# Optimal Recloser Placement in Distribution System Considering Maneuver Points, Practical Limitations, and Recloser Malfunction

Authors: Mohammad Zaher Ghorbani-Juybari; Hossein Gholizade-Narm; Yaser Damchi
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

Improving reliability is one of the most critical problems in power distribution networks. Optimal placement of automatic switches improves system reliability. Practical constraints such as maneuver points and the capacity of neighboring feeders are often overlooked. Reliability indices may also be improved by optimizing maneuver point locations considering the capacities of neighboring feeders. In this paper, a new perspective on the problem of recloser placement in the presence of switch disconnectors (sectionneurs) with the ability to disconnect under load is proposed. The limitations of transmission power capacity at maneuver points are also considered in the proposed method. In addition, by proposing a Markov model, the possibility of malfunction of reclosers is considered. The proposed method is applied to two case studies including Roy Billinton Test System (RBTS) and the real distribution network in Mazandaran, Iran. Real system data are collected during the years 2016–2021. The problem is solved for various scenarios. In the case of 12 fully reliable reclosers, taking into account the optimal maneuver points and without any capacity limitations, compared to the allocation of maneuver points at the endpoints of the feeders show a %4.37 increase in the reliability of the real system. Even by considering practical capacity limitations in the maneuver points, this improvement is %3.47. Also, the results show a %6.684 decrease in the system reliability by considering malfunction in the case of 12 reclosers. This underscores the importance of taking into account the reclosers malfunctions in optimal switch placement for better decision making in practice.


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## Body

## 1. Introduction

Reliability improvement is one of the important goals of PDNs [1]. Improving reliability indices of the PDNs has been interested in recent studies [2–4]. Optimal allocation of fast switches such as reclosers is necessary to reduce the access time and consequently decrease the interruption time [5]. The reliability of PDNs can be improved by the optimal placement of manual and automatic switching devices [6]. In practical cases, selecting the proper maneuver points for the load transfer is crucial [7]. In addition, similar to other elements of the distribution networks, the reclosers do not always work properly. The literature review is presented as follows.In [8], the network automation planning problem is defined in terms of MILP; different switches are located optimally without malfunction probability of the switches. In [9], the system reliability is improved by obtaining the optimum number of sectionalizing switches using the ant colony algorithm, but normally open switches only connect the endpoints of the feeders. In [10], the effects of RCS malfunction on PDN reliability are presented, but the effect of maneuver points and their capacity are not studied. RCS allocation and enhancing reliability by optimizing the reduction of customer interruption cost, the reduction of SAIDI, and the number of restored loads are presented in [11], without studying any malfunction. The genetic algorithm is used in [12] to determine recloser optimal placement, but none of the mentioned considerations such as malfunctions and maneuver points effects are not studied. A new MILP formulation to find the optimum numbers and locations of fault indicators in distribution systems is presented in [13]. A method using analytical hierarchy process for finding the reclosers optimal number and location by evaluating reliability indices such as SAIFI, SAIDI, MAIFI, and ENS is presented in [14], without the effects of maneuver point locations. Optimal placement of the sectionalizing switches based on deterministic algorithms is presented in [15], while the SAIFI, SAIDI, and AENS indices were computed without discussing the effects of the maneuver points and switch malfunctions on the optimal solution. A mathematical model for the placement of protective and controlling devices in PDNs is presented in [16]. In [17], an MILP formulation is proposed for the switch placement problem and guaranties the global optimal solution, but the effect of the maneuver points, switch malfunctions, and maneuver point capacities are not considered. The optimal placement of RCSs considering laterals is presented in [18] using an MILP model. Sectionalizing switch placement, considering switch failure, is studied in [19], and a model based on mixed-integer programming format is proposed to integrate the impacts of a switch failure in switch placement problem, but the effect of different maneuver points and different types of switch defects, with practical concerning, are not studied. In [20], a bidirectional formulation for optimal placement of protective devices and switches such as reclosers and fuses is modified. The model considers the bidirectional power flow at any part of a PDN, while the protective devices are assumed to be fully reliable. Providing the optimal location of reclosers to minimize the power loss cost is presented in [21], but the recloser malfunctions and maneuver point effects are not studied. In [22], an approach to optimize the location of reclosers using the cross-entropy method and reassessment of Monte Carlo sampled states is proposed. However, finding the best neighboring feeders and the effect of the maneuver points on the optimal solution are not studied. Optimal switch placement, using a high-accuracy MILP formulation, is proposed in [23], but the switch malfunction probability is not modelled. In [24], optimal placement of fault indicators and sectionalizing switches are studied with the assumption that section switches and fault indicators do not malfunction. Also, this problem is presented in [25], with the assumption that the fault indicators, RCSs, and disconnectors are all installed at the beginning of each branch, without taking into account their malfunction probability. In [26], the discrete Markov chain model is used, and the effect of malfunction probability of sectionalizing switches is studied, but the maneuver points are considered predetermined at the endpoints of feeders. In [27], a hybrid method for recloser and sectionalizer placement in PDNs considering protection coordination, fault type, and equipment malfunction is proposed, without the practical limitations of the maneuver points. Also, in [28], remodeling of a PDN by optimal placement of auto-reclosers is proposed to enhance system reliability. The limitations for load transfer and the malfunctions are not considered.Reclosers are electrical equipment with a predefined sequence of opening and reclosing [29]. These switches are usually assumed entirely reliable; however, this is not always accurate in practical cases. Some studies such as [10] present models to consider switch malfunctions. However, all of the mentioned practical issues, i.e., effect of different maneuver points, limitation on power transmission capacity in the maneuver points, and the recloser malfunctions are not studied, simultaneously. At the same time, these issues can affect the optimal solution of the problem. In this paper, a particle swarm algorithm is used to solve the problem. The contributions are as follows:(i)
Optimal placement of reclosers(ii)
Considering recloser malfunction using proposed Markov model(iii)
Finding the optimal maneuver points(iv)
Considering the power transmission capacity limitations from neighboring feeders(v)
Finding the optimal neighboring feeders.Nowadays, the DG sources are essential in the PDNs. The DGs can be considered as maneuver points in the view point of implementation (as considered in the proposed method), while those are different from maneuver point technically such as capacity of energy supply, effect on the network loss, and effect on reliability indices.To better illustrate contributions, recent studies are categorized in Table1 according to different perspectives, including optimal maneuver point, optimal recloser placement, recloser malfunction, manual switch, optimal neighboring feeder, and maneuver point capacity. For example, based on Table 1, considering different maneuver points, maneuver point capacity, and finding the best neighboring feeders were not studied in the previous studies. These are practical concerns that influence the PDN reliability indices and optimal placement of reclosers.Table 1
Comparison between the recent approaches in the literature.
ReferenceOptimal maneuver pointsOptimal recloser placementRecloser malfunctionManual switchesOptimal neighboring feederManeuver point capacities[2, 4, 5, 8, 12, 14, 20–22, 28]×✓××××[6, 10, 18, 19, 23, 24, 26]×××✓××[11]×✓×✓××[16]×✓×✓××[27]×✓✓×××Proposed method✓✓✓✓✓✓The rest of the paper is organized as follows. In Section2, the problem formulation consists of the OF, problem constraints, and the proposed Markov model is presented. In addition to their analysis, the simulation results are given in Section 3. Finally, the conclusion is presented in Section 4.


## 2. Problem Formulation

In this section, the problem formulation is presented. At first, the OF is introduced. Then, the constraints of the problem are defined. Finally, a Markov model is proposed to consider the recloser’s malfunctions.


### 2.1. Objective Function Definition

The reliability of the PDNs can be evaluated by many criteria depending on the distribution company goals. Some companies pay more attention to the system costs, while others prioritize energy consumption [30, 31]. Evaluation of a PDN is performed by analyzing a suitable function that should be a good indicator of the system reliability.This paper considers the following OF. This OF is a combination of both customer-orientated and energy-orientated indices.(1)OF=min∑j=1mSAIDIjSAIDIbase+SAIFIjSAIFIbase+CAIDIjCAIDIbase+ENSjENSbase.The variables in equation (1) are as follows:SAIDI (hr/cr) is the system average interruption duration index and is calculated by equation (2) [31].(2)SAIDI=∑UiNi∑Ni.SAIFI (Int/cr) is the system average interruption frequency index and is obtained as follows:(3)SAIFI=∑λiNi∑Ni.ENS (kWh) is the energy not supplied given in equation (4):(4)ENS=∑LaiUi.CAIDI (hr/crI) is customer average interruption duration index formulated as follows:(5)CAIDI=∑UiNi∑λiNi.Indices are normalized by dividing them by their base values: SAIDIbase, SAIFIbase, CAIDIbase, ENSbase, which are the values of these indices without any recloser and maneuver point in the PDN. The decision variables are the recloser locations, maneuver point locations, and the neighboring feeders that must be optimally found.


### 2.2. Constraints

In practice, the number of reclosers is limited due to the high cost of reclosers and budget limitations. Moreover, developing the maneuver points is faced with high costs and difficulties such as legal restrictions and geographical obstacles like passing through the gas transmission branches. Therefore, these financial and technical limitations impose some constraints on the OF. Equation (6) shows the constraint on the number of reclosers that is determined based on the total budget of distribution company. Equation (7) is the constraint on the number of maneuver points. This is specified based on the PDN’s environmental conditions, the total budget, and the legal restrictions. Then, the constraint on the number of neighboring feeders must be regarded, as shown in equation (8). This constraint is dependent on the identity of PDN. The constraint on the number of disconnectors is determined according to the total budget and the PDN structure. Equation (10) shows the limitation on the maneuver capacity, which is specified according to the PDN characteristics such as the number of customers, customer type, and so on.(6)NRecMin≤NRec≤NRecMax,(7)NMPMin≤NMP≤NMPMax,(8)NFeedMin≤NFeed≤NFeedMax,(9)0≤NSec≤NSecMax,(10)CMPMin≤CMP≤CMPMax.When an interruption happens due to a fault in the system, the faultless parts can be isolated and connected through the neighboring feeders [31]. The points that are capable of connecting the neighboring feeders, so-called maneuver points, are assumed to be predetermined in the previous studies. However, these points may be located everywhere in the feeders, which can be fed from the neighboring feeders. Moreover, due to limitations on the power transmission capacities in the maneuver points, it is important to choose an optimal neighboring feeder.


### 2.3. Proposed Markov Model

PDN devices such as reclosers do not always work properly. Switches are usually assumed quite reliable, but in practical conditions, they encounter malfunctions. By considering the recloser malfunctions, their optimal locations can be changed. Different reasons may cause these malfunctions. Solenoid defects, oil leakage or oil pollution in the recloser, energy storage defects, events and faults due to wrong setup and equipment steal, and disarrange in the wiring of recloser control panel are the most common reclosers malfunctions. The solenoid defects such as changes in the magnetic characteristics, spring tension, and plunger malfunctions can influence the recloser performance. The flow of the displaced oil determines the timing before contact opening [32]. Accordingly, the oil leakage in the reclosers can result in delay in contact opening. The events and faults due to wrong setup include every undesirable situation that is caused due to implement and software imperfections. For example, one of the most repetitive setup faults is the lack of coordination between the recloser and the upper-hand substation. Moreover, human errors can cause the wrong setup problems. The environmental conditions include every reason that are originated from the external environment. For example, relay software inaccessibility and recloser equipment steals have occurred in the last six years.In this paper, a Markov model is proposed for reliability analysis of recloser. The states of the recloser operation in the proposed Markov model is illustrated in Figure1 as follows.A: Healthy with on-time isolation (HI)B: Healthy but isolated with delay (HID)C: Healthy without isolation due to environmental conditions (HWIE)D: Healthy without isolation due to wrong setup (HWIS)E: Not healthy (NH).Figure 1
Proposed Markov model for the recloser malfunctions modeling.If a recloser is initially in state A, the recloser performs correctly without delay. State B includes conditions in which a recloser isolates healthily, but with a delay because of equipment malfunctions. For example, if the recloser spring is under tension, this influences the speed of disconnecting, or oil pollution can change its performance, such as pressure and cohesion. However, in many practical cases, the recloser is healthy itself, but it cannot isolate. For example, the reclosers control panel and associated cables may be stolen, or temperature conditions can influence the performance of recloser. These cases belong to state C and are also known as environmental conditions. State D shows that the recloser cannot isolate due to the wrong setup, and the recloser cannot properly detect the feeder faults. Lack of coordination between the recloser and the upper-hand substation is an example of the wrong setup. State E occurs when a recloser is out of service and does not isolate the fault.The transition rate matrixTR for the Markov model is defined as follows [33].(11)TR=TRijn×n,TRij=−∑j≠inaij,i=jaij,i≠j.From Figure1, the transition matrix is obtained according to equation (12).(12)TR=−λAB+λAC+λAD+λAEλABλACλADλAEμBA−μBA+λBE00λBEμCAλCB−μCA+λCB+λCE0λCEμDA00−μDA0μEA000−μEA.To calculate the probability of the recloser states, it is necessary to solve the following equations system.(13)∑σ=15Pσ=1,P×TR=0,where P =  P1,P2,…,Pσ.According to this model, the probability of up and down states of reclosers can be written as follows:(14)PUp=PA+PB,(15)PDown=PC+PD+PE.


## 2.1. Objective Function Definition

The reliability of the PDNs can be evaluated by many criteria depending on the distribution company goals. Some companies pay more attention to the system costs, while others prioritize energy consumption [30, 31]. Evaluation of a PDN is performed by analyzing a suitable function that should be a good indicator of the system reliability.This paper considers the following OF. This OF is a combination of both customer-orientated and energy-orientated indices.(1)OF=min∑j=1mSAIDIjSAIDIbase+SAIFIjSAIFIbase+CAIDIjCAIDIbase+ENSjENSbase.The variables in equation (1) are as follows:SAIDI (hr/cr) is the system average interruption duration index and is calculated by equation (2) [31].(2)SAIDI=∑UiNi∑Ni.SAIFI (Int/cr) is the system average interruption frequency index and is obtained as follows:(3)SAIFI=∑λiNi∑Ni.ENS (kWh) is the energy not supplied given in equation (4):(4)ENS=∑LaiUi.CAIDI (hr/crI) is customer average interruption duration index formulated as follows:(5)CAIDI=∑UiNi∑λiNi.Indices are normalized by dividing them by their base values: SAIDIbase, SAIFIbase, CAIDIbase, ENSbase, which are the values of these indices without any recloser and maneuver point in the PDN. The decision variables are the recloser locations, maneuver point locations, and the neighboring feeders that must be optimally found.


## 2.2. Constraints

In practice, the number of reclosers is limited due to the high cost of reclosers and budget limitations. Moreover, developing the maneuver points is faced with high costs and difficulties such as legal restrictions and geographical obstacles like passing through the gas transmission branches. Therefore, these financial and technical limitations impose some constraints on the OF. Equation (6) shows the constraint on the number of reclosers that is determined based on the total budget of distribution company. Equation (7) is the constraint on the number of maneuver points. This is specified based on the PDN’s environmental conditions, the total budget, and the legal restrictions. Then, the constraint on the number of neighboring feeders must be regarded, as shown in equation (8). This constraint is dependent on the identity of PDN. The constraint on the number of disconnectors is determined according to the total budget and the PDN structure. Equation (10) shows the limitation on the maneuver capacity, which is specified according to the PDN characteristics such as the number of customers, customer type, and so on.(6)NRecMin≤NRec≤NRecMax,(7)NMPMin≤NMP≤NMPMax,(8)NFeedMin≤NFeed≤NFeedMax,(9)0≤NSec≤NSecMax,(10)CMPMin≤CMP≤CMPMax.When an interruption happens due to a fault in the system, the faultless parts can be isolated and connected through the neighboring feeders [31]. The points that are capable of connecting the neighboring feeders, so-called maneuver points, are assumed to be predetermined in the previous studies. However, these points may be located everywhere in the feeders, which can be fed from the neighboring feeders. Moreover, due to limitations on the power transmission capacities in the maneuver points, it is important to choose an optimal neighboring feeder.


## 2.3. Proposed Markov Model

PDN devices such as reclosers do not always work properly. Switches are usually assumed quite reliable, but in practical conditions, they encounter malfunctions. By considering the recloser malfunctions, their optimal locations can be changed. Different reasons may cause these malfunctions. Solenoid defects, oil leakage or oil pollution in the recloser, energy storage defects, events and faults due to wrong setup and equipment steal, and disarrange in the wiring of recloser control panel are the most common reclosers malfunctions. The solenoid defects such as changes in the magnetic characteristics, spring tension, and plunger malfunctions can influence the recloser performance. The flow of the displaced oil determines the timing before contact opening [32]. Accordingly, the oil leakage in the reclosers can result in delay in contact opening. The events and faults due to wrong setup include every undesirable situation that is caused due to implement and software imperfections. For example, one of the most repetitive setup faults is the lack of coordination between the recloser and the upper-hand substation. Moreover, human errors can cause the wrong setup problems. The environmental conditions include every reason that are originated from the external environment. For example, relay software inaccessibility and recloser equipment steals have occurred in the last six years.In this paper, a Markov model is proposed for reliability analysis of recloser. The states of the recloser operation in the proposed Markov model is illustrated in Figure1 as follows.A: Healthy with on-time isolation (HI)B: Healthy but isolated with delay (HID)C: Healthy without isolation due to environmental conditions (HWIE)D: Healthy without isolation due to wrong setup (HWIS)E: Not healthy (NH).Figure 1
Proposed Markov model for the recloser malfunctions modeling.If a recloser is initially in state A, the recloser performs correctly without delay. State B includes conditions in which a recloser isolates healthily, but with a delay because of equipment malfunctions. For example, if the recloser spring is under tension, this influences the speed of disconnecting, or oil pollution can change its performance, such as pressure and cohesion. However, in many practical cases, the recloser is healthy itself, but it cannot isolate. For example, the reclosers control panel and associated cables may be stolen, or temperature conditions can influence the performance of recloser. These cases belong to state C and are also known as environmental conditions. State D shows that the recloser cannot isolate due to the wrong setup, and the recloser cannot properly detect the feeder faults. Lack of coordination between the recloser and the upper-hand substation is an example of the wrong setup. State E occurs when a recloser is out of service and does not isolate the fault.The transition rate matrixTR for the Markov model is defined as follows [33].(11)TR=TRijn×n,TRij=−∑j≠inaij,i=jaij,i≠j.From Figure1, the transition matrix is obtained according to equation (12).(12)TR=−λAB+λAC+λAD+λAEλABλACλADλAEμBA−μBA+λBE00λBEμCAλCB−μCA+λCB+λCE0λCEμDA00−μDA0μEA000−μEA.To calculate the probability of the recloser states, it is necessary to solve the following equations system.(13)∑σ=15Pσ=1,P×TR=0,where P =  P1,P2,…,Pσ.According to this model, the probability of up and down states of reclosers can be written as follows:(14)PUp=PA+PB,(15)PDown=PC+PD+PE.


## 3. Simulation Results

This section investigates the optimal recloser placement for both completely reliable reclosers and malfunctioned reclosers. At first, the two case studies, Roy Billinton and a real distribution network in Mazandaran, Iran, which are used to apply the proposed method, are presented. Then, the problem is stated in three different scenarios. Only the reclosers are optimally placed in the first scenario, and the maneuver points are predetermined in the feeders’ endpoints, without any capacity limitations. The second and third scenarios are concerned with selectable maneuver points, with and without limitations on the power transmission capacities, respectively. In the third scenario, the best neighboring feeders are selected and the maneuver points are found optimally. Scenarios are summarized as follows:Scenario 1: The optimal recloser locations are obtained in the case of predetermined maneuver points and unlimited power transmission conditionScenario 2: With unlimited power transmission capacity, optimal recloser locations and maneuver points are obtained.Scenario 3: With limited power transmission capacity, optimal recloser locations and maneuver points are obtained.Simple implementation and effective response of particle swarm optimization made it one of the most popular metaheuristic optimization methods. The PSO algorithm is thoroughly introduced in [34]. In this paper, the PSO algorithm is used to solve the problem. The inertia weight is w = 0.98, and the population size considered is 100.Figure2 shows a simple flowchart for solving the problem. According to this flowchart, at first the input data of the network are received. Then the problem is solved by PSO for determined iterations IterMax. Finally, if the differences between last K solutions be small than a predefined small value ε, the algorithm will be stopped, otherwise, it is added K iterations in order to reach the solution convergence. It must be mentioned by increasing K the solution has more accuracy. In this paper, the problem is solved with K = 10 and IterMax = 200.Figure 2
A simple flowchart for solving the problem.


### 3.1. RBTS-Bus2

At first, the proposed method is applied to the low-extent RBTS-Bus2. This system is shown in Figure3. This test system with the required data is presented in [35]. In RBTS-Bus2, the number of reclosers is considered one, two, and three for each scenario, and the rest of the switches are assumed as disconnectors. The disconnectors are low-speed in comparison with the reclosers. It is assumed that the total number of switches, including disconnectors and reclosers, equals to the number of all switch possible locations. These locations are shown in Figure 3 using the disconnect symbol. The reclosers can be optimally placed among all possible fourteen locations. The maneuver points are the locations that can be connected via the neighboring feeders and are illustrated by red arrows in Figure 3. Table 2 gives the base values of the reliability indices for this case study. Figure 4 illustrates the convergence curve of PSO for allocating three reclosers in three scenarios.Figure 3
The PDN structure of RBTS-Bus2, Roy Billinton test system-Bus 2.Table 2
Base values of the reliability indices for RBTS-Bus2.
IndicesSAIFIbase (Int/cr)SAIDIbase (hr/cr)CAIDIbase (hr/crI)ENSbase (kWh)Value0.249214.045616.233640.9297Figure 4
Convergence curve of PSO considering three reclosers for all scenarios.PSO algorithm can adequately solve this problem (Figure4). Table 3 shows the reliability indices and optimal solutions of three scenarios for the different number of reclosers. The numbers in the ORP column, mean the feeder segment numbers for optimal recloser locations, and the numbers in the OMPP column mean the load-point numbers for optimal maneuver points.Table 3
Reliability indices and optimal solutions of three scenarios for different number of reclosers in RBTS-Bus2.
ScenarioSAIFI (Int/cr)SAIDI (hr/cr)CAIDI (hr/crI)ENS (kWh)OFORPOMPPONPOne REC10.249213.565214.30637.3573.67522PredeterminedUnlimited20.249213.565214.30637.3573.675224,6,10,14Unlimited30.249213.566214.31037.7113.684423,5,10,14(F1-F2), (F3-F4)Two RECs10.249213.536214.19036.9363.65062, 9PredeterminedUnlimited20.249213.508314.07737.1893.64002, 94,6,9,13Unlimited30.249213.536314.19037.1313.65542, 94,6,10,14(F1-F2), (F3-F4)Three RECs10.249213.507314.07436.6523.62942, 9, 10PredeterminedUnlimited20.249213.478913.95936.9963.62372, 3, 103, 6, 9, 13Unlimited30.249213.507414.07436.8743.63422, 9, 104, 6, 10, 14(F1-F2), (F3-F4)The OF values are improved by increasing the number of reclosers. The effect of different maneuver point locations on the system reliability improvement is clearly observed. By comparing scenario 1 and scenario 2 of three reclosers placements, it is observed that when the maneuver points are placed in 3, 6, 9, and 13 instead of the endpoints 4, 6, 10, and 14, the system reliability is increased by %0.157. However, the results show that the power transmission limitations in maneuver points will affect the system reliability in scenario 3. It is worth to say that SAIFI values are the same and equal to 0.24921 in all solutions. This is because the SAIFI does not depend on the switch speed or load-point repair times. Compared to the base condition, that is the PDN without any reclosers and maneuver points, the system reliability in all scenarios will be modified. For example, in scenario 3, by optimal placement of three reclosers, SAIDI has a %13.3 improvement and ENS has a %9.9 improvement.


### 3.2. Real Test System

The proposed method is applied to a real PDN. This case study is a real PDN in Iran. The structure of this network is illustrated in Figure5. The figure shows that this network includes four feeders, in which feeder 1 has four load-points, feeder 2, 7 load-points, and feeder 3 and feeder 4 have 15 and 23 load-points, respectively. In this network, there are 49 load-points. Therefore, there are 49 possible maneuver point locations. The maneuver points are the locations that can be connected from the neighboring feeders, illustrated by red arrows in Figure 5. The number of reclosers is considered as four, eight, and twelve that should be optimally allocated. These points are 1, 3, 4, 5, 6, 8, 11, 12, 17, 25, 27, 32, 43, and 46. Table 4 provides the general parameters of this network. Table 5 gives the base values of the reliability indices for this case study.Figure 5
The PDN structure of real test system, the real network in Iran.Table 4
General parameters of real test system.
FeederTotal load (MWh)IndustrialCommercialResidentialTotal costumersLength (Km)F13.3532851680013449.54F26.188946131023489.402F312.50102143094456380F45.25476832479289791Total27.28501735768311152189.94Table 5
Base values of the reliability indices for case study 2.
IndicesSAIFIbase (Int/cr)SAIDIbase (hr/cr)CAIDIbase (hr/crI)ENSbase (kWh)Value16.54820.2961.22656434.5Figure6 shows the assumed curves for allocating twelve reclosers in three scenarios. Table 6 demonstrates the reliability indices and optimal solutions of three scenarios for the different number of reclosers.Figure 6
Convergence curves of PSO for twelve reclosers in the real network, for all scenarios.Table 6
Reliability indices and optimal solutions of three scenarios for different numbers of reclosers in real test system.
ScenarioSAIFI (Int/cr)SAIDI (hr/cr)CAIDI (hr/crI)ENS (kWh)OFORPOMPPONPDCLFour RECs116.54818.6961.12984864.83.59842, 3, 4, 21PredeterminedUnlimited1, 5, 6, 8, 11, 12, 17, 25, 27, 32, 43, 46216.54817.7661.07354862.13.50623, 4, 21, 234, 7, 21, 33Unlimited1, 5, 6, 8, 11, 12, 17, 25, 27, 32, 43, 46316.54817.8151.07654861.93.51112, 3, 4, 224, 9, 23, 30(F1-F2), (F3-F4)1, 5, 6, 8, 11, 12, 17, 25, 27, 32, 43, 46Eight RECs116.54818.0291.08954862.73.53232, 3, 4,6, 21, 23, 28, 42PredeterminedUnlimited1, 5, 8, 11, 12, 17, 25, 27, 32, 43, 46216.54816.7581.01274858.53.40642,3,4,9,22,23,29,444, 7, 22, 30Unlimited1, 5, 6, 8, 11, 12, 17, 25,27,32,43,46316.54817.0951.03304860.23.43993, 4, 18, 19, 21, 23, 27, 404, 5, 23, 27(F1–F4), (F2-F3)1, 5, 6, 8, 11, 12, 17, 25, 32, 43, 46Twelve RECs116.54817.2881.04474860.83.45902, 3, 4, 6, 9, 11, 13, 15, 21, 23, 35, 40PredeterminedUnlimited1, 5, 8, 12, 17, 25, 27, 32, 43, 46216.54815.7610.952434855.83.30782, 3, 4, 5, 14, 20, 22, 23, 25, 30, 37, 394, 5, 22, 47Unlimited1, 6, 8, 11, 12, 17, 25, 27, 32, 43, 46316.54816.0780.971554856.43.3392, 3, 4, 6, 7, 15, 20, 22, 23, 28, 38, 404, 8, 23, 27(F1-F2), (F3-F4)1, 5, 8, 11, 12, 17, 25, 27, 32, 43, 46Figure6 shows the convergence of results occurring in less than one hundred iterations. As observed in Figure 6, in scenario 1, the predetermined maneuver points in the feeder endpoints are at 4, 11, 26, and 49. The best result is obtained in scenario 2. According to the optimal solution of scenario 2, the results show the importance of the maneuver point locations. Maneuver point locations may be found everywhere in the possible locations and result in a more reliable system. Also, there are maneuver points that cause larger OF values than in the case of end maneuver points. As shown in Table 6, increasing the number of reclosers decreases the OF in all scenarios. For example, if there are twelve reclosers in scenario 3, the OF will be %4.90 lower than that of four reclosers. In comparison with RBTS-Bus2, by increasing the extent of the network, the number of reclosers will have more effects on the system reliability. The other important point is the effect of maneuver point locations on the system reliability improvement. In case of twelve reclosers placement, in scenario 3, the results show that when the maneuver points are placed in the optimal locations 4, 8, 23, and 27, instead of the endpoints of the feeders, the OF is decreased by %3.47. This result clearly shows the significant effect of the maneuver point locations on the system reliability. Also, in this case study, the impact of maneuver point location dominates the effect of power transmission limitations in maneuver points. In fact, when the optimal maneuver points are selected in all scenarios, the OF is lower than the case with predetermined maneuver points, and with no power transmission limitations. As mentioned before, in practical situations, the power transmission limitations must be considered in maneuver points. From Table 6, it is observed that the optimal recloser locations and maneuver points are changed with this practical viewpoint. Moreover, different neighboring feeder pairs will be resulted to the different OFs. According to Table 6, the optimal locations of the reclosers can be selected on the disconnector locations. For example, in scenario 2 for twelve reclosers, the optimal recloser locations and disconnectors are common in 3, 4, and 5, feeder segments. In these cases, the disconnectors are replaced by the reclosers. Compared to the base condition, the system reliability in all scenarios is improved. For example, in scenario 3, SAIDI has a %20.78 decrease, by optimal placement of twelve reclosers, and ENS has a %24.52 improvement. These decreases for eight optimal reclosers placement are 15.77% and %24.46% and for four optimal reclosers placement are 12.22% and 24.44% for SAIDI and ENS, respectively.


### 3.3. Recloser Malfunction Effect on Optimal Switch Placement

This section finds the optimal locations of the reclosers for real test system by considering the malfunction probabilities. The failure rates and the repair rates of each recloser are obtained from the experts in the distribution company, as shown in Table7. From equations (13)–(15), the up and down probabilities of reclosers are %98 and %2, respectively. Figure 7 shows the convergence curves for solving problems by considering reclosers malfunctions.Table 7
Failure and repair rates of the proposed Markov model for real test system.
Failure ratesValues (failure/year)λAB2.0075λAC0.9855λAD2.9930λAE0.2555λCB0.9855λBE0.4745λCE0.3285Repair ratesValues (repair/year)μBA182.5μCA730μDA1460μEA51.83Figure 7
Convergence curves of PSO for twelve reclosers considering malfunctions in the real network, for all scenarios.From Figure7, the best OF belongs to scenario 2, considering different maneuver points like the previous results. The important point is that when the malfunction probabilities are considered, the system reliability is decreased in all scenarios. Table 8 provides the reliability indices and the optimal solutions in the presence of recloser malfunction probabilities.Table 8
Reliability indices and optimal solutions of three scenarios for twelve reclosers in the real test system by considering the recloser malfunctions.
ScenarioSAIFI (Int/cr)SAIDI (hr/cr)CAIDI (hr/crI)ENS (kWh)OFORPOMPPONPDCLTwelve RECs116.54818.5241.11945447.83.67201, 2, 3, 4, 8, 14, 21, 23, 30, 32, 35, 36PredeterminedUnlimited1, 5, 6, 11, 12, 17, 25, 27, 43, 46216.54817.3951.05115444.23.56022, 3, 4, 8, 10, 14, 19, 22, 23, 35, 39, 414, 7, 23, 27Unlimited1, 5, 6, 11, 12, 17, 25, 27, 32, 43, 46316.54817.4161.05245444.13.56222, 3,4, 19, 20, 22, 23, 40, 43, 44, 46, 474, 5, 23, 29(F1-F2), (F3-F4)1, 5, 6, 8, 11, 12, 17, 25, 27, 32The results given in Table8 clearly show that the reclosers optimal locations and optimal maneuver points are changed by considering malfunction probabilities. For example, by comparing of Tables 7 and 8 in scenario 3, the reclosers in points 6, 7, 15, 28, 38 are replaced by the reclosers in points 19, 43, 44, 46, and 47. Moreover, the OF becomes worse because of the malfunction probability effects on the recloser access times. For example, in scenario 3, by considering twelve reclosers with malfunction probabilities, the OF value has a %6.684 rise, compared to the same case without malfunction probabilities. This indicates with a proper planning by PDN companies, it is possible by means of preventing events and faults, the system reliability can be improved. SAIFI is still unaffected because it is independent of the reach time of the reclosers. Compared to the base condition, that is the PDN without any reclosers and maneuver points, the system reliability is improved. For example, in twelve reclosers placement, SAIDI has a %14.18 shrinkage, and ENS has a %15.39 fall as well. Improvements are lower than that of without reclosers malfunction. This shows, in the practical situation, the malfunction consideration can result in a right and proper allocation of reclosers, maneuver points, and neighboring feeders.


## 3.1. RBTS-Bus2

At first, the proposed method is applied to the low-extent RBTS-Bus2. This system is shown in Figure3. This test system with the required data is presented in [35]. In RBTS-Bus2, the number of reclosers is considered one, two, and three for each scenario, and the rest of the switches are assumed as disconnectors. The disconnectors are low-speed in comparison with the reclosers. It is assumed that the total number of switches, including disconnectors and reclosers, equals to the number of all switch possible locations. These locations are shown in Figure 3 using the disconnect symbol. The reclosers can be optimally placed among all possible fourteen locations. The maneuver points are the locations that can be connected via the neighboring feeders and are illustrated by red arrows in Figure 3. Table 2 gives the base values of the reliability indices for this case study. Figure 4 illustrates the convergence curve of PSO for allocating three reclosers in three scenarios.Figure 3
The PDN structure of RBTS-Bus2, Roy Billinton test system-Bus 2.Table 2
Base values of the reliability indices for RBTS-Bus2.
IndicesSAIFIbase (Int/cr)SAIDIbase (hr/cr)CAIDIbase (hr/crI)ENSbase (kWh)Value0.249214.045616.233640.9297Figure 4
Convergence curve of PSO considering three reclosers for all scenarios.PSO algorithm can adequately solve this problem (Figure4). Table 3 shows the reliability indices and optimal solutions of three scenarios for the different number of reclosers. The numbers in the ORP column, mean the feeder segment numbers for optimal recloser locations, and the numbers in the OMPP column mean the load-point numbers for optimal maneuver points.Table 3
Reliability indices and optimal solutions of three scenarios for different number of reclosers in RBTS-Bus2.
ScenarioSAIFI (Int/cr)SAIDI (hr/cr)CAIDI (hr/crI)ENS (kWh)OFORPOMPPONPOne REC10.249213.565214.30637.3573.67522PredeterminedUnlimited20.249213.565214.30637.3573.675224,6,10,14Unlimited30.249213.566214.31037.7113.684423,5,10,14(F1-F2), (F3-F4)Two RECs10.249213.536214.19036.9363.65062, 9PredeterminedUnlimited20.249213.508314.07737.1893.64002, 94,6,9,13Unlimited30.249213.536314.19037.1313.65542, 94,6,10,14(F1-F2), (F3-F4)Three RECs10.249213.507314.07436.6523.62942, 9, 10PredeterminedUnlimited20.249213.478913.95936.9963.62372, 3, 103, 6, 9, 13Unlimited30.249213.507414.07436.8743.63422, 9, 104, 6, 10, 14(F1-F2), (F3-F4)The OF values are improved by increasing the number of reclosers. The effect of different maneuver point locations on the system reliability improvement is clearly observed. By comparing scenario 1 and scenario 2 of three reclosers placements, it is observed that when the maneuver points are placed in 3, 6, 9, and 13 instead of the endpoints 4, 6, 10, and 14, the system reliability is increased by %0.157. However, the results show that the power transmission limitations in maneuver points will affect the system reliability in scenario 3. It is worth to say that SAIFI values are the same and equal to 0.24921 in all solutions. This is because the SAIFI does not depend on the switch speed or load-point repair times. Compared to the base condition, that is the PDN without any reclosers and maneuver points, the system reliability in all scenarios will be modified. For example, in scenario 3, by optimal placement of three reclosers, SAIDI has a %13.3 improvement and ENS has a %9.9 improvement.


## 3.2. Real Test System

The proposed method is applied to a real PDN. This case study is a real PDN in Iran. The structure of this network is illustrated in Figure5. The figure shows that this network includes four feeders, in which feeder 1 has four load-points, feeder 2, 7 load-points, and feeder 3 and feeder 4 have 15 and 23 load-points, respectively. In this network, there are 49 load-points. Therefore, there are 49 possible maneuver point locations. The maneuver points are the locations that can be connected from the neighboring feeders, illustrated by red arrows in Figure 5. The number of reclosers is considered as four, eight, and twelve that should be optimally allocated. These points are 1, 3, 4, 5, 6, 8, 11, 12, 17, 25, 27, 32, 43, and 46. Table 4 provides the general parameters of this network. Table 5 gives the base values of the reliability indices for this case study.Figure 5
The PDN structure of real test system, the real network in Iran.Table 4
General parameters of real test system.
FeederTotal load (MWh)IndustrialCommercialResidentialTotal costumersLength (Km)F13.3532851680013449.54F26.188946131023489.402F312.50102143094456380F45.25476832479289791Total27.28501735768311152189.94Table 5
Base values of the reliability indices for case study 2.
IndicesSAIFIbase (Int/cr)SAIDIbase (hr/cr)CAIDIbase (hr/crI)ENSbase (kWh)Value16.54820.2961.22656434.5Figure6 shows the assumed curves for allocating twelve reclosers in three scenarios. Table 6 demonstrates the reliability indices and optimal solutions of three scenarios for the different number of reclosers.Figure 6
Convergence curves of PSO for twelve reclosers in the real network, for all scenarios.Table 6
Reliability indices and optimal solutions of three scenarios for different numbers of reclosers in real test system.
ScenarioSAIFI (Int/cr)SAIDI (hr/cr)CAIDI (hr/crI)ENS (kWh)OFORPOMPPONPDCLFour RECs116.54818.6961.12984864.83.59842, 3, 4, 21PredeterminedUnlimited1, 5, 6, 8, 11, 12, 17, 25, 27, 32, 43, 46216.54817.7661.07354862.13.50623, 4, 21, 234, 7, 21, 33Unlimited1, 5, 6, 8, 11, 12, 17, 25, 27, 32, 43, 46316.54817.8151.07654861.93.51112, 3, 4, 224, 9, 23, 30(F1-F2), (F3-F4)1, 5, 6, 8, 11, 12, 17, 25, 27, 32, 43, 46Eight RECs116.54818.0291.08954862.73.53232, 3, 4,6, 21, 23, 28, 42PredeterminedUnlimited1, 5, 8, 11, 12, 17, 25, 27, 32, 43, 46216.54816.7581.01274858.53.40642,3,4,9,22,23,29,444, 7, 22, 30Unlimited1, 5, 6, 8, 11, 12, 17, 25,27,32,43,46316.54817.0951.03304860.23.43993, 4, 18, 19, 21, 23, 27, 404, 5, 23, 27(F1–F4), (F2-F3)1, 5, 6, 8, 11, 12, 17, 25, 32, 43, 46Twelve RECs116.54817.2881.04474860.83.45902, 3, 4, 6, 9, 11, 13, 15, 21, 23, 35, 40PredeterminedUnlimited1, 5, 8, 12, 17, 25, 27, 32, 43, 46216.54815.7610.952434855.83.30782, 3, 4, 5, 14, 20, 22, 23, 25, 30, 37, 394, 5, 22, 47Unlimited1, 6, 8, 11, 12, 17, 25, 27, 32, 43, 46316.54816.0780.971554856.43.3392, 3, 4, 6, 7, 15, 20, 22, 23, 28, 38, 404, 8, 23, 27(F1-F2), (F3-F4)1, 5, 8, 11, 12, 17, 25, 27, 32, 43, 46Figure6 shows the convergence of results occurring in less than one hundred iterations. As observed in Figure 6, in scenario 1, the predetermined maneuver points in the feeder endpoints are at 4, 11, 26, and 49. The best result is obtained in scenario 2. According to the optimal solution of scenario 2, the results show the importance of the maneuver point locations. Maneuver point locations may be found everywhere in the possible locations and result in a more reliable system. Also, there are maneuver points that cause larger OF values than in the case of end maneuver points. As shown in Table 6, increasing the number of reclosers decreases the OF in all scenarios. For example, if there are twelve reclosers in scenario 3, the OF will be %4.90 lower than that of four reclosers. In comparison with RBTS-Bus2, by increasing the extent of the network, the number of reclosers will have more effects on the system reliability. The other important point is the effect of maneuver point locations on the system reliability improvement. In case of twelve reclosers placement, in scenario 3, the results show that when the maneuver points are placed in the optimal locations 4, 8, 23, and 27, instead of the endpoints of the feeders, the OF is decreased by %3.47. This result clearly shows the significant effect of the maneuver point locations on the system reliability. Also, in this case study, the impact of maneuver point location dominates the effect of power transmission limitations in maneuver points. In fact, when the optimal maneuver points are selected in all scenarios, the OF is lower than the case with predetermined maneuver points, and with no power transmission limitations. As mentioned before, in practical situations, the power transmission limitations must be considered in maneuver points. From Table 6, it is observed that the optimal recloser locations and maneuver points are changed with this practical viewpoint. Moreover, different neighboring feeder pairs will be resulted to the different OFs. According to Table 6, the optimal locations of the reclosers can be selected on the disconnector locations. For example, in scenario 2 for twelve reclosers, the optimal recloser locations and disconnectors are common in 3, 4, and 5, feeder segments. In these cases, the disconnectors are replaced by the reclosers. Compared to the base condition, the system reliability in all scenarios is improved. For example, in scenario 3, SAIDI has a %20.78 decrease, by optimal placement of twelve reclosers, and ENS has a %24.52 improvement. These decreases for eight optimal reclosers placement are 15.77% and %24.46% and for four optimal reclosers placement are 12.22% and 24.44% for SAIDI and ENS, respectively.


## 3.3. Recloser Malfunction Effect on Optimal Switch Placement

This section finds the optimal locations of the reclosers for real test system by considering the malfunction probabilities. The failure rates and the repair rates of each recloser are obtained from the experts in the distribution company, as shown in Table7. From equations (13)–(15), the up and down probabilities of reclosers are %98 and %2, respectively. Figure 7 shows the convergence curves for solving problems by considering reclosers malfunctions.Table 7
Failure and repair rates of the proposed Markov model for real test system.
Failure ratesValues (failure/year)λAB2.0075λAC0.9855λAD2.9930λAE0.2555λCB0.9855λBE0.4745λCE0.3285Repair ratesValues (repair/year)μBA182.5μCA730μDA1460μEA51.83Figure 7
Convergence curves of PSO for twelve reclosers considering malfunctions in the real network, for all scenarios.From Figure7, the best OF belongs to scenario 2, considering different maneuver points like the previous results. The important point is that when the malfunction probabilities are considered, the system reliability is decreased in all scenarios. Table 8 provides the reliability indices and the optimal solutions in the presence of recloser malfunction probabilities.Table 8
Reliability indices and optimal solutions of three scenarios for twelve reclosers in the real test system by considering the recloser malfunctions.
ScenarioSAIFI (Int/cr)SAIDI (hr/cr)CAIDI (hr/crI)ENS (kWh)OFORPOMPPONPDCLTwelve RECs116.54818.5241.11945447.83.67201, 2, 3, 4, 8, 14, 21, 23, 30, 32, 35, 36PredeterminedUnlimited1, 5, 6, 11, 12, 17, 25, 27, 43, 46216.54817.3951.05115444.23.56022, 3, 4, 8, 10, 14, 19, 22, 23, 35, 39, 414, 7, 23, 27Unlimited1, 5, 6, 11, 12, 17, 25, 27, 32, 43, 46316.54817.4161.05245444.13.56222, 3,4, 19, 20, 22, 23, 40, 43, 44, 46, 474, 5, 23, 29(F1-F2), (F3-F4)1, 5, 6, 8, 11, 12, 17, 25, 27, 32The results given in Table8 clearly show that the reclosers optimal locations and optimal maneuver points are changed by considering malfunction probabilities. For example, by comparing of Tables 7 and 8 in scenario 3, the reclosers in points 6, 7, 15, 28, 38 are replaced by the reclosers in points 19, 43, 44, 46, and 47. Moreover, the OF becomes worse because of the malfunction probability effects on the recloser access times. For example, in scenario 3, by considering twelve reclosers with malfunction probabilities, the OF value has a %6.684 rise, compared to the same case without malfunction probabilities. This indicates with a proper planning by PDN companies, it is possible by means of preventing events and faults, the system reliability can be improved. SAIFI is still unaffected because it is independent of the reach time of the reclosers. Compared to the base condition, that is the PDN without any reclosers and maneuver points, the system reliability is improved. For example, in twelve reclosers placement, SAIDI has a %14.18 shrinkage, and ENS has a %15.39 fall as well. Improvements are lower than that of without reclosers malfunction. This shows, in the practical situation, the malfunction consideration can result in a right and proper allocation of reclosers, maneuver points, and neighboring feeders.


## 4. Conclusion

In this paper, a new practical approach of the recloser placement problem in RBTS and a real PDN in Iran was proposed. The effects of different maneuver point locations and limitations on power transmission capacity in the maneuver points were studied. The proposed approach was utilized in aforementioned network for different scenarios. Based on these practical constraints, the optimal recloser locations, optimal maneuver points, and the optimal neighboring feeders were found. The results indicated that in a scenario, different maneuver points improved the real test system reliability by %4.37. This improvement with maneuver point capacity consideration is reduced to %3.47. To consider the recloser malfunction, all possible malfunctions and defects were identified and classified from the practical viewpoint of the distribution network company experts. Then, by using this information, a Markov model was proposed to obtain the recloser malfunction probabilities. In all scenarios, the recloser placement was performed in the presence of disconnectors with the ability of disconnection under load. Results revealed that the recloser malfunctions might influence the optimal locations of the maneuver points, reclosers, and neighboring feeders. Compared to the nonpractical full reliable reclosers, considering malfunctions resulted in a %6.684 decrease in the real test system reliability. This confirms the importance of taking into account the recloser malfunctions for better planning in practice. The DG units can be considered as maneuver points in the view point of implementation. However, those are technically different from maneuver point in the capacity of energy supply, effect on the network loss, and reliability indices, etc. Therefore, the effects of DG units by considering their issues such as capacity and type of DGs on the optimal switch placement will be studied in the future work.



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*Source: 5062350-2022-04-22.xml*