Direct-current power distribution network fault positioning system and method based on neural network and optimization algorithm

Abstract

The invention discloses a direct-current power distribution network fault positioning system and method based on a neural network and an optimization algorithm, relates to the field of direct-current power distribution network fault positioning, and designs a fault location strategy in combination with a generalized regression neural network and a grey wolf optimization algorithm. The method comprises the following steps: performing sample expansion on original fault voltage data by adopting an autoregression moving average model to obtain a large number of data samples, performing time-frequency domain feature extraction on a fault transient voltage signal by utilizing S transformation and permutation entropy, constructing a fault feature quantity, inputting the fault feature quantity into a GRNN for training, and optimizing parameters of the GRNN by adopting a GWO of an improved iteration strategy to obtain a fault transient voltage signal; and finally obtaining a fault positioning result. The fault location method designed by the invention is excellent in performance and strong in robustness, and realizes accurate fault location of the MMC type flexible direct-current power distribution network, thereby ensuring safe operation of the flexible direct-current power distribution network.

Description

Technical Field

[0001] The present invention relates to the field of DC distribution network fault location, and in particular to a DC distribution network line fault location method based on a neural network and an optimization algorithm. Background Art

[0002] At present, flexible DC distribution technology is still in its infancy, especially in the research of fault location. There are many difficulties and challenges. The fault duration in the DC distribution network is short. When a fault occurs, the current or voltage rises quickly and reaches the peak value within a few milliseconds. At the same time, since the flexible DC distribution network mostly uses cables to form the transmission channel, it is difficult to accurately determine the fault location once a fault occurs. If the fault is not discovered and cleared in time, it is easy to cause more serious damage such as equipment insulation damage. Although the fault location technology for AC systems is relatively mature, the flexible DC distribution network has great differences from the AC distribution network in system structure and operation control mode, so the traditional fault location method is not applicable. Compared with the DC transmission system that has been studied more by domestic and foreign scholars, the DC distribution network has more lines and converters, more complex topology, and the access of a large number of DC loads and distributed power sources has brought difficulties to the fault feature analysis. Summary of the invention

[0003] The purpose of the present invention is to solve the above shortcomings, ensure the safe and reliable operation of the power system, avoid the damage to the system caused by the difficulty in identifying faults, quickly and accurately realize the precise positioning of single-pole grounding faults in the flexible DC distribution network, accurately measure the location of the fault point, effectively reduce the line patrol time of the staff, and improve the efficiency of fault clearing.

[0004] To achieve the above objectives, the present invention adopts the following technical solutions:

[0005] The present invention discloses a DC distribution network line fault location system based on a neural network and an optimization algorithm, which comprises a sample acquisition and expansion unit, a fault voltage feature extraction unit, a neural network training unit and an optimization algorithm unit;

[0006] The DC distribution network line is divided into multiple topological structures of single-end power supply, double-end power supply and multi-end power supply according to the number of power supply sources; the AC power is converted into DC power by the converter for DC line transmission; the DC line is divided into positive and negative poles, and the corresponding DC distribution network line faults are divided into single-pole faults and double-pole faults;

[0007] The sample collection and expansion unit samples the original data of the fault voltage through the voltage transformers on both sides of the DC distribution line, and expands the fault voltage data using the ARIMA model. The ARIMA model is used to model and predict non-stationary time series data. First, the fault voltage data is differentially processed, and the model order is confirmed through the autocorrelation function and partial autocorrelation function diagram of the fault voltage data. The fitted ARIMA model is used to expand the sample of the original fault voltage data to form a new data sample, which makes up for the problem that the real fault data samples that the flexible DC distribution network can provide are limited, and the generated data samples are transmitted to the fault voltage feature extraction unit;

[0008] The fault voltage feature extraction unit extracts frequency domain energy features and time domain complexity features from the data samples generated by the sample acquisition and expansion unit, and the fault feature quantity is used as the input of the neural network training unit;

[0009] The neural network training unit adopts a generalized regression neural network (GRNN). The learning safety of the GRNN neural network depends on the input data samples. In view of the complex structure and diverse fault conditions of the flexible DC distribution network, a large number of data samples are required for the training of the neural network, 80% of which are used as training sets and 20% as test sets.

[0010] The GRNN neural network consists of four layers, namely, an input layer, a pattern layer, a summation layer and an output layer. The input variable of the input layer is the fault voltage feature obtained by the fault voltage feature extraction unit, and the input variable is directly passed to the pattern layer. The pattern layer passes the input variable to the summation layer through a transfer function. The summation layer performs arithmetic summation and weighted summation on the output of the pattern layer respectively, and divides the two summation results as an output vector and passes them to the output layer. The output result is the fault distance value.

[0011] The optimization algorithm unit adopts the improved grey wolf optimization algorithm with the iterative strategy to obtain the best smooth factor value, so as to achieve the best ranging effect of the GRNN neural network.

[0012] Furthermore, the converter is an MMC converter, and the neutral point of the converter is grounded via a resistor.

[0013] Furthermore, the single-pole grounding fault is determined as a fault location target for a DC distribution line.

[0014] Furthermore, the range of collecting the fault transient voltage signal is 0-20ms.

[0015] Furthermore, the frequency domain energy feature extraction performs an S transform on the original fault signal to obtain the energy value of the original signal at a single frequency; the amplitude of the transient voltage at a single frequency is easily affected by noise and interference signals, and it is difficult to directly extract the amplitude feature. Therefore, the energy spectrum is divided into frequency bands, all single-frequency transient energies contained in the frequency band are added, and the transient energy proportion of each frequency band is calculated, and the energy proportion of each frequency band is used as the frequency domain fault feature.

[0016] Furthermore, the time domain complexity feature extraction is performed by calculating the permutation entropy of the fault transient voltage as a supplement to the frequency domain fault feature. The permutation entropy is a dimensionless indicator used to characterize the complexity of the signal sequence. The larger the entropy value, the greater the complexity of the signal. The fault voltage signal is reconstructed to obtain the phase space matrix. The reconstructed components in the matrix are arranged in ascending order according to the numerical value. The number of occurrences of each sorting is counted, their probabilities are calculated, and the permutation entropy calculation formula is substituted and the data is normalized to obtain the final permutation entropy value.

[0017] Furthermore, in the transfer function, the variables are all fault voltage characteristic quantities, and the only parameter that needs to be manually adjusted is the smoothing factor, and different values ​​of the smoothing factor will affect the performance of the GRNN.

[0018] Furthermore, the optimization process of the gray wolf optimization algorithm first initializes the position of the wolf pack, and each wolf represents a smoothness factor; secondly, the GRNN network under different smoothness factors is trained, and the ranging error is calculated after the test results are obtained. The algorithm terminates when the number of iterations or convergence conditions are met, otherwise the gray wolf position is iterated, and the above steps are repeated until the algorithm terminates.

[0019] Furthermore, the improvement of the iteration strategy is that firstly, a chaotic variable between 0 and 1 is generated by using a chaotic mapping function, and the chaotic variable is mapped into the search space of the decision variable to form an initial population, so as to replace the direct initialization of the population position, and improve the population diversity to improve the search efficiency of the algorithm; secondly, the convergence speed of the algorithm in the early stage is slowed down, so as to prompt the wolf pack to conduct a global search, and improve the convergence speed of the algorithm in the later stage, which is beneficial to the local search accuracy; at the same time, a dynamic weight reflecting the level of the wolf pack is introduced in the update of the wolf pack position, so as to strengthen the guiding role of the optimal solution in the wolf pack and improve the convergence speed and accuracy;

[0020] Furthermore, the DC distribution network line fault location method based on neural network and optimization algorithm has the following implementation steps:

[0021] S1, sample expansion, achieved through sample collection and expansion unit;

[0022] Using the ARIMA model, it is expressed as:

[0023] ARIMA(p,d,q)

[0024] In the formula, p represents the order of autoregression, d represents the number of differences, which is used to convert non-stationary series into stationary series, and q represents the order of moving average term;

[0025] Obtain fault voltage time series data from the power system for differential processing:

[0026] △Y t =Y t -Y t-1

[0027] In the formula, △Y t represents the difference at time t, Y t and Y t-1 Represent the original data at time t and time t-1 respectively. The number of differences d needs to be determined by the results of the stationarity test;

[0028] Plot the autocorrelation function and partial autocorrelation function of the fault voltage data. Based on the AIC information criterion, traverse different combinations of p and q and select the model order that minimizes the information criterion:

[0029] AIC=-2ln(L)+2k

[0030] Where L is the likelihood function value of the model, and k is the number of model parameters;

[0031] The fitted ARIMA model is used to expand the sample of the original fault voltage data to generate multiple sample data, thereby achieving the expansion of the sample data;

[0032] S2, voltage feature extraction, implemented by the fault voltage feature extraction unit, is divided into time domain complexity feature extraction and frequency domain energy feature extraction;

[0033] For frequency domain energy extraction, after a single-pole grounding fault occurs in the DC distribution network, the voltage signal on the fault line is extracted. First, the original signal x(t) is S-transformed:

[0034]

[0035] Where ω(tt,f) is the Gaussian window function, t is the displacement factor, f is the frequency, and j is the imaginary unit;

[0036] Since the electrical signal collected by the computer is discrete, let the discrete time series function of the original signal x(t) be x[αT] (α=0, 1, 2, …, N-1), its discrete Fourier transform is X[αT], and its discrete form of S transform is:

[0037]

[0038] In the formula, N is the number of sampling points, and T is the sampling time interval;

[0039] The transient energy expression of the original signal at a single frequency fn is:

[0040]

[0041] For a certain frequency band, it is only necessary to add up all the single frequency transient energies contained in the frequency band. Considering that the energy value is generally large in magnitude, which affects the weight distribution of the intelligent algorithm, the result obtained cannot be used directly. Therefore, the frequency band energy value is converted into energy proportion, and the result is controlled between 0 and 1 without changing the energy ratio between frequency bands;

[0042] In order to obtain the energy value of a fixed frequency band, it is necessary to divide the energy spectrum into frequency bands, calculate the transient energy proportion of each frequency band, and use the "binary method" to characterize the high-frequency and low-frequency areas of the signal to divide the original signal into 8 fixed frequency bands: d0 area (5kHz, 10kHz), d1 area (2.5kHz, 5kHz), d2 area (1.25kHz, 2.5kHz), d3 area (0.625kHz, 1.25kHz), d4 area (312.5Hz, 625Hz), d5 area (156.25Hz, 312.5Hz), d6 area (78.125Hz, 156.25Hz), and d7 area (0Hz, 78.125Hz) representing the low-frequency area. Since high frequencies (d0, d1, d2) are easily disturbed by lightning strikes, in order to improve the universality and accuracy of the ranging method, the d3 to d7 frequency bands are selected to sum the energy; the energy proportion of each frequency band is calculated as the frequency domain fault feature;

[0043] For time domain complexity extraction, the permutation entropy of the fault voltage signal is calculated and normalized as a supplement to the fault feature information. First, the information entropy of the random variable X is obtained:

[0044]

[0045] Where P(x) is the probability of event x occurring in the random variable X;

[0046] Reconstruct the time series signal x(t) of length N and obtain the phase space matrix X, which is expressed as:

[0047]

[0048] Where m is the embedding dimension, t is the delay time, and k = N-(m-1)t.

[0049] Arrange the reconstructed components of the jth row in X in ascending order according to their numerical values, that is:

[0050] x[j+(j1-1)t]≤x[j+(j2-1)t]≤…≤x[j+(j m -1)t]

[0051] In the formula, j1, j2, ..., jm represent the index of the column where each element is located;

[0052] Count the number of times each sorting occurs and calculate their probability P(i). According to the definition of information entropy, calculate the permutation entropy:

[0053]

[0054] In order to adjust the entropy value range to 0 to 1, the data is normalized and the final entropy value is:

[0055]

[0056] S3, neural network training, is achieved through the neural network training unit. GRNN is based on nonlinear regression analysis and consists of four layers in structure, namely input layer, pattern layer, summation layer and output layer. The fault characteristics are used as neural network input and the fault distance is used as neural network output;

[0057] For the input layer, the S transform converts the fault transient voltage signal into an energy spectrum and divides it into 8 frequency bands. Finally, five frequency bands from d3 to d7 are selected and 5 energy proportions are calculated. The permutation entropy of the fault signal is a numerical value. Therefore, the input vector of the neural network is 6-dimensional in total, which can be expressed as:

[0058] X=[M3, M4, M5, M6, M7, H NPE ] T

[0059] The number of neurons in the pattern layer is equal to the number of learning samples. Each neuron corresponds to a different learning sample, and its transfer function is:

[0060]

[0061] Where X is the input variable of the GRNN network; Xi is the learning sample corresponding to the i-th neuron in the pattern layer, and σ is the smoothing factor;

[0062] There are two types of neurons in the summation layer. The first type of neurons directly perform arithmetic summation on the output of the pattern layer:

[0063]

[0064] The second type of neurons performs weighted summation on the output of the pattern layer. The number of neurons is the same as the sample output dimension. The connection weight between the i-th neuron in the pattern layer and the j-th second type of neuron in the summation layer is the j-th element y in the i-th output sample.ij , the transfer function is:

[0065]

[0066] The number of neurons in the output layer is equal to the dimension of the output vector. The output of the jth neuron in the output layer corresponds to the jth element in the output vector. The expression is:

[0067]

[0068] In the fault location measurement of flexible DC distribution network, the selection of data samples must be representative and comprehensively show various fault conditions. Faults at different locations are samples that must be traversed. Among the fault types, single-pole faults are divided into positive pole faults and negative pole faults, so the fault pole is also a condition that needs to be considered. In actual situations, faults are often not metallic faults, and transition resistance will directly affect the system fault characteristics. Therefore, multiple groups of different transition resistances are set to be added to the network training, and 80% of them are randomly selected as training sets, and the remaining 20% ​​are used as test sets. In actual training, data samples and results are input and output in matrix form.

[0069] S4. Use the gray wolf optimization algorithm to solve the optimal value of the smoothness factor to replace the traditional manual selection. The optimization process of the gray wolf algorithm is divided into three stages: encirclement, pursuit and attack. The first three wolves with the best fitness are defined as alpha, beta and delta respectively, and the omega wolf pack updates the position around the first three levels of wolves; for the initialization of the wolf pack position, introduce a chaotic optimization strategy to improve the population diversity to improve the search efficiency of the algorithm. Set the population size, for each gray wolf individual, use the chaotic mapping function to generate a chaotic variable between 0 and 1; map the chaotic variable to the search space of the decision variable to form the initial population, the chaotic mapping function:

[0070] x n+1 =μx n (1-x n )

[0071] Where μ is the chaos control parameter, x n is the current chaotic variable, x n+1 is the next chaos variable.

[0072] Decision variable mapping formula:

[0073]

[0074] In the formula, is the decision variable of the kth gray wolf in the jth dimension, x minj and x maxj are the search upper and lower bounds of the j-th dimension variable, is a chaotic variable;

[0075] In the gray wolf optimization algorithm, the distance calculation formula between the gray wolf and the prey is:

[0076]

[0077] In the formula, and are the position vector of the prey and the position vector of the gray wolf, respectively, and t is the current iteration number;

[0078] After calculating the distance to the prey, the gray wolf uses the following formula to surround the prey:

[0079]

[0080] In the formula, and are two random one-dimensional vectors with values ​​in [0,1];

[0081] Used to simulate the attack behavior of gray wolves on prey, the value is affected by the convergence factor The convergence factor decreases linearly with the number of iterations from 2 to 0. The convergence factor reduction strategy of the gray wolf algorithm and the wolf group level position iteration strategy are improved. The decreasing strategy is improved from linear decreasing to nonlinear decreasing, using the following formula:

[0082]

[0083] In the formula, T is the total number of iterations, and t is the current number of iterations;

[0084] The larger the convergence factor value, the farther the gray wolf will move from the prey and try to find a more suitable prey, prompting the wolf pack to conduct a global search; the smaller the convergence factor value, the closer the gray wolf will move to the prey, prompting the wolf pack to conduct a local search; the improved strategy slows down the decreasing speed of the convergence factor in the early stage of the algorithm, and the convergence factor maintains a large value for a long time, prompting the wolf pack to conduct a global search; while in the later stage of the algorithm, the convergence factor decreases faster, which is conducive to local search and can improve search accuracy;

[0085] For the wolf pack hierarchical position iteration strategy, alpha, beta and delta wolves are jointly responsible for evaluating the position of the prey, and the remaining wolves use this as a reference to calculate the distance between themselves and the prey and complete the position iteration; in this process, the hierarchy of the wolf pack is not obvious, especially in the later local search of the algorithm, it is necessary to strengthen the optimal solution guidance role of alpha to improve the convergence speed and accuracy. Therefore, a dynamic weight reflecting the wolf pack level is introduced in the wolf pack position update, and its formula is:

[0086]

[0087] In the early stage of the algorithm, in order to prevent the entire wolf pack from gathering in a certain area of ​​the current optimal position of the group too early, the wolf pack's position iteration strategy does not change. Therefore, the improved wolf pack position iteration formula is:

[0088]

[0089] As the number of iterations increases, The value of is decreasing, The fluctuation range will also decrease. When the value of is less than 1, the gray wolf attacks its prey.

[0090] The improved gray wolf algorithm is used to optimize the GRNN smoothing factor. The process is as follows: Figure 7 As shown;

[0091] The improvement of the traditional gray wolf algorithm is located in the "update wolf position" in the flowchart. The wolf position is initialized, each wolf represents a smooth factor, the GRNN network is trained, and the fitness function is calculated after the test results are obtained. The three wolves with the smallest error are marked as alpha, beta and delta, and then the positions of the remaining wolves are recalculated using the improved iterative strategy. The above operations are repeated and the algorithm terminates when the number of iterations or convergence conditions are met. At this time, the position of the head wolf represents the required smooth factor; assuming that the output matrix of the test sample is T = [t1, t2, ..., t 1600 ], and the output of GRNN is A = [a1, a2, ..., a 1600 ], then the fitness value in the flowchart is the root mean square error of the data in the two matrices, that is:

[0092]

[0093] The improved gray wolf optimization algorithm is introduced to improve the computing speed and accuracy of the gray wolf algorithm, further improve the rationality of the smoothing factor selection, thereby improving the GRNN fitting accuracy and increasing the fault distance accuracy;

[0094] Working principle:

[0095] In order to realize fast and accurate fault location after a single-pole grounding fault occurs in an MMC type DC distribution network line, the present invention combines a GRNN neural network with a gray wolf optimization algorithm to design a fault distance measurement strategy; an ARIMA model is used to expand the sample of the original fault voltage data to obtain a large number of data samples; in terms of fault feature extraction, an S transform is selected to obtain the energy spectrum of the fault signal, and the energy proportion is calculated by frequency band as the frequency domain feature of the fault signal; and permutation entropy is used to reflect the complexity and information amount of the signal in the time domain, which together constitute the feature of the fault signal and are then input into a GRNN for training; at the same time, the parameters of the GRNN are optimized by using an improved initialization strategy and an iterative strategy of the gray wolf optimization algorithm, and finally a fault location result is obtained.

[0096] Beneficial effects of the present invention:

[0097] The significance of adopting intelligent algorithms in the research of fault distance measurement in the present invention is that when faced with huge data and complex systems, it can minimize the human error in the fault analysis link and fit the deep relationship between fault characteristics and fault distances; in the fitting of fault characteristics and fault distances, a GRNN neural network is selected, and the network structure and the connection weights between each neuron are only affected by samples, which minimizes the influence of artificially set parameters on the prediction results, and the only parameter that needs to be adjusted in the entire model is the smoothing factor; in order to solve the problem of adjusting the smoothing factor, the gray wolf optimization algorithm is introduced and improved; after testing and comparison, the feature extraction method and ranging algorithm designed by the present invention have excellent ranging accuracy and robustness, and provide a novel and effective solution for fault distance measurement in DC distribution networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 Double-ended power supply type flexible DC distribution network structure diagram;

[0099] Figure 2 Energy distribution diagram of each frequency band at different fault distances;

[0100] Figure 3 Energy distribution diagram of each frequency band under different transition resistance;

[0101] Figure 4 Line mode voltage permutation entropy diagram under different fault conditions;

[0102] Figure 5 The network structure diagram of GRNN;

[0103] Figure 6 GWO wolf pack location update diagram;

[0104] Figure 7 Grey wolf algorithm optimizes GRNN network flow chart;

[0105] Figure 8Fitness value convergence trend graph. DETAILED DESCRIPTION

[0106] In order to better explain the scheme, a detailed description is given below in conjunction with the accompanying drawings and embodiments of the specification.

[0107] A method for locating a DC distribution network line fault based on a neural network and an optimization algorithm, characterized in that it comprises a sample acquisition and expansion unit, a fault voltage feature extraction unit, a neural network training unit and an optimization algorithm unit;

[0108] The core equipment of the converter station in the DC distribution network is a modular multilevel converter (MMC), the neutral point of which is grounded through a resistor, including multiple topologies such as single-end, double-end and multi-end power supply. The distribution line terminal includes AC and DC loads, distributed photovoltaics and energy storage devices, such as Figure 1 As shown in the figure, in addition to the interconnection line between the two MMCs, four power feeders are set up. The ends of feeders 1, 2, and 3 are connected to AC and DC loads, which are 4MW, 1MW, and 6MW respectively. Distributed photovoltaic power is connected to the grid through feeder 4. At 28℃ and 1200W / m2, the output power of photovoltaic power generation is 4MW. The MMC1 converter station adopts constant DC voltage control and constant AC voltage control (Udc / Uac control), and the MMC2 converter station adopts constant active power control and constant reactive power control (P / Q control). The DC lines are all cable lines, and the frequency-variable parameter model is adopted, which is closer to the actual project.

[0109] The fault location is for single-pole grounding fault location of DC distribution lines, which has the basic characteristics of short fault duration, fast rise of current or voltage when a fault occurs, and reaching the peak value within a few milliseconds;

[0110] The sample acquisition and expansion unit samples the original data of the fault voltage through the voltage transformers on both sides of the DC distribution line, the sampling range is the fault transient voltage signal within 20ms from the time of the fault occurrence, and uses the ARIMA model to perform differential processing on the fault voltage data, confirms the model order through the autocorrelation function and partial autocorrelation function diagram of the fault voltage data, uses the fitted ARIMA model to expand the sample of the original fault voltage data, forms a new data sample, compensates for the problem that the real fault data samples that the flexible DC distribution network can provide are limited, and transmits the generated data sample to the fault voltage feature extraction unit;

[0111] The fault voltage feature extraction unit extracts frequency domain energy features and time domain complexity features from the data samples generated by the sample acquisition and expansion unit, and the fault feature quantity is used as the input of the neural network training unit;

[0112] The frequency domain energy extraction first performs an S transform on the original fault signal to obtain the energy value of the original signal at a single frequency. Since the amplitude of the transient voltage at a single frequency is easily affected by noise and interference signals, it is difficult to directly extract the amplitude feature. The fault feature extraction unit divides the energy spectrum into frequency bands, adds all the single-frequency transient energies contained in the frequency band, and calculates the transient energy proportion of each frequency band, and uses the energy proportion of each frequency band as the frequency domain fault feature;

[0113] The time domain complexity feature extraction is performed by calculating the permutation entropy of the fault transient voltage as a supplement to the frequency domain fault feature. The permutation entropy is a dimensionless indicator used to characterize the complexity of the signal sequence. The larger the entropy value, the greater the complexity of the signal. Reconstruct the fault voltage signal to obtain the phase space matrix, sort the reconstructed components in the matrix in ascending order according to the numerical value, count the number of occurrences of each sorting, calculate their probabilities, substitute them into the permutation entropy calculation formula and normalize the data to obtain the final permutation entropy value;

[0114] The neural network training unit adopts a GRNN neural network, which is structurally composed of four layers, namely an input layer, a pattern layer, a summation layer and an output layer, wherein the input variable of the input layer is the fault voltage feature quantity obtained by the fault voltage feature extraction unit, and the input variable is directly passed to the pattern layer, the pattern layer passes the input variable to the summation layer through a transfer function, the summation layer performs arithmetic summation and weighted summation on the output of the pattern layer respectively, and divides the two summation results as an output vector and passes them to the output layer, and the output result is the fault distance value.

[0115] In the transfer function, the variables are all fault voltage characteristic quantities, and the only parameter that needs to be manually adjusted is the smoothing factor, and different values ​​of the smoothing factor will affect the performance of the GRNN.

[0116] The GRNN neural network learning safety depends on the input data samples. Due to the complex structure of the flexible DC distribution network and the diverse fault conditions, the training of the neural network requires a large number of data samples, 80% of which are used as training sets and 20% as test sets.

[0117] The optimization algorithm unit adopts the gray wolf optimization algorithm with improved iteration strategy to obtain the best smooth factor value, so as to achieve the best ranging effect of the GRNN neural network;

[0118] The optimization process of the gray wolf optimization algorithm is as follows: first, the wolf group position is initialized, and each wolf represents a smooth factor; secondly, the GRNN network under different smooth factors is trained, and the ranging error is calculated after the test results are obtained. When the number of iterations or the convergence condition is met, the algorithm is terminated, otherwise the gray wolf position is iterated, and the above steps are repeated until the algorithm is terminated;

[0119] The improvement of the iterative strategy is as follows: first, a chaotic mapping function is used to generate a chaotic variable between 0 and 1, and the chaotic variable is mapped to the search space of the decision variable to form an initial population, so as to replace the direct initialization of the population position, and improve the population diversity to improve the search efficiency of the algorithm; secondly, the convergence speed of the algorithm in the early stage is slowed down, so as to prompt the wolf pack to conduct a global search, improve the convergence speed of the algorithm in the later stage, and facilitate the local search accuracy; at the same time, a dynamic weight reflecting the level of the wolf pack is introduced in the update of the wolf pack position, so as to strengthen the guiding role of the optimal solution in the wolf pack and improve the convergence speed and accuracy.

[0120] The DC distribution network line fault location method based on neural network and optimization algorithm is characterized in that the method implementation steps are as follows:

[0121] S1. Sample expansion, using the ARIMA model, which is expressed as:

[0122] ARIMA(p,d,q)

[0123] In the formula, p represents the order of autoregression, d represents the number of differences, which is used to convert non-stationary series into stationary series, and q represents the order of moving average term.

[0124] Obtain fault voltage time series data from the power system for differential processing:

[0125] △Y t =Y t -Y t-1

[0126] In the formula, △Y t represents the difference at time t, Y t and Y t-1 Represent the original data at time t and time t-1 respectively. The number of differences d needs to be determined by the results of the stationarity test.

[0127] Plot the autocorrelation function and partial autocorrelation function of the fault voltage data. Based on the AIC information criterion, traverse different combinations of p and q and select the model order that minimizes the information criterion:

[0128] AIC=-2ln(L)+2k

[0129] Where L is the likelihood function value of the model and k is the number of model parameters.

[0130] The fitted ARIMA model is used to expand the sample of the original fault voltage data to generate multiple sample data, thereby achieving the expansion of the sample data.

[0131] S2. Voltage feature extraction is divided into time domain complexity feature extraction and frequency domain energy feature extraction.

[0132] For frequency domain energy extraction, after a single-pole grounding fault occurs in the DC distribution network, the voltage signal on the fault line is extracted. First, the original signal x(t) is S-transformed:

[0133]

[0134] Where ω(tt,f) is the Gaussian window function, t is the displacement factor, f is the frequency, and j is the imaginary unit.

[0135] Since the electrical signal collected by the computer is discrete, let the discrete time series function of the original signal x(t) be x[αT] (α=0, 1, 2, …, N-1), its discrete Fourier transform is X[αT], and its discrete form of S transform is:

[0136]

[0137] Where N is the number of sampling points and T is the sampling time interval.

[0138] The transient energy expression of the original signal at a single frequency fn is:

[0139]

[0140] For a certain frequency band, it is only necessary to add up all the single frequency transient energies contained in the frequency band. Considering that the energy value is generally large in magnitude, which affects the weight distribution of the intelligent algorithm, the result obtained cannot be used directly. Therefore, the frequency band energy value is converted into energy proportion, and the result is controlled between 0 and 1 without changing the energy ratio between frequency bands.

[0141] In order to obtain the energy value of a fixed frequency band, it is necessary to divide the energy spectrum into frequency bands, calculate the transient energy proportion of each frequency band, and use the "binary method" to characterize the high-frequency and low-frequency areas of the signal to divide the original signal into 8 fixed frequency bands: d0 area (5kHz, 10kHz), d1 area (2.5kHz, 5kHz), d2 area (1.25kHz, 2.5kHz), d3 area (0.625kHz, 1.25kHz), d4 area (312.5Hz, 625Hz), d5 area (156.25Hz, 312.5Hz), d6 area (78.125Hz, 156.25Hz), and d7 area (0Hz, 78.125Hz) representing the low-frequency area. Since high frequencies (d0, d1, d2) are easily disturbed by lightning strikes, in order to improve the universality and accuracy of the ranging method, the d3~d7 frequency bands are selected to sum the energy. The energy proportion of each frequency band is calculated as the frequency domain fault feature.

[0142] Now set the single-pole grounding fault to occur at 0.1, 0.2, and 0.4 km from the head end of feeder L4, with a transition resistance of 20Ω, and obtain the transient energy distribution of each frequency band of the fault line mode voltage as follows: Figure 2 Then, at a distance of 0.6 km from the head end of line L1, transition resistors of 10, 30, and 50 Ω are set respectively, and the energy distribution of each frequency band is obtained as shown in Figure 3 shown.

[0143] For time domain complexity extraction, the permutation entropy of the fault voltage signal is calculated and normalized as a supplement to the fault feature information. First, the information entropy of the random variable X is obtained:

[0144]

[0145] Where P(x) is the probability of event x occurring in the random variable X.

[0146] Reconstruct the time series signal x(t) of length N and obtain the phase space matrix X, which is expressed as:

[0147]

[0148] Where m is the embedding dimension, t is the delay time, and k = N-(m-1)t.

[0149] Arrange the reconstructed components of the jth row in X in ascending order according to their numerical values, that is:

[0150] x[j+(j1-1)t]≤x[j+(j2-1)t]≤…≤x[j+(j m -1)t]

[0151] In the formula, j1, j2, …, jm represent the index of the column where each element is located.

[0152] Count the number of times each sorting occurs and calculate their probability P(i). According to the definition of information entropy, calculate the permutation entropy:

[0153]

[0154] In order to adjust the entropy value range to 0 to 1, the data is normalized and the final entropy value is:

[0155]

[0156] 21 fault points are set at equal distances on the interconnection line, numbered from 0 to 20, and the line mode voltage permutation entropy values ​​measured on the MMC1 side under different transition resistances are calculated. The results are as follows: Figure 4 shown.

[0157] S3. Neural network training. GRNN is based on nonlinear regression analysis and consists of four layers, such as Figure 5 As shown, they are the input layer, pattern layer, summation layer and output layer respectively. The fault feature is used as the neural network input and the fault distance is used as the neural network output.

[0158] For the input layer, the S transform converts the fault transient voltage signal into an energy spectrum and divides it into 8 frequency bands. Finally, five frequency bands from d3 to d7 are selected and 5 energy proportions are calculated. The permutation entropy of the fault signal is a numerical value. Therefore, the input vector of the neural network is 6-dimensional in total, which can be expressed as:

[0159] X=[M3, M4, M5, M6, M7, H NPE ] T

[0160] The number of neurons in the pattern layer is equal to the number of learning samples. Each neuron corresponds to a different learning sample, and its transfer function is:

[0161]

[0162] Where X is the input variable of the GRNN network; Xi is the learning sample corresponding to the i-th neuron in the pattern layer, and σ is the smoothing factor.

[0163] There are two types of neurons in the summation layer. The first type of neurons directly perform arithmetic summation on the output of the pattern layer:

[0164]

[0165] The second type of neurons performs weighted summation on the output of the pattern layer. The number of neurons is the same as the sample output dimension. The connection weight between the i-th neuron in the pattern layer and the j-th second type of neuron in the summation layer is the j-th element y in the i-th output sample. ij , the transfer function is:

[0166]

[0167] The number of neurons in the output layer is equal to the dimension of the output vector. The output of the jth neuron in the output layer corresponds to the jth element in the output vector. The expression is:

[0168]

[0169] In the fault location measurement of flexible DC distribution network, the selection of data samples must be representative and comprehensively show various fault conditions. Faults in different locations are samples that must be traversed. In the fault type, single-pole faults are divided into positive pole faults and negative pole faults, so the fault pole is also a condition that needs to be considered. In actual situations, faults are often not metallic faults, and transition resistance will directly affect the system fault characteristics. Therefore, multiple groups of different transition resistances are set to join the network training, and 80% of them are randomly selected as training sets, and the remaining 20% ​​are used as test sets. In actual training, data samples and results are input and output in matrix form.

[0170] S4. The gray wolf optimization algorithm is used to solve the optimal value of the smoothness factor to replace the traditional manual selection. The optimization process of the gray wolf algorithm is divided into three stages: encirclement, pursuit and attack. The first three wolves with the best fitness are defined as alpha, beta and delta respectively, and the omega wolf pack updates its position around the first three levels of wolves.

[0171] For the initialization of the wolf pack position, a chaos optimization strategy is introduced to improve the population diversity and thus the search efficiency of the algorithm. The population size is set, and for each individual gray wolf, a chaotic variable between 0 and 1 is generated using a chaos mapping function. The chaotic variable is mapped to the search space of the decision variable to form the initial population. The chaos mapping function is:

[0172] x n+1 =μx n (1-x n )

[0173] Where μ is the chaos control parameter, x n is the current chaotic variable, x n+1 is the next chaos variable.

[0174] Decision variable mapping formula:

[0175]

[0176] In the formula, is the decision variable of the kth gray wolf in the jth dimension, x minj and x maxj are the search upper and lower bounds of the j-th dimension variable, is a chaotic variable.

[0177] In the gray wolf optimization algorithm, the distance calculation formula between the gray wolf and the prey is:

[0178]

[0179] In the formula, and are the position vector of the prey and the position vector of the gray wolf respectively, and t is the current iteration number.

[0180] After calculating the distance to the prey, the gray wolf uses the following formula to surround the prey:

[0181]

[0182] In the formula, and are two random one-dimensional vectors with values ​​in [0,1].

[0183] Used to simulate the attack behavior of gray wolves on prey, the value is affected by the convergence factor The convergence factor decreases linearly with the number of iterations from 2 to 0. The convergence factor reduction strategy of the gray wolf algorithm and the wolf group level position iteration strategy are improved. The decreasing strategy is improved from linear decreasing to nonlinear decreasing, using the following formula:

[0184]

[0185] Where T is the total number of iterations and t is the current number of iterations.

[0186] The larger the convergence factor value, the farther the gray wolf will move from the prey, trying to find a more suitable prey, prompting the wolf pack to conduct a global search; the smaller the convergence factor value, the closer the gray wolf will move to the prey, prompting the wolf pack to conduct a local search. The improved strategy slows down the decreasing speed of the convergence factor in the early stage of the algorithm, and the convergence factor maintains a large value for a long time, prompting the wolf pack to conduct a global search; while in the later stage of the algorithm, the convergence factor decreases faster, which is conducive to local search and can improve search accuracy.

[0187] For the wolf pack hierarchical position iteration strategy, alpha, beta, and delta wolves are jointly responsible for evaluating the location of the prey, and the remaining wolves use this as a reference to calculate the distance between themselves and the prey and complete the position iteration. In this process, the hierarchy of the wolf pack is not obvious, especially in the later local search of the algorithm, it is necessary to strengthen the optimal solution guidance role of alpha to improve the convergence speed and accuracy. Therefore, a dynamic weight reflecting the wolf pack level is introduced in the wolf pack position update, and its formula is:

[0188]

[0189] In the early stage of the algorithm, in order to prevent the entire wolf pack from gathering in a certain area of ​​the current optimal position of the group too early, the wolf pack's position iteration strategy does not change. Therefore, the improved wolf pack position iteration formula is:

[0190]

[0191] The gray wolf's position update diagram is as follows Figure 6 As shown, the alpha, beta, and delta wolves estimate the location of the prey and guide the remaining wolves to update their positions around the prey.

[0192] As the number of iterations increases, The value of is decreasing, The fluctuation range will also decrease. When the value of is less than 1, the gray wolf attacks its prey.

[0193] The improved gray wolf algorithm is used to optimize the GRNN smoothing factor. The process is as follows: Figure 7 shown.

[0194] The improvement to the traditional gray wolf algorithm is located at "update wolf position" in the flowchart. Initialize the wolf position, each wolf represents a smooth factor, train the GRNN network, calculate the fitness function after obtaining the test results, and mark the three wolves with the smallest error as alpha, beta and delta. Then use the improved iterative strategy to recalculate the positions of the remaining wolves, and repeat the above operations. When the number of iterations or convergence conditions are met, the algorithm terminates. At this time, the position of the head wolf represents the required smooth factor. Assume that the output matrix of the test sample is T = [t1, t2, ..., t 1600 ], and the output of GRNN is A = [a1, a2, ..., a 1600 ], then the fitness value in the flowchart is the root mean square error of the data in the two matrices, that is:

[0195]

[0196] The improved gray wolf optimization algorithm is introduced to improve the computing speed and accuracy of the gray wolf algorithm, further improve the rationality of the smoothing factor selection, thereby improving the GRNN fitting accuracy and increasing the fault distance accuracy.

[0197] The optimization performance of GWO on GRNN before and after the improvement is compared, and the convergence trend of the fitness value with the increase of the number of iterations is analyzed, such as Figure 8 As shown, the lower the fitness value, the higher the accuracy of the ranging algorithm, that is, the better the optimization performance of GWO.

Claims

1. A DC distribution network line fault location system based on neural network and optimization algorithm, characterized in that: It includes a sample collection and expansion unit, a fault voltage feature extraction unit, a neural network training unit and an optimization algorithm unit; The DC distribution network line is divided into multiple topological structures of single-end power supply, double-end power supply and multi-end power supply according to the number of power supply sources; the AC power is converted into DC power by the converter for DC line transmission; the DC line is divided into positive and negative poles, and the corresponding DC distribution network line faults are divided into single-pole faults and double-pole faults; The sample collection and expansion unit samples the original data of the fault voltage through the voltage transformers on both sides of the DC distribution line, and expands the fault voltage data using the ARIMA model. The ARIMA model is used to model and predict non-stationary time series data. First, the fault voltage data is differentially processed, and the model order is confirmed through the autocorrelation function and partial autocorrelation function diagram of the fault voltage data. The fitted ARIMA model is used to expand the sample of the original fault voltage data to form a new data sample, which makes up for the problem that the real fault data samples that the flexible DC distribution network can provide are limited, and the generated data samples are transmitted to the fault voltage feature extraction unit; The fault voltage feature extraction unit extracts frequency domain energy features and time domain complexity features from the data samples generated by the sample acquisition and expansion unit, and the fault feature quantity is used as the input of the neural network training unit; The neural network training unit adopts a generalized regression neural network (GRNN). The safety of the GRNN neural network learning depends on the input data samples. In view of the complex structure and diverse fault conditions of the flexible DC distribution network, a large number of data samples are required for the training of the neural network, 80% of which are used as training sets and 20% as test sets. The GRNN neural network consists of four layers, namely, an input layer, a pattern layer, a summation layer and an output layer. The input variable of the input layer is the fault voltage feature obtained by the fault voltage feature extraction unit, and the input variable is directly passed to the pattern layer. The pattern layer passes the input variable to the summation layer through a transfer function. The summation layer performs arithmetic summation and weighted summation on the output of the pattern layer respectively, and divides the two summation results as an output vector and passes them to the output layer. The output result is the fault distance value. The optimization algorithm unit adopts the improved grey wolf optimization algorithm with the iterative strategy to obtain the best smooth factor value, so as to achieve the best ranging effect of the GRNN neural network.

2. A DC distribution network line fault location method based on neural network and optimization algorithm according to claim 1, characterized in that: The converter is an MMC type converter, and the neutral point of the converter is grounded via a resistor.

3. The DC distribution network line fault location method based on neural network and optimization algorithm according to claim 1 is characterized in that: The single-pole grounding fault is determined as a fault location target for a DC distribution line.

4. The method for locating a DC distribution network line fault based on a neural network and an optimization algorithm according to claim 1, characterized in that: The range of collecting fault transient voltage signals is 0-20ms.

5. The method for locating a DC distribution network line fault based on a neural network and an optimization algorithm according to claim 1, characterized in that: The frequency domain energy feature extraction performs an S transform on the original fault signal to obtain the energy value of the original signal at a single frequency; the amplitude of the transient voltage at a single frequency is easily affected by noise and interference signals, and it is difficult to directly extract the amplitude feature. Therefore, the energy spectrum is divided into frequency bands, all single-frequency transient energies contained in the frequency band are added, and the transient energy proportion of each frequency band is calculated, and the energy proportion of each frequency band is used as the frequency domain fault feature.

6. The method for locating a DC distribution network line fault based on a neural network and an optimization algorithm according to claim 1, characterized in that: The time domain complexity feature extraction is performed by calculating the permutation entropy of the fault transient voltage as a supplement to the frequency domain fault feature. The permutation entropy is a dimensionless index used to characterize the complexity of the signal sequence. The larger the entropy value, the greater the complexity of the signal. Reconstruct the fault voltage signal to obtain the phase space matrix, arrange the reconstructed components in the matrix in ascending order according to the numerical value, count the number of occurrences of each sorting, calculate their probabilities, substitute them into the permutation entropy calculation formula and normalize the data to obtain the final permutation entropy value.

7. The method for locating a DC distribution network line fault based on a neural network and an optimization algorithm according to claim 1, characterized in that: In the transfer function, the variables are all fault voltage characteristic quantities, and the only parameter that needs to be manually adjusted is the smoothing factor, and different values ​​of the smoothing factor will affect the performance of the GRNN.

8. The method for locating a DC distribution network line fault based on a neural network and an optimization algorithm according to claim 1, characterized in that: The optimization process of the gray wolf optimization algorithm is as follows: first, the wolf pack positions are initialized, and each wolf represents a smoothness factor; secondly, the GRNN network under different smoothness factors is trained, and the ranging error is calculated after the test results are obtained. When the number of iterations or the convergence condition is met, the algorithm is terminated, otherwise the gray wolf positions are iterated, and the above steps are repeated until the algorithm is terminated.

9. The method for locating a DC distribution network line fault based on a neural network and an optimization algorithm according to claim 1, characterized in that: The improvement of the iterative strategy is as follows: first, a chaotic mapping function is used to generate a chaotic variable between 0 and 1, and the chaotic variable is mapped to the search space of the decision variable to form an initial population, so as to replace the direct initialization of the population position, and improve the population diversity to improve the search efficiency of the algorithm; secondly, the convergence speed of the algorithm in the early stage is slowed down, so as to prompt the wolf pack to conduct a global search, improve the convergence speed of the algorithm in the later stage, and facilitate the local search accuracy; at the same time, a dynamic weight reflecting the level of the wolf pack is introduced in the update of the wolf pack position, so as to strengthen the guiding role of the optimal solution in the wolf pack and improve the convergence speed and accuracy.

10. The method for locating a DC distribution network line fault based on a neural network and an optimization algorithm according to claim 1, characterized in that: The method is implemented in the following steps: S1, sample expansion, achieved through sample collection and expansion unit; Using the ARIMA model, it is expressed as: ARIMA(p,d,q) In the formula, p represents the order of autoregression, d represents the number of differences, which is used to convert non-stationary series into stationary series, and q represents the order of moving average term; Obtain fault voltage time series data from the power system for differential processing: △And t =And t -AND t-1 In the formula, △Y t represents the difference at time t, Y t and Y t-1 Represent the original data at time t and time t-1 respectively. The number of differences d needs to be determined by the results of the stationarity test; Plot the autocorrelation function and partial autocorrelation function of the fault voltage data. Based on the AIC information criterion, traverse different combinations of p and q and select the model order that minimizes the information criterion: AIC=-2ln(L)+2k Where L is the likelihood function value of the model, and k is the number of model parameters; The fitted ARIMA model is used to expand the sample of the original fault voltage data to generate multiple sample data, thereby achieving the expansion of the sample data; S2, voltage feature extraction, implemented by the fault voltage feature extraction unit, is divided into time domain complexity feature extraction and frequency domain energy feature extraction; For frequency domain energy extraction, after a single-pole grounding fault occurs in the DC distribution network, the voltage signal on the fault line is extracted. First, the original signal x(t) is S-transformed: Where ω(tt,f) is the Gaussian window function, t is the displacement factor, f is the frequency, and j is the imaginary unit; Since the electrical signal collected by the computer is discrete, let the discrete time series function of the original signal x(t) be x[αT] (α=0, 1, 2, …, N-1), its discrete Fourier transform is X[αT], and its discrete form of S transform is: In the formula, N is the number of sampling points, and T is the sampling time interval; The transient energy expression of the original signal at a single frequency fn is: For a certain frequency band, it is only necessary to add up all the single-frequency transient energies contained in the frequency band; considering that the energy value is generally of a large order of magnitude, which affects the weight distribution of the intelligent algorithm, the result obtained cannot be used directly, so the frequency band energy value is converted into energy proportion, and the result is controlled between 0 and 1 without changing the energy ratio between frequency bands; In order to obtain the energy value of a fixed frequency band, it is necessary to divide the energy spectrum into frequency bands, calculate the transient energy proportion of each frequency band, and use the "binary method" to characterize the high-frequency and low-frequency areas of the signal to divide the original signal into 8 fixed frequency bands: d0 area (5kHz, 10kHz), d1 area (2.5kHz, 5kHz), d2 area (1.25kHz, 2.5kHz), d3 area (0.625kHz, 1.25kHz), d4 area (312.5Hz, 625Hz), d5 area (156.25Hz, 312.5Hz), d6 area (78.125Hz, 156.25Hz), and d7 area (0Hz, 78.125Hz) representing the low-frequency area; Since high frequencies (d0, d1, d2) are easily disturbed by lightning strikes, in order to improve the universality and accuracy of the ranging method, the d3~d7 frequency bands are selected to sum the energy. The energy proportion of each frequency band is calculated as the frequency domain fault feature; For time domain complexity extraction, the permutation entropy of the fault voltage signal is calculated and normalized as a supplement to the fault feature information. First, the information entropy of the random variable X is obtained: Where P(x) is the probability of event x occurring in the random variable X; Reconstruct the time series signal x(t) of length N and obtain the phase space matrix X, which is expressed as: Where m is the embedding dimension, t is the delay time, and k = N-(m-1)t; Arrange the reconstructed components of the jth row in X in ascending order according to their numerical values, that is: x[j+(j1-1)t]≤x[j+(j2-1)t]≤…≤x[j+(j m -1)t] In the formula, j1, j2, ..., jm represent the index of the column where each element is located; Count the number of times each sorting occurs and calculate their probability P(i). According to the definition of information entropy, calculate the permutation entropy: In order to adjust the entropy value range to 0 to 1, the data is normalized and the final entropy value is: S3, neural network training, is achieved through the neural network training unit. GRNN is based on nonlinear regression analysis and consists of four layers in structure, namely input layer, pattern layer, summation layer and output layer. The fault characteristics are used as neural network input and the fault distance is used as neural network output; For the input layer, the S transform converts the fault transient voltage signal into an energy spectrum and divides it into 8 frequency bands. Finally, five frequency bands from d3 to d7 are selected and 5 energy proportions are calculated. The permutation entropy of the fault signal is a numerical value. Therefore, the input vector of the neural network is 6-dimensional in total, which can be expressed as: X=[M3,M4,M5,M6,M7,H NPE ] T The number of neurons in the pattern layer is equal to the number of learning samples. Each neuron corresponds to a different learning sample, and its transfer function is: Where X is the input variable of the GRNN network; Xi is the learning sample corresponding to the i-th neuron in the pattern layer, and σ is the smoothing factor; There are two types of neurons in the summation layer. The first type of neurons directly perform arithmetic summation on the output of the pattern layer: The second type of neurons performs weighted summation on the output of the pattern layer. The number of neurons is the same as the sample output dimension. The connection weight between the i-th neuron in the pattern layer and the j-th second type of neuron in the summation layer is the j-th element y in the i-th output sample. ij , the transfer function is: The number of neurons in the output layer is equal to the dimension of the output vector. The output of the jth neuron in the output layer corresponds to the jth element in the output vector. The expression is: In the fault location measurement of flexible DC distribution network, the selection of data samples must be representative and comprehensively show various fault conditions. Faults at different locations are samples that must be traversed. Among the fault types, single-pole faults are divided into positive pole faults and negative pole faults, so the fault pole is also a condition that needs to be considered. In actual situations, faults are often not metallic faults, and transition resistance will directly affect the system fault characteristics. Therefore, multiple groups of different transition resistances are set to be added to the network training, and 80% of them are randomly selected as training sets, and the remaining 20% ​​are used as test sets. In actual training, data samples and results are input and output in matrix form. S4. The gray wolf optimization algorithm is used to solve the optimal value of the smoothness factor to replace the traditional manual selection. The optimization process of the gray wolf algorithm is divided into three stages: encirclement, pursuit and attack. The first three wolves with the best fitness are defined as alpha, beta and delta respectively, and the omega wolf pack updates its position around the first three levels of wolves; For the initialization of the wolf pack position, a chaos optimization strategy is introduced to improve the population diversity and thus the search efficiency of the algorithm. The population size is set, and for each individual gray wolf, a chaotic variable between 0 and 1 is generated using a chaos mapping function; the chaotic variable is mapped to the search space of the decision variable to form the initial population. The chaos mapping function is: x n+1 =μx n (1-x n ) Where μ is the chaos control parameter, x n is the current chaotic variable, x n+1 is the next chaos variable. Decision variable mapping formula: In the formula, is the decision variable of the kth gray wolf in the jth dimension, x minj and x maxj are the search upper and lower bounds of the j-th dimension variable, is a chaotic variable; In the gray wolf optimization algorithm, the distance calculation formula between the gray wolf and the prey is: In the formula, and are the position vector of the prey and the position vector of the gray wolf respectively, and t is the current iteration number. After calculating the distance to the prey, the gray wolf uses the following formula to surround the prey: In the formula, and are two random one-dimensional vectors with values ​​in [0,1]; Used to simulate the attack behavior of gray wolves on prey, the value is affected by the convergence factor The convergence factor decreases linearly with the number of iterations from 2 to 0. The convergence factor reduction strategy of the gray wolf algorithm and the wolf group level position iteration strategy are improved. The decreasing strategy is improved from linear decreasing to nonlinear decreasing, using the following formula: In the formula, T is the total number of iterations, and t is the current number of iterations; The larger the convergence factor value, the farther the gray wolf will move from the prey and try to find a more suitable prey, prompting the wolf pack to conduct a global search; the smaller the convergence factor value, the closer the gray wolf will move to the prey, prompting the wolf pack to conduct a local search; the improved strategy slows down the decreasing speed of the convergence factor in the early stage of the algorithm, and the convergence factor maintains a large value for a long time, prompting the wolf pack to conduct a global search; while in the later stage of the algorithm, the convergence factor decreases faster, which is conducive to local search and can improve search accuracy; For the wolf pack hierarchical position iteration strategy, alpha, beta, and delta wolves are jointly responsible for evaluating the location of the prey, and the remaining wolves use this as a reference to calculate the distance between themselves and the prey and complete the position iteration. In this process, the hierarchy of the wolf pack is not obvious, especially in the later local search of the algorithm, it is necessary to strengthen the optimal solution guidance role of alpha to improve the convergence speed and accuracy. Therefore, a dynamic weight reflecting the wolf pack level is introduced in the wolf pack position update, and its formula is: In the early stage of the algorithm, in order to prevent the entire wolf pack from gathering in a certain area of ​​the current optimal position of the group too early, the wolf pack's position iteration strategy does not change. Therefore, the improved wolf pack position iteration formula is: As the number of iterations increases, The value of is decreasing, The fluctuation range will also decrease. When the value of is less than 1, the gray wolf attacks the prey; The improved grey wolf algorithm is used to optimize the GRNN smoothing factor, and its process is shown in Figure 7; The improvement of the traditional gray wolf algorithm is located in the "update wolf position" in the flowchart. The wolf position is initialized, each wolf represents a smooth factor, the GRNN network is trained, and the fitness function is calculated after the test results are obtained. The three wolves with the smallest error are marked as alpha, beta and delta, and then the positions of the remaining wolves are recalculated using the improved iterative strategy. The above operations are repeated. When the number of iterations or convergence conditions are met, the algorithm terminates. At this time, the position of the head wolf represents the required smooth factor; assuming that the output matrix of the test sample is T = [t1, t2, ..., t 1600 ], and the output of GRNN is A = [a1, a2, ..., a 1600 ], then the fitness value in the flowchart is the root mean square error of the data in the two matrices, that is: The introduction of the improved grey wolf optimization algorithm improves the computing speed and accuracy of the grey wolf algorithm, further improves the rationality of the smoothing factor selection, thereby improving the GRNN fitting accuracy and increasing the fault distance measurement accuracy.

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