Efficient Identification Method for Power Quality Disturbance: A Hybrid Data-Driven Strategy

Abstract

The massive integration of distributed renewable energy sources and nonlinear power electronic equipment has given rise to power quality issues such as waveform distortion, voltage instability, and increased harmonic components. Nowadays, the pollution of power quality is becoming increasingly severe, posing a potential threat to the security of the power grid and the stable operation of electrical equipment. Due to the presence of significant noise interference in the collected signals, existing methods still face issues such as low accuracy in disturbance identification and high computational complexity. To address these problems, this paper proposes a hybrid data-driven strategy that can significantly improve the accuracy and speed of identification. Firstly, the wavelet packet transform (WPT) method is employed to denoise the power disturbance signals. Subsequently, the local mean decomposition (LMD) algorithm is used to adaptively decompose the nonlinear and complex time series into multiple product function components. Feature extraction of the disturbance signals is then achieved by calculating entropy values after local mean decomposition, and a feature matrix is constructed from the entropy values of each component for analysis in disturbance identification. Finally, an extreme learning machine (ELM) is employed for the identification and classification of transient power disturbance signals. The verification of numerical examples demonstrates the feasibility and effectiveness of the proposed method in this paper.

1. Introduction

Electricity, as a secondary energy source, is widely utilized across multiple sectors and has become a crucial resource for social development [1]. With the rapid advancement of economy and technology, modern society is gradually stepping into an era of knowledge-based economy, led by automation and intelligent technologies. From the perspective of electricity consumers, modern life and production scenarios are filled with high-precision components that are highly sensitive to the quality of the power supply [2]. Even slight issues with electric energy quality may cause damage to these components and, in extreme cases, lead to the interruption of the entire system, causing unpredictable harm to people’s production and daily lives. Therefore, today’s electricity users demand cleaner and more efficient electric power. From the perspective of power suppliers, as various types of volatile, impulsive, and nonlinear loads [3] are gradually integrated into modern power grids, new electromagnetic interferences are also emerging, accompanied by a significant number of diverse electric energy quality issues. Power suppliers are facing unprecedented challenges [4].

From the perspective of research content and methodology, electricity quality disturbance classification and identification emphasize more on the rapid detection and accurate identification of disturbance signals, while power system harmonic analysis focuses more on the in-depth study of the generation mechanism, characteristics, and impacts of harmonics on the power system. Additionally, electricity quality disturbance classification and identification often employ intelligent methods such as wavelet transform, fuzzy technology, multi-dimensional classification, artificial neural networks, and support vector machines to achieve automatic classification and identification of various disturbance signals. Power system harmonic analysis, on the other hand, may involve more mathematical tools and analytical methods, such as Fourier series decomposition and harmonic measurement techniques. The detection of power quality disturbances typically involves the following two steps: denoising analysis and classification recognition. Firstly, denoising methods are utilized to analyze the relevant disturbance signals, determining whether the signal is normal or contains disturbances. Through mathematical calculations, the moment and the location of the power quality signal disturbance are determined. Secondly, information reflecting the characteristics of various disturbance signals with clear physical meanings is extracted. The differences in feature information between different types of disturbance signals provide data support for subsequent classification and recognition of disturbance signals [5]. Currently, many scholars at home and abroad have conducted in-depth research on noise reduction for power quality disturbances. Common noise reduction methods include Kalman filtering [6], empirical mode decomposition (EMD) [7], mathematical morphology, wavelet threshold denoising, etc. [8]. Kalman filtering is a method that studies the changing trends between the input and output of linear equations to optimally predict the system state. It has advantages such as a simple algorithm structure and strong robustness. However, its limitations include accurate estimation only for linear process models, and it cannot achieve optimal estimation results in nonlinear scenarios. Additionally, the algorithm is sensitive to the initial value settings of state variables, and unreasonable settings can lead to filter divergence [9]. The literature [10] proposes an adaptive maximum likelihood Kalman filtering algorithm, which establishes prediction and updates equations. It continuously estimates the initial state and conditional variance of variables through recursive estimation, but the process is complex and computationally intensive. EMD decomposes signals adaptively into modal components of different frequency bands based on their temporal characteristics and arranges them in order from high to low frequencies [11]. The literature [12] first decomposes the signal into high-frequency noise components and low-frequency useful components using EMD. Then, the wavelet threshold method is introduced to denoise the high-frequency components, while the low-frequency components remain unchanged. The processed high-frequency components are combined with the original low-frequency components to obtain the final denoised signal. The literature [13] constructs a denoising model combining EMD with singular value decomposition. It initially screens the noise signals using EMD and determines the effective singular matrix order by constructing a Hankel matrix to reconstruct the denoised signal. However, EMD can sometimes result in over decomposition or mode mixing when processing signals. When discarding high-frequency components, it may lose effective information from the signal, leading to distortion during reconstruction [14]. Mathematical morphology is a nonlinear filtering method based on lattice theory and topology, characterized by a simple structure and fast computational speed. The literature [15] constructs a denoising algorithm based on a dual-structured element weighted morphological filter. The literature [16] designs a structural element that can adaptively change its scale based on different disturbance types using mathematical morphology. Experimental results show that this method has a significant denoising effect. Due to the complexity of power quality disturbance signal types and their varying waveform characteristics, the denoising effect of mathematical morphology is greatly influenced by the structural elements; therefore, it is challenging to select appropriate structural elements for different types of disturbance signals.

On the other hand, the existing power quality disturbance data identification algorithms primarily rely on digital signal processing techniques such as Fourier transform [17], Hilbert–Huang transform [18], wavelet transform [19], S-transform [20], and compressed sensing [21] to collect and analyze disturbance data. These algorithms extract multiple sets of disturbance data features from different categories and then input them into artificial intelligence algorithms like neural networks, decision trees, and support vector machines for sample learning. Finally, the generated classifier is utilized to categorize the disturbance data [22]. Reference [23] first obtains the approximate and detailed components of the signal through a lifting wavelet transform and then calculates the instantaneous amplitudes of both components using HHT transform. This approach accurately locates the disturbance moments and rapidly identifies the disturbance types based on amplitude characteristics. However, it is susceptible to noise interference. Reference [24] employs generalized S-transform to extract the time–frequency characteristics of disturbance signals and selects the sum of squared time amplitudes, mean values, and characteristic frequency points after transformation as learning samples for neural networks to collect and classify disturbance data. The algorithms mentioned above are based on the Nyquist sampling theorem, increasing the complexity of disturbance data collection, analysis, and feature extraction in power systems [25]. Reference [26] proposes a compressed sensing-based method for power system disturbance data collection and classification. It utilizes the energy feature values and probability of gray level occurrence in the reconstructed gray level co-occurrence matrix texture features to classify and detect the reconstructed signals from compressed sensing. This method has the advantage of low computational complexity, but its reconstruction accuracy is susceptible to the sparsity of the original data. In addition, artificial neural networks have also been widely applied in the field of power system optimization and scheduling and have achieved good results [27].

Although numerous scholars have conducted research on power quality disturbance classification, there are still some issues that need to be addressed.

(1)

Existing methods are greatly influenced by noise. Traditional decomposition algorithms are sensitive to noise and may generate multiple overlapping noise components during the decomposition process. These pseudo-components can slow down the speed of power quality detection. When the noise is too severe, the parameters detected after modal decomposition and reconstruction, such as the start and end times of transient power quality disturbances and the amplitude and frequency of steady-state power quality disturbances, can be affected by high-frequency noise.

(2)

Current algorithms typically treat feature extraction and classification as two separate processes. This means that the quality of the classification results does not feed back into the feature extraction algorithm, leading to the possibility that feature extraction may not fully adapt to the needs of classification. This separated approach limits the performance improvement of the algorithm.

To address these issues, this paper proposes a hybrid data-driven strategy to achieve fast and accurate identification of power quality disturbances. The proposed method is considered a data-driven approach primarily because its processing flow and decision making are entirely based on the characteristics of the input data (i.e., power quality disturbance signals) rather than relying on predefined physical models or theoretical assumptions. Specifically, the following points such as noise preprocessing, feature extraction and decision making embody its data-driven nature. The framework of this paper is organized as follows: First, the WPT and LMD algorithms are employed for noise reduction preprocessing and feature extraction of power quality disturbance signals. Subsequently, the extracted features are input into the ELM classifier. ELM can categorize the disturbance signals based on these features and output classification results.

2. Noise Reduction Method for Disturbance Signals Based on Wavelet Packet Transform Theory

In actual detection, power quality disturbance signals are often accompanied by strong noise interference. In the field of power quality disturbance identification and classification, from an electrical perspective, the criteria for determining power quality disturbances are primarily based on the monitoring and analysis of electrical parameters such as voltage and current in the power system. The changes in these electrical parameters reflect the stability of the power system and the state of power quality. Noise interference can have a negative impact on the detection and classification of power quality disturbances. Considering that WPT is an effective adaptive time–frequency signal processing method that can adaptively extract both low-frequency and high-frequency signals with high computational speed, it has been widely used in various signal processing fields. Therefore, this paper proposes a denoising method for power quality disturbance signals based on the WPT method to preprocess the signals. WPT can simultaneously analyze the high-frequency and low-frequency parts of a signal. In power quality disturbance identification, WPT can effectively extract features of disturbance signals, such as harmonics, transient pulses, voltage sags, etc. It offers more flexible time–frequency analysis and can adjust the decomposition level and frequency resolution according to needs. This makes WPT advantageous in processing nonstationary and nonlinear power quality disturbance signals.

2.1. Introduction to the WPT Method

WPT, as an effective adaptive time–frequency signal processing method, can adaptively extract both low-frequency and high-frequency signals with high computational speed. It is a further improvement and development of wavelet transform. Addressing the shortcoming of wavelet transform in its insufficient decomposition ability for high-frequency signals, WPT can simultaneously subdivide the high-frequency portion of the signal and it possesses a certain degree of adaptivity. That is, based on the characteristic components of the signal, it selects the frequency bands with strong adaptability, which enhances the denoising effect for both stationary and nonstationary signals. In the context of multi-resolution analysis, Equation (1) should be satisfied:

$$L^2(R)=\oplus W_j,j\in Z$$

(1)

In the above equation, $L^2(R)$ represents the Hilbert space and $W_j$ represents the wavelet subspace.

The subspace $x_j^n$ of the power quality disturbance signal is defined as the closure space of signal $x_n(t)$, while the disturbance signal $x_j^{2n}$ is the closure space of $x_{2n}(t)$. Both of them satisfy the two-scale equation, as shown in Equation (2):

$$\left\{\begin{array}{c}{x}_{2n}(t)=\sqrt{2}{\displaystyle \sum _{k\in z}h(k)x_n(2t-k)}\\ x_{2n+1}(t)=\sqrt{2}{\displaystyle \sum _{k\in z}g(k)x_n(2t-k)}\end{array}\right.$$

(2)

where the power quality disturbance signal $x_n(t)$ can be regarded as a wavelet packet determined by the basis function $x_0(t)=\varphi (t)$. The functions g(k) and h(k) in the equation have an orthogonal relationship, and $g(k)={(-1)}^{k}h(1-k)$. When performing multi-resolution analysis of power quality, $\psi (t)$ and $\phi (t)$ also satisfy the two-scale equation, as shown in (3):

$$\left\{\begin{array}{c}\psi (t)={\displaystyle \sum g_k\phi (2t-k),\left\{g_k\right\}\in l^2}\\ \phi (t)={\displaystyle \sum h_k\phi (2t-k),\left\{h_k\right\}\in l^2}\end{array}\right.$$

(3)

Therefore, the wavelet packet sequence for power quality is defined as $x_n(t)$, where the wavelet packet possesses orthogonal characteristics determined by the scaling basis function $u_0(t)=\varphi (t)$.

The essence of wavelet packet denoising for power quality disturbance signals lies in the decomposition and reconstruction of the wavelet packet sequence $x_n(t)$. Firstly, we present Condition (4):

$$g_j^n(t)\in U_j^n$$

(4)

Then, $g_j^n(t)$ can be expressed as (5):

$$g_j^n(t)={\displaystyle \sum d_i^{j,n}{u}_n(2^{j}t-l)}$$

(5)

2.2. Selection of Decomposition Levels

During the denoising process of power quality disturbance signals, it is essential to first determine the number of decomposition levels. The selection of decomposition levels has a significant impact on the denoising results. If the number of decomposition levels is chosen to be too small, it may lead to unsatisfactory denoising effects and only minor improvements in signal-to-noise ratio (SNR) measurements. On the other hand, choosing too many decomposition levels may result in information loss, potentially decreasing the SNR measurement results. Therefore, it is crucial to accurately divide the signal’s frequency bands. The principles for dividing the signal frequency bands are as follows:

Ensure that the fundamental frequency component of the signal is located at the center of the lowest sub-band to limit its influence on other sub-bands. The actual number of decomposition levels for a signal is one less than the number of its sub-bands. A reasonable number of frequency band divisions can be obtained by rounding down the value calculated using the following Formula (6):

$$K={\log }_2(\frac{f_s}{f})+(\sqrt{\frac{1}{8}})$$

(6)

where $f_s$ represents the sampling frequency, and f represents the base frequency. When decomposing wavelet packets, there are various forms of decomposition trees. The optimal tree is selected using Shannon entropy, which reflects the relationship between the amount of information and its uncertainty. The larger the entropy, the greater the amount of information required to determine the event; conversely, the smaller the uncertainty, the smaller the entropy, and the less information needed to determine the event. The feature extraction method based on Shannon entropy (information entropy) primarily utilizes Shannon entropy’s ability to quantify the uncertainty or information content of a random variable when capturing relevant information about the dynamics and complexity of power quality disturbance signals. Shannon entropy describes the uncertainty or information content of a random variable. In the analysis of power quality disturbance signals, the signal can be viewed as a stochastic process, where the signal value at each moment can be regarded as a random variable of that stochastic process. In all, Shannon entropy has the advantages of good stability, complexity quantification, noise robustness, dynamic capture, and high reproducibility.

3. The Principle and Decomposition Steps of the LMD Algorithm

Local mean decomposition (LMD) is a signal decomposition method based on the fundamental idea of breaking down complex signals into multiple local means and local high-frequency components. It is a data-driven approach that lacks strict mathematical derivation but relies on prior knowledge and empirical analysis, yielding results through iterative calculations. As a novel adaptive time–frequency analysis technique, the LMD algorithm can gradually decompose a complex multi-component signal into a sum of several product functions (PF components) and a residual component through multiple iterative cycles based on the signal’s inherent complexity and variation patterns. Each PF is the product of an envelope function and a pure frequency modulation function, essentially representing a single component modulated signal. In theory, combining the instantaneous frequency and amplitude of each PF can reveal the complete time–frequency distribution of the original signal, thus clearly elucidating the distribution patterns of signal energy across various scales.

The LMD algorithm exhibits significant advantages in processing complex signals with amplitude and frequency modulation characteristics, enabling more effective calculation of the signal’s instantaneous amplitude and frequency, thereby better reflecting the state of the actual system. The LMD algorithm can adaptively decompose nonlinear complex time series into multiple PF components, where each PF component is the product combination of an envelope signal and a pure frequency modulation signal. The amplitude of each component is equal to the corresponding envelope signal, and its instantaneous frequency can be calculated from the pure frequency modulation signal. By multiplying the instantaneous frequency and amplitude obtained during the decomposition process, we can obtain all PF components, thus generating the complete time–frequency spectrum of the original time series. To better understand, considering an arbitrary time series x(t), the main decomposition steps of the LMD algorithm are as follows:

Step 1: Identify all local extrema points $n_i$ contained in the time series x(t) and calculate the mean value $m_i$ of the extrema points $n_i$ and $n_{i+1}$ in sequence, as shown in (7).

$$m_i=\frac{n_i+n_{i+1}}{2}$$

(7)

Connect the calculated values $m_i$ with a polyline and smooth it to obtain the local mean function $m_{11}(t)$.

Step 2: Obtain the envelope estimation value $a_i$ by dividing the absolute difference between adjacent extrema points $n_i$ and $n_{i+1}$ by 2.

$$a_i=\frac{\left|n_i-n_{i+1}\right|}{2}$$

(8)

Similarly, connect the calculated values $a_i$ with a polyline in sequence and smooth it to obtain the envelope estimation function $a_{11}(t)$.

Step 3: Separate the local mean function $m_{11}(t)$ from the original time series x(t), as shown in (9).

$$h_{11}(t)=x(t)-m_{11}(t)$$

(9)

By dividing $h_{11}(t)$ by the envelope estimation function $a_{11}(t)$, the demodulation of $h_{11}(t)$ can be achieved, as shown in (10).

$$s_{11}(t)=h_{11}(t)/a_{11}(t)$$

(10)

In ideal circumstances, $s_{11}(t)$ should be a pure frequency modulation signal, meaning that its envelope estimation function $a_{12}(t)$ should match $a_{12}(t)=1$. If $a_{12}(t)\ne 1$, then $s_{11}(t)$ is treated as the original sequence and the above loop steps are repeated n times until $s_{1n}(t)$ becomes a pure frequency modulation signal, satisfying the condition $a_{1(n+1)}(t)=1$. Therefore, the loop process is as follows:

$$\left\{\begin{array}{c}{h}_{11}(t)=x(t)-m_{11}(t)\\ h_{12}(t)=s_{11}(t)-m_{12}(t)\\ ⋮\\ h_{1n}(t)=s_{1(n-1)}(t)-m_{1n}(t)\end{array}\right.$$

(11)

$$\left\{\begin{array}{c}{s}_{11}(t)=h_{11}(t)/a_{11}(t)\\ s_{12}(t)=h_{12}(t)/a_{12}(t)\\ ⋮\\ s_{1n}(t)=h_{1n}(t)/a_{1n}(t)\end{array}\right.$$

(12)

The general termination condition for the iteration is:

$$\underset{n\to \infty }{\lim }{a}_{1n}(t)=1$$

(13)

Step 4: The envelope signal is equal to the product of all envelope estimation functions obtained during the iterative decomposition process, and the envelope signal represents the instantaneous amplitude function. Its mathematical expression can be described as:

$$a_1(t)=a_{11}(t)a_{12}(t)\dots a_{1n}(t)={\displaystyle \prod _{q=1}^n{a}_{1q}(t)}$$

(14)

Step 5: Multiply the envelope signal $a_1(t)$ by the pure frequency modulation signal $s_{1n}(t)$ to obtain the first PF component of the LMD decomposition.

$$P{F}_1(t)=a_1(t)s_{1n}(t)$$

(15)

The LMD algorithm decomposes the signal layer by layer from high to low frequencies, so the frequency of the component $P{F}_1$ is equal to the highest frequency of the sequence x(t). Theoretically, $P{F}_1$ is a single component amplitude-modulated and frequency-modulated signal, with its instantaneous frequency and instantaneous amplitude being $f_1(t)$ and $A_1(t)$, respectively. $A_1(t)$ is equal to the envelope signal $a_1(t)$, and $f_1(t)$ can be obtained by applying Equation (16) to the signal $s_{1n}(t)$.

$$f_1(t)=\frac{1}{2\pi }\frac{d\left[\arccos (s_{1n}(t))\right]}{dt}$$

(16)

Step 6: Remove $P{F}_1(t)$ from the original sequence x(t) to obtain a new time series $u_1(t)$. Repeat Steps 1 to 5 on $u_1(t)$. This process is repeated k times. When $u_k$ becomes a monotonic function, the above loop process is terminated. By following the above steps, k PF components can be obtained.

$$\left\{\begin{array}{c}{u}_1(t)=x(t)-P{F}_1(t)\\ u_2(t)=u_1(t)-P{F}_2(t)\\ ⋮\\ u_k(t)=u_{k-1}(t)-P{F}_k(t)\end{array}\right.$$

(17)

Finally, the time series x(t) will be decomposed into multiple simple signals consisting of k PF components with single components and one monotonic residual component $u_k(t)$, as shown in (18).

$$x(t)={\displaystyle \sum _{p=1}^{k}P{F}_p}(t)+u_k(t)$$

(18)

To gain a better understanding, the detailed flowchart of the LMD decomposition algorithm is shown in Figure 1.

Based on the above decomposition principle, it can be seen that the amplitude frequency characteristics of the time series x(t) can be obtained through the linear combination of the amplitudes and frequencies of all PF components resulting from the decomposition. Therefore, the LMD decomposition method exhibits excellent completeness, as it preserves the complete information in the original signal without causing any loss of information.

4. Disturbance Classification Strategy Based on Extreme Learning Machine

The extreme learning machine (ELM) is a machine learning system or method constructed based on the feedforward neuron network (FNN) suitable for both supervised and unsupervised learning problems. It boasts extremely fast learning capabilities and excellent generalization performance.

As shown in Figure 2, ELM primarily consists of the following three parts: the input layer, the hidden layer, and the output layer. The input layer receives input sample vectors and output sample features. The hidden layer contains multiple hidden nodes, where the output of each node is a weighted sum. The weights are randomly assigned or manually given and do not require updates during the learning process. The output layer has a number of neurons equal to the number of sample categories responsible for generating the final output.

Compared with traditional single hidden-layer neural networks, ELM does not rely on gradient-based backpropagation to adjust weights; instead, it utilizes the Moore–Penrose generalized inverse to set the weights, simplifying the computational process. This confers advantages to ELM in terms of learning speed and generalization capabilities. The connection weights between the input layer and the hidden layer and the thresholds of the hidden layer neurons are randomly generated and do not require adjustment during training. By setting the number of hidden layer neurons, a unique optimal solution can be obtained. Compared with the original feedforward neural networks, ELM offers advantages such as faster learning speeds, better generalization performance, and simpler parameter adjustment.

The mathematical principles underlying ELM are as follows:

Given N arbitrary and distinct datasets $(x_k,y_k)$, where $x_k={[x_{k1},\cdots ,x_{kn}]}^T\in R_n$ represents the training samples and $y_k={[y_{k1},\cdots ,y_{km}]}^T\in R_m$ represents the desired outputs, the ELM model with M hidden nodes can be expressed using the following formula:

$${\displaystyle \sum _{i=1}^M{\beta }_{i}g(x_k)}={\displaystyle \sum _{i=1}^M{\beta }_{i}g(w_i·x_k+b_i)=o_k,k=1,\dots ,N}$$

(19)

where g(·) represents the activation function, β_i denotes the weight vector between the i-th hidden node and the output node, w_i represents the weight vector between the i-th hidden node and the input nodes, and b_i is the bias of the i-th hidden node. The dot product between w_i and x_k is denoted as w_i·x_k. To minimize the output error, it can be expressed as:

$${\displaystyle \sum _{j=1}^N‖o_k-y_k‖=0}$$

(20)

That is, there exist b_i, β_i, and w_i that satisfy the following equation:

$${\displaystyle \sum _{i=1}^N{\beta }_{i}g(w_i·x_k+b_i)=y_k,k=1,\dots ,N}$$

(21)

In matrix form, it can be expressed as the following equation:

$${\displaystyle \sum _{i=1}^N{\beta }_{i}g(w_i·x_k+b_i)=y_k,k=1,\dots ,N}$$

(22)

In matrix form, it can be expressed as the following equation:

$$H\beta =T$$

(23)

where H represents the output matrix of the hidden layer and T represents the desired output. The matrix H can be expressed as (24).

$$H=\left[\begin{array}{cccc}g(w_1{x}_1+b_1)& g(w_2{x}_1+b_2)& \dots & g(w_k{x}_1+b_k)\\ g(w_1{x}_2+b_1)& g(w_2{x}_2+b_2)& \dots & g(w_k{x}_2+b_k)\\ \dots & \dots & \dots & \dots \\ g(w_1{x}_N+b_1)& g(w_2{x}_N+b_2)& \dots & g(w_k{x}_N+b_k)\end{array}\right]$$

(24)

In the ELM, once the biases bi and weights w_i are randomly determined, the hidden layer output matrix H becomes a fixed matrix. This allows the problem to be transformed into solving a linear system of H·β = Y, eliminating the need for extensive parameter adjustments as required in traditional algorithms, which can consume a significant amount of time. Finally, based on Equation (23), we can obtain:

$$\beta =H^{+}T$$

(25)

For a clearer and intuitive understanding of the ELM architecture, this paper delves into the key components of the ELM used in this study and their quantities. Detailed information is given in

Table 1. Key components of the ELM used in this study and their quantities.

Parameters/ Components	Description	Quantities
Input Layer Neurons	Number of corresponding input features	Determined based on the number of features in the power quality data; the value in this paper is 6.
Hidden Layer Neurons	The number of neurons in the ELM architecture affects the complexity and learning capability of the network	Set according to requirements, usually several times the number of input layer neurons; the value in this paper is 18.
Weight Coefficients	Weights from the input layer to the hidden layer and from the hidden layer to the output layer	Number of input layer neurons × number of hidden layer neurons + number of hidden layer neurons × number of output layer neurons.
Bias Terms	Biases of the hidden layer neurons	The value in this paper is 12.
Output Layer Neurons	For classification tasks, it depends on the output categories, using softmax or sigmoid activation functions for multi-class classification	The value in this paper is 6, corresponding to the normal state and five types of power quality disturbances, encoded sequentially as 0–5.
Backpropagation Relationship	ELM typically does not perform backpropagation since its weights are randomly initialized and solved through analytical methods.	/

.

5. Case Study

5.1. Effectiveness Verification of the WPT Denoising Method

In this paper, simulations were conducted in Matlab 2014b software to verify the universality of power quality disturbances. Noise was added to common single power quality disturbances, and comparisons were made with commonly used signal denoising methods, including singular value decomposition (SVD) denoising, wavelet adaptive threshold denoising, and wavelet soft threshold denoising. Simulations were carried out in various noise environments. Among these methods, the wavelet denoising methods all employed the db4 wavelet basis, which exhibits good orthogonality and time–frequency support. For the wavelet packet method, a six-level decomposition was performed, and the optimal wavelet packet tree was selected based on the Shannon entropy principle. Thresholds were selected using the fixed threshold method. The disturbance signals considered in this article included voltage swells, voltage sags, voltage interruptions, transient impulses, and transient oscillations. These five types of signals were generated in MATLAB using Equations (26)–(30) to produce 1000 data samples separately, and the datasets were split into training and testing sets at a ratio of 6:4.

$$\mathrm{normal} \mathrm{voltage} y(t)=A\sin (w_{0}t+\phi )$$

(26)

$$\mathrm{voltage} \mathrm{swells} \begin{array}{l}f(t)=[1+a(u(t-t_1)-u(t-t_2))]\sin (w_{0}t)\\ 0.1<a<0.8,\hspace{0.33em}\hspace{0.33em}T\le (t_2-t_1)\le 9T\end{array}$$

(27)

$$\mathrm{voltage} \mathrm{sags} \begin{array}{l}f(t)=[1-a(u(t-t_1)-u(t-t_2))]\sin (w_{0}t)\\ 0.1<a<0.9,\hspace{0.33em}\hspace{0.33em}T\le (t_2-t_1)\le 9T\end{array}$$

(28)

$$\mathrm{voltage} \mathrm{interruptions} \begin{array}{l}f(t)=[1-a(u(t-t_1)-u(t-t_2))]\sin (w_{0}t)\\ 0.9<a<1,\hspace{0.33em}\hspace{0.33em}T\le (t_2-t_1)\le 9T\end{array}$$

(29)

$$\mathrm{transient} \mathrm{impulses} \begin{array}{l}f(t)=a_1\sin (w_{0}t)+a_3\sin (3w_{0}t)+a_5\sin (5w_{0}t)+a_7\sin (7w_{0}t)\\ 0.9<a_1,a_3,a_5,a_7<1,\hspace{0.33em}\hspace{0.33em}{{\displaystyle \sum (a_i)}}^2=1\end{array}$$

(30)

$$\mathrm{transient} \mathrm{oscillations} \begin{array}{l}f(t)=\sin (w_{0}t)+a{e}^{-(t-t_1)/\tau }(u(t-t_1)-u(t-t_2))\sin (w_{n}t)\\ 0.1<a<0.8,\hspace{0.33em}\hspace{0.33em}T\le (t_2-t_1)\le 3T,\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}8ms\le \tau \le 40ms\\ 300Hz\le f_n\le 500Hz,\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}2\pi f_n=w_n\end{array}$$

(31)

When evaluating the denoising effectiveness of different algorithms, the following two common evaluation metrics are typically used: signal-to-noise ratio (SNR) and mean squared error (MSE). SNR reflects the relationship between the signal and its noise, to a certain extent indicating the smoothness of the signal. MSE, on the other hand, reflects the time delay characteristics of the signal. The calculation methods for these two metrics are as follows:

$$SNR=10\lg \frac{{\displaystyle \sum _{t=1}^N{(\widehat{f}(t))}^2}}{{\displaystyle \sum _{t=1}^N{(\widehat{f}(t)-f(t))}^2}}$$

(32)

$$MSE={\displaystyle \sum _{t=1}^N{(\widehat{f}(t)-f(t))}^2}$$

(33)

The disturbance signals selected in this paper mainly included voltage swells, voltage sags, voltage interruptions, transient impulses, and transient oscillations. The SNR and MSE metrics for different denoising methods are shown in the following Figure 3 and Figure 4.

By observing Figure 3 and Figure 4, it can be found that, compared with traditional methods, the proposed method in this paper demonstrates superior performance in both SNR and MSE metrics. SVD denoising primarily relies on the principle of matrix decomposition, decomposing the signal into singular values and removing those corresponding to noise. However, SVD may not offer the same flexibility in frequency resolution as WPT. Through multi-scale analysis, WPT provides a finer frequency resolution, enabling better capture of detailed information in power quality disturbances. SVD denoising involves matrix operations, which can lead to high computational complexity for large-scale data. In contrast, WPT has a relatively lower computational complexity, making it more suitable for real-time processing or large-scale data processing scenarios. In addition, the SNR metric (in units of dB) measures the strength of noise to further validate the effectiveness of the proposed method under different noise disturbances. The SNR metric provides a quantitative means to evaluate the intensity of noise, enabling a more accurate description of the impact of various noises on power quality disturbances. Measured in decibels (dB), the SNR metric allows us to intuitively understand the relative strength of noise compared with the signal. Through the SNR metric, this quantitative assessment helps us more objectively compare the classification performance of power quality disturbances under different noise disturbances and evaluate the robustness and generalization ability of the classification algorithm, thus ensuring its reliability in practical applications.

The wavelet adaptive threshold denoising method automatically adjusts the threshold based on the characteristics of the signal to remove noise. However, the selection of the threshold can be influenced by the non-stationarity of the signal and noise characteristics, resulting in an unstable denoising performance. The WPT denoising method, through wavelet packet decomposition, can more accurately identify noise and signal components, thereby removing noise more effectively. The WPT denoising method typically provides better denoising results, especially when dealing with non-stationary signals and complex noise environments. It can effectively remove noise while preserving signal characteristics, improving the recognition accuracy of power quality disturbances.

The wavelet soft threshold denoising method can lead to signal discontinuity during the processing due to the introduction of certain biases from the soft thresholding. In contrast, the WPT denoising method can better maintain signal continuity, reducing the distortion introduced during the denoising process. The WPT denoising method generally exhibits higher denoising performance, particularly when dealing with power quality disturbances that have complex structures and multi-scale characteristics. It can more accurately identify and remove noise components while preserving useful information in the signal.

In summary, compared with SVD denoising, wavelet adaptive threshold denoising, and wavelet soft threshold denoising, the WPT denoising method in the field of power quality disturbance denoising offers higher frequency resolution, lower computational complexity, more stable denoising performance, and better signal continuity preservation capabilities. This makes the WPT denoising method more advantageous in handling power quality disturbances and enhancing the accuracy and reliability of disturbance recognition.

5.2. Effectiveness Validation of ELM-Based Disturbance Identification Model

To demonstrate the feasibility and effectiveness of the proposed method more intuitively, this paper compares it with the conventional classification methods of SVM and BPNN. The identification accuracy of each method under different SNR conditions and disturbance types is presented in

Table 2. Identification accuracy of each method under different SNR conditions and disturbance types.

Disturbance Signals		Identification Accuracy/%
		Proposed Method	SVM	BPNN
Voltage swells	SNR = 20 dB	97.9	95.5	94.5
	SNR = 30 dB	98.1	96.9	95.3
	SNR = 40 dB	99.4	98.6	97.6
Voltage sags	SNR = 20 dB	93.4	92.0	91.3
	SNR = 30 dB	95.3	93.4	92.2
	SNR = 40 dB	97.8	95.6	94.5
Voltage interruptions	SNR = 20 dB	95.4	94.9	93.1
	SNR = 30 dB	96.7	95.2	94.3
	SNR = 40 dB	97.7	96.5	93.2
Transient impulses	SNR = 20 dB	96.8	95.6	93.1
	SNR = 30 dB	97.4	96.2	94.7
	SNR = 40 dB	98.6	97.8	96.6
Transient oscillations	SNR = 20 dB	97.5	96.8	95.4
	SNR = 30 dB	98.6	97.1	96.3
	SNR = 40 dB	99.1	98.6	97.0

. The BPNN model has 6 neurons in the input layer, 12 neurons in the hidden layer, and 1 hidden layer, using sigmoid as the activation function. The learning rate was set to 0.01, and the number of iterations was set to 200. For the SVM model, the RBF kernel was used, with a penalty coefficient of 100, a γ value of 0.1, and a soft margin parameter set to 0.01.

Observing the above table, it becomes evident that the extreme learning machine (ELM) exhibits multiple advantages over conventional methods such as backpropagation neural networks (BPNN) and support vector machines (SVM) in the field of power quality disturbance classification. Firstly, in terms of training speed and efficiency, ELM demonstrates significant superiority. ELM is a fast single hidden-layer feedforward neural network learning algorithm. In power quality disturbance identification, ELM can be used as a classifier to categorize disturbance signals based on extracted features. ELM has extremely fast training speed and good generalization ability. Compared with traditional neural networks, ELM does not require iterative parameter adjustment, greatly reducing training time. Additionally, ELM is robust to high-dimensional features and noisy data. The training process of BPNN involves multiple iterations and weight adjustments, often requiring substantial computational resources and time. Conversely, ELM achieves a single training process through random initialization of input weights and biases, along with the use of analytical methods to solve output weights. This enables ELM to rapidly adapt to new data and produce classification results, particularly evident when dealing with large-scale datasets. Although SVM training is also relatively fast, it typically requires the selection of appropriate kernel functions and parameters, whereas ELM’s training process is more concise and efficient. It also should be noted that at the core of the LMD algorithm is its ability to adaptively decompose a complex multicomponent signal into a finite sum of amplitude-modulated and frequency-modulated signals. This means that it does not require pre-assumed or preset conditions for the signal but decomposes based on the signal’s inherent characteristics. This adaptability grants LMD significant flexibility in handling nonlinear and complex time series. During the decomposition process, LMD further calculates the instantaneous amplitude and frequency of each amplitude-modulated and frequency-modulated signal. This approach accurately reflects the dynamic characteristics of the signal, especially in the case of power quality disturbance signals, enabling the capture of abrupt changes and abnormalities. Simultaneously, the LMD algorithm gradually extracts harmonic components of the signal through iterative computation of its local mean and local extreme points. This aids in identifying different frequency components within power quality disturbance signals, providing crucial insights for subsequent disturbance classification and identification.

During the decomposition process, LMD further calculates the instantaneous amplitude and frequency of each amplitude-modulated and frequency-modulated signal. This approach accurately reflects the dynamic characteristics of the signal, especially in the case of power quality disturbance signals, enabling the capture of abrupt changes and abnormalities.

Simultaneously, the LMD algorithm gradually extracts harmonic components of the signal through iterative computation of its local mean and local extreme points. This aids in identifying different frequency components within power quality disturbance signals, providing crucial insights for subsequent disturbance classification and identification.

Secondly, ELM exhibits superior performance in terms of generalization ability. Generalization ability refers to a model’s ability to predict unseen data. Due to its random initialization and analytical solution methods during training, ELM is able to learn the inherent patterns and characteristics of data, resulting in good generalization performance. In contrast, BPNN is susceptible to local optimal solutions, which may compromise its generalization performance. While SVM possesses good generalization ability, its performance heavily depends on the choice of kernel functions and parameter adjustments.

Furthermore, from the perspective of parameter adjustment and model complexity, ELM maintains its advantage. BPNN requires adjustments to parameters such as weights, biases, and learning rates, often relying on extensive experimentation and experience. SVM, on the other hand, necessitates the selection of suitable kernel functions and parameters like penalty coefficients and kernel function parameters, also requiring a certain degree of skill and experience. Comparatively, ELM primarily involves adjusting the number of hidden layer nodes, a relatively straightforward parameter with intuitive effects on model performance. Additionally, the structure of the ELM model is relatively simple, facilitating ease of understanding and implementation.

Moreover, ELM demonstrates excellent stability and robustness. The random initialization and analytical solution methods employed during training render ELM insensitive to the choice of initial parameters, thereby enhancing its stability. Simultaneously, ELM exhibits a certain degree of robustness against noise and outliers, effectively resisting data interference and fluctuations.

Finally, from a practical application perspective, ELM holds broad prospects in the field of power quality disturbance classification. With the development of smart grids and distributed generation in novel power systems, the issue of power quality disturbances is becoming increasingly severe. Rapid and accurate identification and classification of these disturbances are crucial for ensuring the stable operation of power systems. By leveraging its fast learning speed, good generalization ability, and straightforward parameter adjustment, ELM efficiently, accurately, and stably handles complex power quality disturbance data, providing robust technical support for the stable operation of power systems.

6. Conclusions

Electricity is a secondary energy source closely related to people’s livelihood. With the continuous acceleration of social informatization and industrial automation, China’s social electricity consumption has been increasing year by year, posing higher demands on power quality. Therefore, it is crucial to accurately detect and classify various power quality disturbances, serving as the prerequisite and foundation for subsequent governance. This paper analyzes and studies the methods of power quality disturbance detection and classification and applies the combination of WPT and LMD transformations to the detection of disturbances. Based on the detection, the ELM algorithm is introduced to ultimately achieve the classification and recognition of various disturbances.

Although the extreme learning machine has demonstrated good performance, there is still room for optimization. For instance, further improvements in classification accuracy and generalization ability can be achieved by exploring more advanced initialization methods, optimizing the selection of hidden layer nodes, and exploring more efficient activation functions. Additionally, feature selection and extraction are crucial for power quality disturbance identification. Future research can explore how to combine the extreme learning machine with the development of more advanced feature extraction and selection methods, thereby effectively extracting features that contribute to disturbance classification while eliminating redundant features and enhancing the efficiency of the classifier.