ONE of the central features of the emerging Smart Grid

Transcription

1 Towards a Retail Market for Distribution Grids Stefanos Baros, Yasuaki Wasa, Jordan Romvary, Rabab Haider, Kenko Uchida and AM Annaswamy Abstract In this paper, we propose a retail market structure for optimally scheduling Distributed Energy Resources (DERs) including generating units and flexible consumption units in a distribution grid For this purpose, we use a distributed proximal atomic coordination (PAC) algorithm shown to converge faster than the popular ADMM under certain conditions, and requires less amount of information to be exchanged Further, we analyze typical market aspects surrounding the proposed mechanism including the market settlements that dictate how DERs and consumers will be compensated and charged, respectively, and how interactions with the Wholesale Electricity Market (WEM) will occur Finally, we numerically verify the performance of the proposed retail market and underlying PAC algorithm via simulations of a distribution grid in Tokyo, Japan Keywords distributed algorithm, optimal power flow (OPF), distribution grids, distribution grid market I INTRODUCTION ONE of the central features of the emerging Smart Grid is a highly transformed distribution grid with a high penetration of distributed energy resources (DERs) These DERs include units of distributed generation (DG), demand response (DR) compatible consumption, and storage devices such as batteries and electric vehicles The resulting distribution grid is highly desirable, as it allows an efficient integration of renewable generation As these DERs will be owned and operated by different stake holders, what is highly desirable for an efficient and reliable operation of the distribution grid is an overall market structure that allows the procurement and integration of any and all available power generation through DGs, DRs, and storage devices When it comes to procurement and integration of DGs, the current practice is for them to participate in the Wholesale Electricity Market (WEM), for the most part, for providing ancillary services [] While this participation largely pertains to DGs, certain amount of participation also occurs from DR units and storage devices [], an example of which is evidenced by FERC order 84 Despite these recent advances, as the number of DERs grows, which is inevitable, and renewable generation continues to increase, the WEM alone may not suffice in realizing an efficient and reliable power delivery A properly designed retail market that oversees the participation of DERs in the distribution grid and implements a suitable mechanism for their scheduling and compensation is highly necessary In this paper, we propose a market structure Stefanos Baros, Jordan Romvary, Rabab Haider and Anuradha M Annaswamy are with the Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 39, USA, {sbaros, romvary, rhaider, aanna}@mitedu Yasuaki Wasa and Kenko Uchida are with the Department of Electrical Engineering and Bioscience, Waseda University, Tokyo, , Japan, e- mail: wasa@aoniwasedap, kuchida@wasedap This work was supported in part by the NSF Award no EFRI-443, DOE UI-ASSIST, and JST CREST Grant no JPMJCR5K for operation in a distribution grid, through a distributed optimization algorithm, with its solution serving as the schedule for distributed generation The discussion on retail markets for operation in a distribution grid is relatively new [3]-[4] A hierarchical structure is proposed in [3] and [5] to interlace the operation of the WEM with the retail market In [3], a hierarchical market mechanism is proposed where, a distribution network operator (DNO) is responsible for the operation of the retail market and load aggregators for smooth interactions with the WEM In [5], a perspective on the future retail energy market (REM) with increasing activity is presented In [6] and [7], centralized market mechanisms have been proposed Reference [6] focuses on an optimal dispatch of DR units in a distribution grid that participate collectively in WEMs, whereas in [7], a dayahead distribution grid market mechanism is proposed that involves interactions with the WEM and allows diverse types of DERs to competitively participate for the provision of ancillary services All of these papers however retain, by and large features of the WEM and a centralized perspective A main feature of the distribution grid is its distributed nature With several DERs participating in the overall power delivery, the adoption of a centralized perspective of a WEM is highly inefficient Instead, the use of distributed market mechanisms which are computationally efficient as they primarily rely on local computations at each node and peer-to-peer exchange of information among the entities of the distribution grid is preferred Moreover, they are resilient to communication link and single-point failures and, if properly designed, they can preserve the private information of the DERs With this in mind, recent work such as [8] and [4] has focused on the development of distributed market mechanisms for distribution grids The work in [8] introduced an algorithm with a parallel architecture that can concurrently yield price discovery along with optimal scheduling of resources in both transmission and distribution grids Although the problem formulation is very detailed, the complexity of the proposed algorithm is quite high and thus its practical implementation can be quite challenging The work in [4] introduces a decentralized market mechanism with bilateral trading rules that can result in a fair allocation of the line losses However the relation between the trading rules with the optimal dispatch that the local DERs need to follow, or how these trading rules will accommodate interactions with existing WEMs, are not addressed in this paper In this paper, we develop a preliminary retail market structure based on a recently developed distributed algorithm [9] The following are the specific contributions of the paper We propose a recently developed distributed proximal atomic coordination algorithm (PAC) that converges to the solution of the Optimal Power Flow (OPF) problem

2 for distribution grids Compared with the well known ADMM [], [], our proposed algorithm requires less amount of information to be exchanged, and can exhibit faster convergence We propose a retail market mechanism using the PAC and explicit rules for its interactions with the WEM Further, we analyze typical market aspects surrounding the proposed mechanism including the market settlements that dictate how DERs and consumers will be compensated and charged, respectively Finally, we numerically verify the performance of the proposed retail market and underlying PAC algorithm via simulations of a distribution grid in Tokyo, Japan The rest of the paper is organized in the following way In Section II, we present the distributed PAC algorithm as a solution for achieving the OPF in distribution grids In Section III, we introduce an overall structure for a retail market with a distributed market mechanism In Section IV, we illustrate the performance of the proposed retail market and the underlying PAC algorithm via numerical simulations Conclusions are provided in Section V II A DISTRIBUTED PAC ALGORITHM The underlying problem that we address in this paper is optimal power delivery in a distribution grid with different DERs, including DGs, DRs, and storage devices The goal is to determine decision variables that include P G, P L, QG, P L and v at each bus, and the flow variables P i,, Q i,, l i,, in the i- th branch, of active, reactive power, and current, respectively, so that the overall power losses and the total expenditure (payments to generating units less revenue from consumption units) are minimized This problem is formally stated as: min y R y f OPF (y) subect to: P G P G P G, P L P L P L, Q G QG QG, Q L QL QL, v v v, P P i, +Q i, S i,, i, +Q i, v il i,, l i, S i,/v i, ( ) v = v i (R i, P i, +X i, Q i, )+ Ri, +X i, l i,, P G P L = P i, +R i, l i, + k:(,k) T P,k, Q G QL = Q i,+x i, l i, + k:(,k) T Q,k, Pi G P i L = k:(i,k) T P i,k, i F Q G i QL i = k:(i,k) T Q i,k, i F () where the cost function is defined as: { f G-Cost β PG (P G (y) = +β QG (Q G ), λ P P G+λQ QG, if B B\F () f L-Util (y) = f Loss { β PL (P L L P ) β QL (Q Q L ), if B, if F i, (y) = R i, l i,, if (i, ) T (4) f OPF (y) = [ ] [ ] f G-Cost (y) f L-Util (y) +ξ fi, Loss (y) B (i,) T (5) The decision variables are captured by the vector y = [P G ; P L ; Q G ; Q L ; v; l; P; Q] which is a collection of the subvectors y that capture the variables of each bus The bold characters here denote vectors P G, P L, QG, QL, v are local real power generation, real power consumption, reactive power generation, reactive power consumption, and voltage level all at bus, P i,, Q i,, l i, refers to the real power flow, reactive power flow and current flow along the (i, )-branch, R i,, X i, correspond to the resistance and reactance of the (i, )-branch, β PG, β QG, β PL, β QL are cost coefficients of the generation cost and load utility functions respectively, λ P, λq are the locational marginal prices (LMPs) that correspond to the distribution grid feeder, l i, = Îi, and v = ˆV, S refers to the set of substations, F s to the set of feeders per substation s, and B to the set of buses connected to (and including) feeder l at bus #, T B B corresponds to the grid transmission lines, ξ captures the tradeoff between local bus generation costs and global branch losses, P G, P G, P L, P L, QG, QG, QL, QL, v, v represent lower ( ) and upper ( ) limits on local bus variables; Si, represents the thermal limit of the total apparent power that is allowed on branch (i, ) T, P L and Q L correspond to the baseline real and reactive power consumption of the flexible consumers Here, we consider distribution grids with radial topology that can be represented as a directed graph Γ D = B, T D, where B represents the graph vertices and T D T the graph directed edges The compositions of the subvectors y may be different depending upon the types of the corresponding buses In particular, if (i, ), {(, h )} [n] T D, the vector y would be: y = [P G ; P L ; Q G ; Q L ; v ; v i ; P i, ; Q i, ; l i, ; { } ] P ;h ; Q,h If only (i, ) T D (end node) by : y = [ P G ; P L ; Q G ; Q L ; v ; v i ; P i, ; Q i, ; l i, ] If only {(, h )} [n] T D (feeder node) by : y = [P G ; P L ; Q G ; Q L ; v ; { } ] P ;h ; Q,h [n] (3) [n] where h denotes the set of downstream buses connected to bus With the vectors defined above, we can compactly state

3 3 the optimization problem () as: min f OPF (y ) y B subect to: g (y ), G y =, B B where g represents the local bus and branch inequality constraints and G the branch equality constraints We note that the convex relaxation in [] has been employed in the voltage inequality of Problem A Reformulation of the OPF Problem We first design the proximal atomic coordination (PAC) algorithm that will attain solution to the relaxed OPF problem (6) in a fully distributed fashion The ropf problem (6) with the local vectors y is not fully decomposable as the coupling variables v i, P i, and Q i,, appear in both the vectors y and y i of two neighboring buses and i To render it decomposable, we use local copies instead of the actual coupling variables in each y and introduce additional equality constraints that enforce these copies to coincide with the coupling variables at the optimal solution The resulted problem namely, the atomized standard optimization relaxed OPF (asoropf) can then be solved via fully distributed solution methodologies Atomizing each bus variables, yields the asoropf problem: min a R a ˆf OPF (a) subect to: P G P G P G, P L P L P L, Q G QG QG, Q L QL QL, v v v, P i, +Q i, S i,, Pi, i, ṽ[] i l i,, l i, S i,/v i, ( ) v = ṽ [] i (R i, P i, +X i, Q i, )+ Ri, +X i, l i,, P G P L = P i, +R i, l i, + [] k:(,k) T P,k, Q G QL = Q i,+x i, l i, + [] k:(,k) T Q,k, Pi G P i L = k:(i,k) T P i,k, i F Q G i QL i = k:(i,k) T Q i,k, i F ṽ [] P [] i v i =, i B,h P,h =, (, h) T Q [],h Q,h =, (6) (, h) T (7) where the variable ṽ [] i is the local -th atomic copy of the [] [] upstream voltage phasor magnitude and P,h, Q,h are the local -th atomic copies of the downstream real and reactive power flows In general, we assume that the bus i is closer than the the bus to the feeder in a given branch (i, ) Notice that, a represents the atomic version of the subvector y that contains also the local copies of the coupling variables In (7), the last three equalities enforce all local copies of the vector y to coincide with the actual variables that are in y i We can compactly express these constraints in matrix form as: Aa =, (8) where A represents the adacency matrix of Γ D Using (8) and augmenting ˆf OPF (a) ˆf (a ) using an indicator function, B one can state the equivalent of () atomic formulation asoropf problem compactly as: min ˆF (a ) a R a B subect to: G a =, A, a =, B B where A, represents the rows of A that correspond to the coupling variables along (i, ) T D The equation G a = to the Kirchhoff s Voltage Law and power balance constraints Now we introduce the PAC algorithm for solving (9) (see [9] for details), which is based on a distributed linearized variant of the proximal method of multipliers [3], [4] B Algorithm Design We start with the Lagrangian of (9) given by: L (a, µ, ν) = [ ] ˆF (a ) + µ T G a + ν T A, a B = B [ ˆF (a ) + µ T G a + ν T A, a ] B L (a, µ, ν) We note that the two variables that are of most importance are a, the decision variable, which corresponds to the optimal power generation and consumption of active and reactive power, and µ, the price associated with the decision variable By introducing augmentation and proximal regularization terms to L (a, µ, ν) we obtain the augmented Lagrangian: ρ [ L (a, µ, ν) + ργ G a L ρ,γ (a, µ, ν; a ) = B + [ ργ A, a + ] a a ρ B () ) Given that, L (a, µ, ν; a = L (a, µ, ν) + a a we can express it more compactly as: L ρ,γ (a, µ, ν; a ) [ ( L a, µ, ν; a ) ] B + [ ργ G a + ργ ] A, a B () ] (9)

4 4 where ρ > is the step-size and γ > is the over-relaxation term The augmentation terms ) can be linearized around a prior primal iteration (a and a as: ργ G a ργ G a + ργ ( a a )T GT G a () ) T A T, A, a (3) ργ A, a ργ A, a + ργ ( a a Application of () and (3) to () yields: L ρ,γ (a, µ, ν; a ) = [ ( L a, µ, ν; a ) + ργ G a, G ] a B + B [ ργa, a, A, a ] (4) We can express the new predicted dual updates in (4) as: µ = µ + ργ G a, ν = ν + ργa, a, Finally, we can write (4) as: L ρ,γ (a, µ, ν; a ) = B L ( a, µ, ν; a ) (5) We now propose the following PAC algorithm based on a primal-dual method for recovering the optimal solution of (5) We refer the reader to [9] for its analytical properties of convergence Distributed PAC Algorithm { } a [τ + ] = argmin a Lρ,γ (a, µ [τ], ν [τ] ; a [τ]) (6) µ [τ + ] = µ [τ] + ργ G a [τ + ] (7) µ [τ + ] = µ [τ + ] + ργ G a [τ + ] (8) Communicate {a } B according to Γ D (9) ν [τ + ] = ν [τ] + ργa, a [τ + ] () ν [τ + ] = ν [τ + ] + ργa, a [τ + ] () Communicate { ν } B according to Γ D () As shown in [9], the variables a, µ and ν converge to a, µ, and ν The key variables that we will utilize for our proposed retail market mechanism are P G, Q G,P L, Q L, the active and reactive power generation at bus and consumption profiles, and µ P, µ Q, the distribution locational marginal prices (d-lmps) III A RETAIL MARKET MECHANISM We propose our retail market to consist of a distribution grid operator (DSO), the main entity that will decide the scheduling of P G,Q G of the generating units, P L,Q L of the consumption units, as well as their market settlements µ P, µ Q, at node, for all in the distribution grid We denote T and τ to be the market clearing periods of the WEM and the retail market, respectively In what follows, for ease of exposition, we make an assumption that τ T, so that the DSO market clears multiple times within a single WEM Substation Feeder Substation s Feeder l Bus Bus # Bus Multiple iterations between PAC Converges to: Substation S Feeder L Bus J Fig : Proposed retail market clearance period However, in general, these two clearing periods can be chosen independently We make the following additional assumption: Between any two market clearings T and T + T of the WEM, the LMP of all feeder buses λ P l is fixed, for all feeders in a substation This is denoted compactly as λ P l is fixed, l F s, s S (see the hierarchical structure denoted by the gray arrows in Fig ) Thus in (), λ P l is a boundary condition l F s, s S on the scheduling problem, for the N DSO clearings over the time period [T, T + T ] It should be noted however that in (), the power quantities P G, QG are allowed to vary, and will be determined by the PAC algorithm, Note that in PAC, the feeder node # is treated as a generator of infinite capacity (P G, where P G corresponds # # to the upper limit of power generation from (7)) thus, P G # represents power imported from the main grid Likewise, P L # represents power exported to the main grid Depending on whether the power is imported or exported, either P L = or # P G =, respectively Then for time period [T #, T + T ] the average load (generation) of the distribution grid which will be imported from (exported to) the main grid is calculated as Pl,T = N N n= P G #,n P L #,n, l F s, s S With the above assumptions in place we propose that the retail market determines the overall generation, consumption, and prices at each B in the distribution grid, using the PAC algorithm described in ()-(8) over every DSO market clearing period τ Note that the PAC algorithm is run independently for each distribution network connected to the grid by feeder l, l F s, s S Fig shows the proposed retail market and all interactions between the WEM, DSO, and distribution systems downstream of the substations, over one clearing of the WEM The blue arrows show data communication between different entities The retail market will consist of three interactions denoted as (A), (B), and (C), and will be discussed next The first interaction (A) occurs between the WEM and DSO, when the WEM clears: at time T the WEM passes to the DSO the LMPs for each transmission grid connected feeder l F s, s S, and the forecasted load/generation of each feeder bus for the period The second set of interactions (B) occur between the DSO and the distribution grid every τ, prior to the next WEM clearing For each interaction (B), the

5 5 PAC algorithm will run and converge in some K iterations; the converged values of the real and reactive power generation and load for each bus, P G, Q G,P L, Q L, in the distribution grid will be determined, along with their respective shadow prices, µ Our proposition is that the DERs will implement these signals in real time This information will also be passed to the DSO, which will compensate the DGs and DR units for their services during the period, and charge inflexible buses for their consumption based on the shadow prices These prices are valid for the period τ This interaction repeats until the next WEM clearing Finally, the last interaction (C), is between the WEM and DSO, and occurs at the next clearing of the WEM, T + T The DSO will aggregate over the N DSO clearings, the net load (generation) of the distribution grid required from (to be delivered to) the main grid, Pl,T + T, and pass this to the WEM It will then receive the new LMP from the WEM, which will be used in the retail market clearings over the next period, [T + T, T + T ] A Market Settlements The DERs including both generating units and flexible consumers that provide ancillary services through the retail market would have to be appropriately compensated while the inflexible consumers charged for their electricity consumption To this end, we can use the shadow prices µ corresponding to the voltage-balance as well as real and reactive power balance in the PAC algorithm, which correspond, respectively, to: µ = [µ v µ P µ Q ]T R 3 B (3) where µ v is the Lagrange multiplier corresponding to the voltage bus equality constraint, µ P the Lagrange multiplier corresponding to the real power balance equality and µ Q the Lagrange multiplier corresponding to the reactive power balance equality constraint As mentioned earlier, we propose that this retail market clears every τ seconds We group a 4-hour period into 4 hour-long intervals T i = [i, i + ], where i corresponds to the ith hour, i =,, 3, over this 4 hour period Suppose that over this T i, there are N clearings of the retail market, which occur at t = i + n τ, n =,, N, and M clearings of the WEM, which occur at t = i + m T, m =,, M Since τ T, it follows that n > m Denoting n = i + n τ, we represent the DSO s hourly costs over each T i as C G (i) = N n= ( ) µ P (n )P G (n ) + µ Q (n )Q G (n ), B (4) Similarly, over the same interval, the reduction in DSO revenue due to the change in flexible consumption, both active and reactive, is given by: C L (i) = N n= µ P (n ) ( P L (n ) P L (n ) ) + µ Q (n ) ( Q L (n ) Q L (n ) ), B (5) The revenue to the DSO from the inflexible consumers over each T i is given by: C L-inflex (i) = N n= ( ) µ P (n )P L (n ) + µ Q (n )Q L (n ), B (6) In addition to the above, the DSO will make a payment to the WEM over the same interval without the proposed retail market structure (ie, without the PAC algorithm), given by: C WEM l (i) = M m= λ P l (m )P G l (m ), l F s (7) where m = i + m T and M denotes the number of WEM-clearings over T i And we define C WEM,DSO as the corresponding payment from the DSO to the WEM with the proposed market structure, ie when the PAC algorithm is running From (4)-(7), it follows that the revenue of the DSO can be quantified as: R DSO = (C L-inflex C L C G ) B, s S l F s, s S ( C WEM l ) C WEM,DSO l (8) Next, we validate the performance of the proposed retail market via numerical simulations IV NUMERICAL EXPERIMENTS We apply the proposed retail market mechanism using the PAC algorithm to a distribution network in Tokyo, Japan and conduct numerical simulations using real data The distribution network model which is named JST-CREST 6 Distribution Feeder Model is presented in detail in [5] A Set-up and Illustrative Scenario The original network model in [5] represents a distribution grid in Komae city in Tokyo, Japan with an area of 5 km Here we employ a compressed version of that network, shown in Fig Our model contains B =84 nodes and 6 lines all connected to the feeder node in a star topology All the information regarding the electrical lines/loads and generators can be found in Table I and Table II, respectively The parameters P L are obtained randomly satisfying through the total upper capacity values in Table I The baseline P L (i) at the ith hour is defined as P L (i) α(i)p L where the timedependent ratio α(i) varies according to the FY7 average consumption profile in the Tokyo area [6], with i varying between h and 4h The distribution of P L across the network and the 4-hour profile of α(τ) are shown in Fig 3 The base value of the frequency f, v and S are set to 5 Hz, 66 V and 3 kva, which are typical values for power systems in Japan [7] We list the remaining parameters as follows: v = 3 pu (with nominal value 675V), v = 95 pu, v = 5 pu, S i, = pu, Q G = Q G = 5P G, and P G = P L = Q L = Q L = We also define the coefficient

6 6 TABLE I: Line and load node data LINE A B C D E F Nodes in B Branches in T Total # of loads Sum of P L [MW] TABLE II: Generation node data B P G [MW] P L [MW] LINE A LINE C 6 LINE D LINE F LINE E 8 LINE B Fig : An illustration of the distribution network model The filled circles show the nodes B The red, blue and green filled circles indicate loads, local generators and both, respectively 33 parameters of the cost functions so that β PL [4, 8] and β PG, β QG [4, 8] and set ξ = in () We assume that the reactive power can be adusted through proper control of the air-conditioners Further, we assume that the Q-LMP at the feeder node λ Q = while the P-LMP, λp, is either fixed at or is time-varying and varies according to the yearly average profile of the FY7 system price in Japan Electric Power exchange (JEPX) [8] as shown in Fig 4 The numerical simulations are conducted on a 6GHz CPU Intel Core i7-56u PC using MATLAB and CVX B Performance Evaluation For the sake of comparison, we benchmark our results using the following scenarios: () When all the loads in the distribution grid are served only by the main grid, and () when the retail market dispatches local DERs through the PAC algorithm but the P-LMP that comes from the real-time market is either fixed or time varying (see Fig 4) Without loss of generality, here we consider bus to be the feeder, # =, and we assume that the DSO services only this network, ie there is a single substation (S = {}) supplying a single feeder (F = {}); thus for brevity, the hierarchy of Fig can be collapsed We tune the parameters ρ and γ of the PAC algorithm so that convergence of the PAC algorithm is guaranteed (for more details see [9]) and we initiate the vector a at the optimal solution of the asoropf (7) at i = 9h Finally, we assume that τ = min and T = 5min, which implies that N = 6 and M = Before comparing the PAC with Scenario (), we first compare the retail market using the PAC with one using the popular algorithm ADMM [] We run both algorithms for iterations, and the results of the optimization function f OPF in () are shown in Fig 5 We note that, the black graph captures the optimal cost of the global optimization problem () (equivalently of Problem (7)), that can be obtained using a centralized optimization solver Observe that, both the PAC and ADMM algorithm converge to a near-optimal value in roughly 5 iterations while the PAC algorithm converges to the optimal solution slightly faster The total time required to complete iterations with the PAC is 3s (65s/iteration/atom) and with the ADMM, 3s (s/iteration/atom) Hence, when the initial conditions are initiated close to the optimal solution, the proposed PAC algorithm can converge in less than 5 minutes which is the Demand ratio Fig 3: The profile of the time-dependent demand ratio α(i), i =,, 4 LMP [JPY/pu] Fig 4: Profile of P-LMP λ P where red denotes the yearly average profile and blue its mean Cost f opf optimal PAC ADMM Iteration Fig 5: Cost evolution with the PAC algorithm and the ADMM standard time between two WEM clearings, as shown in Fig 5 The results from PAC across the distribution gid are shown in Fig 6 From Fig 6(a), we can see that the voltages across lines A and F are higher than across other lines in the network This is reasonable as the local generators connected to these lines generate power that exceeds the local demand of the loads On the other hand, the voltages across line C are suppressed as the total load connected to line C is higher than the local generated power at node 53 From Fig 6(b), we see that Lagrange multipliers µ V, that correspond to the voltage equality constraint, tend to be lower for nodes with higher voltages and vice versa The local active generation and consumption of the distribution grid can be seen in Fig 6(e) and Fig 6(f) while the reactive power generation and demand response throughout the network in Fig 6(g) and Fig 6(h) In order to evaluate the impact of these LMPs, we benchmark the results of our proposed retail market mechanism against Scenario () in Fig 7 The PAC algorithm was run

7 (a) Bus voltage v and power flow 5 5 (b) Lagrange multiplier µ v [/pu] (c) Lagrange multiplier (P-LMP) µ P [JPY/pu] (d) Lagrange multiplier (Q-LMP) µ Q [/pu] (e) Ratio of active power generation to maximum capacity P G/P G [%] 4 3 (f) Active power consumption P L [pu] (g) Reactive power generation Q G [pu] (h) Ratio of demand response to baseline active power consumption (P L P L (9))/P L (9) [%] Fig 6: Terminal configurations with the PAC algorithm and time-variant P-LMP λ P - using both LMP profiles shown in Fig 4 Fig 7(a) compares the case of scenario () when all loads are served by the main grid (black graph) and the one using the PAC (blue and red graph, corresponding to the two LMP profiles) The latter is much lower, simply because the DR units are sharing some of the load with the proposed market mechanism This is also illustrated in Fig 7(b) which shows that the DR units accommodate about 5 to 6% of the total load The most important results from the proposed market mechanism are shown in Fig 7(c) and 7(d) The hourly cost of the DSO for compensating the generating units, over a 4 hour period, is shown in Fig 7(c) for Scenario (black graph and Scenario (red/blue graph for a constant and timevarying LMP, respectively) Using all of the above data, we now compactly represent the savings that we can obtain from the proposed retail market using the revenue metric of the DSO introduced in (8), which is illustrated in Fig 8 This corroborates the fact that the proposed local retail market can result in lower overall generation cost for serving a given load by efficiently dispatching local generators and DR units through the distributed PAC algorithm C Practical Implementation We have made several assumptions regarding the use of PAC and the working of the corresponding retail market Specifically, the market structure and interactions (A)-(C) outlined in Section III have assumed that the WEM specifies the LMP λ P at T but that the DSO is free to determine the generation and load profiles at the retail market clearing instances, occurring at every τ In practice, such an assumption may not be realistic, as the DSO may be obligated to purchase power quantities Pl,T G, Q G l,t (assuming that the DSO is importing power from the grid, as opposed to exporting to the grid) over the period [T, T + T ] In such an event, the proposed PAC can still be used, but with different boundary conditions: the obligation to import power introduces a second boundary condition, where between any two WEM market clearings T and T + T, the net power from the main grid, Pl,T is constant, l F s, s S Specifically, step (A) is identical to that described in Section III Step (B) is identical except that the boundary conditions will fix both the LMP λ P and power P G, Q G such that the relevant feeder cost function terms in # # ()-(3) are constant and do not influence the PAC optimization for all DSO clearings at [T + i τ, T + (i + ) τ], i [, N ]; over the last interval [T + N τ, T + T ], only λ P is fixed while P G, Q G #, are determined by the PAC,, including the feeder node Another assumption we have made is that the DSO determines the required net load based on the immediately past interval Under this revised approach, the net load over the following WEM period is calculated as Pl,T = + T P G #,N P L #,N, where subscript N indicates the last DSO clearing period Future work will examine, instead, a lookahead approach where the DSO anticipates the net load over the next interval, before bidding into the WEM In such a case, how the variation in the net grid import from P G #,T to

8 8 Sum of P G [pu] Demand response ratio [%] (a) Active power generations ( P G ) (b) Demand response ratio ( (P L P L (τ))/ P L (τ)) Sum of C G [JPY] Sum of C L [JPY] (c) Economic compensation of generators ( CG ) (d) Economic compensation of flexible loads ( CL ) Fig 7: The black graphs correspond to the scenario where all the loads of the distribution grid are served by the main grid, the blue graph to the scenario with the fixed P-LMP and the red graph to the scenario with the time-varying P-LMP λ P R DSO [JPY] Fig 8: The proected savings from the proposed retail market over a 4-hour period P G #,T + τ will affect subsequent LMPs from the WEM will also have to be examined V CONCLUDING REMARKS In this paper, we introduce a retail market structure for optimally scheduling Distributed Energy Resources (DERs) including generating units and flexible consumption units in a distribution grid By leveraging a recently developed distributed PAC algorithm, we designed the retail market with settlement rules that dictate the compensation to DGs and charges to consumers The effectiveness and performance of the proposed retail market were evaluated via numerical experiments with real data of a distribution grid in Tokyo, Japan The results show the potential of the proposed market structure in terms of an overall reduction in the total cost incurred by the grid ACKNOWLEDGMENT The authors would like to thank Dr Anurag Srivastava and Dr Anan Bose of Washington State University for their several useful discussions and comments REFERENCES [] ISO New England Iso new england pricing reports com/isoexpress/web/reports/pricing/-/tree/ancillary, 8 [] P Maloney FERC order opens floodgates for energy storage in wholesale markets ferc-order-opens-floodgates-for-energy-storage-in-wholesale-markets/ 5736/, Feb 8 [3] S D Manshadi and M E Khodayar A Hierarchical Electricity Market Structure for the Smart Grid Paradigm IEEE Transactions on Smart Grid, 7(4): , Jul 6 [4] N Li A Market Mechanism for Electric Distribution Networks In Proceedings of the 54th Conference on Decision and Control (CDC), Dec 5 [5] M Hofling, F Heimgartner, B Litfinski, and M Menth A Perspective on the Future Retail Energy Market In Proceedings of the International Workshops SOCNET 4 and FGENET 4, pages 87 95, 4 [6] S Parhizi, A Khodaei, and S Bahramirad Distribution Market Clearing and Settlement In Proceedings of the IEEE Power and Energy Society General Meeting, Jul 6 [7] L Bai, J Wang, C Wang, C Chen, and F F Li Distribution Locational Marginal Pricing (DLMP) for Congestion Management and Voltage Support IEEE Transactions on Power Systems, Oct 7 [8] M Caramanis, E Ntakou, W W Hogan, A Chakrabortty, and J Schoene Co-Optimization of Power and Reserves in Dynamic T and D Power Markets With Nondispatchable Renewable Generation and Distributed Energy Resources Proceedings of the IEEE, 4(4):87 836, Apr 6 [9] J Romvary and AM Annaswamy A distributed proximal atomic coordination algorithm IEEE Transactions on Automatic Control, 8 [] S Magnússon, P C Weeraddana, and C Fischione A Distributed Approach for the Optimal Power-Flow Problem Based on ADMM and Sequential Convex Approximations IEEE Transactions on Control of Network Systems, (3):38 53, Sep 5 [] Y Zhang, M Hong, E Dall Anese, S Dhople, and Z Xu Distributed Controllers Seeking AC Optimal Power Flow Solutions Using ADMM IEEE Transactions on Smart Grid, Feb 7 [] L Gan, N Li, U Topcu, and S H Low Exact Convex Relaxation of Optimal Power Flow in Radial Networks IEEE Transactions on Automatic Control, 6():7 87, Jan 5 [3] G Chen and M Teboulle A proximal-based decomposition method for convex minimization problems, volume 64 Springer-Verlag, Mar 994 [4] Proximal Algorithms, volume Foundations and Trends in Optimization, 3 [5] Y Hayashi et al Versatile Modeling Platform for Cooperative Energy Management Systems in Smart Cities Proceedings of the IEEE, 6(4):594 6, Mar 8 [6] Tokyo Electric Power Company html/index-ehtml [7] Standard models for Japanese power system IEEJ Tech Report, no 754 (in Japanese), 999 [8] Japan Electric Power exchange [9] R Li, Q Wu, and S S Oren Distribution Locational Marginal Pricing for Optimal Electric Vehicle Charging Management IEEE Transactions on Power Systems, 9():3, Jan 4