Classification Strategy for Power Quality Disturbances Based on Variational Mode Decomposition Algorithm and Improved Support Vector Machine

Abstract

With the continuous improvement in production efficiency and quality of life, the requirements of electrical equipment for power quality are also increasing. Accurate detection of various power quality disturbances is an effective measure to improve power quality. However, in practical applications, the dataset is often contaminated by noise, and when the dataset is not sufficient, the computational complexity is too high. Similarly, in the recognition process of artificial neural networks, the local optimum often occurs, which ultimately leads to low recognition accuracy for the trained model. Therefore, this article proposes a power quality disturbance classification strategy based on the variational mode decomposition (VMD) and improved support vector machine (SVM) algorithms. Firstly, the VMD algorithm is used for preprocessing disturbance denoising. Next, based on the analysis of typical fault characteristics, a multi-SVM model is used for disturbance classification identification. In order to improve the recognition accuracy, the improved Grey Wolf Optimization (IGWO) algorithm is used to optimize the penalty factor and kernel function parameters of the SVM model. The results of the final case study show that the classification accuracy of the proposed method can reach over 98%, and the recognition accuracy is higher than that of the other models.

1. Introduction

With the progress of society and the development of technology, people’s living standards have continuously improved, and at present, electric energy is widely used in the public power grid. As the development of new smart grids and transmission technology routes continues, more and more new electrical equipment is being used in human production and daily life. Ideally, the parameters of the public power grid, such as the frequency, amplitude, and phase, are stable and standardized [1]. However, the introduction and use of a large number of nonlinear loads have had a certain impact on the power system, leading to irregular changes in voltage and current and thus causing pollution to the grid environment, which has greatly increased the imbalance of power systems. In order to ensure the normal operation of a power system, meet people’s production and living needs, and reduce the economic losses caused by instability in a power system, the concept of power quality has emerged accordingly [2]. In contemporary society, automated intelligent technology has developed rapidly, and a large number of high-tech products have been put into mass production and use, which has made the demand for power quality even stricter. Therefore, how to ensure a high-quality power supply has become an important issue that power supply departments need to address [3,4].

The detection of power quality primarily involves data denoising and disturbance classification. Due to factors such as detection equipment and the complex external environment, power quality disturbance signals are susceptible to high-frequency noise or non-stationary noise during transmission, acquisition, and processing. In recent years, many scholars both domestically and internationally have conducted research on denoising for power quality disturbances, and numerous methods for denoising power quality disturbance signals have emerged. The authors of [5] proposed an improved threshold function-based stationary wavelet denoising method that effectively removes noise and preserves the characteristics of mutation points. The wavelet transform, with its excellent time–frequency characteristics and low computational complexity, has been widely used in signal denoising, but the selection of wavelet basis functions and decomposition levels in wavelet transforms is challenging. The authors of [6] introduced a hybrid signal processing method combining mathematical morphology and Walsh theory for power quality disturbances. The authors of [7] proposed a denoising approach for power quality disturbance signals using an adaptive variational mode decomposition (VMD) algorithm. This method first performs adaptive VMD decomposition on the power quality disturbance signal and then selects and removes noise modes using the average periodic energy algorithm, avoiding the modal aliasing issues common in EMD.

The authors of [8] analyzed the principle of the discrete adaptive wavelet algorithm, selected wavelet functions for power quality disturbance signals, performed denoising treatment on the noisy disturbances after detection and analysis, classified and continuously optimized them in a BP neural network, and finally classified and identified them in a new neural network structure. In [9], 12 different statistical features were extracted by passing disturbances through a robust H-infinity filter to minimize the data size and computational complexity. The statistical characteristics of PQ disturbances were then classified using a fast, generalized fuzzy C-means clustering method. With the widespread integration of nonlinear loads, both businesses and consumers are facing issues related to power quality disturbances in the electric grid. Detecting and classifying multiple disturbances is considered a challenging task. The authors of [10] proposed a novel hybrid method based on the Stockwell transform and deep learning for detecting and classifying multiple disturbances. Unlike previous approaches that only considered single or dual disturbances, this paper fully takes into account the existence of multiple disturbances in real-world scenarios and designs a more general and automated feature selection and classification method based on deep learning. The authors of [11] combined the wavelet transform with the decision tree algorithm. They first obtained wavelet energy entropy through transformation, constructed combinations to find the sub-decision tree classifiers, and finally performed simulation experiments under different noise conditions. The authors of [12] first analyzed the interference signals using the fast S-transform to obtain a one-dimensional vector. Then, they extracted the standard deviation of the modulus coefficients of each frequency band (including the coefficients corresponding to the rated frequency) as the interference feature vector. Finally, they classified and identified the disturbance signals using the least squares vector machine. An increasing number of electric vehicles (EVs) are being connected to the power grid, leading to a heightened risk of power quality degradation. Simultaneously, disturbances in power quality (PQDs) pose a direct threat to the safety of EV charging. Therefore, the intelligent identification of complex PQDs serves as a crucial prerequisite for addressing power quality issues, holding significant importance in enhancing the quality of EV charging. In [13], an automatic recognition framework for intricate PQDs was introduced, leveraging an ensemble convolution neural network (ECNN). Practical phasor measurement units (PMUs) are prone to data quality issues arising from communication errors and signal interferences. Consequently, the efficiency of current data-driven methods for disturbance classification can be profoundly influenced. The authors of [14] introduced a swift classification method specifically designed to be resilient against these PMU data quality challenges. Furthermore, the study delved into the consequences of inaccurate PMU measurements on disturbance classification by examining the distribution of features within deep learning frameworks.

Similarly, there are various processing algorithms for signal classification, mainly including artificial neural networks (ANNs) [15,16], convolutional neural networks (CNNs) [17,18], and fuzzy expert systems [19,20]. However, they are prone to issues such as overfitting and local optima. The ANN is an algorithm that simulates the human brain’s neural system to learn data autonomously. It has a simple structure and good fault tolerance, but it can have problems such as long training sample times and slow convergence speeds. Previous research efforts have been directed toward developing algorithms capable of detecting and classifying these disturbances. A comprehensive examination of PQD detector algorithms has revealed that machine learning and deep learning techniques are the most commonly utilized, accurate, and contemporary methods for addressing this challenge. However, a notable limitation of these algorithms is their use of a sliding window approach, which frequently fails to identify multiple disturbances within a single window. In response to this issue, the authors of [21] introduced an innovative architecture known as single-shot PQD detection (SSPQDD). To establish a foundation for effective power–pollution control, the authors of [22] introduced an automated method for classifying PQDs that is well suited for handling complex scenarios. Central to this approach is the ensemble intrinsic timescale decomposition (EITD) technique, which is designed to decompose PQDs. This method addresses the endpoint effect and frequency aliasing issues associated with decomposition levels by incorporating Gaussian noise and integrating multiple subcomponents. The authors of [23] presented a multidimensional feature-driven ensemble model designed to precisely classify intricate power quality disturbances (PQDs). This model is capable of performing self-learning functions directly from data. Distinguishing itself from existing deep learning techniques, the method in [23] takes into account both the spatial features within the time–frequency domain and temporal relational features. Separate submodules tailored for multidimensional feature mining are constructed, leveraging fully convolutional networks and bidirectional gated recurrent units. The authors of [24] utilized an improved support vector machine algorithm to classify composite disturbances. They first introduced two factors into the original support vector machine kernel function to obtain a new and improved algorithm, which reduced the number of support vectors and simplified the computation process. Then, they applied the new algorithm to classify composite disturbances and obtained simulation experimental results. The authors of [25] first combined the S-transform with the TT-transform to extract 60 interference signal functions. After dimension reduction through PCA, they were input into a support vector machine classifier optimized by a particle swarm optimization algorithm. The experiments showed good robustness. The authors of [26] introduced the principles, algorithms, and training processes of convolutional neural networks and their applications in image processing. After a series of simulation experiments, the conclusion was that they had a strong effect in image processing.

The analysis of power quality disturbances is an indispensable part of electrical engineering, involving in-depth research on various power quality signals. Whether they are in a steady or dynamic state, these signals may be subject to interference from various factors such as voltage sag, surge, voltage pulse, and instantaneous power outages, posing a threat to the normal operation of power systems. Therefore, it is crucial to find a method that can quickly and effectively analyze these signals. Such a method can not only clearly present the key parameters in the signal but also infer the type of signal based on these parameters, thereby targeting proposing measures to improve and enhance power quality.

However, multiple challenges arise in the practice of power quality disturbance detection and classification. Firstly, balancing the information in the time domain and the frequency domain is a significant problem. Time domain analysis can intuitively reflect the changes in signals on the time axis, which is helpful for observing the instantaneous behavior of signals. On the other hand, frequency domain analysis can reveal the distribution of signals in frequencies, which is crucial for analyzing harmonics and other issues. However, in practical operations, it is often difficult to consider the information of both domains simultaneously, resulting in incomplete analysis results.

Secondly, the low accuracy of parameter detection and time localization is an urgent issue to be addressed. In power quality disturbance detection, accurately extracting the characteristic parameters of signals and determining the time points of disturbance occurrence are crucial. However, due to the complexity of the signals themselves and the interference of noise, the accuracy of parameter detection is affected, and there may be deviations in time localization. This not only affects the judgment of disturbance types but may also lead to weak targeting of improvement measures.

Lastly, the overly cumbersome selection of feature parameters and low accuracy of disturbance classification are also concerns that need to be addressed. In power quality disturbance classification, it is usually necessary to select a series of feature parameters as the basis for classification. However, the selection of these feature parameters often involves complex calculations and screening processes, which not only increases the difficulty of analysis but may also lead to decreased classification accuracy due to improper parameter selection. This not only affects the identification and handling of power quality disturbances but may also pose potential threats to the stable operation of the power system.

To address the aforementioned issues, this article proposes a novel classification strategy for power quality disturbances based on the VMD algorithm and improved SVM model. The main contributions of this paper are summarized as follows:

(1) This paper designs a comprehensive preprocessing-classification framework for power quality disturbances. Firstly, a preprocessing strategy based on VMD is adopted to denoise the power quality disturbance signals. Compared with the EMD algorithm, the VMD algorithm can effectively extract physically meaningful modal components from complex signals, thereby eliminating noise interference and improving signal quality. This strategy provides a more accurate and reliable data basis for subsequent disturbance classification and identification.

(2) This paper also designs an SVM classification model based on IGWO. The innovation lies in the utilization of the IGWO algorithm to optimize the penalty factor and kernel function parameters of the SVMs, thus improving its classification accuracy. Compared with traditional SVM models, this improved model can more effectively avoid falling into local optimal solutions and achieve higher recognition accuracy when identifying power quality disturbances. The results of the final case study show that the classification accuracy of this method can reach over 98% compared with other models.

The structure of this article is as follows. In Section 2, the principles of the VMD algorithm and the detailed calculation process are given. Then, a multi-SVM model-based disturbance classification strategy is introduced in Section 3, and a corresponding improved algorithm is given in Section 4. Finally, the case study in Section 5 demonstrates the effectiveness and feasibility of the proposed method.

2. Power Quality Disturbance Denoising

2.1. Introduction to the Basic Principles of VMD

Compared with the EMD algorithm, the VMD algorithm has better noise control ability, and the sampling effect is much smaller than in EMD recursive methods, avoiding the phenomenon of mode mixing that the EMD algorithm is prone to. The essence of the VMD algorithm is to transform the signal decomposition process into a process of solving variational problems, decomposing the input real value signal f into k single-component amplitude frequency modulation intrinsic mode functions (IMFs) u_k(t). The constraint condition for the objective function of the corresponding variational problem is to minimize the sum of the estimated bandwidth of k IMF components and ensure that the sum of the IMF components is equal to f. The detailed steps are given below:

(1) The analytical signal and unilateral spectrum of each IMF component obtained through the Hilbert transform are as follows:

$$(\delta (t)+\frac{j}{\pi t})·u_k(t)$$

(1)

(2) Using Equation (2), each IMF component is demodulated to its corresponding estimated center frequency by $e^{-j{w}_{k}t}$, resulting in the transformation of the unilateral spectrum associated with each IMF component into the baseband:

$$[(\delta (t)+\frac{j}{\pi t})·u_k(t)]e^{-j{w}_{k}t}$$

(2)

(3) The variational model defined is constructed as shown in Equation (3):

$$\left\{\begin{array}{c}\min \left\{{\displaystyle \sum _k{‖{\partial }_i\left[(\delta (t)+\frac{j}{\pi t})·u_k(t)\right]e^{-j{w}_{k}t}‖}_2^2}\right\}\\ s.t.{\displaystyle \sum _k{u}_k=f}\end{array}\right.$$

(3)

(4) By introducing the quadratic penalty factor α and the Lagrange multiplier λ, the variational model constructed in Equation (3) can be solved. The introduction of the penalty factor α enhances the robustness of the non-stationary signal during the variational mode decomposition process, while the Lagrange multiplier ensures the rigidity of the model constraints. The augmented Lagrange expression is as follows:

$$L(\left\{u_k\right\},\left\{w_k\right\},\lambda )=a{\displaystyle \sum _k{‖\left[(\delta (t)+\frac{j}{\pi t})·u_k(t)\right]‖}_2^2}+〈\lambda (t),s(t)-{\displaystyle \sum _k{u}_k(t)}〉+{‖s(t)-{\displaystyle \sum _k{u}_k(t)}‖}_2^2$$

(4)

The Lagrange expression in Equation (4) employs the alternating direction method of multipliers (ADMM) to iteratively update $u_k^{n+1},w_k^{n+1},{\lambda }_k^{n+1}$ and seek the optimal solution to the function. By utilizing the Fourier transform (FT), conversion between the time and frequency domains of the iterative parameters $u_k^{n+1}$ is achieved, resulting in the following iterative formula in the frequency domain:

$${\widehat{u}}_k^{n+1}(w)=\frac{\widehat{f}(w)-{\displaystyle \sum _{i\ne k}{\widehat{u}}_i(w)}+\frac{\lambda (w)}{2}}{1+2a{(w-w_k)}^2}$$

(5)

Similarly, the iterative formula for the center frequency in the frequency domain is obtained as follows:

$$w_k^{n+1}=\frac{{\displaystyle {\int }_0^{+\infty }w{\left|{\widehat{u}}_k(w)\right|}^{2}dw}}{{\displaystyle {\int }_0^{+\infty }{\left|{\widehat{u}}_k(w)\right|}^{2}dw}}$$

(6)

To gain a better understanding, the detailed steps of the VMD algorithm are outlined in

Table 1. Detailed steps of the VMD algorithm.

Step	Specific Operations
Step 1	$\mathrm{Initialize} {\widehat{u}}_k^1(w),w_k^1,{\widehat{\lambda }}^1$ and n(n = 0).
Step 2	$\mathrm{n} \leftarrow \mathrm{n}+1, \mathrm{and} \mathrm{update} u_k^{n+1},w_k^{n+1}$ with Equations (5) and (6), respectively.
Step 3	Updated the value of λ with Equation (7):
	${\widehat{\lambda }}^{n+1}(w)={\lambda }^n(w)+\tau (\widehat{f}(w)-{\displaystyle \sum _k{\widehat{u}}_k^{n+1}(w)})$	(7)
Step 4	Repeat steps 2 and 3. When the result of Equation (8) is less than the value of $\epsilon$, stop the iteration and output the result to obtain k modal components and their center frequencies:
	$\frac{{‖{\widehat{u}}_{n+1}^k-{\widehat{u}}_n^k‖}_2^2}{{‖{\widehat{u}}_n^k‖}_2^2}\le \epsilon$	(8)

below.

2.2. Determination Method of the Number of Decomposed Modal Components k

The VMD algorithm involves four main parameters, and the selection of the number of decomposition mode components k has a significant impact. In this section, we introduce a method for determining the parameter k.

Due to the complexity of the environment at power quality disturbance detection points, it is difficult to determine the optimal number of IMF components k when using the VMD algorithm to decompose disturbance signals. Traditional methods for determining k mainly rely on empirical observations of the center frequencies ω to determine the number of IMF components. However, this approach lacks quantitative basis. When the center frequencies ω of adjacent IMF components are too close, this can lead to over-decomposition or under-decomposition, which has a significant impact on the adaptability and effectiveness of the VMD decomposition algorithm.

To address the issue of selecting the modal component k value, this paper proposes a quantitative method using the energy convergence factor algorithm to determine the number of modal components k. This method involves calculating the difference between the energy ratios of the residual signals after decomposition with adjacent k values and the original signal. The decomposition is considered effective when the calculated difference is less than or equal to a threshold η. The detailed calculation process of the energy convergence factor algorithm involves decomposing the original disturbance signal s into m and m + 1 IMF components using the VMD decomposition method. The ratios of the energies of the corresponding residuals after decomposition to the energy of s are denoted as $E_m$ and $E_{m+1}$. The energy convergence factor ${∆}_{mm+1}=E_{m+1}-E_m$ is then calculated as the sum of these ratios, as shown in the following formula:

$${∆}_{mm+1}=\frac{{‖s‖}_2^2-{\displaystyle \sum _{i=1}^{m-1}{‖u_m‖}_2^2}}{{‖s‖}_2^2}-\frac{{‖s‖}_2^2-{\displaystyle \sum _{i=1}^{m-1}{‖u_{m+1}‖}_2^2}}{{‖s‖}_2^2}$$

(9)

This quantitative approach allows for a more accurate determination of the optimal number of IMF components k, improving the adaptability and effectiveness of the VMD decomposition algorithm. On the other hand, through experiments with multiple sets of disturbance signals, this paper determines the threshold η to be 0.02. When the value of the energy convergence factor ${∆}_{mm+1}$ is less than this threshold, it is considered that the energy has converged, and the signal decomposition effect is relatively good at this point.

3. Disturbance Classification Strategy Based on Improved Multi-SVM Model

3.1. The Introduction of the SVM Model

A support vector machine (SVM) primarily employs the theory of statistical learning and can be used to solve data classification problems in the field of pattern recognition with effective performance. The main process of an SVM for classification is as follows. First, it maps the data in a low-dimensional sample set to a high-dimensional functional space. Then, it constructs a decision region such that the closely spaced samples in the original sample space become separable in the new functional space. Each decision surface corresponds to a linear classifier.

Given an observed sample set $\left\{(x_i,y_i)|i=1,2,\dots ,n\right\}$, $x_i\in R,y\in \left\{-1,1\right\}$, where $x_i$ represents the sample points and $y_i$ represents the class labels, the decision surface function in a d-dimensional space is expressed as

$$f(x)=wx+b$$

(10)

where w represents the weight vector and b represents the constant value.

Figure 1 illustrates the schematic diagram of the decision surface in the SVM model. The optimization expression for solving the classification problem in an SVM is shown in Equation (11):

$$\left\{\begin{array}{c}\min \frac{1}{2}{w}^{T}w+C{\displaystyle \sum _{i=1}^n{\zeta }_i}\\ y_i[w^T\phi (x_i)+b]\ge 1-{\zeta }_i,{\zeta }_i\ge 0,i=1,2,\dots ,n\end{array}\right.$$

(11)

In this equation, C represents the penalty factor, which serves to adjust the data outside the error range; ξ_i is the slack variable; and n represents the sample data size. To transform Equation (11) into a dual quadratic programming problem, it is necessary to introduce Lagrange multipliers, which lead to the following classification decision function:

$$f(x)=\mathrm{sgn}({\displaystyle \sum _{i=1,j=1}^n{a}_i^{\ast }{y}_i}(x_i,x_j)+b)$$

(12)

where a^*_i represents the Lagrange multiplier and y_i is the expected output. When classifying complex nonlinear problems, it is necessary to perform nonlinear transformations on the input variables and map them into a high-dimensional space. Then, the optimal classification hyperplane needs to be found. This requires the introduction of a kernel function, as detailed below:

$$K(x_i,x_j)=[\phi (x_i),\phi (x_j)]$$

(13)

By combining Equations (12) and (13), we can obtain Equation (14):

$$f(x)=\mathrm{sgn}({\displaystyle \sum _{i=1,j=1}^n{a}_i^{\ast }{y}_i}K(x_i,x_j)+b)$$

(14)

Commonly used kernel functions include polynomial kernel functions, linear kernel functions, and radial basis function (RBF) kernel functions. To improve the accuracy of SVM classification, this paper adopts the RBF kernel function, whose expression is as follows:

$$K(x_i,x_j)=\exp (\frac{-{‖x_i-x_j‖}^2}{2{\sigma }^2})$$

(15)

where σ represents the kernel parameter, and its value determines the generalization ability of the radial basis function.

The classification object of a support vector machine is mainly binary classification, while the signals include six categories: normal, temporary rise, temporary fall, interruption, pulse, and harmonic. Therefore, it is not possible to directly construct multi-classifiers based on SVMs. To this end, a binary method was used to construct a classifier, and the power quality disturbance recognition classifier is shown in Figure 2. The soft margin SVM classifier allows some training data points to fall within the margin of the decision boundary, handling these “violating” data points by introducing slack variables and corresponding penalty terms. This method is more robust to noise and outliers and better able to handle the complexities of power quality disturbance classification.

Therefore, in most cases, using the soft margin SVM classifier for power quality disturbance classification may be more appropriate. Of course, the specific choice still needs to be determined based on the specific situation of the dataset and the experimental results. If the dataset is quite clean and free of noise, then the hard margin SVM classifier may also be a good choice. However, overall, the soft margin SVM classifier is more popular in power quality disturbance classification due to its better robustness and generalization capabilities. It is important to note that the SVM classifier itself does not directly produce a confusion matrix. A confusion matrix is a tool used to evaluate the performance of a classification model, showcasing the model’s prediction accuracy across different categories. Specifically, a confusion matrix lists the cross-frequencies between the actual categories and the categories predicted by the model. As such, a confusion matrix is a step or tool in evaluating classifier performance, rather than something that is generated by the classifier itself. Various performance metrics, such as accuracy, precision, recall, and F1 score, can be extracted from the confusion matrix to assess the performance of an SVM classifier.

3.2. Introduction of the Traditional Grey Wolf Optimization Algorithm

The Grey Wolf Optimization (GWO) algorithm is a new swarm intelligence algorithm proposed by simulating the hierarchical structure and hunting behavior of grey wolf packs in nature. The grey wolf population executes a strict hierarchical system during prey hunting: the first level is the alpha wolf (α), the leader of the pack who is responsible for directing the activities of the wolves; the second level is the beta wolf (β), who is responsible for assisting the alpha wolf and directing the lower-ranking grey wolves; and the third level is the delta wolf (δ), who is responsible for executing the commands of the alpha and beta wolves and directing the lowest-ranking omega wolves (ω). In the initial stage of searching for prey, the grey wolf population cannot determine the exact location of the prey. The alpha wolf with the best fitness in the population guides the beta and delta wolves to search for prey. By continuously updating their positions, the grey wolf population gradually approaches the location of the prey, ultimately capturing it. Assuming that a population of N grey wolves is formed such that $X=[X_1,X_2,\dots ,X_N]$, if the search space is D-dimensional, then the position of the ith grey wolf in the D-dimensional space is represented by $X_i=(X_i^1,X_i^2,\dots ,X_i^D),i=1,2,\dots ,N$. The changes in the position of the grey wolves during the prey hunt are described in Equations (16)–(19):

$$X_i^d(t+1)=X_p^d(t)-A·\left|C·X_p^d(t)-X_i^d(t)\right|$$

(16)

$$A=2a·r_1-a$$

(17)

$$C=2·r_2$$

(18)

$$a=2-2t/t_{\max }$$

(19)

In the equations, t represents the current iteration, t_max represents the maximum number of iterations, $X_p=(X_P^1,X_P^2,\dots ,X_P^D)$ represents the position of the prey, A and C are coefficients, r₁ and r₂ are random numbers between [0, 1], and a is the control factor, which linearly decreases from 2 to 0 during the iteration process.

However, the actual position of the prey is unknown during the hunting process. Since the alpha, beta, and delta wolves are closer to the prey, their positions are approximately considered to be the prey’s position. The positions of the grey wolves are updated through Equations (16)–(19), and finally, the average position is calculated to obtain the final position of the omega wolf. The specific process of updating the grey wolf’s position is shown in Equations (20) and (21):

$$\left\{\begin{array}{c}{X}_{i,a}^d(t)=X_a^d(t)-A_1·\left|C_1·X_a^d-X_i^d(t)\right|\\ X_{i,\beta }^d(t)=X_{\beta }^d(t)-A_2·\left|C_2·X_{\beta }^d-X_i^d(t)\right|\\ X_{i,\delta }^d(t)=X_{\delta }^d(t)-A_3·\left|C_3·X_{\delta }^d-X_i^d(t)\right|\end{array}\right.$$

(20)

$$X_i^d(t+1)=\frac{X_{i,a}^d(t)+X_{i,\beta }^d(t)+X_{i,\delta }^d(t)}{3}$$

(21)

In the equation, X_α, X_β, and X_δ represent the positions of the top three grey wolves with the best fitness in the current iteration, while A₁, A₂, A₃, C₁, C₂, and C₃ are coefficients generated during each iteration.

4. Algorithm Improvement Strategies and Solution Methods

4.1. Nonlinear Decreasing Strategy for the Control Factor

The traditional GWO algorithm draws inspiration from the natural hierarchy of grey wolf leadership and their collaborative hunting techniques, embodying the principles of swarm intelligence. Its straightforwardness, minimal parameter requirements, straightforward programming, distributed parallel computing compatibility, and robust global search capabilities have made it a popular choice for addressing global optimization challenges across engineering science disciplines. Nevertheless, the standard GWO algorithm exhibits certain limitations, such as a slowdown in convergence during the later stages and a tendency to settle into local optima. Through a randomly weighted position update strategy, a faster convergence speed and higher convergence accuracy can be achieved [27].

On the other hand, the use of the IGWO to optimize the penalty factor and kernel function parameters of the SVM model is primarily aimed at improving the prediction results of the SVM. Among the parameters of the SVM model, based on the RBF kernel, the choice of the penalty factor and kernel function parameters directly impact its learning and generalization capabilities. By optimizing these two parameters using the Grey Wolf Optimization algorithm, the model’s performance can be effectively adjusted to better fit the characteristics of the data, thus improving the prediction accuracy and stability. In the early stages of swarm intelligence algorithms, the focus is on global search, while in the later stages, the focus shifts to local exploitation. A strong global search capability can avoid premature convergence of the algorithm, while a strong local exploitation capability can improve the convergence speed in the later stages. As a type of swarm intelligence algorithm, the balance between the global search and local exploitation capabilities of GWO is crucial for quickly obtaining the global optimal solution.

In the GWO algorithm, when A ≤ 1, the grey wolves attack the prey and perform a local search, while when A > 1, the grey wolves disperse and perform a global search. As can be seen in Equation (17), the parameter A continuously changes with the variation in the control factor a. Therefore, the entire prey encirclement process is primarily completed through the linear variation in the parameter a. The control method of parameter a changing during the iteration process affects the balance between the exploitation and search capabilities of the algorithm. The standard GWO algorithm has a linearly decreasing parameter a. However, the search process of the algorithm is not linear, and thus the linear change of parameter a cannot adapt to the actual search situation. Especially when solving multi-modal function problems, GWO is prone to falling into local optima. To address this issue, this paper proposes a nonlinear control factor strategy:

$$a=\frac{4}{\pi }\arccos \frac{t}{t_{\max }}$$

(22)

In the early stages of iteration, the decay rate of a is relatively small, resulting in larger fluctuations in the value of A in Equation (17). This allows the algorithm to more easily escape from local optima, thereby enhancing its global search capability. In the later stages of iteration, the decay rate of a becomes larger, enabling the algorithm to find the optimal solution locally and more quickly. Therefore, the improved control strategy effectively balances the algorithm’s global search and local exploitation capabilities.

4.2. Randomly Weighted Position Update Strategy

From Equations (20) and (21), it can be seen that the standard GWO algorithm uses the average position of the three best grey wolves as the position of the grey wolves for the next iteration. However, this method does not consider the hierarchical differences within the actual grey wolf population. In the actual optimization process, the fitness of the guiding α, β, and δ wolves decreases in turn, and the position of the α wolf is more likely to be closer to the actual optimal solution. To highlight the global leadership ability of the optimal wolf on the population, we increased the positional weight of the α wolf and decreased the weight of the δ wolf during the position update process. At the same time, to further avoid the algorithm falling into local optima, we adopted a random weight strategy to update the next generation of the population while ensuring that the weight coefficient of the α wolf was greater than that of the δ wolf. In this paper, a randomly weighted position update strategy is introduced:

$$X_i^d(t+1)=\frac{(2-r_3)·X_{i,a}^d+X_{i,\beta }^d(t)+r_3·X_{i,\delta }^d(t)}{3}$$

(23)

In Equation (23), r₃ represents a random number between [0, 1].

4.3. Classification Model Based on IGWO-SVM

The penalty factor C in the SVM model represents the tolerance level for misclassification when using the optimal hyperplane to classify samples. It balances the relationship between the classification accuracy of SVMs and the complexity of the model. As C increases, the classification accuracy on the training dataset improves, but the classification margin decreases, leading to potential overfitting and a reduction in the generalization ability of the classifier. Conversely, as C decreases, the probability of misclassifying samples in the training dataset increases, and the classification margin widens, but this may lead to underfitting and a decrease in the generalization ability of the classifier.

In the Gaussian kernel function, g determines the mapping relationship between the original data feature space and the high-dimensional data feature space. When g is large, the value of the Gaussian kernel function tends to approach zero, and the SVM will correctly classify all training samples, but the classification hyperplane becomes more complex, reducing the generalization ability of the model. Conversely, when g is small, the discriminant function of the SVM approaches one, and the model will classify all test samples as belonging to the majority class represented by the training samples, resulting in poor generalization ability. Finding the appropriate penalty factor C and kernel function g is crucial for enhancing the generalization ability of SVMs. In this paper, the improved GWO algorithm is used to optimize the parameters of the SVM algorithm.

The process of optimizing the SVM parameters using IGWO is as follows:

Step 1: Input the experimental data. To eliminate the influence of the dimension on classification, normalize the original dataset using the following formula:

$$y=\frac{x-x_{\min }}{x_{\max }-x_{\min }}$$

(24)

where x represents the original data feature, x_min and x_max are the minimum and maximum values of each feature group, respectively, and y is the normalized data.

Step 2: Randomly divide the entire dataset into a training set and a validation set according to a certain proportion. The training set is used to train the SVM model, while the validation set is used to evaluate and select the SVM model.

Step 3: Set the parameters C and g as the position parameters of the grey wolves, and initialize the population size, individual dimension, parameter optimization range, and maximum iteration number of the algorithm.

Step 4: Use the parameters C and g to obtain an SVM model on the training set, and evaluate the model on the validation set by classifying the samples. The classification accuracy is used as the fitness value for each wolf.

Step 5: Divide the grey wolf population into four levels—α, β, γ, and ω—based on their fitness values.

Step 6: Update the position of each grey wolf in the population using Equations (20)–(23).

Step 7: Check if the maximum iteration number has been reached. If it has, then the parameter optimization process ends. Otherwise, return to step 4, and continue iterating with the updated position parameters of the grey wolves.

Step 8: At the end of the iteration, output the optimal wolf position (i.e., the values of C and g), and establish an SVM classification model using these optimized parameters.

5. Case Study

5.1. Effectiveness Verification of the Effectiveness of Power Quality Disturbance Denoising

For the noise reduction of complex component disturbance signals, this paper employs an improved VMD algorithm to achieve noise reduction of the disturbance signals, such as transient oscillations. The ideal mathematical model for this is as follows:

$$x(t)=310.2\times (\cos wt+0.65e^{-18(t-0.8)})(\epsilon (t-0.125))\times \cos 8wt)$$

(25)

Firstly, we determined the value of k, which represents the number of IMF components for the transient oscillation disturbance signal after adding noise using the VMD decomposition. By employing the energy convergence factor method mentioned earlier, we calculated the values of the energy convergence factor Δ for different modal components. Given that Δ₁₂ = 0.9325 and Δ₂₃ = 0.0174 < η, the value of k for decomposition was set to 2.

The simulation diagram of the transient oscillation disturbance signal with noise after VMD decomposition is shown in Figure 3. Additionally, the denoised IMF components were superimposed and reconstructed to obtain the final denoised disturbance signal. A comparison of the original signal, the disturbed signal after adding noise, and the denoised signal is presented in Figure 4.

The VMD algorithm utilizes a variational mode decomposition model to break down complex power quality disturbance signals into a series of modal components with distinct frequency characteristics. These modal components accurately reflect the features of the disturbance signals, enabling us to identify and analyze the nature of the disturbance signals with greater precision. Additionally, the VMD algorithm effectively suppresses noise interference during the decomposition process, enhancing the signal-to-noise ratio of the disturbance signals and consequently extracting useful information from the disturbance signals with increased accuracy.

The transient oscillation disturbance signal was denoised using both the method proposed in this paper and the SVD algorithm. The results of the signal-to-noise ratio (SNR) and root mean square error (RMSE) calculations for the denoised disturbance signals are compared in

Table 2. The results for the signal-to-noise ratio using different methods.

Method	Signal-to-Noise Ratio before Denoising (dB)	Signal-to-Noise Ratio after Denoising (dB)	RMSE (%)
The proposed method	14	19.27	12.3
SVD method	14	16.56	15.8

. The results show that the proposed algorithm achieved a higher SNR and a lower RMSE for the denoised disturbance signal. Therefore, the improved VMD algorithm demonstrated better denoising performance for complex component disturbance signals containing multiple frequencies.

In all, compared with other algorithms, the advantages of the VMD algorithm in noise reduction are mainly reflected in the following aspects:

Adaptive decomposition capability: The VMD algorithm can adaptively decompose complex signals into a series of narrow-bandwidth intrinsic mode functions (IMFs). This adaptive decomposition characteristic enables the VMD algorithm to effectively process different types of noise and disturbance signals without the need to preset a decomposition mode.

Noise robustness: The VMD algorithm can effectively suppress noise interference during the decomposition process and improve the signal-to-noise ratio. This means that even in environments with high noise levels, the VMD algorithm can accurately extract useful signals and achieve high-quality noise reduction effects.

Avoidance of endpoint effects: Compared with some traditional signal decomposition algorithms, the VMD algorithm avoids the problem of endpoint effects. Traditional signal decomposition methods may lead to inaccurate decomposition results due to insufficient information at the signal endpoints. However, the VMD algorithm theoretically solves this issue, thereby improving the accuracy and stability of noise reduction.

Low computational complexity: The VMD algorithm has a relatively low computational complexity and can quickly process large-scale data. This makes the VMD algorithm more efficient and practical in practical applications, especially in scenarios that require real-time processing.

5.2. Effectiveness Verification of the Effectiveness of Power Quality Disturbance Denoising

In this section, 6000 data samples were randomly generated using MATLAB for 6 types of disturbance signals, including normal, temporary rise, temporary drop, interruption, pulse, and harmonic. The number of data samples for each type of signal was 1000. We selected 700 disturbance signals from various sources as the training set, and the remaining ones were the testing set.

The classification accuracy of various disturbance signals of the algorithm proposed in this paper under different noise intensities is shown in

Table 3. The classification accuracy of various disturbance signals under different noise intensities.

Disturbance Signal	Accuracy (%)
	Signal-to-Noise Ratio: 0 dB	Signal-to-Noise Ratio: 40 dB
normal	100	100
temporary rise	98.6	99.2
temporary drop	99.3	98.2
interruption	100	98.4
pulse	99.5	98.5
harmonic	100	98.6

. From the table, it can be seen that the accuracy of various signals was relatively high, with an average of 99.20%. At 0 dB and 40 dB, the highest accuracy could reach 100%. Overall, the analysis shows that the classifier can achieve good classification and recognition results, indicating that the method has high robustness. The numerical examples successfully verified the effectiveness of the method proposed in this article, which can achieve accurate recognition of disturbance signals. However, in recent years, with the rapid development of artificial intelligence technology and scientific research equipment, new classification model algorithms have emerged, and each algorithm has its own advantages and disadvantages. Therefore, in subsequent experimental research, we need to select appropriate algorithms based on specific research objects to achieve the desired goals.

To further demonstrate the effectiveness of the proposed method in this paper, we tested the disturbance identification accuracy of different models under different data samples. The relevant test results are shown in the following Figure 5.

From observation of the above figure, it can be seen that the power quality disturbance identification accuracy of the proposed method in this paper was superior to the traditional deep learning model and CNN model. The advantage was even more prominent under small sample training sets. In fact, SVMs are adept at handling small sample data, and their classification effect was not only related to the number of training samples but also to the distribution of the training samples. When the number of training samples was small, the SVM model could better handle uneven data distribution, thus maintaining high accuracy. In the case of small samples, the deep learning models and CNN models tended to overfit, leading to a decrease in performance on the test data. However, by utilizing the principle of structural risk minimization and selection of the optimal hyperplane, SVMs can reduce the generalization error while ensuring training error, thus exhibiting higher accuracy in small sample scenarios.

To further verify the feasibility of the method proposed in this paper in the distribution network, we also conducted corresponding case studies for verification in the IEEE-33 distribution network. The structural diagram of the IEEE-33 node system is shown in Figure 6 below, where random disturbance signals are superimposed onto the voltage curves under normal conditions at nodes 14, 18, and 26 to obtain a fault disturbance dataset. The final test results are shown in Figure 7 below.

It is not difficult to observe that the accuracy of power quality disturbance identification at node 18 was higher than that at nodes 14 and 26. Noise signal sources near the root node can influence subsequent child nodes, making the randomness of the superimposed noise more prominent. The noise signal source at node 18 affected nodes 14 and 26, increasing the difficulty of identification. However, overall, the proposed method could still maintain an identification accuracy of over 91% under complex conditions.

6. Conclusions

This article proposes a classification strategy for power quality disturbances based on the VMD algorithm and improved SVM model. Firstly, the VMD algorithm was used to denoise the signal, followed by the multi-SVM model for disturbance classification. Meanwhile, in order to improve the accuracy of disturbance identification, the IGWO algorithm was used for parameter optimization. In the future, the following potential research directions need to be further explored:

(1) Power quality disturbances often involve multiple signals and data sources, such as the voltage, current, and power factor. Studying how to effectively integrate information from different sources using multi-source information fusion techniques to improve the accuracy and reliability of disturbance classification is a challenging and promising research direction.

(2) With the development of smart grid and Internet of Things technologies, higher requirements have been placed on the online real-time monitoring and classification of power quality disturbances. Studying how to implement fast and accurate online real-time classification algorithms to meet the needs of practical applications is a research direction with practical application value.