Surge arrester resistive current prediction method and system based on combination of vmd-mvo-esn

Abstract

This invention discloses a method and system for predicting the resistive current of surge arresters based on a combination of VMD-MVO-ESN. To select and design suitable surge arresters, evaluate and compare their lightning protection capabilities in power systems, and ensure their performance and reliability under specific operating conditions, accurate prediction of the resistive current of surge arresters is necessary. In this invention, the original resistive current sequence is decomposed using variational mode decomposition (VMD), eliminating internal noise. Multiple signal components after decomposition are simultaneously used to build models. The structural parameters in the reservoir of the echo state network are optimized using a multiverse algorithm. Finally, the predictions of each signal component are completed, and the results are combined and accumulated to achieve accurate prediction of the resistive current of the surge arrester, ensuring the safe and stable operation of the power system.

Description

Technical Field

[0001] This invention belongs to the field of power system protection technology, specifically relating to a method and system for predicting resistive current of surge arresters based on the combination of VMD-MVO-ESN. Background Technology

[0002] A surge arrester is an electrical device used to protect equipment and systems from lightning strikes and overvoltages. When a lightning strike or overvoltage occurs, the surge arrester conducts current, diverting the voltage overload exceeding the equipment or system's withstand capability to the ground, thereby protecting the safe operation of the equipment and system. Therefore, accurate research on the resistive current of surge arresters has very important theoretical significance.

[0003] Combining signal decomposition with neural networks and optimization algorithms is a relatively novel technology in the field of power system protection. Since the original resistive current of the surge arrester is a highly nonlinear time series, the original sequence needs to be processed by variational mode decomposition before the model is built. In the ESN neural network, the intermediate reservoir structure replaces the traditional hidden layer, which increases the mapping capability of the network. At the same time, the introduction of the MVO algorithm to obtain the optimal values ​​of the four parameters in the reservoir and substituting them into the ESN model can effectively solve the defect of poor prediction performance of the single model.

[0004] To address the problems in existing technologies, this invention proposes a method and system for predicting the resistive current of surge arresters based on a combination of VMD, MVO, and ESN. Taking into account the characteristics of the original energy storage of the resistive current in surge arresters, the VMD algorithm is combined with the ESN neural network model optimized by the MVO algorithm, achieving excellent results. Summary of the Invention

[0005] In view of the limitations and bottlenecks of existing technologies, this invention proposes a method and system for predicting resistive current of surge arresters based on the combination of VMD-MVO-ESN, which can effectively solve the problem of difficulty in predicting resistive current.

[0006] On the one hand, this invention provides a method for predicting the resistive current of surge arresters based on a combination of VMD-MVO-ESN, which includes the following steps:

[0007] Step 1: Obtain the raw data of the resistive current of the surge arrester, and use the VMD algorithm to decompose it to obtain the various IMF components of the resistive current signal, and divide it into corresponding training and test samples.

[0008] Step 2: Simultaneously establish MVO-ESN resistive current prediction models for each IMF component, optimize the four parameters of the storage pool in the ESN model structure using the MVO algorithm, and then re-substitute the obtained optimal parameters into the ESN model for training.

[0009] Step 3: Substitute the resistive current test data into the combined prediction model to obtain the prediction results of each component, and recombine the prediction results to obtain the output sequence.

[0010] Furthermore, the specific steps of the VMD algorithm in step 2 are as follows:

[0011] 1) Obtain the analytic signal by performing Hilbert transform on each mode:

[0012]

[0013] 2) Combine the transformed analytical signal with the center frequency to obtain the corresponding modal spectrum.

[0014]

[0015] 3) Based on the L2 norm of the squared gradient of the demodulated signal, and transforming it into a constrained variational model, the formula is as follows:

[0016]

[0017] Formula {μ k}:={μ1,L,μ k} and {ω k}:={ω1,L,ω k All modal numbers and their center frequencies.

[0018] 4) Introducing the Lagrange operator λ and the quadratic penalty factor α, the problem is transformed into an unconstrained problem, with the specific functional expression as follows:

[0019]

[0020] 5) To solve the problem of finding the optimal objective function in equation 4), the parameters are updated using the alternating direction multiplier method. and

[0021] Regarding parameters The update formula is:

[0022]

[0023] Regarding parameters The update formula is:

[0024]

[0025] Regarding parameters The update formula is:

[0026]

[0027] 6) Repeat the above iterative process to update until the condition is met and then stop iterating.

[0028]

[0029] Furthermore, in the MVO-ESN algorithm constructed in step 2, the specific formula for updating the optimal cosmic black hole position in the MVO is as follows:

[0030]

[0031] In the formula, TDR represents the travel distance rate, H is the threshold for judgment, and r3 and r4 represent random numbers in the range of 0-1. This represents the optimal position of a black hole in the universe under its current state.

[0032] Furthermore, in the MVO-ESN algorithm built in step 2, after updating the optimal cosmic black hole position, the corresponding wormhole existence rate (WEP) and travel distance rate (TDR) will also be updated accordingly, as shown in the following expressions:

[0033]

[0034] In the formula, l is the current iteration number, L is the maximum iteration number, and max and min are taken as the maximum and minimum values ​​based on experience. The expression for Travel Distance Rate (TDR) is as follows:

[0035]

[0036] Furthermore, in the MVO-ESN algorithm built in step 2, x(t+1) is the current state of the reserve pool, and μ(t+1) is the current input. The output state equation of the ESN model can be established by the following formula.

[0037] y(t+1)=f out ×(ω out ×(μ(t+1), x(t+1)))

[0038] In the formula, f out This is the activation function for the output layer.

[0039] Furthermore, when using the MVO algorithm to optimize the reservoir parameters of the ESN structure, the root mean square error between the actual and predicted values ​​of the resistive current is selected as the objective function of the algorithm, which can be specifically expressed as:

[0040] (1) Root Mean Square Error (RMSE)

[0041]

[0042] In the formula, M is the length of the resistive current time series, and y(k) represents the actual value of the resistive current time series. This represents the predicted value of the resistive current time series.

[0043] Secondly, the present invention provides a surge arrester resistive current prediction system based on the combination of VMD-MVO-ESN, comprising:

[0044] The acquisition module is used to acquire the raw data of the resistive current signal of the surge arrester, and decompose it using the VMD algorithm to obtain each IMF component of the resistive current signal, and divide it into corresponding training and test samples.

[0045] The multivariate optimization module is used to simultaneously establish an MVO-ESN arrester resistive current combination prediction model for each IMF component. It uses the MVO algorithm to optimize the four parameters of the storage pool in the ESN model structure and re-substitutes the optimal parameters into the ESN model for training.

[0046] The prediction module is used to input the test data of the resistive current signal into the combined prediction model to obtain the prediction results of each component, and then reassemble the prediction results to obtain the output sequence.

[0047] Third, the present invention also provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the program is executed by a processor, it implements the above-described arrester resistive current prediction method based on the combination of VMD-MVO-ESN.

[0048] The beneficial effects of this invention are:

[0049] This invention provides a method and system for predicting the resistive current of surge arresters based on a combination of VMD-MVO-ESN. Due to the complexity and nonlinearity of the original resistive current sequence of surge arresters, it is necessary to process the original sequence using variational mode decomposition before establishing the model. In the ESN neural network, the intermediate reservoir structure replaces the traditional hidden layer, increasing the network's mapping capability. At the same time, the introduction of the MVO algorithm to obtain the optimal values ​​of the four parameters in the reservoir and substituting them into the ESN model can effectively solve the defect of poor prediction performance of a single model, which has good theoretical guiding significance. Attached Figure Description

[0050] Figure 1 The flowchart below shows the surge arrester resistive current prediction method based on the combination of VMD-MVO-ESN in a specific embodiment of the present invention.

[0051] Figure 2 ESN Network Topology Diagram

[0052] Figure 3Time series diagram of resistive current of the original surge arrester.

[0053] Figure 4 This is a diagram showing the decomposition of the resistive current sequence of the surge arrester using the VMD algorithm.

[0054] Figure 5 This is a comparison chart of the resistive current prediction of surge arresters using the method of this invention, the traditional ESN method, and the MOV-ESN method. Detailed Implementation

[0055] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, these descriptions are merely exemplary and are not intended to limit the scope of the present invention.

[0056] Before explaining the method of the present invention, a basic theoretical introduction to the content of echo state networks will be given.

[0057] Echo State Networks (ESNs) are a type of feedback neural network. Unlike traditional feedforward neural networks, ESNs use a reservoir structure inside the network to replace the original hidden layers, making them essentially sparse networks that overcome the shortcomings of traditional neural networks.

[0058] At time n, the input is represented by u(n), the number of nodes is N, the state of the reserve pool is denoted by x(n), the number of nodes is M, and the output is represented by y(n), the number of nodes is O. The above layers can be transformed into:

[0059]

[0060] In the next stage, the state equation and output equation of the ESN model are expressed as follows:

[0061]

[0062] In the equation f and f out These are the activation functions for the model's state equation and output equation, respectively; typically, the tanh function is chosen. Meanwhile, W... in W represents the connection weights (M*N order) between the input layer and the reservoir, and W represents the connections (M*M order) within the reservoir. out Represented as the connection between the reservoir and the output layer (order O*(M+N+O)), W back It is represented as the feedback output weight (M*O order), but it is not necessary in the actual prediction process, so it can be simplified to zero.

[0063] The specific prediction process of the ESN model can be represented as follows:

[0064] 1) Initialize the parameters SR, N, IS, and SD in the ESN model pool. Initial parameter settings are usually selected based on experience and then adjusted based on the results of subsequent predictions.

[0065] 2) Train the ESN network using input data while simultaneously updating the state of the reservoir. Utilize the predicted output... Approximating the expected output y(k):

[0066]

[0067] This means that to minimize the system MSE error by calculating the weight matrix, we need to solve the following objective:

[0068]

[0069] The final, organized form can be expressed as:

[0070] W out =(M -1 ×T) T

[0071] Based on the above echo state network, this invention provides a surge arrester resistive current prediction method and system based on the combination of VMD-MVO-ESN, such as... Figure 1 As shown, it includes the following steps:

[0072] Step 1: Obtain the raw data of the resistive current of the surge arrester, and use the VMD algorithm to decompose it to obtain the various IMF components of the resistive current signal, and divide it into corresponding training and test samples.

[0073] Step 2: Simultaneously establish MVO-ESN resistive current prediction models for each IMF component, optimize the four parameters of the storage pool in the ESN model structure using the MVO algorithm, and then re-substitute the obtained optimal parameters into the ESN model for training.

[0074] Step 3: Substitute the resistive current test data into the combined prediction model to obtain the prediction results of each component, and recombine the prediction results to obtain the output sequence.

[0075] Variational mode decomposition (VMD) is an adaptive, non-recursive signal decomposition method that effectively addresses mode aliasing and endpoint effects compared to traditional empirical mode decomposition (EMD). The algorithm matches the bandwidth and center frequency of each mode, divides the signal into components and frequency domains, and finally obtains the decomposed signal. The implementation process is as follows:

[0076] 1) Obtain the analytic signal by performing Hilbert transform on each mode:

[0077]

[0078] 2) Combine the transformed analytical signal with the center frequency to obtain the corresponding modal spectrum.

[0079]

[0080] 3) Based on the L2 norm of the squared gradient of the demodulated signal, and transforming it into a constrained variational model, the formula is as follows:

[0081]

[0082] Formula {μ k}:={μ1,L,μ k} and {ω k}:={ω1,L,ω k All modal numbers and their center frequencies.

[0083] 4) Introducing the Lagrange operator λ and the quadratic penalty factor α, the problem is transformed into an unconstrained problem, with the specific functional expression as follows:

[0084]

[0085] The VMD parameters are set as follows: penalty factor α = 4000, number of decomposition layers K = 8.

[0086] 5) To solve the problem of finding the optimal objective function in equation 4), the parameters are updated using the alternating direction multiplier method. and

[0087] Regarding parameters The update formula is:

[0088]

[0089] Regarding parameters The update formula is:

[0090]

[0091] Regarding parameters The update formula is:

[0092]

[0093] 6) Repeat the above iterative process to update until the condition is met and then stop iterating.

[0094]

[0095] The MVO algorithm is a swarm intelligence optimization algorithm that simulates the direct interaction of a population within white holes, black holes, and wormholes. It has relatively few parameters, is easy to operate, and exhibits good performance. The position update formula for this algorithm is:

[0096]

[0097] In the formula, TDR represents the travel distance rate, H is the threshold for judgment, and r3 and r4 represent random numbers in the range of 0-1. This represents the optimal position of a black hole in the universe under its current state.

[0098] After updating the optimal location of the black hole in the universe, the corresponding wormhole existence rate (WEP) and travel distance rate (TDR) will also be updated accordingly, as shown in the following expressions:

[0099]

[0100] In the formula, l is the current iteration number, L is the maximum iteration number, and max and min are taken as the maximum and minimum values ​​based on experience. The expression for Travel Distance Rate (TDR) is as follows:

[0101]

[0102] ESN neural network is a feedback neural network that can solve many nonlinear and complex problems compared to traditional neural networks. In ESN neural network, x(t+1) is the current state of the reservoir and μ(t+1) is the current input. The output state equation of ESN model can be established by the following formula.

[0103] y(t+1)=f out ×(ω out ×(μ(t+1), x(t+1)))

[0104] In the formula, f out This is the activation function for the output layer.

[0105] Furthermore, when using the MVO algorithm to optimize the reservoir parameters of the ESN structure, the root mean square error between the actual and predicted values ​​of the resistive current is selected as the objective function of the algorithm, which can be specifically expressed as:

[0106] (1) Root Mean Square Error (RMSE)

[0107]

[0108] In the formula, M is the length of the resistive current time series, and y(k) represents the actual value of the resistive current time series. This represents the predicted value of the resistive current time series.

[0109] This example uses 110kV surge arrester detection data from a 220kV substation in North China as support. The number of data samples collected is 500. In the experiment, the ratio of training samples to test samples is 0.7 and 0.3, respectively. The number of neurons in the reservoir is set to 100. Based on experience, the reservoir size N of the initial single echo state network is set to 100, the shrinkage factor IS is 0.1, the spectral radius SR is 0.6, and the sparsity SD is 0.1. The optimal reservoir parameters of the ESN network after optimization by the MOV algorithm are shown in Table 1.

[0110] Table 1 Comparison of Reserve Pool Parameters Before and After Optimization

[0111]

[0112] like Figure 4 The VMD algorithm decomposes the resistive current sequence of the surge arrester, as shown in the diagram. The original resistive current sequence is decomposed into eight IMF components and one RS margin. Simultaneously, a combined prediction model of the MOV algorithm-optimized ESN is established to predict each component of the resistive current and accumulates them to form the final predicted value. This prediction is then compared with the single ESN without decomposition and the MOV-ESN model. Figure 5 The comparison chart of the resistive current prediction of surge arresters by the method of this invention, the traditional ESN and MOV-ESN methods is shown. It can be seen that the algorithm can effectively and accurately predict the resistive current of surge arresters.

[0113] Table 2 Comparison of error metrics for various model algorithms

[0114]

[0115] As shown in Table 2, which compares the error indices of various model algorithms, in this invention, the combined model of variational mode and multiverse algorithm to optimize the echo state network has the best effect on the resistive current prediction of the surge arrester, and all prediction error indices are improved compared with those before decomposition and before model optimization.

[0116] Research shows that the ratio of training set to test set, the size of the buffer pool, and the parameter settings of the algorithm all have a significant impact on the performance of the ESN model. Therefore, in actual simulations, the optimal algorithm parameters are determined by conducting multiple experiments.

[0117] Although embodiments have been shown and described, it will be understood by those skilled in the art that modifications, variations, and substitutions may be made to the shown and described embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the resistive current of surge arresters based on a combination of VMD-MVO-ESN, characterized in that, include: Step 1: Obtain the raw data of the resistive current signal of the surge arrester, and decompose it using the VMD algorithm to obtain each IMF component of the resistive current signal, and divide it into corresponding training and test samples. Step 2: Simultaneously establish an MVO-ESN arrester resistive current combination prediction model for each IMF component. Optimize the four parameters of the reservoir in the ESN model structure using the MVO algorithm. These four parameters include: reservoir size, shrinkage factor, spectral radius, and sparsity. Substitute the optimal parameters back into the ESN model for training. Specific steps are as follows: 1) Obtain the analytic signal from each mode using the Hilbert transform: In the formula, μ k Let t be the Kth mode function, and δ(t) be the Dirac function; 2) The transformed analytical signal is combined with the center frequency to obtain the corresponding modal spectrum: In the formula, μ k Let ω be the Kth mode function. k The Kth center frequency; 3) Obtain the L2 norm of the squared gradient of the demodulated signal and transform it into a constrained variational model, as shown in the following formula: In the formula, {μ k }:={μ1,L,μ k } and {ω k }:={ω1,L,ω k All modal numbers and their center frequencies, For the sign of differentiation, It is an exponential signal; 4) Introducing the Lagrange operator λ and the quadratic penalty factor α, the problem is transformed into an unconstrained problem, with the specific functional expression as follows: In the formula, is the λ-Lagrange operator, α is the quadratic penalty factor, and μ is the λ-Lagrange operator. k This is the Kth mode function; 5) To solve the problem of finding the optimal objective function in equation 4), update the parameters using the alternating direction multiplier method. Regarding parameters The update formula is: Regarding parameters The update formula is: Regarding parameters The update formula is: 6) Repeat the above iterative process to update until the condition is met, then stop iterating. In the formula, e represents the discrimination precision; Step 3: Substitute the test data of the resistive current signal into the combined prediction model to obtain the prediction results of each component, and reassemble the prediction results to obtain the output sequence.

2. The surge arrester resistive current prediction method based on VMD-MVO-ESN combination as described in claim 1, characterized in that, When using the MVO algorithm to optimize the reservoir parameters of the ESN structure, the root mean square error (RMSE) between the actual and predicted resistive current values ​​is selected as the objective function of the algorithm. In the formula, M is the length of the resistive current time series, and y(k) represents the actual value of the resistive current time series. This represents the predicted value of the resistive current time series.

3. The surge arrester resistive current prediction method based on VMD-MVO-ESN combination as described in claim 1, characterized in that, In the MVO-ESN algorithm built in step 2, the specific formula for updating the optimal cosmic black hole position in MVO is as follows: In the formula, TDR represents the travel distance rate, H is the threshold for judgment, and r3 and r4 represent random numbers in the range of 0-1. This represents the optimal position of a black hole in the universe under its current state.

4. The surge arrester resistive current prediction method based on VMD-MVO-ESN combination as described in claim 3, characterized in that, In the MVO-ESN algorithm built in step 2, after updating the optimal cosmic black hole position, the corresponding wormhole existence rate (WEP) and travel distance rate (TDR) will also be updated accordingly, as shown in the following expressions: In the formula, l is the current iteration number, L is the maximum iteration number, and max and min are taken as the maximum and minimum values ​​based on experience; The expression for Travel Distance Rate (TDR) is as follows:

5. The surge arrester resistive current prediction method based on VMD-MVO-ESN combination as described in claim 4, characterized in that, In the MVO-ESN algorithm built in step 2, x(t+1) represents the current state of the reservoir, and μ(t+1) represents the current input. The output state equation of the ESN model is then established using the following formula: y(t+1)=f out ×(ω out ×(μ(t+1),x(t+1))) In the formula, f out This is the activation function for the output layer.

6. A surge arrester resistive current prediction system based on VMD-MVO-ESN combination, used to implement the surge arrester resistive current prediction method based on VMD-MVO-ESN combination as described in claim 1, characterized in that, include: The acquisition module is used to acquire the raw data of the resistive current signal of the surge arrester, and decompose it using the VMD algorithm to obtain each IMF component of the resistive current signal, and divide it into corresponding training and test samples. The multivariate optimization module is used to simultaneously establish an MVO-ESN arrester resistive current combination prediction model for each IMF component. It uses the MVO algorithm to optimize the four parameters of the storage pool in the ESN model structure and re-substitutes the optimal parameters into the ESN model for training. The prediction module is used to input the test data of the resistive current signal into the combined prediction model to obtain the prediction results of each component, and to reassemble the prediction results to obtain the output sequence.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the surge arrester resistive current prediction method based on the combination of VMD-MVO-ESN as described in any one of claims 1-5.

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