# Optimal Location and Sizing of BESS for Performance Improvement of Distribution Systems with High DG Penetration

Authors: Sirote Khunkitti; Punyawoot Boonluk; Apirat Siritaratiwat
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

This work proposes an optimal location and sizing of battery energy storage system (BESS) installation for performance improvement of distribution systems with high distributed generation (DG) penetration level where the DGs comprise photovoltaics (PV) and wind turbines (WT). The installation of the BESS can reduce costs incurred in the systems, alleviate reverse power flow when the systems are in the high DG penetration level, and also achieve peak shaving during high demand. To find the optimal location and sizing of the BESS, three optimization algorithms, genetic algorithm (GA), particle swarm optimization (PSO), and salp swarm algorithm (SSA), are applied, and their performances are compared. The considered objective function is the system costs consisting of transmission loss cost, peak power cost, and voltage deviation cost. The system performance improvement is compared in terms of transmission loss, peak demand, and voltage regulation reductions. IEEE 33- and 69-bus distribution systems with high DG penetration are tested to investigate the performance improvement of the BESS installation. The results found that the installation of the BESS could successfully decrease system cost, improve voltage profile, reduce power losses, alleviate reverse power flow, and achieve peak shaving where PSO and SSA are found to be the best competitive algorithms. So, the proposed method can be further applied to find the optimal location and sizing of the BESS to improve the performance of practical systems in the future.


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## Body

## 1. Introduction

Nowadays, with the development of technologies together with the growth of power demand, renewable energy sources (RESs), connected to distribution systems as the distributed generation (DG), are one of the popular choices to support power generation with the saving cost and clean energy [1–3]. However, RESs such as photovoltaics (PV) and wind turbines (WT) are from natural sources which cannot be controlled resulting in power fluctuations caused by the difference in voltage and frequency of different RESs, especially in systems with high DG penetration levels [4–7]. Energy storage system (ESS) is increasingly being incorporated into distribution systems to solve the aforementioned problems and provide different technical and economic benefits [8–12]. Moreover, ESS also reduces power losses [13–16], improves voltage profile or alleviates voltage deviation [17, 18], achieves peak shaving [19], mitigates reverse power flow [20], and decreases system cost [21].Although the ESS provides various benefits, the appropriate location and sizing of BESS have a considerable impact on the economic term when it comes to placing it in networks, as improper placement and excessive size of ESS can raise investment costs [22]. Consequently, finding a minimum cost solution together with improving system performance is the inspiration of this work. The optimal location and sizing of the ESS, introduced in various works, have been investigated based on different expectations, and several algorithms and solutions have been applied to solve the problem [23–32].In [23], an optimal allocation and sizing of battery energy storage system (BESS) are evaluated to decrease voltage deviation, transmission losses, and line loading in the IEEE 33-bus system. An optimal location of distributed community-based BESS in distribution systems is proposed to accomplish the advantages of energy arbitrage, loss and emission reductions, and peaking PV generation [24]. In [25], an optimal location and sizing of ESS are introduced to enhance voltage profile and minimize system cost in a distribution system with WT penetration. An optimal location strategy of ESS is presented in [26] to simultaneously minimize voltage deviation, operation cost, and emission in a power system with WT penetration. The optimal location and operation of BESS in a distribution network for enhancing generation and load hosting capability in order to reduce peak power, improve voltage regulation, and decrease power loss are proposed in [27]. The ESS optimal location is investigated in [28, 29] for alleviating voltage fluctuation problems occurring from PV penetration; however, transmission loss is not evaluated. In [30], an optimal management strategy of BESS is presented to decrease network power losses, emissions, and generation costs in a distribution system with RES penetration. The location of ESS installation is proposed in [31] for minimizing transmission losses, reducing costs, and supporting voltage by congestion management. In [32], an optimal location of BESS is found to minimize the costs of BESS installation, power losses, maintenance, interruption, and system improvement. In [33], an optimal location and sizing problem of BESS is solved for improving voltage profile, reducing line loading, minimizing power losses, and minimizing cost in the IEEE 33-bus distribution system. An improved optimization algorithm is proposed in [34] to find optimal location and sizing of BESS in a distribution network for mainly minimizing system losses. From the extensive review on optimal location and sizing of BESS problem, an optimal location and sizing of BESS for minimizing system costs and improving system performance in terms of power loss reduction, voltage profile improvement, and peak shaving achievement in the systems with high DG, including PV and WT DGs penetration, have been rarely investigated.In [35], optimal siting and sizing of BESS in distribution networks with connected RESs were evaluated in order to minimize the costs incurred in the distribution networks comprising costs of voltage deviation, power losses, and peak demand. The performances of GA and PSO are also compared to find a better algorithm for solving this problem. However, this work was only investigated in the IEEE 33-bus distribution system which is a small distribution system. So, it was difficult to conclude whether these algorithms are still efficient and which algorithm is better when the system is larger, and the DG penetration level is increased. The considered costs of this work have not been compared to the costs of the system without BESS installation, so the cost improvement from the BESS installation has not been evaluated. Besides, the adopted algorithms in this work which are GA and PSO are very traditional, although several new efficient optimization algorithms have been proposed, and the statistical analysis of the considered algorithms has not been investigated. In [12], an optimal siting and sizing of BESSs are proposed to improve performance, in terms of voltage regulation, real loss, and peak demand reductions, of a distribution network in Thailand. However, this work only considers one PV as a DG in a 56-bus distribution network.Thus, this paper proposes an optimal location and sizing of the BESS installation for minimizing system costs and improving system performance in the high DG penetration situation. The load demand and the DGs including PV and WT DGs are varied across a day. Traditional algorithms consisting of genetic algorithm (GA) [36] and particle swarm optimization (PSO) [37] and a new efficient algorithm which is salp swarm algorithm (SSA) [38, 39] are used to solve the problem, and their performances are compared before and after the BESS installation. The IEEE 33- and 69-bus distribution systems with high DG penetration levels are tested to compare the system cost and performance enhancement after the BESS installation.The main contributions of this work are as follows:(1)
The optimal location and sizing of the BESS in the IEEE 33- and 69-bus distribution systems with high DG penetration are investigated in order to minimize an objective function which is the system costs from power losses, voltage deviation, and peak power.(2)
The performance of the distribution systems is improved in terms of power loss reduction, peak power reduction, and voltage profile improvement.(3)
Three optimization algorithms, GA, PSO, and SSA, are applied to solve the optimization problems, and the performance comparison is investigated.The rest of the paper is organized as follows: The battery energy storage is depicted in Section2. Section 3 introduces the problem formulation. The optimization algorithms and implementation are described in Section 4. Section 5 presents the simulation results and implementation. Finally, the conclusion is given in Section 6.


## 2. Battery Energy Storage

The type of BESS simulated in this work is Li-ion batteries due to their several advantages. As the usage of Li-ion batteries in electric vehicles (EV) has grown because of their reusable property [40], the price of these batteries has tended to fall [41, 42]. Li-ion batteries are also notable for their high capacity and energy per volume, as well as their quick charge and discharge times and low self-discharge rate. Moreover, Li-ion batteries provide several advantages, including the ability to perform at a variety of voltage levels, a high energy density per volume, easy power and capacity adjustment, and long life cycles [43].


### 2.1. Battery Energy Storage System (BESS)

BESS operating condition and performance can be represented by the state of charge (SoC) and state of health (SoH) [44]. SoC is the battery capacity at one state compared to the actual maximum capacity of the battery where the reduction in the daily SoC swing can improve the cycle life of the battery. SoH is the actual maximum capacity divided by the ideal capacity representing battery lifetime, the potentiality to accept a charge, the number of charge-discharge cycles, and the temperature of the battery during its previous uses [45]. So these various parameters should be considered in order to maximize battery life. The appropriate temperature of Li-ion battery is approximately 15–35°C, and a good cooling system is required. The depth of discharge (DOD) of Li-ion battery should be around 80% of the rated capacity where the charging or discharging rate should not be high to avoid the high temperaure shortening the battery life [46].


### 2.2. Modelling of BESS

To investigate the dispatch of the BESS, a BESS energy vector (CiT) is evaluated to provide the charging or discharging rate of the BESS within a day. The BESS energy vector dimension can be obtained depending on the divided interval during a day. For example, dividing one-day hours (24 hours) by 15 minutes, 30 minutes, and 1 hour gives the BESS energy vector dimension (m) of 96, 48, and 24, respectively. So, the BESS energy vector is formulated as presented below.(1)CiT=EB1⋮EBm,where CiT is the BESS energy vector and EB(t) is the BESS energy (MWh) at time t when t = 1, 2, …, m.The BESS energy vector must be constrained by energy balance to ensure that charging or discharging is within its limits at the end of a cycle and also to facilitate the next-day operation.The energy of the battery,EB (t), which is periodic is more simply expressed by using Fourier coefficient vector (CiF) such that [47](2)CiF=a1,b1⋮am,bm,(3)EBt=a0+a1cos2πtT+b1sin2πtT+…+amcos2πtT+bmsin2πtT,where CiF is the Fourier coefficient vector, EB (t) is the energy of the battery at time t, a0, am, and bm are constant Fourier coefficient, Fourier cosine coefficients, and Fourier sine coefficient, respectively, m is the number of Fourier coefficients which is set to 8 [47], and T is a period.As can be seen from equation (2), coefficient a0 which is constant is excluded because it does not affect the charging or discharging power of the battery and energy cost. Coefficient a0 is applied to verify that the energy curve of the battery is not negative or lower than the DOD requirements.Two consecutive energies of the battery are computed by (3) in order to find the battery power as in (4) and (5) where the battery power is positive when it is charging and negative when it is discharging as shown below.(4)ΔEB=EBt−EBt−1,(5)PBt=ΔEB/Δt×ηc;PBt>0,(6)PBt=ΔEB×ηd/Δt;PBt<0,where ΔEB represents the two consecutive energies of the battery, ηc =  ηd =  ηbat, ηbat = 0.9 is the battery efficiency in a round trip cycle, ηc and ηd are battery charging and discharging efficiencies, respectively, PB (t) is the battery power at time t, and Δt is the sampling time interval.The battery size can be found from the different values of maximum and minimum BESS energy values divided by the maximum DOD as a presented equation.(7)Battery sizekWh=EBmax−EBminDODmax,where EBmax and EBmin are maximum and minimum values of BESS energy, respectively, and DODmax = 0.8 is the maximum DOD.The battery life is also evaluated to indicate the performance of BESS by using a cycle as the expressed equations.(8)Cycle=12∑t=1TEBt−EBt−1DODmax⋅Battery Size,Battery Lifeyears=Cycle LifeCycles×D,where BatteryLife is the actual life of the battery (years), CycleLife = 3221 is the nominal cycle life of Li-ion battery [46], and D = 365 is the number of operating days.


## 2.1. Battery Energy Storage System (BESS)

BESS operating condition and performance can be represented by the state of charge (SoC) and state of health (SoH) [44]. SoC is the battery capacity at one state compared to the actual maximum capacity of the battery where the reduction in the daily SoC swing can improve the cycle life of the battery. SoH is the actual maximum capacity divided by the ideal capacity representing battery lifetime, the potentiality to accept a charge, the number of charge-discharge cycles, and the temperature of the battery during its previous uses [45]. So these various parameters should be considered in order to maximize battery life. The appropriate temperature of Li-ion battery is approximately 15–35°C, and a good cooling system is required. The depth of discharge (DOD) of Li-ion battery should be around 80% of the rated capacity where the charging or discharging rate should not be high to avoid the high temperaure shortening the battery life [46].


## 2.2. Modelling of BESS

To investigate the dispatch of the BESS, a BESS energy vector (CiT) is evaluated to provide the charging or discharging rate of the BESS within a day. The BESS energy vector dimension can be obtained depending on the divided interval during a day. For example, dividing one-day hours (24 hours) by 15 minutes, 30 minutes, and 1 hour gives the BESS energy vector dimension (m) of 96, 48, and 24, respectively. So, the BESS energy vector is formulated as presented below.(1)CiT=EB1⋮EBm,where CiT is the BESS energy vector and EB(t) is the BESS energy (MWh) at time t when t = 1, 2, …, m.The BESS energy vector must be constrained by energy balance to ensure that charging or discharging is within its limits at the end of a cycle and also to facilitate the next-day operation.The energy of the battery,EB (t), which is periodic is more simply expressed by using Fourier coefficient vector (CiF) such that [47](2)CiF=a1,b1⋮am,bm,(3)EBt=a0+a1cos2πtT+b1sin2πtT+…+amcos2πtT+bmsin2πtT,where CiF is the Fourier coefficient vector, EB (t) is the energy of the battery at time t, a0, am, and bm are constant Fourier coefficient, Fourier cosine coefficients, and Fourier sine coefficient, respectively, m is the number of Fourier coefficients which is set to 8 [47], and T is a period.As can be seen from equation (2), coefficient a0 which is constant is excluded because it does not affect the charging or discharging power of the battery and energy cost. Coefficient a0 is applied to verify that the energy curve of the battery is not negative or lower than the DOD requirements.Two consecutive energies of the battery are computed by (3) in order to find the battery power as in (4) and (5) where the battery power is positive when it is charging and negative when it is discharging as shown below.(4)ΔEB=EBt−EBt−1,(5)PBt=ΔEB/Δt×ηc;PBt>0,(6)PBt=ΔEB×ηd/Δt;PBt<0,where ΔEB represents the two consecutive energies of the battery, ηc =  ηd =  ηbat, ηbat = 0.9 is the battery efficiency in a round trip cycle, ηc and ηd are battery charging and discharging efficiencies, respectively, PB (t) is the battery power at time t, and Δt is the sampling time interval.The battery size can be found from the different values of maximum and minimum BESS energy values divided by the maximum DOD as a presented equation.(7)Battery sizekWh=EBmax−EBminDODmax,where EBmax and EBmin are maximum and minimum values of BESS energy, respectively, and DODmax = 0.8 is the maximum DOD.The battery life is also evaluated to indicate the performance of BESS by using a cycle as the expressed equations.(8)Cycle=12∑t=1TEBt−EBt−1DODmax⋅Battery Size,Battery Lifeyears=Cycle LifeCycles×D,where BatteryLife is the actual life of the battery (years), CycleLife = 3221 is the nominal cycle life of Li-ion battery [46], and D = 365 is the number of operating days.


## 3. Problem Formulation

An optimal location and sizing of the BESS are evaluated in order to minimize system costs considered as an objective function while satisfying a set of constraints as explained in the following subsections.


### 3.1. Objective Function

The objective of this work is to find the optimal location and sizing of BESS while minimizing costs incurred in the distribution system (Csystem) consisting of transmission loss cost (CLoss), peak power cost (CPP), and voltage regulation cost (CVR). So, the truly appropriate optimal location and sizing of BESS for mainly enhancing the efficiency of the distribution network can be obtained, the system cost is reduced, and the system performance is improved. The equation of the objective function is thus presented below.(9)minfCiF=Csystem=CLoss+CPP+CVR,where Csystem is the total system cost incurred in the distribution system.(10)CLoss=∑t=1T∑k=1NLgkVi2+Vj2−2ViVjcosθij⋅rLoss,CPP=Pmax⋅Δt⋅rPP,CVR=∑t=1T∑i=1NVi−Vr⋅rVR.From the provided equations,CLoss is the transmission loss cost, CPP is the peak power cost, CVR is the voltage regulation cost, rLoss = 0.284 $/kWh, rPP = 200 $/kWh/year, rVR = 0.142 $/p.u. are loss cost rate, voltage regulation cost rate, and peak demand cost rate, respectively [23, 27], NL is the number of transmission lines, gk is the conductance of branch k, Vi and Vj are the voltage magnitudes of buses i and j, θij is the different voltage angle between buses i and j, Pmax is the slack bus maximum power over the period, N is the number of buses, and Vr = 1 p.u. is the voltage magnitude at the reference bus.


### 3.2. Constraints

The considered objective function is minimized while the voltage magnitude must be bounded within a limit called voltage constraint as the given equation.(11)Vmin<Vit<Vmax,where Vmin and Vmax are the minimum and maximum voltage magnitudes, respectively, and Vit is the voltage magnitude of bus i at time t.Also, the power and energy of the BESS must be limited in the battery security ranges while charging or discharging status which is called battery constraints as expressed in the following equation:(12)PBmin<PBt<PBmax,EBmin<EBt<EBmax,where PBmin, PBmax, EBmin, and EBmax are minimum and maximum powers of BESS and minimum and maximum capacities of BESS, and PBt and EBt are the power and capacities of BESS at time t, respectively.


## 3.1. Objective Function

The objective of this work is to find the optimal location and sizing of BESS while minimizing costs incurred in the distribution system (Csystem) consisting of transmission loss cost (CLoss), peak power cost (CPP), and voltage regulation cost (CVR). So, the truly appropriate optimal location and sizing of BESS for mainly enhancing the efficiency of the distribution network can be obtained, the system cost is reduced, and the system performance is improved. The equation of the objective function is thus presented below.(9)minfCiF=Csystem=CLoss+CPP+CVR,where Csystem is the total system cost incurred in the distribution system.(10)CLoss=∑t=1T∑k=1NLgkVi2+Vj2−2ViVjcosθij⋅rLoss,CPP=Pmax⋅Δt⋅rPP,CVR=∑t=1T∑i=1NVi−Vr⋅rVR.From the provided equations,CLoss is the transmission loss cost, CPP is the peak power cost, CVR is the voltage regulation cost, rLoss = 0.284 $/kWh, rPP = 200 $/kWh/year, rVR = 0.142 $/p.u. are loss cost rate, voltage regulation cost rate, and peak demand cost rate, respectively [23, 27], NL is the number of transmission lines, gk is the conductance of branch k, Vi and Vj are the voltage magnitudes of buses i and j, θij is the different voltage angle between buses i and j, Pmax is the slack bus maximum power over the period, N is the number of buses, and Vr = 1 p.u. is the voltage magnitude at the reference bus.


## 3.2. Constraints

The considered objective function is minimized while the voltage magnitude must be bounded within a limit called voltage constraint as the given equation.(11)Vmin<Vit<Vmax,where Vmin and Vmax are the minimum and maximum voltage magnitudes, respectively, and Vit is the voltage magnitude of bus i at time t.Also, the power and energy of the BESS must be limited in the battery security ranges while charging or discharging status which is called battery constraints as expressed in the following equation:(12)PBmin<PBt<PBmax,EBmin<EBt<EBmax,where PBmin, PBmax, EBmin, and EBmax are minimum and maximum powers of BESS and minimum and maximum capacities of BESS, and PBt and EBt are the power and capacities of BESS at time t, respectively.


## 4. Optimization Algorithms and Implementation

To provide the optimal location and sizing of BESS, the optimization problem was solved by using two well-known efficient algorithms, GA and PSO, and one recent efficient algorithm which is SSA to both investigate the performance of the used algorithms and also provide the best feasible solution for the problem. The formulations of these algorithms and the implementation are presented.


### 4.1. Genetic Algorithms (GA)

GA is one of the most well-known evolutionary algorithms (EAs) inspired by natural genetics and natural selection [36, 48]. In the simulation, GA simulates the process of biological evolution in a domain of binary numbers. The decision variables in each population have equal binary numbers multiplied by the bit number (nBit), which is 16 in this work, allocated to each decision variable. In the GA optimization process, the initial population is firstly generated in a search space to evaluate the objective value. Parents are then selected from the initial population in the selection process, and crossover is performed by those parents to create the next generation called offspring to provide a new solution and improve stochastic behavior based on the crossover percentage (pc), which is equal to 0.7 in this work. The offspring are mutated in the mutation process to improve the exploration based on the mutation rate (mu), which is 0.5 in this work, and the main population and the offspring are merged. The objective function is then evaluated by those. The objective values are sorted, and the only population containing a good objective value is selected. Finally, if the termination condition is met, the feasible solution is obtained; otherwise, the algorithm is operated again from the selection process.


### 4.2. Particle Swarm Optimization (PSO)

PSO is a population-based stochastic optimization algorithm proposed by Eberhart and Kennedy [37]. It is one of the most well-known and popular optimization algorithms due to its high efficiency in obtaining a feasible solution and its quickness to provide the solution. PSO was introduced by imitating behaviors of bird flocking and fish schooling. In the PSO simulation, particles spread around the search space where each particle is initialized with randomly generated position and velocity. A personal best position which is the best position of each particle and a global best position which is the best position among all particles are defined. Then, the velocity of each particle is updated according to the personal best and global best found so far, and the position is also updated as the provided equations.(13)ViIt+1=ωIt×ViIt+C1×rand1×XpbestiIt−XiIt+C2×rand2×XgbestIt−XiIt,XiIt+1=XiIt+ViIt+1,where ViIt+1 and ViIt are the velocities of particle i at iterations It + 1 and t, respectively, XiIt+1 and XiIt are the positions of particle i at iterations It + 1 and It, respectively, C1 and C2 are positive acceleration constants which are both set to 2, rand1 and rand2 are uniformly randomly generated numbers in the range of [0,1], XItpbesti is the personal best position of particle i at iteration It, XItgbest is the global best position among all particles at iteration It, and ωIt is the inertia weight at iteration It calculated as follows:(14)ωIt=ωmax−ωmax−ωminItItmax,where ωmax = 0.9, ωmax = 0.4, It is the current iteration number, and Itmax is the maximum iteration number.


### 4.3. Salp Swarm Algorithm (SSA)

SSA is inspired by salps which are creatures in the deep ocean [38]. Salps generally build themselves as salp chain to achieve better movement and quick foraging. To formulate this behavior, the salp chain is divided into two groups. The first one is a leader which is the salp in front of the chain, and its role is to lead the swarm to the food source. The other group contains followers which are the other salps of the chain. The followers’ role is to follow each other. Thus, the leader position can be mathematically formulated as follows:(15)xj1=Fj+c1ULj−LLjc2+LLjifc3≥0Fj−c1ULj−LLjc2+LLjifc3<0,where x1j is the leader position in dimension j, Fj is the food source position in dimension j, c2 and c3 are numbers randomly and uniformly generated between 0 and 1 to enhance the stochastic behavior, ULj and LLj are upper and lower limits of dimension j, respectively, and c1 is a parameter used to balance exploration and exploitation phases in the optimization process defined as follows:(16)c1=2exp−4⋅ItItmax2.The positions of the followers are updated based on the concept of Newton’s law of motion where time is instead considered as the iteration. So the followers’ positions are updated as the provided equation.(17)xji=12xji+xji−1i≥2,where xij is the follower’s position of salp i in dimension j.


### 4.4. System Performance Investigation

After the implementation of the BESS installation, the system cost is compared with the case without the BESS, and system performance improvement is investigated in terms of voltage profile improvement, power loss reduction, and peak power reduction.


#### 4.4.1. Voltage Deviation Index (VDI)

In this work, the percentage of voltage deviation index (VDI) is calculated to investigate the voltage profile improvement where the less percentage of VDI indicates more improvement of the voltage profile. The percentage of VDI can be computed as follows:(18)%VDIi=maxTVref−Vi,%VDI=∑i=1Nbus%VDIi,where %VDIi is the maximum value of VDI of bus i during time interval T, Vref is the reference voltage which is set to 1 p.u., Vi is the voltage of bus i, %VDI is the total percentage of VDI of the system, and Nbus is the total bus number.


#### 4.4.2. Real, Reactive, and Apparent Power Losses

Real, reactive, and apparent power losses are also calculated to investigate the system performance after the BESS installation in terms of the power loss reductions. The losses can be formulated as the given equations.(19)PL=∑t=1T∑l=1NLPlt,QL=∑t=1T∑l=1NLQlt,SL=∑t=1T∑l=1NLSlt,where PL, QL, and SL are the total system active power loss, reactive power loss, and apparent power loss during time interval T, respectively, Plt, Qlt, and Slt are active power loss, reactive power loss, and apparent power loss of branch l at time t, respectively, NL is the number of system branches, and T is the considered time interval.


### 4.5. Implementation

The implementation to find the optimal location and sizing of the BESS in the distribution systems is presented in Figure1, where each considered algorithm including GA, PSO, and SSA is separately operated.Figure 1
Implementation of battery energy storage system (BESS) installation.


## 4.1. Genetic Algorithms (GA)

GA is one of the most well-known evolutionary algorithms (EAs) inspired by natural genetics and natural selection [36, 48]. In the simulation, GA simulates the process of biological evolution in a domain of binary numbers. The decision variables in each population have equal binary numbers multiplied by the bit number (nBit), which is 16 in this work, allocated to each decision variable. In the GA optimization process, the initial population is firstly generated in a search space to evaluate the objective value. Parents are then selected from the initial population in the selection process, and crossover is performed by those parents to create the next generation called offspring to provide a new solution and improve stochastic behavior based on the crossover percentage (pc), which is equal to 0.7 in this work. The offspring are mutated in the mutation process to improve the exploration based on the mutation rate (mu), which is 0.5 in this work, and the main population and the offspring are merged. The objective function is then evaluated by those. The objective values are sorted, and the only population containing a good objective value is selected. Finally, if the termination condition is met, the feasible solution is obtained; otherwise, the algorithm is operated again from the selection process.


## 4.2. Particle Swarm Optimization (PSO)

PSO is a population-based stochastic optimization algorithm proposed by Eberhart and Kennedy [37]. It is one of the most well-known and popular optimization algorithms due to its high efficiency in obtaining a feasible solution and its quickness to provide the solution. PSO was introduced by imitating behaviors of bird flocking and fish schooling. In the PSO simulation, particles spread around the search space where each particle is initialized with randomly generated position and velocity. A personal best position which is the best position of each particle and a global best position which is the best position among all particles are defined. Then, the velocity of each particle is updated according to the personal best and global best found so far, and the position is also updated as the provided equations.(13)ViIt+1=ωIt×ViIt+C1×rand1×XpbestiIt−XiIt+C2×rand2×XgbestIt−XiIt,XiIt+1=XiIt+ViIt+1,where ViIt+1 and ViIt are the velocities of particle i at iterations It + 1 and t, respectively, XiIt+1 and XiIt are the positions of particle i at iterations It + 1 and It, respectively, C1 and C2 are positive acceleration constants which are both set to 2, rand1 and rand2 are uniformly randomly generated numbers in the range of [0,1], XItpbesti is the personal best position of particle i at iteration It, XItgbest is the global best position among all particles at iteration It, and ωIt is the inertia weight at iteration It calculated as follows:(14)ωIt=ωmax−ωmax−ωminItItmax,where ωmax = 0.9, ωmax = 0.4, It is the current iteration number, and Itmax is the maximum iteration number.


## 4.3. Salp Swarm Algorithm (SSA)

SSA is inspired by salps which are creatures in the deep ocean [38]. Salps generally build themselves as salp chain to achieve better movement and quick foraging. To formulate this behavior, the salp chain is divided into two groups. The first one is a leader which is the salp in front of the chain, and its role is to lead the swarm to the food source. The other group contains followers which are the other salps of the chain. The followers’ role is to follow each other. Thus, the leader position can be mathematically formulated as follows:(15)xj1=Fj+c1ULj−LLjc2+LLjifc3≥0Fj−c1ULj−LLjc2+LLjifc3<0,where x1j is the leader position in dimension j, Fj is the food source position in dimension j, c2 and c3 are numbers randomly and uniformly generated between 0 and 1 to enhance the stochastic behavior, ULj and LLj are upper and lower limits of dimension j, respectively, and c1 is a parameter used to balance exploration and exploitation phases in the optimization process defined as follows:(16)c1=2exp−4⋅ItItmax2.The positions of the followers are updated based on the concept of Newton’s law of motion where time is instead considered as the iteration. So the followers’ positions are updated as the provided equation.(17)xji=12xji+xji−1i≥2,where xij is the follower’s position of salp i in dimension j.


## 4.4. System Performance Investigation

After the implementation of the BESS installation, the system cost is compared with the case without the BESS, and system performance improvement is investigated in terms of voltage profile improvement, power loss reduction, and peak power reduction.


### 4.4.1. Voltage Deviation Index (VDI)

In this work, the percentage of voltage deviation index (VDI) is calculated to investigate the voltage profile improvement where the less percentage of VDI indicates more improvement of the voltage profile. The percentage of VDI can be computed as follows:(18)%VDIi=maxTVref−Vi,%VDI=∑i=1Nbus%VDIi,where %VDIi is the maximum value of VDI of bus i during time interval T, Vref is the reference voltage which is set to 1 p.u., Vi is the voltage of bus i, %VDI is the total percentage of VDI of the system, and Nbus is the total bus number.


### 4.4.2. Real, Reactive, and Apparent Power Losses

Real, reactive, and apparent power losses are also calculated to investigate the system performance after the BESS installation in terms of the power loss reductions. The losses can be formulated as the given equations.(19)PL=∑t=1T∑l=1NLPlt,QL=∑t=1T∑l=1NLQlt,SL=∑t=1T∑l=1NLSlt,where PL, QL, and SL are the total system active power loss, reactive power loss, and apparent power loss during time interval T, respectively, Plt, Qlt, and Slt are active power loss, reactive power loss, and apparent power loss of branch l at time t, respectively, NL is the number of system branches, and T is the considered time interval.


## 4.4.1. Voltage Deviation Index (VDI)

In this work, the percentage of voltage deviation index (VDI) is calculated to investigate the voltage profile improvement where the less percentage of VDI indicates more improvement of the voltage profile. The percentage of VDI can be computed as follows:(18)%VDIi=maxTVref−Vi,%VDI=∑i=1Nbus%VDIi,where %VDIi is the maximum value of VDI of bus i during time interval T, Vref is the reference voltage which is set to 1 p.u., Vi is the voltage of bus i, %VDI is the total percentage of VDI of the system, and Nbus is the total bus number.


## 4.4.2. Real, Reactive, and Apparent Power Losses

Real, reactive, and apparent power losses are also calculated to investigate the system performance after the BESS installation in terms of the power loss reductions. The losses can be formulated as the given equations.(19)PL=∑t=1T∑l=1NLPlt,QL=∑t=1T∑l=1NLQlt,SL=∑t=1T∑l=1NLSlt,where PL, QL, and SL are the total system active power loss, reactive power loss, and apparent power loss during time interval T, respectively, Plt, Qlt, and Slt are active power loss, reactive power loss, and apparent power loss of branch l at time t, respectively, NL is the number of system branches, and T is the considered time interval.


## 4.5. Implementation

The implementation to find the optimal location and sizing of the BESS in the distribution systems is presented in Figure1, where each considered algorithm including GA, PSO, and SSA is separately operated.Figure 1
Implementation of battery energy storage system (BESS) installation.


## 5. Simulation Results and Discussion

In the simulation process, the optimal location and sizing of the BESS are tested in two IEEE distribution systems with high DG, including PV and WT DGs, penetration level. Firstly, the IEEE 33-bus distribution system was tested to evaluate the performance of the BESS installation. The IEEE 69-bus distribution system was then used to verify the BESS installation performance in a larger system. In each system, the performance after the BESS installation was investigated in terms of system cost, loss reduction, voltage profile improvement, and peak power comparison when three optimization algorithms, GA, PSO, and SSA, were applied. The population size and the maximum number of iterations of all algorithms are set to 60 and 1000, respectively. The detailed data of the two systems and the simulation results are presented in the following subsections.


### 5.1. IEEE 33-Bus Distribution System

The IEEE 33-bus distribution system was applied to find the optimal location and sizing of the BESS. A single-line diagram of this system is presented in Figure2, and the network data can be obtained from [27]. The voltage at the substation is 12.66 kV, and the base value is 10 MVA. WT and PV DGs were installed in the system to simulate the high DG penetration situation as expressed in Figure 2. Two 1 MW·WT DGs are located at the 18th and 24th buses, three 400 kVA PV DGs are installed at the 5th, 21th, and 31st buses, and four 500 kVA PV DGs are connected at the 8th, 12th, 28th, and 33rd buses. The PV and WT are operating at a constant unity power factor. The maximum active and reactive power demands are 3.556 MW and 2.191 MVAr, respectively. The time-variant load demand and generation of DGs from WT and PV are plotted in Figure 3 [23].Figure 2
Single-line diagram of the IEEE 33-bus distribution system.Figure 3
Time-variant load demand and generation of distributed generations (DGs) from wind turbines (WT) and photovoltaics (PV) for the IEEE 33-bus system.


#### 5.1.1. Optimal Location and Sizing of the BESS

Firstly, the optimal location and sizing of the BESS installation were obtained in the IEEE 33-bus system by using GA, PSO, and SSA. The best five-bus locations where system cost was considered as the objective function to be minimized provided by each algorithm are compared to the case without the BESS which is the base case as expressed in Table1. It can be observed from the top three best objective values that PSO could give the least system costs with 47.89%, 47.61%, and 47.53% reductions compared to that of the base case when installing the BESS at the 6th, 26th, and 7th buses, respectively. SSA provided the second-best system costs with 46.79%, 45.79%, and 45.68% decreases when the BESS was located at the 26th, 7th, and 8th buses, respectively, while GA found the worst system cost values with 42.37%, 42.35%, and 41.71% reductions when the locations of the BESS were at the 6th, 7th, and 26th buses, respectively, compared to that of the base case. However, the size, power, and lifetime of the BESS provided by each algorithm were slightly different. For the best bus location of BESS installation, SSA provided the least battery size and power of the battery followed by PSO and GA, while all considered algorithms gave the same values of battery lifetime. The final optimized decision variable values of the best bus for this system are shown in Table 2.Table 1
Optimal location and sizing of the BESS for the IEEE 33-bus system.
AlgorithmsBest bus locationsBattery size (MWh)Power of battery (MW)Battery lifetime (years)Csystem ($)Base————2100.13GA615.23142.14718.82471210.20715.53512.12718.82471212.852615.57552.44158.82471224.172714.9551.99838.82471258.93813.67821.98828.82471269.52PSO614.70781.96408.82471094.352614.69371.93438.82471100.23714.54851.94358.82471102.032714.64571.94968.82471107.31814.62291.95258.82471108.56SSA2614.25021.94578.82471117.57715.24962.02428.82471138.43815.00521.97948.82471140.792713.60881.90178.82471155.51914.10201.84958.82471165.91Table 2
Final optimized decision variable values of the best bus for the IEEE 33-bus system.
AlgorithmsBest bus locationFourier coefficient valuesGA6a1b1a2b2a3b3a4b5−0.0002−5.6252−1.38360.79310.00010.0516−0.01950.0006a5b5a6b6a7b7a8b8−0.0662−0.0125−0.1265−0.00780.00010.0183−0.00250.0781PSO6a1b1a2b2a3b3a4b50.6633−5.3813−1.28460.6520−0.10310.02730.03160.0829a5b5a6b6a7b7a8b8−0.00400.0380−0.02180.01310.0154−0.00520.00400.0351SSA26a1b1a2b2a3b3a4b50.7946−5.1942−1.35660.6203−0.07130.0188−0.00950.1346a5b5a6b6a7b7a8b8−0.01400.0194−0.00910.02850.0023−0.01700.03090.0159From Figure4, the state of energy (SoE) expressing the energy stored in the BESS for 24 hours provided by each algorithm is presented, and the SoC can also be observed. It is seen from the figure that the GA needed the largest size of BESS at 15.23 MWh to store the energy from DGs followed by PSO at 14.71 MWh, while SSA needed the smallest BESS size at 14.25 MWh.Figure 4
State of energy (SoE) of the BESS of each algorithm for the IEEE 33-bus system.


#### 5.1.2. System Performance Improvement Investigation

The system performance improvements after installing BESS in the IEEE 33-bus system are compared in terms of VDI, real power loss, reactive power loss, and apparent power loss by using each algorithm as presented in Table3, where the base case is the case without the BESS installation. It is observed that the BESS installation could significantly reduce the VDI, real power loss, reactive power loss, and also apparent power loss. PSO provided the best values for all considered terms followed by SSA which gave slightly worse values than those of PSO, while GA obtained the worst improvement compared to those of the other algorithms.Table 3
System performance comparison for the IEEE 33-bus system.
AlgorithmsVoltage deviation index (VDI) (%)Real power loss (MW)Reactive power loss (MVAr)Apparent power loss (MVA)Base127.321.831.262.22GA83.881.591.111.94PSO79.081.561.101.91SSA80.171.581.111.93The voltage profile improvement after the BESS installation can be noticed in Figure5. In this figure, the voltage profiles of the 33rd bus, which generated the worst voltage profile for this system, for 24 hours before and after the BESS installation are shown. Before installing the BESS, in the base case, the voltage was below the lower limit after 7 p.m. However, the voltage profile was moved to be within the limits after the BESS was installed by adopting each algorithm.Figure 5
Voltage profile improvement comparison of each algorithm for the IEEE 33-bus system.The all-day real power loss comparison is expressed in Figure6. It is seen that the real loss was noticeably decreased from 1 a.m. to 9 a.m. after the BESS installation. However, the real power loss was slightly moved up from 9.00 a.m. to 6.00 p.m. after locating the BESS in the system because the BESS also supplied power to the load demand. After 6.00 p.m., the real loss was extremely dropped from the case with the BESS installation, so the all-day real power loss was improved for the case with BESS installation as evident in Table 3.Figure 6
Real power loss comparison of each algorithm for the IEEE 33-bus system.


#### 5.1.3. Peak Power Comparison

The peak power comparison at the slack bus for the IEEE 33-bus system is shown in Figure7. It is observed from the base case that the peak power had two directions, flowing into and out of the system. From 1.00 a.m. to 11 a.m. and from about 5.00 p.m. until midnight, the peak power was positive which means the system supplied power to the load demand. However, from 8.00 a.m., the peak power tended to be obviously decreased until the peak power was negative from after 11.00 a.m. to 5.00 p.m. because of the high DG penetration causing the reverse power flow. Moreover, from 5.00 p.m. until midnight, the peak power was increased to almost 3 MW at 10.00 p.m. because of the high demand and low DG penetration resulting in a need for high power generation from the system. After the BESS installation by using each algorithm, the BESS starts charging during the high DG penetration and discharging when the demand rises achieving the peak shaving. So, the peak power was reduced to 1.18 MW, 1.22 MW, and 1.38 MW for PSO, SSA, and GA, respectively, as evident in Figure 7.Figure 7
Peak power comparison of each algorithm for the IEEE 33-bus system.


#### 5.1.4. Performance Comparison of the Optimization Algorithms

To further investigate the performance of the optimization algorithms in this system, the comparison of the convergence graphs for the best bus location provided by each algorithm is presented in Figure8. Figure 8(a) shows the convergence graph comparison of each algorithm, and Figure 8(b) presents the expanded version of the convergence curve to clearly notice how each algorithm converged to the optimal solution. It is noticeable that GA firstly converged to its feasible solution, and PSO and SSA converged to their feasible solutions at around the same iteration. However, the last solution obtained by GA is the worst, while that obtained by PSO is the best.Figure 8
(a) Convergence graphs for the best bus location of each algorithm for the IEEE 33-bus system. (b) Expanded version of the convergence graphs.
(a)(b)Moreover, the statistical analysis and convergence time of all algorithms are presented in Table4 to also analyze the performance of the optimization algorithms. It is seen that GA still provided the worst values of worst cost, mean cost, standard deviation, and time. Although PSO generated the best cost value, SSA could give the best mean cost leading to the best standard deviation. The convergence time of PSO is the fastest one followed by SSA and GA, respectively.Table 4
Performance analysis of the optimization algorithm in the IEEE 33-bus system.
AlgorithmsBest cost ($)Worst cost ($)Mean cost ($)Standard deviationTime (s)GA1210.201479.181290.5691.315991PSO1094.351365.771201.8081.275895SSA1117.571430.231196.7478.225947For the IEEE 33-bus system, when compared to the base case, PSO could provide the best system cost reduction when installing the BESS at bus 6, while SSA gave the second-best system cost reduction when the BESS was located at bus 26, and GA obtained the worst system cost reduction when the BESS was installed at bus 6. PSO was also the best algorithm to improve system performance in terms of VDI, real power loss, reactive power loss, and apparent power loss reductions followed by SSA and GA; however, all considered algorithms could significantly decrease all-day real loss and also move the out-of-bound voltage profile to be within the limits. In the peak power comparison, PSO was the best algorithm to reduce the peak power followed by SSA and GA, while all algorithms could vanish the reverse power flow caused by the high DG penetration. To summarize the performance of the considered algorithm for the IEEE 33-bus system, PSO was the best algorithm to find the optimal location and sizing of the BESS installation for minimizing system cost and enhancing system performance. SSA and GA were the second- and third-best algorithms for obtaining the location and sizing of the BESS; however, the performance of SSA was slightly worse than that of PSO, while the performance of GA was obviously worse than that of PSO and SSA.


### 5.2. IEEE 69-Bus Distribution System

The optimal location and sizing of the BESS are also investigated in a larger system which is the IEEE 69-bus distribution system. The network diagram can be found in Figure9 [49], and the detailed parameter can be obtained from [50]. The substation voltage is 12.66 kV, and the base is set at 10 MVA. To simulate the high DG penetration situation, twelve DGs are installed in this system as shown in Figure 9. Five 0.6 MW wind DGs are installed at the 8th, 12th, 59th, 61st, and 64th buses, and seven 0.6 MW PV DGs are located at the 27th, 33rd, 34th, 35th, 38th, and 41st buses. The PV and WT operating power factor is unity. The active and reactive power demands are 3.802 MW and 2.695 MVAr, respectively. The time-variant load demand and generation of DGs from WT and PV of this system are shown in Figure 10 [23].Figure 9
Single-line diagram of the IEEE 69-bus distribution system.Figure 10
Time-variant load demand and generation of DGs from WT and PV for the IEEE 69-bus system.


#### 5.2.1. Optimal Location and Sizing of the BESS

In this system, the optimal location and sizing of the BESS were also found by adopting three algorithms: GA, PSO, and SSA. The best five bus locations of the BESS installation obtained from each algorithm by considering the minimum system cost as the objective function are depicted in Table5 compared to the base case. It is noticeable that PSO provided the best system cost with a 57.41% reduction when the BESS was installed at the 20th bus followed by 57.27% and 57.26% reductions at the 15th and 16th buses, respectively, compared to the cost of the base case. In addition, SSA could obtain system costs with 57.27%, 57.00%, and 56.87% decreases, which were very competitive with those of PSO, when locating the BESS at the 15th, 12th, and 59th buses, respectively. However, GA gave the worst system costs, which were much more than those of PSO and SSA, with only 28.87%, 23.39%, and 20.05% reductions when the BESS was located at the 67th, 11th, and 7th buses, respectively. It can also be observed that the battery size and power of the battery provided by GA were much more than those of PSO and SSA. Besides, the battery lifetime solved by GA was slightly shorter than those of PSO and SSA. The final optimized decision variable values of the best bus for this system are presented in Table 6.Table 5
Optimal location and sizing of the BESS for the IEEE 69-bus system.
AlgorithmsBest bus locationsBattery size (MWh)Power of battery (MW)Battery lifetime (years)Csystem ($)Base————2029.32GA6717.65203.56518.74841493.851114.91192.92578.20111608.96726.75094.07018.66871679.08616.46064.09747.67931689.156615.63843.12007.80201986.10PSO206.70441.21918.8247894.48156.73221.21228.8154897.39167.02551.21168.8247897.62147.06341.20618.8247899.93137.57351.20148.8247902.05SSA156.88221.21048.8247897.37128.01031.19708.8247903.01594.36670.76718.8247905.84604.10240.72798.8247906.17613.81660.68448.8247906.40Table 6
Final optimized decision variable values of the best bus for the IEEE 69-bus system.
AlgorithmBest bus locationFourier coefficient valuesGA67a1b1a2b2a3b3a4b51.8151−5.6228−2.11360.23910.3124−0.6408−0.23520.1795a5b5a6b6a7b7a8b8−0.0823−0.2849−0.1567−0.2150−0.01200.07490.1181−0.1581PSO20a1b1a2b2a3b3a4b50.4767−2.2149−0.77090.2915−0.0956−0.14120.00720.1798a5b5a6b6a7b7a8b8−0.06350.08070.08160.01500.05370.09480.0054−0.0175SSA15a1b1a2b2a3b3a4b50.5586−2.2881−0.75070.2439−0.1036−0.10440.00790.2130a5b5a6b6a7b7a8b8−0.08730.07750.06950.00740.04540.0683−0.0034−0.0260The SoE of the BESS of all considered algorithms is plotted in Figure11, and the SoC can be noticed in this figure. It is observed from the best BESS location that the SoE provided by GA was maximum at 17.65 MWh, while the SoE generated by PSO and SSA were maximum at only 6.70 and 6.88 MWh, respectively. So, the BESS of GA needed a much larger battery size than those of PSO and SSA.Figure 11
SoE of the BESS of each algorithm for the IEEE 69-bus system.


#### 5.2.2. System Performance Improvement Investigation

Table7 presents the performance improvement comparison after the BESS installation by applying the considered algorithms for the IEEE 69-bus system, where the base case is the case without the BESS. It can be seen from the table that SSA provided the best VDI compared to that of other algorithms and the base case followed by PSO, while GA obtained worse VDI compared to the other algorithms including the base case. For the power loss comparison, PSO could provide the least real power loss, reactive power loss, and also apparent power loss, and SSA could give the second-least power losses. However, GA gave more losses than those of the base case.Table 7
System performance comparison for the IEEE 69-bus system.
AlgorithmsVoltage deviation index (VDI) (%)Real power loss (MW)Reactive power loss (MVAr)Apparent power loss (MVA)Base133.802.1300.9832.346GA142.192.4161.0822.648PSO110.721.9840.9212.188SSA106.251.9950.9242.198Figure12 shows the all-day voltage profile of the 65th bus, which is the bus with the worst voltage profile of this system, for all cases. It is observed from the base case that the voltage was below the lower limit from 8.00 a.m. to 10.00 a.m. and from 9.00 p.m. to 11.30 p.m. After the BESS installation by using each algorithm, the all-day voltage profiles were progressed to be within the limits. Although the VDI provided by GA as in Table 7 was more than that of the base case, the all-day voltage profile generated by GA was within the voltage limits, while the base case produced the out-of-bound voltage profile.Figure 12
Voltage profile improvement comparison of each algorithm for the IEEE 69-bus system.The real loss comparison for 24 hours for each case is depicted in Figure13. This figure can confirm (Table 7) that the power losses after the BESS installation by using PSO and SSA were enhanced from the base case. It is observed that the real loss provided by GA was much larger than those of SSA, PSO, and the base case from 9.00 a.m. to 4.00 p.m. This means that installing BESS by using GA provided a huge amount of real loss when the BESS supplied power to the load demand during the day, while some real loss was decreased during the night. However, the total real loss for 24 hours generated from installing BESS by GA was more than that of the base case as evident in Table 7.Figure 13
Real power loss comparison of each algorithm for the IEEE 69-bus system.


#### 5.2.3. Peak Power Comparison

The peak power comparison between the cases with and without BESS is plotted in Figure14. From the base case, the peak power of the system without the BESS started dropping from 8.00 a.m. until the reverse power flow occurred at around 9.30 a. m. until 6.00 p.m. due to the high DG penetration. In addition, the peak demand reached the maximum value which is 2.59 MW at 10.00 p.m. when the DG penetration was low. For the case with the BESS installation, the reverse power flow still occurred; however, the amount of the reverse power flow was improved from −2.50 MW for the base case to −1.46 MW, −1.62 MW, and −1.63 MW for GA, SSA, and PSO, respectively, when the BESS started charging. Besides, the installed BESS could also accomplish the peak shaving from 2.59 MW for the base case to 1.47 MW, 1.70 MW, and 1.78 MW for GA, SSA, and PSO, respectively, because of the BESS discharging.Figure 14
Peak power comparison of each algorithm for the IEEE 69-bus system.


#### 5.2.4. Performance Comparison of the Optimization Algorithms

The convergence graphs for the best bus location of all algorithms are expressed in Figure15 to verify the performance of the optimization algorithm in the large 69-bus system, where Figure 15(a) presents the full convergence graphs of each algorithm and Figure 15(b) shows the expanded convergence graphs to obviously observe the convergence of each algorithm. It can be seen that GA quickly starts converging at around the 20th iteration, while SSA and PSO start converging at about the 520th and 640th iterations, respectively. However, the last solution generated by GA was much more than those of PSO and SSA, and the last solutions provided by PSO and SSA are very competitive.Figure 15
(a) Convergence graphs for the best bus location of each algorithm for the IEEE 33-bus system. (b) Expanded version of the convergence graphs.
(a)(b)To further analyze the performance of these optimization algorithms in this system, the statistical results and convergence time of all algorithms were obtained as in Table8. It is noticeable that the best cost, worst cost, and mean cost values of GA are much worse than those of PSO and SSA, leading to the very higher value of standard deviation, while PSO and SSA gave close values of best and worst, as well as mean costs, resulting in small standard deviation values. The convergence time of GA is also twice those of PSO and SSA. This means that GA has a problem finding the optimal solution or it might be stuck in the local optima.Table 8
Performance analysis of the optimization algorithm in the IEEE 69-bus system.
AlgorithmsBest cost ($)Worst cost ($)Mean cost ($)Standard deviationTime (s)GA1493.853181.322285.80515.7314482PSO894.48929.98909.579.227731SSA897.37929.93912.667.267857For the IEEE 69-bus distribution system, the best location of the BESS was at the 20th bus giving the most system cost reduction which was solved by PSO, and SSA found slightly less system cost reduction compared to PSO when locating the BESS at the 15th bus. However, GA generated much less system cost reduction compared to the other algorithms when installing the BESS at the 67th bus which was the best bus found by GA. SSA was the algorithm to achieve the best voltage profile improvement by providing the least VDI followed by PSO, while PSO could generate the least losses followed by SSA. GA provided more VDI and all losses compared to SSA, PSO, and also the base case. However, all algorithms could enhance the voltage profile to be within the limits. For the comparison of peak power, GA was the best one to improve the reverse power flow followed by SSA and PSO when the DG penetration was high. GA was also the best algorithm to shave the peak demand followed by SSA and PSO. In conclusion for this system, although GA was the best algorithm for improving the reverse power flow and shaving the peak, it generated very high system cost, VDI, and losses compared to those of PSO and SSA. So, GA is considered to be the worst algorithm for this system. The performances of SSA and PSO are very competitive, since they could achieve the improvement in different terms.Overall, in the small distribution system which is the IEEE 33-bus system, PSO was the best algorithm to find the optimal location and sizing of the BESS installation for minimizing system cost and improving system performance, while SSA was the second-best one with a very competitive performance. However, GA was obviously the worst algorithm for this system. In the larger distribution system which is the IEEE 69-bus system, PSO and SSA also have a competitive performance where they could obtain the enhancement in different terms, while GA was the worst algorithm to find the optimal location and sizing of the BESS. Thus, PSO must be selected to find the optimal location and sizing of the BESS in the IEEE 33-bus system while, in the IEEE 69-bus system, PSO and SSA could be judiciously chosen for enhancing the system performance in different terms.


## 5.1. IEEE 33-Bus Distribution System

The IEEE 33-bus distribution system was applied to find the optimal location and sizing of the BESS. A single-line diagram of this system is presented in Figure2, and the network data can be obtained from [27]. The voltage at the substation is 12.66 kV, and the base value is 10 MVA. WT and PV DGs were installed in the system to simulate the high DG penetration situation as expressed in Figure 2. Two 1 MW·WT DGs are located at the 18th and 24th buses, three 400 kVA PV DGs are installed at the 5th, 21th, and 31st buses, and four 500 kVA PV DGs are connected at the 8th, 12th, 28th, and 33rd buses. The PV and WT are operating at a constant unity power factor. The maximum active and reactive power demands are 3.556 MW and 2.191 MVAr, respectively. The time-variant load demand and generation of DGs from WT and PV are plotted in Figure 3 [23].Figure 2
Single-line diagram of the IEEE 33-bus distribution system.Figure 3
Time-variant load demand and generation of distributed generations (DGs) from wind turbines (WT) and photovoltaics (PV) for the IEEE 33-bus system.


### 5.1.1. Optimal Location and Sizing of the BESS

Firstly, the optimal location and sizing of the BESS installation were obtained in the IEEE 33-bus system by using GA, PSO, and SSA. The best five-bus locations where system cost was considered as the objective function to be minimized provided by each algorithm are compared to the case without the BESS which is the base case as expressed in Table1. It can be observed from the top three best objective values that PSO could give the least system costs with 47.89%, 47.61%, and 47.53% reductions compared to that of the base case when installing the BESS at the 6th, 26th, and 7th buses, respectively. SSA provided the second-best system costs with 46.79%, 45.79%, and 45.68% decreases when the BESS was located at the 26th, 7th, and 8th buses, respectively, while GA found the worst system cost values with 42.37%, 42.35%, and 41.71% reductions when the locations of the BESS were at the 6th, 7th, and 26th buses, respectively, compared to that of the base case. However, the size, power, and lifetime of the BESS provided by each algorithm were slightly different. For the best bus location of BESS installation, SSA provided the least battery size and power of the battery followed by PSO and GA, while all considered algorithms gave the same values of battery lifetime. The final optimized decision variable values of the best bus for this system are shown in Table 2.Table 1
Optimal location and sizing of the BESS for the IEEE 33-bus system.
AlgorithmsBest bus locationsBattery size (MWh)Power of battery (MW)Battery lifetime (years)Csystem ($)Base————2100.13GA615.23142.14718.82471210.20715.53512.12718.82471212.852615.57552.44158.82471224.172714.9551.99838.82471258.93813.67821.98828.82471269.52PSO614.70781.96408.82471094.352614.69371.93438.82471100.23714.54851.94358.82471102.032714.64571.94968.82471107.31814.62291.95258.82471108.56SSA2614.25021.94578.82471117.57715.24962.02428.82471138.43815.00521.97948.82471140.792713.60881.90178.82471155.51914.10201.84958.82471165.91Table 2
Final optimized decision variable values of the best bus for the IEEE 33-bus system.
AlgorithmsBest bus locationFourier coefficient valuesGA6a1b1a2b2a3b3a4b5−0.0002−5.6252−1.38360.79310.00010.0516−0.01950.0006a5b5a6b6a7b7a8b8−0.0662−0.0125−0.1265−0.00780.00010.0183−0.00250.0781PSO6a1b1a2b2a3b3a4b50.6633−5.3813−1.28460.6520−0.10310.02730.03160.0829a5b5a6b6a7b7a8b8−0.00400.0380−0.02180.01310.0154−0.00520.00400.0351SSA26a1b1a2b2a3b3a4b50.7946−5.1942−1.35660.6203−0.07130.0188−0.00950.1346a5b5a6b6a7b7a8b8−0.01400.0194−0.00910.02850.0023−0.01700.03090.0159From Figure4, the state of energy (SoE) expressing the energy stored in the BESS for 24 hours provided by each algorithm is presented, and the SoC can also be observed. It is seen from the figure that the GA needed the largest size of BESS at 15.23 MWh to store the energy from DGs followed by PSO at 14.71 MWh, while SSA needed the smallest BESS size at 14.25 MWh.Figure 4
State of energy (SoE) of the BESS of each algorithm for the IEEE 33-bus system.


### 5.1.2. System Performance Improvement Investigation

The system performance improvements after installing BESS in the IEEE 33-bus system are compared in terms of VDI, real power loss, reactive power loss, and apparent power loss by using each algorithm as presented in Table3, where the base case is the case without the BESS installation. It is observed that the BESS installation could significantly reduce the VDI, real power loss, reactive power loss, and also apparent power loss. PSO provided the best values for all considered terms followed by SSA which gave slightly worse values than those of PSO, while GA obtained the worst improvement compared to those of the other algorithms.Table 3
System performance comparison for the IEEE 33-bus system.
AlgorithmsVoltage deviation index (VDI) (%)Real power loss (MW)Reactive power loss (MVAr)Apparent power loss (MVA)Base127.321.831.262.22GA83.881.591.111.94PSO79.081.561.101.91SSA80.171.581.111.93The voltage profile improvement after the BESS installation can be noticed in Figure5. In this figure, the voltage profiles of the 33rd bus, which generated the worst voltage profile for this system, for 24 hours before and after the BESS installation are shown. Before installing the BESS, in the base case, the voltage was below the lower limit after 7 p.m. However, the voltage profile was moved to be within the limits after the BESS was installed by adopting each algorithm.Figure 5
Voltage profile improvement comparison of each algorithm for the IEEE 33-bus system.The all-day real power loss comparison is expressed in Figure6. It is seen that the real loss was noticeably decreased from 1 a.m. to 9 a.m. after the BESS installation. However, the real power loss was slightly moved up from 9.00 a.m. to 6.00 p.m. after locating the BESS in the system because the BESS also supplied power to the load demand. After 6.00 p.m., the real loss was extremely dropped from the case with the BESS installation, so the all-day real power loss was improved for the case with BESS installation as evident in Table 3.Figure 6
Real power loss comparison of each algorithm for the IEEE 33-bus system.


### 5.1.3. Peak Power Comparison

The peak power comparison at the slack bus for the IEEE 33-bus system is shown in Figure7. It is observed from the base case that the peak power had two directions, flowing into and out of the system. From 1.00 a.m. to 11 a.m. and from about 5.00 p.m. until midnight, the peak power was positive which means the system supplied power to the load demand. However, from 8.00 a.m., the peak power tended to be obviously decreased until the peak power was negative from after 11.00 a.m. to 5.00 p.m. because of the high DG penetration causing the reverse power flow. Moreover, from 5.00 p.m. until midnight, the peak power was increased to almost 3 MW at 10.00 p.m. because of the high demand and low DG penetration resulting in a need for high power generation from the system. After the BESS installation by using each algorithm, the BESS starts charging during the high DG penetration and discharging when the demand rises achieving the peak shaving. So, the peak power was reduced to 1.18 MW, 1.22 MW, and 1.38 MW for PSO, SSA, and GA, respectively, as evident in Figure 7.Figure 7
Peak power comparison of each algorithm for the IEEE 33-bus system.


### 5.1.4. Performance Comparison of the Optimization Algorithms

To further investigate the performance of the optimization algorithms in this system, the comparison of the convergence graphs for the best bus location provided by each algorithm is presented in Figure8. Figure 8(a) shows the convergence graph comparison of each algorithm, and Figure 8(b) presents the expanded version of the convergence curve to clearly notice how each algorithm converged to the optimal solution. It is noticeable that GA firstly converged to its feasible solution, and PSO and SSA converged to their feasible solutions at around the same iteration. However, the last solution obtained by GA is the worst, while that obtained by PSO is the best.Figure 8
(a) Convergence graphs for the best bus location of each algorithm for the IEEE 33-bus system. (b) Expanded version of the convergence graphs.
(a)(b)Moreover, the statistical analysis and convergence time of all algorithms are presented in Table4 to also analyze the performance of the optimization algorithms. It is seen that GA still provided the worst values of worst cost, mean cost, standard deviation, and time. Although PSO generated the best cost value, SSA could give the best mean cost leading to the best standard deviation. The convergence time of PSO is the fastest one followed by SSA and GA, respectively.Table 4
Performance analysis of the optimization algorithm in the IEEE 33-bus system.
AlgorithmsBest cost ($)Worst cost ($)Mean cost ($)Standard deviationTime (s)GA1210.201479.181290.5691.315991PSO1094.351365.771201.8081.275895SSA1117.571430.231196.7478.225947For the IEEE 33-bus system, when compared to the base case, PSO could provide the best system cost reduction when installing the BESS at bus 6, while SSA gave the second-best system cost reduction when the BESS was located at bus 26, and GA obtained the worst system cost reduction when the BESS was installed at bus 6. PSO was also the best algorithm to improve system performance in terms of VDI, real power loss, reactive power loss, and apparent power loss reductions followed by SSA and GA; however, all considered algorithms could significantly decrease all-day real loss and also move the out-of-bound voltage profile to be within the limits. In the peak power comparison, PSO was the best algorithm to reduce the peak power followed by SSA and GA, while all algorithms could vanish the reverse power flow caused by the high DG penetration. To summarize the performance of the considered algorithm for the IEEE 33-bus system, PSO was the best algorithm to find the optimal location and sizing of the BESS installation for minimizing system cost and enhancing system performance. SSA and GA were the second- and third-best algorithms for obtaining the location and sizing of the BESS; however, the performance of SSA was slightly worse than that of PSO, while the performance of GA was obviously worse than that of PSO and SSA.


## 5.1.1. Optimal Location and Sizing of the BESS

Firstly, the optimal location and sizing of the BESS installation were obtained in the IEEE 33-bus system by using GA, PSO, and SSA. The best five-bus locations where system cost was considered as the objective function to be minimized provided by each algorithm are compared to the case without the BESS which is the base case as expressed in Table1. It can be observed from the top three best objective values that PSO could give the least system costs with 47.89%, 47.61%, and 47.53% reductions compared to that of the base case when installing the BESS at the 6th, 26th, and 7th buses, respectively. SSA provided the second-best system costs with 46.79%, 45.79%, and 45.68% decreases when the BESS was located at the 26th, 7th, and 8th buses, respectively, while GA found the worst system cost values with 42.37%, 42.35%, and 41.71% reductions when the locations of the BESS were at the 6th, 7th, and 26th buses, respectively, compared to that of the base case. However, the size, power, and lifetime of the BESS provided by each algorithm were slightly different. For the best bus location of BESS installation, SSA provided the least battery size and power of the battery followed by PSO and GA, while all considered algorithms gave the same values of battery lifetime. The final optimized decision variable values of the best bus for this system are shown in Table 2.Table 1
Optimal location and sizing of the BESS for the IEEE 33-bus system.
AlgorithmsBest bus locationsBattery size (MWh)Power of battery (MW)Battery lifetime (years)Csystem ($)Base————2100.13GA615.23142.14718.82471210.20715.53512.12718.82471212.852615.57552.44158.82471224.172714.9551.99838.82471258.93813.67821.98828.82471269.52PSO614.70781.96408.82471094.352614.69371.93438.82471100.23714.54851.94358.82471102.032714.64571.94968.82471107.31814.62291.95258.82471108.56SSA2614.25021.94578.82471117.57715.24962.02428.82471138.43815.00521.97948.82471140.792713.60881.90178.82471155.51914.10201.84958.82471165.91Table 2
Final optimized decision variable values of the best bus for the IEEE 33-bus system.
AlgorithmsBest bus locationFourier coefficient valuesGA6a1b1a2b2a3b3a4b5−0.0002−5.6252−1.38360.79310.00010.0516−0.01950.0006a5b5a6b6a7b7a8b8−0.0662−0.0125−0.1265−0.00780.00010.0183−0.00250.0781PSO6a1b1a2b2a3b3a4b50.6633−5.3813−1.28460.6520−0.10310.02730.03160.0829a5b5a6b6a7b7a8b8−0.00400.0380−0.02180.01310.0154−0.00520.00400.0351SSA26a1b1a2b2a3b3a4b50.7946−5.1942−1.35660.6203−0.07130.0188−0.00950.1346a5b5a6b6a7b7a8b8−0.01400.0194−0.00910.02850.0023−0.01700.03090.0159From Figure4, the state of energy (SoE) expressing the energy stored in the BESS for 24 hours provided by each algorithm is presented, and the SoC can also be observed. It is seen from the figure that the GA needed the largest size of BESS at 15.23 MWh to store the energy from DGs followed by PSO at 14.71 MWh, while SSA needed the smallest BESS size at 14.25 MWh.Figure 4
State of energy (SoE) of the BESS of each algorithm for the IEEE 33-bus system.


## 5.1.2. System Performance Improvement Investigation

The system performance improvements after installing BESS in the IEEE 33-bus system are compared in terms of VDI, real power loss, reactive power loss, and apparent power loss by using each algorithm as presented in Table3, where the base case is the case without the BESS installation. It is observed that the BESS installation could significantly reduce the VDI, real power loss, reactive power loss, and also apparent power loss. PSO provided the best values for all considered terms followed by SSA which gave slightly worse values than those of PSO, while GA obtained the worst improvement compared to those of the other algorithms.Table 3
System performance comparison for the IEEE 33-bus system.
AlgorithmsVoltage deviation index (VDI) (%)Real power loss (MW)Reactive power loss (MVAr)Apparent power loss (MVA)Base127.321.831.262.22GA83.881.591.111.94PSO79.081.561.101.91SSA80.171.581.111.93The voltage profile improvement after the BESS installation can be noticed in Figure5. In this figure, the voltage profiles of the 33rd bus, which generated the worst voltage profile for this system, for 24 hours before and after the BESS installation are shown. Before installing the BESS, in the base case, the voltage was below the lower limit after 7 p.m. However, the voltage profile was moved to be within the limits after the BESS was installed by adopting each algorithm.Figure 5
Voltage profile improvement comparison of each algorithm for the IEEE 33-bus system.The all-day real power loss comparison is expressed in Figure6. It is seen that the real loss was noticeably decreased from 1 a.m. to 9 a.m. after the BESS installation. However, the real power loss was slightly moved up from 9.00 a.m. to 6.00 p.m. after locating the BESS in the system because the BESS also supplied power to the load demand. After 6.00 p.m., the real loss was extremely dropped from the case with the BESS installation, so the all-day real power loss was improved for the case with BESS installation as evident in Table 3.Figure 6
Real power loss comparison of each algorithm for the IEEE 33-bus system.


## 5.1.3. Peak Power Comparison

The peak power comparison at the slack bus for the IEEE 33-bus system is shown in Figure7. It is observed from the base case that the peak power had two directions, flowing into and out of the system. From 1.00 a.m. to 11 a.m. and from about 5.00 p.m. until midnight, the peak power was positive which means the system supplied power to the load demand. However, from 8.00 a.m., the peak power tended to be obviously decreased until the peak power was negative from after 11.00 a.m. to 5.00 p.m. because of the high DG penetration causing the reverse power flow. Moreover, from 5.00 p.m. until midnight, the peak power was increased to almost 3 MW at 10.00 p.m. because of the high demand and low DG penetration resulting in a need for high power generation from the system. After the BESS installation by using each algorithm, the BESS starts charging during the high DG penetration and discharging when the demand rises achieving the peak shaving. So, the peak power was reduced to 1.18 MW, 1.22 MW, and 1.38 MW for PSO, SSA, and GA, respectively, as evident in Figure 7.Figure 7
Peak power comparison of each algorithm for the IEEE 33-bus system.


## 5.1.4. Performance Comparison of the Optimization Algorithms

To further investigate the performance of the optimization algorithms in this system, the comparison of the convergence graphs for the best bus location provided by each algorithm is presented in Figure8. Figure 8(a) shows the convergence graph comparison of each algorithm, and Figure 8(b) presents the expanded version of the convergence curve to clearly notice how each algorithm converged to the optimal solution. It is noticeable that GA firstly converged to its feasible solution, and PSO and SSA converged to their feasible solutions at around the same iteration. However, the last solution obtained by GA is the worst, while that obtained by PSO is the best.Figure 8
(a) Convergence graphs for the best bus location of each algorithm for the IEEE 33-bus system. (b) Expanded version of the convergence graphs.
(a)(b)Moreover, the statistical analysis and convergence time of all algorithms are presented in Table4 to also analyze the performance of the optimization algorithms. It is seen that GA still provided the worst values of worst cost, mean cost, standard deviation, and time. Although PSO generated the best cost value, SSA could give the best mean cost leading to the best standard deviation. The convergence time of PSO is the fastest one followed by SSA and GA, respectively.Table 4
Performance analysis of the optimization algorithm in the IEEE 33-bus system.
AlgorithmsBest cost ($)Worst cost ($)Mean cost ($)Standard deviationTime (s)GA1210.201479.181290.5691.315991PSO1094.351365.771201.8081.275895SSA1117.571430.231196.7478.225947For the IEEE 33-bus system, when compared to the base case, PSO could provide the best system cost reduction when installing the BESS at bus 6, while SSA gave the second-best system cost reduction when the BESS was located at bus 26, and GA obtained the worst system cost reduction when the BESS was installed at bus 6. PSO was also the best algorithm to improve system performance in terms of VDI, real power loss, reactive power loss, and apparent power loss reductions followed by SSA and GA; however, all considered algorithms could significantly decrease all-day real loss and also move the out-of-bound voltage profile to be within the limits. In the peak power comparison, PSO was the best algorithm to reduce the peak power followed by SSA and GA, while all algorithms could vanish the reverse power flow caused by the high DG penetration. To summarize the performance of the considered algorithm for the IEEE 33-bus system, PSO was the best algorithm to find the optimal location and sizing of the BESS installation for minimizing system cost and enhancing system performance. SSA and GA were the second- and third-best algorithms for obtaining the location and sizing of the BESS; however, the performance of SSA was slightly worse than that of PSO, while the performance of GA was obviously worse than that of PSO and SSA.


## 5.2. IEEE 69-Bus Distribution System

The optimal location and sizing of the BESS are also investigated in a larger system which is the IEEE 69-bus distribution system. The network diagram can be found in Figure9 [49], and the detailed parameter can be obtained from [50]. The substation voltage is 12.66 kV, and the base is set at 10 MVA. To simulate the high DG penetration situation, twelve DGs are installed in this system as shown in Figure 9. Five 0.6 MW wind DGs are installed at the 8th, 12th, 59th, 61st, and 64th buses, and seven 0.6 MW PV DGs are located at the 27th, 33rd, 34th, 35th, 38th, and 41st buses. The PV and WT operating power factor is unity. The active and reactive power demands are 3.802 MW and 2.695 MVAr, respectively. The time-variant load demand and generation of DGs from WT and PV of this system are shown in Figure 10 [23].Figure 9
Single-line diagram of the IEEE 69-bus distribution system.Figure 10
Time-variant load demand and generation of DGs from WT and PV for the IEEE 69-bus system.


### 5.2.1. Optimal Location and Sizing of the BESS

In this system, the optimal location and sizing of the BESS were also found by adopting three algorithms: GA, PSO, and SSA. The best five bus locations of the BESS installation obtained from each algorithm by considering the minimum system cost as the objective function are depicted in Table5 compared to the base case. It is noticeable that PSO provided the best system cost with a 57.41% reduction when the BESS was installed at the 20th bus followed by 57.27% and 57.26% reductions at the 15th and 16th buses, respectively, compared to the cost of the base case. In addition, SSA could obtain system costs with 57.27%, 57.00%, and 56.87% decreases, which were very competitive with those of PSO, when locating the BESS at the 15th, 12th, and 59th buses, respectively. However, GA gave the worst system costs, which were much more than those of PSO and SSA, with only 28.87%, 23.39%, and 20.05% reductions when the BESS was located at the 67th, 11th, and 7th buses, respectively. It can also be observed that the battery size and power of the battery provided by GA were much more than those of PSO and SSA. Besides, the battery lifetime solved by GA was slightly shorter than those of PSO and SSA. The final optimized decision variable values of the best bus for this system are presented in Table 6.Table 5
Optimal location and sizing of the BESS for the IEEE 69-bus system.
AlgorithmsBest bus locationsBattery size (MWh)Power of battery (MW)Battery lifetime (years)Csystem ($)Base————2029.32GA6717.65203.56518.74841493.851114.91192.92578.20111608.96726.75094.07018.66871679.08616.46064.09747.67931689.156615.63843.12007.80201986.10PSO206.70441.21918.8247894.48156.73221.21228.8154897.39167.02551.21168.8247897.62147.06341.20618.8247899.93137.57351.20148.8247902.05SSA156.88221.21048.8247897.37128.01031.19708.8247903.01594.36670.76718.8247905.84604.10240.72798.8247906.17613.81660.68448.8247906.40Table 6
Final optimized decision variable values of the best bus for the IEEE 69-bus system.
AlgorithmBest bus locationFourier coefficient valuesGA67a1b1a2b2a3b3a4b51.8151−5.6228−2.11360.23910.3124−0.6408−0.23520.1795a5b5a6b6a7b7a8b8−0.0823−0.2849−0.1567−0.2150−0.01200.07490.1181−0.1581PSO20a1b1a2b2a3b3a4b50.4767−2.2149−0.77090.2915−0.0956−0.14120.00720.1798a5b5a6b6a7b7a8b8−0.06350.08070.08160.01500.05370.09480.0054−0.0175SSA15a1b1a2b2a3b3a4b50.5586−2.2881−0.75070.2439−0.1036−0.10440.00790.2130a5b5a6b6a7b7a8b8−0.08730.07750.06950.00740.04540.0683−0.0034−0.0260The SoE of the BESS of all considered algorithms is plotted in Figure11, and the SoC can be noticed in this figure. It is observed from the best BESS location that the SoE provided by GA was maximum at 17.65 MWh, while the SoE generated by PSO and SSA were maximum at only 6.70 and 6.88 MWh, respectively. So, the BESS of GA needed a much larger battery size than those of PSO and SSA.Figure 11
SoE of the BESS of each algorithm for the IEEE 69-bus system.


### 5.2.2. System Performance Improvement Investigation

Table7 presents the performance improvement comparison after the BESS installation by applying the considered algorithms for the IEEE 69-bus system, where the base case is the case without the BESS. It can be seen from the table that SSA provided the best VDI compared to that of other algorithms and the base case followed by PSO, while GA obtained worse VDI compared to the other algorithms including the base case. For the power loss comparison, PSO could provide the least real power loss, reactive power loss, and also apparent power loss, and SSA could give the second-least power losses. However, GA gave more losses than those of the base case.Table 7
System performance comparison for the IEEE 69-bus system.
AlgorithmsVoltage deviation index (VDI) (%)Real power loss (MW)Reactive power loss (MVAr)Apparent power loss (MVA)Base133.802.1300.9832.346GA142.192.4161.0822.648PSO110.721.9840.9212.188SSA106.251.9950.9242.198Figure12 shows the all-day voltage profile of the 65th bus, which is the bus with the worst voltage profile of this system, for all cases. It is observed from the base case that the voltage was below the lower limit from 8.00 a.m. to 10.00 a.m. and from 9.00 p.m. to 11.30 p.m. After the BESS installation by using each algorithm, the all-day voltage profiles were progressed to be within the limits. Although the VDI provided by GA as in Table 7 was more than that of the base case, the all-day voltage profile generated by GA was within the voltage limits, while the base case produced the out-of-bound voltage profile.Figure 12
Voltage profile improvement comparison of each algorithm for the IEEE 69-bus system.The real loss comparison for 24 hours for each case is depicted in Figure13. This figure can confirm (Table 7) that the power losses after the BESS installation by using PSO and SSA were enhanced from the base case. It is observed that the real loss provided by GA was much larger than those of SSA, PSO, and the base case from 9.00 a.m. to 4.00 p.m. This means that installing BESS by using GA provided a huge amount of real loss when the BESS supplied power to the load demand during the day, while some real loss was decreased during the night. However, the total real loss for 24 hours generated from installing BESS by GA was more than that of the base case as evident in Table 7.Figure 13
Real power loss comparison of each algorithm for the IEEE 69-bus system.


### 5.2.3. Peak Power Comparison

The peak power comparison between the cases with and without BESS is plotted in Figure14. From the base case, the peak power of the system without the BESS started dropping from 8.00 a.m. until the reverse power flow occurred at around 9.30 a. m. until 6.00 p.m. due to the high DG penetration. In addition, the peak demand reached the maximum value which is 2.59 MW at 10.00 p.m. when the DG penetration was low. For the case with the BESS installation, the reverse power flow still occurred; however, the amount of the reverse power flow was improved from −2.50 MW for the base case to −1.46 MW, −1.62 MW, and −1.63 MW for GA, SSA, and PSO, respectively, when the BESS started charging. Besides, the installed BESS could also accomplish the peak shaving from 2.59 MW for the base case to 1.47 MW, 1.70 MW, and 1.78 MW for GA, SSA, and PSO, respectively, because of the BESS discharging.Figure 14
Peak power comparison of each algorithm for the IEEE 69-bus system.


### 5.2.4. Performance Comparison of the Optimization Algorithms

The convergence graphs for the best bus location of all algorithms are expressed in Figure15 to verify the performance of the optimization algorithm in the large 69-bus system, where Figure 15(a) presents the full convergence graphs of each algorithm and Figure 15(b) shows the expanded convergence graphs to obviously observe the convergence of each algorithm. It can be seen that GA quickly starts converging at around the 20th iteration, while SSA and PSO start converging at about the 520th and 640th iterations, respectively. However, the last solution generated by GA was much more than those of PSO and SSA, and the last solutions provided by PSO and SSA are very competitive.Figure 15
(a) Convergence graphs for the best bus location of each algorithm for the IEEE 33-bus system. (b) Expanded version of the convergence graphs.
(a)(b)To further analyze the performance of these optimization algorithms in this system, the statistical results and convergence time of all algorithms were obtained as in Table8. It is noticeable that the best cost, worst cost, and mean cost values of GA are much worse than those of PSO and SSA, leading to the very higher value of standard deviation, while PSO and SSA gave close values of best and worst, as well as mean costs, resulting in small standard deviation values. The convergence time of GA is also twice those of PSO and SSA. This means that GA has a problem finding the optimal solution or it might be stuck in the local optima.Table 8
Performance analysis of the optimization algorithm in the IEEE 69-bus system.
AlgorithmsBest cost ($)Worst cost ($)Mean cost ($)Standard deviationTime (s)GA1493.853181.322285.80515.7314482PSO894.48929.98909.579.227731SSA897.37929.93912.667.267857For the IEEE 69-bus distribution system, the best location of the BESS was at the 20th bus giving the most system cost reduction which was solved by PSO, and SSA found slightly less system cost reduction compared to PSO when locating the BESS at the 15th bus. However, GA generated much less system cost reduction compared to the other algorithms when installing the BESS at the 67th bus which was the best bus found by GA. SSA was the algorithm to achieve the best voltage profile improvement by providing the least VDI followed by PSO, while PSO could generate the least losses followed by SSA. GA provided more VDI and all losses compared to SSA, PSO, and also the base case. However, all algorithms could enhance the voltage profile to be within the limits. For the comparison of peak power, GA was the best one to improve the reverse power flow followed by SSA and PSO when the DG penetration was high. GA was also the best algorithm to shave the peak demand followed by SSA and PSO. In conclusion for this system, although GA was the best algorithm for improving the reverse power flow and shaving the peak, it generated very high system cost, VDI, and losses compared to those of PSO and SSA. So, GA is considered to be the worst algorithm for this system. The performances of SSA and PSO are very competitive, since they could achieve the improvement in different terms.Overall, in the small distribution system which is the IEEE 33-bus system, PSO was the best algorithm to find the optimal location and sizing of the BESS installation for minimizing system cost and improving system performance, while SSA was the second-best one with a very competitive performance. However, GA was obviously the worst algorithm for this system. In the larger distribution system which is the IEEE 69-bus system, PSO and SSA also have a competitive performance where they could obtain the enhancement in different terms, while GA was the worst algorithm to find the optimal location and sizing of the BESS. Thus, PSO must be selected to find the optimal location and sizing of the BESS in the IEEE 33-bus system while, in the IEEE 69-bus system, PSO and SSA could be judiciously chosen for enhancing the system performance in different terms.


## 5.2.1. Optimal Location and Sizing of the BESS

In this system, the optimal location and sizing of the BESS were also found by adopting three algorithms: GA, PSO, and SSA. The best five bus locations of the BESS installation obtained from each algorithm by considering the minimum system cost as the objective function are depicted in Table5 compared to the base case. It is noticeable that PSO provided the best system cost with a 57.41% reduction when the BESS was installed at the 20th bus followed by 57.27% and 57.26% reductions at the 15th and 16th buses, respectively, compared to the cost of the base case. In addition, SSA could obtain system costs with 57.27%, 57.00%, and 56.87% decreases, which were very competitive with those of PSO, when locating the BESS at the 15th, 12th, and 59th buses, respectively. However, GA gave the worst system costs, which were much more than those of PSO and SSA, with only 28.87%, 23.39%, and 20.05% reductions when the BESS was located at the 67th, 11th, and 7th buses, respectively. It can also be observed that the battery size and power of the battery provided by GA were much more than those of PSO and SSA. Besides, the battery lifetime solved by GA was slightly shorter than those of PSO and SSA. The final optimized decision variable values of the best bus for this system are presented in Table 6.Table 5
Optimal location and sizing of the BESS for the IEEE 69-bus system.
AlgorithmsBest bus locationsBattery size (MWh)Power of battery (MW)Battery lifetime (years)Csystem ($)Base————2029.32GA6717.65203.56518.74841493.851114.91192.92578.20111608.96726.75094.07018.66871679.08616.46064.09747.67931689.156615.63843.12007.80201986.10PSO206.70441.21918.8247894.48156.73221.21228.8154897.39167.02551.21168.8247897.62147.06341.20618.8247899.93137.57351.20148.8247902.05SSA156.88221.21048.8247897.37128.01031.19708.8247903.01594.36670.76718.8247905.84604.10240.72798.8247906.17613.81660.68448.8247906.40Table 6
Final optimized decision variable values of the best bus for the IEEE 69-bus system.
AlgorithmBest bus locationFourier coefficient valuesGA67a1b1a2b2a3b3a4b51.8151−5.6228−2.11360.23910.3124−0.6408−0.23520.1795a5b5a6b6a7b7a8b8−0.0823−0.2849−0.1567−0.2150−0.01200.07490.1181−0.1581PSO20a1b1a2b2a3b3a4b50.4767−2.2149−0.77090.2915−0.0956−0.14120.00720.1798a5b5a6b6a7b7a8b8−0.06350.08070.08160.01500.05370.09480.0054−0.0175SSA15a1b1a2b2a3b3a4b50.5586−2.2881−0.75070.2439−0.1036−0.10440.00790.2130a5b5a6b6a7b7a8b8−0.08730.07750.06950.00740.04540.0683−0.0034−0.0260The SoE of the BESS of all considered algorithms is plotted in Figure11, and the SoC can be noticed in this figure. It is observed from the best BESS location that the SoE provided by GA was maximum at 17.65 MWh, while the SoE generated by PSO and SSA were maximum at only 6.70 and 6.88 MWh, respectively. So, the BESS of GA needed a much larger battery size than those of PSO and SSA.Figure 11
SoE of the BESS of each algorithm for the IEEE 69-bus system.


## 5.2.2. System Performance Improvement Investigation

Table7 presents the performance improvement comparison after the BESS installation by applying the considered algorithms for the IEEE 69-bus system, where the base case is the case without the BESS. It can be seen from the table that SSA provided the best VDI compared to that of other algorithms and the base case followed by PSO, while GA obtained worse VDI compared to the other algorithms including the base case. For the power loss comparison, PSO could provide the least real power loss, reactive power loss, and also apparent power loss, and SSA could give the second-least power losses. However, GA gave more losses than those of the base case.Table 7
System performance comparison for the IEEE 69-bus system.
AlgorithmsVoltage deviation index (VDI) (%)Real power loss (MW)Reactive power loss (MVAr)Apparent power loss (MVA)Base133.802.1300.9832.346GA142.192.4161.0822.648PSO110.721.9840.9212.188SSA106.251.9950.9242.198Figure12 shows the all-day voltage profile of the 65th bus, which is the bus with the worst voltage profile of this system, for all cases. It is observed from the base case that the voltage was below the lower limit from 8.00 a.m. to 10.00 a.m. and from 9.00 p.m. to 11.30 p.m. After the BESS installation by using each algorithm, the all-day voltage profiles were progressed to be within the limits. Although the VDI provided by GA as in Table 7 was more than that of the base case, the all-day voltage profile generated by GA was within the voltage limits, while the base case produced the out-of-bound voltage profile.Figure 12
Voltage profile improvement comparison of each algorithm for the IEEE 69-bus system.The real loss comparison for 24 hours for each case is depicted in Figure13. This figure can confirm (Table 7) that the power losses after the BESS installation by using PSO and SSA were enhanced from the base case. It is observed that the real loss provided by GA was much larger than those of SSA, PSO, and the base case from 9.00 a.m. to 4.00 p.m. This means that installing BESS by using GA provided a huge amount of real loss when the BESS supplied power to the load demand during the day, while some real loss was decreased during the night. However, the total real loss for 24 hours generated from installing BESS by GA was more than that of the base case as evident in Table 7.Figure 13
Real power loss comparison of each algorithm for the IEEE 69-bus system.


## 5.2.3. Peak Power Comparison

The peak power comparison between the cases with and without BESS is plotted in Figure14. From the base case, the peak power of the system without the BESS started dropping from 8.00 a.m. until the reverse power flow occurred at around 9.30 a. m. until 6.00 p.m. due to the high DG penetration. In addition, the peak demand reached the maximum value which is 2.59 MW at 10.00 p.m. when the DG penetration was low. For the case with the BESS installation, the reverse power flow still occurred; however, the amount of the reverse power flow was improved from −2.50 MW for the base case to −1.46 MW, −1.62 MW, and −1.63 MW for GA, SSA, and PSO, respectively, when the BESS started charging. Besides, the installed BESS could also accomplish the peak shaving from 2.59 MW for the base case to 1.47 MW, 1.70 MW, and 1.78 MW for GA, SSA, and PSO, respectively, because of the BESS discharging.Figure 14
Peak power comparison of each algorithm for the IEEE 69-bus system.


## 5.2.4. Performance Comparison of the Optimization Algorithms

The convergence graphs for the best bus location of all algorithms are expressed in Figure15 to verify the performance of the optimization algorithm in the large 69-bus system, where Figure 15(a) presents the full convergence graphs of each algorithm and Figure 15(b) shows the expanded convergence graphs to obviously observe the convergence of each algorithm. It can be seen that GA quickly starts converging at around the 20th iteration, while SSA and PSO start converging at about the 520th and 640th iterations, respectively. However, the last solution generated by GA was much more than those of PSO and SSA, and the last solutions provided by PSO and SSA are very competitive.Figure 15
(a) Convergence graphs for the best bus location of each algorithm for the IEEE 33-bus system. (b) Expanded version of the convergence graphs.
(a)(b)To further analyze the performance of these optimization algorithms in this system, the statistical results and convergence time of all algorithms were obtained as in Table8. It is noticeable that the best cost, worst cost, and mean cost values of GA are much worse than those of PSO and SSA, leading to the very higher value of standard deviation, while PSO and SSA gave close values of best and worst, as well as mean costs, resulting in small standard deviation values. The convergence time of GA is also twice those of PSO and SSA. This means that GA has a problem finding the optimal solution or it might be stuck in the local optima.Table 8
Performance analysis of the optimization algorithm in the IEEE 69-bus system.
AlgorithmsBest cost ($)Worst cost ($)Mean cost ($)Standard deviationTime (s)GA1493.853181.322285.80515.7314482PSO894.48929.98909.579.227731SSA897.37929.93912.667.267857For the IEEE 69-bus distribution system, the best location of the BESS was at the 20th bus giving the most system cost reduction which was solved by PSO, and SSA found slightly less system cost reduction compared to PSO when locating the BESS at the 15th bus. However, GA generated much less system cost reduction compared to the other algorithms when installing the BESS at the 67th bus which was the best bus found by GA. SSA was the algorithm to achieve the best voltage profile improvement by providing the least VDI followed by PSO, while PSO could generate the least losses followed by SSA. GA provided more VDI and all losses compared to SSA, PSO, and also the base case. However, all algorithms could enhance the voltage profile to be within the limits. For the comparison of peak power, GA was the best one to improve the reverse power flow followed by SSA and PSO when the DG penetration was high. GA was also the best algorithm to shave the peak demand followed by SSA and PSO. In conclusion for this system, although GA was the best algorithm for improving the reverse power flow and shaving the peak, it generated very high system cost, VDI, and losses compared to those of PSO and SSA. So, GA is considered to be the worst algorithm for this system. The performances of SSA and PSO are very competitive, since they could achieve the improvement in different terms.Overall, in the small distribution system which is the IEEE 33-bus system, PSO was the best algorithm to find the optimal location and sizing of the BESS installation for minimizing system cost and improving system performance, while SSA was the second-best one with a very competitive performance. However, GA was obviously the worst algorithm for this system. In the larger distribution system which is the IEEE 69-bus system, PSO and SSA also have a competitive performance where they could obtain the enhancement in different terms, while GA was the worst algorithm to find the optimal location and sizing of the BESS. Thus, PSO must be selected to find the optimal location and sizing of the BESS in the IEEE 33-bus system while, in the IEEE 69-bus system, PSO and SSA could be judiciously chosen for enhancing the system performance in different terms.


## 6. Conclusions

In this work, the optimal location and sizing of the BESS installation for performance improvement in high DG penetration distribution network are presented, where the DGs consist of WT and PV. Three algorithms, GA, PSO, and SSA, were applied to find the optimal solutions in the IEEE 33- and 69-bus distribution systems. The system performance improvement was compared in terms of system cost, voltage profile improvement, power losses, and peak power. The simulation results found that PSO was the best algorithm to find the optimal location and sizing of the BESS with the least system cost, the best voltage profile improvement, the least power losses, and the best peak shaving for the IEEE 33-bus system. In this system, SSA was the second-best algorithm to provide optimal location and sizing of the BESS with solutions that are very competitive with those of PSO, while GA was the worst algorithm. All three algorithms could vanish the reverse power flow that occurred from the high DG penetration during the day. For the IEEE 69-bus system, PSO was the best algorithm to give the optimal location and sizing of the BESS with the least system cost followed by SSA with slightly more system cost. SSA was the best one to improve the voltage profile with the least VDI followed by PSO, while PSO could find the least power losses followed by SSA. Although GA could achieve the best peak shaving and reverse power flow decreasing in this system, the system cost, VDI, and power losses provided by GA were very high. In conclusion, PSO and SSA were, respectively, the best and second-best algorithms for providing the optimal location and sizing in the IEEE 33-bus system, and PSO and SSA were the best algorithms for providing better solutions in different terms with very competitive performance for the IEEE 69-bus system. GA was considered the worst algorithm for both IEEE 33- and 69-bus distribution systems in finding the optimal location and sizing of the BESS. However, all of the considered algorithms could improve the voltage profile by moving the out-of-bound voltage profile to be within the limits in all considered systems. So, the operators must judiciously select the suitable algorithms to find the optimal location and sizing for improving the system performance in different aspects and system sizes.In future work, this approach can be applied to find the optimal location and sizing of the BESS installation in real distribution networks to improve the performance of high DG penetration distribution networks. Moreover, if the size of the distribution system increases, the BESS candidate bus should be considered as the decision variable of the optimization algorithm to decrease the operator burden. Two candidate buses can also be considered at a time to further improve system performance at a high DG penetration level.



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*Source: 6361243-2022-06-01.xml*