Optimization Based Method for Fault Section Estimation on Distribution Systems

Faults are inevitable in power systems and the accurate fault location is essential for system restoration and prompt response to customers demands. An alternative to identify the fault section in power distribution systems is to monitor the alarms and status of the protective devices. This paper presents a novel approach for fault section estimation in power distribution systems. The fault section location is treated as a 0–1 integer programming problem. The fault hypothesis is based on the actual and expected status of protective relays, circuit breakers, reclosers and fault indicators. Aiming to solve the programming problem, a new objective function is proposed and the genetic algorithm is used. The proposed method is applied to a typical 33 bus distribution system. The performance and effectiveness of the proposed method are assessed in challenging scenarios, including spurious data and operating failures of protective devices. The results show the feasibility of the proposed method for fault section estimation on power distribution systems.

voltage/current monitoring. In this scenario, monitoring the 26 alarms and status of the protective devices (PD) can ensure 27 the fault detection. For this purpose, the power system can be 28 The associate editor coordinating the review of this manuscript and approving it for publication was Ali Raza . divided into sections, according to its topology. In this paper, 29 a section is a part of the system (e.g: line, bus, etc) delim- 30 ited by PD, such as circuit breakers (CB), protective relays 31 (PR), etc. In general, the fault section estimation problem 32 is straightforward when the PD operate correctly. However, 33 in the cases of failure and/or malfunctioning of PD, the fault 34 diagnosis is not always trivial [5]. 35 The fault section estimation was initially proposed by [6]. 36 In that paper, an expert system (ES) was presented and data 37 from PR and CB were used. Other ES-based methods for 38 fault diagnosis are presented in [7], [8], and [9]. In general, 39 ES-based methods use a rule-based database and apply a 40 reasoning system to locate the faulted section. However, the 41 design and maintenance of the database are laborious tasks. 42 In addition to ES, several techniques have been applied to 43 the fault section estimation problem, such as neural networks 44 (NN) [ [18]. Despite their good perfor-46 mance, NN-based methods inevitably require a lot of data for 47 by applying GA. In addition, the OF considers failure 104 indexes that improve the fault section estimation even in 105 cases with spurious data (PD operating logic errors or 106 communication errors). 107 • A simple procedure is derived to attribute the weight 108 factors to each element of the OF, including the PD and 109 the corresponding sections. This procedure highlights 110 the importance level of each PD and each corresponding 111 section for the fault diagnosis.

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• The proposed method has been successfully tested in 113 several challenging cases, including spurious status of 114 PD. Unlike the existing methods, the proposed one dis-115 tinguishes true FH from false, showing superior perfor-116 mance and demonstrating its applicability to cases with 117 abnormal or missing PD status, in addition to spurious 118 data.

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The fault section estimation problem refers to the identifi-121 cation of the most probable fault hypothesis that explains 122 the information taken from the protective devices opera-123 tions [19]. Thus, the goal is to model a mathematical func-124 tion that reflects the logical relationship between the status 125 of power system protective devices and the possible fault 126 sections.

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The FH describes how the reported alarms can be logically 129 explained as a function of the status of the sections and 130 the PD. If a FH is consistent with the reported alarms, the 131 expected status of PD should correspond to the alarms as 132 closely as possible. Therefore, the FH can be expressed as 133 follows where:

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• S = {s 1 , s 2 , · · · , s n s } is the set of possible fault sections 137 and s k represents the status of the k-th element of S, with 138 s k = 1 and s k = 0 equivalent to its faulted and normal 139 status, respectively. S is a vector to be determined;

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• R m = {r 1m , r 2m , · · · , r n r m } is the set of main PR related 141 to S and r km denotes the status of the k-th element 142 of R m . If it operates, r km = 1, otherwise r km = 0; 143 • R b = {r 1b , r 2b , · · · , r n r b } is the set of backup PR related 144 to S and r kb corresponds to the status of the k-th element 145 of R b , with r kb = 1 and r kb = 0 equivalent to its 146 operating and non-operating status, respectively;

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• R c = {r 1c , r 2c , · · · , r n c c } is the set of CB failure relays 148 related to S and r kc denotes the k-th element of R c . If r kc 149 operates, then r kc = 1, otherwise r kc = 0; x e k + y e k , (4) 196 where: s k represents the status of the k-th section; x ξ denotes 197 the misoperation index of equipment ξ (ξ ∈ {r k µ , c k , e k }); 198 y ξ represents the operating failure index of equipment ξ ; 199 w s k is the weight factor of the k-th section; w rµ z , w c z and 200 w e z denotes the weight factors for failure or misoperation of 201 PR with a µ characteristic, CB, and FI, respectively; n s is the 202 number of power system sections.
The expected status of main PR is defined as The expected status of backup PR corresponds to where and ⊗ represent the logical NOT and AND operators, 213 respectively.

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The expected status of a CB failure relay can be formulated 215 as follows where R(c k ) is the set of PR that can trip c k , and r n ∈ 218 The expected status of a FI is given by where S(e k ) is the set containing the sections supervised 222 by e k .

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The expected status of a CB can be determined as

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The misoperating index points to an inappropriate operation 227 of a certain equipment. This index will be 1 when the device 228 operates and its expected status indicates otherwise. Hence, 229 its value can be obtained as The operating failure index represents a failure in the oper-232 ation of a certain equipment. This index will be 1 when the 233 equipment has not operated and its expected status indicates 234 otherwise. Therefore, its value is formulated as follows   The GA flowchart is shown in Fig. 1, it starts with a random

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A widely used arrangement to study distribution systems 285 is the IEEE 33 bus distribution system, originally proposed 286 by [39]. This system comprises 33 buses, 32 lines, and no 287 reactive power compensation unit. The grid is supplied by a 288 feeder connected to the first bus, without additional power 289 generating units. Over years, this test system has been used to 290 study several problems in conventional distribution systems. 291 Recently, a modification to the IEEE 33 bus distribution 292 system was proposed in [40], which inserted PD along the 293 system. The test system adopted here is based on [40], which 294 is depicted in Fig. 2. The protective scheme consists of CB, 295 PR, and FI.

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The weights for the proposed OF are presented in Table 2, 304 which were determined after a detailed sensitivity analysis.

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The used GA parameters are:   Table 3.

TABLE 3. Ideal status of PD for faults in each section of test system.
However, PD operational failures may occur, resulting in 315 abnormal PD status. Also, the status of PD may present 316 spurious information. These conditions are challenging for 317 fault diagnosis and can be represented by a large number of 318 scenarios. The proposed method for fault section estimation 319 was tested for several fault scenarios and performed with high 320 accuracy. Due to space limitation, only some challenging sce-321 narios are presented and detailed in this paper, followed by the 322 performance evaluation of the proposed method. Some fault 323 scenarios listed in Table 4 Table 4, the fault scenarios comprise spurious 326 data from PD related to the fault sections, spurious status 327 from PD related to sound sections and operational failures 328 of PD. Besides evaluating the feasibility and effectiveness 329 of the proposed method, for comparison purposes, the fault 330 scenarios were also applied to two well-established meth-331 ods in the literature, termed here as methods M1 [24] and 332 M2 [29]. Additionally, since the aforementioned methods do 333 not include FI status on their problem formulation, the test 334  The results for the evaluated fault scenarios are shown in 353   Table 5. It can be seen that M1 and M2 failed for many cases.  Generally, M1 and M2 performed well for scenarios where 390 there were information from both CB and main PR related to 391 the fault section. However, those methods failed when only 392 the status of the main PR was available (e.g: scenario 1.2), 393 besides other cases with spurious or missing data.

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A new genetic algorithm based method for fault location 396 in distribution systems was presented in this paper. Here, 397 the fault hypothesis was defined according to the protective 398 devices status, such as protective relays, circuit breakers and 399 fault indicators status. The proposed objective function is 400 based on the actual and expected status of those protective 401 devices, taking into account their malfunctioning. Moreover, 402 a simple procedure to attribute the weight factors to each 403 element of the objective function, including the protective 404 devices and the corresponding sections, was proposed. Thus, 405 an analytic model to accurately determine the faulted sections 406 in distribution networks was presented. 407 A typical distribution system were used for case studies 408 and the proposed method presented a good performance to 409 locate the faulted section in most of them. The results show 410 that the proposed method is appropriate even for challenging 411 scenarios with spurious status and operational failure of PD. 412 Additionally, the proposed method was compared to two 413 well-established methods in the literature, demonstrating its 414 effectiveness and suitability to locate the faulted sections in 415 distribution networks. As the proposed method is based only 416 on PD status, it is also suitable for distribution systems with 417 distributed generation. In this case, bi-directional PD should 418 be taken into account.