An elastic power distribution network multi-source fault locating method based on adaptive chaotic evolutionary cooperative optimization

Abstract

The application relates to a flexible power distribution network multi-source fault positioning method based on adaptive chaotic evolution cooperative optimization, and belongs to the technical field of power distribution network automation. The method generates an initial population by combining a chaotic mapping and reverse learning, adaptively adjusts a chaotic sampling number based on population distribution entropy, and introduces a simulated annealing criterion to enhance global optimization capability. Meanwhile, a multi-source information positioning model is constructed by fusing an FTU switch function, muPMU synchronous phasor data, action signals and fault frequency constraints, so that single information source error can be corrected and the solution space can be reduced. The method can effectively improve the positioning accuracy and robustness of the flexible power distribution network when facing complex faults caused by low-frequency high-influence or high-frequency gradualness.

Description

Technical Field

[0001] This invention relates to a method for locating multi-source faults in a resilient distribution network based on adaptive chaotic evolutionary co-optimization. Background Technology

[0002] In recent years, the resilience of distribution networks has received widespread attention. Compared with traditional distribution networks, resilient distribution networks face two types of unconventional disturbances: low-frequency, high-impact disturbances, such as major natural disasters; and high-frequency, gradual disturbances, such as the integration of a high proportion of distributed generation (DG). These events can lead to the loss of control over the distribution network. Fault location is the foundation for resilient distribution networks to achieve "self-healing" and "proactive control." Accurate fault location is of great significance for supporting the intelligent and resilient development of distribution networks.

[0003] With the development of distribution network automation, the method of building an optimization model based on feeder terminal unit (FTU) information for fault location has been widely used [1-3]. The technical route is as follows: collect actual switch state information through FTU, build a mathematical model of the approximate relationship between it and the expected state, and thus locate the fault. Reference [4] establishes a switching function based on non-logic operation and uses a linear integer programming model to solve it, but it cannot locate multiple faults. To solve this problem, references [5-6] improved the switching function so that it can effectively characterize the current direction of single and simple multiple faults. However, it still has limitations in complex multiple faults, which affects the applicability of the location model. The switching function proposed in references [7-8] fails to fully consider the current direction characteristics of the main power source and distributed power source in the fault state in the shared branch of the distribution network, which affects its reliability in such scenarios.

[0004] Intelligent algorithms have attracted the attention of scholars at home and abroad for their powerful global search capabilities, adaptability to complex problems and flexible improvement space[9]. Reference

[10] improved the initial population quality by introducing Tent chaotic mapping and enhanced the global optimization capability by incorporating the golden sine algorithm. However, the accuracy dropped significantly under multiple faults and the robustness of the algorithm was poor. The algorithm proposed in References [11-12] improved the convergence, but the key parameters need to be set based on experience and lack an adaptive parameter optimization mechanism. The applicability needs to be further improved. Reference

[13] adopted the improved vulture search algorithm and introduced a partitioning strategy to reduce the solution dimension. However, its partitioning depends on the network topology and is limited in its application in flexible elastic distribution networks. Reference

[14] improved the accuracy and efficiency of fault location through hierarchical dimensionality reduction and algorithm improvement. However, its location model depends on FTU. In addition, researchers have proposed a variety of improved and fused algorithms, such as artificial fish swarm algorithm

[15] , gray wolf particle swarm algorithm

[16] , sparrow algorithm

[17] , quantum ant colony algorithm

[18] , black-winged kite algorithm

[19] .

[0005] In summary, the development of fault location research has shifted from single-factor to multi-factor, with gradually enhanced robustness and convergence. However, existing research suffers from some common problems: 1. Location models rely solely on FTU data, which is prone to false alarms and missed alarms. When complex multi-factor faults occur in the distribution network, relying solely on FTU weakens the reliability of location. 2. Low-frequency high-impact or high-frequency asymptotic faults increase the probability of complex faults in the distribution network, leading to fundamentally different fault characteristics and a decline in the performance of existing location models. Therefore, the key to improving fault location in resilient distribution networks lies in overcoming the reliability problem of location under the dual constraints of complex multi-factor faults and information distortion.

[0006] References:

[0007] [1] Wang Shouxiang, Liu Qi, Zhao Qianyu, et al. Analysis and research prospect of the elasticity connotation of distribution network [J]. Automation of Electric Power System, 2021, 45(09):1-9.

[0008] [2] GE Leijiao, LI Yuanliang, CHEN Yanbo, et al. Key technologies of situation awareness and implementation effectiveness evaluation in smart distribution network[J]. High Voltage Engineering, 2021, 47(7): 2269-2280.

[0009] [3] Jin Fanfan, Guo Ruipeng, Lin Zhenzhi, et al. Optimal configuration of FTU considering power supply reliability and economy in distribution network [J]. Electric Power Automation Equipment, 2024, 44(12):132-139. DOI:10.16081 / j.epae.202410023.

[0010] [4] He Ruijiang, Hu Zhijian, Li Yan, et al. Linear integer programming method for fault location in distribution network with distributed generation [J]. Power System Technology, 2018, 42(11):3684-3692. DOI:10.13335 / j.1000-3673.pst.2018.0612.

[0011] [5]JIANG Yazhou. Data-driven fault location of electric powerdistribution systems with distributed generation[J]. IEEE Transactions onSmart Grid, 2020, 11(1): 129-137.

[0012] [6]WANG Qiujie, JIN Tao, MOHAMED A, et al. A novel linear optimization method for section location of single-phase ground faults in neutralnoneffectively grounded systems[J]. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 1-10.

[0013] [7] Wang Yushan, Wang Chen, Wang Shuxia, et al. Fault location method for distribution network based on IWOA [J]. Smart Power, 2024, 52(11):98-105. DOI:10.20204 / j.sp.2024.11013.

[0014] [8] Zheng Cong, Zhou Haifeng, Zheng Dongqiang, et al. Research on active distribution network fault location method based on improved multiverse algorithm [J]. Power System Protection and Control, 2023, 51(02):169-179. DOI:10.19783 / j.cnki.pspc.220601.

[0015] [9] Zhan Huiyu, Liu Keyan, Sheng Wanxing, et al. Review and prospect of fault diagnosis and location methods for active distribution networks [J]. High Voltage Engineering, 2023, 49(02):660-671. DOI:10.13336 / j.1003-6520.hve.20211604.

[0016]

[10] Mai Zhangqu, Zeng Ying, Zhang Luliang, et al. Fault location in active distribution network based on improved Harris Eagle optimization algorithm [J]. Smart Power, 2022, 50(11):104-111.

[0017]

[11] Zhao Qiao, Wang Zengping, Dong Wenna, et al. Research on fault location method of distribution network based on immune binary particle swarm optimization algorithm [J]. Power System Protection and Control, 2020, 48(20):83-89. DOI:10.19783 / j.cnki.pspc.191527.

[0018]

[12] Gao Fengyang, Li Zhaojun, Yuan Cheng, et al. Active power distribution network fault location based on quantum computing and immune optimization algorithm [J]. High Voltage Engineering, 2021, 47(02):396-406. DOI:10.13336 / j.1003-6520.hve.20200507021.

[0019]

[13] Yang Guohua, Feng Ji, Liu Xuan, et al. Fault location in distribution network with distributed power source based on improved vulture search algorithm [J]. Power System Protection and Control, 2022, 50(18):1-9. DOI:10.19783 / j.cnki.pspc.211674.

[0020]

[14] Ji Xingquan, Zhang Shuo, Zhang Yumin, et al. Fault location in distribution network based on IELM algorithm [J]. Automation of Electric Power Systems, 2021, 45(22):157-166.

[0021]

[15] Hu Jue, Wei Gang, Xie Sujuan, et al. Active distribution network fault location based on artificial fish swarm algorithm [J]. Smart Power, 2020, 48(06):112-118+124. Xiong Rui, Zhao Linjun, Zhang Yuhang.

[0022]

[16] Fault location in active distribution network based on gray wolf-particle swarm algorithm [J]. Journal of Electric Power System and Automation, 2025, 37(05): 141-148+158. DOI: 10.19635 / j.cnki.csu-epsa.001501.

[0023]

[17] Wu Xiaomeng, Han Kang, Dang Bo, et al. Active fault location in distribution network based on improved sparrow search algorithm [J]. Science Technology and Engineering, 2025, 25(28):12059-12067.

[0024]

[18] Bi Zhongqin, Yu Xiaowan, Wang Baonan, et al. Rapid location technology for fault sections in distribution network based on quantum ant colony algorithm [J]. Journal of Shanghai Jiaotong University, 2024, 58(05):693-708. DOI:10.16183 / j.cnki.jsjtu.2023.004.

[0025]

[19] Wang Qiujie, Ji Chenxu, Tan Hong, et al. A method for locating complex multi-fault sections in flexible distribution networks based on improved switching functions [J]. Electric Power Automation Equipment, 2025, 45(10):84-91. DOI:10.16081 / j.epae.202509003. Summary of the Invention

[0026] The purpose of this invention is to address the problems of existing technologies' over-reliance on easily distorted FTU data and insufficient reliability under complex multiple faults by providing a method for locating multi-source faults in resilient distribution networks based on adaptive chaotic evolutionary collaborative optimization.

[0027] To achieve the above objectives, the technical solution of this invention is: a method for locating multi-source faults in a resilient distribution network based on adaptive chaotic evolutionary cooperative optimization, comprising:

[0028] Read fault information, obtain status information uploaded by each feeder terminal unit (FTU) and microphasor measurement unit (μPMU), and encode to generate an actual status matrix;

[0029] Initialize the parameters related to the ICEO algorithm, and generate an initial population based on combinatorial chaotic mapping and reverse learning;

[0030] The iteration begins, and the number of chaotic samples is adaptively determined based on the current population's distribution entropy. ;

[0031] Perform chaotic evolution operations on each individual in the population, including random pairing, chaotic mapping based on exponential discrete memristor mapping, mutation and crossover, to generate experimental individuals;

[0032] Calculate the fitness of all experimental individuals, decide whether to accept experimental individuals based on the simulated annealing criterion to update the current solution, and update the global optimal solution;

[0033] The iteration process is repeated until the iteration termination condition is met, and the global optimal solution is output as the fault location result. The global optimal solution is a coded combination of the feeder section state.

[0034] Furthermore, an initial population is generated based on combinatorial chaotic mapping and reverse learning, including:

[0035] A combined chaotic sequence is generated based on the Tent map and the Logistic map, wherein the kernel function expression of the Tent map is:

[0036]

[0037] In the formula: For the initial population, the first The first individual in the population is randomly generated. A factor that controls the intensity of the chaotic behavior of the mapping;

[0038] The kernel function expression for the Logistic mapping is:

[0039]

[0040] Mapping the tentative-logistic combination values ​​to the interval [−1, 1] and then performing a cosine transform yields the initial population. The transformation formula is:

[0041]

[0042]

[0043] Constructing the reverse population of the initial population X :

[0044]

[0045] For population search space;

[0046] Merge the initial population and the reverse population:

[0047]

[0048] Calculate the merged population Based on fitness, select the one with the best fitness. Each individual is used as the final initial population. .

[0049] Furthermore, the number of chaotic samples is adaptively determined based on the current population's distribution entropy. ,include:

[0050] The final initial population Mapped to space:

[0051]

[0052] In the formula: The initial population after mapping The i-th individual, For the final initial population The i-th individual, These are the upper and lower bounds of the variable;

[0053] Divide the interval [0,1] into B equal-width bins and calculate the population distribution entropy H:

[0054]

[0055]

[0056] in, For the first The percentage of individual items in each container This is an indicator function; it takes the value 1 if the condition is met, and 0 otherwise. As a dimension, It is a very small positive number;

[0057] Calculate the number of chaotic samples in the current iteration based on the distribution entropy H. :

[0058]

[0059] in, , These represent the maximum and minimum number of samples, respectively, and round is the rounding function.

[0060] Furthermore, the decision on whether to accept trial individuals is based on simulated annealing criteria, including:

[0061] Calculate candidate solutions With the current solution Poor adaptability :

[0062]

[0063] Update the current solution using the following formula:

[0064]

[0065] Where T is the annealing temperature and rand is a random number function.

[0066] Furthermore, the fitness of an individual is calculated based on the objective function:

[0067]

[0068]

[0069] in, For the number of FTU switches, This refers to the number of feeders. Encode the actual state of the s-th switch. Let be the desired state function of the s-th switch. The status encoding for the j-th feeder segment. These are the weighting coefficients. For correction factor, Let be the change in current of the s-th switch. and For all switches The maximum and minimum values ​​in the range. The change in current supplied by the distributed power source to the s-th switch; The change in current supplied by the main grid power supply to the s-th switch; Let be the change in load current at the s-th switch.

[0070] Furthermore, the desired state function Is*(L) of the switch is:

[0071]

[0072] in, This represents the expected function of the fault current originating from upstream of switch s. This represents the expected function of the fault current originating downstream of switch s.

[0073] Furthermore, the aforementioned and Calculate using the following formula:

[0074]

[0075]

[0076] in, , These represent the total number of power supplies located upstream and downstream of switch s, respectively. , These represent the switching states of the k-th upstream and downstream power sources, respectively. , These represent the total number of feeder segments on the power path from switch s to the kth upstream and downstream power source, respectively. , These represent the states of the j-th feeder segment on the k-th upstream and downstream power paths, respectively; , These represent the total number of all feeder sections downstream and upstream of switch S, respectively. These represent the states of the j-th feeder segment upstream and downstream of switch s, respectively.

[0077] Furthermore, when calculating fitness, action signal constraints are introduced, expressed as follows:

[0078]

[0079] in, This refers to the collection of all feeder segments within the area protected by the protection device PD.

[0080] Furthermore, when calculating fitness, a fault multiplicity constraint is introduced, expressed as:

[0081]

[0082] in, This is the preset maximum number of faults.

[0083] Furthermore, when calculating fitness, the μPMU fault domain constraint is introduced, expressed as:

[0084]

[0085] in, This is the set of all feeder segments within the fault area determined by the μPMU.

[0086] Compared with existing technologies, this invention has the following advantages: Based on the explanation of the chaotic evolution optimization (CEO) algorithm, this invention proposes the IECO algorithm, which uses a combination of Tent-Logistic-Cosine chaotic mapping and reverse learning to generate an initial population, thereby improving the diversity of initial solutions. It introduces an adaptive mechanism based on population distribution entropy to dynamically adjust the number of EDM mapping samples, balancing exploration and development capabilities. It incorporates simulated annealing criteria to accept inferior solutions with probability, thereby enhancing the ability to escape local optima. It incorporates strong constraints such as action signals, fault multiplicity, and μPMU fault domain to weaken the impact of FTU information distortion, further narrowing the search range and improving positioning accuracy and speed. Attached Figure Description

[0087] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0088] Figure 2 This is a schematic diagram of the positive fault current distribution.

[0089] Figure 3 This is a schematic diagram of the reverse fault current distribution. Detailed Implementation

[0090] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0091] This invention provides a method for locating multi-source faults in a resilient distribution network based on adaptive chaotic evolutionary co-optimization, comprising:

[0092] Read fault information, obtain status information uploaded by each feeder terminal unit (FTU) and microphasor measurement unit (μPMU), and encode to generate an actual status matrix;

[0093] Initialize the parameters related to the ICEO algorithm, and generate an initial population based on combinatorial chaotic mapping and reverse learning;

[0094] The iteration begins, and the number of chaotic samples is adaptively determined based on the current population's distribution entropy. ;

[0095] Perform chaotic evolution operations on each individual in the population, including random pairing, chaotic mapping based on exponential discrete memristor mapping, mutation and crossover, to generate experimental individuals;

[0096] Calculate the fitness of all experimental individuals, decide whether to accept experimental individuals based on the simulated annealing criterion to update the current solution, and update the global optimal solution;

[0097] The iteration process is repeated until the iteration termination condition is met, and the global optimal solution is output as the fault location result. The global optimal solution is a coded combination of the feeder section state.

[0098] The following is a detailed implementation process of the present invention.

[0099] This invention presents a multi-source fault location method for resilient distribution networks based on adaptive chaotic evolutionary cooperative optimization. Building upon the explanation of the chaotic evolution optimization (CEO) algorithm, the IECO algorithm is proposed. It employs a combined Tent-Logistic-Cosine chaotic mapping and back-learning to generate an initial population, enhancing the diversity of initial solutions. An adaptive mechanism based on population distribution entropy is introduced to dynamically adjust the EDM mapping sampling number, balancing exploration and development capabilities. Simulated annealing criteria are incorporated to probabilistically accept inferior solutions, enhancing the ability to escape local optima. Strong constraints based on action signals, fault multiplicity, and μPMU fault domain are integrated to mitigate the impact of FTU information distortion, further narrowing the search range and improving location accuracy and speed.

[0100] 1. IECO Algorithm

[0101] 1.1 CEO Algorithm

[0102] The CEO algorithm, a novel metaheuristic algorithm proposed in 2025, uses a two-dimensional discrete memristor hyperchaotic mapping to provide an evolutionary direction for the population. Combined with the mutation, crossover, and selection mechanisms of differential evolution, it effectively solves the "zero bias" problem of existing metaheuristic algorithms. The algorithm flowchart can be found in the literature.

[19] This will not be elaborated upon here.

[0103] 1.2 Improvement Strategies

[0104] The original CEO algorithm suffers from problems such as large initial population randomness, fixed chaotic sampling number, and easy getting trapped in local optima. Three improvement strategies are proposed, which are applied to initialization, adaptive adjustment of chaotic sampling, and selection mechanism, respectively.

[0105] 1.2.1 Reverse Learning Initialization Based on Combinatorial Chaotic Mapping

[0106] The original CEO algorithm uses random initialization, which makes it difficult to guarantee the uniform distribution and diversity of the initial population. To address this, a combined chaotic mapping integrating Tent mapping, Logistic mapping, and cosine transform is proposed. This method generates ergodic and random sequences through nonlinear iteration, providing a uniformly distributed initial solution for population initialization, and introduces back-learning to select superior individuals. The Tent mapping kernel function expression is as follows:

[0107] (1)

[0108] In the formula: For the initial population, the first The first individual in the population is randomly generated. A factor that controls the intensity of the chaotic behavior of the mapping.

[0109] The core function expression for the Logistic mapping is:

[0110] (2)

[0111] Combining equations (1) and (2), the tentative-logistic combination value is mapped to the interval [−1,1], and then the uniformity of the sequence is enhanced by the cosine function, while avoiding zero-value divergence:

[0112] (3)

[0113] (4)

[0114] The initial population was The population search space is generated by equations (1)–(4). Construct a reverse population:

[0115] (5)

[0116] (6)

[0117] In the formula: , Given a reversed population and a merged population, calculate the fitness of all individuals and select the top individuals in ascending fitness order. Each individual is used as the final initial population. .

[0118] 1.2.2 Adaptive Chaotic Sampling Number Based on Population Distribution Entropy

[0119] In the original CEO algorithm, the number of chaotic samples The number of chaotic directions generated by each individual remains constant and cannot be dynamically adjusted according to the population's evolutionary state. To balance exploration and development capabilities, population distribution entropy is introduced to adaptively adjust the sampling number. The final initial population generated in Section 1.2.1 is used... Mapped to space:

[0120] (7)

[0121] In the formula: These are the upper and lower bounds of the variable.

[0122] Divide the interval [0,1] into B equal-width bins and calculate the population distribution entropy:

[0123] (8)

[0124] (9)

[0125] In the formula: For the first The percentage of individual items in each container This is an indicator function; it takes the value 1 if the condition is met, and 0 otherwise. As a dimension, The population distribution entropy.

[0126] The number of mappings is based on changes in entropy; the higher the entropy, the stronger the population diversity. The smaller the value, the less redundant computation is required for EDM mapping; the lower the entropy value, the closer the population converges. The larger the value, the greater the global exploration capability of the EDM mapping. Number of chaotic samples in the current iteration:

[0127] (10)

[0128] In the formula: , These are the maximum and minimum number of samples, respectively.

[0129] 1.2.3 Solution Update Mechanism Based on Simulated Annealing Rules

[0130] The original CEO selection operation uses a greedy criterion, accepting only the offspring if it is superior to the parent, which easily leads to premature convergence of the population. Borrowing from simulated annealing, we accept inferior solutions probabilistically, balancing the exploration and utilization of the algorithm. The solution update rule is:

[0131] (11)

[0132] (12)

[0133] In the formula: For the current solution, As a candidate solution, and These correspond to the fitness levels, Due to poor adaptability. The annealing temperature is the temperature at which the algorithm can be annealed. The higher the temperature, the greater the probability of accepting inferior solutions, thus ensuring the algorithm's global exploration in the early stages. The lower the temperature, the more the algorithm gradually converges to the optimal solution.

[0134] 2. Fault location model for flexible distribution networks

[0135] 2.1 Switch and feeder coding

[0136] When a system failure occurs, the following encoding is applied to any feeder segment:

[0137] (13)

[0138] For any switch The state function can be obtained from the actual information collected by the FTU and then encoded.

[0139] (14)

[0140] In the formula: For the first The fault current of each switch, For the first The overcurrent setting value of each switch.

[0141] For any switch Its expected function is closely related to the state of each feeder segment and the power supply connection state, and the fault current is the first... Using the switch as a dividing point, the fault current is broken down into "forward fault current" and "reverse fault current," the sources and conditions of which are shown in Table 1. Figure 2 , Figure 3 As shown.

[0142] Table 1 Fault Current Source Conditions

[0143]

[0144] Therefore, the switching function is:

[0145] (15)

[0146] (16)

[0147] (17)

[0148] In the formula: , They are located at the switch Total number of upstream and downstream power sources; , The first The switching status of a power supply, 1 for on and 0 for off; , From the switch To the The total number of feeder sections on the upstream and downstream power paths; , They are respectively from the switch To the The first upstream and downstream power path The status of each feeder section; , Switches The total number of all feeder sections in the downstream and upstream areas; Switches Upstream and downstream The status of each feeder section.

[0149] 2.2 Objective Function

[0150] The closer the expected function is to the data actually collected by the FTU, the higher the fitness. The objective function is established as follows:

[0151] (18)

[0152] In the formula: This represents the number of FTU switches in the distribution network. This represents the total number of feeders in the distribution network. The weighting coefficients are used to prioritize the hypothesis with the fewest faulty feeders when multiple hypotheses with the same fitness are present.

[0153] To further improve the accuracy of multi-source fault location in the distribution network, based on the high-precision synchronous phasor data provided by μPMU or voltage, current and phase data provided by other devices, a correction parameter for the objective function is introduced, and the improved equation (18) is:

[0154] (19)

[0155] In the formula: k is the correction coefficient, usually taken as 1.05, and 0 indicates that the objective function is not corrected; for The maximum value in; yes The minimum value in; For the first The change in current of each switch, i.e.:

[0156] (20)

[0157] In the formula: The change in current supplied by the distributed power source to the s-th switch; The change in current supplied by the main grid power supply to the s-th switch; Let be the change in load current at the s-th switch.

[0158] 2.3 Constraints

[0159] 2.3.1 Action Signal Constraints

[0160] Currently, the power distribution network mainly uses a three-stage overcurrent protection scheme. As its protection principle states, after a fault occurs, the switch closest to the fault point and whose current exceeds its predetermined protection setting will trip to isolate the fault.

[22] Therefore, the faulty section can be identified based on the switch action signal, and the action signal constraint is defined as follows:

[0161] (twenty one)

[0162] In the formula: This refers to the collection of all feeder segments within the area protected by the protection device PD.

[0163] 2.3.2 Fault Multiplicity Constraint

[0164] According to the N-2 criterion, in extreme events, it is extremely rare for a distribution network to experience three or more faults simultaneously. Therefore, the fault multiplicity constraint is defined as follows:

[0165] , Take 3 (22)

[0166] 2.3.3 μPMU Fault Domain Constraints

[0167] The precise synchronization phasor data provided by the μPMU can serve as an independent and reliable information source, helping to verify and correct the expected state of the switching function calculation, providing "adjudication-level" high-precision data. The hard constraint forming the fault region dictates that the fault segment must be located on the fault branch indicated by the μPMU.

[23] Therefore, the μPMU fault domain constraint is defined as follows:

[0168] (twenty three)

[0169] In the formula: This is the set of all feeder segments within the fault area identified by the μPMU.

[0170] 2.4 Fault Location Process

[0171] like Figure 1As shown, the fault location process for the resilient distribution network based on ICEO is as follows:

[0172] Step 1: Read fault information, obtain the status information uploaded by each FTU and μPMU, and encode it to generate the actual status matrix S. Initialize the ICEO related parameters.

[0173] Step 2: Initialize the population. Generate the initial population according to equations (1)–(6) and calculate the individual fitness value according to equation (19).

[0174] Step 3: Iteration begins. .

[0175] Step 4: Calculate the adaptive chaotic sampling number according to equations (7)–(10). .

[0176] Step 5: Perform chaotic evolution operations on each individual in the population:

[0177] 1. Random pairing: Randomly selecting another pair from the population that is different from the target population. individual .

[0178] 2. Chaotic mapping: , Mapping to the initial chaotic range, substituting into the exponential discrete memristor mapping, generates For the chaotic candidate vectors, we then back-map them to the actual search space to obtain the chaotic directions. , , .

[0179] 3. Mutation: Generate mutated individuals with a probability of 0.5 by either global exploration or local development. , .

[0180] 4. Crossover: Perform a binomial crossover between the mutated individual and the current individual to generate experimental individuals. , And perform boundary constraint processing.

[0181] Step 6: Calculate the fitness of all experimental individuals, retaining the optimal value in the formula. Based on formulas (11)-(12), use the simulated annealing criterion to decide whether to accept the experimental individual. If the optimal value of the experimental individual is better than the current global optimum, update the global optimum until the iteration ends.

[0182] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for locating multi-source faults in a resilient distribution network based on adaptive chaotic evolutionary co-optimization, characterized in that, include: Read fault information, obtain status information uploaded by each feeder terminal unit (FTU) and microphasor measurement unit (μPMU), and encode to generate an actual status matrix; Initialize the parameters related to the ICEO algorithm, and generate an initial population based on combinatorial chaotic mapping and reverse learning; The iteration begins, and the number of chaotic samples is adaptively determined based on the current population's distribution entropy. ; Perform chaotic evolution operations on each individual in the population, including random pairing, chaotic mapping based on exponential discrete memristor mapping, mutation and crossover, to generate experimental individuals; Calculate the fitness of all experimental individuals, decide whether to accept experimental individuals based on the simulated annealing criterion to update the current solution, and update the global optimal solution; The iteration process is repeated until the iteration termination condition is met, and the global optimal solution is output as the fault location result. The global optimal solution is a coded combination of the feeder section state.

2. The method for multi-source fault location in a resilient distribution network based on adaptive chaotic evolutionary cooperative optimization as described in claim 1, characterized in that, The initial population is generated based on combinatorial chaotic mapping and reverse learning, including: A combined chaotic sequence is generated based on the Tent map and the Logistic map, wherein the kernel function expression of the Tent map is: In the formula: For the initial population, the first The first individual in the population is randomly generated. A factor that controls the intensity of the chaotic behavior of the mapping; The kernel function expression for the Logistic mapping is: Mapping the tentative-logistic combination values ​​to the interval [−1, 1] and then performing a cosine transform yields the initial population. The transformation formula is: Constructing the reverse population of the initial population X : For population search space; Merge the initial population and the reverse population: Calculate the merged population Based on fitness, select the one with the best fitness. Each individual is used as the final initial population. .

3. The method for multi-source fault location in a resilient distribution network based on adaptive chaotic evolutionary cooperative optimization according to claim 2, characterized in that, The number of chaotic samples is adaptively determined based on the current population's distribution entropy. ,include: The final initial population Mapped to space: In the formula: The initial population after mapping The i-th individual, For the final initial population The i-th individual, These are the upper and lower bounds of the variable; Divide the interval [0,1] into B equal-width bins and calculate the population distribution entropy H: in, For the first The percentage of individual items in each container This is an indicator function; it takes the value 1 if the condition is met, and 0 otherwise. As a dimension, It is a very small positive number; Calculate the number of chaotic samples in the current iteration based on the distribution entropy H. : in, , These represent the maximum and minimum number of samples, respectively, and round is the rounding function.

4. The method for multi-source fault location in a resilient distribution network based on adaptive chaotic evolutionary cooperative optimization according to claim 1, characterized in that, The decision to accept trial subjects is based on simulated annealing criteria, including: Calculate candidate solutions With the current solution Poor adaptability : Update the current solution using the following formula: Where T is the annealing temperature and rand is a random number function.

5. The method for multi-source fault location in a resilient distribution network based on adaptive chaotic evolutionary cooperative optimization according to claim 1, characterized in that, The objective function used to calculate the fitness of an individual is: in, For the number of FTU switches, This refers to the number of feeders. Encode the actual state of the s-th switch. Let be the desired state function of the s-th switch. The status encoding for the j-th feeder segment. These are the weighting coefficients. For correction factor, Let be the change in current of the s-th switch. and For all switches The maximum and minimum values ​​in the range. The change in current supplied by the distributed power source to the s-th switch; The change in current supplied by the main grid power supply to the s-th switch; Let be the change in load current at the s-th switch.

6. The method for multi-source fault location in a resilient distribution network based on adaptive chaotic evolutionary cooperative optimization according to claim 5, characterized in that, The desired state function Is*(L) of the switch is: in, This represents the expected function of the fault current originating from upstream of switch s. This represents the expected function of the fault current originating downstream of switch s.

7. The method for multi-source fault location in a resilient distribution network based on adaptive chaotic evolutionary cooperative optimization according to claim 6, characterized in that, The and Calculate using the following formula: in, , These represent the total number of power supplies located upstream and downstream of switch s, respectively. , These represent the switching states of the k-th upstream and downstream power sources, respectively. , These represent the total number of feeder segments on the power path from switch s to the kth upstream and downstream power source, respectively. , These represent the states of the j-th feeder segment on the k-th upstream and downstream power paths, respectively; , These represent the total number of all feeder sections downstream and upstream of switch S, respectively. These represent the states of the j-th feeder segment upstream and downstream of switch s, respectively.

8. The method for multi-source fault location in a resilient distribution network based on adaptive chaotic evolutionary cooperative optimization according to claim 5, characterized in that, When calculating fitness, action signal constraints are introduced, expressed as follows: in, This refers to the collection of all feeder segments within the area protected by the protection device PD.

9. The method for multi-source fault location in a resilient distribution network based on adaptive chaotic evolutionary co-optimization according to claim 5, characterized in that, When calculating fitness, a fault multiplicity constraint is introduced, expressed as: in, This is the preset maximum number of faults.

10. The method for multi-source fault location in a resilient distribution network based on adaptive chaotic evolutionary cooperative optimization according to claim 5, characterized in that, When calculating fitness, the μPMU fault domain constraint is introduced, and the expression is: in, This is the set of all feeder segments within the fault area determined by the μPMU.

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