Power grid fault traveling wave positioning device point distribution method based on improved genetic algorithm

Abstract

The invention discloses a power grid fault traveling wave positioning device stationing method based on an improved genetic algorithm. The method comprises the following steps: S1, establishing a mathematical model: establishing a mathematical model of a target function and a reclosing time function; encoding the information into a graph structure; s2, initial population generation: numbering lines to form an initial population; converting the node information into individual codes according to a coding rule, and calculating individual fitness through a fitness function; s3, genetic manipulation: performing selection, crossover and mutation operations on the initial population to generate new individuals; s4, algorithm termination judgment: if the optimal individual in the chromosomes has a plurality of genes, terminating the algorithm; and if the optimal individual has no gene, continuing genetic manipulation until a termination condition is met. The bidirectional fault current caused by the distributed power supply is accurately captured through three-state switch coding, the crossing / mutation probability is adjusted in real time through the Sigmoid function to achieve the dynamic genetic algorithm, and the convergence speed is increased; and the complex network is disassembled into non-overlapping sub-regions by an original topology grading strategy, so that the calculation complexity is reduced.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of fault positioning, in particular to a power grid fault traveling wave positioning device point arrangement method based on an improved genetic algorithm. BACKGROUND

[0002] With the increasing application of distributed power supply in distribution networks, the bidirectional power flow characteristics completely overturn the traditional radial power grid architecture, causing instability of the fault detection system: the reverse current of the power supply during a fault causes confusion in the fault direction criterion, and the misjudgment rate of the traditional one-way detection strategy increases sharply; island operation and grid switching also cause frequent changes in the topological structure, and the fixed point arrangement scheme frequently mismatches, resulting in serious delay in fault isolation, which seriously threatens power supply reliability.

[0003] Existing fault positioning technologies such as the traveling wave detection method have the potential for millisecond-level response, but are subject to high cost of nanosecond-level clock synchronization equipment and large signal attenuation distortion caused by multiple branches of short lines. Commonly used point arrangement optimization algorithms such as mathematical programming are only suitable for power networks with a small number of nodes; traditional genetic algorithms cannot represent bidirectional current due to binary coding, and the number of iterations increases due to the lack of hierarchical processing of the topology.

[0004] To ensure power supply reliability, the application accurately captures bidirectional fault currents caused by distributed power supply through three-state switch coding, uses a Sigmoid function to adjust the crossover / mutation probability in real time to realize a dynamic genetic algorithm, and improves the convergence speed; the unique hierarchical topology strategy decomposes the complex network into non-overlapping sub-regions, reducing the computational complexity.

[0005] The comparison with the prior art is as follows:

[0006] Comparison with the technology of patent CN112557811A "Fault positioning of distribution network containing distributed power supply based on improved genetic algorithm"

[0007] 1. In patent CN112557811A, the individual crossover is improved, and the single crossover is used instead of the group crossover to improve the operation efficiency. However, the population diversity is not considered, making it more difficult for individuals with multiple optimal genes to appear, which indirectly leads to unsatisfactory output results.

[0008] The patent designs the crossover and mutation probability with a Sigmoid function, which depends on the maximum and average values of the fitness, helps to select individuals with higher fitness, increases population diversity, and improves the performance of the algorithm. It solves the problem of lack of population diversity in traditional genetic algorithms, premature convergence, and inability to retain optimal individuals. It greatly improves the solving speed and also improves the probability of occurrence, retention and output of optimal solutions.

[0009] There is an essential difference between the two in terms of "improvement ideas and implementation schemes".

[0010] 2. Patent CN112557811A uses different populations to represent different fault types, directly ignoring irrelevant populations during diagnosis, thus improving operational efficiency. This requires adding judgment operations to the algorithm, and the accuracy of the final output largely depends on the judgment results, indirectly reducing the algorithm's reliability and applicability. Furthermore, increasing the number of populations negatively impacts computational efficiency.

[0011] This patent uses each gene locus on each chromosome to represent whether each branch has a device installed, without requiring additional steps in the algorithm structure. Furthermore, the chromosome length is only the total number of branches to ensure coverage, eliminating the need to expand the initial population. This ensures both the stability and applicability of the algorithm while maintaining its computational efficiency.

[0012] The two differ fundamentally in terms of "algorithm structure and encoding scheme". Summary of the Invention

[0013] To address the above problems, this invention discloses a method for deploying power grid fault traveling wave location devices based on an improved genetic algorithm.

[0014] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0015] A method for deploying power grid fault traveling wave location devices based on an improved genetic algorithm includes the following steps:

[0016] S1 establishes a mathematical model:

[0017] To address the issue of offline fault location device deployment in distribution networks, a mathematical model is established that includes the distribution network topology, fault location parameters, power supply reliability objective function, and reclosing time function; the information of distribution network nodes, switching equipment, and circuit breakers is encoded into a graph structure.

[0018] S2 Initial Population Generation:

[0019] An initial population is formed by assigning line numbers, and the initial positions of nodes are determined based on the topology. Node information is converted into individual codes according to coding rules, and individual fitness is calculated using a fitness function.

[0020] S3 genetic operations:

[0021] Select, crossover, and mutation operations are performed on the initial population to generate new individuals;

[0022] S4 Algorithm Termination Check:

[0023] If the best individual in the chromosome has multiple genes, the algorithm terminates; if the best individual has no genes, the genetic operation continues until the termination condition is met.

[0024] As a further improvement of the application, the switch device coding in step S1 adopts a tri-state coding mode.

[0025] Switch state coding rule:

[0026] Encoding as 1 when the fault current direction is the same as the positive direction;

[0027] Encoding as 0 when there is no non-fault current passing through;

[0028] Encoding as -1 when the fault current direction is inconsistent with the positive direction.

[0029] In the distribution network, the coding mode of the switch usually adopts binary coding, that is, the switch through which the fault current passes is encoded as 1, and the switch through which the non-fault current passes is encoded as 0. In order to accurately reflect the current attribute and direction in the distribution network containing distributed power, the binary coding is expanded on the basis of the binary coding;

[0030] Switch function expression:

[0031] ;

[0032] In the formula:

[0033] is the line switch expectation function;

[0034] is the switch switching coefficient;

[0035] , are the upper and lower half section feeder fault states, respectively;

[0036] , are the upper and lower half section feeder fault states, respectively;

[0037] The improved switch function is also applicable to the distribution network containing distributed power and forming a complex power grid topology after the switching operation, ensuring the applicability and accuracy of the switch function under different power grid topologies.

[0038] As a further improvement of the application, the fitness function in step S2 is improved as follows:

[0039] ;

[0040] In the formula:

[0041] is the switch variable;

[0042] is the number of upper half section feeders; ​

[0043] The improved fitness function adds a regularization term, which ensures that the value of the fitness function is always positive, and avoids the occurrence of missed and misjudged by adjusting the judgment of the switch state;

[0044] In order to improve the accuracy and response speed, the optimization target is converted into a dual problem, i.e. the minimum value problem is changed into a maximum value problem, and the maximum value of the current fitness function is found:

[0045] ;

[0046] In terms of chromosome coding, a branch direct mapping coding method is adopted, i.e. each branch corresponds to an independent chromosome gene site, and the total length of the chromosome is equal to the total number of branches;

[0047] Based on this, economic and reliability indicators are added to the fitness function, which are quantified by the cumulative device cost of the gene site value and the proportion of locatable fault branches, respectively.

[0048] The constraint conditions include:

[0049] The main line route needs to be configured with ≥1 set of multi-terminal devices, the distributed power access branch gene site value ≥1, the number of devices on the critical path ≥2, and the upper limit threshold of the total cost;

[0050] When performing specific genetic operations, the crossover operator exchanges the configuration between adjacent branches with an electrical distance ≤3 first; the mutation operator is set according to the branch type; and the probability elite retention strategy ensures that at least 20 high-quality individuals with 100% coverage are retained in each generation.

[0051] As a further improvement of the present application, the genetic operation in step S3 adopts dynamic adaptive crossover and mutation probabilities, which are defined as follows:

[0052] ;

[0053] In the formula:

[0054] 、 are the maximum and minimum values of the crossover probability;

[0055] 、 are the maximum and minimum values of the mutation probability;

[0056] is the maximum fitness in the population;

[0057] is the average fitness of the population at iteration.

[0058] The Sigmoid function similar to the activation function of neural network is used to design the crossover and mutation probability, wherein the nonlinear characteristic depends on the maximum and average value of the fitness, which is helpful to screen out the individual with higher fitness, increase the population diversity and improve the performance of the algorithm.

[0059] As a further improvement of the application, the S4 algorithm termination judgment further comprises hierarchical processing and power supply reliability index:

[0060] Hierarchical processing:

[0061] Determine the main line of the distribution network, and divide the network into non-overlapping independent sub-regions;

[0062] Obtain fault information through the SCADA system and FTU equipment, and optimize the distribution by using the fitness function;

[0063] With the application of distributed power in the distribution network, the topology of the distribution network gradually changes and becomes complex, the demand for the number of switch FTU monitoring points is further increased, which leads to the expansion of the population size of the genetic algorithm, increases the number of iterations and the solution time of the algorithm. In view of the problem, the main line of the distribution network is first determined, and then the entire network is divided into multiple independent sub-regions based on this, each sub-region is contained in the distribution network, and there is no overlapping region, which reduces the number of feasible solutions and facilitates the optimization and solution of the genetic algorithm;

[0064] The power supply reliability index calculation includes:

[0065] System average interruption duration index (SAIDI):

[0066] ;

[0067] Average service availability index (ASAI):

[0068] ;

[0069] System energy not supplied (ENS):

[0070] ;

[0071] System average energy not supplied (AENS):

[0072] ;

[0073] In the formula:

[0074] N is the total number of load points;

[0075] N is the number of users connected to the load point

[0076] ​ is the load point of the annual average fault duration;

[0077] is the load point of the total average load connected.

[0078] In the above technical solution, the power grid fault traveling wave positioning device point arrangement method based on the improved genetic algorithm has the following technical advantages:

[0079] 1. Accurately capture the bidirectional fault current caused by distributed power supply through tri-state switch coding.

[0080] 2. Real-time adjustment of crossover / mutation probability with Sigmoid function to realize dynamic genetic algorithm, so as to improve the convergence speed.

[0081] 3. The unique topological hierarchical strategy decomposes the complex network into non-overlapping sub-regions, and the calculation complexity is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0082] Figure 1 is the flowchart of the power grid fault traveling wave positioning device point arrangement method based on the improved genetic algorithm in the embodiment of the application;

[0083] Figure 2 is the power grid structure topology identified in the embodiment of the application;

[0084] Figure 3 is the optimal point arrangement scheme output by the algorithm in the embodiment of the application;

[0085] Figure 4 is the traditional optimal point arrangement scheme in the embodiment of the application. DETAILED DESCRIPTION

[0086] The application will be further described in detail below in combination with the drawings and specific embodiments:

[0087] As Figure 1 shown, a power grid fault traveling wave positioning device point arrangement method based on an improved genetic algorithm, characterized in that it comprises the following steps:

[0088] S1: Establish a mathematical model: for the distribution network offline fault positioning device point arrangement problem, a mathematical model is established, which includes the distribution network topology structure, fault positioning parameters, power supply reliability objective function and reclosing time function; the distribution network nodes, switch devices and circuit breaker information are coded into a graph structure;

[0089] S2 Initial Population Generation: An initial population is formed by assigning line numbers, and the initial positions of nodes are determined based on the topology. Node information is converted into individual codes according to coding rules, and individual fitness is calculated using a fitness function.

[0090] S3 genetic operations: Perform selection, crossover, and mutation operations on the initial population to generate new individuals;

[0091] S4 Algorithm Termination Criteria: The algorithm terminates if the optimal individual in the chromosome has multiple genes; otherwise, the genetic operation continues until the termination condition is met.

[0092] like Figure 2 After identifying the power grid topology, traditional binary switch coding cannot characterize the reverse fault current after distributed generation (DG) integration, directly leading to a high misjudgment rate in the final deployment scheme. To improve the adaptability to the new power grid after DG integration in step S1, a three-state coding method is adopted for the switch coding, and the switch function is improved to make it applicable to multi-source networks.

[0093] Switch status coding rules:

[0094] The code is 1 when the fault current direction is the same as the positive direction;

[0095] The code is 0 when no non-fault current passes through;

[0096] The code is -1 when the direction of the fault current is not in the positive direction.

[0097] In distribution networks, switches are typically encoded using binary encoding, where a switch carrying fault current is coded as 1, and a switch carrying non-fault current is coded as 0. To accurately reflect current attributes and direction in distribution networks containing distributed generation sources, this binary encoding method is extended.

[0098] Switch function expression:

[0099]

[0100] In the formula:

[0101] Let be the desired function of the circuit switch.

[0102] This is the switching coefficient.

[0103] , The fault statuses are for the upper and lower sections of the feeder, respectively.

[0104] , The upper and lower halves of the switch are respectively the first The feeder segment is in fault condition.

[0105] The improved switching function is also applicable to the distribution network problem containing distributed power supply and forming a complex power grid topology after the switching operation, and ensures the applicability and accuracy of the switching function under different power grid topologies.

[0106] In order to improve the accuracy and calculation speed of the algorithm, the fitness function in step S2 should be improved as follows:

[0107]

[0108] In the formula:

[0109] is a switching variable.

[0110] is the number of upper half sections of the switching.

[0111] The improved fitness function increases the regularization term, which on the one hand ensures that the value of the fitness function is always positive, and on the other hand, by adjusting the judgment of the switching state, avoids the occurrence of missed judgment and misjudgment

[0112] In order to improve the accuracy and response speed, the optimization target is converted into a dual problem, that is, the minimum value problem is converted into a maximum value problem, and the maximum value of the current fitness function is found:

[0113]

[0114] The genetic algorithm is deeply integrated into the power grid traveling wave positioning device point optimization, and the core implementation logic is to establish an accurate mapping relationship between the chromosome and the power grid branch: each branch of the distribution network is regarded as an independent gene site of the chromosome, and the length of the chromosome is equal to the total number of target distribution network branches. The direct mapping mechanism of the gene site-branch completely eliminates the decoupling problem of device type and installation location in the traditional scheme.

[0115] In the design of the fitness function, the economic and reliability double targets are creatively integrated: the function body contains a device cost summation term and a fault coverage ratio term, wherein the cost term is calculated according to the value difference of the gene site, and the coverage term quantifies the proportion of the fault branch that can be accurately positioned. The function dynamically adjusts the value of γ / δ to respond to changes in the power grid environment in real time.

[0116] The constraint condition construction fully embodies the physical characteristics of the power grid: the topology constraint requires that at least one set of multi-terminal devices must be deployed at the first and last ends of the main line, and the gene bit value of all distributed power access branches must be ≥1; the performance constraint forces the number of devices on the critical path to be ≥2 sets through mathematical inequalities; and the economic constraint sets an upper threshold for the total cost. These constraints are converted into evolution rules in genetic operations: the crossover operator exchanges the configuration between adjacent branches with an electrical distance ≤3, and the probability elite reservation strategy is set according to the branch type to ensure that at least 20 high-quality individuals with 100% coverage are retained in each generation.

[0117] Fixed crossover and mutation probabilities can easily cause loss of population diversity in genetic algorithms, and generally lead to premature convergence, ultimately resulting in missing the optimal solution. The present invention introduces dynamic crossover and mutation probabilities in step S3, defined as follows:

[0118]

[0119] In the formula:

[0120] , are the maximum and minimum values of the crossover probability.

[0121] , are the maximum and minimum values of the mutation probability.

[0122] is the maximum fitness in the population.

[0123] is the average fitness of the population at iteration.

[0124] The Sigmoid function similar to the activation function of a neural network is used to design the crossover and mutation probabilities, where the nonlinear characteristics depend on the maximum and average values of the fitness, which helps to filter out individuals with higher fitness while increasing population diversity and improving algorithm performance.

[0125] In genetic algorithms, the population size grows exponentially with the number of nodes. In order to further reduce the computational complexity, the hierarchical blocking method in topology is introduced into the processing of power grid topology, and the specific implementation method and test index are as follows.

[0126] Hierarchical processing:

[0127] Determine the main line of the distribution network, divide the network into non-overlapping independent sub-regions;

[0128] Obtain fault information through the SCADA system and FTU devices, and optimize the distribution of points using the fitness function.

[0129] With the application of distributed power in distribution network, the topology of distribution network is gradually changing complex, the demand for the number of monitoring points of switch FTU is further increased, and the population size of genetic algorithm is expanded, the number of iterations is increased and the solution time of algorithm is increased. In view of the problem, the main line of distribution network is determined first, and then the whole network is divided into multiple independent sub-regions based on this, each sub-region is contained in the distribution network and there is no overlapping region, the number of feasible solutions is reduced, and the genetic algorithm is optimized for solving

[0130] The power supply reliability index calculation includes:

[0131] System average interruption duration index (SAIDI):

[0132]

[0133] Average service availability index (ASAI):

[0134]

[0135] System energy not supplied (ENS):

[0136]

[0137] System average energy not supplied (AENS):

[0138]

[0139] In the formula:

[0140] The total number of load points.

[0141] The number of users connected to the load point .

[0142] The annual average failure duration of the load point .

[0143] The total average load connected to the load point .

[0144] The final output is shown in Figure 3 , and Figure 4 compared with the traditional distribution scheme, the number of devices to be installed is reduced from 11 to 7.

[0145] It should be noted that the above listed embodiments are only used to illustrate the technical principles and application modes of the present application, and do not constitute a limitation on the protection scope of the present application. Although the present application has been described in detail in combination with a plurality of preferred embodiments, it should be understood by those skilled in the art that various forms of modification, transformation or equivalent replacement of related technical details can still be made without departing from the core technical idea of the present application. For example, simplification of the graph construction mode, replacement of the graph neural network structure, switching of the reinforcement learning algorithm, adjustment of the interface protocol between the modules, etc. should be regarded as reasonable technical extensions of the present application. Therefore, any equivalent changes or replacements made within the scope of the spirit and technical principles of the present application should be covered within the protection scope of the present application.

Claims

1. A method for deploying power grid fault traveling wave location devices based on an improved genetic algorithm, characterized in that, Includes the following steps: S1 establishes a mathematical model: To address the issue of offline fault location device deployment in distribution networks, a mathematical model is established that includes the distribution network topology, fault location parameters, power supply reliability objective function, and reclosing time function; the information of distribution network nodes, switching equipment, and circuit breakers is encoded into a graph structure. S2 initial population generation: An initial population is formed by assigning line numbers, and the initial positions of nodes are determined based on the topology. The node information is then converted into individual codes according to the coding rules, and the individual fitness is calculated using a fitness function. S3 genetic operations: Select, crossover, and mutation operations are performed on the initial population to generate new individuals; S4 Algorithm Termination Check: If the best individual in the chromosome has multiple genes, the algorithm terminates; if the best individual has no genes, the genetic operation continues until the termination condition is met.

2. The method for deploying a power grid fault traveling wave location device based on an improved genetic algorithm according to claim 1, characterized in that, The switching device coding in step S1 adopts a three-state coding method; Switch status coding rules: The code is 1 when the fault current direction is the same as the positive direction; The code is 0 when no non-fault current passes through; The code is -1 when the direction of the fault current is not in the positive direction; In distribution networks, switches are typically encoded using binary encoding, where a switch carrying fault current is coded as 1, and a switch carrying non-fault current is coded as 0. To accurately reflect current attributes and direction in distribution networks containing distributed generation, this binary encoding method is extended. Switch function expression: ； In the formula: The desired function of the circuit switch; This refers to the switching coefficient; , These represent the feeder fault statuses for the upper and lower sections, respectively. , The upper and lower halves of the switch are respectively the first The feeder segment is in fault condition.

3. The method for deploying a power grid fault traveling wave location device based on an improved genetic algorithm according to claim 1, characterized in that, The fitness function in step S2 is improved as follows: ； In the formula: For switching variables; This refers to the number of feeders in the upper half section of the switch. To improve accuracy and response speed, the optimization objective is transformed into a dual problem, i.e., the minimum problem is transformed into a maximum problem, finding the maximum value of the current fitness function: ； In terms of chromosome coding, a branch direct mapping coding method is adopted, that is, each branch corresponds to an independent chromosome gene locus, and the total length of the chromosome is equal to the total number of branches. Based on this, economic and reliability indicators are added to the fitness function, which are determined by the cumulative cost of the device for obtaining gene loci and the quantification of the proportion of locatable fault branches, respectively. The constraints include: The first and last ends of the main line must be equipped with at least one multi-terminal device, the distributed power supply access branch gene value must be at least 1, and the number of critical path devices must be at least 2. Total cost cap threshold; When performing specific genetic operations, the crossover operator is preferentially exchanged between adjacent branches with an electrical distance of ≤3; the mutation operator is set in a hierarchical manner according to the branch type; and the probabilistic elite retention strategy ensures that at least 20 high-quality individuals with 100% coverage are retained in each generation of the population.

4. The method for deploying a power grid fault traveling wave location device based on an improved genetic algorithm according to claim 1, characterized in that, The genetic operation in step S3 employs dynamic adaptive crossover and mutation probabilities, defined as follows: ； In the formula: , These represent the maximum and minimum crossover probabilities; , These represent the maximum and minimum mutation probabilities; The maximum fitness in the population; This represents the average fitness of the population during iteration.

5. The method for deploying a power grid fault traveling wave location device based on an improved genetic algorithm according to claim 1, characterized in that, The S4 algorithm termination judgment also includes hierarchical processing and power supply reliability indicators: Hierarchical processing: Determine the main distribution network lines and divide the network into non-overlapping independent sub-regions; Fault information is obtained through SCADA system and FTU equipment, and the placement of points is optimized using fitness function; First, determine the main lines of the distribution network, and then divide the entire network into multiple independent sub-regions based on these lines. Each sub-region is contained within the distribution network and there are no overlapping areas, which reduces the number of feasible solutions and facilitates optimization by the genetic algorithm. The calculation of power supply reliability indicators includes: System Mean Outage Duration (SAIDI): ； Average power supply reliability (ASAI): ； Low system battery (ENS): ； System average battery level is insufficient (AENS): ； In the formula: This is the total number of load points; For load point The number of users connected; It is the load point The average annual duration of failures; For load point The total average load received.

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