Applied Energy 195 (2017) 974–990 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Network-aware approach for energy storage planning and control in the network with high penetration of renewables Khashayar Mahani ⇑, Farbod Farzan, Mohsen A. Jafari Rutgers, The State University of New Jersey, USA h i g h l i g h t s  Approximate solution for energy storage (ES) sizing and operation planning.  Approximate solution significantly reduces the complexity of problem.  Approximate solution for complex network with multiple applications of ESs.  A rule-based control scheme for the near real-time operation of complex ES network.  The control schema has been developed by mining the I/O statistical relationship. a r t i c l e i n f o Article history: Received 6 December 2016 Received in revised form 23 March 2017 Accepted 24 March 2017 Keywords: Network-aware planning and control Energy storage network Data-driven control Optimal planning Community level micro-grid a b s t r a c t In this paper, we consider multiple energy storage nodes distributed over a power distribution network, and are purposed for multiple applications. The research problems of interests are to optimally locate these nodes over the distribution network and to create day-ahead plans according to planned applications. The two problems are formulated as stochastic optimization problems, and hourly and timeaggregated approximate solutions are presented. The approximation identifies time periods where load and generation patterns demonstrate low variability, and marks the whole period as a single time zone, thus significantly reducing the number of decision variables and the overall problem size. We show that aggregate and hourly planning solutions are close. The planning problem can handle any number of storage nodes with general topology and load connections, and deterministic or stochastic capacities. In this paper, we focus on network of static energy storages with deterministic capacity. Finally, we build a novel rule based control scheme for the near real time operation of the storage network by mining the statistical relationship between input and optimal charge and discharge patterns. Ó 2017 Elsevier Ltd. All rights reserved. 1. Introduction Energy storage (ES) has the potential to offer a new means of added flexibility on the electricity distribution systems. This flexibility can be used in a number of ways, including adding value towards asset management, power quality and reliability. An important factor in evaluating the feasibility of ES technology is the application(s) for which the storage is used for [1]. ES can provide local level services such as, peak shaving and renewable integration [2,3], and network level services, such as voltage and frequency control [4]. It can also be utilized for loss minimization and deferral of network infrastructure upgrades. With the use of energy storage in a distribution networks for multiple applications, however, comes the challenge of determining how best to control ⇑ Corresponding author. E-mail address: km723@scarletmail.rutgers.edu (K. Mahani). http://dx.doi.org/10.1016/j.apenergy.2017.03.118 0306-2619/Ó 2017 Elsevier Ltd. All rights reserved. these storage units under load and system state uncertainties. For example, with increasing number of Electrical Vehicles (EVs) the uncertainty in the electricity demand rises due to EV charging demand [5–7]. But, on the other hand, Vehicle-to-Grid (V2G) technology, while mitigating some of this uncertainly, can add system dynamics complexities to the network [8–10]. Han et al. [11] and Wong et al. [12] provide control algorithms to maximize EV owner’s profit, which comes from selling power to grid and participating in the frequency regulation market. They formulate the problem as a discrete-time Markov decision process and solve it by introducing an online learning algorithm which iterates every hours based on available information. Koutsopoulos et al. [13] study the optimal energy storage control problem by taking the point of view of a utility operator and focuses on arbitrage application of energy storage. The authors show that the model can be extended to account for a renewable source that feeds the storage device. The same problem was considered in [14], where the K. Mahani et al. / Applied Energy 195 (2017) 974–990 975 Nomenclature Ens;max Ps;max time index static storage node index demand node index renewable node index temporal zone index day index year index scenario (cluster) index tree index in tree-bagging method number of clusters annual inflation rate (%/year) annual discount rate (%/year) storage unit s energy capacity (kWh) energy storage s rated capacity (kW) Inv Cap s investment unit cost on storage capacity ($/kWh) Inv PR s LSc ðj; iÞ investment unit cost on power rating ($/kW) total electricity demand during zone i at demand node j for cluster Sc (kWh) total renewable generation during zone i at renewable node k for cluster Sc (kWh) demand matrix for day ‘‘d” in year ‘‘y” renewable generation matrix for day ‘‘d” in year ‘‘y” electricity price matrix for day ‘‘d” in year ‘‘y” representative demand matrix for cluster Sc representative renewable generation matrix for cluster Sc representative electricity price matrix for cluster Sc t s j k i d y Sc b CL c a RSc ðk; iÞ Ld;y ð:Þ Rd;y ð:Þ Pr d;y ð:Þ LSc ð:Þ RSc ð:Þ PrSc ð:Þ ech;g s;i;Sc ech;r s;k;i;Sc eds;j;i;Sc total energy charged from grid during zone i in storage unit s for cluster Sc (kWh) total energy charged from renewable node k during zone i in storage unit s for cluster Sc (kWh) total energy discharged during zone i from storage s to demand node j for cluster Sc (kWh) cost of energy is minimized subject to both user demands and prices using a Markov Decision Process. Dufo-Lopez et al. [15] consider the energy storage in private facility to reduce the electricity bill. They conclude that electricity price variation has a great effect on the profitability of storage system. Renewable resource integration is an important application of energy storage, and chargedischarge control policy of energy storage to serve this application is presented by Wang et al. [16]. Renewable energy sources are considered by Teleke et al. [17] too, where an open-loop optimal control scheme was developed which incorporates the operating constraints of battery energy storage. They use the battery energy storage in a smoothing application where a wind farm is dispatched on an hourly basis based on the forecasted wind conditions. Earlier works on component sizing or optimal operation employ different approaches, which are differentiated by decisional variables. Studies that take into account both sizing and scheduling problems are generally scarce. Ru et al. in [18] determine the optimal size of a grid-connected PV-battery system which is used in an arbitrage application. Their objective is to minimize the net power purchase cost plus battery capacity loss, without considering any initial capital investment. Khalilpour et al. [19] introduce a decision support tool for sizing and operation of PV-battery system in a single facility, with the objective of maximizing the net present value generated by bill reduction. Zhang et al. [20] introduce a rule based charge and discharge strategy which simultaneously optimizes the battery sizing and operation in a bill management edem;g j;i;Sc total energy from grid during zone i to demand node j for cluster Sc (kWh) edem;r total energy from renewable k during zone i to demand j;k;i;Sc node j for cluster Sc (kWh) ci;j configuration number between nodes i and j Effch;s energy storage ‘‘s” charging efficiency energy storage ‘‘s” discharging efficiency Effdis;s average electricity whole sale price during the hours of Pr w Sc ðiÞ zone i for cluster Sc ($/kWh) Pnsub penalty for damage to substation due to reverse flow of power ($/kWh) Dem demand charge for peak demand ($/kW) storage s energy level at the end of zone i (kWh) SOC s;i dri duration of temporal zone i Enmax maximum energy reservoir capacity Pmax maximum power rating safety reserve capacity for storage unit s SF s ESL Storage - Demand Eligibility Matrix ERS Renewable - Storage Eligibility Matrix ERL Renewable - Demand Eligibility Matrix ST t network state vector at time t ps control policy for storage s control action of storage s at time t ast rwst (ST, ast Þ reward function for storage s when action ast is taken in state ST s Vp value storage s under control policy ps Y classification response vector (Control action vector) LR level of on-site renewable generation LD level of demands EP electricity price X classification feature matrix B number of bags s memory window in control module dn nth digit in control action code application. The introduced rule-based approach works well for a single PV-battery system with in the facility, however the interaction between multiple battery units in more complex distribution network has not been investigated. The similar problem was considered by Brekken et al. [21], where sizing and control methodologies for a battery-based energy storage system is presented for wind farm applications. The sizing problem of distributed generator and energy storage system (single application – electricity cost reduction) for demand response applications in smart households has been studied in [22,23]. Andreotti et al. [24] consider a network of renewable generation units and formulate a singleobjective optimization problem whose objective function is power loss minimization while satisfying constraints on active and reactive power at the interconnection bus. Nick et al. [25] studied the optimal allocation of storage systems in an active distribution network by defining a multi-objective optimization problem. The application of renewable generation integration is also considered in [26–29]. Van de ven et al. [30] present a battery control policy, which minimizes the total discounted costs, taking into account arbitrage application of energy storage. Jayawarna et al. [31] studied the energy storage power reliability application and present the concept of using central energy storage system as the main fault current source in micro-grid islanded mode. To the best of our knowledge, there is a major gap in understanding how multiple storage units programmed for multiple applications should operate in a distribution network. This paper intends to fill this gap by developing simple but verifiable control 976 K. Mahani et al. / Applied Energy 195 (2017) 974–990 strategies, which directly take into account system characteristics and states. The proposed approach is applicable to connected energy storage units in distribution networks with multiple applications. More specifically, we consider a system with multiple storage nodes distributed over an arbitrary power distribution network, and given that there are infrastructure limitations on the use of energy storage over this power network. Capacity of each node is assumed to be static and deterministic. Stochastic energy storage nodes are also possible, and will be examined in another paper under preparation by the same team. A good example of energy storage with dynamic capacity is a parking lot with multiple spaces for EV and V2G connections, where arrival and departure of vehicles are random and only a random portion of parked vehicles can serve vehicle to grid flow [32]. In this paper, energy storage is considered as a node with two main parameters, namely; energy capacity (in kWh) and rated capacity (in kW). The behavior of storage nodes is deterministic. We also assume that the voltage of nodes across the distribution network will be maintained in the proper feasible region by network operator. Fig. 1 gives an example of a power distribution network with multiple loads or demand nodes, storage nodes, and renewable generation nodes as well as connectivity to a macro power grid. We are interested in the following problems: (i) Where to locate static storage nodes and how much capacity to allocate to each node for optimal sizing and operation; (ii) How to day-ahead plan for the charge and discharge of these nodes, and (iii) How to control their operation in a near real time basis. In this paper, we use a network-aware distributed planning and control approach to solve these problems. Network-aware planning and control is an approach for near real time control of assets in an arbitrary interconnected network. Such a network has multiple nodes with different functionality and criticality. Planning and real time control decisions need to be made in reference to the characteristics and state of constituent elements (nodes and arcs) of the network and the overall control objective. The state description of an element includes, among other attributes, the element’s availability and efficiency factors. We will present two models: (i) A model for optimal location and capacity planning that also solves for day-ahead operational plan, and (ii) A model for optimal charge and discharge control of storage nodes in a near real time basis. The paper is structured as follows. In Section 2, we describe the first model. Some illustrative case studies for planning phase are demonstrated in Section 3. Section 4 gives a data-driven network-aware control scheme with a number of case studies. To investigate the impact of behavior changes of stochastic input processes on the network planning and control we include sensitivity analysis in section 5. Conclusion and future work are explained in Section 6. 2. Optimal planning In this study, we consider a power distribution network, which could be utility-owned or a community level micro-grid, with high penetration of renewable resources, such that renewable output may exceed system load from time to time (see Fig. 1). The reverse flow of power, resulting from the high level of renewable output and inability to absorb excessive power at loads, could damage the distribution network infrastructure. The storage nodes absorb this excessive power and mitigate the damages (Renewable reverse flow reduction). The energy charged from excessive renewable output can be used to reduce the cost of purchased energy from grid during peak hours, given that renewable peak and price peak do not coincide (Time of Use). The energy charged from renewable during off-peak hours can be utilized during on-peak hours to shave the peak demand as well (Peak Reduction). Here we formulate a stochastic optimal planning problem that takes into account the long-term cost of investment on a network of storage nodes and their short-term operation costs calculated on the basis of day-ahead planning schemes. The formulation is general in such a way that time units can vary from sub-hourly to hourly to more aggregate temporal zones that are constructed on the basis of stochastic pattern changes of some or all of the input sources (e.g., electricity price and power demand). The aggregation is done in a way that the designated input processes have small variations within these temporal zones. Fig. 2 illustrates a simple example of the temporal aggregation scheme over three stochastic input processes, namely, renewable generation, demand (in this specific example our network has two demand nodes) and electricity price. Coefficient of variation is used to measure the variation of the stochastic processes. In order to aggregate several hours into one temporal zone, we start from the first time slot (hour 1). The consecutive time slots (hours) are aggregated into a single temporal zone as long as the coefficient of variation (CV) for each input parameter (namely, demand, on-site power generation and electricity price) remains less than the selected threshold (0.3 in this example) for that temporal zone. If adding the next hour increases the inputs’ CVs for the current temporal zone to more than 0.3 (in either of the input parameter), that hour is then considered for the Fig. 1. An example circuit with multiple storage units, renewable energy resources and demand nodes. K. Mahani et al. / Applied Energy 195 (2017) 974–990 977 Fig. 2. Temporal zone aggregation example. next temporal zone. It is intuitive that decreasing (or increasing) the threshold value for coefficient of variation increases (or decreases) the number of zones in the aggregate model. Fig. 2(a)–(c) shows the example patterns of stochastic input processes. We note that within each temporal zone the input patterns are fixed at their average values (Fig. 2d, e and f). The advantage of the temporal aggregation over common hourly mixed integer programming is that, in the aggregate model, the planning period is decomposed into zones (usually in several hours), and the only variable which is moved from one zone to the next is the state of charge at the end of the zone. By the virtue of this decomposition, a problem with long planning periods and a complex network configuration does not suffer from excessive computational times. Hereafter, we will use the term temporal zone to commonly refer to a time unit (sub-hourly or hourly). The objective function is the total operation and investment cost defined over these temporal zones, and energy storage capacity (both energy capacity and rated capacity), aggregate charge and discharge amounts within each zone (in kWh) are the decision variables. Multiple applications of energy storage are considered, namely, ‘‘Time of Use”, ‘‘Renewable Reverse Flow Reduction” and ‘‘Peak Shaving”. We borrow ideas from the classical multi-period inventory control problem [33], where each temporal zone represents a single period and the remaining energy in storage at the end of each period defines the storage state of charge at the beginning of the next period. The total cost function is measured in net present value and includes the present value of investment costs and operation costs of the installed nodes during a lifetime period. That is, MinimizeðOBJ Inv þ OBJ op Þ ðO:1Þ For the investment part we have OBJInv ¼ X ðCAPS  Inv Cap þ PS  Inv PR s s Þ ðO:2Þ s where Inv Cap is investment cost related to the capacity of storage s node s (measured in $/kWh) and Inv PR s is cost related to power rating of the node (measured in $/kW). For the short-term operation costs, we must cover the uncertainties over the planning horizon. We assume that input daily profiles of demand, renewable power generation and electricity price each follow a stochastic pattern, and together they can be clustered into groups of profiles over the planning horizon. We note that one can always form such clusters using historical data over the subject distribution network. Total operation cost (OBJop ) of network will be the sum of daily operation costs over the planning horizon. Daily operation cost is 978 K. Mahani et al. / Applied Energy 195 (2017) 974–990 stochastic because of the uncertainty in daily profile of demand, renewable power generation and electricity price. OBJ op ¼ " X  1 þ c y 1  1þa y # 365 X DailyOperationCostðd; yÞ ðO:3Þ d¼1 For the above problem, stochastic scenarios are generated over the stochastic inputs namely, demand, electricity price and renewable power generation, and on the basis of historical data from several years (we choose 3 for illustration). To reduce the computational complexity, we apply a high-dimensional data clustering method [34] to group these profiles and reduce the number of scenarios [25]. Daily demand profile, electricity price and renewable power generation are considered as features in this clustering. Suppose that a total of ‘‘CL” clusters of input profiles exist. In each cluster we consider the representative average profile (over a cluster) for each demand node, renewable resources and electricity price. Now, depending on the size of each cluster the chance of its occurrence is calculated (ProbSc Þ: OBJ op ¼ " X  1 þ c y y 1  1þa CL X 365  ProbSc  DailyOperationCostðScÞ Sc¼1 # ðO:4Þ where c and a are annual inflation and discount rates (%/year), ‘‘Sc” is the index of scenarios according to the input data and ProbSc is the probability of scenario ‘‘Sc”. DailyOperationCostðScÞ is the daily operation cost given scenario ‘‘Sc”, which is the representative scenario for cluster ‘‘Sc”. Since multiple applications are considered, the daily operation cost includes multiple sections as described below: 1. Within each zone a portion of electricity at each demand node is served by the renewable nodes, which are connected to it. Also, a percentage of demand at that demand node is served by discharging energy from its connected energy storage nodes. The rest of the demand plus any amount to be stored in storage nodes are supplied by purchasing electricity from the grid. 2. The owner of the distribution system is usually charged for peak demand. High peak demand could also cause more depreciation of distribution devices. Charging storage nodes during off-peak hours and discharging during on-peak hours reduce the peak. Demand charge is usually defined in a monthly term. Here, we use the same concept in daily planning. In order to consider the hourly peak demand in time aggregate approach we assume that the aggregate power flow is distributed uniformly within each zone. 3. It is assumed that the remaining power from renewable creates a reverse flow at the substation if it is not absorbed by storage. Cost of damage to substation due to the reverse power is estimated by multiplying the remaining renewable output by a penalty factor (Pnsub Þ. þ w3  Obj 3ðScÞÞ Obj 1ðScÞ ¼ i j ( Obj 3ðScÞ ¼ " X i " X Pnsub RSc ðk; iÞ k ðO:5Þ !# 1 X dem;g X ch;g ej;i;Sc þ es;i;Sc dr i s j Obj 2ðScÞ ¼ Dem  max i s !) X dem;r X ch;r ej;k;i;Sc þ es;k;i;Sc j 0 6 P s 6 Pmax ; s !## 8s ðC:1Þ 8s ðC:2Þ Operation Constraints: Operation constraints are valid in every scenario (Sc). The total amount of inflow and outflow electricity for each static storage node is limited due to its power rating, ech;g s;i;Sc þ X ech;r s;k;i;Sc þ X eds;j;i;Sc 6 Ps  dr i;Sc 8s; i; Sc ðC:3Þ j k As we mentioned before, storage level (state of charge) is moved from one temporal zone to the next. Storage level at the end of a zone is calculated based on the amount of energy charged and discharged during that zone. It is obvious that storage level cannot exceed its maximum capacity. Also, SFs as a safety reserve capacity is considered for storage nodes. Since, according to (O.5), daily operation cost is calculated in objective function the initial state of charge in each individual day will be important. For daily optimization, we assume that all nodes have the same initial state of charge (e.g., 80% of maximum energy capacity ðCAPS Þ). Furthermore, the SOC of each storage at the end of a day is the same as its daily initial state. SOC s;i;Sc ¼ SOC s;i 1;Sc þ Effch;s  ech;g s;i;Sc þ X ech;r s;k;i;Sc k X ed j s;j;i;Sc 8s; i; Sc Effdis;s SF s  CAPs 6 SOC s;i 6 CAP s ! ðC:4Þ 8s; i ðC:5Þ We assume that the electricity load at each demand node has to be satisfied, so: LSc ðj; iÞ ¼ X dem;r X ej;k;i;Sc þ eds;j;i;Sc þ edem;g j;i;Sc 8j; i; Sc ðC:6Þ s k Electricity generated by a renewable unit is used to serve demand nodes and charge the storage nodes which are connected to it. The remaining generation from renewable creates a reverse flow of power at the substation. X dem;r X ch;r ej;k;i;Sc þ es;k;i;Sc j DailyOperationCostðScÞ ¼ ðw1  Obj 1ðScÞ þ w2  Obj 2ðScÞ X dem;g X ch;g PrSc ðiÞ ej;i;Sc þ es;i;Sc 0 6 CAP S 6 Enmax ; RSc ðk; iÞ P The daily operation cost is then given by: " X where PrSc ðiÞ is the average electricity price during the hours of zone i for cluster Sc. w1 ; w2 and w3 represent the importance of different storage applications in the planning phase. The constraints of the above problem are defined in two categories: ESS installation constraints and operation constraints. ‘‘j”, ‘‘k” and ‘‘s” representing sets of demand nodes, renewable nodes and static storage respectively. Installation Constraints: Constraints 5 and 6 show the maximum capacity (energy and power rating) of ESS that can be installed on possible node ‘‘s”. 8k; i; Sc ðC:7Þ s The power distribution network has ‘‘S” possible nodes for static ESS installation, ‘‘J” demand nodes and ‘‘K” renewable resources. Power can flow between two nodes if they are connected physically. The topology of the network is defined by configuration numbers (ci1 ;i2 Þ. Configuration numbers have binary value; 1 means physical connection exists. ci1 ;i2 ¼ 1 means that nodes i1 and i2 are connected. Following equations illustrate the network configuration constraints: 0 6 edem;r 8j; k; i; Sc j;k;i;Sc 6 M  c k;j ðiÞ ðC:8Þ 0 6 eds;j;i;Sc 6 M  cSs ;d ðiÞ 8j; s; i; Sc ðC:9Þ 979 K. Mahani et al. / Applied Energy 195 (2017) 974–990 0 6 ech;r 8s;k; i; Sc s;k;i;Sc 6 M  c k;Ss ðiÞ ðC:10Þ where ‘‘M” is a very big number (e.g. 10 millions). Solution methodology is illustrated using the following example. 3. Illustrative example A modified IEEE 13 node test feeder as a community level distribution system with high penetration of renewable resources is used as a case study (see Fig. 3). We start with the clustering of stochastic input profiles and grouping of days in the planning horizon. Then we show optimal capacities for different network configurations with different applications. Finally, the day-ahead operation results will be demonstrated. As shown in Fig. 3 eight demand nodes are considered in this network. Four residential sectors are considered in nodes D2, D5, D7 and D8. The other four demand nodes (D1, D3, D4 and D6) assumed to be commercial facilities. Four PV solar systems with generation rated capacity of, respectively, 1500 kW, 1600 kW, 800 kW and 600 kW are assumed as renewable resources at nodes R1 - R4. The hourly power generation of these nodes is related to hourly solar intensity (radiation). We assume the same solar radiation at the locations of solar systems. Four nodes with renewable resources are considered as the potential nodes for energy storage installation. Following eligibility matrices are assumed in this case study: Fig. 3. Distribution network. 5. c = 2%/year and a = 10%/year are assumed as annual inflation and discount rate [35]. Three years data for residential and commercial sectors, solar radiation and electricity price are grouped into several clusters. High Dimensional Data Clustering (HDDC) method is used to allocate input data into smaller number of groups [34]. This method is available in CRAN server and can be used in R. By applying HDDC algorithm, three years input data are grouped into fortyeight (48) clusters with each cluster associated with daily operation cost that varies in a small range. Fig. 4 shows the input data with hourly mean value in one of these 48 clusters. More information about these clusters can be found in Appendix A. The cluster shown in Fig. 4 (cluster 13) has population size of 41. All of these 41 individual input data are within a heating season, specifically from December to February. Since the total sample size is 1095 (3  365), the probability of having inputs similar to data in cluster 13 is 41=1095 ¼ 0:0374. Next, we present our results for the optimal capacity planning with different weights for different storage applications. This will be followed by the optimal operation planning for some sample clusters. 3.1. Capacity planning As an example based on the defined eligibility matrices, storage at node S2 can be charged from renewable R2. Furthermore, this storage node can serve electricity demand in nodes D3 to D8. The following assumptions are considered in this case study: 1. Sodium-Sulfur energy storage with 15 years lifetime is candidate technology to install as energy storage system. 2. According to [35] 350 $/kWh and 350 $/kW are considered as investment unit cost related to ESS energy capacity and power rated capacity (Inv Cap and Inv PR s s ). 3. Both charging and discharging efficiency are assumed at 90%. 4. 5% power loss is assumed for long distance transmission. Note that nodes shown in Fig. 3 are grouped into four classes, class 1 includes D1, D2, R1 and Storage 1, class 2 contains D3, D4, R2 and Storage 2. D5, D6, R3 and storage 3 are in class 3 and class 4 includes the other nodes. Transferring power between two different classes is considered as long distance transmission. The capacity planning optimization problem is solved using both hourly and aggregate temporal zones. The same optimal capacity plans were obtained from both cases; the reason being that the variation of stochastic input processes within each temporal zone is small, as per approximation scheme. Multiple applications of storage with weights w1, w2 and w3 are considered in both cases. Note that each storage application has its own cost elements, and using these weights we are able to obtain a weighted objective function that includes multiple applications. Table 1 shows four different combinations of storage applications with different weights. In the first three cases a single application is considered in planning and in the last case (Case 4) multiple applications are investigated. This table also shows the optimal capacity for these cases. Clearly, capacity plans depend on the intended storage applications. For instance, for renewable reverse flow reduction application installing storage system in nodes S3 and S4 is sufficient. The reason is that renewable R1 and R2, which respectively can charge storage S1 and S2, are serving more electricity demands, therefor there exist less excessive reverse power flow in these two nodes. In the following section the day-ahead planning results will be demonstrated for some sample clusters. The hourly model is used for the day-ahead planning problem. The results from the aggregate model are then compared to the results from the hourly model. 980 K. Mahani et al. / Applied Energy 195 (2017) 974–990 Fig. 4. Input data in cluster 13. Table 1 Capacity planning results. Case 1 2 3 4 (W1, W2, W3) Storage 1 Capacity (kWh) Power Rate (kW) Capacity (kWh) Power Rate (kW) Capacity (kWh) Power Rate (kW) Capacity (kWh) Power Rate (kW) (0, (0, (1, (1, 17,000 0 6200 10,000 1500 0 2000 1500 700 0 6600 2000 90 0 2200 500 290 80 1000 900 40 20 300 160 690 1500 600 1800 90 300 120 300 1, 0, 0, 1, 0) 1) 0) 1) Storage 2 Storage 3 3.2. Aggregate model validation In the aggregate model electricity flows from the main grid and DER resources are distributed uniformly within each temporal zone. Hence, the aggregate state of charge at storage nodes and the overall objective function are expected to closely approximate the hourly results. Moreover, one would expect that the computational complexity of the aggregate model to be significantly lower than the exact hourly model especially for large networks and higher temporal resolution. Next, we compare the results of aggregate model to the exact hourly model. Note that both aggregate and hourly models produce the same optimal sizing. We illustrate results from one of the representative clusters that we will later use for daily planning, as shown in Table 2. Fig. 5 compares the state of charge of ESSs in hourly and aggregate models when the optimal configuration of case 3 (EBM application) is installed in the distribution network and inputs come from cluster 47. As demonstrated in the above figure the state of charges at the end of each temporal zone in aggregate model are close to the hourly model. Table 2 compares the two models in different cases. As illustrated in Table 2 the values of objectives in aggregate and hourly model are close. Recent table compares the objective values for different cases for one specific cluster. Analyzing the results from aggregate model Storage 4 shows the little error for all input clusters. Following Table 3 illustrates the mean value and standard deviation of error over all input clusters for each objective in different applications. Table 3 verifies that proposed aggregate model is a good approximation for exact hourly model in day-ahead planning. Using aggregate model lowers the computational complexity of optimization problem significantly. For instance, in our example case (Fig. 3 – Distribution network, which is defined by configuration matrices ESL, ERS and ERL; there are 56 possible directions for power flow in the distribution network. Also as mentioned earlier 48 input clusters exist based on historical input data. Using hourly model results in 56  48  24 ¼ 64512 operational decision variables in the capacity planning problem, however, using the aggregate model reduces the decision variables to 56  672 ¼ 37632 (almost % 45 reduction). Reduction in the number of decision variables has a significant value especially in the complex and large networks. 3.3. Daily operation planning In this section, daily operation planning for different capacity configuration (shown in Table 1) are discussed for some sample input clusters. For each capacity arrangement the impact of different application weighting values on daily operation planning are Table 2 Aggregate model vs. Hourly model (inputs from cluster 47). Case Application Electricity cost ($) Hourly 1 2 3 4 Peak shaving Reverse flow reduction EBM Bundle 46,246 46,940 Peak value (kW) Aggregate 47,498 48,044 Total reverse flow (kWh) Hourly Aggregate 7331 7849 7696 7912 Hourly Aggregate 0 0 0 0 981 K. Mahani et al. / Applied Energy 195 (2017) 974–990 Fig. 5. Aggregate model vs. Hourly model (SOC), Application: EBM. Table 3 Percentage error over all input clusters (Aggregate model vs. Hourly model). % error for each objective for different applications (average over all clusters) Case Application Electricity cost ($) Mean value 1 2 3 4 Peak shaving Reverse flow reduction EBM Bundle % 3.5 %3 Peak value (kW) Standard deviation % 0.8 % 0.6 studied. For daily operation planning analysis, we focus on three different clusters of input data (clusters 44, 46 and 47) – Fig. 6 shows the mean value of input data for these clusters. Cluster 44 has low level residential demand, but a high-level commercial demand. It also represents days with medium-level of solar intensity. Cluster 46 has low levels of residential and commercial demand with a high-level of solar intensity. Cluster 47 represents days with a high mean value and variance in hourly electricity price. Both residential and commercial nodes have a high-level of demand in this cluster. In each cluster, a 24-h planning horizon is divided into temporal zones and used to find the optimal amount of charge and discharge for a given cluster representative profiles. Table 4 shows the number of zones and their duration (in hours) for each input cluster. In this example, we assume that ESS units are installed for TOU application to reduce the cost of purchasing electricity from the main grid. So according to the capacity planning results, shown in Table 1, ESSs with capacities given by case 3 are installed in the subject distribution network. Based on capacity planning results, this configuration is optimal when reducing the cost of purchasing electricity from grid is the only goal for ESS installation. Total reverse flow (kWh) Mean value Standard deviation %6 % 1.5 % 5.5 % 1.2 Mean value Standard deviation % 0.2 % 0.05 % 0.2 % 0.05 Figs. 7–9 show the optimal power dispatch of DER assets (renewable resources and energy storages) to demand nodes 1 and 8 when the input data, respectively, come from clusters 44, 46 and 47. Note that aggregate model is used to find the optimal dispatch and aggregated amount of power is depicted uniformly within each temporal zone in these figures. As illustrated in the above figures the optimal dispatch of DER resources is sensitive to input profile. For instance, in all the three clusters a major portion of demands are satisfied from renewable resources during the noon time when sunlight is available, and stored energy in ESSs is utilized in peak price periods. As shown in Fig. 6 peak price times are different in the three representative clusters. In cluster 44 peak price is at 1:00 AM and as illustrated in Fig. 7 during that period stored power in ESS is discharged to supply electricity demand and reduce the network electricity cost. The above figures also show that the configuration of network affects the dispatch of DERs. For example, demand 8 is connected to all storage and renewable resources, but because of the higher power loss in long transmission, R4 and S4 are used to serve this demand node. As an another example, D1 could be served only by R1 and S1, so these two resources are used to provide electricity 982 K. Mahani et al. / Applied Energy 195 (2017) 974–990 Fig. 6. Average Input data in clusters 44, 46 and 47. Table 4 Local zones’ duration for different clusters (Clusters 44, 46 and 47). Cluster number Number of temporal zones Duration of temporal zones 44 46 47 13 16 12 [1, 4, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 7] [3, 4, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2] [6, 1, 1, 1, 1, 1, 2, 1, 1, 4, 1, 4] Fig. 8. DER optimal dispatch with input data from cluster 46. 4. Network-aware real-time control Fig. 7. DER optimal dispatch with input data from cluster 44. to D1. The optimal dispatch of DERs to other six demand nodes are presented in Appendix B. Finally Table 5 illustrates the interaction between storage application and optimal operation for input cluster 47. The above Day-ahead planning was performed based on the forecast of stochastic input processes. But what happens if the real-time inputs are not close to the forecast values? For real time control, one could always update the forecast values of input patterns and repeatedly carry online optimization by solving the optimization problem at some predefined time steps [36,37] (online optimization). Running on-line optimization for complex networks with large number of components and inputs is not practical, however. Here, we propose a rule-based control approach that determines the optimal real-time actions for each storage node by 983 K. Mahani et al. / Applied Energy 195 (2017) 974–990 renewable nodes, (iii) state of charge at each storage unit, and (iv) electricity price trend. That is, ST t ¼ ½LDd;t s ; . . . ; LDd;t ; LRk;t s ; . . . ; LRk;t ; EPt s ; . . . ; EP t ; SOC i;t ŠT 2 SS ð1Þ 8d 2 Demand nodes; 8k 2 Renewable nodes; 8i 2 Storage units Fig. 9. DER optimal dispatch with input data from cluster 47. Table 5 peak value, total reverse flow and total electricity cost when ESSs are used for different applications. Case Weights ([w1,w2, w3]) Application Peak value (kW) Total reverse flow (kWh) Electricity cost ($) 1 2 [0, 1, 0] [0, 0, 1] 7849 9313 955 0 48,499 50,376 3 [1, 0, 0] 8559 374 47,498 4 [1, 1, 1] Peak shaving Reverse flow reduction EBM (Energy Bill Management) Bundle 7912 0 48,044 monitoring the state of components and inputs across the network. We adopt a reinforcement learning approach and build a control policy, which maps the actions and network state, by a supervised learning classification model. In the proposed Network-aware control model the near optimal actions are taken in each individual storage unit based on the partial knowledge of the whole network state. The state space SS of the distribution network is defined by: (i) electricity consumption trend at demand nodes, (ii) renewable power generation trend at where LDd;t represents the level of electricity demand at node d at time step t, LRk;t represents the level of power generation at renewable k at time step t, EP t represents the electricity price at time step t and SOC i;t represents the level of energy at storage node i at the beginning of time t. In order to investigate time series impact of these variables we define a new variable ‘‘s” for a time window. At each time step t, control agent s (for storage s) receives state STt of the network and selects an action ast 2 As (STt) # As , where As (STt) is the set of actions available for storage s in state STt and As is the set of all possible actions for storage s. As is defined by the amount and direction of power at any given state. Since As has a finite possible actions the amount of power has to be discretized. Power directions are: charging from grid, charging from different connected renewable nodes and discharging to different demand nodes. We note that depending on the network topology, storage nodes will have different action spaces. For illustration, storage unit S4 in our example case study is connected to two demand nodes (D7 and D8), renewable node R4 and also main electricity grid (4 directions). If the amount of power in each direction discretized into three levels, then 43 will be the maximum number of actions in action set A4 . We should note that some of these actions won’t be feasible because of rated capacity limit on storage unit, hence will be removed from the action set. Since our focus in this section is electricity bill management as a primary application of storage units, for each individual storage s, the reward function rwst ðST t ; ast Þ during time interval t, is the saving in network electricity cost as a result of storage s. Since action ðast Þ at time t affects the state of network at the next time step (ST tþ1 Þ, ast should be taken in a way to maximize rewards during that and all future time intervals. For storage s we seek a control policy ps , s such that as t ¼ p (STt), which minimizes the overall network electricity cost. Value of the storage s under the control policy ps when network starts in state ST at time t is defined as: ps V ðSTÞ ¼ rwst ðST; ast Þ þE ( 1 X i e i¼1 Fig. 10. Stochastic Input pattern when charging from grid is the optimal action for ESS1. rwstþi ðST tþi ; astþi Þ ) ð2Þ 984 K. Mahani et al. / Applied Energy 195 (2017) 974–990 Fig. 11. Stochastic Input pattern when discharging to D1 is the optimal action for ESS1. where X rwst ðST; ast Þ ¼ PrðtÞ  eds;j;t j ech;g s;t ! ð3Þ ech;g s;t is the amount of power flow from grid to the storage s during P time interval t and j eds;j;t represents the total amount of power flow discharged from storage s to serve connected demand nodes. These quantities are determined according to action ast . Note that future states and rewards are not only dependent on the action taken by storage unit s, but also are dependent on the actions of the other agents. This brings uncertainty to the future rewards, hence, expected value of the value function is used. A threshold value 0 < e < 1 is introduced to ensure convergence. The optimal policy ps then maximizes the value of storage s, so that, s ps ¼ ArgmaxðV p ðSTÞÞ actions. After a predefined time window (usually a day), the state space and action spaces will be updated and rules will be reconstructed (repeat steps (i) and (ii)). This will ensure that the control model is robust to the changes in the input patterns. ð4Þ ps The above optimal control problem is solved using the following three steps: (i) Compute the optimal hourly charging and discharging actions for each storage node in the network using the above hourly optimization model. Several points are in order: (a) Hourly model is used since control actions are to be made at the top of each hour; (b) The optimization model is run for 365 days per year times the number of years for which historical data exist. In practice the sample size (N S Þ can be very large. For illustration, we will use a sample size N S ¼ 3  365  24 hourly data each described by a state vector STt and a set of corresponding actions ast for storage unit s. For the illustrative distribution network, there are four storage units, so in each sample data there exist four sets of actions (ast ; 8sf1; 2; 3; 4g). (ii) Construct simple rules that characterize the optimal actions as a function of network state and its stochastic input patterns. The output of this step is ps for all storage units (8sf1; 2; 3; 4gÞin illustraive case. The construction is carried out using a classification algorithm, which will be discussed next in details. (iii) Monitor and match the real-time values of inputs and the network state to the most similar stored patterns computed in step (i). Use rule set from Step (ii) to take the optimal Algorithm 1 (Offline classifier construction algorithm). Estimate the optimal control policy ps For (8s) repeat: /storage index/ 1.1 – Construct the response vector: Y = [as1 , as2 ;


; asN S ]T 1.2 – Construct the feature matrix: X = [ST 1 , ST 2 ;


; ST N S ]T For ð8bÞ repeat: /tree index in tree bagging method (denoted by ‘‘B”)/ 1.3 – Calculate classifier psb (ST) based on bootstrapped training data set (X b , Y b ) End 1.4 – Calculate ps ðSTÞ ¼ B1 End PB b¼1 psb ðSTÞ ð5Þ As described in ‘‘Algorithm 1” a classification technique is used to characterize the optimal actions as a function of state of the network components and stochastic inputs. The hourly optimization model is utilized to generate the required data for classification. The hourly decision variables of the day-ahead optimization problem, namely, charge and discharge quantities for each storage node, are the designated response variables in the classification (optimal control actions). A unique class label is then assigned to each action for the classification purposes. We note that the number of classes changes according to the configuration and topology of distribution network. The response of the classification for each storage system is a vector with labels associated with optimal actions for that storage unit. Tree bagging technique [38] is used to build a classification model to predict the optimal action in each individual storage node as a function of stochastic input values and the SOC of ESSs in the entire network. Tree bagging creates and ensembles decision trees for predicting response variable (optimal action at each time step) as a function of predictors (network state). Given a training set of predictors with corresponding 985 K. Mahani et al. / Applied Energy 195 (2017) 974–990 Table 6 Storage 4 control action representation. a Value of each digit (dn ; n = 1, 2, 3 and 4) d1 (level of charging from grid) d2 (level of charging from R4) d3 (level of discharging to D7) d4 (level of discharging to D8) 0 1 2 0% of rated powera 50% of rated power 100% of rated power 0% of rated power 50% of rated power 100% of rated power 0% of rated power 50% of rated power 100% of rated power 0% of rated power 50% of rated power 100% of rated power In the focused case in control problem (case 3) rated power is 120 kW for storage 4. responses, tree bagging repeatedly selects a random sample with replacement of the training set and fits trees to these samples (Algorithm 1 – step 1.3). Number of trees ‘‘B” is not a critical parameter with bagging; using a very large number of ‘‘B” will not lead to overfitting [38]. We used a sufficiently big number (e.g., 500) to achieve a good performance with low out-of-bag error. After training, predictions for unseen samples may be created by taking the average of predictions from all the individual trees (Eq. (5) in step 1.4). Since the classification model is built based on the optimization model, which has been solved for all available data in historical data set, this classifier is expected to be a good estimation of optimal control policy. However, this control policy is updated continuously according to the new occurred network state as described below in ‘‘Algorithm 2”. Algorithm 2 (Online monitoring and classification). Figs. 10 and 11 confirm the correlation between charge/discharge controls of electricity storage and input patterns. According to Fig. 10a and d, charging from grid actions of S1 should follow decreasing trends in electricity price and solar radiation. This is expected since electricity storage application is intended to reduce the electricity bill. Fig. 11a–d illustrate that discharging to commercial demand D1 follow the increasing trends in demand profiles and electricity price. According to the illustrative network configuration, the possible directions for power flow in storage ‘‘S4” are: discharge to demand nodes D7 and D8, charge from renewable R4 and charge from grid. In each of these directions the amount of electricity flow is discretized into three levels based on power rating: at 0%, between 0% and 50% and greater than 50%. As a result, there are 34 (=81) total possible actions for storage ‘‘S4” during a given time step. A four-digit number in turnary (the base-3 numeral) system Assign the optimal action ast For (8d) repeat: /day index/ For (8t) repeat: /time interval index/ 2.1 – Monitor the state of the network; ST t For (8s) repeat: /storage index/ 2.2 – Assign action ast ¼ ps ðST t Þ to storage unit s End End 2.3 – Solve the exact optimization problem for day ‘‘d” and update the state space SS and action space As ; 8sðstorage indexÞ 2.4 – Repeat the steps in ‘‘Algorithm 1” with updated response vector and feature matrix and update the optimal policy ps ðSTÞ8sðstorage indexÞ End Fig. 12. Daily cost deviation (%) – (a) s = 0 – (b) s = 4. Next, the proposed control algorithm is applied to our example distribution network. The configuration defined in ‘‘Case 3” with electricity cost reduction application is considered for the illustration. To devise a classifier, we explore the relationship between stochastic patterns of input variables and optimal actions. This is followed by a discretization process according to the network configuration and topology. We also discuss the accuracy of the control model using sensitivity analysis. Our hypothesis is that there exists a strong correlation between the stochastic input patterns and optimal charge and discharge actions. Here we investigate this hypothesis by analyzing input patterns in a time window defined by (t-s;t). In Figs. 10 and 11 (with s = 4) we show the average patterns for these inputs with two different actions at storage node 1. We assume that the solar radiation at renewable nodes are close (due to the same geographical zone), therefore, there is no need to consider separate levels of renewable electricity generation for different PV systems in the classification phase. Hence, instead of analyzing the level of generation at the renewable nodes we look at the solar intensity patterns. Fig. 13. Example day electricity price and outputs profile – (a) Purchased electricity from grid, (b) electricity price. 986 K. Mahani et al. / Applied Energy 195 (2017) 974–990 Fig. 14. Hourly demand profile boxplot (Heating season and cooling season). Table 7 Capacity planning for different electricity demand growth. Growth in elec. demand Storage 1 Storage 2 Storage 3 Capacity (kWh) Power rate (kW) Capacity (kWh) Power rate (kW) Capacity (kWh) Power rate (kW) Capacity (kWh) Power rate (kW) Baseline (0%) 5% 10% 15% 20% 6200 6500 6900 7200 7500 2000 2200 2300 2500 2600 6600 6800 7200 7500 7800 2200 2300 2400 2500 2600 1000 1000 1100 1150 1200 300 300 350 350 400 600 600 600 650 650 120 120 130 130 130 Fig. 15. Deviation from the daily optimal cost when elec. Demand increase by 5% – s = 4. ðd1 d2 d3 d4 Þ3 is used to represent each action for this storage. Each digit represents the amount of electricity flow in specific direction. The following Table 6 shows the meaning of each digit for control actions in storage 4. For example, action number 3, which is represented as ð0 0 1 0Þ3 in turnary system, represents discharging to D7 with 50% power rating. Control actions for other storage units are defined similarly. It is obvious that some of these actions (for instance, multiple charging and discharging during same time step) are not feasible because of the limitation on the power rating (see Eq. (C.3)). Finally, we note that, in addition to state of charge of ESSs at time ‘‘t”, the level of renewable generation, electricity demands and electricity price from time ‘‘t-s” to ‘‘t” will be considered as Storage 4 classification features. Furthermore, we expect that higher values of s will improve the misclassification and control errors. Next, we present the above methodology for our case study network with two different values of s. First, we assume s = 0, which means that no memory is considered for the control algorithm. Therefore, only the current state of charge of ESS nodes, electricity generation in renewable nodes, electricity demand and electricity price are taken into account. Two-third (2/3) of the sample data (the same three years historical data) is used to train the classification model. The daily cost is calculated for each individual day and the deviation from optimal daily cost is also calculated. Fig. 12a shows the histogram chart of daily cost deviation when s = 0. The mean value of the cost deviation from optimal case (with exact information) is 6%, which means that by using approximation rule-based control (with zero-hour memory); on the average, the daily operation cost will be 6% more than the optimal cost. Repeating the above for s = 4 demonstrates that deviation from the optimal cost reduces significantly with the size of time memory window (Fig. 12b). The mean value of the cost deviation from optimal case (with exact information) is 4% when memory window of 4 h considered for control algorithm. As expected, by increasing the memory window the error of model decreases. In the following Fig. 13a the amount of electricity required to be purchased from the main grid as a result of executing control actions (for both s = 0 and s = 4) during an example day are illustrated. Fig. 13b shows the electricity price this example day. Fig. 13a shows that by increasing the memory window the rulebased control assigns charge and discharge actions to storage nodes in a way to reduce the purchasing electricity from grid 987 K. Mahani et al. / Applied Energy 195 (2017) 974–990 during the peak hours. Note that, none of controllers (s = 0 and s = 4) has information about future and they assign control actions according to their prediction ability. But it seems that higher sizes of the memory window improve the future prediction capability of patterns, which results in less daily cost and better performance of the control model. any changes in network components’ behavior and increase the robustness of control module. Appendix A Following table shows the population size and corresponding probability value for each cluster. 5. Sensitivity analysis on stochastic parameter changes Thus, far, the planning and real-time controlling models have been made based on the available historical data. In this section, we conduct a sensitivity analysis and investigate the impact of load changes on planning decisions and control actions. We will experiment with data of Fig. 14 which gives the hourly profile boxplot for two demand nodes in our distribution network during cooling season and heating seasons. We fit a multi-variate log-normal distribution to each demand data and compute mean value and covarriance matrix. We consider 5%, 10%, 15% and 20% growth in demand for each node and investigate the impact of these increases on capacity planning and control for distribution network. We focuse on energy bill management application. The following Table 7 confirms that increasing in electricity demand results in higher value of investment in energy storage, therefore capacity planning model suggests higher capacity of energy storages. Now let’s move to the proposed network aware control model. Capacity of storage units are same as baseline (no growth in electricity demand). The initial control policy is determined based on base-line demand scenario (Step ‘‘A” in Algorithm 1). Now consider that the level of demand is increasing with 5% growth. This results in new state vectors which do not exist in the initial state space. As described in steps B-3 and B-4 in Algorithm 1, the control policy will be updated continuously according to the new occurred states to adjust control actions with new states and maintain the performance of control module. Following Fig. 15 demonstrates the deviation from optimal cost as a result of applying proposed network aware control algorithm on the new state space with %5 growth in electricity demand. The mean value of the cost deviation from optimal case is %4.5. 6. Conclusion The paper proposed ‘‘Network-aware planning and control approach” for multiple energy storage nodes distributed over power distribution network. We were interested in optimally locate these storage units over distribution network and to create day-ahead plans according to planned application. An approximation model has been proposed for planning purpose, which lowers the computational complexity of optimization problem by 45% in our illustrative example (in terms of number of decision variables). Two types of storage system with static and dynamic capacity are considered in the planning model. Furthermore, a novel rule based control scheme for the near real time operation of the storage network has been built. Tree-bagging classification technique is utilized to determine the near optimal control policy, which maximizes the value of storage nodes. In the proposed Network-aware control model the near optimal actions at a time ‘‘t” are taken in each individual storage unit based on the partial knowledge of the whole network state from time ‘‘ts” to ‘‘t. Comparing the daily costs of approximate control model with the exact optimal case when s = 0 shows 6% difference in average. Increasing the memory (s) of the model from 0 h to 4 h reduces this deviation to 4%. In the proposed model the control policy is being updated frequently to adjust the control rules with Cluster number Population size Cluster probability 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 11 43 10 14 14 9 11 42 34 12 33 19 41 12 11 21 40 12 49 11 45 49 12 13 13 41 52 45 14 11 12 9 15 28 44 22 12 9 11 22 11 41 16 40 18 16 13 12 0.01005 0.03927 0.00913 0.01279 0.01279 0.00822 0.01005 0.03836 0.03105 0.01096 0.03014 0.01735 0.03744 0.01096 0.01005 0.01918 0.03653 0.01096 0.04475 0.01005 0.04110 0.04475 0.01096 0.01187 0.01187 0.03744 0.04749 0.04110 0.01279 0.01005 0.01096 0.00822 0.01370 0.02557 0.04018 0.02009 0.01096 0.00822 0.01005 0.02009 0.01005 0.03744 0.01461 0.03653 0.01644 0.01461 0.01187 0.01096 Appendix B Optimal dispatch to different demand nodes in different example clusters (case study without parking-lot). Optimal dispatch to different demand nodes in an example cluster (case study with parking-lot): (see Figs. 16–19). 988 K. Mahani et al. / Applied Energy 195 (2017) 974–990 Fig. 16. Optimal dispatch to 8 demand nodes (Cluster 44). Fig. 17. Optimal dispatch to 8 demand nodes (Cluster 46). K. Mahani et al. / Applied Energy 195 (2017) 974–990 Fig. 18. Optimal dispatch to 8 demand nodes (Cluster 47). Fig. 19. Optimal dispatch to 8 demand nodes (With dynamic energy storage) – (Cluster 47). 989 990 K. Mahani et al. / Applied Energy 195 (2017) 974–990 References [1] Carnegie R, Gotham D, Nderitu D, Preckel PV. Utility scale energy storage systems, benefuts, applications, and technologies. State Utility Forcasting Group; 2013. [2] Oudalov A, Cherkaoui R, Beguin A. Sizing and optimal operation of battery energy storage system for peak shaving application. In: IEEE Lausanne Powertech, Lausanne. [3] Barton JP, Infield DG. Energy storage and its use with intermittent renewable energy. IEEE Trans Energy Convers 2004;19(2):441–8. [4] Wang P, Liang DH, Yi J, Lyons PF, Davison PJ, Taylor PC. Integrating electric energy storage into coordinated voltage control schemes for distribution network. IEEE Transact Smart Grid 2014;5(2):1018–32. [5] Energy OoEEaR. MULTI-YEAR PROGRAM PLAN; Vehicle Technologies Program (2011-2015). US Department of Energy; 2010. [6] Posey J. Air quality conformity analysis of the 2014 constrained long range plan and the FY2015-2020 transportation improvement program for the Washington Metropolitan Region. NATIONAL CAPITAL REGION TRANSPORTATION PLANNING BOARD; 2014. [7] Richtel M. In California, Electrictric Cars Outpace Plugs, and Sparks Fly. The New York Times; 2015. [8] Kempton JTaW. Using fleets of electric-drive vehicles for grid support. J Power Sources 2007;168(2):2459–68. [9] Tomic WKaJ. Vehicle-to-grid power implementation: from stabilizing the grid to supporting large-scale renewable energy. J Power Sources 2005;144 (1):280–94. [10] Gross CGaG. Design of a conceptual framework for the V2G implementation. In: IEEE Energy2030, Atlanta, GA. [11] Han SHaKSS. Development of an optimal vehicle-togrid aggregator for frequency regulation. IEEE Trans. Smart Grid 2010;1(1):65–72. [12] Wong WSaVW. Real-Time Vehicle-to-Grid Control Algorithm under price uncertainty. In: Smart Grid Communications (SmartGridComm), IEEE International Conference. [13] Koutsopoulos I, Hatzi V, Tassiulas L. Optimal energy storage control policies for the smart power grid. In: IEEE International Conference on Smart Grid Communications (SmartGridComm). [14] van de Ven P, Hedge N, Massoulie L, Salonidis T. Optimal control of residential energy storage under price fluctuatuion; 2011. [15] Dufo-López R. Optimisation of size and control of grid-connected storage under real. Appl Energy 2015;140:395–408. [16] Wang Z, Li X, Li G, Zhou M, Lo K. Energy storage control for the photovoltaic generation system in a micro-grid. In: 5th International conference on critical infrastructure (CRIS). [17] Teleke S, Baran ME, Bhattacharya S, Huang AQ. Optimal control of battery energy storage for wind farm dispatching. IEEE Trans Energy Convers 2010;25 (3):787–94. [18] Ru Y, Jan K, Sonia M. Storage size determination for grid-connected Photovoltaic systems. IEEE Transact Sutain Energy 2013;4:68–81. [19] Khalilpour R, Vassallo A. Planning and operation scheduling of PV-battery systems: a novel methodology. Renew Sustain Energy 2016;53:196–208. [20] Zhang Y, Lundblad A, Campana PE, Benavente F, Yan J. Battery sizing and rulebased operation of grid-connected photovoltaic-battery system: a case study in Sweden. Energy Convers Manage 2017;133:249–63. [21] Brekken T, Yokochi A, von Jouanne A, Yen Z, Hapke H, Halamay D. Optimal energy storage sizing and control for wind power applications. IEEE Transact Sustain Energy 2011;2(1):69–77. [22] Erdinc O, Paterakis NG, Pappi IN, Bakirtzis AG, Catalão JP. A new perspective for sizing of distributed generation and energy. Appl Energy 2015;143:26–37. [23] Farzan F, Farzan F, Jafari MA, Gong J. Integration of demand dynamics and investment decisions on distributed energy resources. IEEE Transactions on Smart Grid 2015. [24] Andreotti A, Carpinelli G, Mottola F. Optimal energy storage system control in a smart grid including renewable generation units. In: International conference on renewable energies and power quality (ICREPQ’11), Las Palmas de Gran Canaria, Spain. [25] Nick M, Cherkaoui R, Paolone M. Optimal allocation of dispersed energy storage system in active distribution networks for energy balance and grid support. IEEE Trans Power Syst 2014;29(5):2300–10. [26] Chandy K, Low S, Topcu U, Xu H. A simple optimal power flow model with energy storage. In: 49th IEEE conference on decision and control (CDC), Atlanta, GA, USA. [27] Kanoria Y, Montanari A, Tse D, Zhang B. Distributed storage for intermittent energy sources: control design and performance limits. arXiv:1110.4441v1[cs. SY]; 2011. [28] Silventea J, Kopanosb GM, Pistikopoulos EN, Espuña A. A rolling horizon optimization framework for the simultaneous energy supply and demand planning in microgrids. Appl Energy 2015;155:485–501. [29] Harsha P, Dahleh M. Optimal sizing of energy storage for efficient integration of renewable energy. In: 50th IEEE conference on decision and control and European control conference (CDC-ECC), Orlando, Fl, USA. [30] van de Ven PM, Hedge N, Massoulie L, Salonidis T. Optimal control of end-user energy storage. arXiv:1203.1891; 2012. [31] Jayawarna N, Barnes M, Jones C, Jenkins N. Operating MicroGrid energy storage control during network faults. In: IEEE international conference on system of systems engineering. [32] Mahani K, Jafari M. Electric Vehicles Parking Lot operation as an energy storage in the power market. IEEE Transactions 2017. submitted for publication. [33] Choi T-M, Chiu C-H, Fu P-L. Periodic review multiperiod inventory control under a mean-variance optimization objective. IEEE Transact Syst, Man, Cybernet - A: Syst Humans 2011;41(4):678–82. [34] Bouveyron C, Girad S, Schemid C. High-dimensional data clustering. Comput Stat Data Anal 2007;52(1):502–19. [35] Schoenung S. Energy storage system cost update. Sandia National Laboratories; 2011. [36] Ferrari ML, Pascenti M, Sorce A, Traverso A, Massardo AF. Real-time tool for management of smart polygeneration grids including thermal energy storage. Appl Energy 2014;130:670–8. [37] Kwak Y, Huh J-H, Jang C. Development of a model predictive control framework through real-time building energy management system data. Appl Energy 2015;155:1–13. [38] Hastie T, Tibshirani R, Friedman J. The elements of statistical learning. Springer-Verlag; 2009.