Enhanced Fault Detection and Classification in AC Microgrids Through a Combination of Data Processing Techniques and Deep Neural Networks

Abstract

This paper introduces an innovative method for the intelligent protection of AC microgrids that incorporate renewable energy sources and electric vehicle charging stations. To extract relevant features, current signals from both sides of the distribution line are sampled. Subsequently, the differential current is calculated, and the resultant signals are processed using Compressed Sensing Theory and Variational Mode Decomposition to extract key features. These extracted features serve as input data for training the proposed wide and deep learning model. The proposed method was evaluated on a microgrid that incorporated electric vehicle chargers and wind turbines. The results indicate that this approach can effectively identify and categorize different types of faults in AC microgrids. Moreover, it demonstrates stable and dependable performance in the face of typical transients, and its accuracy is not influenced by uncertainties in the microgrid topology.

1. Introduction

One of the primary obstacles impeding the advancement of microgrids is ensuring the protection of these systems [1]. Conventional fault detection techniques for distribution networks typically depend on the magnitude and direction of short-circuit currents. Nevertheless, the incorporation of electric vehicles (EVs) and distributed generators (DGs) has altered the formerly passive characteristics of traditional distribution networks, resulting in bidirectional power flow within microgrids [2,3]. The uncertainty in microgrid topology, arising from the diverse types of DGs and EVs, as well as the dynamic nature of their connection to the grid, further complicates the protection process. Given these uncertainties, designing a protection scheme capable of detecting and classifying faults across all operational topologies of microgrids is highly complex [4].

In addition to their efficiency in various operational topologies, fault detection and classification methods must be capable of distinguishing between transient and permanent faults, as well as detecting high-impedance faults [4]. The inherent uncertainty in microgrid topology makes it susceptible to transients caused by switching operations. These switching surges, primarily resulting from the connection and disconnection of DGs and EVs, as well as mode transitions within the microgrid, can potentially be misidentified as faults by fault detection methods, especially when multiple surges occur simultaneously [5,6,7].

Several studies have explored fault detection and classification methods for microgrids. These methods can be categorized into various approaches [4,8]. A significant portion of these studies focuses on processing sampled voltage and current signals. For instance, the authors of [9,10] propose fault detection techniques by transforming signals from the abc to the dq reference frame. However, these methods may not effectively address transient disturbances arising from microgrid topology changes. Other studies, such as reference [11], employ zero-sequence and negative-sequence components for low-impedance fault detection and transient components for high-impedance fault detection. While this approach can be effective, it may not fully account for the impact of network topology variations and transients. Wavelet-based techniques, as explored in references [12,13,14,15], have been utilized for fault detection. These methods, including the combination of wavelet analysis and cross-overlap differential transformation proposed in [16], can be sensitive to noise and transient waves caused by switching operations in microgrid topologies. Other techniques, such as those based on signal energy differentials in references [17,18,19] and harmonic analysis in references [20,21], have also been proposed. While these methods can be effective in certain scenarios, they may require data synchronization or may be limited to specific fault types. For instance, the method proposed in [21] detects faults by calculating the ratio of zero-sequence current to positive-sequence current in the fifth harmonic of the current. Due to its reliance on zero-sequence current, this method is limited to ground fault detection. In reference [22], the direction of active power flow, current amplitude, and voltage flash are used to detect low-impedance faults in microgrids equipped with inverter-based DGs. In reference [23], phase difference and admittance amplitude measurements at each bus are utilized for fault detection. Traveling-wave-based methods in reference [24] offer high-speed fault detection but require high sampling rates and complex calculations to determine the traveling wave propagation speed [25]. Statistical-based methods, such as the one proposed in [26], detect faults by calculating the standard deviation of the average voltage and frequency from their normal values. However, these methods may be less sensitive to certain fault types. In summary, while various fault detection methods have been proposed for microgrids, many of them have limitations in terms of their ability to handle dynamic topologies, transient disturbances, and diverse fault types.

In contrast to signal-processing-based methods, machine learning methods have gained significant attention for addressing the challenges of microgrid protection due to the increasing availability and reliability of data [26]. In reference [27], various machine learning methods in microgrid protection were categorized. Accordingly, machine learning patterns have been categorized into two general categories: shallow-based algorithms and deep-based algorithms [27]. Shallow learning methods, such as the Decision Tree (DT) in [28], Support Vector Machine (SVM) in [29], Adaptive Neuro-Fuzzy Inference System (ANFIS) in [30], Extreme Learning Machine (ELM) in [31], K-Nearest Neighbor Regression (KNN) in [32], and Random Forest (RF) in [33], have been widely applied to microgrid fault detection. However, these methods may struggle to capture complex patterns [34], particularly in microgrids with significant topological uncertainty and transient states caused by frequent switching operations. This limitation has motivated the development of more sophisticated methods that can effectively address these challenges and accurately distinguish between permanent faults and transient disturbances. The authors of [35] introduced a hybrid method that integrates discrete wavelet transform and deep neural networks (DWT-DNN) to detect and classify fault types in AC microgrids. Reference [36] presents a hybrid method based on wavelet transform and deep neural networks. The most significant issues with these references are their low accuracy in error detection and classification and their failure to consider the wind turbine and electric vehicle charger.

Accordingly, this paper presents a novel approach to fault detection and classification based on wide and deep learning (WDL) models. The proposed method leverages a dual signal processing algorithm, combining Compressed Sensing Theory (CST) proposed in [37] and Variational Mode Decomposition (VMD) proposed in [38], to extract features from time-series signals. The extracted features from the CST and VMD are then fed separately into the WDL model. The CST-derived features primarily contribute to fault detection, while the VMD-derived features play a crucial role in fault classification. Importantly, the WDL model’s interconnected layers enable information sharing between both sections, enhancing overall accuracy. The microgrid under study was simulated in MATLAB Simulink 2023b, and various fault scenarios were implemented and analyzed. Signal processing and feature extraction were carried out in Python. The extracted features were stored in a CSV file and used to train the WDL model. Results from various studies demonstrate the proposed method’s ability to detect faults while considering microgrid topological uncertainties. Additionally, it effectively distinguishes between transient states caused by switching operations and permanent faults. Comparative analysis with previous studies highlights the superior performance of the proposed method.

The organization of this paper is outlined as follows: Section 2 details the formulation of the proposed method. Section 3 presents the simulation results of the proposed method applied to a sample network, along with a comparative analysis with prior studies. Section 4 contrasts the key functionalities of the proposed method with the latest developments in fault detection techniques.

2. Problem Formulation

To address the necessity of a comprehensive method for fault detection and classification in AC microgrids, this section presents the new formulation proposed in this paper, as well as the intelligent algorithm designed to achieve the intended objectives.

2.1. Feature Exctraction

In this study, dual signal processing was used to extract features. First, the current signal from both sides of the protected line is sampled. The current data from both sides of the line are then summed together, and their absolute values are calculated for each phase. The first signal processing model is the CST, which will be discussed in the following to express the governing relations of this model. The CST is a signal processing method that has attracted much attention from power system protection researchers in recent years due to the need for low sampling rates and high speed in fault detection [37,39,40]. When using the CST, many of the less important sampling data are zeroed. Essentially, the CST relies on non-adaptive random sampling. The structure of the CST model can be described using Equation (1) [41].

$$y=\phi x$$

(1)

where $x\in R^n$ or $x\in C^n$ represents the input signal of length $n$, $\phi \in R^{m\times n}$ or $\phi \in C^{m\times n}$ denotes a random measurement matrix $m\times n$, and $y\in R^m$ or $y\in C^m$ is a measurement vector length $n$. Compression is performed by multiplying the input signal with a random measurement matrix. The measured data size, denoted as $m<<n$, is much smaller than the length of the input signal.

Signal compression necessitates the use of a random matrix, which is commonly referred to as and can be computed using Equation (2) [42,43].

$$\phi =HP$$

(2)

Matrices $P$ and $H$ are shown in Equations (3) and (4) [41]. Accordingly, the matrix $P$ is a diagonal matrix $n\times n$ with elements $p_i\in +/-1$. The matrix $H$ is a matrix $m\times n$. The number of samples in each row of matrix $H$ determines the number of samples needed for the measurement by the ratio $R=[n/m]$.

$$P=\left[\begin{array}{ccc}{p}_1& & \\ & ...& \\ & & p_n\end{array}\right]$$

(3)

$$H=\left[\begin{array}{ccc}111...& & \\ & 111...& \\ & & 111...\end{array}\right]$$

(4)

Variable $\tilde{x}$ can be calculated as Equation (5).

$$\tilde{x}=Px$$

(5)

Accordingly, Equation (1) can be rewritten as Equation (6).

$$y=H\tilde{x}$$

(6)

Equation (6) effectively describes the signal compression process. In this equation, the compressed signal $y$ is defined as the product of the matrix $H$ and the transformed signal $\tilde{x}$. This implies that $H$ has a structure comprising a finite number of samples and serves the purpose of data compression. Since $H$ consists of rows with correlated and repeated values, it effectively eliminates unnecessary parts of the signal while retaining only the essential information. As a result, the dimensions of the signal $\tilde{x}$ are reduced, producing a signal $y$ that is prepared for further analysis or processing. Given the established structure for $H$ and $P$, Equation (6) illustrates that the original signal $x$ is transformed into a more optimal form after applying the random diagonal matrix $P$ and subsequently compressed using the matrix $H$. This approach is highly efficient due to its preservation of the signal’s sparsity property and the reduction in the number of samples while simultaneously ensuring that the original information of the signal remains intact in the compressed state $y$.

In this study, the Discrete Fourier Transform Matrix (DFTM) was utilized to create the random matrix. The method for using DFTM to apply the CST to a signal is explained in reference [37].

Figure 1 shows the changes in the real and imaginary parts obtained by applying the CST to the current signal in phase a. As clearly shown, the features extracted from the CST signal can be very suitable for fault detection, but using these features does not seem suitable for fault classification. For this reason, an auxiliary signal processing method needs to be used.

The VMD signal processing technique is a method that can dynamically separate a signal into a collection of Intrinsic Mode Functions (IMFs). Overall, employing VMD can significantly mitigate the challenges related to the signal processing techniques of Local Mean Decomposition (LMD) and Empirical Mode Decomposition (EMD) [44]. In reality, using Equation (7), a raw signal stream $y(t)$ can be broken down into a set of IMFs ($u_k$) [44].

$$y(t)=\sum _k{u}_k$$

(7)

where $\left\{u_k\right\}=\{u_1,u_2,\dots ,u_k\}$ is the set of IMFs.

The essential factors for attaining optimal decomposition performance when addressing the constrained variational model are detailed in Equation (8) [44].

$$\underset{\left\{u_k\right\}\left\{{\omega }_k\right\}}{{\displaystyle \min }}\left\{{\displaystyle \sum _k\left|\right|{\partial }_t\left[\left(\delta (t)+\frac{j}{\pi t}\right)\ast u_k(t)\right]e^{-j{\omega }_{k}t}|{|}_2^2}\right\}$$

(8)

Here, $\left\{{\omega }_k\right\}=\{{\omega }_1,{\omega }_2,\dots ,{\omega }_k\}$ denotes the collection of central frequencies for each IMF. Furthermore, $\delta$, $\left|\right|•|{|}_2$, and $\ast$ signify the Dirac distribution, the Euclidean norm, and the convolution operator, respectively.

To change the constrained problem into an unconstrained one, a Lagrangian coefficient $\lambda \left(t\right)$ and a quadratic penalty term $a$ are defined, resulting in the establishment of the associated unconstrained variation model as specified in Equation (9) [44].

$$\begin{array}{l}L\left(\left\{u_k\right\},\left\{{\omega }_k\right\},\lambda \right)=\Vert y(t)-{\displaystyle \sum _k}{u}_k\left(t\right){\Vert }_2^2\\ +⟨\lambda (t),y(t)-{\displaystyle \sum _k}{u}_k\left(t\right)⟩\\ +a{\displaystyle \sum _k}\Vert {\partial }_t\left[\left(\delta (t)+{\displaystyle \frac{j}{\pi t}}\right)*u_k(t)\right]e^{-j{\omega }_{k}t}{\Vert }_2^2\end{array}$$

(9)

where $u_k$, ${\omega }_k$, and $\lambda \left(t\right)$ can be calculated from Equations (10)–(12) [44].

$${\widehat{u}}_k^{n+1}(\omega )={\displaystyle \frac{\widehat{y}(\omega )-{\sum }_{i>k}{\widehat{u}}_i(\omega )+(\widehat{\lambda }(\omega )/2)}{1+2\alpha (\omega -{\omega }_k{)}^2}}$$

(10)

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

(11)

$${\widehat{\lambda }}^{n+1}(\omega )={\widehat{\lambda }}^n(\omega )+\tau \left(\widehat{y}(\omega )-\sum _k{\widehat{u}}_k^{n+1}\left(\omega \right)\right)$$

(12)

In which $\tau$ represents the update parameter, and the symbol $\wedge$ denotes the update values of $u_k$, ${\omega }_k$, $\lambda \left(t\right)$ and $y$, respectively.

Figure 2 shows the IMF values extracted by VMD from the phase a current signal during the network’s normal state and at the time of fault occurrence.

In the final step of the feature extraction section, it is necessary to calculate the $MEAN,$ $RMS$, and $MAX$ values based on Equations (13)–(15) for each signal window after applying the CST and VMD separately to the current signal. It should be noted that, after feature extraction, these features are used to train the proposed WDL model, which will be examined in the next section.

$$MEAN={\displaystyle \frac{abs\left(Signal\right)}{lentgh\left(Signal\right)}}$$

(13)

$$RMS=\sqrt{\sum _{i=n}^N{\displaystyle \frac{Signa{l}^2}{N}}}$$

(14)

$$MAX=\mathit{max}\left(Signal\right)$$

(15)

2.2. Proposed WDL Model

Figure 3 illustrates the proposed WDL model and Algorithm 1, demonstrating the operation of the proposed method. As shown, after applying signal processing techniques to the current signal and extracting features, the data obtained from the CST and VMD processes are input as two separate entries into the proposed WDL model.

WDL models combine two distinct approaches to machine learning. In the wide learning approach, the model includes a wide layer that receives a large set of features as input and employs linear methods. While these models can effectively capture linear relationships between inputs and outputs, they face limitations in modeling more complex relationships. In the deep learning approach, the model is composed of multiple deep layers designed to extract more complex features from the data. These models are capable of capturing nonlinear relationships, but they may not perform as well on simple linear relationships. WDL models aim to combine the advantages of both approaches. They consist of a wide component (wide layers) and a deep component (deep neural networks). The wide component allows the model to effectively capture linear relationships, while the deep component enables the modeling of more complex relationships. By integrating these two approaches, WDL models can achieve better performance than either approach alone.

Algorithm 1: Fault Classification in AC Microgrids Using Signal Processing and Deep Learning
Input:			$I\left(t\right)$: Current signal of the microgrid.
Output:			$Y_{pred}$: Softmax probability vector for 11 fault classes.
	Algorithm Steps:
		1. Signal Processing and Feature Extraction:
			$1.1.\mathrm{Apply}\mathrm{VMD}\mathrm{to}I\left(t\right)$:
				$\mathrm{Decompose}I\left(t\right)$ into IMFs
			$1.2.\mathrm{Apply}\mathrm{CST}\mathrm{to}I\left(t\right)$:
				Extract real and image features using CST.
			1.3. Compute statistical features for both VMD and CST outputs:
				Mean, RMS, and MAX.
				$\mathrm{Construct}\mathrm{feature}\mathrm{matrices}{X}_{VMD}$ and $X_{CST}$
				Split the dataset into training (70%) and testing (30%) subsets.
				Further split the training data into training (70%) and validation (30%) subsets.
		2. Input Layers:
			2.1. Define two input layers:
				$X_{VMD}$ $\mathrm{and}{X}_{CST}$
		3. Branch 1 (VMD Feature Processing):
			3.1. Dense layer (100 units, SELU, L2 regularization)→Batch Normalization.
			3.2. Dense layer (50 units, SELU, L2 regularization)→Batch Normalization.
			3.3. Dense layer (25 units, SELU, L2 regularization).
		4. Branch 2 (CST Feature Processing):
			4.1. Dense layer (50 units, SELU, L2 regularization)→Batch Normalization.
			4.2. Dense layer (25 units, SELU, L2 regularization).
		5. Feature Concatenation:
			$5.1.\mathrm{Concatenate}{X}_{VMD},X_{CST},Branc{h}_1,Branc{h}_2$
		6. Regularization:
			6.1. Apply Dropout with a rate of 0.1 to the concatenated features.
		7. Output Layer:
			7.1. Dense layer with 11 units and softmax activation to produce class probabilities.
		8. Training and Validation:
			8.1. Train the model using the training subset (70% of the total data).
			8.2. Use the validation subset (30% of the training data) for hyperparameter tuning and monitoring.
		9. Testing:
			9.1. Evaluate the trained model on the test subset (30% of the total data) to assess performance metrics such as accuracy, precision, recall, and F1-score.

As is well known, the WDL model utilizes dense layers with scaled exponential linear unit (SELU) activation as its primary layers. Dense layers in deep neural networks are those where each neuron is connected to all neurons in the subsequent layer, meaning they are fully connected. Such layers are extensively used in artificial neural networks.

The SELU is an activation function that has recently gained attention in deep neural networks. It is specifically designed to enhance the convergence and stability of these networks. The SELU is similar to the ReLU function but has two key differences: first, the SELU continually scales positive values and decreases negative values, rather than mapping negative values to zero. Second, the SELU includes a scaling factor that enables the network to automatically maintain constant output variance across layers. These characteristics enable neural networks using the SELU to automatically normalize and converge more quickly, particularly in deep networks. As a result, the SELU is an attractive choice for designing deep neural networks.

In this deep learning model, two different inputs from two separate datasets (VMD and CST) are provided to the model. Each input is processed through separate branches, which include dense layers with SELU activation and L2 regularization set at a coefficient of 0.01. Following each dense layer, BatchNormalization layers are added to normalize the data and improve the model’s performance. After the inputs are processed, the features from each branch are combined in a Concatenate layer. To mitigate the risk of overfitting, a Dropout layer with a rate of 10% is applied after the feature concatenation stage. The model’s output consists of a dense layer with 11 nodes that utilize Softmax activation to predict the classification labels. For model optimization, the Adam algorithm is employed along with the sparse categorical crossentropy loss function, while accuracy is considered the performance evaluation metric. The model is trained for 500 epochs with a batch size of 32, and to prevent overfitting, the “early stopping” callback is utilized. The settings and parameters of the deep learning model’s input are presented in

Table 1. Configuration and input parameters of the proposed WDL model.

Parameters	Details
Inputs	Input_1 (VMD), Input_2 (CST)
Branch 1	Dense: 100 Hidden Layers, Activation: SELU
	Dense: 50 Hidden Layers, Activation: SELU
	Dense: 25 Hidden Layers, Activation: SELU
Branch 2	Dense: 50 Hidden Layers, Activation: SELU
	Dense: 25 Hidden Layers, Activation: SELU
Dropout	10%
Output	Dense: 11 Hidden Layers, Activation: Softmax
Optimizer	Adam
Loss function	Sparse categorical crossentropy
Metric	Accuracy
Epochs	500
Batch size	32
Callbacks	Early stopping

.

3. Simulation Results

The effectiveness of the proposed method in handling various faults and transient conditions occurring in microgrids needs to be demonstrated. Therefore, this section evaluates the performance of the proposed method by applying it to a sample microgrid.

3.1. Case Study

To assess the effectiveness of the proposed method, the 19-bus network shown in Figure 4 is employed [45]. This network consists of 18 primary lines and two backup lines. The backup lines (L19 and L20) serve to provide power to loads in case one of the primary lines experiences a failure. Further details regarding this network can be found in [46].

It should be noted that various studies, including [45,46], have conducted simulations using three DGs with capacities of 4, 3, and 5 MVA installed on the grid depicted in Figure 4. However, as mentioned, wind turbines and Vehicle-to-Grid (V2G) systems can pose challenges for protection systems. Therefore, in this study, three wind turbines are connected to buses 5, 8 and 13, replacing the previously used DGs. Additionally, several electric vehicle chargers are connected to buses 3, 4, 6 and 14. The IDE is evaluated once for protecting line L9 and once for line L10. The dataset for fault types consists of 1470 instances, and there are 220 instances representing different states in which the relay should not operate. These states include transient events such as load switching, capacitor bank switching, DG entry and exit, various EV operating conditions, and out-of-zone faults. Of the entire simulated dataset, 30% is allocated for testing, and 70% is used for training. Furthermore, 30% of the training dataset is reserved for validation.

The microgrid under study was implemented in MATLAB Simulink, with various faults introduced and analyzed. Signal processing methods and feature extraction algorithms were also executed within MATLAB. After extracting the desired features, the data were saved as a CSV file and imported into Python for training the WDL model.

3.2. Accuracy of the Proposed Method When Protecting the L9 Line

To illustrate the effectiveness of the proposed protection method, simulations were conducted for single-phase, two-phase, and three-phase faults with different impedances and at various locations along the L9 line. Subsequently, feature extraction was conducted, and the resulting data were used to train the intelligent model in Python. Figure 5 illustrates the training progress of the proposed WDL model. Notably, a callbacks function was employed to prevent the model from overfitting. As evident from Figure 5, the proposed WDL model demonstrates successful training. The trends observed in loss and accuracy typically offer valuable insights into the model’s performance over time. For instance, a continuous decrease in the loss value during the training periods usually signifies an improvement in model performance and a reduction in prediction errors. Conversely, if the loss remains constant or increases at certain stages, it may indicate issues such as overfitting or inadequate model fitting to the data. An increase in accuracy indicates that the model is making more correct predictions, thereby demonstrating improved performance.

After completing model training, test data were applied to evaluate the model’s performance. In this study, two parameters—$Accuracy$ and $F1$-score—were used to assess the performance of the proposed method. The values of these parameters can be calculated using Equations (16) and (17) [47].

$$Accuracy={\displaystyle \frac{\mathrm{Number}\mathrm{of}\mathrm{correctly}\mathrm{classified}\mathrm{samples}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{samples}}}\times 100$$

(16)

$$F1={\displaystyle \frac{\mathrm{Precision}\times \mathrm{Recall}}{\mathrm{Precision}+\mathrm{Recall}}}$$

(17)

Additionally, the values of $\mathrm{Precision}$ and $\mathrm{Recall}$ can be calculated using Equations (18) and (19) [47].

$$\mathrm{Precision}={\displaystyle \frac{TP}{TP+FP}}$$

(18)

$$\mathrm{Recall}={\displaystyle \frac{TP}{TP+FN}}$$

(19)

where $TP$ is the count of true positive samples, $FP$ represents the count of false positive samples, and $FN$ indicates the count of false negative samples.

The results of the model performance are shown in Figure 6. According to this figure, the proposed model demonstrates high accuracy (99.9%). Additionally, the confusion matrix (CM) of the model is presented in Figure 7. As is evident from these figures, the proposed method performs very well under various fault conditions.

3.3. Accuracy of the Proposed Method When Protecting the L10 Line

To demonstrate the efficiency of the presented model at various points in the network, this section will examine the model’s performance during the protection of the L10 line. Different fault states, as described in previous sections, were simulated on this line. After signal processing, the extracted features were exported to train the intelligent model in Python.

Figure 8 demonstrates the training progression of the suggested WDL model in the protection of the L10 line. As evidenced by this figure, the proposed WDL model was trained accurately. The results of the model’s performance are also presented in Figure 9, which indicates that the proposed model achieves high accuracy (99%). Additionally, the CM of the model is depicted in Figure 10. These figures demonstrate that the proposed method performs exceptionally well under various fault conditions.

4. Performance Comparison of the Proposed Approach

As previously reviewed, various methods have been proposed in past studies for fault detection and classification in AC microgrids. Accordingly, this section compares the proposed method in this paper with previous approaches, highlighting its advantages over past methods.

4.1. Comparison with Alternative Intelligent Methods

In this section, the performance of the proposed method is compared with KNN, SVM, RF, and XGBoost models based on $\mathrm{Precision}$, $\mathrm{Recall}$, and $F1$-score criteria, as shown in

Table 2. Comparison of the proposed approach with alternative intelligent models.

Case	Proposed Method			KNN			SVM			RF			XGBOOST
	PR *	RE **	F1	PR	RE	F1	PR	RE	F1	PR	RE	F1	PR	RE	F1
AG	1	1	1	0.98	1	0.99	0.98	1	0.99	0.98	1	0.99	0.98	1	0.99
BG	1	1	1	1	0.98	0.99	1	0.98	0.99	1	0.98	0.99	0.98	0.98	0.98
CG	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
AB	1	1	1	1	0.98	0.99	1	0.98	0.99	1	0.98	0.99	1	0.98	0.99
AC	1	1	1	0.98	1	0.99	0.98	1	0.99	0.98	1	0.99	0.98	1	0.99
BC	1	0.98	0.99	1	1	1	0.82	1	0.9	1	1	1	1	0.98	0.99
ABG	1	1	1	1	0.98	0.99	1	0.98	0.99	1	0.98	0.99	1	0.96	0.98
ACG	1	1	1	1	0.98	0.99	1	0.98	0.99	1	0.98	0.99	1	0.98	0.99
BCG	1	0.98	0.99	0.98	0.98	0.98	0.97	0.77	0.86	0.98	0.98	0.98	0.98	0.98	0.98
ABC	1	1	1	1	1	1	1	1	1	0.89	1	0.94	0.89	1	0.94
No fault	0.97	1	0.99	0.93	0.96	0.94	0.93	0.96	0.94	0.94	0.91	0.93	0.91	0.9	0.91

* $\mathrm{Precision}$, ** $\mathrm{Recall}$.

, for fault detection and classification on line L9.

Additionally, Figure 11 illustrates the CM obtained from the test performance results of each method. The results indicate that the proposed method outperforms the other models across all criteria. Notably, in fault classification and accurate detection, the proposed model achieves higher $\mathrm{Precision}$ and $\mathrm{Recall}$. This improvement is attributed to the more effective feature extraction from signals and the use of the WDL model, which offers a comprehensive combination of deep and wide learning.

4.2. Comparison with Alternative Methods Discussed in Studies

The proposed method in this paper is based on hybrid signal processing and the WDL model. This method is capable of fault detection across various operational topologies of microgrids and effectively distinguishes between transient network states and permanent faults. Accordingly,

Table 3. Comparison of the proposed approach with prior research.

Ref.	Feature Extraction Method	Intelligent Model	Microgrid Topology Uncertainty	Distinction Between Permanent Faults and Transient Waves	Fault Detection	Fault Classification	Wind	EV
[35]	Discrete wavelet transform	DNN	✓	✓	✓	✓	✗	✗
[36]	Discrete wavelet transform	GRU	✓	✓	✓	✓	✗	✗
[48]	2D modeling	BWO-BiLSTM	✓	✓	✓	✗	✗	✓
[49]	FP-growth-K-means-mini-batch gradient descent		✗	✗	✓	✗	✗	✗
[50]	Discrete wavelet transform	RBFNN neuronal network	✓	✗	✓	✓	✗	✗
[51]	Discrete wavelet transform	DT	✓	✓	✓	✓	✗	✗
Proposed method	CST-VMD	WDL	✓	✓	✓	✓	✓	✓

presents a comparison between this method and those presented in previous studies. As is evident from this table, many previous studies based on machine learning and deep learning methods have not considered the uncertainties imposed on microgrids by the presence of electric vehicles. Additionally, some studies have only focused on fault detection within microgrids and have not taken fault classification into account.

5. Conclusions

In this paper, a novel method for the intelligent protection of AC microgrids, including renewable energy sources and electric vehicle chargers, was presented. This method is designed based on hybrid signal processing and the WDL learning model. Utilizing features extracted from current signals, it accurately identified and classified various faults with high precision. In addition to comparisons with intelligent methods such as KNN, SVM, RFC, and XGBoost—where results indicated a significant advantage of the proposed method across all metrics, including $\mathrm{Precision}$, $\mathrm{Recall}$, and $F1$-score—further analyses and comparisons with different approaches in this field were conducted. These comparisons demonstrated that the proposed method, leveraging the WDL model and advanced signal processing, not only performs better in fault detection accuracy but also exhibits enhanced adaptability to topological changes and common transient states in microgrids.

The stability and flexibility of the proposed method under various operational conditions and topological changes are among its significant advantages. However, future studies can further enhance its effectiveness by focusing on reducing the computational complexity of this method and evaluating its performance on larger scales and more complex systems. Additionally, developing predictive algorithms for better resource management during critical conditions and employing reinforcement learning to enhance the method’s adaptability to environmental changes can further improve this approach. Integrating this method with new artificial intelligence techniques and comparing it with more advanced algorithms in the field of microgrid protection can also pave the way for further enhancements in this area.