# Dual Strategy of Reconfiguration with Capacitor Placement for Improvement Reliability and Power Quality in Distribution System

Authors: Ali Nasser Hussain; Wathiq Rafa Abed; Mohanad Muneer Yaqoob
Journal: Journal of Engineering
 (2023)

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## Abstract

The demand for electrical power has been increasing rapidly due to higher industrial output and deregulation. The concerns have been raised about the ability of distribution networks to provide adequate power for the customers with an appropriate level of quality and reliability. To ameliorate the performance of the radial distribution system (RDS), the optimal capacitor placement (OCP), and the distribution system reconfiguration (DSR) strategies have been implemented in the current work to achieve the highest power quality and system reliability in a balanced manner at the same time. Three different scenarios were implemented, the first scenario of dual sequential (OCP after DSR), the second scenario of dual sequential (DSR after OCP), and the third scenario of dual simultaneous (DSR with OCP). These scenarios were tested on typical 33 and 69 bus IEEE RDS using the binary salp swarm algorithm (BSSA) based on the multiobjective functions (MOFs), in order to identify the most effective scenario performance that achieved the highest power quality and system reliability. The MOF was formulated to improve the power quality by increasing the voltage buses and reducing the power losses. While the constraints include limits of system reliability indices to provide optimal constraints on negative interactions of power quality. The simulation results demonstrate that the second scenario of dual sequential (DSR after OCP) provide superior in comparison with the first scenario of dual sequential (OCP after DSR) for enhancing the RDS reliability indices, voltage buses, and reducing power losses. Finally, the best result can be realized with dual simultaneous (DSR and OCP) in the third scenario compared to the dual sequential scenarios.


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## Body

## 1. Introduction

Distribution system failures cause 80% of all consumer outages, according to utility data. Moreover, the majority of customers are linked at the level of distribution, which represents the highest proportion of investment expenditures. Consequently, enhancing the reliability of RDS leads to raising the chances of the overall electrical power system to operate without failure. Therefore, efficient computing methodologies are required to assess the reliability of RDS [1, 2].The electrical network operator needs to provide electric power to the consumers while maintaining suitable levels of reliability and keeping the node voltages within allowable limits [3]. To reduce the fault currents and an efficient configuration of protective devices, the distribution system (DS) is built as a radial structure [4, 5]. RDS is reconfigured utilizing the normally open (N.O), as well as normally close (N.C) switches to establish the radial limitation, which improves overall performance [6, 7]. Numerous issues with RDS, including increased active losses, bus voltage variations, overloading, and off-balance loads can be resolved by utilizing a variety of ways. The following methods are suggested for resolving the aforementioned RDS issues: distributed generation (DG), OCP, and DSR [8–10].In conjunction with increased the demand for electric power, the scarcity of fossil fuel resources with its high costs, as well as the environmental problems resulting from it such as global warming for example. So, the need to preserve the environment by reducing air pollution is essential [11–13]. This explained why the OCP and DSR techniques have been an important topic for researchers in the recent years. The ability of capacitors to provide the reactive power has contributed to the improvement of the voltage profile and power factor and thus reduced the losses. So, the optimal placement of capacitors in DS is one of the important things nowadays. Depending on how and where the capacitors are positioned in the system, the advantages of this sort of correction may vary [14–17]. Also, the RDS reconfiguration technique is presented as the most economical strategy because the installation and operating costs for DG or capacitors are not included [18]. The optimal solutions for these problems are solved using artificial intelligence and optimization-based algorithms. Moreover, the OCP and DSR have been subjected to numerous studies, and various approaches with various objective functions have been used to model the network and address the problems using optimization algorithms such as improved particle swarm optimization (IPSO), grey wolf optimization (GWO), and flower pollination algorithm (FPA) [19–21].Sudhakara and Reddy for the best placement of DSR published a metaheuristic optimization method that depends on the whale optimization algorithm (WOA) in IEEE DS using 33 and 119 buses. The DSR problem was solved using the WOA algorithm. This method provides a high voltage for the buses despite having small active power losses of 139.5697 kW, which is utilized to lower active losses and raise the voltage for each bus in the standard networks [22]. Furthermore, Diab and Rezk used a new optimization algorithm to detect the OCP and DSR using dragonfly optimization (DFO), GWO, and moth-flame algorithm (MFA). In this work, the performance and efficiency of these algorithms are validated using 33, 69, and 118-bus IEEE systems. Also, the MATLAB/Simulink software was used to assess the convergence performance for tested RDSs [23]. Chakrabarti et al. presented a DSR technique which maximizes the reliability of IEEE 13-bus RDS using the binary PSO algorithm that is used to determine the optimal configuration of switches in the network. The reliability is calculated by using the Monte Carlo simulation technique [24]. Sedighizadeh et al. presented a new approach based on the dual and simultaneous of DSR and OCP technologies with a usual optimization process of improving the binary PSO. This method has been tested for 16 and 33 bus RDSs to improve the voltage profile and reduce active losses [25]. Reddy and Reddy have applied a sequential approach to solving DSR and OCP problems. Ant line optimization algorithm (ALO) is used to find the best OCP size and location for RDS after implementing the DSR technique. The test was conducted to reduce active loss and improve saving on the two IEEE-33 and IEEE-69 RDS. The results demonstrate the success of the proposed approach in which the active power losses are reduced by 44.97% and 67.31% when the OCP is installed for the reconfigured network of 33 buses and 69 buses, respectively, and the net savings are increased to 82,944 $ and 75,456 $ [26]. Gallego et al. introduced the mixed linear programming (MILP) model for simultaneous DSR and OCP solution in RDS. This optimization process is carried out in order to reduce the overall cost, reduce active loss, and optimize the voltage profile. This approach is applied to IEEE-(33, 69, 83, 119, 136, 202, and 417) bus RDSs. The optimal result obtained via this technique demonstrated that the simultaneous technique of optimal DSR with OCP is able to improve the voltage profile and reduce both total and capacitor costs. Also, the results show the active loss percentage reduced to 54.28%, 68.93%, 30.81%, 46.95%, 21.12%, 26.65%, and 27.90%, respectively, for the RDSs that were used in this test [27]. However, the previous studies had a number of drawbacks, where many of these papers focused on the improvement of power quality or reliability that dealt with separately from others. For example, Tamilselvan et al. presented a single objective function to reduce the losses for RDS, while neglecting to include the improvement of voltage profile and system reliability as well [28]. In contrast, other researchers presented several studies to improve the reliability individually without paying attention to the effect of power quality.As a result to avoid these drawbacks, the current work presented a new study in which the improvement process considers both aspects of the power quality and reliability of RDS together. The optimization process has been carried out in a balanced manner, where reducing the total losses and enhancing the voltage profile for the distribution system are included as a MOF, and the improvement of reliability was also included as a constraint and a prerequisite for the optimization process.In this study, three scenarios for dual sequentially OCP after DSR, DSR after OCP, and dual-simultaneous DSR and OCP based on the BSSA optimization method were implemented on 33 and 69 IEEE buses RDS. Therefore, the best capacitor placement, size, and optimum structure of RDS are chosen to reduce the active losses and improve voltage for all buses with a comprehensive enhancement of system reliability using this optimization method. Moreover, MATLAB software environmental is used to test the presented RDS with using the m-file function tool.


## 2. Materials and Methods

The load flow, MOF, reliability assessment, RDS constraints, and BSSA algorithm that applied in this study are described and explained in detail in this section.


### 2.1. Load Flow Analysis for RDS

The distribution networks use conductors that have a high ratio of R/X, a radial construction with many nodes (buses), branches, DG, and complicated topology configurations that can be altered for repair tasks and contingency operations [17, 29]. Also, the ability of load flow techniques to perform the calculations relating for RDS such as current, voltage, active power losses, and total cost has enhanced their significance recently.Due to RDS radial construction, high resistance to reactance ratio, and imbalanced nature of the loads, standard approaches were unable to provide quick convergence for load flow solution. The backward/forward sweep technique was created and published [30]. However, when applied the computer code of the backward/forward sweep algorithm, the authors did not clarify how determined each branch end in automatically form or where to begin the backward computation. The answer is found by straightforward matrix multiplication of the two matrices bus injection to bus current (BIBC) and bus current to bus voltage (BCBV), which were developed from the network topological structure as part of a direct technique of backward/forward sweep reported in reference [31]. The next three crucial stages are defined beginning at the terminal node, while taking into account the electrical properties shown in Figure 1.Step 1 (computation of the nodal current): by using equation (1), the current injection at each node i can be obtained as follows [31]:(1)Iik=conjPn−i+j∗Qn−iVn−ik,i=1,2,3,⋯,n,wherePn−i and Qn−i are active and reactive power injection at node i, respectively, and the node voltage Vn−ik.Step 2 (backward sweep): beginning with the last branch, the currentJi+1 for any branch from node i to the node i+1 is calculated from equation (2) as follows:(2)Jn−ik=−conjPn−i+j∗Qn−iVn−ik+∑rJn−rkr=1,where∑rJn−rk represents current in branches coming from node (i).Step 3 (forward sweep): using equation (3), the node adjusted voltages beginning at the root bus.(3)Vik=Vi−1k−ZiJik,i=1,2,⋯,n,whereZi symbolize the impedance of the branch.Figure 1
The load flow analysis in RDS.The aforementioned three processes are repeated until the voltage levels in all nodes at the current iteration and the preceding fall below a tolerance limitε.(4)VK+1−VK<ε.


### 2.2. Objective Function

Figure2 shows the MOF schematic used in this study. The MOF was formulated to minimize the active power losses and maximize the voltage profile. The MOF is used in this instance to achieve the best OCP and DSR in the RDS.Figure 2
The MOF diagram.The MOF can be represented as the following equations [32]:(5)OF1=MinimizePT,L,PT,L=∑a=1NbPL,aKW,PL,a=Ia2∗RaKW,where PT,L, PL,a, Nb, Ia, and Ra represent the total real power loss, the loss per branch a, number of branches, flow of current in branch a, and resistance of branch a.To enhancement the voltage profile, the voltage must stay within normal limits.(6)OF2=VG∗rev+CG∗rei,where VG, CG, rev, and rei represent consecutively bus voltage limits, current of branch limits, penalty factor for bus voltage (when the bus voltage is within permissible limits, this factor equals 0), and penalty factor for branch current (if the branch current does not exceed the thermal limit, this equals 0).Therefore,(7)MOF=OF1+OF2.


### 2.3. Reliability Assessment

The word reliability refers to a system’s ability to execute its intended purpose, i.e., analysis of the ability of the distribution system to meet the needs of load [33]. The reliability evaluation of the entire network is based on the reliability of each part included in this network which has two states, either an operating state or a failed state. This enables to distinct the network state by identifying the state of components. The failure probability of power system components owing to outages of lines, transformers, and generators may be used to calculate the system’s reliability. A line, transformer, and generator outage may have more than one failure condition so the reliability analysis of RDS is of high importance for continuous operation [34].Different reliability indices can be used to represent the results of a reliability study. Reliability indices are used to assess the degree or relevance of a system outage [33]. To execute the reliability evaluation, a suitable set of indices must be determined based on the application. It is generally typical practice in the electric utility business to measure and assess reliability performance using standard IEEE reliability indices. The amount of outage length, repetition of outages, availability of a system, and reaction time are among the reliability indices. The reliability indices standard deviation informs distribution engineers about the expected range of yearly values.Three fundamentals load point indices may be used to computation the indices of reliability for RDS as the following [35]:(1)
Average failure rate at load point (i), λi which is written as following equation (8):(8)λi=∑jϵNeλe,j,whereNe represents the total number of elements whose fault would interrupt load point (i) and λe,j represents the average failure rate at load point (i).(2)
Annual outage duration at load point (i), Ui (an hour per year):(9)Ui=∑jϵNeλe,j∙ri,j,whereri,j is failure duration at load point (i) owing to a failed element j.(3)
Average outage duration at load point (i), ri (hours) as follows:(10)ri=Uiλi.Typically, a measure of RDS reliability is considered as the effects of a prolonged interruption in terms of the number of users disconnected by an outage. The equations are used to compute sustained interruption indices [36–38].(i)
SAIDI: system average interruption duration index.(11)SAIDI=TotaldurationofallinterruptionTotalnumberofcustomersconnected,SAIDI=∑i=1kUiNi∑i=1kNi,hrC∙yr.(ii)
SAIFI: system average interruption frequency index.(12)SAIFI=TotalnumberofallinterruptionsTotalnumberofcustomersconnected,SAIFI=∑i=1kλiNi∑i=1kNifC∙yr.(iii)
CAIDI: customer average interruption duration index.(13)CAIDI=TotaldurationofallinterruptionTotalnumberofallinterruptions,CAIDI=∑i=1kUiNi∑i=1kλiNihr.(iv)
ASAI: average service availability index.(14)ASAI=TotalnumberofhoursavailabilityTotaldemandhours,ASAI=∑i=1k8760Ni−∑i=1kUiNi∑i=1k8760Nip.u..(v)
EENS: expected energy not supplied.(15)EENS=∑i=1kpiUiMWhryr,wherepi represent the average load for load point i(vi)
AENS: average energy not supplied.(16)AENS=TotaleneragenotsupplieTotalnumberofcustomersconnected,AENS=∑i=1kEENS∑i=1kNiMWhrC∙yr.(vii)
Average service unavailability index (ASUI).(17)ASUI=1−ASAIp.u..


### 2.4. Power Flow and Reliability Assessment Constraints

The following is a description of the power flow and reliability assessment procedure time constraints:


#### 2.4.1. Capacitor Size

The capacitor bank is injected maximum value reactive power into the RDS it should not be above the entire reactive power load and indicated by the following equation (18) [32, 39]:(18)QC,MAX<QL,where QC,MAX is the maximum needed of reactive power amount from capacitor bank in KVAR and QL is the all reactive power for a load of the network. However, in the optimal design of the OCP technique, the size of capacitors in the RDS is very important and it must be less than QL.


#### 2.4.2. Voltage and Current Limit

This limitation is used to ensure that the voltage value of each bus keeps within the required tolerances based on the following equation (19):(19)VMIN≤Vi≤VMAX,where the allowable values of node voltage limited by Vmax=1.05p.u and Vmin=0.95p.u.However, the current at each brunch must be limited as shown in equation (20) as follows:(20)Ii≤Ii,max.


#### 2.4.3. Reliability Constraints

Reliability indices after the optimization process must be better than the base case, as shown in equations as follows:(21)0<SAIDI<SAIDIB,0<SAIFI<SAIFIB,0<CAIDI<CAIDIB,0<AENS<AENSB,ASAI>ASAIB,0<EENS>EENSB,0<ASUI>ASUIB,where SAIDIB, SAIFIB, CAIDIB, AENSB, ASAIB, and ASUIB represent the indices in the base case, and SAIDI, SAIFI, CAIDI, AENS, ASAI, and ASUI are indices after optimization [37].


### 2.5. Optimization-Based BSSA

In 2017, Mirjalili et al. [40] proposed the SSA where this algorithm depends on the navigation and foraging behavior in the seas and oceans as shown in Figure 3. To update the leader location, the following equation (22) is presented [41]:(22)Xj1=Fj+C1ubj−lbjC2+lbj,C3≥0.5,Fj−C1ubj−lbjC2+lbj,C3<0.5,where Xj1 represents the first location of salp in the jth dimension, Fj represents the location of food supply, ubj,lbj are the upper and lower bounds of jth dimension, and the random numbers are denoted by C2 and C3 [0, 1]. While the coefficient C1 is written using the following equation (23):(23)C1=2×e−4t/T2,where t represents the present iteration and T is the total number of iterations. The location of the followers can be written as equation (24) [42] as follows:(24)Xjn=12Xjn+Xjn−1,where n≥2 and Xjn is the site of nth follower in j dimension.Figure 3
Chain of SSA.The salp population is seen as a binary bound of dimension in a binary search issue. The velocity and position values for each particle must be limited to (0 or 1) in order for this method to search in discrete space. So that, the transfer function T.F may be applied as follows [43]:(25)T.FXjnt=11+e−Xjnt.By using T.F, (24) will be changed to as follows:(26)Xjdt+1=0ifrand<T.FXjdt+1,1ifrand≥T.FXjdt+1,where Xjdt+1 is the j−th element at dth dimension in X solution.The proposed BSSA is implemented to find the optimal size and location of OCP and optimal topology of DSR that reduces the real power losses, and enhance the voltage profile and reliability. The switches of RDS are represented here as discrete values, where 0 denotes an open switch and 1 denotes a closed switch. The BSSA was carried out which depend on the following steps: (Algorithm1).Algorithm 1: The main steps of binary salp swarm algorithm (BSSA) [43].
(1)
Initialize the search agents, maximum number of iterations, and salp population with considering of the binary bound of dimension(2)
Retain the search agents that satisfies all the constraints(3)
Run the load flow and evaluate the objective function using equation (7)(4)
Calculate the reliability indices of each bus(5)
Obtain the best salp position or leader salp position using equation (22)(6)
Update the value ofC1 using equation (23)(7)
Update the location of the leader using equation (22)(8)
Calculate the probabilities using equation (25) which take the output of equation (22) as an input to equation (26)(9)
Update the followers using equation (24)(10)
Check the program stopping condition, ifiteration<themaximumnumber, go to step 6, otherwise go to step 11(11)
Print the optimal results(12)
End


## 2.1. Load Flow Analysis for RDS

The distribution networks use conductors that have a high ratio of R/X, a radial construction with many nodes (buses), branches, DG, and complicated topology configurations that can be altered for repair tasks and contingency operations [17, 29]. Also, the ability of load flow techniques to perform the calculations relating for RDS such as current, voltage, active power losses, and total cost has enhanced their significance recently.Due to RDS radial construction, high resistance to reactance ratio, and imbalanced nature of the loads, standard approaches were unable to provide quick convergence for load flow solution. The backward/forward sweep technique was created and published [30]. However, when applied the computer code of the backward/forward sweep algorithm, the authors did not clarify how determined each branch end in automatically form or where to begin the backward computation. The answer is found by straightforward matrix multiplication of the two matrices bus injection to bus current (BIBC) and bus current to bus voltage (BCBV), which were developed from the network topological structure as part of a direct technique of backward/forward sweep reported in reference [31]. The next three crucial stages are defined beginning at the terminal node, while taking into account the electrical properties shown in Figure 1.Step 1 (computation of the nodal current): by using equation (1), the current injection at each node i can be obtained as follows [31]:(1)Iik=conjPn−i+j∗Qn−iVn−ik,i=1,2,3,⋯,n,wherePn−i and Qn−i are active and reactive power injection at node i, respectively, and the node voltage Vn−ik.Step 2 (backward sweep): beginning with the last branch, the currentJi+1 for any branch from node i to the node i+1 is calculated from equation (2) as follows:(2)Jn−ik=−conjPn−i+j∗Qn−iVn−ik+∑rJn−rkr=1,where∑rJn−rk represents current in branches coming from node (i).Step 3 (forward sweep): using equation (3), the node adjusted voltages beginning at the root bus.(3)Vik=Vi−1k−ZiJik,i=1,2,⋯,n,whereZi symbolize the impedance of the branch.Figure 1
The load flow analysis in RDS.The aforementioned three processes are repeated until the voltage levels in all nodes at the current iteration and the preceding fall below a tolerance limitε.(4)VK+1−VK<ε.


## 2.2. Objective Function

Figure2 shows the MOF schematic used in this study. The MOF was formulated to minimize the active power losses and maximize the voltage profile. The MOF is used in this instance to achieve the best OCP and DSR in the RDS.Figure 2
The MOF diagram.The MOF can be represented as the following equations [32]:(5)OF1=MinimizePT,L,PT,L=∑a=1NbPL,aKW,PL,a=Ia2∗RaKW,where PT,L, PL,a, Nb, Ia, and Ra represent the total real power loss, the loss per branch a, number of branches, flow of current in branch a, and resistance of branch a.To enhancement the voltage profile, the voltage must stay within normal limits.(6)OF2=VG∗rev+CG∗rei,where VG, CG, rev, and rei represent consecutively bus voltage limits, current of branch limits, penalty factor for bus voltage (when the bus voltage is within permissible limits, this factor equals 0), and penalty factor for branch current (if the branch current does not exceed the thermal limit, this equals 0).Therefore,(7)MOF=OF1+OF2.


## 2.3. Reliability Assessment

The word reliability refers to a system’s ability to execute its intended purpose, i.e., analysis of the ability of the distribution system to meet the needs of load [33]. The reliability evaluation of the entire network is based on the reliability of each part included in this network which has two states, either an operating state or a failed state. This enables to distinct the network state by identifying the state of components. The failure probability of power system components owing to outages of lines, transformers, and generators may be used to calculate the system’s reliability. A line, transformer, and generator outage may have more than one failure condition so the reliability analysis of RDS is of high importance for continuous operation [34].Different reliability indices can be used to represent the results of a reliability study. Reliability indices are used to assess the degree or relevance of a system outage [33]. To execute the reliability evaluation, a suitable set of indices must be determined based on the application. It is generally typical practice in the electric utility business to measure and assess reliability performance using standard IEEE reliability indices. The amount of outage length, repetition of outages, availability of a system, and reaction time are among the reliability indices. The reliability indices standard deviation informs distribution engineers about the expected range of yearly values.Three fundamentals load point indices may be used to computation the indices of reliability for RDS as the following [35]:(1)
Average failure rate at load point (i), λi which is written as following equation (8):(8)λi=∑jϵNeλe,j,whereNe represents the total number of elements whose fault would interrupt load point (i) and λe,j represents the average failure rate at load point (i).(2)
Annual outage duration at load point (i), Ui (an hour per year):(9)Ui=∑jϵNeλe,j∙ri,j,whereri,j is failure duration at load point (i) owing to a failed element j.(3)
Average outage duration at load point (i), ri (hours) as follows:(10)ri=Uiλi.Typically, a measure of RDS reliability is considered as the effects of a prolonged interruption in terms of the number of users disconnected by an outage. The equations are used to compute sustained interruption indices [36–38].(i)
SAIDI: system average interruption duration index.(11)SAIDI=TotaldurationofallinterruptionTotalnumberofcustomersconnected,SAIDI=∑i=1kUiNi∑i=1kNi,hrC∙yr.(ii)
SAIFI: system average interruption frequency index.(12)SAIFI=TotalnumberofallinterruptionsTotalnumberofcustomersconnected,SAIFI=∑i=1kλiNi∑i=1kNifC∙yr.(iii)
CAIDI: customer average interruption duration index.(13)CAIDI=TotaldurationofallinterruptionTotalnumberofallinterruptions,CAIDI=∑i=1kUiNi∑i=1kλiNihr.(iv)
ASAI: average service availability index.(14)ASAI=TotalnumberofhoursavailabilityTotaldemandhours,ASAI=∑i=1k8760Ni−∑i=1kUiNi∑i=1k8760Nip.u..(v)
EENS: expected energy not supplied.(15)EENS=∑i=1kpiUiMWhryr,wherepi represent the average load for load point i(vi)
AENS: average energy not supplied.(16)AENS=TotaleneragenotsupplieTotalnumberofcustomersconnected,AENS=∑i=1kEENS∑i=1kNiMWhrC∙yr.(vii)
Average service unavailability index (ASUI).(17)ASUI=1−ASAIp.u..


## 2.4. Power Flow and Reliability Assessment Constraints

The following is a description of the power flow and reliability assessment procedure time constraints:


### 2.4.1. Capacitor Size

The capacitor bank is injected maximum value reactive power into the RDS it should not be above the entire reactive power load and indicated by the following equation (18) [32, 39]:(18)QC,MAX<QL,where QC,MAX is the maximum needed of reactive power amount from capacitor bank in KVAR and QL is the all reactive power for a load of the network. However, in the optimal design of the OCP technique, the size of capacitors in the RDS is very important and it must be less than QL.


### 2.4.2. Voltage and Current Limit

This limitation is used to ensure that the voltage value of each bus keeps within the required tolerances based on the following equation (19):(19)VMIN≤Vi≤VMAX,where the allowable values of node voltage limited by Vmax=1.05p.u and Vmin=0.95p.u.However, the current at each brunch must be limited as shown in equation (20) as follows:(20)Ii≤Ii,max.


### 2.4.3. Reliability Constraints

Reliability indices after the optimization process must be better than the base case, as shown in equations as follows:(21)0<SAIDI<SAIDIB,0<SAIFI<SAIFIB,0<CAIDI<CAIDIB,0<AENS<AENSB,ASAI>ASAIB,0<EENS>EENSB,0<ASUI>ASUIB,where SAIDIB, SAIFIB, CAIDIB, AENSB, ASAIB, and ASUIB represent the indices in the base case, and SAIDI, SAIFI, CAIDI, AENS, ASAI, and ASUI are indices after optimization [37].


## 2.4.1. Capacitor Size

The capacitor bank is injected maximum value reactive power into the RDS it should not be above the entire reactive power load and indicated by the following equation (18) [32, 39]:(18)QC,MAX<QL,where QC,MAX is the maximum needed of reactive power amount from capacitor bank in KVAR and QL is the all reactive power for a load of the network. However, in the optimal design of the OCP technique, the size of capacitors in the RDS is very important and it must be less than QL.


## 2.4.2. Voltage and Current Limit

This limitation is used to ensure that the voltage value of each bus keeps within the required tolerances based on the following equation (19):(19)VMIN≤Vi≤VMAX,where the allowable values of node voltage limited by Vmax=1.05p.u and Vmin=0.95p.u.However, the current at each brunch must be limited as shown in equation (20) as follows:(20)Ii≤Ii,max.


## 2.4.3. Reliability Constraints

Reliability indices after the optimization process must be better than the base case, as shown in equations as follows:(21)0<SAIDI<SAIDIB,0<SAIFI<SAIFIB,0<CAIDI<CAIDIB,0<AENS<AENSB,ASAI>ASAIB,0<EENS>EENSB,0<ASUI>ASUIB,where SAIDIB, SAIFIB, CAIDIB, AENSB, ASAIB, and ASUIB represent the indices in the base case, and SAIDI, SAIFI, CAIDI, AENS, ASAI, and ASUI are indices after optimization [37].


## 2.5. Optimization-Based BSSA

In 2017, Mirjalili et al. [40] proposed the SSA where this algorithm depends on the navigation and foraging behavior in the seas and oceans as shown in Figure 3. To update the leader location, the following equation (22) is presented [41]:(22)Xj1=Fj+C1ubj−lbjC2+lbj,C3≥0.5,Fj−C1ubj−lbjC2+lbj,C3<0.5,where Xj1 represents the first location of salp in the jth dimension, Fj represents the location of food supply, ubj,lbj are the upper and lower bounds of jth dimension, and the random numbers are denoted by C2 and C3 [0, 1]. While the coefficient C1 is written using the following equation (23):(23)C1=2×e−4t/T2,where t represents the present iteration and T is the total number of iterations. The location of the followers can be written as equation (24) [42] as follows:(24)Xjn=12Xjn+Xjn−1,where n≥2 and Xjn is the site of nth follower in j dimension.Figure 3
Chain of SSA.The salp population is seen as a binary bound of dimension in a binary search issue. The velocity and position values for each particle must be limited to (0 or 1) in order for this method to search in discrete space. So that, the transfer function T.F may be applied as follows [43]:(25)T.FXjnt=11+e−Xjnt.By using T.F, (24) will be changed to as follows:(26)Xjdt+1=0ifrand<T.FXjdt+1,1ifrand≥T.FXjdt+1,where Xjdt+1 is the j−th element at dth dimension in X solution.The proposed BSSA is implemented to find the optimal size and location of OCP and optimal topology of DSR that reduces the real power losses, and enhance the voltage profile and reliability. The switches of RDS are represented here as discrete values, where 0 denotes an open switch and 1 denotes a closed switch. The BSSA was carried out which depend on the following steps: (Algorithm1).Algorithm 1: The main steps of binary salp swarm algorithm (BSSA) [43].
(1)
Initialize the search agents, maximum number of iterations, and salp population with considering of the binary bound of dimension(2)
Retain the search agents that satisfies all the constraints(3)
Run the load flow and evaluate the objective function using equation (7)(4)
Calculate the reliability indices of each bus(5)
Obtain the best salp position or leader salp position using equation (22)(6)
Update the value ofC1 using equation (23)(7)
Update the location of the leader using equation (22)(8)
Calculate the probabilities using equation (25) which take the output of equation (22) as an input to equation (26)(9)
Update the followers using equation (24)(10)
Check the program stopping condition, ifiteration<themaximumnumber, go to step 6, otherwise go to step 11(11)
Print the optimal results(12)
End


## 3. Results and Discussion

The MATLAB environment software was used to do the suggested BSSA algorithm for two IEEE standard test systems. The first is 33-bus RDS with 3715 kW, 2300 kVA, and 37 branches with (32 closed and 5 opened switches) as illustrated in Figure4. The second test system is 69-bus RDS with 100 MVA, 3.8015 MW, 2.6946 MVAr, and 12.66 kV containing 73 branches. The system included, 5 opened tie switches and 68 closed sectionalizing switches as shown in Figure 5. The reliability and line bus data are obtained from references [3, 37] for both systems, respectively. Three scenarios were used to evaluate the effectiveness of the suggested techniques:Scenario 1: sequentially (OCP after DSR)Scenario 2: sequentially (DSR after OCP)Scenario 3: simultaneously (DSR and OCP)Figure 4
33-bus IEEE system used in this work.Figure 5
69-bus IEEE system used in this work.


### 3.1. IEEE-33 Bus

The effects of adding OCP as well as changing the state of tie switches to build a new radial structure in the DSR on the test systems is examined in these three scenarios and described in Table1, which calculates the main results of the proposed BSSA including the tie switches for these scenarios. Active power loss, capacitor location, capacitor size, reliability indices (SAIDI, SAIFI, EENS, AENS, ASAI, and CAIDI), minimum voltage, maximum voltage, and % loss reduction are listed in both tables. All these parameters have been improved in these scenarios from the base case for both test system.Table 1
The results and comparison among the scenarios for the IEEE 33-bus RSD.
ParameterScenariosSequentiallySimultaneouslyBase caseCOP after DSRDSR after OCPDSR and OCPTie switch number33, 34, 35, 36, and 377, 14, 30, 35, and 3711, 27, 33, 34, and 367, 11, 17, 34, and 37Total power loss (kW)202.6771115.7382105.9175104.5116Capacitor location—19, 23, and 306, 24, and 3319, 30, and 33Capacitor size KVAR—100, 600, and 100600, 600, and 600600, 600, and 600Vmin (p.u.)0.913060.950.950.95732Vmax (p.u.)1111Execution time (sec)0.23802391.1491761.0816789.1659Convergence iterations—12937Percentage loss reduction—42.895347.740848.4344SAIDI (hr/c.yr)2.04361.78721.54241.5151SAIFI (f/c.yr)2.41262.27162.09642.0839EENS (MWhr/yr)2066.64461918.65441894.01941605.2589AENS (MWhr/C.yr)0.1135500.1054200.1040700.088201ASAI (p.u.)0.999770.999810.999810.99984CAIDI (hr/c.Int.)0.847030.786750.735760.72703ASUI (p.u.)0.000233280.000194820.000187140.00015796The results of Table1 indicate that the topology of RDS changes in each scenario according to the change of open tie switches. Figures 6–8 show the position and value of OCP, as well as the new structure of RDS after the optimization process.Figure 6
33-bus IEEE system for scenario 1.Figure 7
33-bus IEEE system for scenario 2.Figure 8
33-bus IEEE system for scenario 3.The voltage profile is shown in Figure9 using the BSSA for the test RDS under three scenarios with the base case, it offers a significant improvement in the voltage for all buses of the system, which contributes to increasing the efficiency of system.Figure 9
Voltage profile for 33-bus using BSSA algorithm for three scenarios with the base case.The results obtained show a clear superiority of the technique that used in scenario 3, in term of losses reduced to 104.5116 kW, while keeping all RDS constraints within the permissible range. Figures10 and 11 show the improvement in active and reactive losses for all buses of RDS in the three scenarios compared with the base case. Furthermore, Figure 12 reports the convergence of active losses using the suggested BSSA algorithm for three scenarios used in this work.Figure 10
Active losses curve for 33-bus with using the BSSA algorithm for three scenarios with the base case.Figure 11
Reactive losses curve for 33-bus with using the BSSA algorithm for three scenarios with the base case.Figure 12
Convergence active power losses (kW) for 33-bus using the suggested BSSA algorithm.According to the results of Table1, the simulation results indicate that the optimization process using BSSA is successful in improvement the RDS reliability. By increasing the reserve of power supplied for consumers, the EENS and AENS indices will reduction for this reason. Detailed reliability analysis may also prevent the undesirable issues and minimize interruptions, hence then enhancing the power quality. The reliability indicators that depend on the number of outages SAIDI, SAIFI, ASAI, CAIDI, and ASUI show a significant improvement from the base case.Figure13 shows the values of reliability indices studied in this paper after the optimization process with the base case. According to this figure, when comparing the three implemented scenarios, the best results are obtained for optimization in scenario 3, which outperforms both scenarios 1 and 2.Figure 13
Reliability indices for 33-bus with using the BSSA algorithm for three scenarios with the base case.


### 3.2. IEEE-69 Bus

The BSSA algorithm for 69-bus RDS is applied to perform another test to verify the success of techniques in the three proposed scenarios. To find out the effect of implementing the DSR technique and OCP technique sequentially or simultaneously for large distribution systems to improving the reliability and power quality. The results of three scenarios for the optimization process are listed in Table2.Table 2
The results and comparison among the scenarios for the IEEE 69-bus RSD.
ParameterScenariosSequentiallySimultaneouslyBase caseCOP after DSRDSR after OCPDSR and OCPTie switch number69, 70, 71, 72, and 7316, 21, 40, 45, and 5614, 42, 55, 62, and 7014, 18, 38, 57, and 63Total power loss (kW)224.960695.219886.403985.4559Capacitor location—28, 60, 6615, 47, 6039, 61, 65Capacitor size KVAR—1200, 900, and 500500, 1000, and 1000700, 1100, and 500Vmin (p.u.)0.909010.950.950.96632Vmax (p.u.)1111Execution time (sec.)1.772511390.255112383.00418857.2237Convergence iterations—49376Percentage loss reduction—57.672761.591562.0129SAIDI (hr/c.yr)1.008600.723520.711900.66594SAIFI (f/c.yr)1.53541.27971.27021.1240EENS (MWhr/yr)8.32873.68414.24573.5237AENS (MWhr/C.yr)0.000668970.000295910.000341020.00028303ASAI (p.u.)0.999880.999920.999920.99992CAIDI (hr/c.Int.)0.656910.63660.604270.58151ASUI (p.u.)0.000115148.2594 × 10−58.1267 × 10−57.6021 × 10−5The results of Table2 indicated that the radial topology of 69-bus RDS is changed in each scenario according to the change of the tie switches. Also, the places and values of injected capacitors differ in each scenario about the other. These differences are illustrated in the following Figures 14–16.Figure 14
69-bus IEEE system for scenario 1.Figure 15
69-bus IEEE system for scenario 2.Figure 16
69-bus IEEE system for scenario 3.The voltage profile in Figure17 shows a significant improvement in the three scenarios compared to the base case. The BSSA algorithm achieved significant success in optimizing the objective of the voltage profile function, whereby the voltages of all network buses were optimized. Improving the voltage of buses for RDS helps for reducing the voltage drop in all branches of the network and this contributes effectively to improving the losses reduction. Minimizing the active losses is the primary goal of this research, and the proposed algorithm has succeeded in finding the optimal radial structure of 69-bus RDS and the best values and locations of capacitors based on the OCP technique. These scenarios contributed for reducing the losses to the lowest possible value according to the established system constraints. Figure 18 shows the active power loss reduction in RDS for three scenarios with the base case where the scenario 3 shows superiority in reducing losses. Figure 19 shows the effect of KVAR compensation through OCP injection that contributes to reducing the reactive losses of the network compared to the base case.Figure 17
Voltage profile for 69-bus using BSSA algorithm for three scenarios with the base case.Figure 18
Active losses curve for 69-bus with using the BSSA algorithm for three scenarios with the base case.Figure 19
Reactive losses curve for 69-bus with using the BSSA algorithm for three scenarios with the base case.The convergence of active losses using the suggested BSSA algorithm for three scenarios that used in this work is shown in Figure20.Figure 20
Convergence active power losses (kW) for 69-bus using the suggested BSSA algorithm.The simulation results of Table2 indicate the success of the BSSA algorithm for maximizing the voltages of system buses with reducing losses in a balanced way, while improving the reliability of 69 RDS as a prerequisite for the optimization process. The reliability indices also show a significant improvement in the three scenarios compared with the base case. Figure 21 shows a comparison among the reliability indices for three scenarios.Figure 21
Reliability indices for 69-bus with using the BSSA algorithm for three scenarios with the base case.


## 3.1. IEEE-33 Bus

The effects of adding OCP as well as changing the state of tie switches to build a new radial structure in the DSR on the test systems is examined in these three scenarios and described in Table1, which calculates the main results of the proposed BSSA including the tie switches for these scenarios. Active power loss, capacitor location, capacitor size, reliability indices (SAIDI, SAIFI, EENS, AENS, ASAI, and CAIDI), minimum voltage, maximum voltage, and % loss reduction are listed in both tables. All these parameters have been improved in these scenarios from the base case for both test system.Table 1
The results and comparison among the scenarios for the IEEE 33-bus RSD.
ParameterScenariosSequentiallySimultaneouslyBase caseCOP after DSRDSR after OCPDSR and OCPTie switch number33, 34, 35, 36, and 377, 14, 30, 35, and 3711, 27, 33, 34, and 367, 11, 17, 34, and 37Total power loss (kW)202.6771115.7382105.9175104.5116Capacitor location—19, 23, and 306, 24, and 3319, 30, and 33Capacitor size KVAR—100, 600, and 100600, 600, and 600600, 600, and 600Vmin (p.u.)0.913060.950.950.95732Vmax (p.u.)1111Execution time (sec)0.23802391.1491761.0816789.1659Convergence iterations—12937Percentage loss reduction—42.895347.740848.4344SAIDI (hr/c.yr)2.04361.78721.54241.5151SAIFI (f/c.yr)2.41262.27162.09642.0839EENS (MWhr/yr)2066.64461918.65441894.01941605.2589AENS (MWhr/C.yr)0.1135500.1054200.1040700.088201ASAI (p.u.)0.999770.999810.999810.99984CAIDI (hr/c.Int.)0.847030.786750.735760.72703ASUI (p.u.)0.000233280.000194820.000187140.00015796The results of Table1 indicate that the topology of RDS changes in each scenario according to the change of open tie switches. Figures 6–8 show the position and value of OCP, as well as the new structure of RDS after the optimization process.Figure 6
33-bus IEEE system for scenario 1.Figure 7
33-bus IEEE system for scenario 2.Figure 8
33-bus IEEE system for scenario 3.The voltage profile is shown in Figure9 using the BSSA for the test RDS under three scenarios with the base case, it offers a significant improvement in the voltage for all buses of the system, which contributes to increasing the efficiency of system.Figure 9
Voltage profile for 33-bus using BSSA algorithm for three scenarios with the base case.The results obtained show a clear superiority of the technique that used in scenario 3, in term of losses reduced to 104.5116 kW, while keeping all RDS constraints within the permissible range. Figures10 and 11 show the improvement in active and reactive losses for all buses of RDS in the three scenarios compared with the base case. Furthermore, Figure 12 reports the convergence of active losses using the suggested BSSA algorithm for three scenarios used in this work.Figure 10
Active losses curve for 33-bus with using the BSSA algorithm for three scenarios with the base case.Figure 11
Reactive losses curve for 33-bus with using the BSSA algorithm for three scenarios with the base case.Figure 12
Convergence active power losses (kW) for 33-bus using the suggested BSSA algorithm.According to the results of Table1, the simulation results indicate that the optimization process using BSSA is successful in improvement the RDS reliability. By increasing the reserve of power supplied for consumers, the EENS and AENS indices will reduction for this reason. Detailed reliability analysis may also prevent the undesirable issues and minimize interruptions, hence then enhancing the power quality. The reliability indicators that depend on the number of outages SAIDI, SAIFI, ASAI, CAIDI, and ASUI show a significant improvement from the base case.Figure13 shows the values of reliability indices studied in this paper after the optimization process with the base case. According to this figure, when comparing the three implemented scenarios, the best results are obtained for optimization in scenario 3, which outperforms both scenarios 1 and 2.Figure 13
Reliability indices for 33-bus with using the BSSA algorithm for three scenarios with the base case.


## 3.2. IEEE-69 Bus

The BSSA algorithm for 69-bus RDS is applied to perform another test to verify the success of techniques in the three proposed scenarios. To find out the effect of implementing the DSR technique and OCP technique sequentially or simultaneously for large distribution systems to improving the reliability and power quality. The results of three scenarios for the optimization process are listed in Table2.Table 2
The results and comparison among the scenarios for the IEEE 69-bus RSD.
ParameterScenariosSequentiallySimultaneouslyBase caseCOP after DSRDSR after OCPDSR and OCPTie switch number69, 70, 71, 72, and 7316, 21, 40, 45, and 5614, 42, 55, 62, and 7014, 18, 38, 57, and 63Total power loss (kW)224.960695.219886.403985.4559Capacitor location—28, 60, 6615, 47, 6039, 61, 65Capacitor size KVAR—1200, 900, and 500500, 1000, and 1000700, 1100, and 500Vmin (p.u.)0.909010.950.950.96632Vmax (p.u.)1111Execution time (sec.)1.772511390.255112383.00418857.2237Convergence iterations—49376Percentage loss reduction—57.672761.591562.0129SAIDI (hr/c.yr)1.008600.723520.711900.66594SAIFI (f/c.yr)1.53541.27971.27021.1240EENS (MWhr/yr)8.32873.68414.24573.5237AENS (MWhr/C.yr)0.000668970.000295910.000341020.00028303ASAI (p.u.)0.999880.999920.999920.99992CAIDI (hr/c.Int.)0.656910.63660.604270.58151ASUI (p.u.)0.000115148.2594 × 10−58.1267 × 10−57.6021 × 10−5The results of Table2 indicated that the radial topology of 69-bus RDS is changed in each scenario according to the change of the tie switches. Also, the places and values of injected capacitors differ in each scenario about the other. These differences are illustrated in the following Figures 14–16.Figure 14
69-bus IEEE system for scenario 1.Figure 15
69-bus IEEE system for scenario 2.Figure 16
69-bus IEEE system for scenario 3.The voltage profile in Figure17 shows a significant improvement in the three scenarios compared to the base case. The BSSA algorithm achieved significant success in optimizing the objective of the voltage profile function, whereby the voltages of all network buses were optimized. Improving the voltage of buses for RDS helps for reducing the voltage drop in all branches of the network and this contributes effectively to improving the losses reduction. Minimizing the active losses is the primary goal of this research, and the proposed algorithm has succeeded in finding the optimal radial structure of 69-bus RDS and the best values and locations of capacitors based on the OCP technique. These scenarios contributed for reducing the losses to the lowest possible value according to the established system constraints. Figure 18 shows the active power loss reduction in RDS for three scenarios with the base case where the scenario 3 shows superiority in reducing losses. Figure 19 shows the effect of KVAR compensation through OCP injection that contributes to reducing the reactive losses of the network compared to the base case.Figure 17
Voltage profile for 69-bus using BSSA algorithm for three scenarios with the base case.Figure 18
Active losses curve for 69-bus with using the BSSA algorithm for three scenarios with the base case.Figure 19
Reactive losses curve for 69-bus with using the BSSA algorithm for three scenarios with the base case.The convergence of active losses using the suggested BSSA algorithm for three scenarios that used in this work is shown in Figure20.Figure 20
Convergence active power losses (kW) for 69-bus using the suggested BSSA algorithm.The simulation results of Table2 indicate the success of the BSSA algorithm for maximizing the voltages of system buses with reducing losses in a balanced way, while improving the reliability of 69 RDS as a prerequisite for the optimization process. The reliability indices also show a significant improvement in the three scenarios compared with the base case. Figure 21 shows a comparison among the reliability indices for three scenarios.Figure 21
Reliability indices for 69-bus with using the BSSA algorithm for three scenarios with the base case.


## 4. Conclusions and Future Work

Several previous researches presented studies for improving the power quality of RDS by reducing the active losses and optimizing the system voltage profile without observance the system reliability concerns. So, a new method was devised to improve the power quality and reliability of RDS in an equiponderant manner to address these concerns. In this research, three different scenarios were used for 33 and 69 bus IEEE RDS, the first one OCP after DRS, the second DSR after OCP, and the third simultaneous DSR and OCP. The modern artificial intelligence algorithm, known as BSSA has been applied for these three scenarios to raise the reliability and performance of RDS by selecting the best locations and sizes of capacitors in addition to modifying the system topology. The main conclusions of this study are summarized as follows:(1)
The DSR and OCP techniques need a strong load flow method; therefore, backward/forward sweep load flow provides this capability due to its efficiency and speed when compared with NRM(2)
Simulation results expose the effectiveness and robustness of the proposed algorithm in implementing a MOF for reducing the system losses and amelioration the voltage profile in the three mentioned scenarios(3)
All RDS reliability indices are enhanced through three different optimization scenarios which can be helped for increasing the reserve power supplied to consumers and reducing the number of interruptions(4)
The optimal dual sequential and dual-simultaneous techniques (OCP after DRS, DSR after OCP, and simultaneous DSR and OCP) based on BSSA have been contributed successfully to improve the percentage of loss reduction in the three scenarios (42.8953%, 47.7408%, and 48.4344%), respectively, in 33-bus RDS and to (57.6727%, 61.5915%, and 62.0129%), respectively, in 69-bus RDS(5)
The dual-simultaneous technique (scenario 3) demonstrates its superiority over dual sequential techniques (scenarios 1 and 2) for improving the loss reduction, better voltage optimization, and a significant increase in the network reliabilityBased on the results of this study, the following studies that can be addressed as a possible extension in the future:(i)
Kinds of disturbances might be applied to the system under study such as symmetrical three-phase fault, unsymmetrical faults, and switching failure(ii)
Achieve the improvement of loss reduction, voltage profile, and network reliability by using other dual sequential and dual-simultaneous techniques or optimization methods



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*Source: 1943535-2023-03-15.xml*