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: S t , f = ∫ − ∞ + ∞ h τ w τ − t , f e − j 2 π f τ d τ (1) where h τ represents the input signal, and ω τ − t , f is the Gaussian window function, defined as shown in Equation 2: ω τ − t , f = f 2 π e − τ − t 2 f 2 2 (2)

In this study, the S-transform is employed to extract the time-frequency features of PQD signals. The detailed steps are as follows:

1. Signal Preprocessing: The collected power signals are normalized to adjust their amplitudes to the range of [0,1].

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.

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 F 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 M c , represented as M c = σ MLP GAP F + MLP GMP F .

Finally, the original input feature F is weighted by the channel attention map M c to obtain the enhanced feature F ′ , as shown in Equation 3: F ′ = M c · F (3)

After generating the channel-enhanced features F ′ , the spatial attention module then focuses on the prominent regions of the features along the spatial dimension. Initially, the input feature F ′ 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 M s , represented as shown in Equation 4: M s = σ f 7 × 7 GAP F ; GMP F (4)

Finally, the channel-enhanced feature F ′ is weighted by the spatial attention map M s to generate the final enhanced feature F ″ , as shown in Equation 5: F ″ = M s · F ′ (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.

The overall model construction of PowerMobileNet is shown in 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 ): L b i a s = − 1 N ∑ i = 1 N ∑ j = 1 K z v i y i j ⁡ log ⁡ f j x i ; θ (6) z v i = exp v i × α − β (7) here, N represents the number of samples, and K is the number of categories. The term y i j corresponds to the ground truth label encoded using one-hot representation, while f j x i ; θ denotes the predicted probability of sample x i belonging to class j. The key innovation lies in introducing the scaling function z v i , where v i represents the feature variance of sample x i . The parameters α and β are tunable hyperparameters designed to regulate the dynamic range of the scaling function. A higher value of α increases the emphasis on samples with higher feature variance, thus focusing the model more on these samples during optimization. Conversely, β 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.

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.

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.

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 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%.

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.

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.

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.

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.

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%).

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.