Physics-inspired time-frequency feature extraction and lightweight neural network for power quality disturbance classification

Abstract

This study proposes a lightweight and efficient classification method for Power Quality Disturbances (PQDs) using the PowerMobileNet model, which combines the S-transform for time-frequency feature extraction and the MobileNetV3-CBAM neural network for enhanced classification performance. Extensive experiments demonstrate that PowerMobileNet achieves a prediction accuracy of 99.33%, significantly surpassing traditional Convolutional Neural Networks (CNNs) at 97.07% and MobileNetV3-SE at 98.58%. Compared to other state-of-the-art models, PowerMobileNet outperforms KELM (97.4%), SqueezeNet (99.0%), ShuffleNet V2 (98.6%), and AlexNet (98.3%) in terms of classification accuracy. Additionally, it exhibits superior robustness under various signal-to-noise ratio (SNR) conditions, maintaining high accuracy even at low SNR levels (e.g., 90% accuracy at 20 dB). The model’s parameter count is drastically reduced to 374,632 (1.43 MB), compared to the traditional CNN’s 112,094,345 (427.61 MB), making it highly suitable for resource-constrained environments. Furthermore, PowerMobileNet demonstrates the shortest runtime, with a training duration of 925 s and a classification time of 0.57 s. These results validate the effectiveness and efficiency of PowerMobileNet for real-time PQD classification, offering significant potential for practical power quality monitoring applications.

1 Introduction

In modern power systems, the rapid development of renewable energy generation, along with the widespread adoption of distributed generation and microgrid control strategies, has introduced a substantial number of nonlinear signals into the power system [1, 2]. From a physics perspective, the intermittency and volatility of wind and photovoltaic power generation are rooted in the inherent variability of natural energy sources. Wind speeds and solar irradiance fluctuate over time, leading to voltage fluctuations [3, 4], flicker, and harmonic distortion in the electrical domain. These phenomena can be understood through the lens of electromagnetic theory and signal processing principles, which highlight the complex interactions between renewable energy sources and the power grid [5–7]. Furthermore, the power electronic converters associated with these energy sources are highly susceptible to PQDs, such as harmonic distortion and voltage imbalance [8]. This susceptibility can be attributed to the fundamental principles of power electronics, where the conversion of electrical energy between different forms (e.g., AC-DC, DC-AC) introduces nonlinearities and potential instabilities into the system. The frequent occurrence of power quality events not only causes significant inconvenience to users but also results in substantial economic losses [9]. From a physics standpoint, accurately identifying and classifying PQDs is crucial for ensuring the stable operation of microgrids and the safe functioning of related equipment [10, 11]. This involves the application of advanced signal processing techniques and machine learning algorithms to extract meaningful features from complex, nonlinear signals. The underlying physics of these disturbances provides a foundation for developing robust and efficient detection methods, which are essential for maintaining the integrity and reliability of modern power systems.

However, PQDs in microgrids are often highly complex and exhibit multiple characteristics, making feature extraction a fundamental prerequisite for effective disturbance classification [12–15]. Traditional detection methods rely on manual operations, such as using oscilloscopes, multimeters, and power quality analyzers, whose efficiency and accuracy are increasingly inadequate for the demands of modern power systems. In contrast, fast and accurate intelligent detection methods not only reduce labor costs but also significantly mitigate equipment degradation and system failures caused by power quality issues. Therefore, developing an efficient and precise PQD detection algorithm is essential not only for minimizing production costs but also for its substantial practical significance and broad application prospects.

Regarding feature extraction, the main methods include Fast Fourier Transform (FFT) [17], Wavelet Transform [4], S-Transform [18], Hilbert-Huang Transform (HHT) [19], Short-Time Fourier Transform (STFT) [20], Singular Value Decomposition (SVD) [21], and Kalman Filtering (KF) [22]. The STFT has a fixed window length and shape, which limits its ability to simultaneously capture high-frequency and low-frequency signal characteristics. Although Wavelet Transform enables multi-scale analysis, the relationship between its transformation scales and frequencies is fixed, making flexible adjustments challenging. Additionally, both SVD and Kalman Filtering lack the capability to describe signal features in the frequency domain.

In contrast, S-Transform, which integrates the advantages of both Wavelet Transform and FFT as a reversible time-frequency analysis technique, has gained widespread application in PQD feature extraction in recent years [23]. By employing an analysis window that adapts to frequency variations, S-Transform provides frequency-dependent resolution [18], effectively overcoming the fixed-resolution limitation of STFT in handling high- and low-frequency signals [24]. Compared to Wavelet Transform, S-Transform not only expands its application scope but also significantly reduces sensitivity to noise [25]. This is particularly beneficial in complex power systems with substantial noise interference, as it enables more accurate extraction of time-frequency features, offering superior temporal and spectral resolution. These characteristics make S-Transform particularly advantageous for analyzing nonlinear, non-stationary, and transient PQDs, thereby providing more reliable technical support for power quality monitoring and fault diagnosis [11, 26].

In the field of PQD classification, machine learning and deep learning methods have been extensively studied and applied. Traditional machine learning techniques, such as Support Vector Machines (SVM) [27], Decision Trees [28], and Bayesian Classifiers [29], are widely used due to their efficiency and interpretability in handling classification tasks. However, these methods exhibit certain limitations when dealing with complex PQD signals. For instance, although SVM achieves high classification accuracy, its computational burden during parameter optimization is significant, particularly when processing large-scale datasets, leading to prolonged training times that fail to meet real-time requirements. Additionally, Decision Trees and Bayesian Classifiers tend to suffer from overfitting when handling high-dimensional features and complex signals, thereby reducing classification performance. Another common drawback of these conventional approaches is their reliance on manual feature extraction, which not only increases preprocessing complexity but may also result in insufficient or redundant feature selection, further impacting classification efficiency.

In recent years, the rise of deep learning has presented new opportunities for PQD classification. CNNs, as a powerful deep learning model, have been widely applied in image recognition, signal processing, and related fields [30]. By leveraging convolutional and pooling layers, CNNs can automatically extract features from signals, reducing the need for manual feature engineering while enhancing classification accuracy to some extent [31, 32]. However, CNNs also face challenges when applied to PQD signals. First, CNN models are typically highly complex and require a large number of parameters for training, which not only increases computational resource consumption but also prolongs training time, making real-time applications difficult. Second, CNNs struggle with distinguishing highly similar disturbance signals (e.g., interruptions and voltage sags), often leading to misclassification. This issue is further exacerbated by the potential introduction of redundant, non-essential features during feature extraction, which reduces classification efficiency.

In parallel, Transformer-based models, such as Vision Transformers (ViTs) and Swin Transformers, have recently emerged as competitive alternatives to CNNs in image and signal classification tasks [33, 34]. These models leverage self-attention mechanisms to capture global dependencies across the input, demonstrating strong performance in various vision applications [35]. However, despite their promising results, Transformer models exhibit several limitations in the context of PQD classification. First, they typically require substantial computational resources and memory, which hampers their feasibility for real-time deployment in embedded or resource-constrained power systems. Second, while Transformers excel at modeling global structures, they may overlook subtle local disturbances that are critical for fine-grained classification of PQD types. This limitation affects their robustness and accuracy when applied to transient and high-noise scenarios frequently encountered in real-world power systems. Similarly, popular deep learning models such as BiLSTM [36], GRU [37], and Deep Belief Networks (DBN) [38] improve classification accuracy but face challenges related to model size and computational speed.

To overcome the limitations of traditional CNNs and Transformer-based models in PQD classification, researchers have increasingly turned to lightweight neural networks such as EfficientNet (B0), GhostNet, and MobileNetV3, which have attracted considerable attention in recent years due to their efficiency and compact design [39]. However, each exhibits varying degrees of limitations in terms of feature extraction capability, architectural flexibility, or deployment adaptability. Table 1 lists the comparative analysis and shows their differences.

From Table 1, it is evident that EfficientNet, despite its high accuracy, has a complex structure and challenges in integrating attention mechanisms flexibly. GhostNet, while extremely lightweight, shows slightly lower accuracy and high module encapsulation, hindering further improvements. MobileNetV3 strikes a balance between efficiency and performance, but further refinement is needed.

To address the limitations of traditional methods in PQD classification, we propose a lightweight deep learning model, PowerMobileNet, based on an improved MobileNet V3 architecture. Compared to CNNs, BiLSTMs, and other deep learning models, MobileNet offers advantages in computational efficiency and parameter reduction. However, its feature extraction capabilities remain insufficient. To enhance this aspect, we incorporate the Convolutional Block Attention Module (CBAM). This integration does not significantly increase computational complexity, as CBAM is relatively lightweight and can be implemented using simple convolutional and pooling operations. As a result, MobileNet retains its lightweight nature while benefiting from enhanced feature extraction. Consequently, PowerMobileNet achieves high classification accuracy while substantially reducing model parameters and computational complexity, making it more suitable for real-time PQD classification tasks.

The experimental results demonstrate that PowerMobileNet achieves a prediction accuracy of 99.33%, significantly surpassing traditional CNN (97.11%) and MobileNet V3-SE (98.58%). The model excels under high SNR conditions and maintains high classification accuracy even in low-SNR environments, validating its effectiveness and efficiency in practical applications. Through these improvements, PowerMobileNet not only addresses the challenges of high computational complexity and poor real-time performance associated with traditional methods but also enhances model performance and applicability by incorporating a lightweight architecture and an optimized loss function.

The structure of this paper is organized as follows: Section 1 reviews related work on PQD classification. Section 2 provides a detailed description of the feature extraction process, the proposed method, and its key modules. Section 3 presents the experimental results and compares them with state-of-the-art algorithms to validate the effectiveness of the proposed approach. Finally, Section 4 concludes the study and discusses future research directions.

2 Models

2.1 S-transform and feature extraction

The S-transform is a reversible time-frequency analysis method that introduces a Gaussian window function into the Fourier transform framework [44]. This allows the analysis window’s width to vary with frequency, thereby overcoming the fixed window width limitation of the short-time Fourier transform. The S-transform exhibits multi-resolution analysis capabilities, making it suitable for analyzing nonlinear, non-stationary, and transient PQD signals. The continuous S-transform is defined as shown in Equation 1 below:where represents the input signal, and is the Gaussian window function, defined as shown in Equation 2:

2.2 The construction of the MobileNetV3-CBAM model

To enhance the precision and efficiency of PQD classification, we employed the lightweight neural network model MobileNet V3, which is fundamentally based on depthwise separable convolutions [45]. By decomposing standard convolutions into depthwise convolutions and pointwise convolutions, the former reduces spatial computation, while the latter decreases channel computation, thereby significantly reducing both parameter count and computational cost. Additionally, the model integrates the CBAM, which focuses on critical features across channel and spatial dimensions, further improving the model’s accuracy and representational capacity [38]. The structure of CBAM is shown in Figure 1.

FIGURE 1

Specifically, the traditional MobileNet integrates the Squeeze-and-Excitation (SE) module, which focuses solely on channel-level features while neglecting spatial dimensions. In contrast, the CBAM module processes features across both channel and spatial dimensions while maintaining low computational overhead. The channel attention module assigns a weight to each channel by analyzing the significance of the input features along the channel dimension. Initially, the input feature undergoes global average pooling (GAP) and global max pooling (GMP), resulting in two global feature description vectors. These vectors are processed through a shared multilayer perceptron (MLP), their outputs are then summed, and a Sigmoid activation function is applied to generate the channel attention map , represented as .

Finally, the original input feature is weighted by the channel attention map to obtain the enhanced feature , as shown in Equation 3:

After generating the channel-enhanced features , the spatial attention module then focuses on the prominent regions of the features along the spatial dimension. Initially, the input feature undergoes both global average pooling and global max pooling to obtain two spatial feature maps. These two maps are concatenated along the channel dimension to form a comprehensive representation. This representation is then processed through a 7 × 7 convolution operation to capture local spatial correlations. Finally, a Sigmoid activation function is applied to generate the spatial attention map , represented as shown in Equation 4:

Finally, the channel-enhanced feature is weighted by the spatial attention map to generate the final enhanced feature , as shown in Equation 5:

The MobileNet V3 model designed in this study consists of a series of Inverted Residual Blocks and Dense Layers, as shown in Table 2.

The initial layer employs a Conv2D 3 × 3 convolution with 3 input channels and an output size of 112 × 112, using the ReLU activation function and a stride of 2. This is followed by multiple Inverted Residual Blocks, with the number of input channels ranging from 16 to 40, and the output size gradually decreasing. Finally, a GlobalAveragePooling2D layer is applied to compress the feature map size to 1 × 1. The last two layers are fully connected layers: the first layer uses the Hard-swish activation function, with 1 × 1 input channels and an output size of 1,280; the second layer applies the Softmax activation function, with 1,280 input channels, and outputs probability scores for 9 classes. MobileNetV3 block is shown in Figure 2.

FIGURE 2

The overall model construction of PowerMobileNet is shown in Figure 3.

FIGURE 3

Regarding the loss function, cross-entropy loss optimizes model performance by calculating the difference between the predicted probability distribution and the ground truth labels. However, the traditional cross-entropy loss function may fail to adequately account for data diversity, particularly when data points lack rich features, leading the model to generate random predictions. To address this issue, we adopt the Bias Loss function, which dynamically adjusts the weight of each data point, allowing the model to focus on samples with distinctive features during the optimization process. It is defined as follows, with Equation 6 representing the bias loss and Equation 7 defining the function z(v_i):here, N represents the number of samples, and K is the number of categories. The term corresponds to the ground truth label encoded using one-hot representation, while denotes the predicted probability of sample belonging to class j. The key innovation lies in introducing the scaling function , where represents the feature variance of sample . The parameters and are tunable hyperparameters designed to regulate the dynamic range of the scaling function. A higher value of increases the emphasis on samples with higher feature variance, thus focusing the model more on these samples during optimization. Conversely, provides a baseline offset, ensuring that samples with low feature variance are not completely ignored. By carefully tuning these parameters, we can control how much emphasis the model places on samples with different feature variances, which is crucial for improving the model’s ability to generalize from the training data to unseen data.

3 Experimental design

3.1 Data sample

Since the performance of deep learning networks heavily depends on the quantity and quality of training samples, it is crucial to have as many high-quality training data as possible. Adequate and well-annotated data can significantly enhance the generalization ability of the model, reducing the risk of overfitting and improving its robustness in real-world applications [46]. To validate the effectiveness of PowerMobileNet, we therefore generated nine different types of PQD signals using MATLAB R2024a, adhering to the IEEE 1159–2019 standard [47], referring to Li et al. and Khetarpal et al. ’s research [48, 49]. The nine types of signals include: Normal, Harmonics, Interruption, Sag, Swell, Flicker, Sag+Harmonics, Swell+Harmonics, and Transient Oscillation. The mathematical model of PQD is shown in Table 3. The original signal, the image after S transformation and the image after CBAM processing are shown in Figure 4. The MATLAB rand function was used, with a base frequency of 50 Hz and a sampling frequency of 3.2 kHz. The generated signals exhibit random amplitude and random disturbance occurrence times, within specified parameter ranges and sampling durations. After S-transformation, the image data is divided into training, testing and validation sets in a 4:1:1 ratio, with 9,000 samples for training, 2,250 samples for testing and 2,250 samples for validation, ensuring balanced class distribution.

FIGURE 4

To train the PowerMobileNet model, we used the SGD optimizer with a learning rate of 0.01 and momentum set to 0.9. The model was trained for 100 epochs with a batch size of 32. All input images were resized to 224 × 224 × 3 and normalized to the range [0, 1]. During training, data augmentation was applied including shear transformation (range: 0.2), zoom (range: 0.2), and horizontal flipping to improve generalization and prevent overfitting.

3.2 Comparison of the model with mainstream methods

Figures 5, 6 illustrate the variation of accuracy and loss function over the number of iterations for the compared models. It can be observed that PowerMobileNet stabilizes after approximately 25 epochs, with relatively minor fluctuations after convergence. In contrast, CNN exhibits poor convergence performance, with higher loss values and significant oscillations during training. Even after 100 epochs, its accuracy only hovers around 97%. When MobileNet V3 integrates the CBAM module, the validation accuracy steadily approaches 98.5%, and the loss function stabilizes around 0.10 after 40 iterations. Furthermore, replacing the cross-entropy loss function with Bias Loss and incorporating the CBAM module further improves classification accuracy by 0.76% and reduces the loss by 0.07. These results demonstrate that introducing the Bias Loss function mitigates random prediction issues in the optimization process, highlighting the robustness of PowerMobileNet and validating the effectiveness of the proposed method.

FIGURE 5

FIGURE 6

Figure 7 compare the confusion matrices of CNN, MobileNet-SE, and PowerMobileNet. The CNN model selected for comparison consists of 12 layers, similar to the layer count of the MobileNetV3 used in this study. It includes two convolutional blocks, each containing convolutional layers, LeakyReLU activation layers, and max-pooling layers. The convolutional output gradually increases to 192 channels. A flattening layer transforms the output into a fully connected layer with 4,096 neurons, followed by a Softmax activation function for 9-class classification. We added 30 dB white noise to each simulated signal to simulate random disturbances. As shown in Table 4, despite the presence of disturbance, PowerMobileNet achieved the highest prediction accuracy of 99.33%.

FIGURE 7

To provide a more comprehensive and rigorous evaluation and to validate the effectiveness of the proposed approach, we conducted comparative experiments between MobileNet-CBAM and state-of-the-art methods. These methods include the optimized KELM model [51] after feature vector extraction, as well as deep learning models such as SqueezeNet [50], ShuffleNet V2 [52], and AlexNet [53]. All experiments were performed on the same computing platform, which consists of an NVIDIA GeForce RTX 3060 GPU and an AMD Ryzen 7 5800H CPU, with Jupyter Notebook 7.0.8 as the programming environment. The Table 4 summarizes the average classification results of different models on various types of PQD signals over 10 experimental runs. The experimental results indicate that KELM and AlexNet require substantial memory and computational resources when processing large-scale PQD signal data, resulting in inefficiencies. In contrast, SqueezeNet and ShuffleNet V2 employ Fire Modules and layered convolution [54], respectively, to reduce the number of parameters, thereby improving test accuracy while maintaining a more compact model. The results in the table demonstrate that PowerMobileNet achieved the highest classification accuracy, outperforming KELM, SqueezeNet, ShuffleNet V2, and AlexNet by 1.95%, 0.30%, 0.71%, and 1.02%, respectively. Moreover, PowerMobileNet exhibited the shortest runtime, with a training duration of 925 s and a classification duration of 0.57 s, further validating its superior performance in PQD signal classification tasks.

3.3 The impact of noise on classification results

In real-world scenarios, PQD signals are inevitably affected by various unpredictable factors, leading to different levels of noise [48]. To demonstrate the robustness and generalizability of the proposed algorithm across different environments, we introduced noise with SNR of 40 dB, 30 dB, and 20 dB into the original signals and compared the classification performance. As shown in Table 5, the classification accuracy of PowerMobileNet exhibits a decreasing trend as the SNR decreases. However, even in a high-noise environment with an SNR of 20 dB, the lowest classification accuracy remains around 90%, highlighting its superior noise resistance.

Figure 8 also presents the performance of the three models under varying SNR in the simulation dataset. Experiments conducted under four different conditions demonstrated that the MobileNet-CBAM model has fewer misclassified PQD instances, indicating strong robustness and exceptional performance.

FIGURE 8

3.4 Ablation study

To quantitatively evaluate the contribution of the CBAM module to model performance, we conducted an ablation study by comparing the classification accuracy of two configurations: PowerMobileNet and its variant without CBAM module. The results are summarized in Table 6.

As shown, the inclusion of CBAM results in a 1.7% improvement over the baseline with a minor time increase. This demonstrates that CBAM effectively enhances the focus on relevant features in both spatial and channel dimensions, thereby improving classification performance.

3.5 The comparison of model size and parameter count

In Table 7, we can clearly observe the differences in the parameter count of each model. When compared with CNNs that have similar layers and functionality, the MobileNetV3-CBAM significantly reduces computational complexity and parameter count. Moreover, while maintaining parameters comparable to MobileNetV3-SE, MobileNetV3-CBAM not only improves accuracy but also better satisfies the practical requirements for deployment on mobile devices and embedded systems.

3.6 Validation on real-world dataset

To evaluate the real-world performance and generalization capability of PowerMobileNet, we conducted experiments on the publicly available SEED Power Quality Disturbance Dataset (SEED-PQD-v1), which is available at https://www.kaggle.com/datasets/sumairaziz/seed-power-quality-disturbance-dataset. This dataset contains 17 power disturbance classes, each with 1,000 signals sampled at 5 kHz. We compared PowerMobileNet against six representative models: CNN, MobileNet-SE, KELM, SqueezeNet, ShuffleNet V2, and AlexNet. The experimental conditions were exactly the same as the previous setup. The classification accuracy for each class and the overall average are reported.

As presented in Figure 9, PowerMobileNet achieved the highest overall classification accuracy (96.78%) across all 17 power quality disturbance (PQD) classes in the SEED-PQD-v1 dataset. This significantly outperforms the traditional CNN (88.03%), classical machine learning method KELM (85.11%), and several lightweight or well-established deep models including MobileNet-SE (91.91%), SqueezeNet (89.91%), ShuffleNet V2 (92.45%), and AlexNet (91.22%).

FIGURE 9

In detail, for PQ2 (Sag), it outperforms CNN by 13.0% and ShuffleNet V2 by 4.3%. In PQ3 (Swell), PowerMobileNet achieves an improvement of 19.9% over CNN and 3.6% over ShuffleNet V2. Notably, PowerMobileNet exhibits improvement in several challenging PQD classesinvolving compound or transient disturbances. For instance, for PQ11 (Flicker with Sag) and PQ15 (Sag with Harmonics), the proposed model surpasses CNN by 20.5% and 16.3%, respectively, while also outperforming ShuffleNet V2 and AlexNet by 11.9% and 9.2%. These categories typically involve compound or transient features that are difficult to model using standard CNNs or shallow classifiers.

Furthermore, compared to models such as MobileNet-SE and ShuffleNet V2, which are known for their computational efficiency, PowerMobileNet still yields a clear 4%–5% accuracy gain on average, with only a modest increase in training time. These results validate the architectural enhancements introduced by CBAM and Bias Loss components.

4 Conclusion

In this study, we successfully developed a highly efficient and lightweight method for PQD classification using the PowerMobileNet model. The proposed approach integrates the S-transform for robust time-frequency feature extraction and the MobileNetV3-CBAM architecture for enhanced classification accuracy and efficiency. We compared PowerMobileNet with mainstream models in terms of accuracy, loss function, noise impact, model size and number of parameters. The experimental results achieved a classification accuracy of 99.33%, significantly surpassing traditional CNN (97.07%), MobileNetV3-SE (98.58%), and other state-of-the-art models such as KELM (97.4%), SqueezeNet (99.0%), ShuffleNet V2 (98.6%), and AlexNet (98.3%). The model also demonstrates remarkable robustness under varying SNR conditions, maintaining high accuracy even at low SNR levels (e.g., 90% accuracy at 20 dB). Additionally, PowerMobileNet achieves a substantial reduction in computational complexity, with a total parameter count of 374,632 (1.43 MB) compared to traditional CNNs (112,094,345 parameters, 427.61 MB). This efficiency is further evidenced by its short training duration of 925 s and classification time of 0.57 s. This makes it particularly well-suited for deployment in resource-constrained environments. Our research provides an efficient and accurate tool for power quality monitoring, indicating great potential for practical applications in power systems. Future research will focus on further optimizing the model structure and validating its generalization ability on broader datasets. In addition, we plan to deploy the model on embedded platforms such as Raspberry Pi or Jetson Nano in our subsequent research, in order to systematically evaluate its latency, memory consumption, and real-time performance, thereby promoting the transition of the algorithm from experimental validation to practical deployment in real-world power monitoring systems.

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