The sophisticated nature of PQD signals, characterized by their nonlinearity and non-stationarity, necessitates a robust feature extraction method to yield accurate disturbance identification. The empirical mode decomposition (EMD) technique is widely utilized for this purpose, enabling the extraction of multiple intrinsic mode functions (IMFs) from PQD signals. These IMFs are instrumental in isolating various frequency components, thereby providing detailed insights into disturbances and facilitating the analysis of non-stationary signals. Nevertheless, a significant limitation of the EMD method is its susceptibility to mode mixing, a phenomenon that can introduce errors in the decomposition of complex PQD signals. To mitigate this issue and enhance the accuracy of EMD, the ensemble empirical mode decomposition (EEMD) is developed. The EEMD approach augments the decomposition efficacy by averaging the results from numerous EMD iterations, each with a unique instantiation of white noise added to the PQD signal.

For the PQD signal x(t), the EMD is carried out M times. In each EMD trial, x(t) is superimposed with an independent white noise w _m (t), which can be expressed as shown in Eq. 1. x m t = x t + w m t , m = 1,2 , … , M . (1)

After the EMD operation, x _m (t) is decomposed into multiple IMFs I _mp (t) and a residual r _m (t). The number of IMFs is denoted by K, and the decomposition result can be described as shown in Eq. 2. x m t = ∑ p = 1 K I m p t + r m t . (2)

Then, to eliminate the influence of white noise on real IMF components, the mean values of the corresponding IMFs and residuals are computed, as shown in Eqs 3, 4, respectively. I M F p t = 1 M ∑ m = 1 M I m p t , (3) r e t = 1 M ∑ m = 1 M r m t , (4) where IMF _p (t) denotes the pth IMF component after the EEMD operation.

Based on these IMF components and the residual, the EEMD result of the original PQD signal x(t) can be further obtained as shown in Eq. 5. x t = ∑ p = 1 K I M F p t + r e t . (5)

Relative to the EMD method, the EEMD technique offers an enhanced ability to diminish noise impact and alleviate the mode mixing issue, leading to a more precise extraction of PQD signal modes. However, the typical empirical approach to determining the number of IMFs can introduce artifacts or omit vital information when handling complex PQD signals. To address this, the novel optimized mode decomposition strategy is introduced. This method adaptively configures the number of IMFs based on the specific characteristics of the PQD signal, thereby optimizing the decomposition process and ensuring a more accurate signal representation.

In essence, EEMD builds upon the foundation of the EMD method, with each IMF correlating to a specific frequency range. Within this range, EEMD effectively extracts the inherent oscillatory elements of the PQD signal (Prosvirin et al., 2019). Consequently, EEMD’s operation can be likened to a form of band-pass filtering, where signal energy divergent from the central frequency is attenuated. It follows that the cumulative energy across all IMFs may decrease if the number of decompositions is either excessively high or low. Furthermore, the aggregate energy of the IMFs is invariably less than that of the original PQD signal.

Considering this analysis, an effective selection method of the decomposition number is presented. This method involves comparing the total energy of all IMFs subsequent to the EEMD process. The cornerstone of the optimized mode decomposition technique is the dynamic adjustment of the decomposition number K, aiming to maximize the total IMF energy. This enhancement renders the original EEMD more adaptable, thereby significantly bolstering the precision of disturbance identification across a spectrum of complex PQD signals.

The PQD signal is denoted as x(t), and the initial total energy can be defined as follows: E x = ∑ j = 1 S x 2 j , (6) where S represents the number of sampling points and x(j) represents the amplitude of x(t) at different sampling points.

After the EEMD operation, multiple mode signals are obtained, and the total energy of these IMFs can be expressed as follows: E I M F = ∑ p = 1 K E I M F p , (7) and there is E I M F p = ∑ j = 1 S I M F p 2 j , (8) where E (IMF) represents the energy summation of the IMF signals when the corresponding decomposition number is K and IMF _p (t) is the pth IMF signal.

Based on Eqs 6–8, the energy ratio between the IMFs and the original PQD signal can be further computed, which is given as shown in Eq. 9. ξ = E I M F E x × 100 % . (9)

In OMD, when the sampling frequency and sampling period are determined, the corresponding sampling points S are fixed. Namely, the original disturbance energy E(x) is a fixed value. Therefore, once the energy ratio ξ reaches the maximum, the corresponding total energy of all IMFs also obtains the maximum, which demonstrates that the decomposition number K is optimal.

After the OMD-based feature extraction process, an improved attention convolutional neural network model is further proposed to identify different complex PQD signals based on the IMFs provided by OMD.

As a quintessential archetype of deep learning, convolutional neural networks (CNNs) are distinguished for their superior feature extraction proficiency. The CNN architecture uniquely integrates feature extraction with classification, thereby optimizing the utilization of informational resources. This dual capability has propelled its adoption across a broad spectrum of applications, including image recognition, fault diagnosis, and natural language processing. Complementing its practical applications, scholarly inquiries have substantiated CNNs’ effectiveness in PQD signal identification, consistently delivering a commendable performance. Consequently, this paper selects the CNN as the primary model for PQD signal classification, leveraging its validated strengths in this specialized area of study.

Generally, the CNN contains the input layer, convolutional layer, pooling layer, fully connected layer, and output layer. When it is used for PQD identification in this article, the input layer is the IMFs of the PQD signals. The feature information of IMFs is extracted by the convolutional layer. Then, the pooling layer is utilized to reduce feature dimensions to improve network efficiency. Thus, the pooling layer is also called the downsampling layer. The classification performance of the CNN is usually reflected by combining multiple convolutional layers and pooling layers. The fully connected layer is used to combine the extracted features in a nonlinear manner and then transfer the feature information to the output layer. Namely, the fully connected layer is not expected to have feature extraction ability, but it attempts to use existing higher-order features to complete the identification goal. Finally, the output layer outputs the classification result of the CNN.

For some simple PQD signals, a traditional CNN can typically yield satisfactory classification outcomes by increasing the count of the convolutional and pooling layers. However, this approach tends to escalate processing time, making it challenging to fulfill the real-time processing demands of PQD detection. Furthermore, when it comes to complex PQD signals, classification accuracy may suffer. To achieve a balance between high identification accuracy and expedient detection time, this work introduces an advanced attention convolutional neural network. This innovative model intends to significantly amplify the inherent feature extraction prowess of the CNN. This approach aims to deliver precise classification of PQD signals while adhering to the time-sensitive requirements of real-time detection.

In the improved attention convolutional neural network, the enhancement of feature extraction is approached from two strategic angles. First, the deployment of multiple convolutional kernels of varying sizes supplants the traditional singular kernel, enabling the capture of both global and local signal characteristics. This variety allows for the integration of diverse feature sets, culminating in a composite feature that encapsulates more detailed information.

Second, the integration of an attention module subsequent to the convolutional layers serves a pivotal role. Its primary function is to direct the IACNN’s focus toward salient features of disturbances while diminishing the influence of non-essential elements. The objective is to streamline the flow of pertinent information within the model. The configuration of the proposed IACNN architecture is illustrated in Figure 1, with an in-depth exposition provided in the subsequent sections.

Instead of the single convolution kernel, the sizes of 3 × 3 and 7 × 7 are used to obtain the local and global information, respectively. Taking the 3 × 3 convolution as an example, the output of the convolutional layer can be determined as shown in Eq. 10. Z c 3 = f W p * X + b p , (10) where W ^p denotes the weight of the convolutional kernel in the pth layer, b ^p is the corresponding bias, X is the input, * denotes the convolution operator, and f is the activation function. In this article, the scaled exponential linear unit (SELU) activation is used in both the convolution layers and fully connected layers. The description of SELU can be expressed as shown in Eq. 11. S E L U x = λ x ,  if  x > 0 α e x − α ,  if  x ≤ 0 , (11) where λ = 1.0507 denotes the scale constant and α is a constant.

In addition, to increase the convergence speed and accelerate the network stability, batch normalization is added in the convolutional layer, and the convolution result is normalized to a Gaussian distribution before the activation operation.

After the convolutional layer, motivated by the work of Woo et al. (2018), the attention modules are placed to emphasize the important disturbance feature. The attention modules consist of channel attention and spatial attention modules, where channel attention is used to reflect ‘what’ is meaningful, and spatial attention is used to find ‘where’ is an informative part. These two attention modules are placed as shown in Figure 2. The PQD feature extracted by the convolutional layer is first processed by the channel attention. The description of the channel attention can be expressed as shown in Eq. 12. M c Z c 3 = σ M L P A v g P o o l Z c 3 + M L P M a x P o o l Z c 3 , (12) where Z _c3 is the output of convolution 3 × 3, AvgPool and MaxPool represent the average-pooling and max-pooling operations, respectively, MLP denotes the multi-layer perceptron, and σ represents the sigmoid function.

After the channel attention, the output of the disturbance feature is adjusted as shown in Eq. 13. Z c 3 ′ = M c Z c 3 ⊗ Z c 3 , (13) where ⊗ represents the element-wise multiplication.

Next, the new disturbance feature is processed by the spatial attention, which can be described as shown in Eq. 14. M s Z c 3 ′ = σ C o n v n × n A v g P o o l Z c 3 ′ ; M a x P o o l Z c 3 ′ , (14) where Conv _n×n denotes the convolutional layer with the size of n × n.

The attention layer output can be obtained after the spatial attention, which can be expressed as shown in Eq. 15. Z c 3 ′ ′ = M c Z c 3 ′ ⊗ Z c 3 ′ . (15)

Then, the pooling layer is deployed for downsampling, and the pooling size is 2 × 2. The convolution, attention, and pooling are carried out twice in the proposed IACNN. After that, the features from convolutions 3 × 3 and 7 × 7 are fused to provide more comprehensive disturbance information. In this way, the IACNN can further improve its classification performance. Finally, the IACNN can output the classification result after the fully connected (FC) layer. The number of FC layers is set to five in the proposed IACNN model.

The features extracted by the OMD method directly affect the classification accuracy. In OMD, the decomposition number ranges from 6 to 10, and the specific number is determined based on the energy ratio of IMFs. Taking one complex PQD signal C27 as an example to explain the set of decomposition numbers for OMD, when the decomposition number ranges in OMD, different energy ratios of IMFs are listed in Table 2.

From Table 2, it can be seen that the energy ratio has a lower value when the IMF number is small, which demonstrates that the PQD signal is not fully decomposed. When the IMF number is over eight, the energy ratio decreases with the increase in its number, indicating some false components are generated. Therefore, the optimal number of OMD is set to eight for proper decomposition. The corresponding decomposition result is shown in Figure 3. It is worth mentioning that IMF0 denotes the original C27 signal and RES denotes the residual. In this way, different PQD signals can be set the optimal decomposition number.

In addition, to verify the improvement of OMD and the IACNN for the PQD classification performance, the accuracy of OMD–IACNN is compared with other combination methods, including EEMD–IACNN, OMD–ACNN, and EEMD–CNN. It is important to note that the ACNN model differs from the IACNN in that it utilizes a singular convolutional approach as opposed to the latter’s advanced attention-fused convolutional strategy. For the input features of the various CNN architectures, a fixed dimension of 640 × 10 was established, where 640 represents the length of IMFs and 10 represents the highest decomposition level. In instances where the decomposition level of OMD fell short of 10, null values were padded with zeros to maintain a consistent input size. The comparison results under different noise levels are presented in Figure 4.

Figure 4 shows that both the feature extraction and the classifier have an obvious effect on PQD identification. On the one hand, the OMD–IACNN has higher classification accuracy compared to the EEMD–IACNN under different noise levels. This demonstrates that the OMD can provide more reliable disturbance feature information by adjusting the decomposition number adaptively, proving its effectiveness. Furthermore, the superior performance of OMD–IACNN over OMD–ACNN and EEMD–CNN underscores the advantages of incorporating an attention mechanism and a convolution fusion strategy into the CNN framework. This combination bolsters the CNN’s ability to discern disturbances more accurately. Notably, the OMD–IACNN maintains a high accuracy rate of 99.2% even under 20 dB noise, affirming its robustness against noise interference. In addition, Figure 4 also shows an increase in model accuracy when the noise level shifts from 40 dB to 20 dB; the reason is that the PQD signals are changeable before the noise is added, which can reflect the randomness of the classification result. Such results are indicative of the model’s strong anti-noise capabilities, making it a suitable tool for PQD identification under challenging conditions.

To further verify the proposed OMD–IACNN, some existing PQD detection frameworks are selected for a comprehensive comparison. The comparison result is given in Table 3.

It can be seen from Table 3 that the proposed OMD–IACNN model has a higher PQD identification accuracy compared with some other popular detection frameworks. First, more PQD types are considered in our OMD–IACNN, which is important to address the challenges of power grid complexity. In addition, under the same noise level, the proposed OMD–IACNN can obtain the highest accuracy. For example, the accuracy of the OST–KSVM and the EITD–GSCNN is 98.82% and 98.56%, respectively, while that the OMD–IACNN is 99.20%. The result demonstrates that the optimal mode decomposition and improved network structure can significantly enhance disturbance detection performance. Therefore, the proposed OMD–IACNN is more suitable for complex PQD identification.

To further ascertain the practical applicability of the proposed methodology, a hardware experimental platform was employed to capture authentic PQDs signals. The hardware platform is presented in Figure 5.

Figure 5 shows that the hardware platform is based on the AC6801 series AC power source. After the experimental PQD signals are collected, they can be identified by the proposed OMD–IACNN model in PC. The experiment encompasses a suite of PQD scenarios: C1 (normal), C2 (sag), C3 (swell), C4 (interrupt), and C5 (harmonics). We adhered to a sampling frequency of 3,200 Hz and a total sampling duration of 10 s. To reinforce the robustness of the identification process, each PQD category was subjected to 160 random tests, with the results presented in Table 4.

The data in Table 4 attest to the resilience of the OMD–IACNN approach when applied to experimental PQD signals. An average classification accuracy of 97.37% was achieved with the OMD–IACNN, underscoring its efficacy in accurate detection. Moreover, the average time taken to test each PQD sample was less than the time required for signal sampling, highlighting the model’s commendable real-time performance. Collectively, these experimental findings reinforce the OMD–IACNN model’s superiority in the identification of multiple PQD types.