Katayoun Rahbar, Mohammad R. Vedady Moghadam, and Sanjib Kumar Panda. Abstract. Index Terms I. INTRODUCTION

Transcription

1 Real-tie Shared Energy Storage Manageent for Renewable Energy Integration in Sart Grid Katayoun Rahbar, Mohaad R. Vedady Moghada, and Sanjib Kuar Panda Abstract arxiv:176.62v1 [cs.sy] 2 Jun 217 Energy storage systes (ESSs) are essential coponents of the future sart grids with high penetration of renewable energy sources. However, deploying individual ESSs for all energy consuers, especially in large systes, ay not be practically feasible ainly due to high upfront cost of purchasing any ESSs and space liitation. As a result, the concept of shared ESS enabling all users charge/discharge to/fro a coon ESS has becoe appealing. In this paper, we study the energy anageent proble of a group of users with renewable energy sources and controllable (i.e., deand responsive) loads that all share a coon ESS so as to iniize their su weighted energy cost. Specifically, we propose a distributed algorith to solve the forulated proble, which iteratively derives the optial values of charging/discharging to/fro the shared ESS, while only liited inforation is exchanged between users and a central controller; hence, the privacy of users is preserved. With the optial charging and discharging values obtained, each user needs to independently solve a siple linear prograing (LP) proble to derive the optial energy consuption of its controllable loads over tie as well as that of purchased fro the grid. Using siulations, we show that the shared ESS can achieve lower energy cost copared to the case of distributed ESSs, where each user owns its ESS and does not share it with others. Next, we propose online algoriths for the real-tie energy anageent, under non-zero prediction errors of load and renewable energy. The proposed algoriths differ in coplexity and the inforation required to be shared between the users and central controller, where their perforance is also copared via siulations. Index Ters Shared energy storage syste, energy anageent, distributed algorith, online algorith, renewable energy, convex optiization. I. INTRODUCTION FAST-GROWING electric energy consuption is a serious concern for existing power systes. According to the study reported by the US energy inforation adinistration (EIA), the worldwide energy consuption will grow by 56% fro 21 to 24 [1]. An appealing sustainable solution to this concern is to widely integrate renewable energy sources into power systes and satisfy the deand of individual users locally. Besides, it helps to effectively reduce both the carbon dioxide eissions of fossil fuel based power plants and the transission losses fro power plants to the users. The inherently stochastic nature of renewable energy generation can cause ibalanced supply and deand, which yields fluctuations in the power syste frequency and/or voltage [2]. To overcoe this

2 2 issue, various techniques have been proposed. For instance, deand response (DR) techniques adjust the power consuption of each user over tie to closely atch it with renewable energy generation and/or electricity prices [2], [3]. This reduces the need of purchasing power fro the grid, especially during peakdeand periods when the electricity price is high. However, relying solely on DR capability ay not be sufficient to alleviate the stochastic renewable energy generation, since users have ust-run loads such as lighting that cannot be deferred in general. In this case, energy storage systes (ESSs) can be deployed to be charged during renewable energy surplus and/or low electricity price and be later discharged during renewable energy deficit and/or high electricity price. Thanks to the technology advances, integrating ESSs at the user level, e.g., residential and coercial users, is viable. For instance, Powerwall by Tesla [4] and SipliPhi [5] have anufactured various battery odules for residential and coercial buildings. However, integrating individual ESSs for all users, especially in large systes, ay not be practically feasible. This is ainly due to the high upfront cost of purchasing any ESSs (particularly in the absence of sufficient governent funding) and the space liitation for installing the. As a result, the concept of shared ESS that enables the surplus renewable energy of soe users to be charged into a shared (coon) ESS and then be discharged by other users with renewable energy deficit has becoe appealing in recent years [8], [9]. Specifically, in countries with high population density and land scarcity such as Singapore and Hong Kong that a large nuber of users live in high-rise buildings, the concept of shared ESS is even ore practically viable. The energy anageent proble for users with ESSs has been well studied in the literature. However, ost of the previous works, e.g., [6], [7], [11], [12], assued that each user (or icrogrid) owns an ESS that is not shared with others. The idea of sharing a coon ESS aong users and network operator was introduced in [8] and interesting preliinary results were reported. The policy proposed in [8] for charging/discharging to/fro the shared ESS and satisfying the deand responsive loads akes decisions heuristically and only based on the hourly electricity prices offered by the grid operator, while other practical criteria that can affect the policy of using the shared ESS are neglected. Beside, [9] solved the cost iniization proble for a syste of ultiple users with deand response capability and a shared ESS, but without integration of renewable energy sources. The algorith given in [9] ais at iniizing the total energy cost of all users, after which the total resulted benefit in cost reduction is fairly shared

3 3 aong all users according to their flexibility in load shifting. Last but not least, [1] introduced an auction based approach to capture the interaction between the shared ESS and users, where a gae theoretical technique was eployed to derive the equilibriu point of such syste. In this paper, we consider a syste of ultiple users each with their individually owned renewable energy generators, fixed and controllable loads, and one ESS shared aong all of the. We assue that users exchange inforation with a central controller using an existing two-way counication syste, where the central controller optiizes the charging/discharging energy to/fro the shared ESS by each user. The ain contributions of this paper are as follows: We first forulate the off-line energy anageent proble by assuing that the users renewable energy generation and load are perfectly known ahead of tie. We then propose an iterative based algorith to optially solve the off-line energy anageent proble in a distributed anner. The proposed algorith requires a central controller to exchange necessary inforation with users so as to optially derive charging/discharging values to/fro the shared ESS. Next, given the optial charging and discharging values, each user independently derives the optial energy consuption of its controllable loads and that of purchased fro the grid. Next, for the real-tie energy anageent under the practical setup of stochastic renewable energy generation/load, we deploy receding horizon control (RHC) based online algorith [21], also known as odel predictive control, by utilizing the developed distributed algorith for the off-line energy anageent. For ease of practical ipleentation in systes with large nuber of users and/or liited counication support, we devise alternative online algoriths that are of lower coplexity, but still perfor well in practice. Specifically, we propose proportional sharing (PS) and one-bit feedback (OBF) online algoriths that require the exchange of very liited aount of inforation at each tie slot, and converge uch faster than RHC. It is shown via siulations that the proposed online algoriths perfor close to the optial off-line solution, with perforance gaps saller that 7.5% with about 25% of renewable energy prediction errors. We ake coparison with benchark case of distributed ESSs, where each user owns its relatively saller-scale ESS, which is not shared with others. To have a fair coparison, we assue that the su capacity of all individual ESSs in this case is equal to the capacity of the shared ESS. Our

4 4 siulation results show that the shared ESS can potentially decrease the total energy cost of all users copared to the case of distributed ESSs (up to 11.5% in our siulations). This is because the surplus renewable energy of one user can be utilized by others with renewable energy deficit, and also the energy curtailent is avoided ore effectively due to the higher capacity of the shared ESS. We further highlight the ipact of renewable energy sources diversity on the effectiveness of shared ESS in energy cost reduction. In contrast to the prior works [6] [12], we propose a distributed algorith for the energy anageent of users with a shared ESS. Our recent works on shared ESS anageent in [15], [16] provide preliinary results on the effectiveness of shared ESS in energy cost reduction [15] and how self-interested users can trade energy with the shared ESS to siultaneously achieve lower energy costs while preserving their privacy [16]. In contrast to [15], [16], in this paper, we investigate online algoriths for the real-tie energy anageent of a syste constituting of a shared ESS, which to the best of our knowledge has not been rigorously studied yet. Note that the real-tie energy anageent for users with a shared ESS highly differs fro that of distributed ESSs and/or no ESS integration that has been coprehensively studied in the literature, e.g., see [12] [14], since users are all coupled together through the shared ESS. The rest of this paper is organized as follows. Section II presents the syste odel and forulates the optiization proble. Section III presents a distributed algorith to optially solve the off-line energy anageent proble and also provides a benchark setup of users with distributed ESSs. Section IV presents three online algoriths for the real-tie energy anageent. Section V presents siulation results. Last, we conclude the paper in Section VI. II. SYSTEM MODEL AND PROBLEM FORMULATION As shown in Fig. 1, we consider a syste of M > 1 users, indexed by, M = {1,..., M}, each of which can be a single residential, coercial, or industrial energy consuer or even a group of consuers anaged by an aggregator. We consider that each user has its own renewable energy generator that supplies a part or all of its deand over tie, but it is still grid-connected and can draw energy fro the grid whenever necessary. We also consider that each user has two different types of loads, naely fixed and controllable, where each fixed load (e.g., lighting) should be instantly satisfied upon the request of the user, while each controllable load (e.g., sart electric water heater) can be satisfied within a desired

5 5 GG 1nn Grid GG MMMM GG User 1 Renewable Energy, Aggregate Fixed Load ΔΔ LL qqqqqq s User Controllable Loads User M DD αα αα CC DD 1nn CC 1nn αα αα Shared ESS αα αα DD MMMM CC MMMM Figure 1. Syste odel: Users with a shared ESS. tie period specified by the user a priori, subject to certain practical considerations. Furtherore, we consider that there is an energy storage syste (ESS) shared aong all users, where the surplus energy of soe users can be charged into it and be then discharged by others with renewable energy deficit at the sae tie and/or later. A central controller is then assued for coordinating the use of the shared ESS by exchanging the required inforation with users through an existing bidirectional counication syste. Specifically, the central control unit is responsible for joint optiization of energy charged/discharged to/fro the shared ESS by all users to iniize their su weighted energy cost. Last, for convenience, we adopt a tie-slotted syste with slot index n, n N = {1,..., N}, with N 1 denoting the total nuber of scheduling ties slots, where the duration of each slot is noralized to a unit tie, hence power and energy are used interchangeably in this paper. In the following, we define the syste odel in detail. 1) Grid Energy Cost: Let G n denote the energy drawn fro the distribution copany/grid by user at tie slot n, where the corresponding cost for the user is odeled by f n (G n ). We assue that f n ( ), which is tie-varying in general, is a convex and onotonically increasing function over G n. 2) Shared ESS: Let C n and D n, with C n C and D n D, denote the energy charged/discharged to/fro the shared ESS by user at tie slot n, respectively, where C > and D > are the given axiu charging and discharging rates of the shared ESS per user, respectively.

6 6 The energy losses during charging and discharging processes are specified by charging and discharging efficiency paraeters, denoted by < α < 1 and < α < 1, respectively. Denote S n as the available energy in the shared ESS at the beginning of tie slot n, which can be derived recursively fro the state, charging, and discharging values of all users in the previous tie slot as follows: M S n+1 = S n + α C n 1 α M D n. (1) =1 A practical ESS has a finite capacity and cannot be fully discharged to avoid deep discharging. Hence, we consider the following constraints for the states of the shared ESS: M n S 1 + ( αc i 1/ αd i ) S, n N (2) S 1 + =1 i=1 M =1 i=1 =1 n ( αc i 1/ αd i ) S, n N (3) where S > and S > S are the iniu and axiu allowable states of the shared ESS, respectively. We set S S 1 S by default. 3) Controllable and Fixed Loads: Denote ˆL n as the aggregate fixed loads of user at tie slot n. We assue that each user has ultiple controllable loads whose energy consuption can be scheduled flexibly, discussed as follows. Let Q 1 denote the nuber of controllable loads of user, indexed by q, q Q = {1,..., Q }. Specifically, we consider that controllable load q of user requires E q > aount of energy to coplete its task over tie slots n q n n q, where 1 n q < N and n q < n q N are the start and terination tie slots, respectively, which are specified by user. Accordingly, we define N q = {n q,..., n q }. Let L qn denote the energy allocated to controllable load q of user at tie slot n. Due to practical considerations, L qn should be higher (lower) than a given iniu (axiu) threshold L q (L q > L q ) over tie slots n N q. Without loss of generality, we set L q = L q =, n N q. By default, we set (n q n q )L q < E q < (n q n q )L q, to ensure that controllable load q of user is practically schedulable. 1 We thus have the following constraints for controllable loads: n q n=n q L qn = E q, q Q, M, (4) L q L qn L q, q Q, M, n N. (5) 1 We assue that the energy consuption of deand responsive loads can be continuously changed over tie which accurately odels electric water heaters, heating, and cooling systes, that account for the largest energy consuption of residential consuers.

7 7 4) Energy Neutralization: By denoting R n as the renewable energy generation of user at tie slot n, we define n = R n ˆL n as renewable energy generation offset by the aggregate fixed load, where n indicates that renewable energy generation can fulfill the aggregate fixed load of user at tie slot n and ay also eet all or part of its controllable load deand and/or charge the shared ESS. On the other hand, n < indicates that the generated renewable energy of user at tie slot n cannot even eet its aggregate fixed load. We assue that renewable energy generation and fixed load of each user are practically predictable but with finite prediction errors. 2 By denoting n as the predictable net energy profile, we have n = n + δ n, where δ n denotes prediction errors. Finally, we assue that each user needs to satisfy its fixed and controllable loads at each tie slot n, using its renewable energy generation, shared ESS, and/or purchasing fro the grid. We then have the following energy neutralization constraints for all users: G n C n +D n + n Q q=1 L qn, M, n N. (6) With the syste odel defined above, we now proceed to iniize the su weighted energy cost of all users, subject to practical constraints of their loads as well as the shared ESS. We thus forulate the following optiization proble. (P1) : in {X } M M =1 n=1 s.t. (2) (6), N β f n (G n ) where X { C n C, D n D, G n, L qn, q Q, n N } denotes the set of all decision variables for user. Moreover, β s, with β 1, M and M =1 β = 1, are the given cost weight coefficients for different users. 3 III. SHARED ESS MANAGEMENT: OFF-LINE OPTIMIZATION In this section, we first propose an algorith to optially solve (P1) in a distributed anner, by assuing that n s are perfectly known to each user without any prediction errors. To do so, we use the so-called duality principle. We also forulate the benchark case of distributed ESSs, where users have their individually owned ESS that is not shared with others. 2 We assue that there is no randoness in starting/terination ties of the controllable loads and their total energy consuption throughout their scheduling period. 3 In practice, there are different approaches to set the cost weight coefficients β s. For instance, consider the scenario that users invest to purchase a bulk ESS. In this case, β n s can be set such that users benefit fro the shared ESS according to their initial investent.

8 8 A. Distributed Algorith for (P1) For convenience, we introduce vector presentation for decision variables in (P1) as well as soe syste paraeters as g = [G 1,..., G N ] T, c = [C 1,..., C N ] T, d = [D 1,..., D N ] T, l q = [L q1,..., L qn ] T, ˆl = [ˆL 1,..., ˆL N ] T, r = [R 1,..., R N ] T, and = r ˆl = [ 1,..., N ] T. Moreover, let y = [Y 1,, Y N ] T, with Y n, n N, denote the Lagrange variables corresponding to energy neutralization constraints in (6). The Lagrangian of (P1) is thus expressed as M N M L({X } M, {y } M ) = β f n (G n ) y T (g c + d + =1 n=1 The dual function of L( ) is given by g({y } M ) = Hence, the dual proble of (P1) is derived as (D1) : =1 in {X } M L({X } M, {y } M ) Q q=1 l q ). (7) s.t. (2) (5). (8) ax {y } M g({y } M ). (9) Since (P1) is a convex optiization proble and satisfies the Slater s condition [17], strong duality holds between (P1) and (D1). Therefore, (P1) can be solved by investigating the optial solution to its dual proble (D1) equivalently. To solve (D1), we use the subgradient ethod [18], which can be ipleented via an iterative algorith as follows. Let {X (k) } M, with X (k) = {c (k), d (k), g (k), l (k) q, q Q }, and {y (k) } M denote the values of prial and dual (Lagrange) variables of (P1), respectively, at each iteration k, k = 1, 2,. At iteration k, (8) is firstly solved with fixed {y (k 1) } M, where {y () } M denotes an initial point that is randoly generated. Hence, (8) can be decoupled into the following sub-probles: in g,{l q} q Q N n=1 β f n (G n ) y (k 1) T (g Q q=1 l q ) s.t. (4) and (5), (1) for = 1,..., M, and in M { c C} M,{ d D} M =1 y (k 1) T (c d ) s.t. (2) (3). (11)

9 9 1) Initialize {y () 2) Repeat: a) Given y (k 1) } M. Table I ALGORITHM FOR THE OPTIMAL OFF-LINE ENERGY MANAGEMENT Algorith 1 received fro the central controller, user solves (1) and saves the obtained solution as g (k) in (13), and sends it to the central controller via the existing counication syste; Accordingly, user evaluates z (k) and {l (k) q} q Q. b) Given {y (k 1) } M, the central controller solves (11), and then by eploying the averaging technique [19], [2] derives {c (k) } and {d (k) }. Furtherore, the central controller evaluates the subgradients v (k), M, in (12), and accordingly updates the dual variable via e.g. the ellipsoid ethod [18], where the updated dual variables are saved as {y (k) } M. 3) Until the dual variables all convergence within a prescribed accuracy. 4) The central controller sets y y(k), M, and broadcasts c(k) and d (k) to each user. 5) Each user sets c c (k) and d d (k), g g(k), and {l q} q Q {l (k) q} q Q. For each, g (k) and {l (k) q} q Q are set as the optial solution to (1), which is unique due to the fact that every cost function f n (G n ) is assued to be convex and onotonically increasing over G n. However, the optial solution to the linear prograing (LP) in (11) is generally not unique. In this case, to ensure the sooth convergence of algorith, the so-called running average technique [19], [2] is used, under which c (k) = 1/k k i=1 ĉ(i) and d (k) = 1/k k (i) i=1 ˆd, M, with {ĉ (k) } M and {ˆd (k) } M denoting any optial solution to (11). With {X (k) } M obtained as above, the dual function g({y } M ) in (8) is fored, where it can be shown that the resulted dual function is concave but not necessarily differentiable [17]. Nevertheless, it can be verified that the subgradient of g({y } M ) always exists [18], where the subgradient corresponding to user at iteration k is given by v (k) = z (k) c (k) + d (k), (12) with z (k) = g (k) Q q=1 l (k) q +. (13) Accordingly, the dual variables can be updated by using subgradient based ethods such as the ellipsoid ethod [18], where the updated dual variables are denoted by {y (k) } M. The algorith terinates when the dual variables all converge within a prescribed accuracy. Let {X }, with X = {c, d, g, l q, q Q }, and {y } denote the optial prial and dual variables of (P1), respectively. The aforeentioned algorith to optially solve (P1) is thus suarized in Table I, as Algorith 1.

10 1 GG 1nn Grid GG GG MMMM User 1 User User M CC 1nn αα αα ESS DD 1nn CC αα DD αα ESS CC MMMM αα DD MMMM αα ESS Figure 2. Syste odel: Users with distributed ESSs. It is worth noting that at each iteration of Algorith 1, the updates in (1) (13) can be ipleented in a fully distributed anner, discussed as follows. First, given y (k 1) announced by the central controller to each user, the user derives g (k) z (k) and {l (k) q} q Q by solving (1) independently, after which it coputes in (13) and sends the obtained value to the central controller via the existing counication syste. On the other hand, the central controller obtains {c (k) } M and {d (k) } M by solving (11) and also applying the averaging technique [19], [2]. Moreover, the central controller coputes the subgradients v (k), = 1,..., M, in (12) and updates the dual variables via e.g. the ellipsoid ethod [18], where the updated dual variables are saved as {y (k) } M. Reark III.1. Algorith 1 preserves the privacy of users, since at each iteration, user only needs to share z (k) in (13) with the central controller. Hence, the user do not need to share the detailed inforation of its load characteristics, renewable energy profile, etc. with the central controller and/or other users. B. Benchark: Distributed ESSs In this subsection, we consider a syste of distributed ESSs, where users own their individual sallscale ESSs that are not shared with any other user. In this case, the state of the ESS for each user, denoted by S n at tie slot n, is given by S n+1 = S n + α C n 1 αd D n, (14) where < α < 1 and < α < 1 are charging and discharging efficiency paraeters, respectively. Siilar to the shared ESS, we have the following constraints: S S n S, n N, (15)

11 11 where S and S are the iniu and axiu allowed states of the ESS owned by user. The charging and discharging values should satisfy C n C and D n D, where C > and D > are axiu charging and discharging rates, respectively. To have a fair coparison with the case of shared ESS, we set S = M =1 S, S = M =1 S, C = M =1 C, and D = M =1 D. We also set α = α and α = α, M. We now forulate the optiization proble as follows. M N (P2) : in β f n (G n ) {X } =1 n=1 s.t. S S n S, M, n N (4) (6). It can be readily verified that (P2) is convex [17] and separable over all users, since ESS constraints are not coupled over users. In this case, (P2) can be decoposed into M subprobles, one for each user, and be solved without the need of inforation exchange between users and the central controller. IV. ONLINE ENERGY MANAGEMENT In Section III, we have discussed an off-line scenario where the renewable energy generation and energy consuption of (fixed) loads of the users are all known a priori, i.e., predicted without error. However, this assuption does not hold in practice, even by using the ost advanced forecasting techniques. As a result, in the following, we consider three online algoriths for the real-tie energy anageent of the syste with non-zero prediction errors, i.e., δ n, M, n N. A. Receding Horizon Control (RHC) Based Online Algorith In this algorith, starting fro tie slot n = 1 to n = N, the energy anageent proble is solved via Algorith 1 over windows with receding sizes of N n 1. Specifically, at each tie slot n, actual values of renewable energy generation/load of past and current tie slots, i.e., 1,..., n, and the predictable values of the future i.e., n + 1,..., N, are used in Algorith 1 to derive the decision variables of the current tie slot n, i.e., {C n, D n, G n, L qn, q Q, M}. Please refer to [11], [21] for ore detail of RHC algorith. Although RHC is a conventional technique for real-tie energy anageent and has a close-to-optial perforance in general, its ipleentation for systes with large nuber of users (N 1) and/or liited

12 12 counication support is challenging due to the high coputational coplexity and large aount of inforation exchange between users and the central controller. For ease of practical ipleentation, in the following, we devise two alternative online algoriths of low coplexity that require liited inforation sharing between users and the central controller, have relatively faster convergence rates, and also perfor close to the optial off-line solution derived by assuing zero prediction errors. B. Proportional Sharing (PS) Online Algorith At each tie slot n, starting fro user 1 to M, if user has energy deficit, it announces its odified net energy profile to the central controller, where the odified net energy profile will be discussed later in the following. Accordingly, the central controller fors a set, denoted by M D, whose eleents are users with energy deficit. On the other hand, users with energy surplus firstly satisfy their fixed and controllable loads as uch as possible, but subject to their constraints. Then, they send their surplus renewable energy (if any) to the shared ESS (either to be stored in the shared ESS and/or curtailed when the ESS is full). Next, the central controller proportionally divides the available energy in the shared ESS aong users M D based on their energy deficit feedbacked. The reaining energy deficit of users (if any) is finally satisfied fro the grid. The PS based online algorith akes decisions based on the instantaneous energy surplus/deficit of users and the available energy in the shared ESS, hence it needs to ensure that the total energy requireents of controllable loads of all users are et by their given terination tie slots. To do so, at tie slot n, each user firstly needs to evaluate L qn = [E q n 1 i=1 L qn] + /(n q n + 1), with L q L qn L q, which shows the unsatisfied energy of its controllable load q noralized over the nuber of tie slots left to reach its terination tie slot n q. Hence, if L qn aount of energy is assigned to this controllable load over tie slots n,..., n q, its energy requireent will be et surely. Accordingly, user can set its odified fixed load as L n = ˆL n + Q q=1 L qn. The odified net energy profile for user at tie slot n is thus obtained as n = R n L n. With such odified net energy profiles, the central controller proportionaly divides the energy in the shared ESS aong users M D as D n = γ n, where γ = in{ αs n, D}/ M D n. To suarize, the aforeentioned PS online algorith is presented in Fig. 3.

13 13 =1 User sends to central controller Central controller updates No > Yes User satisfies its controllable loads as uch as possible User sends the extra energy (if any) to shared ESS = +1 Yes < No At this point, users with surplus renewable energy have satisfied their controllable loads and charged the shared ESS as uch as possible END Yes = No Central controller proportionally divides the energy in the shared ESS aong users : = END Yes Deficit of all users et? No Draw fro the grid to itigate the deficit Figure 3. PS online algorith at each tie slot n. C. One-Bit Feedback (OBF) Online Algorith This algorith perfors the sae as that in PS online algorith except that at each tie slot n, each user after calculating its odified net energy profile n, sends only one bit feedback to the central controller to indicate its energy surplus/deficit (no need to send the exact value of surplus/deficit). For instance, by sending 1 when n <, the central controller is notified of energy deficit, while is sent when n, indicating energy surplus or zero net energy profile. Due to receiving only one bit of inforation, the central controller evenly divides the available energy in the shared ESS aong all users with energy deficit, i.e., M D, regardless of the aount of their deficit. Last, note that RHC based online algorith uses an iterative algorith given in Table I at each tie slot n, which requires the large aount of inforation exchange between the central controller and different users. However, PS and OBF online algoriths require the exchange of very liited aount of inforation at each tie slot and converge faster; hence, can be ipleented in systes with large nuber of users and/or liited counication support. However, the perforance of PS and OBF online algoriths is

14 14 Energy profiles (kw) Energy profiles (kw) 4 Wind and solar Fixed load n (hour) (a) 4 Solar Fixed load Energy profiles (kw) Energy profiles (kw) 3 Solar Fixed load n (hour) (b) 2 Wind Fixed load n (hour) (c) n (hour) (d) Figure 4. Energy profiles of renewable energy generation and fixed loads of: (a) user 1, (b) user 2, (c) user 3, and (d) user 4. Table II CONTROLLABLE LOADS PARAMETERS Controllable Loads Type 1: Electric vehicle Type 2: EWH-orning Type 3: EWH-evening Type 4: Dryer n q n q L q (kw) L q (kw) E q(kwh) expected to degrade copared to RHC based online algorith, as will be shown in Section V-B. V. SIMULATION RESULTS We consider a syste of four residential users M = 4, each integrating its renewable energy generators, solar and/or wind, over one day N = 24. We consider that n = 1 indicates tie : AM, n = 2 tie 1: AM, and finally n = 24 tie 11: PM. Energy profiles of renewable energy generation and users fixed loads are shown in Fig. 4 [22] [24]. We assue that each user has one or ultiple types of controllable loads. Details of the users

15 15 controllable loads are given in Table II. It is shown that the EV needs to be charged fro : AM to 8: AM (tie slots 1 n 9) to receive the total energy of 5 kwh during this period. Electrical water heater (EWH) is considered to be used either in the orning or evening and needs to receive 8.85 kwh to war 5 gallons of water fro 4: AM to 7: AM (tie slots 5 n 8) and/or fro 2: PM to 5: PM (tie slots 16 n 19), respectively [25]. Finally, the dryer can operate flexibly during 8: AM to 8: PM (tie slots 9 n 21) and consue 3.19 kwh during this tie [26]. We assue that user 1 has controllable loads of Class 1, user 2 Classes 2 and 4, user 3 Classes 3 and 4, and finally user 4 Classes 2 and 3. For the shared ESS, we consider sodiu-sulfur batteries with axiu and iniu capacities of S = 18 kwh and S =.1S, respectively, charging and discharging efficiencies of α = α =.87, and axiu charging and discharging rates of C = D =.15S [27]. We also set S 1 = S. Last, we consider β =.25,, set the price of purchasing energy fro the grid as.2 $/kw [28], and odel the cost function as f n =.2G n. In the following, we provide nuerical exaples to first show the energy cost saving resulting fro the shared ESS, copared to the case of distributed ESSs. Next, we evaluate the perforance of the three online algoriths. Finally, we highlight the ipact of renewable energy diversity on the effectiveness of shared ESS in energy cost saving. A. Shared versus Distributed ESSs In this subsection, we ai to show the effectiveness of the shared ESS over distributed ESSs (with the optiization proble given in (P2)) in energy cost saving. The total energy cost of all users resulting fro shared and distributed ESSs schees over ρs (ρs for distributed ESSs) are shown in Fig. 5. It is observed that the total energy cost of users decreases over ESS capacity, which is due to less waste in surplus energy. Furtherore, it is observed that users with a shared ESS can achieve a total energy cost target with a saller ESS capacity as copared to the case of distributed ESSs. For instance, to achieve the total energy cost of $22, the capacity of the shared ESS can be set as S = 7 kwh. However, for the case of distributed ESSs, we need to set S 1 = 4.7 kwh, S 2 = 4.7 kwh, S 3 = 9.3 kwh, and S 4 = 9.3 kwh, where the overall capacity in this case is 28 kwh. This shows that the shared ESS significantly reduces the overall ESS capacity requireent by enabling energy sharing aong users. In addition, the

16 16 Total energy cost of all users ($) S = 7 kwh 11.5% S 1 = 4.7 kwh S 2 = 4.7 kwh S 3 = 9.3 kwh S 4 = 9.3 kwh Shared ESS Distributed ESSs 7.4% ρ Figure 5. Total energy cost fro shared and distributed ESSs schees. Total energy cost of all users ($) Off-line Optiization RHC based Online Algorith PS OnlineAlgorith OBI Online Algorith 7.4% 4.4% 1.6% σ 2 (k 2 W 2 ) Figure 6. Total energy cost versus the variance of prediction errors. shared ESS can avoid renewable energy curtailents ore effectively over the case of distributed ESSs, due to its higher capacity copared to each individual distributed ESS. B. Perforance Evaluation of Online Algoriths In this subsection, we ai to evaluate the perforance of the online algoriths in Section IV, under unknown prediction errors. We assue that prediction errors δ n s follow independent and identical Gaussian distributions with zero ean and variance σn. 2 We then set σn 2 = σ 2, M, n N. Fig. 6 shows the average total energy cost versus the prediction error variance σ 2. First, the off-line optiization is observed to outperfor the three online algoriths, since it is under the ideal assuption that renewable energy generation/load are copletely known. It is also observed that RHC based online algorith achieves its cost very close to the iniu cost by off-line optiization, and also outperfors

17 17 Energy profiles (kw) User 1 User 2 User 3 User n (hour) Figure 7. Solar energy profiles of users in the low diversity case. over PS and OBF online algoriths. This is expected, since RHC deploys Algorith 1 to solve the energy anageent proble at each tie slot n, by iteratively exchanging inforation between users and the central controller and exploiting the future predictable values of net energy profiles. Therefore, the capacity of the shared ESS and the flexibility of controllable loads are fully utilized and the resulting energy cost is lower copared to the other two alternative online algoriths that ake decisions only based on the current state of the syste and liited inforation received fro users. However, the proposed PS and OBF online algoriths still perfor close to the optial off-line solution with perforance losses of 4.4% and 7.4%, respectively, in the noisy environent with σ 2 = 1.2 k 2 W 2. C. Ipact of Renewable Energy Diversity By keeping the fix load profiles of users unchanged, we consider that users 1 and 4, siilar to users 2 and 3, only have solar energy sources. Renewable energy profiles of all four users in this case are shown in Fig. 7. The goal is to copare the effectiveness of the shared ESS in energy cost saving in two different setups of only solar (low diversity) and diverse renewable energy sources of solar, wind, or both (high diversity). The total energy cost saving of all users for the two cases of high and low renewable energy diversities are shown in Fig. 8-a and 8-b, respectively. It is observed that energy cost saving in the high diversity case in Fig. 8-a reains unchanged over the shared ESS capacity increase for S 18 kwh, while in 8-b, it happens for S 36 kwh, which shows that the highest achievable energy cost saving is attainable in significantly lower ESS capacity when the diversity is high. This is because when diversity

18 18 Energy cost saving (%) S = 18 kwh S (kwh) (a) Energy cost saving (%) S = 36 kwh S (kwh) (b) Figure 8. Energy cost saving: (a) High diversity (wind and solar energy generators), (b) Low diversity (only solar energy generators) Charging values (kw) c 1 c 2 c 3 c n (hour) (a) Discharging values (kw) d 1 d 2 d 3 d n (hour) (b) Charging values (kw) c 1 c 2 c 3 c n (hour) (c) Discharging values (kw) 1.5 d 1 d 2 d 3 d n (hour) (d) Figure 9. Charging and discharging values given S = 18 kw: (a) and (b) for high diversity; (c) and (d) for low diversity. is high, it is ore likely that the energy surplus/deficit in users renewable energy profiles do not happen at the sae tie. In this case, the surplus energy of soe users can copensate the energy deficit in others and charging/discharging to/fro the shared ESS do not happen concurrently, as validated in Figs. 9-a and 9-b. This in contrast to the low diversity case in which charging and discharging values happen alost at the sae tie slots, as shown in Figs. 9-c and 9-d. VI. CONCLUSION In this paper, we address the energy anageent proble of a syste of ultiple renewable energy integrated users sharing a coon ESS. First, we propose an algorith for the optial off-line energy

19 19 anageent that can be ipleented in a distributed anner and by exchanging liited aount of inforation aong users and the central controller. Next, we propose three online algoriths that differ in coplexity, inforation sharing, and perforance. We discuss each algorith in detail and evaluate their perforance via siulations, using a practical syste setup. We also ake coparison with the case of distributed ESSs, where each user owns its relatively saller-scale ESS, which is not shared with others. The siulation results show that the shared ESS can potentially decrease the total energy cost of all users copared to the case of distributed ESSs by enabling energy sharing aong the. REFERENCES [1] U.S. Energy Inforation Adinistration (EIA): International energy outlook 214, available online at pdf/484(214).pdf. [2] M. R. V. Moghada, R. T. B. Ma, and R. Zhang, Distributed frequency control in sart grids via randoized deand response, IEEE Trans. Sart Grid, vol. 5, no. 6, pp , Nov [3] J. Aghaei and M. I. Alizadeh, Deand response in sart electricity grids equipped with renewable energy sources: A review, Renewable and Sustainable Energy Reviews, vol. 18, pp , Feb [4] Tesla hoe battery: Powerwall, available online at [5] Sipliphi: Products, available online at [6] Y. Zhang, N. Gatsis, and G. B. Giannakis, Robust energy anageent for icrogrids with high-penetration renewables, IEEE Trans. Sustainable Energy, vol. 4, no. 4, pp , Oct [7] I. Atzeni, L. G. Ordonez, G. Scutari, D. P. Paloar, and J. R. Fonollosa, Deand-Side Manageent via Distributed Energy Generation and Storage Optiization, IEEE Trans. Sart Grids, vol. 4, no. 2, pp , June 213. [8] Z. Wang, C. Gu, F. Li, P. Bale, and H. Sun, Active deand response using shared energy storage for household energy anageent, IEEE Trans. Sart Grid, vol. 4, no. 4, pp , Dec [9] K. Paridari, A. Parisio, H. Sandberg, and K. H. Johansson, Deand response for aggregated residential consuers with energy storage sharing, in Proc. IEEE Conf. Decision and Control (CDC), pp , Dec [1] W. Tushar, B. Chai, C. Yuen, S. Huang, D. B. Sith, H. V. Poor, and Z. Yang, Energy storage sharing in sart grid: a odified auction based approach, IEEE Trans. Sart Grids, vol. 7, no. 3, pp , May 216. [11] K. Rahbar, J. Xu, and R. Zhang, Real-tie energy storage anageent for renewable integration in icrogrids: an off-line optiization approach, IEEE Trans. Sart Grid, vol. 6, no. 1, pp , Jan [12] K. Rahbar, C. C. Chai, and R. Zhang, Energy cooperation optiization in icrogrids with renewable energy integration, IEEE Trans. Sart Grid, Early access. [13] M. Fathi and H. Bevrani, Adaptive energy consuption scheduling for connected icrogrids under deand uncertainty, IEEE Trans. Power Delivery, vol. 28, no. 3, pp , July 213. [14] A. Ouai, H. Dagdougui, and R. Sacile, Optial control of power flows and energy local storages in a network of icrogrids odeled as a syste of systes, IEEE Trans. Control Sys. Tech., vol. 23, no. 1, pp , Jan [15] K. Rahbar, M. R. V. Moghada, S. K. Panda, and T. Reindl, Shared energy storage anageent for renewable energy integration in sart grid, in Proc. IEEE PES Innovative Sart Grid Technologies Conference (ISGT), pp. 1-5, Sept [16] K. Rahbar, M. R. V. Moghada, S. K. Panda, and T. Reindl, Energy anageent for deand responsive users with shared energy storage syste, in Proc. IEEE SartGridCo, pp , Nov [17] S. Boyd and L. Vandenberghe, Convex Optiization, Cabridge University Press, 24. [18] S. Boyd, Convex optiization II: Subgradient ethods, Stanford University. Available online at lectures.htl. [19] Angelia Nedic and Asuan Ozdaglar, Approxiate prial solutions and rate analysis for dual subgradient ethods, SIAM Journal on Optiization, vol. 19, no. 4, pp , Dec. 28.

20 2 [2] K. C. Kiwiel, Convergence of approxiate and increental subgradient ethods for convex optiization, SIAM J. Opti., vol. 14, no. 3, pp , 24. [21] E. F. Caacho and C. B. Alba, Model Predictive Control, Springer, 213. [22] Open energy inforation, Coercial and residential hourly load profiles for all TMY3 locations in the United States, available online at [23] NREL, Data & resources: Western wind dataset, available online at wind ethodology.htl. [24] NREL, Solar power data for integration studies datasets: California, available online at solar integration ethodology.htl. [25] Rhee: Residential water heaters, available online at residential-water-heaters. [26] Ma. Pipattanasoporn, M. Kuzlu, S. Rahan, and Y. Teklu, Load profiles of selected ajor household appliances and their deand response opportunities, IEEE Trans. Sart Grid, vol. 5, no. 2, Mar [27] Keet engineering center, Sodiu-sulfur batteries and supercapacitors, available online at [28] Singapore Energy Market Authority (EMA): Electricity Tariffs. Available online at Electricity Tariffs.aspx.