus on the measurement data n Tate s Carn (TC), where solar and wnd powers have a negatve correlaton. set. Such technque has been wdely used n economcs and engneerng research [15], [16] for the purpose of modelng stochastc processes. We appled the forward scenaro reducton algorthm [16] (detals descrbed n our onlne techncal report [23]) to fnd a best scenaro subset, and assgn new probabltes to the smaller number scenaros. The key dea s to select a subset of scenaros to preserve, such that the correspondng reduced probablty measure s the closest to the orgnal measure. We set the number of preserved scenaros as 10, and generate selected scenaros for the solar power n KP (whch we assume s the same as n TC) and wnd power n TC, shown n Fg. 2. Therefore, for the renewable generaton, we have a set of = 100 scenaros denoted as Ω, and each renewable generaton scenaro ω Ω has one solar power scenaro and one wnd power scenaro. 3 Comparng (a) and (b), we can see that the solar power has a peak at noontme, whle wnd power s often adequate durng nght tme. Therefore, solar power and wnd power have a complementary relaton, whch motvates us to consder hybrd deployment of both. The data we use can be found at [24]. Lantau Island New Terrtores TPK SHA SKG Kowloon TC SKG WGL Meteorologcal staton measurng solar radaton and wnd speed Meteorologcal staton measurng wnd speed KP Hong Kong Island TMT Fg. 1: Locatons of meteorologcal statons Based on the solar power model [13] and wnd power model [14], we calculate the daly realzaton of hourly solar and wnd power productons n 365 days based on the measurement of data of solar radaton and wnd speed. 2 Each daly power producton realzaton s called a scenaro, and thus we obtan 365 scenaros for solar power and wnd power respectvely. We model the renewable energy generaton scenaros as all the combnatons of each solar power scenaro and each wnd power scenaro, and the total number of renewable scenaros s Due to the large number of scenaros whch lmts the computatonal tractablty of the nvestment optmzaton problem, t s useful to choose a smaller subset of scenaros that can well approxmate the orgnal scenaro 1 We compute the correlatons accordng to [12]. 2 The techncal parameters of the solar power model and wnd power model are shown n [23]. Fg. 2: Solar and wnd power scenaros per 1kW capacty III. SYSTEM MODEL Fg. 3 llustrates a typcal mcrogrd, whch conssts of dfferent sources of power supply and responsve demand. Wthn the mcrogrd, there s a local generaton system, consstng of solar and wnd renewable power generaton. Besdes the local energy generatons, the mcrogrd s also connected to the man grd that provdes power through conventonal generaton methods. The demand sde conssts of a set of electrcty users N = {1,...,N}, and each user N s equpped wth a smart meter and energy schedulng module. The operator runs the mcrogrd, determnes the nvestment n renewable energy capactes at a large tme scale (years), as well as energy prces at a small tme scale (hours and days). The users determne ther energy consumptons based on the prces set by the operator (as the demand response). From the operator s perspectve, t needs to decde optmal renewable capacty nvestment and power schedulng, n whch nvestment and schedulng decsons affect each other. We formulate the jont nvestment and operatons problem as a stochastc program wth two perods, as shown n Fg. 4. Specfcally, the frst-perod problem s a long term renewable energy capacty nvestment problem, wth the objectve of mn- 3 For smplcty, we have assumed that the solar and wnd power generatons are ndependent. We wll take the correlaton between solar power scenaro and wnd power scenaro as our future work to explore.

3 Man Grd Mcrogrd Smart Meters The flexble load schedulng for all users needs to satsfy the followng two constrants. Solar Power Wnd Power Operator Power Fg. 3: System model Demand Responsve Users Communcatons mzng the expected overall cost over an nvestment horzon H = {1,..., D} of D days, subject to a budget constrant. An nvestment horzon usually corresponds to several years. The second-perod problem s a power schedulng problem, wth the objectve of mnmzng the socal operatonal costs of both operator and users under a specfc realzaton of renewable power generaton wthn a smaller tme wndow. The operatonal horzon s one day, whch ncludes T = {1,...,T} of T tme slots (say 24 hours). Investment horzon 1 2 D 1 2 Operatonal horzon T Days Hours Fg. 4: Investment and operatonal horzons Note that n the second perod, the optmal power schedulng s affected by both power supply and demand, and the renewable power supply depends on the capacty nvestment decson made n the frst perod and the actual realzed scenaro. On the other hand, the expected overall cost n the frst perod ncludes both the one-tme nvestment cost and the recurrng socal cost n all D days. Hence the decsons n two perods are coupled. In the followng, we wll frst formulate the operaton problem n the second perod, and then formulate the nvestment problem n the frst perod. A. Perod 2: Mcrogrd operatons Mcrogrd operator acts as a socal planner, wth the objectve of mnmzng the socal cost ncludng both operator s cost and users costs n an operatonal horzon. In ths subsecton, we frst present the models of users and the operator, and then formulate the operator s socal cost mnmzaton problem. 1) User s model: We classfy each user s load nto two types: the flexble load and the nflexble load. The flexble load corresponds to the energy usage of those applances such as electrc vehcles, washng machnes, and vdeo game consoles, as a user may shft the flexble load over tme wthout sgnfcant negatve mpact. The nflexble load corresponds to the energy usage of applances such as lghtng, refrgerators, and such load cannot be easly shfted over tme. The demand response can only control the flexble load. We denote the correspondng decsons as x ω = {x ω,t, t T }, where x ω,t s user s flexble load energy consumpton n tme slot t T under scenaro ω. d t xω,t d t, t T, N, (1) x ω,t D, N. (2) t T Constrant (1) provdes a mnmum power consumptond t and a maxmum power consumpton d t for the user n each tme slot t. Constrant (2) corresponds to the maxmum total flexble power demand D for user n the entre operatonal horzon. We further ntroduce a dscomfort cost C ( ), whch measures user s experence under x ω = {x ω,t, t T } whch devates from hs preferred power consumpton y = {y t, t T } under a tme-ndependent (and low enough) prce. However, f the operator sets tme-dependent prces, a user wll schedule ts flexble load to mnmze the cost (more detals n Secton IV),.e. shftng power consumpton from hgh prce tme slots to low prce tme slots. The correspondng dscomfort (or nconvenence) [17] s C (x ω ) = ( x ω,t 2. y) t (3) t T 2) Operator s model: We assume that the operator can predct the renewable energy producton scenaro ω accurately at the begnnng of an operatonal horzon (a day). 4 In scenaro ω and each tme slot t, the operator determnes the renewable power supply and the conventonal power procurement to meet the total users demand, whch conssts of the flexble power consumpton x ω from each user N and the aggregate nflexble load {b t, t T } of all the users. The renewable power supply r ω = {r ω,t, t T } and conventonal power procurement q ω = {q ω,t, t T } should satsfy the followng constrants. 0 r ω,t rmax ω,t, t T, (4) q ω,t 0, t T, (5) r ω,t +q ω,t = b t + N x ω,t, t T, (6) wherermax ω,t n constrant (4) depends on the nvested capactes of solar powerα s and wnd powerα w, whch are the operator s decson varables n the frst perod. For each unt of nvested solar capacty and wnd capacty, the correspondng solar power and wnd power n scenaro ω and tme t wll be η ω s = {ηs ω,t, t T } and η ω w = {ηw ω,t, t T }, respectvely. Hence we have rmax ω,t = ηs ω,t α s +ηw ω,t α w. Constrant (5) means that the operator can only purchase power from the man grd, but cannot sell power to the man grd, assumng that the man grd does not accommodate dstrbuted generatons n the mcrogrd. We assume that the man grd has adequate power to meet the demand of the mcrogrd, hence there s no upper-bound of q ω,t n (5). Constrant (6) s the power balance constrant between supply and demand n tme slot t. Dfferent from the conventonal power generaton, the renewable power generaton does not consume fuel sources, so we assume zero cost of generatng renewable power. Therefore, 4 The short-run (day-ahead) renewable energy forecast can be qute accurate n practce [18], [19]. We wll consder the mpact of predcton error n the future work.

4 the operator wll try to use as much renewable power as possble to meet the demand. We let Q ω = {Q ω,t, t T } denote the aggregate supply,.e., Q ω,t = r ω,t + q ω,t, and rewrte the power balance constrant (6) as follows: Q ω,t = b t + x ω,t, t T. (7) N If the operator has enough renewable power to meet the aggregate demand,.e. rmax ω,t Qω,t, then there s no need to purchase any conventonal power,.e. q ω,t = 0. On the other hand, f rmax ω,t < Qω,t, the operator wll frst use all the renewable power r ω,t = rmax ω,t, and then purchase conventonal power q ω,t = Q ω,t rmax ω,t to meet the power defct. The producton cost of conventonal power has a quadratc form [20], and thus we defne the operator s cost as C o (Q ω ) = [ (Q ω,t ηs ω,t α s η ω,t ) ] + 2, w α w (8) t T where (z) + = max{z,0} for any value z. 3) The second-perod problem: Next we state the second perod problem, where the operator coordnates aggregate power supply Q ω and schedules users power consumptons x ω to mnmze the socal cost consstng of the operator s cost C o (Q ω ) and all the users costs C (x ω ) as follows. Socal cost mnmzaton problem n the second perod P2: mn βc o (Q ω )+(1 β) C (x ω Q ω,x ω ) (9) N s.t. (1),(2),(7). The operator adopts the same parameter β selected by ndvdual users n (16) to tradeoff the costs for the operator and users. Problem P2 s convex, and can be solved effcently f a centralzed optmzaton s possble. However, ths may not be feasble n practce, as the operator cannot drectly control users power consumptons. We wll dscuss the desgn of a decentralzed algorthm n Secton IV. B. Perod 1: Hybrd renewable energy nvestment In the frst nvestment perod, the operator needs to determne the capactes of the solar power and wnd power facltes (α s and α w ) for the entre nvestment horzon, subject to a budget constrant B. These capacty decsons wll determne the renewable power producton n each day of the second perod, and consequently affect the power schedulng and operatonal cost. The operator wants to make optmal nvestment decsons to mnmze the overall cost, ncludng both the captal nvestment and the expected operatonal cost n the second perod. The captal nvestment cost can be represented as C I (α s,α w ) = c s α s +c w α w, (10) where c s and c w denote the nvestment costs of solar power and wnd power per kw, respectvely. The nvestment cost covers all expendtures, e.g., nstallaton and mantenance of photovoltac panel for solar energy, turbne for wnd energy, controllers, nverters, and cables. The expected operatonal cost E ω [f( )] s a functon of the nvested capactes α s and α w, E ω Ω [f(α s,α w,ω)] = ω Ωπ ω [f(α s,α w,ω)], (11) where ω Ω denotes the renewable power scenaro wth a realzaton probablty π ω, whch s obtaned by the scenaro reducton algorthm n Secton II. Specfcally, the operatonal cost functon n scenaro ω s the optmzed second-perod objectve value (.e. mnmzed socal cost) n scenaro ω: ( f(α s,α w,ω) = mn Q ω,x ω βc o (Q ω )+(1 β) N C (x ω ) ), (12) where the cost depends on the renewable power supply n scenaro ω and users demand responses n the second perod. The frst-perod optmzaton problem s subject to a budget constrant c s α s +c w α w B, and the solar power and wnd power capactes must be non-negatve. To summarze, the frst-perod problem s as follows. The frst-perod problem P1: mn δc I (α s,α w )+(1 δ)d E ω Ω [f(α s,α w,ω)] (13) α s,α w s.t. c s α s +c w α w B, (14) α s 0, α w 0, (15) where the objectve functon conssts of captal nvestment cost C I and expected operatonal cost E ω [f( )] over all scenaros ω Ω. The weght parameter δ [0,1] trades off the longterm nvestment cost and the short-term operatonal cost, and D s the number of days over the nvestment horzon. IV. SOLUTION METHOD To solve the above two-perod stochastc programmng problem, we start wth the second-perod problem P2 and solve t usng a dstrbuted algorthm, and then solve the frst-perod problem P1 to obtan the optmal renewable energy nvestment. A. Perod 2: Optmal power schedulng As mentoned n Secton III, t s not practcal for the operator to solve P2 centrally and control users power consumptons drectly. Instead, the operator can set day-ahead prces p ω = {p ω,t, t T } for the users n scenaro ω, and let users choose the proper power schedulng accordngly. In the followng, we frst present a user s total cost mnmzaton problem gven the prces. Then we dscuss the operator s optmal choces of prces so that the users power schedulng decsons concde wth the optmal soluton of Problem P2. 1) User s problem: In scenaro ω, user receves the prce sgnals p ω and schedules the power consumpton x ω to mnmze the total cost. Specfcally, user s total cost conssts of two parts: energy cost C e and dscomfort cost C. The energy cost 5 of user depends on the prce and user s power consumpton, whch can be represented as C e (x ω ) = t T pω,t x ω,t. Therefore, we have the followng total cost mnmzaton problem for user n scenaro ω. User s total cost mnmzaton problem Pu: mn x ω βc e (x ω )+(1 β)c (x ω ) (16) s.t. (1),(2), where the users choose β to tradeoff the energy cost and user s dscomfort cost. The operator chooses the same β n the socal cost mnmzaton problem P2. 5 The user cannot change the energy cost related to nflexble load, hence we do not consder that n user s optmzaton problem.

5 2) Optmal prcng and decentralzed algorthm: We denotep ω = {p ω,t, t T } as the optmal prcng that nduces the socally optmal power consumpton {x ω, N} n scenaro ω (.e. the optmal soluton of Problem P2). We have the followng theorem. Theorem 1: In each scenaro ω, the optmal prcng scheme p ω that nduces the socally optmal power consumptonsx ω for each user satsfes the followng relatonshp, p ω,t = { Co(Q ω ) Q Q ω,t ω,t =Q ω,t,, when Qω,t > rmax, ω,t (17) 0, when Q ω,t rmax ω,t. Theorem 1 motvates us to desgn a decentralzed algorthm n Algorthm 1, where the operator sets the day-ahead prces and users respond to the prces by determnng ther power consumptons. At the begnnng of each day, the operator and each user s smart power control module compute the electrcty prces and power consumptons teratvely. Algorthm 1 Decentralzed algorthm n the mcrogrd 1: Intalzaton: teraton ndex k = 0, error tolerance ǫ > 0, stepsze γ > 0, predcted scenaro ω, and x ω,t (0) = y t. 2: repeat 3: Operator: At the k-th teraton, the operator collects each user s consumpton and computes the aggregate supply Q ω, and sets the prces p ω,t (k) accordng to (17). 4: Users: Each user solves Problem Pu by updatng the power consumptonx ω,t (k+1) based on the prce p ω,t (k): ˆx ω,t (k +1) = x ω,t (k) ( γ(k) (1 β) C (x ω (k)) x ω,t (k) ) +βp ω,t (k). 5: Project the power consumpton on the feasble set by solvng the followng problem: mn x ω x ω (k+1) (k +1) ˆxω (k +1) s.t. (1),(2). 6: k = k +1; 7: untl p ω (k) p ω (k 1) ǫ. 8: end We can see that the decentralzed Algorthm 1 requres mnmum nformaton exchange between the operator and users. The users only report ther power consumptons to the operator, and the operator broadcasts the prces to all users based on the aggregate power load. There s no need for the users to drectly coordnate wth each other or to reveal ther prvate nformaton such as cost functon and consumpton constrants. The prces set by the operator are the same for all users, and reflect the total power load wthout dsclosng ndvdual user s power consumpton. Theorem 2: Algorthm 1 s a sub-gradent projecton algorthm for solvng P2, and wth a dmnshng stepsze t converges to the socally optmal prce and power consumpton {p ω,x ω } for each ω. Note that the dmnshng stepsze satsfes the followng condtons: lm k γ(k) = 0 and lm k kγ(k) =. B. Perod 1: Optmal hybrd renewable energy nvestment After solvng the second-perod problem P2, we solve the frst-perod problem P1 as follows. Theorem 3: The operator s nvestment problem P1 s equvalent to the followng sngle optmzaton problem EP1. mn α s,α w,q ω,x ω δ[c sα s +c w α w ] +(1 δ)d E ω [ βc o (Q ω )+(1 β) N C (x ω ) s.t. (1),(2),(7),(14),(15), whch s a convex quadratc program and can be solved usng a standard nteror-pont method [21]. We assume that the operator can estmate the nformaton about user s power consumpton behavors through a survey or daly operatons, and the parameters n (1) and (2) are known to the operator. Then the operator solves the equvalent problem EP1 for optmal nvestment n a centralzed manner. For the proofs of Theorems, please refer to [23]. V. SIMULATION RESULTS We assume that the nvestment horzon ncludes D = 3650 days (10 years). We use the load curve n [22] as the preferred power consumpton, and set δ = 0.1 and β = 0.5. The nvestment costs of solar power and wnd power per kw are set as c s = HKDs and c w = 5500 HKDs [3]. We obtan renewable power scenaros as dscussed n Secton II, wth detals descrbed n our techncal report [23]. A. Beneft of demand response Frst, we study the beneft of adoptng the ncentve-based demand sde management scheme. The result s shown n Fg. 5, where we assume that the nvestment budget n the frst perod s 5 mllon HKDs. Wthout ncentves (hence keepng the prces low and the same for 24 hours), a user wll choose the power consumpton accordng to y. In that case, smulaton shows that t s optmal for the operator to use the entre 5 mllon HKDs budget durng the frst perod. Wth ncentves, the operator sets day-ahead prces so that to steer the users power consumptons to the socally optmal values. The total optmal nvestment expendture reduces to 4.1 mllon HKDs, whch mples that the demand response may sgnfcantly reduce the system cost and avod over-nvestment. B. Beneft of hybrd renewable nvestment We compare the optmal hybrd renewable capactes wth the cases where the operator only nvests n a sngle renewable source. Fg. 6 shows the optmal capactes n three cases: solar alone, wnd alone, and hybrd renewable sources. The red bar represents the capacty nvested n the solar power, and the blue bar represents the capacty nvested n the wnd power. We can see that the hybrd renewable soluton has the smallest total capacty 549 kw, wth 99 kw n solar power and 450 kw n wnd power. Compared wth the sngle renewable energy nvestment, the hybrd renewable energy nvestment saves up to 37 kw renewable generaton capacty. The results demonstrate the beneft of the hybrd renewable nvestment n terms of reducng the need of the total generaton capacty. ],

6 Fg. 5: Investment expendture Fg. 6: Optmal capacty nvestment Fg. 7: Optmal rato of nvestment n solar and wnd power C. Impact of budget We study the mpact of budget on the optmal rato of nvestment n solar power and wnd power, as shown n Fg. 7. When the budget s tght (as 1 mllon HKDs), the nvestment prorty s wnd power because t s more economcal. Whle the budget ncreases, the nvestment prefers more solar power, because the solar power fts the daly demand better (.e., more energy use durng the day) even though t s more expensve. VI. CONCLUSION We propose a theoretcal framework to study the jont nvestment and operaton problem wth renewable energy n the mcrogrd. Wth realstc meteorologcal data, our model provdes the optmal nvestment decsons on hybrd renewable powers and optmal daly operaton (prcng and power schedulng) of the mcrogrd. The smulaton studes demonstrate the economc beneft of demand response and hybrd renewable nvestment. In the future, we wll further consder the nvestment problem at dfferent locatons wth dfferent wnd power scenaros, and mpacts of key system parameters on optmal nvestment, operaton and power schedulng. REFERENCES [1] X. Fang, S. Msra, G. Xue, and D. Yang, Smart grd-the new and mproved power grd: a survey," IEEE Communcatons Surveys and Tutorals, 14: , [2] H. Xu, U. Topcu, S.H. Low, C.R. Clarke, and K.M. Chandy, Load-sheddng probabltes wth hybrd renewable power generaton and energy storage", n Proc. of Allerton Conference, [3] L. Xu, X. Ruan, C. Mao, B. Zhang, Y. Luo, An mproved optmal szng method for wn-solar-battery hybrd power system", IEEE Trans. Sustanable Energy, 4(3): , [4] Y. Cao, M. He, Z. Wang, T. Jang, J. Zhang, Multple resource expanson plannng n smart grds wth hgh penetraton of renewable generaton", n Proc. of IEEE Smartgrdcomm, [5] D.W.H. Ca, Y. Xu, and S.H. Low, Optmal nvestment of conventonal and renewable generaton assets", n Proc. of Allerton Conference, [6] A.H. Mohsenan-Rad, V.W.S. Wong, J. Jatskevch, R. Schober, A. Leon-Garca, Autonomous demand-sde management based on game-theoretc energy consumpton schedulng for the future smart grd", IEEE Trans. on Smart Grd, 1(3): , [7] N. L, L. Chen, and S.H. Low, Optmal demand response based on utlty maxmzaton n power networks", n Proc. of IEEE PES General Meetng, [8] L. Qan, Y. Zhang, J. Huang, and Y. Wu, Demand response management va real-tme electrcty prce control n smart grds", IEEE JSAC, 31(7): , [9] H. Wang, J. Huang, X. Ln, and H. Mohsenan-Rad, Explorng smart grd and data center nteractons for electrc power load balancng", n Proc. of ACM Greenmetrcs, [10] C. Wu, H. Mohsenan-Rad, and J. Huang, PEV-based reactve power compensaton for wnd DG unts: a stackelberg game approach", n Proc. of IEEE Smartgrdcomm, [11] S. Jn, A. Botterud, and S.M. Ryan, Impact of demand response on thermal generaton nvestment wth hgh wnd penetraton", IEEE Trans. on Smart Grd, 4(4): , [12] J. Wdén, Correlatons between large-scale solar and wnd power n a future scenaro for Sweden", IEEE Trans. Sustanable Energy, 2(2): , [13] F.O. Hocaoglu, O.N. Gerek, and M. Kurban, A novel hybrd (wnd-photovoltac) system szng procedure", Solar Energy, 83: , [14] Y. L, V.G. Agelds, and Y. Shrvastava, Wnd-solar resource complementarty and ts combned correlaton wth electrcty load demand", n Proc. of IEEE ICIEA, [15] A. Möller, W. Römsch, and K. Weber, A new approach to O & D revenue management based on scenaro trees", Journal of Revenue and Prcng Management, 3(3): , [16] N. Gröwe-Kuska, H. Hetsch, and W. Römsch, Scenaro reducton and scenaro tree constructon for power management problems", n Proc. IEEE Bologna Power Tech Conference, [17] L. Jang and S.H. Low, Mult-perod Optmal Energy Procurement and Demand Response n Smart Grd wth Uncertan Supply", n Proc. of IEEE CDC, [18] R.H. Inman, H.T.C. Pedro, and C.F.M. Combra, Solar forecastng methods for renewable energy ntegraton", Progress n Energy and Combuston Scence, 39(6): , [19] A.M. Foley, P.G. Leahy, A. Marvugla, and E.J. McKeogh, Current methods and advances n forecastng of wnd power generaton", Renewable Energy, 37(1): 1-8, [20] D. Krschen and G. Strbac, Fundamentals of power system economcs", Wley, [21] S. Boyd and L. Vandenberghe, Convex Optmzaton", Cambrdge Unv. Press, [22] G. Carpnell et al., Optmal ntegraton of dstrbuted energy storage devces n smart grds", IEEE Trans. on Smart Grd, 4(2): , [23] H. Wang and J. Huang, Techncal Report.[Onlne] HybrdRenewableInvestmentReport.pdf [24] Summary of Wnd and Solar Meteorologcal Data n Hong Kong,