Voltage sag signal identification and classification method based on improved NGO algorithm

By optimizing variational mode decomposition and cross-correlation coefficient screening using the improved Northern Eagle optimization algorithm, and combining it with refined composite multi-scale fuzzy entropy for feature extraction, an INGO-ELM classifier is constructed. This solves the problems of noise interference and insufficient feature extraction in complex scenarios for voltage sag signal recognition methods, and achieves efficient voltage sag signal recognition.

CN120995303APending Publication Date: 2025-11-21HUBEI ENERGY GRP EZHOU POWER GENERATION CO LTD
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Patent Information

Application Number
CN202511085446.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-08-04
Publication Date
2025-11-21

AI Technical Summary

Technical Problem

Existing voltage sag signal identification methods suffer from noise interference and insufficient feature extraction in complex scenarios, resulting in low identification accuracy.

Method used

An improved Northern Eagle Optimization Algorithm (INGO) is used to optimize the penalty factor and the number of decomposition layers K in variational mode decomposition (VMD). The intrinsic mode function (IMF) components are screened by combining the cross-correlation coefficient method, and features are extracted by fine composite multiscale fuzzy entropy (RCMFE). An INGO-ELM classifier is then constructed for signal classification.

Benefits of technology

It improves the accuracy of signal reconstruction and the ability to represent features, significantly enhances the recognition accuracy of voltage sag signals, and achieves efficient classification of complex voltage sag signals.

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Abstract

A voltage sag signal identification and classification method based on an improved NGO algorithm relates to the technical field of power system signal processing, and comprises the steps of building a micro-grid simulation model, adding noise to simulate an actual environment, optimizing VMD parameters by using INGO, screening IMF components to reconstruct signals, extracting features and constructing vectors by using RCMFE, and optimizing ELM classifier parameters to complete a classification task. According to the method, through multi-stage optimization and multi-level feature extraction, the problems of noise interference and insufficient features are effectively solved, the voltage sag signal identification precision is remarkably improved, and technical support is provided for accurate classification of a power system in a complex scene.
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Description

Technical Field

[0001] This invention belongs to the field of power system signal processing and intelligent optimization technology, and specifically relates to a voltage sag signal identification and classification method based on an improved NGO algorithm. Background Technology

[0002] Voltage sags are a critical aspect of power quality issues, and their accurate identification is crucial for timely fault location and intervention. Currently, common identification and classification methods typically combine feature extraction with classification. For feature extraction, commonly used methods include S-transform, HHT (Hilbert-Huang Transform), and wavelet transform. However, these methods suffer from poor real-time performance, frequent spurious spectra, and endpoint effects, limiting the effectiveness of feature extraction. Furthermore, while support vector machines, decision trees, and fuzzy comprehensive evaluation algorithms are widely used for classification, their results often fall short of ideal levels in complex situations. Therefore, effectively improving the accuracy of voltage sag signal identification and classification has become a pressing technical challenge. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a voltage sag signal identification and classification method based on an improved NGO algorithm, so as to solve the technical problem of low voltage sag signal identification accuracy caused by noise interference and insufficient feature extraction in complex scenarios of power systems.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A voltage sag signal identification and classification method based on an improved NGO algorithm, comprising the following steps: A microgrid voltage sag simulation model was built, and different types of voltage signals were collected. Noise was added to the collected voltage signals to simulate the actual operating environment. The improved Northern Eagle Optimization Algorithm (INGO) was used to optimize the penalty factor and the number of decomposition layers K in Variational Mode Decomposition (VMD), where the fitness function is the minimum value of the permutation entropy of each mode component. The Intrinsic Mode Function (IMF) components after INGO-VMD decomposition were screened by the cross-correlation coefficient method, and the signals were reconstructed. The Refined Composite Multiscale Fuzzy Entropy (RCMFE) was used to extract features from the reconstructed signals and construct feature vectors. The INGO algorithm was used to optimize the input layer weights and hidden layer biases of the Extreme Learning Machine (ELM) classifier to construct the INGO-ELM classifier. The feature vectors were then input into the INGO-ELM classifier to complete the classification task.

[0005] Preferably, the steps of building a microgrid voltage sag simulation model include: designing a simulation circuit topology based on common voltage sag types in the power grid; collecting five typical voltage signals: normal operating condition, single-phase ground fault, two-phase ground fault, three-phase ground fault, and two-phase short-circuit fault; and simulating random interference in the actual operating environment by introducing Gaussian white noise.

[0006] Preferably, the step of optimizing the penalty factor and decomposition level K in variational mode decomposition (VMD) using the improved Northern Eagle Optimization Algorithm (INGO) includes: initializing the population position and search range of the Northern Eagle Optimization Algorithm, defining the objective function as the minimum value of the permutation entropy of each mode component; updating the population position through iterative search until the convergence condition is met; and outputting the optimal penalty factor and decomposition level K.

[0007] Preferably, the step of screening the intrinsic mode function (IMF) components after INGO-VMD decomposition by using the cross-correlation coefficient method includes: calculating the cross-correlation coefficient between each IMF component and the original signal; setting a threshold to screen out IMF components with cross-correlation coefficients greater than a preset value; and superimposing the screened IMF components to reconstruct the signal. Preferably, the step of using fine composite multiscale fuzzy entropy (RCMFE) to extract features from the reconstructed signal includes: dividing the reconstructed signal into multiple time windows and calculating the multiscale fuzzy entropy in each window; taking the average of the multiscale fuzzy entropy of all windows to obtain the fine composite multiscale fuzzy entropy value of the signal; and combining the fine composite multiscale fuzzy entropy values ​​of different signals into a feature vector.

[0008] Preferably, the step of optimizing the input layer weights and hidden layer biases of the Extreme Learning Machine (ELM) classifier using the INGO algorithm includes: initializing the population position and search range of the Northern Eagle optimization algorithm, defining the objective function as the minimum classification error on the classifier training set; updating the population position through iterative search until the convergence condition is met; and outputting the optimal input layer weights and hidden layer biases. Preferably, the step of inputting the feature vector into the INGO-ELM classifier to complete the classification task includes: inputting the feature vector into the trained INGO-ELM classifier; the classifier calculates the output result through the activation function, and the output result corresponds to one of the five voltage sag types.

[0009] The present invention also provides an electronic device, which includes a memory and a processor. The memory is used to store executable program code; the processor is connected to the memory and runs a computer program corresponding to the executable program code by reading the executable program code, so as to perform the steps in any of the aforementioned voltage sag signal identification and classification methods based on the improved Northern Eagle optimization algorithm. The present invention also provides a voltage sag signal identification and classification system based on an improved Northern Eagle optimization algorithm, characterized in that it includes the aforementioned electronic device.

[0010] This invention provides a voltage sag signal identification and classification method and system based on an improved NGO algorithm. By optimizing the parameter selection of variational mode decomposition using the improved Northern Eagle optimization algorithm, it can effectively decompose complex signals and extract key mode components, thereby improving the accuracy of signal reconstruction. The application of the cross-correlation coefficient method further filters out mode components with large noise interference, ensuring the quality of signal reconstruction. In addition, the fine composite multi-scale fuzzy entropy as a feature extraction tool can comprehensively characterize the nonlinear characteristics of the signal at multiple scales, significantly improving feature representation ability. Combining the INGO algorithm to optimize the parameters of the extreme learning machine classifier enables efficient classification of complex voltage sag signals. The above technical solution, through multi-stage optimization and multi-level feature extraction, solves the defects of traditional methods in terms of noise interference and insufficient feature extraction, providing reliable technical support for the accurate identification of voltage sag signals.

[0011] The present invention can achieve the following beneficial effects: 1. The INGO algorithm used in this patent enhances the algorithm's optimization and global search capabilities by improving the NGO algorithm.

[0012] 2. By combining the INGO algorithm with VMD and ELM, the efficiency of signal processing is effectively improved.

[0013] 3. This patent utilizes the INGO algorithm to optimize the parameter selection problem in VMD, thereby improving the stability of the signal processing process.

[0014] 4. By combining INGO-VMD and the correlation coefficient method, the processing and reconstruction of noisy signals demonstrates strong capabilities in resisting mode mixing and interference.

[0015] 5. By combining RCMFE feature extraction with the INGO-ELM classifier, the signal recognition capability is effectively improved. Attached Figure Description

[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is the microgrid voltage sag simulation model used in this invention; Figure 2 This is a flowchart illustrating an example of the present invention; Figure 3 This is a flowchart of the improved Northern Eagle optimization algorithm of the present invention; Figure 4 The figures show six different voltage sag signals after adding noise to the voltage sag signal of this invention. Figure 5 These are images of six different voltage sag signals after denoising processing according to the present invention. Figure 6 This invention provides six types of voltage sag signals at different scale factors. RCMFE below; Figure 7 This is the recognition and classification result of the INGO-ELM classifier of this invention and its confusion matrix. Detailed Implementation In this embodiment, six types of voltage sag sources were collected based on a microgrid voltage sag simulation model. The voltage configuration of this simulation model was 20kV / 0.4kV, with both high-voltage and low-voltage line voltages at 0.4kV, and the induction motor power was set to 4kW. Figure 2 As shown, the specific steps of this method are as follows: Step 1: To address common voltage sag signals in power grids, a microgrid voltage sag simulation model is built, and different types of voltage signals are collected, followed by the addition of noise. For example... Figure 4 As shown, six different voltage sag signals were obtained after adding noise to the voltage sag signal. The noise-added signals exhibited a coarse waveform. The reconstructed signal, however, displayed a smooth time-domain waveform with natural and stable transitions between peaks and troughs, without abrupt fluctuations or abrupt changes. This verifies that the method combining the INGO-VMD algorithm and the cross-correlation coefficient method can effectively filter noise and significantly improve signal quality for six different types of voltage signals under noisy conditions. Through this method, a clearer and more accurate voltage signal can be obtained.

[0017] First, a simulation environment is built using a microgrid voltage sag simulation model. This model includes circuit topologies for common voltage sag types in power grids, simulating five typical voltage signals: normal operating conditions, single-phase ground fault, two-phase ground fault, three-phase ground fault, and two-phase short-circuit fault. A noise addition module is connected to the microgrid voltage sag simulation model to introduce Gaussian white noise into the acquired voltage signals to simulate random interference in the actual operating environment. The output signal of the noise addition module serves as the input signal for subsequent processing, ensuring that the acquired voltage signals reflect the real-world conditions under complex scenarios.

[0018] Step 2: Optimize the penalty factor in Variational Mode Decomposition (VMD) using the improved Northern Eagle Optimization Algorithm (INGO). and decomposition layer number K The fitness function is the minimum entropy of the arrangement of each modal component.

[0019] The INGO-VMD decomposition module receives the signal from the noise addition module and optimizes the penalty factor and decomposition level K in Variational Mode Decomposition (VMD) using the improved Northern Eagle Optimization Algorithm (INGO). During optimization, the population position and search range of the Northern Eagle Optimization Algorithm are initialized, the objective function is defined as the minimum of the permutation entropy of each modal component, and the population position is updated iteratively until the convergence condition is met. Finally, the optimal penalty factor and decomposition level K are output. The INGO-VMD decomposition module decomposes the signal into multiple intrinsic mode function (IMF) components, which are then passed to the cross-correlation coefficient filtering module.

[0020] like Figure 3 As shown, improvements are made to the initialization, first, and second stages of the NGO algorithm. Specifically, firstly, a Reflection Backward Learning (ROBL) mechanism is introduced to enhance the diversity of the initial population; secondly, a golden sine strategy is introduced to update the position of the Northern Eagle optimization algorithm in the first stage; and thirdly, a Levy flight strategy is adopted to avoid the algorithm getting trapped in local optima.

[0021] Step 3: Use the cross-correlation coefficient method to screen the IMF components after INGO-VMD decomposition and then reconstruct the signal.

[0022] The cross-correlation coefficient filtering module receives the IMF components output by the Ingo-VMD decomposition module, calculates the cross-correlation coefficient between each IMF component and the original signal, and sets a threshold to filter out IMF components with cross-correlation coefficients greater than a preset value. The filtered IMF components are superimposed and reconstructed into a new signal, which serves as the input signal for subsequent feature extraction. The function of the cross-correlation coefficient filtering module is to eliminate modal components with significant noise interference, thereby improving the quality of signal reconstruction.

[0023] Step 4: Use Refined Composite Multiscale Fuzzy Entropy (RCMFE) to extract features from the reconstructed signal and construct a feature vector.

[0024] The RCMFE feature extraction module receives the reconstructed signal output from the cross-correlation coefficient filtering module, divides it into multiple time windows, and calculates the multi-scale fuzzy entropy within each window. The average of the multi-scale fuzzy entropies across all windows yields the refined composite multi-scale fuzzy entropy value of the signal, which is then combined to form a feature vector. The RCMFE feature extraction module comprehensively characterizes the nonlinear properties of the signal through multi-scale analysis, significantly improving its feature representation capability. Figure 6 As shown, the RCMFE value can effectively distinguish between six different types of voltage sag signals.

[0025] Step 5: The INGO algorithm is used to optimize the input layer weights and hidden layer biases of the ELM classifier, thereby constructing the INGO-ELM classifier. Then, the feature vector is input into the INGO-ELM classifier.

[0026] The INGO-ELM classifier receives feature vectors generated by the RCMFE feature extraction module and optimizes the input layer weights and hidden layer biases of the Extreme Learning Machine (ELM) classifier using an improved Northern Eagle optimization algorithm. During optimization, the population position and search range of the Northern Eagle optimization algorithm are initialized, the objective function is defined as the minimum classification error on the classifier training set, and the population position is updated iteratively until the convergence condition is met. Finally, the optimal input layer weights and hidden layer biases are output. The INGO-ELM classifier inputs the feature vectors into the trained classifier and calculates the output result using an activation function. The output result corresponds to one of five voltage sag types.

[0027] like Figure 7 As shown, the INGO-ELM classifier exhibits excellent recognition accuracy. To simulate noise interference in a real-world environment, six different types of voltage sag signals were collected, and 30dB of Gaussian white noise was added to these signals. The INGO-VMD algorithm was then used to denoise these noisy voltage sag signals, and the RCMFE algorithm was used for feature extraction. 100 samples were selected for each type of voltage sag signal, totaling 600 samples. 50 samples from the feature vectors of each voltage sag signal were selected as the training dataset for the classifier, while the remaining 50 samples were used as the test dataset to evaluate the classifier's performance. For the six different types of faults, corresponding voltage sag signal labels were assigned as 1, 2, 3, 4, 5, and 6, respectively.

[0028] The various modules are interconnected via signal flow. The signal output from the microgrid voltage sag simulation model sequentially passes through the noise addition module, the INGO-VMD decomposition module, the cross-correlation coefficient filtering module, and the RCMFE feature extraction module, and is finally classified by the INGO-ELM classifier. The cooperative relationship between the modules ensures a complete process from signal acquisition to classification output, overcoming the shortcomings of traditional methods in terms of noise interference and insufficient feature extraction.

[0029] This invention also provides an electronic device including a memory and a processor. The memory stores executable program code, and the processor is connected to the memory and runs a computer program corresponding to the executable program code by reading the executable program code, thereby executing the steps in the aforementioned voltage sag signal identification and classification method based on the improved Northern Eagle optimization algorithm. This electronic device, together with the aforementioned module, constitutes a voltage sag signal identification and classification system based on the improved Northern Eagle optimization algorithm, achieving efficient classification of complex voltage sag signals.

[0030] To enable those skilled in the art to fully understand and implement this invention, the specific implementation principle of this invention is further explained below in conjunction with a specific application scenario.

[0031] In real-world power grid operation environments, the identification and classification of voltage sag signals face challenges such as noise interference and insufficient feature extraction. To address this issue, an experimental environment was first established using a microgrid voltage sag simulation model. This model is designed based on the circuit topology of common power grid voltage sag types and can simulate five typical voltage signals: normal operating conditions, single-phase ground faults, two-phase ground faults, three-phase ground faults, and two-phase short-circuit faults. These signals are used as raw data input to noise addition module 2, where Gaussian white noise is introduced to simulate random interference in the actual operating environment. The role of noise addition module 2 is to ensure that the signals processed subsequently reflect the real situation under complex scenarios, thereby improving the robustness of the algorithm.

[0032] Subsequently, the signal processed by the noise addition module 2 is passed to the INGO-VMD decomposition module 3. In this module, the improved Northern Eagle Optimization Algorithm (INGO) is used to optimize key parameters of Variational Mode Decomposition (VMD), including the penalty factor and the number of decomposition levels K. Specifically, the Northern Eagle Optimization Algorithm initializes the population position and search range, defines the objective function as the minimum of the permutation entropy of each modal component, and iteratively searches to update the population position. When the algorithm meets the convergence condition, it outputs the optimal penalty factor and the number of decomposition levels K. The optimization of these parameters enables VMD to more accurately decompose the signal into multiple intrinsic mode function (IMF) components, thereby effectively separating noise and useful information in the signal.

[0033] The decomposed IMF components are then passed to the cross-correlation coefficient filtering module 4. This module calculates the cross-correlation coefficient between each IMF component and the original signal, filtering out IMF components with cross-correlation coefficients greater than a preset threshold. The filtered IMF components are then superimposed and reconstructed into a new signal, which serves as the input signal for subsequent feature extraction. The role of the cross-correlation coefficient filtering module 4 is to eliminate modal components with significant noise interference, thereby improving the quality of signal reconstruction. This process ensures that the input signal in the subsequent feature extraction stage has a high signal-to-noise ratio, providing a reliable foundation for subsequent analysis.

[0034] Next, the RCMFE feature extraction module 5 receives the reconstructed signal output from the cross-correlation coefficient filtering module 4 and performs Refined Composite Multiscale Fuzzy Entropy (RCMFE) analysis on it. Specifically, this module divides the reconstructed signal into multiple time windows and calculates the multiscale fuzzy entropy within each window. By averaging the multiscale fuzzy entropies of all windows, the refined composite multiscale fuzzy entropy value of the signal is obtained. These values ​​are combined into a feature vector to comprehensively characterize the nonlinear properties of the signal. The RCMFE feature extraction module 5 significantly improves the feature representation capability through multiscale analysis, providing more discriminative features for subsequent classification tasks.

[0035] Finally, the INGO-ELM classifier 6 receives the feature vectors generated by the RCMFE feature extraction module 5 and optimizes the input layer weights and hidden layer biases of the Extreme Learning Machine (ELM) classifier using the improved Northern Eagle optimization algorithm. During optimization, the Northern Eagle optimization algorithm initializes the population position and search range, defines the objective function as the minimum classification error on the classifier training set, and iteratively searches to update the population position. When the algorithm meets the convergence condition, it outputs the optimal input layer weights and hidden layer bias parameters. The optimization of these parameters enables the ELM classifier to achieve efficient classification in complex scenarios. The classifier calculates the output result through an activation function, and the final output corresponds to one of the five voltage sag types.

[0036] The modules described above are interconnected via signal flow, ensuring a complete process from signal acquisition to classification output. The signal output from the microgrid voltage sag simulation model 1 sequentially passes through the noise addition module 2, the INGO-VMD decomposition module 3, the cross-correlation coefficient filtering module 4, and the RCMFE feature extraction module 5, finally being classified by the INGO-ELM classifier 6. The cooperative relationship between these modules overcomes the shortcomings of traditional methods in terms of noise interference and insufficient feature extraction, achieving efficient classification of complex voltage sag signals.

[0037] Furthermore, the present invention also provides an electronic device including a memory and a processor. The memory stores executable program code, and the processor is connected to the memory and runs a computer program corresponding to the executable program code by reading the executable program code, thereby performing the steps in the aforementioned voltage sag signal identification and classification method based on the improved Northern Eagle optimization algorithm. This electronic device, together with the aforementioned module, constitutes a voltage sag signal identification and classification system based on the improved Northern Eagle optimization algorithm, achieving efficient classification of complex voltage sag signals.

[0038] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A voltage sag signal identification and classification method based on an improved NGO algorithm, characterized in that... Includes the following steps: A simulation model of voltage sag in a microgrid was built, and different types of voltage signals were collected; Noise is added to the acquired voltage signal to simulate the actual operating environment; An improved Northern Eagle optimization algorithm is used to optimize the penalty factor and the number of decomposition layers K in variational mode decomposition, where the fitness function is the minimum value of the permutation entropy of each mode component; The intrinsic mode function components obtained from variational mode decomposition optimized by the improved Northern Eagle optimization algorithm were screened using the cross-correlation coefficient method, and then the signal was reconstructed. The reconstructed signal is feature extracted using fine composite multi-scale fuzzy entropy, and a feature vector is constructed. An improved Northern Eagle optimization algorithm is used to optimize the input layer weights and hidden layer biases of an Extreme Learning Machine (ELM) classifier, and an ELM classifier optimized by the improved Northern Eagle optimization algorithm is constructed. The feature vectors are input into an optimized Extreme Learning Machine classifier based on the improved Northern Eagle optimization algorithm to complete the classification task.

2. The voltage sag signal identification and classification method based on the improved NGO algorithm according to claim 1, characterized in that: The steps for building a microgrid voltage sag simulation model include: designing a simulation circuit topology based on common voltage sag types in the power grid; collecting five typical voltage signals: normal operating condition, single-phase ground fault, two-phase ground fault, three-phase ground fault, and two-phase short-circuit fault; and simulating random interference in the actual operating environment by introducing Gaussian white noise.

3. The voltage sag signal identification and classification method based on the improved NGO algorithm according to claim 1, characterized in that: The steps for optimizing the penalty factor and decomposition level K in variational mode decomposition using the improved Northern Eagle optimization algorithm include: initializing the population position and search range of the Northern Eagle optimization algorithm, defining the objective function as the minimum value of the permutation entropy of each mode component; updating the population position through iterative search until the convergence condition is met; and outputting the optimal penalty factor and decomposition level K.

4. The voltage sag signal identification and classification method based on the improved NGO algorithm according to claim 1, characterized in that: The step of filtering intrinsic mode function components obtained by variational mode decomposition optimized by the improved Northern Eagle optimization algorithm using the cross-correlation coefficient method includes: calculating the cross-correlation coefficient between each intrinsic mode function component and the original signal; setting a threshold to filter intrinsic mode function components with cross-correlation coefficients greater than a preset value; and superimposing the filtered intrinsic mode function components to reconstruct the signal.

5. The voltage sag signal identification and classification method based on the improved NGO algorithm according to claim 1, characterized in that: The steps for feature extraction of the reconstructed signal using fine composite multi-scale fuzzy entropy include: dividing the reconstructed signal into multiple time windows and calculating the multi-scale fuzzy entropy in each window; taking the average of the multi-scale fuzzy entropy of all windows to obtain the fine composite multi-scale fuzzy entropy value of the signal; and combining the fine composite multi-scale fuzzy entropy values ​​of different signals into a feature vector.

6. The voltage sag signal identification and classification method based on the improved NGO algorithm according to claim 1, characterized in that: The steps for optimizing the input layer weights and hidden layer biases of the Extreme Learning Machine classifier using the improved Northern Eagle optimization algorithm include: initializing the population position and search range of the Northern Eagle optimization algorithm, defining the objective function as the minimum classification error on the classifier training set; updating the population position through iterative search until the convergence condition is met; and outputting the optimal input layer weights and hidden layer biases.

7. The voltage sag signal identification and classification method based on the improved NGO algorithm according to claim 1, characterized in that: The steps of inputting the feature vector into the Extreme Learning Machine classifier optimized by the improved Northern Eagle optimization algorithm to complete the classification task include: inputting the feature vector into the trained Extreme Learning Machine classifier optimized by the improved Northern Eagle optimization algorithm; the classifier calculates the output result through the activation function, and the output result corresponds to one of the five voltage sag types.

8. The voltage sag signal identification and classification method based on the improved NGO algorithm according to claim 1, characterized in that: The improved Northern Eagle optimization algorithm enhances global search capabilities by adjusting the population position update formula.

9. A voltage sag signal identification and classification method based on an improved NGO algorithm according to claim 1, characterized in that: The permutation entropy is calculated based on the time series distribution characteristics of the signal, and the order and embedding dimension of the permutation entropy are preset fixed values.

10. A voltage sag signal identification and classification system based on an improved Northern Eagle optimization algorithm, characterized in that: A voltage sag signal identification and classification method based on an improved NGO algorithm, as described in any one of claims 1-9, was adopted.