Optimal Storage Planning in Active Distribution Network Considering ...

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Optimal Storage Planning in Active Distribution Network Considering Uncertainty of Wind Power Distributed Generation Mahdi Sedghi, Ali Ahmadian, Student Member, IEEE, and Masoud Aliakbar-Golkar

Abstract—The penetration of renewable distributed generation (DG) sources has been increased in active distribution networks due to their unique advantages. However, non-dispatchable DGs such as wind turbines raise the risk of distribution networks. Such a problem could be eliminated using the proper application of energy storage units. In this paper, optimal planning of batteries in the distribution grid is presented. The optimal planning determines the location, capacity and power rating of batteries while minimizing the cost objective function subject to technical constraints. The optimal long-term planning is based on the short-term optimal power flow considering the uncertainties. The point estimate method (PEM) is employed for probabilistic optimal power flow. The batteries are scheduled optimally for several purposes to maximize the benefits. A hybrid Tabu search/particle swarm optimization (TS/PSO) algorithm is used to solve the problem. The numerical studies on a 21-node distribution system show the advantages of the proposed methodology. The proposed approach can also be applied to the realistic sized networks when some sensitive nodes are considered as candidate locations for installing the storage units. Index Terms—Distribution network, optimal planning, point estimate method, storage, wind power uncertainty.

NOMENCLATURE

Capacity of the th storage unit (kWh). Power rating of the th storage unit (kVA). Number of all storage units. Total operation cost in th season ($). Duration of the th season in one year (days). Inflation rate. Interest rate. Period of the project (years). Operation and maintenance cost function of storage units ($). Operation cost of the th HV/MV substation at time of the th season ($). Active energy price at th hour of the th season ($/MWh). Injected active power in th HV/MV substation at time of the th season (MW). Reactive energy price at th hour of the th season ($/MVARh). Injected reactive power in th HV/MV substation at time of the th season (MVAR). Number of all HV/MV substations.

Cost objective function ($).

Average failure rate of the th event (f/year).

Investment cost of storage units ($).

Binary variable associated to the outage of th load node due to th failure event. Outage cost function ($). Power of interrupted load in th node (kW).

Total operation cost ($). Total reliability cost ($). Penalty factor. Installation cost related to capacity of storage ($). Installation cost related to the power rating of storage ($). Replacement cost related to the capacity of storage ($). Replacement cost related to the power rating of storage ($).

Type of the th load node. Duration of outage due to th failure event (hour). Number of all failure events. Number of all load nodes. Power of equipment

(kVA).

Allowed maximum power of equipment

(kVA).

Number of all the equipment. Manuscript received June 15, 2014; revised September 08, 2014, December 11, 2014, and January 26, 2015; accepted February 12, 2015. Paper no. TPWRS00811-2014. The authors are with the Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2015.2404533

Voltage magnitude in th node at time (p.u.). Allowed minimum voltage magnitude (p.u.). Allowed maximum voltage magnitude (p.u.). Power of the th HV/MV substation at th hour (kVA). Power of th DG unit at th hour (kVA).

0885-8950 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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Number of all DG units. Charge power of the th storage unit at th hour (kVA). Demand of the th load node at th hour (kVA). Total power loss in distribution network at th hour (kVA). Number of all nodes where at least a constraint is violated in th hour of a day in th season. Number of all feeder sections where at least a constraint is violated in th hour of a day in th season. Active power of th storage unit at time (kW). Reactive power of th storage at time (kVAR). State of charge of th storage at time (kWh). Charge efficiency of the storage unit. Discharge efficiency of the storage unit. Generated power of DG unit in th node at th hour (kVA). Generated power of storage unit in th node at th hour (kVA). Load power of th node at th hour, including the power loss of LV network (kVA). Expected value. First estimated point in 2-PEM. Second estimated point in 2-PEM. Corresponding probability of the first point in 2-PEM. Corresponding probability of the second point in 2-PEM. Output variable of probabilistic load flow. PDF of input variable in 2-PEM. Dirac's delta function. Rate of searching for active power of storage.

iter

Active power of the th storage unit at time in new neighbor solution of TS (kW). Reactive power of the th storage unit at time in new neighbor solution of TS (kVAR). iterth iteration of PSO algorithm. First period of storage scheduling that stands for charge (hour). Second period of storage scheduling that stands for discharge (hour). I. INTRODUCTION

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OWADAYS the penetration of renewable distributed generation (DG) sources is greatly increased in active distribution networks (ADNs). The advantages of the renewable DGs are power loss reduction, peak shaving, voltage regulation, ancillary services, higher power quality, reliability enhancement, deferral of transmission and distribution systems reinforcement, and decreasing the emission of greenhouse gases and environmental concerns [1]. Among all renewable DGs, wind generation has been matter of more attention because it has many

commercial products and can provide larger power in the distribution system [2]. However, extensive penetration of the wind power raises the risks of secure and economical operation of distribution network due to intermittent wind speed [3]. To solve the problem, storage units or conventional DGs can be used [4]. Regarding the advantages of storage units, in the literature the optimal scheduling and planning of storage units in distribution networks which include wind turbines has been considered. In [5], active-reactive optimal power flow (A-R-OPF) in distribution networks with embedded wind generation and battery units based on a fixed length in the charge and discharge cycle for daily operations of battery units was presented. Furthermore, the authors extended their work in [6] with a flexible battery management system and higher profit was achieved as compared with a fixed operation strategy of battery units. The works in [5] and [6] have been further developed in [7] to ensure both feasible and optimal operation strategies. This was achieved by considering a flexible A-R-OPF with a flexible on-load-tap-changer (OLTC) control system. While the works in [5]–[7] focused on the optimal operation of battery units, different planning studies have been done in [8] and [9] to include battery units in ADNs. In [8], the reactive power capability of DG sources was optimally utilized based on the A-R-OPF. It was shown that high annual energy costs can be saved and there is no need to use battery units to save curtailed/spilled renewable power/energy of renewable DG sources in a low voltage network. In a medium voltage network, the relationships between the needed battery units (to save curtailed/spilled renewable power/energy) and allowed reverse active power flow, load density and electric vehicle penetration were established in [9]. It was also demonstrated that no need for battery units to save lost renewable energy if a high level of allowed reverse power flow is ensured. It is to note that four variables were introduced for upper bounds of active and reactive power in forward and reverse direction at so called slack/infinite bus [10]. More recently, a comprehensive assessment of the performance of ADNs with wind and battery units when reverse A-R-OPF is allowed was carried out in [11]. It was shown that planning battery units is related strongly to the location of renewable DG sources and feeder layout. In the works [5]–[11], however, reliability aspects were not considered. In [12]–[14] the optimal sizing of storage for reducing the supplying cost in isolated systems containing wind power generators has been presented. However, in these references, the placement of storage and its effects on distribution network are not considered. The optimal placement and sizing of batteries in distribution system considering multistage expansion of the network is shown in [15]. Although the battery units are scheduled for both peak cutting and reliability improvement simultaneously, non-dispatchable DG such as wind turbine has not been considered in this reference. Moreover, some optimal simple strategies are used considering three-level model of load. As the optimal power flow is not employed in [15], it may not result in optimal solutions. The optimal allocation of the batteries in distribution network with a high penetration of wind energy is firstly proposed in [16], where the storage units are allocated to minimize the annual cost of electricity.

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In addition, the optimal placement of the battery units in a distribution system to improve performance of the wind power DGs has been utilized in [17] and [18]. On the other hand, the uncertainty effects of non-dispatchable renewable DG sources on the optimal storage planning needs critically appropriate stochastic models [19], [20]. However, most of the papers such as [15]–[18], [21], and [22] have used deterministic models to optimize the battery planning in distribution network. In this paper, an active distribution network which includes wind-based DGs is developed by obtaining optimal location, capacity and power rating of the battery units. The storage investment cost as well as the operation and reliability cost is considered directly in the cost objective function. In addition, in this paper, the owner of distribution network is the institute that invests for storage units. The optimal long-term planning of the batteries is based on the optimal short-term charge/discharge scheduling as optimal power flow (OPF) approach under uncertainty. Here, the OPF is investigated in various seasons separately because their properties are different significantly. Although using the batteries for several purposes makes the optimal planning more complex compared with the previous works, it brings more benefits to distribution network from technical and economic points of view. Hence, in this paper, the batteries are scheduled simultaneously for several objects, i.e., peak shaving, voltage regulation and reliability enhancement. The reactive power injection/absorption of batteries is also considered to help optimal scheduling and planning. This study determines the influence of reactive power consideration in optimal sizing and allocation of the batteries. All the objectives are incorporated in a single cost function as a criterion to select the global optimal solution. The uncertainty of load and wind power is modeled using point estimate method (PEM), and a hybrid TS/PSO algorithm is employed for optimization. II. PROBLEM STATEMENT Optimal planning of the batteries in a distribution network determines the location, capacity and power rating of the storage units while minimizing the cost objective function under technical constraints. Here, the objectives are as follows: 1) minimization of the storage investment cost; 2) minimization of O&M cost; 3) minimization of reliability cost; 4) minimization of the number of technical constraints' violations. Consequently, the objective function consists of four parts, i.e., the installation cost, operation cost, reliability cost and penalty factor, as follows: (1) The first part consists of investment cost of the battery units' installation and replacement. The investment is a function of the storage capacity and power rating, as follows:

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In the current work, the lifetime of battery is modeled by restricted number of charge/discharge cycles. Whenever the number of cycles exceeds the maximum value, the replacement cost is added to the investment cost in (2). The operation cost is categorized into the operation and maintenance cost of the batteries and the cost of electrical energy purchased by the distribution utility at HV/MV substation which depends on the charge/discharge power of the storage units. The cost of energy is used instead of power loss because it is more important than the power loss for distribution utility from economic point of view. However, this strategy usually results in power loss reduction. In this paper, the operation cost has separately been calculated for four seasons of a year in long-term optimal planning, because the uncertainty parameters are considerably different for these four periods. Moreover, the operation cost should be evaluated considering the interest and inflation rates [15], as follows: (3) where (4) According to [11], in the general form, the energy purchased at HV/MV substations is a function of the injected active/reactive power and the price, as follows: (5) The energy purchased at HV/MV substation is a negative value when the power is exported. Here, the power may be exported if it is beneficial from economic points of view. In the current work, the cost of energy not supplied (ENS) is considered as the reliability cost of the distribution network. The ENS term appears due to the failure events in HV/MV substation or feeder sections. The outage cost is estimated considering the interrupted load, type of the customer and outage duration [15], as follows:

(6) The penalty factor is embedded in the objective function to penalize the solutions which do not satisfy the technical constraints. In an acceptable solution, the power of the equipment should not exceed the maximum capacity, the voltage magnitude of all nodes of the network should be limited to the allowed boundary, and the required load should be supplied in a normal condition. The constraints are formulated as follows: (7)

(2)

(8)



(9) The active/reactive power balance in distribution network is shown in (9), where all the power variables are complex values. The power of the HV/MV substation as well as the power loss is obtained from the load flow analysis to satisfy the power balance constraint. Moreover, some special constraints have to be applied to the battery units as follows: 1) The discharge power of the batteries is a function of the stored energy within the previous operating hours, the battery efficiency, and the pulse power capability of the battery as shown in [23]. 2) The batteries should be charged and discharged only once in each day because of lifetime limitations and reducing the replacement cost. 3) At the end of short-term scheduling, the batteries should be discharged as much as possible to prevent partial discharging; however, the batteries should not be discharged completely. This strategy increases the battery's lifetime [24]. In order to satisfy these constraints, in a diurnal basis, the battery is allowed to be discharged only after the state-of-charge (SOC) achieved its maximum level. Discharge power is regulated to reduce the SOC until it reaches to the minimum allowed level. Then, the discharge power is updated considering the storage efficiency and pulse power capability of the battery. Afterwards, the battery is not permitted to be charged again in that day. If this constraint is not considered, the battery units are not helpful components from economic point of view [24]. In some papers, the maximum SOC of the battery is limited to an upper bound which is less than the capacity of the battery [5], [6];however, in the current work, the upper bound is set equal to the battery capacity according to [24]. In this paper, the number of all the nodes and feeder sections, where at least a technical constraint is violated, is taken as the penalty factor. The penalty factor is investigated for 24 h of a typical day in four seasons, as follows: (10) Since the technical constraint violations turn the solution infeasible, all of the probable violations (1% violation to 100% violation) are forbidden. As a result, the number of all voltage and current violations with non-zero corresponding probability is taken into account in (10). Unlike the penalty factor, the first three objectives are monetary and they are simply added in (1). However, a non-zero penalty factor makes the monetarily optimized planning infeasible. In order to intensify the impact of penalty factor, the term of is multiplied to the financial objective function. As a result, the infeasible solutions are not preferred compared with the feasible candidate solutions which may have higher corresponding cost.

Although the main problem of storage planning is to minimize (1) for determining the optimal location and capacity of the batteries in long-term, it is needed to optimize the charge/discharge power of the batteries in a diurnal basis as a sub-problem which is a short-term scheduling problem. The scheduling subproblem obtains the power rating of the batteries considering the maximum charge/discharge power during the scheduling period. Unlike the conventional methods, in the proposed economical scheduling (described in Section III-A) the charge/discharge power of the batteries is optimized to minimize the objective function using OPF and probabilistic load flow (PLF) considering the wind power uncertainty. However, in the shortterm scheduling optimization, i.e., OPF, the decision variables are only the charge/discharge power and power rating of the batteries. As a result, the location and capacity of the batteries are kept fixed when the OPF is executed. Here, the inputs of OPF analysis are stochastic variables to deal with the uncertainty of the optimal planning, unlike using the OPF for one snapshot of time. The probabilistic variation of the inputs makes the OPF analysis useful for optimal planning over many years with a resolution down to hours. III. PROPOSED METHODOLOGY A. Proposed Short-Term Scheduling To maximize the benefits of batteries in distribution network, it is proposed here to use the installed battery storage units for the following three purposes simultaneously: 1) peak shaving; 2) voltage regulation; 3) reliability enhancement. The batteries can be used for peak shaving in distribution network. From economic point of view, the storage units are charged during off-peak periods, and then they are discharged during on-peak times. However, the non-dispatchable DG sources such as wind power generators affect the peak shaving strategy. The battery storage units can store the excess energy generated by the wind turbines when the load level is not high, and also when the energy price is too low to sell the excess energy to the upstream network. Accordingly, the battery energy storage units are discharged when the wind speed is low. The peak shaving strategy is developed to optimize the overall operation cost, in an order that the cost of purchased energy from upstream network is reduced. This strategy usually results in power loss reduction. As the second objective, the storage units can be used to improve the voltage level of distribution network especially when the wind power penetration is high. During periods in which wind speed is high, the wind turbines inject a large amount of active power to the network [25]. Hence the voltage magnitude of some nodes is increased so that the maximum voltage constraint is violated. On the other hand, when the wind speed is not high, the wind turbines may absorb such a great reactive power from distribution network [25] that the minimum allowed voltage level constraint of some nodes is not satisfied. Unlike the capacitor banks, the battery storage units can both inject and absorb active and reactive power to regulate the voltage in distribution network. So they are more useful than capacitors for


voltage regulation, especially when the wind power penetration is high. The scheduling optimization should not only determine the injected or absorbed active power of the batteries, but also it should determine the injected or absorbed reactive power of them. As a result, based on the formulation shown in [5], the power rating of the batteries should be calculated considering both the active and the reactive power as follows:

(11) In addition, the SOC of the batteries should be updated in each hour using the following equation [5]:

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conditions, the network may be also operated in islanding mode, considering the price, generation and load level in OPF stage. The best scheduling to increase the reliability is to keep the batteries fully charged in standby mode, until a failure event occurs [23]. However, in the proposed scheduling, the SOC of the batteries should be optimized by simultaneously considering peak shaving, voltage regulation and reliability enhancement. So the batteries can be charged/discharged within 24 h and they may not be remained fully charged only for reliability improvement. Here, the optimal scheduling approach determines the final decision to minimize the total objective function. The mentioned three purposes, i.e., peak shaving, voltage regulation and reliability enhancement, correspond to the three terms of (1), as they can reduce operation cost (OC), penalty factor (PF) and reliability cost (RC), respectively. B. Point Estimate Method

(12) where may be a positive or negative value. In (12), and denote the overall efficiency of the battery and converter. The voltage regulation objective affects the total objective function with reducing penalty factor in (1). The storage units which are embedded in MV distribution network can also reduce the ENS during outage times. In this case, the failed equipment (i.e., a power transformer or a feeder section) is disconnected from the network using normally closed switches, and then the interrupted loads of downstream LV networks are restored by the storage units at MV/LV nodes that are operated in islanding mode. In every hour of a day, the probability of every failure event in distribution network should be investigated, and the SOC of the storage units should be estimated for each hour. Whereas the SOC is a time-dependent variable and it may not be enough to restore the whole load, the loads are restored regarding their priority. The wind power generators which can be dispatched by the storage units from technical point of view are also used to restore the loads in islanding mode. In every hour of islanding, firstly the power of wind turbine is used to restore the loads if a storage unit is available (i.e., it is existing with nonzero SOC value) for dispatching the wind power. The excess energy of the wind power can charge the storage unit. If the wind power does not meet the requirements, the battery is discharged to supply the demand and the SOC is updated using (12). The loads which cannot be restored are considered for calculating ENS and the outage cost. If the existing storage unit is empty, the loads cannot be restored but the wind power charges the battery for the next hour restoration. In islanding mode, the wind power can be used to charge the batteries which are directly connected to the wind turbine. The flowchart of the islanding mode management for th node is shown in Fig. 1. In this algorithm, the expected value of wind power is used to estimate the wind power in each hour. The generated power of DG and storage are set equal to zero for load nodes in which no wind turbine and battery unit is existing, respectively. All of the technical constraints should be satisfied in islanding mode operation as well. The algorithm is used for operation only when a failure event occurs. However, in normal

To calculate the objective function in (1) with probabilistic input variables, i.e., load and wind power, the PLF analysis is needed. Because the Monte Carlo simulation method is very time consuming, the PEM is used for the PLF analysis. The PEM has been applied to PLF problem successfully [26], [27]. The inputs of the PEM are the probability density functions (PDFs) of the load and wind power variables. Then the moments and PDFs of the output variables, e.g., voltage magnitude of all nodes, can be estimated subject to the deterministic load flow equations as shown in Fig. 2. This figure presents the two-point estimate method (2-PEM) approach as an example. In Fig. 2, denotes the deterministic load flow equations. In 2-PEM, some discrete states of inputs, i.e., , and their corresponding weights, i.e., , are used to approximate the PDF of inputs, as follows: (13) In other words, the PDF is concentrated in a few points. The moments of the outputs are estimated using the Taylor series ex. For instance, the expected value of the output pansion of is obtained from the following equation [28]: (14) , and are determined regarding the moments where of input variables as shown in [28]. The location of the points, i.e., , and the corresponding probabilities, i.e., , are functions of the mean value, standard deviation, and skewness of the input variables. Application of various types of PEM, such as 3-PEM and 5-PEM, has been provided in [26]–[30]. The accuracy of the PEM improves when the number of points increases. The details of PEM are shown in these references and are not presented in this paper. In the current work, the 5-PEM is used for PLF as shown in [30]. Unlike the transmission network, distribution network is not usually too wide. So the outputs of wind turbines are approximately similar from different nodes' point of view. Consequently, the load profiles of commercial nodes are similar, while the residential load profiles are similar together as well. Since the wind and load are correlated and dependent on weather conditions, the power profiles should be investigated



Fig. 1. Proposed algorithm for islanding mode management.

separately in different seasons in long-term planning. In addition, wind and load are correlated in time domain, so the real data is used in OPF analysis to model the correlation between expected values in the time intervals. However, in every single hour, wind and load power are approximately independent for long-term planning study over several years. So they are formulated in independent manner for point estimate method which is employed in every single hour separately. It is needed to execute the deterministic load flow only for a few times in PEM unlike in Monte Carlo simulation method. In this paper, the expected value of the PLF output is used to estimate the objective function. Fig. 2. Two-point estimate method approach [28].


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C. Hybrid TS/PSO Algorithm The planning of battery units in an active distribution network is a combinatorial problem which should be solved using powerful metaheuristic methods. Due to its suitable capabilities in dealing with such problems, the particle swarm optimization (PSO) algorithm has been employed to solve the problem. PSO is a swarm intelligent algorithm. It is based on the movement of some groups of particles which share their explorations among themselves. Each individual in PSO called particle flies in the searching space with a velocity, which is dynamically adjusted according to its own flying experience and its components' flying experience. The details of PSO can be found in [31]. Here, every particle denotes a candidate solution of location and capacity of storage units. In other words, the th component of a particle represents the capacity of storage in the th node of the network. As a result, the global best particle of PSO specifies the optimal best location and capacity of the batteries. As mentioned earlier, the optimal storage planning contains the OPF as a sub-problem. In each iteration of PSO, the OPF should be executed several times completely for several candidate locations and capacities of the batteries. Therefore, a heuristic algorithm with fast convergence is needed to solve the OPF problem. According to the literature, e.g., [32], Tabu search (TS) is an efficient combinatorial method that can achieve an optimal solution within a reasonably short time when the dimension of the problem is not too high. So it is more suitable to be applied to the OPF problem in the current work. The advantages of the TS to solve the OPF problem are shown in [33] and [34]. TS is based on iterative local search along a trajectory. Starting from a feasible solution as the current solution, some neighbor solutions are evaluated. Then the best neighbor solution is selected as the new current solution to continue the local search. This process is iterated until a termination criterion is satisfied. To prevent cycling, a Tabu list is used in TS. More details of TS algorithm can be found in [31]. The following rules and steps are developed to generate a neighbor solution in TS algorithm: Step 1) Set and , where . Step 2) Select the th storage unit among all storage units, randomly. Step 3) If , then go to step 4; otherwise go to step 6. Step 4) Select the th and th hours randomly ( , , and ). Step 5) Make , and , and stop. Step 6) Select the th hour randomly . , Step 7) Make and stop. is a constant controller parameter within the range of (for example: ). In step 1, the neighbor solutions are set to the current solutions initially. If (in step 3), then the active power of storage is changed, otherwise the reactive power is manipulated. , and may be positive or negative.

Fig. 3. Flowchart of the TS/PSO algorithm.

In step 5, rand is a random variable within (0, 1) which is allowed to be equal to 1 as well. The value of is a percentage of



Fig. 4. Two main loops in proposed optimal planning of storage.

the charging/discharging power at time , that is moved from time to the time . In this case, maximum SOC of the batteries in the new neighbor solution should not be different from the maximum SOC of the current solution. This maximum SOC is equal to the capacity of the battery units. In this strategy, neither charge/discharge power nor charge/discharge time is fixed. However, two charge/discharge periods, i.e., and , are considered instead of three periods like in [6]. In this case, the first period stands for charge, while the second period stands for discharge. If three or more charge/discharge periods within the time intervals more than 24 h are used, the scheduling approach would be more flexible. This more flexible strategy may results in less operation cost and greater storage capacity, when the wind penetration is very high; however, it makes the problem more complex. It is not considered in the current work because the wind penetration is not very high. In this paper, the OPF is solved using TS algorithm for the four seasons separately, because the time series and the stochastic inputs are different considerably in various seasons, but they are dependent on each other in every season. The TS algorithm provides the best active and reactive power profiles of the batteries in separate four intervals where the maximum power is taken as the power rating of the battery according to (11). This strategy guarantees that the power does not exceed the rated value. The flowchart of the proposed TS/PSO algorithm is shown in Fig. 3. It contains two main loops as briefly shown in Fig. 4. It should be noted that use of metaheuristic methods in the proposed methodology may be problematic in practice, because they do not typically provide any performance guarantees. However, according to the literature [35]–[37], this problem is solved if the algorithms are executed several times. In the current work, the distribution company is the owner of storage units. However, a different institute may invest for storage units in a distribution network. In this case, the optimal planning should be performed based on the cost/benefit of the distribution company and the storage owner. As a result, the mentioned purposes in this paper can be categorized to some objectives, e.g., distribution company cost and storage owner benefit similar to [38]. In this way, the proposed method can be modified to address the multi-objective optimization using Pareto optimal set. In the modified method, the member of the Pareto optimal set that gives the minimum distance is assigned

Fig. 5. Distribution network under study.

as the global best solution [39]; however, the cost/benefit analysis is needed to take the final decision [38]. IV. NUMERICAL STUDY The system used for the case study, as shown in Fig. 5, is a typical 13.8-kV distribution network obtained from [40]. The total peak load of the network is 6.2 (MW) and the capacity of the existing HV/MV substation is 10 (MVA). The maximum allowed active/reactive power in forward direction at slack bus is limited to the rated apparent power of HV/MV transformer, while upper bound of active/reactive power in reverse direction is 0.25 of the transformer capacity like in [9]. In addition, it is assumed that both active and reactive reverse power flow to the transmission network is allowed without any rejection in comparison with the work in [41]. Using OLTC at HV/MV transformer for voltage regulation results in more flexible operation as shown in [7]; however, it reduces the lifetime of transformer and the reliability of the network [42]. Hence, in the current case study, the OLTC is limited to keep the voltage of slack bus fixed at 1.05 (p.u.) according to [40]. In the other cases, a further work is required to optimize the voltage of slack bus in presence of intermittent wind power. Firstly, all the lines are upgraded as much as possible, regarding the data shown in [40]; and then six wind-based DG units are embedded at buses 5, 15, and 18–21. In 30 (%) penetration of wind, the maximum wind power is 210 (kW) at nodes 5, 18, and 20, while it is 410 (kW) at nodes 15, 19, and 21. Nodes number 5, 13, 17, and 20 are commercial loads and the other nodes are residential loads. The customer sector interruption cost of different load types is shown in Table I which is adopted from [15]. The wind power is extracted from real wind speed data in Ganjeh, Iran [43], considering a typical wind turbine power curve. Fig. 6 shows the box plots of wind speed in four seasons. It represents the uncertainty of wind speed around main time series. The mean value of the active power profiles of the loads is based on the real data of a distribution system in Iran [44] as shown in Fig. 7. The reactive power profiles can be obtained from the power factor of loads as well. The normal distribution


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Fig. 7. Mean value of the active power profile (in percentage of peak) for residential (Re.) and commercial (Co.) loads, in spring (Sp.), summer (Su.), fall (Fa.), and winter (Wi.).

Fig. 6. Box plots of wind speed data used in case study: (a) spring, (b) summer, (c) fall, and (d) winter.

TABLE I SECTOR INTERRUPTION COST FOR RELIABILITY COST EVALUATION

Fig. 8. Active power price profile in two sections of a year.

function is used for modeling uncertainty of load. The threelevel electrical energy price based on time-of-use [6], [45], is considered for active energy price profiles as shown in Fig. 8. The same price is assigned to the imported/exported active energy, wind energy and active energy losses in this paper. A fixed price of reactive energy may be investigated in some networks as presented in [11]; however, in this case study, it is neglected according the tariff of reactive power for a typical residential and commercial network in Iran [45]. The other parameters of the system are shown in Table II. The parameters of the batteries are obtained from [46]. Regarding the cost/benefit analysis provided in [16], only feasible economic storage technology is Zn/Br. So, in this paper, only Zn/Br technology is used for energy storage. The high penetration of wind is not considered in case studies, because of technical and geographical limitations in the typical distribution system. Consequently, the wind power curtailment is neglected in simulations except in the islanding mode. The proposed algorithm has been run several times and the best results of optimal storage integration with distribution network are shown in Table III. In this table, the optimal location, capacity and power rating of the batteries in different wind power penetrations are given. The results reveal that the battery units are helpful and economical even if the wind turbines are not embedded in distribution network. The reason is that the storage units are used for several purposes which minimize the operation and reliability costs simultaneously. However, in presence of the renewable generators, the required capacity of storage increases considerably. For example, the total capacity

TABLE II PARAMETERS OF THE SYSTEM UNDER STUDY

of batteries increases from 1.930 (MWh) to 3.775 (MWh), when the wind turbines are embedded with 10 (%) penetration. The capacity of storage units is increased as the wind penetration increases. The power rating is proportional to the capacity of every storage unit. In addition, the location of storage units depends on the wind penetration. For instance, the node 11 is more suitable than node 17 for installing the storage unit when the penetration of wind increases to 30 (%). According to the optimization results, batteries are usually located far from the HV/MV substation. The reason is that the higher power loss, voltage deviation, and outage probability are important challenges in these nodes.



TABLE III RESULTS OF OPTIMAL STORAGE PLANNING FOR DIFFERENT WIND POWER PENETRATION

Fig. 9. Results of the OPF in summer, for 10 (%) penetration of wind power.

The result of probabilistic OPF, for example in summer, is represented in Fig. 9, where the optimal active and reactive power and the SOC profiles of the batteries are shown. This figure indicates that both absorbing and injecting reactive power are needed for optimal scheduling. As a result, in active distribution networks the battery storage units are more appropriate than capacitor banks for voltage regulation. If the deterministic OPF is used instead of the probabilistic OPF, the required capacity of storage decreases. The reason is that the number of violations and operation cost are reduced when the deterministic OPF is employed. For example, the total capacity of battery units decreases from 8.585 (MWh) to 6.970 (MWh), if the deterministic OPF is used for 30 (%) penetration of wind. However, it does not mean that the deterministic approach is better. Because the real conditions of the system are neglected in the deterministic analysis. Hence, the operation cost and the number of violations will not be acceptable in practice, if the results of deterministic approach are taken into account. Therefore it is necessary to investigate the probabilistic OPF instead of the deterministic approach to address the real conditions. In order to show the impact of reactive power management and of the islanding operation on optimal planning, the main approach is compared with two other scenarios. In the first scenario, the batteries are optimized without reactive power injection/absorption, while in the second one, the islanding mode operating is neglected. The results of this study are presented in Table IV. It shows that if the batteries are scheduled without absorbing/injecting reactive power, the total capacity of storage decreases in 0 (%) and 10 (%) penetration of wind,

but it increases in 30 (%) penetration (compared with the main approach). Therefore, in the high penetration of wind power, i.e., 30 (%), more active power needs for voltage regulation, so that the capacity of the batteries as well as the installation cost and the total cost objective function increase. The cost function is higher when the reactive power is not considered in nonzero penetrations. In addition to the voltage regulation, the batteries have been scheduled for other purposes as well. According to Table IV, the required capacity of storage as well as the investment cost decreases when the islanding mode operation is not considered as a decision for optimal planning. However, the total cost objective function increases. As a result, the proposed strategy raises the optimal capacity of the batteries and it makes them more economical in distribution network. Fig. 10 represents the impact of storage units on operation cost, reliability cost, penalty factor and average power loss in proposed optimal planning. The results show that using the storage units optimally improves all terms of the objective function separately, even if the overall cost objective function is investigated for optimization. In addition, the average power loss is reduced as a result of peak shaving; however, it may not be improved in all times. In these conditions, unlike the power loss, the cost of power loss decreases thanks to the lower price in off-peak times. The cost improvement is more considerable in high penetration of wind. Although the lines are upgraded, the penalty factor is not zero without storage units in 10 (%) and 30 (%) penetration of wind. On the other hand, feeder reinforcement does not influence the peak cutting and reliability enhancement considerably, but the batteries can improve the objective function from several points of view. The total cost of storage in period of the project is compared with the total benefits of distribution utility due to storage installation in Fig. 11. The penalty factor of the constraint viola-


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TABLE IV RESULTS OF OPTIMAL PLANNING FOR DIFFERENT SCENARIOS

Fig. 10. Impact of optimal storage planning on operation cost, reliability cost, penalty factor, and power loss in different wind penetrations.

Fig. 11. Total cost/benefit of using storage in distribution network.

tions is neglected in this cost/benefit analysis. However, it can be seen that the benefit of storage is more than the corresponding cost in all wind penetrations and the net profit increases as the wind penetration grows. In addition to the economic benefits, the storage units are useful from technical points of view as well. According to Fig. 10, the number of probable violations is considerable in 10 (%) and 30 (%) penetrations of wind when the storage units are not optimally embedded. In order to show the results of several runs, the PDF of the objective function is presented in Fig. 12 for a single case as an example. This figure is obtained from several runs of the TS algorithm and then fitting the results to a PDF. In this case, the location and capacity of the batteries are according to Table III for 10 (%) penetration of wind. This study provides a bound on solution quality. Consequently the results show that the TS algorithm is more reliable when it is run for several times. Although the execution time is not usually an important criterion in off-line issues such as the long-term planning, it may become unacceptable for high dimension problems. In these cases, it is

Fig. 12. PDF of the objective function in several runs of TS.

necessary to limit the search of TS and PSO. For example, according to the optimization results in Table III, only the nodes which are electrically far from the HV/MV substation are suitable for installing the storage units. As a result, it does not need to consider all the nodes in search space. This strategy simplifies the real sized networks and reduces the computation cost efficiently. V. CONCLUSION In this paper, the planning procedure determines optimal location, capacity and power rating of the batteries while minimizing the cost function under technical constraints. The objective function consists of the monetary parts, i.e., investment, operation and reliability costs, and the technical penalty factor which is intensified to penalize the violations. Unlike the previous researches, the optimal planning is performed subject to probabilistic OPF in presence of wind turbines and batteries. Regarding their specifications, the PSO and TS algorithms are combined and employed to solve the optimal planning and OPF



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Mahdi Sedghi was born in Behshahr, Iran, in 1982. He received the B.Sc. and M.Sc. degrees in electrical engineering from K. N. Toosi University of Technology, Tehran, Iran, in 2006 and 2008, respectively. He is currently pursuing the Ph.D. degree from the Electrical Engineering Department of K. N. Toosi University of Technology, Tehran, Iran. His research interests include distribution network planning and reliability, electrical energy storage, and soft computing.

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Ali Ahmadian (S'11) was born in Ahar, Iran, on May 12, 1988. He received the B.Sc. and M.Sc. degrees in electrical engineering in 2010 and 2012, respectively. He is currently pursuing the Ph.D. degree from the Electrical Engineering Department of K. N. Toosi University of Technology, Tehran, Iran. His research interests include active distribution network's operation and planning, smart grid, and power market.

Masoud Aliakbar-Golkar was born in Tehran, Iran, in 1954. He received the B.Sc. degree from the Sharif University of Technology, Tehran, Iran, in 1977, the M.Sc. degree from the Oklahoma State University, Stillwater, OK, USA, in 1979, and the Ph.D. degree from the Imperial College of Science, Technology, and Medicine, The University of London, U.K., in 1986, all in electrical engineering (power systems). Since 1979, he has been teaching and doing research at K. N. Toosi University of Technology, Tehran, Iran. He is the advisor of many electricity boards and has successfully conducted many projects for different electricity utilities in Iran. He conducted some research groups on Electrical Distribution Systems and Reactive Power studies at the Electric Power Research Center (EPRC) for more than 10 years. From January 2002 to July 2005, he has served as a Senior Lecturer at Curtin University of Technology in Malaysia. His main research areas are smart grid, distributed generation, and renewable generations studies, electric distribution systems and reactive power studies, voltage collapse studies, and load and energy management. He is the author of some books and has more than 200 papers in national and international journals and conferences. Currently, he is a Professor at K. N. Toosi University of Technology in Tehran, Iran.