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

Optimal Recloser Placement in Distribution System Considering Maneuver Points, Practical... Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 5062350, 12 pages https://doi.org/10.1155/2022/5062350 Research Article Optimal Recloser Placement in Distribution System Considering Maneuver Points, Practical Limitations, and Recloser Malfunction Mohammad Zaher Ghorbani-Juybari , Hossein Gholizade-Narm , and Yaser Damchi Shahrood University of Technology, Faculty of Electrical Engineering, Shahrood, Iran Correspondence should be addressed to Hossein Gholizade-Narm; gholizade@shahroodut.ac.ir Received 12 December 2021; Revised 1 March 2022; Accepted 14 March 2022; Published 22 April 2022 Academic Editor: Santi A. Rizzo Copyright © 2022 Mohammad Zaher Ghorbani-Juybari et al. +is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. +e 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. +e 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. +e 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. +is underscores the importance of taking into account the reclosers malfunctions in optimal switch placement for better decision making in practice. optimally without malfunction probability of the switches. 1. Introduction In [9], the system reliability is improved by obtaining the Reliability improvement is one of the important goals of optimum number of sectionalizing switches using the ant PDNs [1]. Improving reliability indices of the PDNs has been colony algorithm, but normally open switches only connect interested in recent studies [2–4]. Optimal allocation of fast the endpoints of the feeders. In [10], the effects of RCS switches such as reclosers is necessary to reduce the access malfunction on PDN reliability are presented, but the effect of maneuver points and their capacity are not studied. RCS time and consequently decrease the interruption time [5]. +e reliability of PDNs can be improved by the optimal allocation and enhancing reliability by optimizing the re- duction of customer interruption cost, the reduction of placement of manual and automatic switching devices [6]. In practical cases, selecting the proper maneuver points for the SAIDI, and the number of restored loads are presented in load transfer is crucial [7]. In addition, similar to other [11], without studying any malfunction. +e genetic algo- elements of the distribution networks, the reclosers do not rithm is used in [12] to determine recloser optimal place- always work properly. +e literature review is presented as ment, but none of the mentioned considerations such as follows. malfunctions and maneuver points effects are not studied. A In [8], the network automation planning problem is new MILP formulation to find the optimum numbers and defined in terms of MILP; different switches are located locations of fault indicators in distribution systems is 2 International Transactions on Electrical Energy Systems models to consider switch malfunctions. However, all of the presented in [13]. A method using analytical hierarchy process for finding the reclosers optimal number and lo- mentioned practical issues, i.e., effect of different maneuver points, limitation on power transmission capacity in the cation by evaluating reliability indices such as SAIFI, SAIDI, MAIFI, and ENS is presented in [14], without the effects of maneuver points, and the recloser malfunctions are not maneuver point locations. Optimal placement of the sec- studied, simultaneously. At the same time, these issues can tionalizing switches based on deterministic algorithms is affect the optimal solution of the problem. In this paper, a presented in [15], while the SAIFI, SAIDI, and AENS indices particle swarm algorithm is used to solve the problem. +e were computed without discussing the effects of the ma- contributions are as follows: neuver points and switch malfunctions on the optimal so- (i) Optimal placement of reclosers lution. A mathematical model for the placement of (ii) Considering recloser malfunction using proposed protective and controlling devices in PDNs is presented in Markov model [16]. In [17], an MILP formulation is proposed for the switch placement problem and guaranties the global optimal so- (iii) Finding the optimal maneuver points lution, but the effect of the maneuver points, switch mal- (iv) Considering the power transmission capacity lim- functions, and maneuver point capacities are not considered. itations from neighboring feeders +e optimal placement of RCSs considering laterals is (v) Finding the optimal neighboring feeders. presented in [18] using an MILP model. Sectionalizing switch placement, considering switch failure, is studied in Nowadays, the DG sources are essential in the PDNs. +e [19], and a model based on mixed-integer programming DGs can be considered as maneuver points in the view point format is proposed to integrate the impacts of a switch of implementation (as considered in the proposed method), failure in switch placement problem, but the effect of dif- while those are different from maneuver point technically ferent maneuver points and different types of switch defects, such as capacity of energy supply, effect on the network loss, with practical concerning, are not studied. In [20], a bidi- and effect on reliability indices. rectional formulation for optimal placement of protective To better illustrate contributions, recent studies are devices and switches such as reclosers and fuses is modified. categorized in Table 1 according to different perspectives, +e model considers the bidirectional power flow at any part including optimal maneuver point, optimal recloser of a PDN, while the protective devices are assumed to be placement, recloser malfunction, manual switch, optimal fully reliable. Providing the optimal location of reclosers to neighboring feeder, and maneuver point capacity. For minimize the power loss cost is presented in [21], but the example, based on Table 1, considering different ma- recloser malfunctions and maneuver point effects are not neuver points, maneuver point capacity, and finding the studied. In [22], an approach to optimize the location of best neighboring feeders were not studied in the previous reclosers using the cross-entropy method and reassessment studies. +ese are practical concerns that influence the of Monte Carlo sampled states is proposed. However, PDN reliability indices and optimal placement of finding the best neighboring feeders and the effect of the reclosers. maneuver points on the optimal solution are not studied. +e rest of the paper is organized as follows. In Section Optimal switch placement, using a high-accuracy MILP 2, the problem formulation consists of the OF, problem formulation, is proposed in [23], but the switch malfunction constraints, and the proposed Markov model is presented. probability is not modelled. In [24], optimal placement of In addition to their analysis, the simulation results are fault indicators and sectionalizing switches are studied with given in Section 3. Finally, the conclusion is presented in the assumption that section switches and fault indicators do Section 4. not malfunction. Also, this problem is presented in [25], with the assumption that the fault indicators, RCSs, and 2. Problem Formulation disconnectors are all installed at the beginning of each branch, without taking into account their malfunction In this section, the problem formulation is presented. At probability. In [26], the discrete Markov chain model is used, first, the OF is introduced. +en, the constraints of the and the effect of malfunction probability of sectionalizing problem are defined. Finally, a Markov model is proposed to switches is studied, but the maneuver points are considered consider the recloser’s malfunctions. predetermined at the endpoints of feeders. In [27], a hybrid method for recloser and sectionalizer placement in PDNs considering protection coordination, fault type, and 2.1. Objective Function Definition. +e reliability of the equipment malfunction is proposed, without the practical PDNs can be evaluated by many criteria depending on the limitations of the maneuver points. Also, in [28], remodeling distribution company goals. Some companies pay more of a PDN by optimal placement of auto-reclosers is proposed attention to the system costs, while others prioritize energy to enhance system reliability. +e limitations for load consumption [30, 31]. Evaluation of a PDN is performed by transfer and the malfunctions are not considered. analyzing a suitable function that should be a good indicator Reclosers are electrical equipment with a predefined of the system reliability. sequence of opening and reclosing [29]. +ese switches are +is paper considers the following OF. +is OF is a usually assumed entirely reliable; however, this is not always combination of both customer-orientated and energy-ori- accurate in practical cases. Some studies such as [10] present entated indices. International Transactions on Electrical Energy Systems 3 Table 1: Comparison between the recent approaches in the literature. Optimal Optimal recloser Recloser Manual Optimal Maneuver point Reference maneuver points placement malfunction switches neighboring feeder capacities [2, 4, 5, 8, 12, 14, 20–22, 28] × ✓ × × × × [6, 10, 18, 19, 23, 24, 26] × × × ✓ × × [11] × ✓ × ✓ × × [16] × ✓ × ✓ × × [27] × ✓ ✓ × × × Proposed method ✓ ✓ ✓ ✓ ✓ ✓ +is constraint is dependent on the identity of PDN. +e SAIDI SAIFI CAIDI ENS j j j j OF � min 􏽘 + + + . 􏼠 􏼡 constraint on the number of disconnectors is determined SAIDI SAIFI CAIDI ENS base base base base j�1 according to the total budget and the PDN structure. Equation (10) shows the limitation on the maneuver ca- (1) pacity, which is specified according to the PDN character- +e variables in equation (1) are as follows: istics such as the number of customers, customer type, and SAIDI (hr/cr) is the system average interruption dura- so on. tion index and is calculated by equation (2) [31]. Min Max N ≤ N ≤ N , (6) Rec Rec Rec 􏽐 U N i i SAIDI � . (2) Min Max 􏽐 N i (7) N ≤ N ≤ N , MP MP MP SAIFI (Int/cr) is the system average interruption fre- Min Max (8) N ≤ N ≤ N , quency index and is obtained as follows: Feed Feed Feed 􏽐 λ N i i Max SAIFI � . (3) 0≤ N ≤ N , (9) Sec Sec 􏽐 N Min Max ENS (kWh) is the energy not supplied given in equation C ≤ C ≤ C . (10) MP MP MP (4): When an interruption happens due to a fault in the ENS � 􏽘 L U . (4) a(i) i system, the faultless parts can be isolated and connected through the neighboring feeders [31]. +e points that are CAIDI (hr/crI) is customer average interruption dura- capable of connecting the neighboring feeders, so-called tion index formulated as follows: maneuver points, are assumed to be predetermined in the 􏽐 U N previous studies. However, these points may be located i i CAIDI � . (5) everywhere in the feeders, which can be fed from the 􏽐 λ N i i neighboring feeders. Moreover, due to limitations on the Indices are normalized by dividing them by their base power transmission capacities in the maneuver points, it is values: SAIDI , SAIFI , CAIDI , ENS which are important to choose an optimal neighboring feeder. base base base base, the values of these indices without any recloser and ma- neuver point in the PDN. +e decision variables are the 2.3. Proposed Markov Model. PDN devices such as reclosers recloser locations, maneuver point locations, and the do not always work properly. Switches are usually assumed neighboring feeders that must be optimally found. quite reliable, but in practical conditions, they encounter malfunctions. By considering the recloser malfunctions, 2.2. Constraints. In practice, the number of reclosers is their optimal locations can be changed. Different reasons limited due to the high cost of reclosers and budget limi- may cause these malfunctions. Solenoid defects, oil leakage tations. Moreover, developing the maneuver points is faced or oil pollution in the recloser, energy storage defects, events with high costs and difficulties such as legal restrictions and and faults due to wrong setup and equipment steal, and geographical obstacles like passing through the gas trans- disarrange in the wiring of recloser control panel are the most common reclosers malfunctions. +e solenoid defects mission branches. +erefore, these financial and technical limitations impose some constraints on the OF. Equation (6) such as changes in the magnetic characteristics, spring shows the constraint on the number of reclosers that is tension, and plunger malfunctions can influence the recloser determined based on the total budget of distribution performance. +e flow of the displaced oil determines the company. Equation (7) is the constraint on the number of timing before contact opening [32]. Accordingly, the oil maneuver points. +is is specified based on the PDN’s leakage in the reclosers can result in delay in contact environmental conditions, the total budget, and the legal opening. +e events and faults due to wrong setup include restrictions. +en, the constraint on the number of neigh- every undesirable situation that is caused due to implement boring feeders must be regarded, as shown in equation (8). and software imperfections. For example, one of the most 4 International Transactions on Electrical Energy Systems repetitive setup faults is the lack of coordination between the HWIS recloser and the upper-hand substation. Moreover, human errors can cause the wrong setup problems. e environ- D mental conditions include every reason that are originated BA AB LR from the external environment. For example, relay software AD inaccessibility and recloser equipment steals have occurred DA AB HI HID NH in the last six years. Up LR In this paper, a Markov model is proposed for reliability EA CA analysis of recloser. e states of the recloser operation in the λ λ λ AE BE CB Down proposed Markov model is illustrated in Figure 1 as follows. CE A: Healthy with on-time isolation (HI) B: Healthy but isolated with delay (HID) AC C: Healthy without isolation due to environmental LR conditions (HWIE) HWIE D: Healthy without isolation due to wrong setup Figure 1: Proposed Markov model for the recloser malfunctions (HWIS) modeling. E: Not healthy (NH). If a recloser is initially in state A, the recloser performs an example of the wrong setup. State E occurs when a correctly without delay. State B includes conditions in which recloser is out of service and does not isolate the fault. a recloser isolates healthily, but with a delay because of e transition rate matrix TR for the Markov model is equipment malfunctions. For example, if the recloser spring deˆned as follows [33]. is under tension, this in†uences the speed of disconnecting, or oil pollution can change its performance, such as pressure TR  TR , ij n × n and cohesion. However, in many practical cases, the recloser   is healthy itself, but it cannot isolate. For example, the −  a ,i  j (11) ij reclosers control panel and associated cables may be stolen, TR  . j ≠ i ij or temperature conditions can in†uence the performance of a ,i ≠ j ij recloser. ese cases belong to state C and are also known as environmental conditions. State D shows that the recloser From Figure 1, the transition matrix is obtained cannot isolate due to the wrong setup, and the recloser according to equation (12). cannot properly detect the feeder faults. Lack of coordina- tion between the recloser and the upper-hand substation is − λ + λ + λ + λ λ λ λ λ AB AC AD AE AB AC AD AE                    μ − μ + λ 00 λ     BA BA BE BE                        TR  μ λ − μ + λ + λ  0 λ . (12)      CA CB CA CB CE CE                             μ 0 0 −μ 0     DA DA    μ 0 00 −μ EA EA P  P + P , (14) Up A B To calculate the probability of the recloser states, it is necessary to solve the following equations system. P  P + P + P . (15) Down C D E P  1, (13) σ1 3. Simulation Results P × TR  0, is section investigates the optimal recloser placement for where P [P ,P , ... ,P ]. both completely reliable reclosers and malfunctioned 1 2 σ According to this model, the probability of up and down reclosers. At ˆrst, the two case studies, Roy Billinton and a states of reclosers can be written as follows: real distribution network in Mazandaran, Iran, which are International Transactions on Electrical Energy Systems 5 used to apply the proposed method, are presented. +en, the reclosers. +e numbers in the ORP column, mean the feeder problem is stated in three different scenarios. Only the segment numbers for optimal recloser locations, and the numbers in the OMPP column mean the load-point reclosers are optimally placed in the first scenario, and the maneuver points are predetermined in the feeders’ end- numbers for optimal maneuver points. points, without any capacity limitations. +e second and +e OF values are improved by increasing the number of third scenarios are concerned with selectable maneuver reclosers. +e effect of different maneuver point locations on points, with and without limitations on the power trans- the system reliability improvement is clearly observed. By mission capacities, respectively. In the third scenario, the comparing scenario 1 and scenario 2 of three reclosers best neighboring feeders are selected and the maneuver placements, it is observed that when the maneuver points are points are found optimally. Scenarios are summarized as placed in 3, 6, 9, and 13 instead of the endpoints 4, 6, 10, and follows: 14, the system reliability is increased by %0.157. However, the results show that the power transmission limitations in Scenario 1: +e optimal recloser locations are obtained maneuver points will affect the system reliability in scenario in the case of predetermined maneuver points and 3. It is worth to say that SAIFI values are the same and equal unlimited power transmission condition to 0.24921 in all solutions. +is is because the SAIFI does not Scenario 2: With unlimited power transmission ca- depend on the switch speed or load-point repair times. pacity, optimal recloser locations and maneuver points Compared to the base condition, that is the PDN without are obtained. any reclosers and maneuver points, the system reliability in Scenario 3: With limited power transmission capacity, all scenarios will be modified. For example, in scenario 3, by optimal placement of three reclosers, SAIDI has a %13.3 optimal recloser locations and maneuver points are obtained. improvement and ENS has a %9.9 improvement. Simple implementation and effective response of particle swarm optimization made it one of the most popular 3.2. Real Test System. +e proposed method is applied to a metaheuristic optimization methods. +e PSO algorithm is real PDN. +is case study is a real PDN in Iran. +e structure thoroughly introduced in [34]. In this paper, the PSO al- of this network is illustrated in Figure 5. +e figure shows gorithm is used to solve the problem. +e inertia weight is that this network includes four feeders, in which feeder 1 has w � 0.98, and the population size considered is 100. four load-points, feeder 2, 7 load-points, and feeder 3 and Figure 2 shows a simple flowchart for solving the feeder 4 have 15 and 23 load-points, respectively. In this problem. According to this flowchart, at first the input data network, there are 49 load-points. +erefore, there are 49 of the network are received. +en the problem is solved by possible maneuver point locations. +e maneuver points are PSO for determined iterations Iter . Finally, if the dif- Max the locations that can be connected from the neighboring ferences between last K solutions be small than a predefined feeders, illustrated by red arrows in Figure 5. +e number of small value ε, the algorithm will be stopped, otherwise, it is reclosers is considered as four, eight, and twelve that should added K iterations in order to reach the solution conver- be optimally allocated. +ese points are 1, 3, 4, 5, 6, 8, 11, 12, gence. It must be mentioned by increasing K the solution has 17, 25, 27, 32, 43, and 46. Table 4 provides the general more accuracy. In this paper, the problem is solved with parameters of this network. Table 5 gives the base values of K � 10 and Iter � 200. Max the reliability indices for this case study. Figure 6 shows the assumed curves for allocating twelve reclosers in three scenarios. Table 6 demonstrates the reli- 3.1. RBTS-Bus2. At first, the proposed method is applied to ability indices and optimal solutions of three scenarios for the low-extent RBTS-Bus2. +is system is shown in Figure 3. +is test system with the required data is presented in [35]. the different number of reclosers. Figure 6 shows the convergence of results occurring in In RBTS-Bus2, the number of reclosers is considered one, two, and three for each scenario, and the rest of the switches less than one hundred iterations. As observed in Figure 6, in scenario 1, the predetermined maneuver points in the feeder are assumed as disconnectors. +e disconnectors are low- endpoints are at 4, 11, 26, and 49. +e best result is obtained speed in comparison with the reclosers. It is assumed that the in scenario 2. According to the optimal solution of scenario total number of switches, including disconnectors and 2, the results show the importance of the maneuver point reclosers, equals to the number of all switch possible loca- locations. Maneuver point locations may be found every- tions. +ese locations are shown in Figure 3 using the where in the possible locations and result in a more reliable disconnect symbol. +e reclosers can be optimally placed system. Also, there are maneuver points that cause larger OF among all possible fourteen locations. +e maneuver points values than in the case of end maneuver points. As shown in are the locations that can be connected via the neighboring feeders and are illustrated by red arrows in Figure 3. Table 2 Table 6, increasing the number of reclosers decreases the OF in all scenarios. For example, if there are twelve reclosers in gives the base values of the reliability indices for this case study. Figure 4 illustrates the convergence curve of PSO for scenario 3, the OF will be %4.90 lower than that of four reclosers. In comparison with RBTS-Bus2, by increasing the allocating three reclosers in three scenarios. extent of the network, the number of reclosers will have PSO algorithm can adequately solve this problem more effects on the system reliability. +e other important (Figure 4). Table 3 shows the reliability indices and optimal point is the effect of maneuver point locations on the system solutions of three scenarios for the different number of 6 International Transactions on Electrical Energy Systems Start Input PDN Data Iter = 1 Particle Swarm Optimization OF Iter Iter = Iter +K Iter = Iter+1 Max Max NO YES YES NO Differences between < ε Iter<Iter Output = OF Max Iter OF , (γ = Iter -K,..,Iter ) γ Max Max End Figure 2: A simple †owchart for solving the problem. LP19 LP17 LP22 MP13 MP14 MP11 MP12 F4 12 13 11 14 LP21 LP16 LP18 LP20 NO LP11 LP13 F3 7 8 9 MP7 MP8 MP9 MP10 LP14 LP15 LP10 LP12 11KV MP5 MP6 F2 LP9 LP8 NO LP5 LP1 LP3 F1 1 23 MP3 MP4 MP1 MP2 LP4 LP6 LP7 LP2 Maneuver Point MP Normally Open NO Disconnect Transformer Breaker Fuse Figure 3: e PDN structure of RBTS-Bus2, Roy Billinton test system-Bus 2. Table 2: Base values of the reliability indices for RBTS-Bus2. Indices SAIFI (Int/cr) SAIDI (hr/cr) CAIDI (hr/crI) ENS (kWh) base base base base Value 0.24921 4.0456 16.2336 40.9297 International Transactions on Electrical Energy Systems 7 3.66 3.655 3.65 3.645 3.64 3.635 3.63 3.625 3.62 0 20 40 60 80 100 120 140 160 180 200 Iteration Scenario1 Scenario2 Scenario3 Figure 4: Convergence curve of PSO considering three reclosers for all scenarios. Table 3: Reliability indices and optimal solutions of three scenarios for di¢erent number of reclosers in RBTS-Bus2. Scenario SAIFI (Int/cr) SAIDI (hr/cr) CAIDI (hr/crI) ENS (kWh) OF ORP OMPP ONP One REC 1 0.24921 3.5652 14.306 37.357 3.6752 2 Predetermined Unlimited 2 0.24921 3.5652 14.306 37.357 3.6752 2 4,6,10,14 Unlimited 3 0.24921 3.5662 14.310 37.711 3.6844 2 3,5,10,14 (F1-F2), (F3-F4) Two RECs 1 0.24921 3.5362 14.190 36.936 3.6506 2, 9 Predetermined Unlimited 2 0.24921 3.5083 14.077 37.189 3.6400 2, 9 4,6,9,13 Unlimited 3 0.24921 3.5363 14.190 37.131 3.6554 2, 9 4,6,10,14 (F1-F2), (F3-F4) ree RECs 1 0.24921 3.5073 14.074 36.652 3.6294 2, 9, 10 Predetermined Unlimited 2 0.24921 3.4789 13.959 36.996 3.6237 2, 3, 10 3, 6, 9, 13 Unlimited 3 0.24921 3.5074 14.074 36.874 3.6342 2, 9, 10 4, 6, 10, 14 (F1-F2), (F3-F4) reliability improvement. In case of twelve reclosers place- can be selected on the disconnector locations. For example, ment, in scenario 3, the results show that when the maneuver in scenario 2 for twelve reclosers, the optimal recloser lo- points are placed in the optimal locations 4, 8, 23, and 27, cations and disconnectors are common in 3, 4, and 5, feeder instead of the endpoints of the feeders, the OF is decreased segments. In these cases, the disconnectors are replaced by by %3.47. is result clearly shows the signiˆcant e¢ect of the reclosers. Compared to the base condition, the system the maneuver point locations on the system reliability. Also, reliability in all scenarios is improved. For example, in in this case study, the impact of maneuver point location scenario 3, SAIDI has a %20.78 decrease, by optimal dominates the e¢ect of power transmission limitations in placement of twelve reclosers, and ENS has a %24.52 im- maneuver points. In fact, when the optimal maneuver points provement. ese decreases for eight optimal reclosers are selected in all scenarios, the OF is lower than the case placement are 15.77% and %24.46% and for four optimal with predetermined maneuver points, and with no power reclosers placement are 12.22% and 24.44% for SAIDI and transmission limitations. As mentioned before, in practical ENS, respectively. 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 3.3. Recloser Malfunction E ect on Optimal Switch Placement. changed with this practical viewpoint. Moreover, di¢erent is section ˆnds the optimal locations of the reclosers for neighboring feeder pairs will be resulted to the di¢erent OFs. real test system by considering the malfunction probabilities. According to Table 6, the optimal locations of the reclosers e failure rates and the repair rates of each recloser are Objective function 8 International Transactions on Electrical Energy Systems LP35 LP36 LP37 LP43 LP44 LP45 Real Power Distribution Network in Iran MP34 MP35 LP33 MP36 MP27 MP43 MP44 MP37 MP33 MP29 MP31 43 44 F4 35 MP30 MP32 LP31 34 MP42 45 MP45 32 LP34 31 39 40 41 47 48 49 MP49 MP41 28 MP39 MP28 MP38 MP40 LP46 LP42 46 MP46 MP48 MP47 LP19 LP21 LP20 LP32 LP27 LP28 LP29 LP30 LP38 LP39 LP40 LP41 LP48 LP49 LP47 MP18 LP23 MP16 MP13 MP21 MP15 MP25 F3 12 MP17 19 23 MP14 LP13 MP12 15 17 20 22 MP24 MP26 . 21 18 LP18 LP22 13 MP20 MP19 MP23 MP22 LP15 LP16 LP17 LP24 20 KV LP12 LP14 LP26 LP11 MP9 LP25 LP9 MP11 MP6 MP7 MP5 F2 MP10 MP8 Maneuver Point MP LP7 LP5 LP8 LP6 LP10 Disconnect Sectioner LP3 3 Feeder Segment Number Red Numbers MP1 F1 MP3 2 MP2 MP4 LP2 LP1 LP4 Figure 5: e PDN structure of real test system, the real network in Iran. Table 4: General parameters of real test system. Feeder Total load (MWh) Industrial Commercial Residential Total costumers Length (Km) F1 3.353 28 516 800 1344 9.54 F2 6.18 8 946 1310 2348 9.402 F3 12.50 10 214 3094 4563 80 F4 5.25 4 7683 2479 2897 91 Total 27.28 50 1735 7683 11152 189.94 Table 5: Base values of the reliability indices for case study 2. Indices SAIFI (Int/cr) SAIDI (hr/cr) CAIDI (hr/crI) ENS (kWh) base base base base Value 16.548 20.296 1.2265 6434.5 obtained from the experts in the distribution company, as example, by comparing of Tables 7 and 8 in scenario 3, the shown in Table 7. From equations (13)–(15), the up and reclosers in points 6, 7, 15, 28, 38 are replaced by the down probabilities of reclosers are %98 and %2, respectively. reclosers in points 19, 43, 44, 46, and 47. Moreover, the OF Figure 7 shows the convergence curves for solving problems becomes worse because of the malfunction probability ef- by considering reclosers malfunctions. fects on the recloser access times. For example, in scenario 3, From Figure 7, the best OF belongs to scenario 2, by considering twelve reclosers with malfunction proba- considering di¢erent maneuver points like the previous bilities, the OF value has a %6.684 rise, compared to the same results. e important point is that when the malfunction case without malfunction probabilities. is indicates with a probabilities are considered, the system reliability is de- proper planning by PDN companies, it is possible by means creased in all scenarios. Table 8 provides the reliability in- of preventing events and faults, the system reliability can be dices and the optimal solutions in the presence of recloser improved. SAIFI is still una¢ected because it is independent malfunction probabilities. of the reach time of the reclosers. Compared to the base e results given in Table 8 clearly show that the condition, that is the PDN without any reclosers and ma- reclosers optimal locations and optimal maneuver points are neuver points, the system reliability is improved. For ex- changed by considering malfunction probabilities. For ample, in twelve reclosers placement, SAIDI has a %14.18 International Transactions on Electrical Energy Systems 9 3.7 3.65 3.6 3.55 3.5 3.45 3.4 3.35 3.3 0 20 40 60 80 100 120 140 160 180 200 Iteration Scenario1 Scenario2 Scenario3 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 di¢erent numbers of reclosers in real test system. SAIFI SAIDI CAIDI ENS Scenario OF ORP OMPP ONP DCL (Int/cr) (hr/cr) (hr/crI) (kWh) Four RECs 1, 5, 6, 8, 11, 12, 17, 1 16.548 18.696 1.1298 4864.8 3.5984 2, 3, 4, 21 Predetermined Unlimited 25, 27, 32, 43, 46 1, 5, 6, 8, 11, 12, 17, 2 16.548 17.766 1.0735 4862.1 3.5062 3, 4, 21, 23 4, 7, 21, 33 Unlimited 25, 27, 32, 43, 46 (F1-F2), 1, 5, 6, 8, 11, 12, 17, 3 16.548 17.815 1.0765 4861.9 3.5111 2, 3, 4, 22 4, 9, 23, 30 (F3-F4) 25, 27, 32, 43, 46 Eight RECs 1, 5, 8, 11, 12, 17, 25, 1 16.548 18.029 1.0895 4862.7 3.5323 2, 3, 4,6, 21, 23, 28, 42 Predetermined Unlimited 27, 32, 43, 46 1, 5, 6, 8, 11, 12, 17, 2 16.548 16.758 1.0127 4858.5 3.4064 2,3,4,9,22,23,29,44 4, 7, 22, 30 Unlimited 25,27,32,43,46 (F1–F4), 1, 5, 6, 8, 11, 12, 17, 3 16.548 17.095 1.0330 4860.2 3.4399 3, 4, 18, 19, 21, 23, 27, 40 4, 5, 23, 27 (F2-F3) 25, 32, 43, 46 Twelve RECs 2, 3, 4, 6, 9, 11, 13, 15, 1, 5, 8, 12, 17, 25, 27, 1 16.548 17.288 1.0447 4860.8 3.4590 Predetermined Unlimited 21, 23, 35, 40 32, 43, 46 2, 3, 4, 5, 14, 20, 22, 23, 1, 6, 8, 11, 12, 17, 25, 2 16.548 15.761 0.95243 4855.8 3.3078 4, 5, 22, 47 Unlimited 25, 30, 37, 39 27, 32, 43, 46 2, 3, 4, 6, 7, 15, 20, 22, (F1-F2), 1, 5, 8, 11, 12, 17, 25, 3 16.548 16.078 0.97155 4856.4 3.339 4, 8, 23, 27 23, 28, 38, 40 (F3-F4) 27, 32, 43, 46 Table 7: Failure and repair rates of the proposed Markov model for real test system. Failure rates Values (failure/year) λ 2.0075 AB λ 0.9855 AC λ 2.9930 AD λ 0.2555 AE λ 0.9855 CB λ 0.4745 BE λ 0.3285 CE Repair rates Values (repair/year) μ 182.5 BA μ 730 CA μ 1460 DA μ 51.83 EA Objective function 10 International Transactions on Electrical Energy Systems 3.76 3.74 3.72 3.7 3.68 3.66 3.64 3.62 3.6 3.58 3.56 0 20 40 60 80 100 120 140 160 180 200 Iteration Scenario1 Scenario2 Scenario3 Figure 7: Convergence curves of PSO for twelve reclosers considering malfunctions in the real network, for all scenarios. Table 8: Reliability indices and optimal solutions of three scenarios for twelve reclosers in the real test system by considering the recloser malfunctions. SAIFI SAIDI CAIDI ENS Scenario OF ORP OMPP ONP DCL (Int/cr) (hr/cr) (hr/crI) (kWh) Twelve RECs 1, 2, 3, 4, 8, 14, 21, 1, 5, 6, 11, 12, 17, 1 16.548 18.524 1.1194 5447.8 3.6720 Predetermined Unlimited 23, 30, 32, 35, 36 25, 27, 43, 46 2, 3, 4, 8, 10, 14, 19, 1, 5, 6, 11, 12, 17, 2 16.548 17.395 1.0511 5444.2 3.5602 4, 7, 23, 27 Unlimited 22, 23, 35, 39, 41 25, 27, 32, 43, 46 2, 3,4, 19, 20, 22, 23, (F1-F2), (F3- 1, 5, 6, 8, 11, 12, 17, 3 16.548 17.416 1.0524 5444.1 3.5622 4, 5, 23, 29 40, 43, 44, 46, 47 F4) 25, 27, 32 shrinkage, and ENS has a %15.39 fall as well. Improvements malfunctions and defects were identiˆed and classiˆed from the practical viewpoint of the distribution network are lower than that of without reclosers malfunction. is shows, in the practical situation, the malfunction consid- company experts. en, by using this information, a eration can result in a right and proper allocation of Markov model was proposed to obtain the recloser mal- reclosers, maneuver points, and neighboring feeders. function probabilities. In all scenarios, the recloser placement was performed in the presence of disconnectors with the ability of disconnection under load. Results 4. Conclusion revealed that the recloser malfunctions might in†uence the In this paper, a new practical approach of the recloser optimal locations of the maneuver points, reclosers, and placement problem in RBTS and a real PDN in Iran was neighboring feeders. Compared to the nonpractical full reliable reclosers, considering malfunctions resulted in a % proposed. e e¢ects of di¢erent maneuver point locations and limitations on power transmission capacity in the 6.684 decrease in the real test system reliability. is conˆrms the importance of taking into account the recloser maneuver points were studied. e proposed approach was utilized in aforementioned network for di¢erent scenarios. malfunctions for better planning in practice. e DG units Based on these practical constraints, the optimal recloser can be considered as maneuver points in the view point of locations, optimal maneuver points, and the optimal implementation. However, those are technically di¢erent neighboring feeders were found. e results indicated that from maneuver point in the capacity of energy supply, in a scenario, di¢erent maneuver points improved the real e¢ect on the network loss, and reliability indices, etc. test system reliability by %4.37. is improvement with erefore, the e¢ects of DG units by considering their maneuver point capacity consideration is reduced to %3.47. issues such as capacity and type of DGs on the optimal To consider the recloser malfunction, all possible switch placement will be studied in the future work. Objective function International Transactions on Electrical Energy Systems 11 International Journal of Electrical Power & Energy Systems, Abbrevations vol. 55, pp. 602–611, 2014. [2] A. Alam, M. Tariq, M. 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Billinton, Reliability Evaluation of Power Systems, Springer US, Berlin, Germany, 2013. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Transactions on Electrical Energy Systems Hindawi Publishing Corporation

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

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Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 5062350, 12 pages https://doi.org/10.1155/2022/5062350 Research Article Optimal Recloser Placement in Distribution System Considering Maneuver Points, Practical Limitations, and Recloser Malfunction Mohammad Zaher Ghorbani-Juybari , Hossein Gholizade-Narm , and Yaser Damchi Shahrood University of Technology, Faculty of Electrical Engineering, Shahrood, Iran Correspondence should be addressed to Hossein Gholizade-Narm; gholizade@shahroodut.ac.ir Received 12 December 2021; Revised 1 March 2022; Accepted 14 March 2022; Published 22 April 2022 Academic Editor: Santi A. Rizzo Copyright © 2022 Mohammad Zaher Ghorbani-Juybari et al. +is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. +e 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. +e 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. +e 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. +is underscores the importance of taking into account the reclosers malfunctions in optimal switch placement for better decision making in practice. optimally without malfunction probability of the switches. 1. Introduction In [9], the system reliability is improved by obtaining the Reliability improvement is one of the important goals of optimum number of sectionalizing switches using the ant PDNs [1]. Improving reliability indices of the PDNs has been colony algorithm, but normally open switches only connect interested in recent studies [2–4]. Optimal allocation of fast the endpoints of the feeders. In [10], the effects of RCS switches such as reclosers is necessary to reduce the access malfunction on PDN reliability are presented, but the effect of maneuver points and their capacity are not studied. RCS time and consequently decrease the interruption time [5]. +e reliability of PDNs can be improved by the optimal allocation and enhancing reliability by optimizing the re- duction of customer interruption cost, the reduction of placement of manual and automatic switching devices [6]. In practical cases, selecting the proper maneuver points for the SAIDI, and the number of restored loads are presented in load transfer is crucial [7]. In addition, similar to other [11], without studying any malfunction. +e genetic algo- elements of the distribution networks, the reclosers do not rithm is used in [12] to determine recloser optimal place- always work properly. +e literature review is presented as ment, but none of the mentioned considerations such as follows. malfunctions and maneuver points effects are not studied. A In [8], the network automation planning problem is new MILP formulation to find the optimum numbers and defined in terms of MILP; different switches are located locations of fault indicators in distribution systems is 2 International Transactions on Electrical Energy Systems models to consider switch malfunctions. However, all of the presented in [13]. A method using analytical hierarchy process for finding the reclosers optimal number and lo- mentioned practical issues, i.e., effect of different maneuver points, limitation on power transmission capacity in the cation by evaluating reliability indices such as SAIFI, SAIDI, MAIFI, and ENS is presented in [14], without the effects of maneuver points, and the recloser malfunctions are not maneuver point locations. Optimal placement of the sec- studied, simultaneously. At the same time, these issues can tionalizing switches based on deterministic algorithms is affect the optimal solution of the problem. In this paper, a presented in [15], while the SAIFI, SAIDI, and AENS indices particle swarm algorithm is used to solve the problem. +e were computed without discussing the effects of the ma- contributions are as follows: neuver points and switch malfunctions on the optimal so- (i) Optimal placement of reclosers lution. A mathematical model for the placement of (ii) Considering recloser malfunction using proposed protective and controlling devices in PDNs is presented in Markov model [16]. In [17], an MILP formulation is proposed for the switch placement problem and guaranties the global optimal so- (iii) Finding the optimal maneuver points lution, but the effect of the maneuver points, switch mal- (iv) Considering the power transmission capacity lim- functions, and maneuver point capacities are not considered. itations from neighboring feeders +e optimal placement of RCSs considering laterals is (v) Finding the optimal neighboring feeders. presented in [18] using an MILP model. Sectionalizing switch placement, considering switch failure, is studied in Nowadays, the DG sources are essential in the PDNs. +e [19], and a model based on mixed-integer programming DGs can be considered as maneuver points in the view point format is proposed to integrate the impacts of a switch of implementation (as considered in the proposed method), failure in switch placement problem, but the effect of dif- while those are different from maneuver point technically ferent maneuver points and different types of switch defects, such as capacity of energy supply, effect on the network loss, with practical concerning, are not studied. In [20], a bidi- and effect on reliability indices. rectional formulation for optimal placement of protective To better illustrate contributions, recent studies are devices and switches such as reclosers and fuses is modified. categorized in Table 1 according to different perspectives, +e model considers the bidirectional power flow at any part including optimal maneuver point, optimal recloser of a PDN, while the protective devices are assumed to be placement, recloser malfunction, manual switch, optimal fully reliable. Providing the optimal location of reclosers to neighboring feeder, and maneuver point capacity. For minimize the power loss cost is presented in [21], but the example, based on Table 1, considering different ma- recloser malfunctions and maneuver point effects are not neuver points, maneuver point capacity, and finding the studied. In [22], an approach to optimize the location of best neighboring feeders were not studied in the previous reclosers using the cross-entropy method and reassessment studies. +ese are practical concerns that influence the of Monte Carlo sampled states is proposed. However, PDN reliability indices and optimal placement of finding the best neighboring feeders and the effect of the reclosers. maneuver points on the optimal solution are not studied. +e rest of the paper is organized as follows. In Section Optimal switch placement, using a high-accuracy MILP 2, the problem formulation consists of the OF, problem formulation, is proposed in [23], but the switch malfunction constraints, and the proposed Markov model is presented. probability is not modelled. In [24], optimal placement of In addition to their analysis, the simulation results are fault indicators and sectionalizing switches are studied with given in Section 3. Finally, the conclusion is presented in the assumption that section switches and fault indicators do Section 4. not malfunction. Also, this problem is presented in [25], with the assumption that the fault indicators, RCSs, and 2. Problem Formulation disconnectors are all installed at the beginning of each branch, without taking into account their malfunction In this section, the problem formulation is presented. At probability. In [26], the discrete Markov chain model is used, first, the OF is introduced. +en, the constraints of the and the effect of malfunction probability of sectionalizing problem are defined. Finally, a Markov model is proposed to switches is studied, but the maneuver points are considered consider the recloser’s malfunctions. predetermined at the endpoints of feeders. In [27], a hybrid method for recloser and sectionalizer placement in PDNs considering protection coordination, fault type, and 2.1. Objective Function Definition. +e reliability of the equipment malfunction is proposed, without the practical PDNs can be evaluated by many criteria depending on the limitations of the maneuver points. Also, in [28], remodeling distribution company goals. Some companies pay more of a PDN by optimal placement of auto-reclosers is proposed attention to the system costs, while others prioritize energy to enhance system reliability. +e limitations for load consumption [30, 31]. Evaluation of a PDN is performed by transfer and the malfunctions are not considered. analyzing a suitable function that should be a good indicator Reclosers are electrical equipment with a predefined of the system reliability. sequence of opening and reclosing [29]. +ese switches are +is paper considers the following OF. +is OF is a usually assumed entirely reliable; however, this is not always combination of both customer-orientated and energy-ori- accurate in practical cases. Some studies such as [10] present entated indices. International Transactions on Electrical Energy Systems 3 Table 1: Comparison between the recent approaches in the literature. Optimal Optimal recloser Recloser Manual Optimal Maneuver point Reference maneuver points placement malfunction switches neighboring feeder capacities [2, 4, 5, 8, 12, 14, 20–22, 28] × ✓ × × × × [6, 10, 18, 19, 23, 24, 26] × × × ✓ × × [11] × ✓ × ✓ × × [16] × ✓ × ✓ × × [27] × ✓ ✓ × × × Proposed method ✓ ✓ ✓ ✓ ✓ ✓ +is constraint is dependent on the identity of PDN. +e SAIDI SAIFI CAIDI ENS j j j j OF � min 􏽘 + + + . 􏼠 􏼡 constraint on the number of disconnectors is determined SAIDI SAIFI CAIDI ENS base base base base j�1 according to the total budget and the PDN structure. Equation (10) shows the limitation on the maneuver ca- (1) pacity, which is specified according to the PDN character- +e variables in equation (1) are as follows: istics such as the number of customers, customer type, and SAIDI (hr/cr) is the system average interruption dura- so on. tion index and is calculated by equation (2) [31]. Min Max N ≤ N ≤ N , (6) Rec Rec Rec 􏽐 U N i i SAIDI � . (2) Min Max 􏽐 N i (7) N ≤ N ≤ N , MP MP MP SAIFI (Int/cr) is the system average interruption fre- Min Max (8) N ≤ N ≤ N , quency index and is obtained as follows: Feed Feed Feed 􏽐 λ N i i Max SAIFI � . (3) 0≤ N ≤ N , (9) Sec Sec 􏽐 N Min Max ENS (kWh) is the energy not supplied given in equation C ≤ C ≤ C . (10) MP MP MP (4): When an interruption happens due to a fault in the ENS � 􏽘 L U . (4) a(i) i system, the faultless parts can be isolated and connected through the neighboring feeders [31]. +e points that are CAIDI (hr/crI) is customer average interruption dura- capable of connecting the neighboring feeders, so-called tion index formulated as follows: maneuver points, are assumed to be predetermined in the 􏽐 U N previous studies. However, these points may be located i i CAIDI � . (5) everywhere in the feeders, which can be fed from the 􏽐 λ N i i neighboring feeders. Moreover, due to limitations on the Indices are normalized by dividing them by their base power transmission capacities in the maneuver points, it is values: SAIDI , SAIFI , CAIDI , ENS which are important to choose an optimal neighboring feeder. base base base base, the values of these indices without any recloser and ma- neuver point in the PDN. +e decision variables are the 2.3. Proposed Markov Model. PDN devices such as reclosers recloser locations, maneuver point locations, and the do not always work properly. Switches are usually assumed neighboring feeders that must be optimally found. quite reliable, but in practical conditions, they encounter malfunctions. By considering the recloser malfunctions, 2.2. Constraints. In practice, the number of reclosers is their optimal locations can be changed. Different reasons limited due to the high cost of reclosers and budget limi- may cause these malfunctions. Solenoid defects, oil leakage tations. Moreover, developing the maneuver points is faced or oil pollution in the recloser, energy storage defects, events with high costs and difficulties such as legal restrictions and and faults due to wrong setup and equipment steal, and geographical obstacles like passing through the gas trans- disarrange in the wiring of recloser control panel are the most common reclosers malfunctions. +e solenoid defects mission branches. +erefore, these financial and technical limitations impose some constraints on the OF. Equation (6) such as changes in the magnetic characteristics, spring shows the constraint on the number of reclosers that is tension, and plunger malfunctions can influence the recloser determined based on the total budget of distribution performance. +e flow of the displaced oil determines the company. Equation (7) is the constraint on the number of timing before contact opening [32]. Accordingly, the oil maneuver points. +is is specified based on the PDN’s leakage in the reclosers can result in delay in contact environmental conditions, the total budget, and the legal opening. +e events and faults due to wrong setup include restrictions. +en, the constraint on the number of neigh- every undesirable situation that is caused due to implement boring feeders must be regarded, as shown in equation (8). and software imperfections. For example, one of the most 4 International Transactions on Electrical Energy Systems repetitive setup faults is the lack of coordination between the HWIS recloser and the upper-hand substation. Moreover, human errors can cause the wrong setup problems. e environ- D mental conditions include every reason that are originated BA AB LR from the external environment. For example, relay software AD inaccessibility and recloser equipment steals have occurred DA AB HI HID NH in the last six years. Up LR In this paper, a Markov model is proposed for reliability EA CA analysis of recloser. e states of the recloser operation in the λ λ λ AE BE CB Down proposed Markov model is illustrated in Figure 1 as follows. CE A: Healthy with on-time isolation (HI) B: Healthy but isolated with delay (HID) AC C: Healthy without isolation due to environmental LR conditions (HWIE) HWIE D: Healthy without isolation due to wrong setup Figure 1: Proposed Markov model for the recloser malfunctions (HWIS) modeling. E: Not healthy (NH). If a recloser is initially in state A, the recloser performs an example of the wrong setup. State E occurs when a correctly without delay. State B includes conditions in which recloser is out of service and does not isolate the fault. a recloser isolates healthily, but with a delay because of e transition rate matrix TR for the Markov model is equipment malfunctions. For example, if the recloser spring deˆned as follows [33]. is under tension, this in†uences the speed of disconnecting, or oil pollution can change its performance, such as pressure TR  TR , ij n × n and cohesion. However, in many practical cases, the recloser   is healthy itself, but it cannot isolate. For example, the −  a ,i  j (11) ij reclosers control panel and associated cables may be stolen, TR  . j ≠ i ij or temperature conditions can in†uence the performance of a ,i ≠ j ij recloser. ese cases belong to state C and are also known as environmental conditions. State D shows that the recloser From Figure 1, the transition matrix is obtained cannot isolate due to the wrong setup, and the recloser according to equation (12). cannot properly detect the feeder faults. Lack of coordina- tion between the recloser and the upper-hand substation is − λ + λ + λ + λ λ λ λ λ AB AC AD AE AB AC AD AE                    μ − μ + λ 00 λ     BA BA BE BE                        TR  μ λ − μ + λ + λ  0 λ . (12)      CA CB CA CB CE CE                             μ 0 0 −μ 0     DA DA    μ 0 00 −μ EA EA P  P + P , (14) Up A B To calculate the probability of the recloser states, it is necessary to solve the following equations system. P  P + P + P . (15) Down C D E P  1, (13) σ1 3. Simulation Results P × TR  0, is section investigates the optimal recloser placement for where P [P ,P , ... ,P ]. both completely reliable reclosers and malfunctioned 1 2 σ According to this model, the probability of up and down reclosers. At ˆrst, the two case studies, Roy Billinton and a states of reclosers can be written as follows: real distribution network in Mazandaran, Iran, which are International Transactions on Electrical Energy Systems 5 used to apply the proposed method, are presented. +en, the reclosers. +e numbers in the ORP column, mean the feeder problem is stated in three different scenarios. Only the segment numbers for optimal recloser locations, and the numbers in the OMPP column mean the load-point reclosers are optimally placed in the first scenario, and the maneuver points are predetermined in the feeders’ end- numbers for optimal maneuver points. points, without any capacity limitations. +e second and +e OF values are improved by increasing the number of third scenarios are concerned with selectable maneuver reclosers. +e effect of different maneuver point locations on points, with and without limitations on the power trans- the system reliability improvement is clearly observed. By mission capacities, respectively. In the third scenario, the comparing scenario 1 and scenario 2 of three reclosers best neighboring feeders are selected and the maneuver placements, it is observed that when the maneuver points are points are found optimally. Scenarios are summarized as placed in 3, 6, 9, and 13 instead of the endpoints 4, 6, 10, and follows: 14, the system reliability is increased by %0.157. However, the results show that the power transmission limitations in Scenario 1: +e optimal recloser locations are obtained maneuver points will affect the system reliability in scenario in the case of predetermined maneuver points and 3. It is worth to say that SAIFI values are the same and equal unlimited power transmission condition to 0.24921 in all solutions. +is is because the SAIFI does not Scenario 2: With unlimited power transmission ca- depend on the switch speed or load-point repair times. pacity, optimal recloser locations and maneuver points Compared to the base condition, that is the PDN without are obtained. any reclosers and maneuver points, the system reliability in Scenario 3: With limited power transmission capacity, all scenarios will be modified. For example, in scenario 3, by optimal placement of three reclosers, SAIDI has a %13.3 optimal recloser locations and maneuver points are obtained. improvement and ENS has a %9.9 improvement. Simple implementation and effective response of particle swarm optimization made it one of the most popular 3.2. Real Test System. +e proposed method is applied to a metaheuristic optimization methods. +e PSO algorithm is real PDN. +is case study is a real PDN in Iran. +e structure thoroughly introduced in [34]. In this paper, the PSO al- of this network is illustrated in Figure 5. +e figure shows gorithm is used to solve the problem. +e inertia weight is that this network includes four feeders, in which feeder 1 has w � 0.98, and the population size considered is 100. four load-points, feeder 2, 7 load-points, and feeder 3 and Figure 2 shows a simple flowchart for solving the feeder 4 have 15 and 23 load-points, respectively. In this problem. According to this flowchart, at first the input data network, there are 49 load-points. +erefore, there are 49 of the network are received. +en the problem is solved by possible maneuver point locations. +e maneuver points are PSO for determined iterations Iter . Finally, if the dif- Max the locations that can be connected from the neighboring ferences between last K solutions be small than a predefined feeders, illustrated by red arrows in Figure 5. +e number of small value ε, the algorithm will be stopped, otherwise, it is reclosers is considered as four, eight, and twelve that should added K iterations in order to reach the solution conver- be optimally allocated. +ese points are 1, 3, 4, 5, 6, 8, 11, 12, gence. It must be mentioned by increasing K the solution has 17, 25, 27, 32, 43, and 46. Table 4 provides the general more accuracy. In this paper, the problem is solved with parameters of this network. Table 5 gives the base values of K � 10 and Iter � 200. Max the reliability indices for this case study. Figure 6 shows the assumed curves for allocating twelve reclosers in three scenarios. Table 6 demonstrates the reli- 3.1. RBTS-Bus2. At first, the proposed method is applied to ability indices and optimal solutions of three scenarios for the low-extent RBTS-Bus2. +is system is shown in Figure 3. +is test system with the required data is presented in [35]. the different number of reclosers. Figure 6 shows the convergence of results occurring in In RBTS-Bus2, the number of reclosers is considered one, two, and three for each scenario, and the rest of the switches less than one hundred iterations. As observed in Figure 6, in scenario 1, the predetermined maneuver points in the feeder are assumed as disconnectors. +e disconnectors are low- endpoints are at 4, 11, 26, and 49. +e best result is obtained speed in comparison with the reclosers. It is assumed that the in scenario 2. According to the optimal solution of scenario total number of switches, including disconnectors and 2, the results show the importance of the maneuver point reclosers, equals to the number of all switch possible loca- locations. Maneuver point locations may be found every- tions. +ese locations are shown in Figure 3 using the where in the possible locations and result in a more reliable disconnect symbol. +e reclosers can be optimally placed system. Also, there are maneuver points that cause larger OF among all possible fourteen locations. +e maneuver points values than in the case of end maneuver points. As shown in are the locations that can be connected via the neighboring feeders and are illustrated by red arrows in Figure 3. Table 2 Table 6, increasing the number of reclosers decreases the OF in all scenarios. For example, if there are twelve reclosers in gives the base values of the reliability indices for this case study. Figure 4 illustrates the convergence curve of PSO for scenario 3, the OF will be %4.90 lower than that of four reclosers. In comparison with RBTS-Bus2, by increasing the allocating three reclosers in three scenarios. extent of the network, the number of reclosers will have PSO algorithm can adequately solve this problem more effects on the system reliability. +e other important (Figure 4). Table 3 shows the reliability indices and optimal point is the effect of maneuver point locations on the system solutions of three scenarios for the different number of 6 International Transactions on Electrical Energy Systems Start Input PDN Data Iter = 1 Particle Swarm Optimization OF Iter Iter = Iter +K Iter = Iter+1 Max Max NO YES YES NO Differences between < ε Iter<Iter Output = OF Max Iter OF , (γ = Iter -K,..,Iter ) γ Max Max End Figure 2: A simple †owchart for solving the problem. LP19 LP17 LP22 MP13 MP14 MP11 MP12 F4 12 13 11 14 LP21 LP16 LP18 LP20 NO LP11 LP13 F3 7 8 9 MP7 MP8 MP9 MP10 LP14 LP15 LP10 LP12 11KV MP5 MP6 F2 LP9 LP8 NO LP5 LP1 LP3 F1 1 23 MP3 MP4 MP1 MP2 LP4 LP6 LP7 LP2 Maneuver Point MP Normally Open NO Disconnect Transformer Breaker Fuse Figure 3: e PDN structure of RBTS-Bus2, Roy Billinton test system-Bus 2. Table 2: Base values of the reliability indices for RBTS-Bus2. Indices SAIFI (Int/cr) SAIDI (hr/cr) CAIDI (hr/crI) ENS (kWh) base base base base Value 0.24921 4.0456 16.2336 40.9297 International Transactions on Electrical Energy Systems 7 3.66 3.655 3.65 3.645 3.64 3.635 3.63 3.625 3.62 0 20 40 60 80 100 120 140 160 180 200 Iteration Scenario1 Scenario2 Scenario3 Figure 4: Convergence curve of PSO considering three reclosers for all scenarios. Table 3: Reliability indices and optimal solutions of three scenarios for di¢erent number of reclosers in RBTS-Bus2. Scenario SAIFI (Int/cr) SAIDI (hr/cr) CAIDI (hr/crI) ENS (kWh) OF ORP OMPP ONP One REC 1 0.24921 3.5652 14.306 37.357 3.6752 2 Predetermined Unlimited 2 0.24921 3.5652 14.306 37.357 3.6752 2 4,6,10,14 Unlimited 3 0.24921 3.5662 14.310 37.711 3.6844 2 3,5,10,14 (F1-F2), (F3-F4) Two RECs 1 0.24921 3.5362 14.190 36.936 3.6506 2, 9 Predetermined Unlimited 2 0.24921 3.5083 14.077 37.189 3.6400 2, 9 4,6,9,13 Unlimited 3 0.24921 3.5363 14.190 37.131 3.6554 2, 9 4,6,10,14 (F1-F2), (F3-F4) ree RECs 1 0.24921 3.5073 14.074 36.652 3.6294 2, 9, 10 Predetermined Unlimited 2 0.24921 3.4789 13.959 36.996 3.6237 2, 3, 10 3, 6, 9, 13 Unlimited 3 0.24921 3.5074 14.074 36.874 3.6342 2, 9, 10 4, 6, 10, 14 (F1-F2), (F3-F4) reliability improvement. In case of twelve reclosers place- can be selected on the disconnector locations. For example, ment, in scenario 3, the results show that when the maneuver in scenario 2 for twelve reclosers, the optimal recloser lo- points are placed in the optimal locations 4, 8, 23, and 27, cations and disconnectors are common in 3, 4, and 5, feeder instead of the endpoints of the feeders, the OF is decreased segments. In these cases, the disconnectors are replaced by by %3.47. is result clearly shows the signiˆcant e¢ect of the reclosers. Compared to the base condition, the system the maneuver point locations on the system reliability. Also, reliability in all scenarios is improved. For example, in in this case study, the impact of maneuver point location scenario 3, SAIDI has a %20.78 decrease, by optimal dominates the e¢ect of power transmission limitations in placement of twelve reclosers, and ENS has a %24.52 im- maneuver points. In fact, when the optimal maneuver points provement. ese decreases for eight optimal reclosers are selected in all scenarios, the OF is lower than the case placement are 15.77% and %24.46% and for four optimal with predetermined maneuver points, and with no power reclosers placement are 12.22% and 24.44% for SAIDI and transmission limitations. As mentioned before, in practical ENS, respectively. 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 3.3. Recloser Malfunction E ect on Optimal Switch Placement. changed with this practical viewpoint. Moreover, di¢erent is section ˆnds the optimal locations of the reclosers for neighboring feeder pairs will be resulted to the di¢erent OFs. real test system by considering the malfunction probabilities. According to Table 6, the optimal locations of the reclosers e failure rates and the repair rates of each recloser are Objective function 8 International Transactions on Electrical Energy Systems LP35 LP36 LP37 LP43 LP44 LP45 Real Power Distribution Network in Iran MP34 MP35 LP33 MP36 MP27 MP43 MP44 MP37 MP33 MP29 MP31 43 44 F4 35 MP30 MP32 LP31 34 MP42 45 MP45 32 LP34 31 39 40 41 47 48 49 MP49 MP41 28 MP39 MP28 MP38 MP40 LP46 LP42 46 MP46 MP48 MP47 LP19 LP21 LP20 LP32 LP27 LP28 LP29 LP30 LP38 LP39 LP40 LP41 LP48 LP49 LP47 MP18 LP23 MP16 MP13 MP21 MP15 MP25 F3 12 MP17 19 23 MP14 LP13 MP12 15 17 20 22 MP24 MP26 . 21 18 LP18 LP22 13 MP20 MP19 MP23 MP22 LP15 LP16 LP17 LP24 20 KV LP12 LP14 LP26 LP11 MP9 LP25 LP9 MP11 MP6 MP7 MP5 F2 MP10 MP8 Maneuver Point MP LP7 LP5 LP8 LP6 LP10 Disconnect Sectioner LP3 3 Feeder Segment Number Red Numbers MP1 F1 MP3 2 MP2 MP4 LP2 LP1 LP4 Figure 5: e PDN structure of real test system, the real network in Iran. Table 4: General parameters of real test system. Feeder Total load (MWh) Industrial Commercial Residential Total costumers Length (Km) F1 3.353 28 516 800 1344 9.54 F2 6.18 8 946 1310 2348 9.402 F3 12.50 10 214 3094 4563 80 F4 5.25 4 7683 2479 2897 91 Total 27.28 50 1735 7683 11152 189.94 Table 5: Base values of the reliability indices for case study 2. Indices SAIFI (Int/cr) SAIDI (hr/cr) CAIDI (hr/crI) ENS (kWh) base base base base Value 16.548 20.296 1.2265 6434.5 obtained from the experts in the distribution company, as example, by comparing of Tables 7 and 8 in scenario 3, the shown in Table 7. From equations (13)–(15), the up and reclosers in points 6, 7, 15, 28, 38 are replaced by the down probabilities of reclosers are %98 and %2, respectively. reclosers in points 19, 43, 44, 46, and 47. Moreover, the OF Figure 7 shows the convergence curves for solving problems becomes worse because of the malfunction probability ef- by considering reclosers malfunctions. fects on the recloser access times. For example, in scenario 3, From Figure 7, the best OF belongs to scenario 2, by considering twelve reclosers with malfunction proba- considering di¢erent maneuver points like the previous bilities, the OF value has a %6.684 rise, compared to the same results. e important point is that when the malfunction case without malfunction probabilities. is indicates with a probabilities are considered, the system reliability is de- proper planning by PDN companies, it is possible by means creased in all scenarios. Table 8 provides the reliability in- of preventing events and faults, the system reliability can be dices and the optimal solutions in the presence of recloser improved. SAIFI is still una¢ected because it is independent malfunction probabilities. of the reach time of the reclosers. Compared to the base e results given in Table 8 clearly show that the condition, that is the PDN without any reclosers and ma- reclosers optimal locations and optimal maneuver points are neuver points, the system reliability is improved. For ex- changed by considering malfunction probabilities. For ample, in twelve reclosers placement, SAIDI has a %14.18 International Transactions on Electrical Energy Systems 9 3.7 3.65 3.6 3.55 3.5 3.45 3.4 3.35 3.3 0 20 40 60 80 100 120 140 160 180 200 Iteration Scenario1 Scenario2 Scenario3 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 di¢erent numbers of reclosers in real test system. SAIFI SAIDI CAIDI ENS Scenario OF ORP OMPP ONP DCL (Int/cr) (hr/cr) (hr/crI) (kWh) Four RECs 1, 5, 6, 8, 11, 12, 17, 1 16.548 18.696 1.1298 4864.8 3.5984 2, 3, 4, 21 Predetermined Unlimited 25, 27, 32, 43, 46 1, 5, 6, 8, 11, 12, 17, 2 16.548 17.766 1.0735 4862.1 3.5062 3, 4, 21, 23 4, 7, 21, 33 Unlimited 25, 27, 32, 43, 46 (F1-F2), 1, 5, 6, 8, 11, 12, 17, 3 16.548 17.815 1.0765 4861.9 3.5111 2, 3, 4, 22 4, 9, 23, 30 (F3-F4) 25, 27, 32, 43, 46 Eight RECs 1, 5, 8, 11, 12, 17, 25, 1 16.548 18.029 1.0895 4862.7 3.5323 2, 3, 4,6, 21, 23, 28, 42 Predetermined Unlimited 27, 32, 43, 46 1, 5, 6, 8, 11, 12, 17, 2 16.548 16.758 1.0127 4858.5 3.4064 2,3,4,9,22,23,29,44 4, 7, 22, 30 Unlimited 25,27,32,43,46 (F1–F4), 1, 5, 6, 8, 11, 12, 17, 3 16.548 17.095 1.0330 4860.2 3.4399 3, 4, 18, 19, 21, 23, 27, 40 4, 5, 23, 27 (F2-F3) 25, 32, 43, 46 Twelve RECs 2, 3, 4, 6, 9, 11, 13, 15, 1, 5, 8, 12, 17, 25, 27, 1 16.548 17.288 1.0447 4860.8 3.4590 Predetermined Unlimited 21, 23, 35, 40 32, 43, 46 2, 3, 4, 5, 14, 20, 22, 23, 1, 6, 8, 11, 12, 17, 25, 2 16.548 15.761 0.95243 4855.8 3.3078 4, 5, 22, 47 Unlimited 25, 30, 37, 39 27, 32, 43, 46 2, 3, 4, 6, 7, 15, 20, 22, (F1-F2), 1, 5, 8, 11, 12, 17, 25, 3 16.548 16.078 0.97155 4856.4 3.339 4, 8, 23, 27 23, 28, 38, 40 (F3-F4) 27, 32, 43, 46 Table 7: Failure and repair rates of the proposed Markov model for real test system. Failure rates Values (failure/year) λ 2.0075 AB λ 0.9855 AC λ 2.9930 AD λ 0.2555 AE λ 0.9855 CB λ 0.4745 BE λ 0.3285 CE Repair rates Values (repair/year) μ 182.5 BA μ 730 CA μ 1460 DA μ 51.83 EA Objective function 10 International Transactions on Electrical Energy Systems 3.76 3.74 3.72 3.7 3.68 3.66 3.64 3.62 3.6 3.58 3.56 0 20 40 60 80 100 120 140 160 180 200 Iteration Scenario1 Scenario2 Scenario3 Figure 7: Convergence curves of PSO for twelve reclosers considering malfunctions in the real network, for all scenarios. Table 8: Reliability indices and optimal solutions of three scenarios for twelve reclosers in the real test system by considering the recloser malfunctions. SAIFI SAIDI CAIDI ENS Scenario OF ORP OMPP ONP DCL (Int/cr) (hr/cr) (hr/crI) (kWh) Twelve RECs 1, 2, 3, 4, 8, 14, 21, 1, 5, 6, 11, 12, 17, 1 16.548 18.524 1.1194 5447.8 3.6720 Predetermined Unlimited 23, 30, 32, 35, 36 25, 27, 43, 46 2, 3, 4, 8, 10, 14, 19, 1, 5, 6, 11, 12, 17, 2 16.548 17.395 1.0511 5444.2 3.5602 4, 7, 23, 27 Unlimited 22, 23, 35, 39, 41 25, 27, 32, 43, 46 2, 3,4, 19, 20, 22, 23, (F1-F2), (F3- 1, 5, 6, 8, 11, 12, 17, 3 16.548 17.416 1.0524 5444.1 3.5622 4, 5, 23, 29 40, 43, 44, 46, 47 F4) 25, 27, 32 shrinkage, and ENS has a %15.39 fall as well. Improvements malfunctions and defects were identiˆed and classiˆed from the practical viewpoint of the distribution network are lower than that of without reclosers malfunction. is shows, in the practical situation, the malfunction consid- company experts. en, by using this information, a eration can result in a right and proper allocation of Markov model was proposed to obtain the recloser mal- reclosers, maneuver points, and neighboring feeders. function probabilities. In all scenarios, the recloser placement was performed in the presence of disconnectors with the ability of disconnection under load. Results 4. Conclusion revealed that the recloser malfunctions might in†uence the In this paper, a new practical approach of the recloser optimal locations of the maneuver points, reclosers, and placement problem in RBTS and a real PDN in Iran was neighboring feeders. Compared to the nonpractical full reliable reclosers, considering malfunctions resulted in a % proposed. e e¢ects of di¢erent maneuver point locations and limitations on power transmission capacity in the 6.684 decrease in the real test system reliability. is conˆrms the importance of taking into account the recloser maneuver points were studied. e proposed approach was utilized in aforementioned network for di¢erent scenarios. malfunctions for better planning in practice. e DG units Based on these practical constraints, the optimal recloser can be considered as maneuver points in the view point of locations, optimal maneuver points, and the optimal implementation. However, those are technically di¢erent neighboring feeders were found. e results indicated that from maneuver point in the capacity of energy supply, in a scenario, di¢erent maneuver points improved the real e¢ect on the network loss, and reliability indices, etc. test system reliability by %4.37. is improvement with erefore, the e¢ects of DG units by considering their maneuver point capacity consideration is reduced to %3.47. issues such as capacity and type of DGs on the optimal To consider the recloser malfunction, all possible switch placement will be studied in the future work. Objective function International Transactions on Electrical Energy Systems 11 International Journal of Electrical Power & Energy Systems, Abbrevations vol. 55, pp. 602–611, 2014. [2] A. Alam, M. Tariq, M. 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International Transactions on Electrical Energy Systems – Hindawi Publishing Corporation

Published: Apr 22, 2022

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