Research on the Enhancement of Provincial AC/DC Ultra-High Voltage Power Grid Security Based on WGAN-GP

Abstract

With the advancement in the “dual carbon” strategy and the integration of high proportions of renewable energy sources, AC/DC ultra-high-power grids are facing new security challenges such as commutation failure and multi-infeed coupling effects. Fault diagnosis, as an important tool for assisting power grid dispatching, is essential for maintaining the grid’s long-term stable operation. Traditional fault diagnosis methods encounter challenges such as limited samples and data quality issues under complex operating conditions. To overcome these problems, this study proposes a fault sample data enhancement method based on the Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP). Firstly, a simulation model of the AC/DC hybrid system is constructed to obtain the original fault sample data. Then, through the adoption of the Wasserstein distance measure and the gradient penalty strategy, an improved WGAN-GP architecture suitable for feature learning of the AC/DC hybrid system is designed. Finally, by comparing the fault diagnosis performance of different data models, the proposed method achieves up to 100% accuracy on certain fault types and improves the average accuracy by 6.3% compared to SMOTE and vanilla GAN, particularly under limited-sample conditions. These results confirm that the proposed approach can effectively extract fault characteristics from complex fault data.

1. Introduction

China’s energy resources and load centers are distributed in an inverse pattern, which has driven national transmission strategy projects such as “West-to-East Power Transmission” and “North-to-South Power Transmission.” [1]. Ultra-high voltage direct current (UHVDC) transmission, characterized by significant capacity, minimal losses, and capability for long-distance power delivery, has become a key technical support for realizing cross-regional energy allocation. As of 2023, more than 20 UHVDC projects have been built and put into operation in China, and the AC/DC ultra-high-power grid covers the country’s main economic regions, becoming an important form of the provincial backbone power grid.

However, with the extension of transmission distances and the increase in the complexity of the grid structure, the AC/DC hybrid system faces many new security challenges [2]. Differences in geographical environments lead to an increase in the probability of line failures, and frequent extreme climate events exacerbate the risks of system operation [3]. Moreover, the response of converter stations to failures has nonlinear, discrete, and time-varying characteristics, making fault features more complex and traditional fault diagnosis methods difficult to apply. Particularly during practical operation, real fault samples are limited because of the system’s sustained stable performance, causing current fault diagnosis methods to fall short in accuracy and real-time effectiveness. Therefore, there is an urgent need for technological innovation to break through the data bottleneck and enhance the safety and intelligence level of the power grid.

The fault diagnosis of AC/DC hybrid power grids faces two core challenges: first, the scarcity of real fault samples makes it difficult to comprehensively reflect various fault characteristics; second, the system’s multi-source heterogeneous structure leads to complex nonlinear correlations in fault data. Traditional data augmentation methods, such as linear interpolation algorithms like SMOTE [4] and ADASYN [5], can alleviate the problem of sample insufficiency; however, the generated data is limited within the initial feature space and does not adequately represent the intricate characteristics of actual faults. In recent years, Generative Adversarial Networks (GAN) have demonstrated significant potential in image synthesis, time-series data generation, and other fields, providing a new approach for data augmentation in power systems [6]. Reference [7] utilizes GAN to detect partial discharge conditions in high-voltage AC systems, but due to differences in model structure and fault characteristics, the transferability and stability of this method need further improvement. Reference [8] combines WGAN with DT-SVM models, proposing a new hybrid DC transmission system commutation fault diagnosis method. This method effectively enhances diagnostic accuracy by augmenting sample data through WGAN, but its stability has not been practically verified. In reference [9], an enhanced GAN structure is introduced to strengthen the model’s capability for detailed feature extraction, effectively increasing the training performance of the generative model; however, the method still exhibits inadequate training stability. These studies collectively highlight the challenges of unstable training and mode collapse associated with conventional GANs, causing the generated samples to fall short of the stringent reliability standards required by power systems [10].

In response to these challenges, this study introduces a fault data augmentation approach utilizing the Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP). By introducing the Wasserstein distance as the loss function and using a gradient penalty mechanism instead of weight clipping, the convergence stability and quality of generated samples are improved. This approach effectively overcomes the gradient vanishing issue commonly observed in traditional GANs, while also improving the diversity and realism of the generated samples, thus offering reliable, high-quality data for building fault datasets in AC/DC hybrid systems.

At present, extensive research has been conducted on the application of deep learning techniques for fault diagnosis within the power system domain. For example, reference [11] proposes a method based on convolutional sparse autoencoders, overcoming the cumbersome process of fault signal processing, which can reliably and accurately achieve fault diagnosis in HVDC transmission lines. Reference [12] adopts parallel neural networks to extract (here, “convolutional” is removed based on the context) electrical feature quantities, improving fault diagnosis efficiency. Reference [13] utilizes convolutional neural networks to process multidimensional fault data, enhancing fault classification accuracy. Reference [14] presents a novel fault identification approach that combines wavelet packet energy spectrum analysis with convolutional neural networks (CNN). By extracting time-domain and frequency-domain fault feature information, the fault identification capability of hybrid DC transmission systems is significantly improved. These studies have demonstrated the effectiveness of deep learning in fault diagnosis for single-grid structures like AC or high-voltage DC systems; however, they remain inadequate in addressing the multi-modal nature and strong coupling characteristics of AC/DC hybrid systems.

This study centers on the fault diagnosis challenge within AC/DC hybrid transmission systems, aiming to solve problems such as complex topology, strong coupling of fault characteristics, and complicated information in the dispatching process. By constructing a data enhancement mechanism based on WGAN-GP, the diversity and representativeness of fault samples are improved, thereby assisting in the establishment of a more robust and efficient fault diagnosis model. This method can quickly mine key features from a large amount of fault alarm information, accurately determine the nature of the fault, and provide reliable support for dispatching and maintenance decisions. Moreover, compared with previous applications of WGAN-GP in single-mode AC or DC systems, this paper focuses on its advantages in AC/DC hybrid systems, which feature strong nonlinear coupling, asynchronous control, and limited fault samples. These characteristics make traditional models less effective in capturing fault features. The proposed WGAN-GP model enhances the learning of complex fault characteristics under such constraints, ensuring improved training stability and diversity of generated samples, thereby making it more suitable for small-sample learning scenarios in AC/DC hybrid transmission grids. It can reduce the workload of fault troubleshooting for maintenance personnel, effectively avoid economic risks caused by incomplete fault recovery, and contribute positively to ensuring the reliable and efficient operation of AC/DC hybrid transmission systems.

In conclusion, the AC/DC hybrid transmission system has a complex structure and long transmission distances, making fault detection and troubleshooting difficult [15]. The WGAN-GP based fault diagnosis method proposed in this study not only enhances the stability and safety of power grid operations but also offers a valuable theoretical foundation and technical pathway for the advancement of future smart grids.

2. Fault Diagnosis and Data Augmentation Principles

2.1. Fault Diagnosis Principles Based on Convolutional Neural Networks

The transmission line fault diagnosis explored in this paper primarily consists of two aspects: identifying faulted lines and determining fault types. The CNN architecture employed for this task, as illustrated in Figure 1, comprises two main components: an input feature extraction network and a fault classification network.

(1)

Fault Feature Extraction Network

(1) Input Layer

The input to the network consists of fault sample data, while the output target corresponds to the specific fault type. In this process, the output labels are represented using one-hot encoding, where only the node corresponding to a particular fault category is assigned a value of “1” within a zero vector whose length matches the total number of fault categories. Together, the input data and their corresponding output labels form the complete set of fault diagnosis samples. To mitigate the impact of varying data scales on model training, the sample set is further processed using min–max normalization. The normalization function is defined as follows:

$$x^{\ast }={\displaystyle \frac{x-x_{\min }}{x_{\max }-x_{\min }}}$$

(1)

where $x^{*}$ represents the data after the normalization transformation of the collected quantity; $x$ represents the raw data collected; $x_{\min }$ and $x_{\max }$ represent the minimum and maximum values in the sample data, respectively.

(2) Convolutional Layer

The convolutional layer realizes feature mapping by sliding a two-dimensional convolution kernel across the input matrix to perform inner product operations. The ability of the convolutional layer to extract fault features is affected by multiple influencing factors. To develop a network architecture tailored for fault diagnosis in hybrid AC/DC transmission systems, it is necessary to clarify the correlation between the dimensions of the input matrix $h_1\times w_1\times d_1$, the size of the convolution kernel $a\times b$, the number of convolution kernels $K$, the sliding step $S$, and the size of the output matrix $h_2\times w_2\times d_2$. The relationship is as follows:

$$\left\{\begin{array}{l}{h}_2=(h_1-a)/S+1\\ w_2=(w_1-b)/S+1\\ d_2=K\end{array}\right.$$

(2)

The convolution operation first generates the output feature map by performing a linear activation response on the input, and then further extracts fault features through nonlinear activation functions [16]. To alleviate the network’s gradient vanishing phenomenon and make its representation sparse, the activation function employed is the Rectified Linear Unit (ReLU). The activation function makes the feature map sparse by rewriting values less than 0 as 0, thereby realizing the extraction of relevant features. The activation function is as follows:

$$f(x)=\max (0,x)$$

(3)

(3) Pooling Layer

The pooling operation aggregates adjacent elements within the convolutional feature map into a single representative value. The selection of the number of elements to be merged is a critical process in training the power system fault diagnosis model. Currently, pooling operations applied to CNN models include average pooling, maximum pooling, and stochastic pooling. Among these, maximum pooling, which selects the maximum value within a region, can, to some extent, mitigate the impact of noise interference. Therefore, maximum pooling is adopted for fault diagnosis [17].

The fault feature extraction network conveys the features obtained from the input samples to the fault classification network through multiple layers of convolution and pooling. The classification network then performs the final categorization based on these features.

(2)

Fault Classification Network

The fault classification network transforms the output features into a linear fully connected structure. To enable the fault classification network to focus on the overall information of the input layer and the correlation of output nodes, the Softmax function is used for the classification output of fault features [18]. Its expression and conditions are as follows:

$$y_i=\phi ({\upsilon }_i)={\displaystyle \frac{e^{{\upsilon }_i}}{e^{{\upsilon }_1}+e^{{\upsilon }_2}+e^{{\upsilon }_3}+\dots +e^{{\upsilon }_M}}}={\displaystyle \frac{e^{{\upsilon }_i}}{{\displaystyle \sum _{k=1}^M{e}^{{\upsilon }_k}}}}$$

(4)

$$\phi ({\upsilon }_1)+\phi ({\upsilon }_2)+\phi ({\upsilon }_3)+\dots +\phi ({\upsilon }_M)=1$$

(5)

where $\phi ({\upsilon }_i)$ is the weighted sum of the ith output node, and M is the number of output nodes.

Equation (5) takes into account the relative magnitudes of each output value, setting their sum always equal to 1, which helps to present a multi-class neural network.

In summary, considering the operational characteristics of AC/DC hybrid transmission systems, the CNN-based fault feature extraction and classification model is capable of thoroughly mining fault features, thereby enhancing the effectiveness of fault diagnosis.

2.2. Based on the Data Augmentation Principle of Generative Adversarial Networks

Generative Adversarial Networks (GAN) are a type of data generation model based on the principles of zero-sum games and Nash equilibrium from game theory and are widely used for data generation and sample augmentation [19].

The fundamental concept involves alternately training two adversarial neural networks—the generator (G) and the discriminator (D)—to capture the distribution characteristics of real data and generate new samples that closely resemble authentic ones, thereby expanding and enriching the sample set. Among them, the generator aims to generate realistic fault samples that are indistinguishable from the real samples by the discriminator, thereby effectively enriching the training dataset, using random noise z to forge samples that are close to reality. The role of the discriminator is to distinguish between real and generated samples. The training objectives of the two networks are contradictory, and they are alternately trained in an adversarial manner. When a dynamic Nash equilibrium is reached, the network successfully converges, and at this point, the features of the generated samples are highly similar to those of the real samples. The fundamental architecture of the network is illustrated in Figure 2.

The loss functions for the aforementioned two parts of the network are, respectively,

$$L_G=E_{z~P_z}\left[\log \left(1-D\left(G\left(z\right)\right)\right)\right]$$

(6)

$$L_D=-E_{x~P_r}\left[\log D\left(x\right)\right]-E_{z~P_z}\left[\log \left(1-D\left(G\left(z\right)\right)\right)\right]$$

(7)

where $E$ represents the expected function, $p_r$ and $p_z$ are the distributions of real samples and random noise, respectively, and $G(\cdot )$ and $D(\cdot )$ are functions differentiable with respect to both the generator and discriminator networks, respectively, with G(z) representing the generated samples.

However, the traditional GAN model faces challenges related to training instability and convergence difficulties, primarily reflected in the following two aspects.

On one hand, there is the problem of mode collapse in the network. The generator and discriminator are trained alternately in an interleaved fashion. When the discriminator’s learning is not ideal, i.e., it is in a state of overfitting or underfitting, the generator’s sole goal is to perfectly fit the real samples, resulting in limited diversity among the generated samples. During the training process, the discriminator’s loss function assigns the same penalty value to non-real generated samples, causing the generator to excessively pursue the accuracy of the generated data while neglecting diversity, and the problem of mode collapse in the network gradually becomes prominent.

On the other hand, there is the problem of gradient vanishing. The generator’s loss function is formulated as the minimization of the Jensen–Shannon (JS) divergence between the real and generated sample distributions. The corresponding loss expressions are presented in Equations (8) and (9). From these equations, it can be seen that the JS divergence has a flat region where the loss function is constant, resulting in the phenomenon of gradient vanishing, which is not conducive to updating network parameters, and the adversarial training process is difficult to maintain.

$$L_G=2JS\left(P_r\left|\right|P_g\right)-2\log 2$$

(8)

where JS divergence is an indicator that measures the similarity between two distributions, and its definition is as follows:

$$JS\left(P_r\left|\right|P_g\right)={\displaystyle \frac{1}{2}}{E}_{x~P_r}\log {\displaystyle \frac{2P_r}{P_r+P_g}}+{\displaystyle \frac{1}{2}}{E}_{x~P_g}\log {\displaystyle \frac{2P_g}{P_r+P_g}}$$

(9)

where $p_r$ and $p_g$ represent the distributions of real samples and generated samples, respectively.

3. Data Augmentation Model Based on WGAN-GP

3.1. WGAN-GP Network

Original GAN experience problems like training instability and mode collapse, which are partly due to the improper design of the loss function within the network model. In particular, the Kullback–Leibler (KL) divergence and Jensen–Shannon (JS) divergence are not well-suited for quantifying the distance between the distributions of generated and real samples [20,21]. Wasserstein GAN (WGAN) provides an effective solution to these problems, improving the stability of network training to a certain extent.

WGAN adopts the Wasserstein distance as its loss function because it offers meaningful gradient information even when the sample distributions have little or no overlap, thus intuitively representing the closeness or divergence between distributions [22]. WGAN-GP is selected over other GAN variants due to its improved training stability and effectiveness under smallsample conditions. Unlike vanilla GAN or DCGAN, it uses Wasserstein distance and gradient penalty to avoid mode collapse and provide stable gradients. Moreover, non-GAN methods such as SMOTE or ADASYN cannot effectively model the temporal structure and nonlinear features of fault waveforms, making WGAN-GP more suitable for fault sample augmentation in this context. In contrast, both the Kullback–Leibler (KL) divergence and Jensen–Shannon (JS) divergence tend to exhibit discontinuous or abrupt variations, such as shifting from 0 to infinity or log (2), when faced with non-overlapping distributions, failing to accurately represent the distance between sample distributions. The definition of the Wasserstein distance is given by the following equation:

$$W(P_r,P_g)=\underset{\gamma ~\Pi (P_r,P_g)}{\inf }{{\rm E}}_{(x,y)~\gamma }\left[‖x-y‖\right]$$

(10)

where $\Pi (P_r,P_g)$ represents the set of joint distributions bounded by $P_r$ and $P_g$; $\gamma$ represents a joint distribution of $P_r$ and $P_g$; ${{\rm E}}_{(x,y)~\gamma }\left[‖x-y‖\right]$ denotes the expected value of the distance between the generated sample y and the real sample x under the joint distribution $\gamma$. The practical significance of this equation is to find the minimum value of the expected distance for all possible joint distributions between the distributions of generated samples and real samples. Where $\Pi (P_r,P_g)$ represents the set of joint distributions bounded by $P_r$ and $P_g$. Each fault sample contains 500 eigenvalues, i.e., the true sample distribution and the generated sample distribution each contain 500 probability distributions. There are a total of 500 joint distributions in $\Pi (P_r,P_g)$, corresponding to the joint distribution composed of each fault characteristic value. $\gamma$ represents a joint distribution of $P_r$ and $P_g$; ${{\rm E}}_{(x,y)~\gamma }\left[‖x-y‖\right]$ denotes the expected value of the distance between the generated sample y and the real sample x under the joint distribution $\gamma$. The practical significance of this equation is to find the minimum value of the expected distance for all possible joint distributions between the distributions of generated samples and real samples.

However, the distance definition in the above equation $\underset{\gamma ~\Pi (P_r,P_g)}{\inf }$ cannot be directly solved. We introduce the Lipschitz continuous conditions for the calculations. In most cases, the Lipschitz continuity constraint can be relaxed to K-Lipschitz continuity. The K-Lipschitz continuity constraint is represented as follows:

$$\left|f(x_1)-f(x_2)\right|\le K\left|x_1-x_2\right|$$

(11)

According to the Kantorovich–Rubinstein duality theorem, the Wasserstein distance between $P_r$ and $P_g$ can be converted into a function of dual form that satisfies the Lipschitz continuous condition, as shown below.

$$W(P_r,P_g)=\underset{f(x)}{\max }\left\{{\displaystyle \int \left[P_{r}f(x)-P_{g}f(x)\right]\mathrm{d}x\left|\left|f(x_1)-f(x_2)\right|\le K\left|x_1-x_2\right|\right.}\right\}$$

(12)

Since $P_r$ and $P_g$ represents the probability distribution, Equation (3) can be written as a sample, as shown below.

$$W(P_r,P_g)=\underset{f(x),{‖f‖}_L\le K}{\max }\left\{E_{x~P_r}\left[f(x)\right]-E_{x~P_g}\left[f(x)\right]\right\}$$

(13)

where ${‖f‖}_L$ represents the Lipschitz constant of function $f(x)$; K represents a constant value not less than 0. The above Equation (11) represents the K-Lipschitz continuity constraint condition. Equation (12) represents the upper bound of the difference between the expected values of distributions $P_r$ and $P_g$ for all possible f that satisfy the condition under the constraint that the Lipschitz constant of function $f(x)$ does not exceed K. The practical significance of this equation is to convert Equation (10) through the dual theorem and the Lipschitz continuous condition into the maximum value of the expected difference between the two distributions $P_r$ and $P_g$.

Considering the difficulty in accurately solving Equation (13) and given that neural networks have a good fitting ability for complex models, a set of parameters w is used to define a series of possible functions $f_w$ to approximate the Wasserstein distance. At this point, Equation (13) can be approximately transformed into the following form:

$$W(P_r,P_g)\approx {\displaystyle \frac{1}{K}}\underset{w:{\left|f_w\right|}_L\le K}{\max }{{\rm E}}_{x~P_r}\left[f_w(x)\right]-{{\rm E}}_{x~P_g}\left[f_w(x)\right]$$

(14)

Among them, in order to limit the value range of $f_w(x)$, WGAN adopts the method of weight clipping. According to the pre-set truncation range, the parameters of the network model are restricted through artificial hard weight truncation, that is, the value range of $w_i$ is set to $w_i\in [-\alpha ,\alpha ]$, and $\alpha$ is a constant.

WGAN, to some extent, improves the stability of network training, but the method of weight clipping introduces new issues [23,24,25]. On one hand, the artificially set truncation range can easily lead to network parameters being limited to boundary values, greatly wasting the optimized setting of model parameters. This causes the final discriminator to tend to fit a simpler function, significantly affecting the network’s generalization and discrimination capabilities. On the other hand, weight clipping can easily lead to gradient vanishing or gradient explosion because both the discriminator and generator typically have multi-layer structures. If the constraints of weight clipping are too small or too large, it is very likely to encounter issues of gradient vanishing or explosion through multiple layers of the network.

WGAN-GP further improves upon the issues caused by weight clipping in WGAN by replacing weight clipping with gradient penalty constraints on the original network model to satisfy the K-Lipschitz continuity constraint conditions for model training [26]. Its superiority over weight clipping lies in the uniform distribution of training gradients, which greatly enhances the training performance of the network model. The loss functions of the generator and discriminator in WGAN-GP can be expressed as

$$L_g=-E_{\tilde{x}~p_g}\left[f_w\left(\tilde{x}\right)\right]$$

(15)

$$L_d=E_{\tilde{x}~p_g}\left[f_w\left(\tilde{x}\right)\right]-E_{x~p_r}\left[f_w\left(x\right)\right]+\lambda E_{\widehat{x}~P_{\widehat{x}}}\left[{\left({‖{\nabla }_{\widehat{x}}{f}_w\left(\widehat{x}\right)‖}_2-1\right)}^2\right]$$

(16)

In the equation: E represents the expectation function, $f_w(x)$ is the differentiable function of the discriminator in the WGAN-GP model, $\tilde{x}=G(z)$ refers to the generated samples, $\lambda$ is the regularization coefficient, ${‖\cdot ‖}_p$ denotes the p-norm, $\epsilon$ is a random number between 0 and 1, $\widehat{x}$ is the result of random interpolation between real samples and generated samples, and $\widehat{x}=\epsilon x+\left(1-\epsilon \right)\tilde{x}$.

3.2. Data Augmentation of Fault Samples Based on WGAN-GP

In the various operating states of actual AC/DC hybrid transmission systems, obtaining sample data under fault conditions is challenging, which in turn increases the likelihood of diagnostic errors when fault samples are limited. To tackle this problem, this chapter introduces a fault sample data augmentation approach based on WGAN-GP to enhance the accuracy of fault diagnosis. The structure of fault diagnosis based on WGAN-GP is shown in Figure 3.

From the structure of WGAN-GP fault diagnosis, it can be seen that the overall process of data sample expansion and fault diagnosis is mainly divided into four parts: fault data processing, network model training, data sample expansion, and fault diagnosis. The detailed contents are as follows.

Fault data processing: preprocess the fault data to obtain the raw dataset.

Network model training: Train the WGAN-GP network model using samples from the raw dataset. Create the generator G and discriminator D and initialize their weight parameters. Use an alternating iterative training method to update the generator and discriminator networks. After multiple rounds of adversarial training, when WGAN-GP reaches a dynamic game equilibrium, the network model training ends.

Data sample expansion: By inputting random noise signals into the trained generator model, new samples that closely resemble the original data are produced. This process expands the original dataset, enhancing both its scale and quality.

Fault diagnosis: To verify the effectiveness of dataset expansion, use the expanded dataset to diagnose fault lines and fault types, and assess the diagnostic accuracy and reliability using relevant evaluation metrics, thereby verifying the feasibility and effectiveness of the WGAN-GP data augmentation method.

3.3. Comprehensive Evaluation Indicators for Fault Diagnosis

To further analyze and evaluate the results of fault diagnosis, and to meet the requirements of accuracy, rapidity, reliability, and stability for short-circuit fault diagnosis in AC/DC hybrid transmission systems, five indicators are set up to measure the identification results of the network model: accuracy of fault line identification, accuracy of fault type identification, identification time, tolerance to transition resistance, and anti-noise interference ability.

(1) Accuracy

The classification and diagnostic performance of the network model is evaluated based on its accuracy in identifying faulted lines and fault types. The expression for the accuracy of fault diagnosis is as follows:

$$\alpha ={\displaystyle \frac{n}{N}}\times 100\%$$

(17)

(2) Rapidity

The average identification time for a single fault sample is calculated by analyzing the total identification time T of the samples in the fault test set. Its expression is as follows:

$$t={\displaystyle \frac{T}{N}}$$

(18)

(3) Reliability and Stability

Since both noise interference and transition resistance can cause variations in fault-related electrical quantities, thereby affecting the accuracy of fault diagnosis, different transition resistances and noise interferences are introduced into the fault quantities. The reliability and stability of the fault diagnosis model are indicated by the extent of variation in its accuracy metrics.

4. Verification with Examples

4.1. AC/DC Hybrid System Model and Dataset

In this study, a comprehensive model of the AC/DC hybrid system is developed using the PSCAD/EMTDC simulation software (version 4.6.2), with the system parameters detailed in

Table 1. Simulation parameters of the system.

System Parameters	Parameter Values
Rated voltage of the AC side (1, 2, 3)	525 kV
DC rated voltage	±800 kV
Length of DC line L1	932 km
Length of DC line L2	557 km
Rated capacity of converter station 1	8000 MW
Rated capacity of converter station 2	5000 MW
Rated capacity of converter station 3	3000 MW
Inductance value of the smoothing reactor for converter station 1	300 mH
Inductance value of the neutral bus current-limiting reactor for converter stations 2 and 3	75 mH
Inductance value of the DC pole line current-limiting reactor for converter stations 2 and 3	75 mH
Length of AC line L3	30 km

.

The system’s main wiring is a symmetrical true bipolar structure. The sending-end LCC converter station is linked to a major energy base, delivering power to the entire line, using constant current control, constant minimum firing angle control, and low-voltage current limiting control. The receiving-end consists of two MMC converter stations that feed power into the load center. The topology of the conversion units is identical. Converter Station 2 operates under constant DC voltage and reactive power control, whereas Converter Station 3 adopts constant active power and reactive power control.

The simulation wiring diagram of the AC and DC hybrid transmission system is shown in Figure 4.

The fault scenario dataset for the AC and DC hybrid transmission system includes variables such as the fault line, fault type, fault distance, and transition resistance. The AC and DC transmission system comprises two DC lines and one AC line. It is necessary to collect fault samples and set different transition resistances as interferences, totaling 2550 fault samples for the diagnostic model’s input data. The current measurements are collected as a set of inputs, with each input matrix having 5 columns. The sampling window width is 5 ms, and the sampling frequency is set to 20 kHz, resulting in an input row count of A. Therefore, the size of the input matrix is [100, 5]. Each fault sample consists of time-domain current signals obtained from five channels, directly taken from the electromagnetic transient simulations. These signals are not subjected to wavelet or frequency-domain transformations to preserve their original fault waveform characteristics. Before being fed into the CNN model, each signal channel is normalized using min–max scaling, as shown in Equation (1), to ensure consistency in magnitude and facilitate convergence during model training. The fault sample collection is shown in

Table 2. Fault sample collection.

Parameter	DC Line L1	DC Line L2	AC Line L3
Fault initiation point (km)	15	30	1
Spacing distance (km)	20	20	2
Fault end (km)	905	520	30
Fault type	Positive pole fault Negative pole fault Inter-pole short circuit		AG, BG, CG, AB, AC, BC, ABG, ACG, BCG, ABC
Transition resistance ($\Omega$)	0.0140, 80, 120, 160, 200, 240, 280, 320, 360		0, 10, 40

.

4.2. A Fault Diagnosis Model Based on CNN

To fulfill the demands for speed, accuracy, and reliability in fault diagnosis, it is essential to construct a well-designed CNN network model. In this section, the goal is to minimize cross-entropy, and the hyperparameters of the network are selected accordingly. An optimized fault diagnosis network based on CNN is determined, and the optimized network parameters are shown in

Table 3. Optimized parameters for the CNN.

Structure Layer	Network Parameters
	Faulty Line	Line 1 Fault Type	Line 2 Fault Type	Line 3 Fault Type
Input layer	—	—	—	—
2D Convolutional Layer 1	5 × 5, 29, (1)	3 × 4, 52, (1)	3 × 5, 53, (1)	7 × 5, 70, (1)
Max Pooling Layer 1	2 × 2, (2)	2 × 2, (2)	2 × 2, (2)	2 × 2, (2)
2D Convolutional Layer 2	3 × 4, 6, (1)	3 × 2, 20, (1)	3 × 3, 24, (1)	6 × 3, 36, (1)
Max Pooling Layer 2	2 × 2, (2)	2 × 2, (2)	2 × 2, (2)	2 × 2, (2)
Fully Connected Layer 1	128	128	128	128
Fully Connected Layer 2	3	3	3	10
Learning Rate	0.001	0.0033	0.001	0.001

. It is worth noting that the CNN architectures in Table 3 differ across fault types and lines. This is because the electromagnetic transient behaviors of DC Line 1, DC Line 2, and the AC line differ significantly in terms of signal characteristics and sensitivity to noise. To achieve optimal diagnostic performance, each network structure was determined through hyperparameter tuning using cross-validation, balancing diagnostic accuracy with computational efficiency. The optimal recognition performance is obtained when the training and test sets are split in a 7:3 ratio. To prevent information leakage and ensure fair evaluation, all synthetic samples generated by WGAN-GP and baseline augmentation methods were added only to the training set. The validation and test sets were constructed using exclusively real samples, maintaining a strict separation between generated and original data.

To validate the feasibility and effectiveness of the data augmentation method proposed in this chapter, the sample dataset is expanded, and the diagnostic performance of the augmented dataset is subsequently evaluated. The proposed network model is implemented using MATLAB’s Deep Learning Toolbox (R2022b), with the PC configured with an Intel^® Core™ i7-11370H CPU @ 3.30 GHz and an RTX 3050 GPU.

4.3. Data Augmentation Model and Training Effects Based on WGAN-GP

4.3.1. Parameters of the Data Augmentation Model Based on WGAN-GP

As shown in

Table 4. The structure and parameter settings of the generator network.

Network Layer	Type	Network Layer Parameters
1	Input Layer	Input Noise Data Dimension: 4
2	Signal Reshaping Layer	Network Layer Size: 1 × 50 × 32
3	Transposed Convolution Layer	1 × 2, 32, (1) Activation Function: Relu
4	Transposed Convolution Layer	1 × 3, 16, (1) Activation Function: Relu
5	Transposed Convolution Layer	1 × 3, 1, (1) Activation Function: Relu
6	Fully Connected Layer	Output data dimension: 500 Activation Function: tanh

, the generator network model consists of 6 layers. The ReLU function is selected as the activation function for the transposed convolutional layers due to its benefits of fast convergence, reduced sensitivity to gradient vanishing, and improved stability during convolution. For the final fully connected layer, the tanh function is employed, as it facilitates sample generation optimization to a certain extent.

The discriminator network structure is similar to the generator network structure, as shown in

Table 5. Structure and parameter settings of the discriminator network.

Network Layer	Type	Network Layer Parameters
1	Input Layer	Input Noise Data Dimension: 1 × 500
2	Convolutional Layer	1 × 3, 16, (1) Activation Function: LeakyRelu
3	Convolutional Layer	1 × 3, 32, (1) Activation Function: LeakyRelu
4	Convolutional Layer	1 × 3, 64, (1) Activation Function: LeakyRelu
5	Convolutional Layer	1 × 3, 1, (1) Activation Function: LeakyRelu
6	Fully Connected Layer	Output Dimension: 1 Activation Function: sigmoid

. It also comprises multiple convolutional layers; however, the key difference is that the activation function of the final fully connected layer is a sigmoid function. This function maps the output to the interval (0, 1), representing the discriminant result of the similarity between the input sample and the real sample.

4.3.2. Training Effects of Data Augmentation Model Based on WGAN-GP

Based on the fundamental theory of WGAN-GP, the training process of the generator and discriminator is inherently adversarial in nature, which can be formulated as a min–max optimization problem. The training parameters of the enhanced model are configured as follows: the Adam optimizer is employed for updating network weights, with a learning rate of 0.001, and the number of pre-training epochs is set to 20,000. To clearly and intuitively demonstrate the generation of AC/DC hybrid transmission line fault samples by the WGAN-GP model, the training process is analyzed through three aspects: the change curve of the network loss function, the iterative evolution of the generated sample data by the generator, along with the visualization of features for both generated and real samples.

(1) Changes in the network model loss function

The loss function value of the discriminator adopts the Wasserstein distance function, which can reflect the disparity between the generated samples and the real samples. In Figure 5, the change curve of the loss function shows the change curve of the discriminator loss function.

In the early stages of training, the generated samples lack the characteristic features present in the real samples, and the discriminator can easily distinguish between the authenticity of the input samples, resulting in a large loss value. At the 2500th iteration, the generator has preliminarily learned the features of the samples, and although the loss value of the discriminator is still oscillating, it indicates that the effect of the generated samples simulating the original samples is not yet stable. By the 20,000th iteration, the loss value of the discriminator fluctuates very little around 0, to a certain extent indicating that the generated samples closely resemble real samples. In addition, by comparing the two curves of WGAN and WGAN-GP in the figure, it is found that after adding gradient penalty constraints, the convergence speed of the discriminator loss value is greatly accelerated, and there are fewer burrs during the training process, which confirms that the method proposed in this paper is capable of generating new samples rapidly and stably.

(2) Iterative changes in the generated sample data by the generator

Taking the real sample of the positive ground short-circuit fault on DC Line 1 as an example, the data of a single fault sample is input into the WGAN-GP network model for iterative training. The changes in the generator loss and discriminator loss are shown in Figure 6. During the iterative training process of the WGAN-GP network, after 5000 iterations, the generator loss value gradually tends to 0, indicating that the generated samples can learn the deep-seated fault characteristics of the real samples at this point, and finally, samples that are highly similar to the real samples are obtained. Figure 7a to f, respectively, show the characteristic performance of the original real sample of a single fault and the generated samples after 100, 1000, 5000, 10,000, and 20,000 iterations.

From the generated samples of different iteration numbers, it can be seen that after 100 iterations of WGAN-GP, the generated samples by the generator differ greatly from the real samples, containing a large amount of noise signals, indicating that the generator has not learned the distribution characteristics of the fault samples. With the increase in the number of iterations, after 1000 iterations, the generated samples have begun to gradually resemble the real samples in shape and feature distribution but still contain a lot of noise. When the network iterates to 5000 times, the generated sample data only have poor simulation effects in some areas compared to the real fault samples, mixed with a small amount of noise signals. The generated samples after 10,000 iterations and 20,000 iterations have a high similarity to the original samples, and the curves are relatively smooth, fully learning the fault signal characteristics of the original samples. The above iterative change process shows that the WGAN-GP adopted in this chapter enables the generator to grasp the deeper characteristics of the original fault samples in the process of adversarial learning with the discriminator.

(3) Visualization Analysis of Characteristics of Generated Samples and Real Samples

To further evaluate the generation performance, a positive pole grounding fault sample from DC Line 1 is selected as an example. A subset of generated and real samples is randomly chosen, and t-SNE is applied to reduce the dimensionality of both the generated and original data for visual inspection and analysis. Figure 8 presents the data distribution after dimensionality reduction using t-SNE.

As can be seen from Figure 7, most of the generated samples highly overlap with the real samples, indicating a high degree of feature similarity; however, some discrepancies remain between certain generated samples and real samples, suggesting that the generated data retains a certain level of diversity. The samples generated by the WGAN-GP network not only exhibit high similarity to the original data but also enhance the diversity of the dataset, thereby contributing to the improved generalization capability of the network model.

4.4. Analysis of Fault Diagnosis Effect

To verify the superiority of the WGAN-GP network for data augmentation in AC/DC hybrid transmission system fault diagnosis, a fault diagnosis of the generated samples is conducted using a CNN fault diagnosis network.

The trained WGAN-GP network model is used to generate fault samples. For DC Line 1, 1800 samples are generated for each fault type, while for DC Line 2, 1000 samples are generated per fault type. For AC lines, 180 samples are generated for each type of fault. The CNN fault diagnosis network is used to identify the nature of the faults in the generated samples, and the diagnosis results are shown in

Table 6. Generates a sample of fault line diagnostic results.

Faulty Line	Total Number of Generated Samples	Number of Test Set Samples	Number of Misdiagnosed Samples	Diagnostic Accuracy Rate/%
DC Line 1	5400	1620	0	100
DC Line 2	3000	900	0	100
AC Line	1800	540	4	99.26

and

Table 7. Generates a sample of fault type diagnostic results.

Fault Type		Total Number of Generated Samples	Number of Misdiagnosed Samples	Diagnostic Accuracy Rate/%
DC Line 1	Positive pole fault	540	0	100
	Negative pole fault	540	0	100
	Inter-pole short circuit	540	0	100
	Total	1620	0	100
DC Line 2	Positive pole fault	300	0	100
	Negative pole fault	300	0	100
	Inter-pole short circuit	300	0	100
	Total	900	0	100
AC Line	Single-phase grounding	162	2	98.77
	Phase-to-phase short circuit	162	0	100
	Two-phase grounding	162	2	98.77
	Three-phase short circuit	54	0	100
	Total	540	4	99.26

, respectively.

From the above two tables, it can be seen that the overall diagnostic accuracy of the samples generated by the WGAN-GP network is high, with a diagnostic accuracy rate of 100% for fault lines, and the diagnostic accuracy rate for fault types is not lower than 99.26%. Thanks to the enrichment of the diversity of the generated fault sample set based on the original fault samples, the diagnostic effect of the fault diagnosis network is very good. Therefore, it can be explained that the generator in the WGAN-GP network can learn to extract feature information from real fault samples during the training process, and the generated samples have good practical application value. To further validate the effectiveness of the WGAN-GP network in fault sample data augmentation, a comparative test is conducted between the original sampling scenario and the scenario after dataset expansion with samples generated by WGAN-GP using the CNN fault diagnosis network. Using the fault type diagnosis of DC Line 1 as an example, the test results are presented in

Table 8. Fault diagnosis results for original and expanded sets.

Sample Conditions	Number of Training Set Samples	Number of Test Set Samples	Number of Misdiagnosed Samples	Diagnostic Accuracy Rate/%	Diagnostic Duration/ms
Original Dataset	1645	705	3	99.57	0.646
GAN Augmented Dataset	8225	3525	2	99.94	0.641
WGAN Augmented Dataset	8225	3525	2	99.94	0.639
WGAN-GP Augmented Dataset	8225	3525	0	100	0.637

. In order to emphasize the necessity of data augmentation, we clarify that the original dataset for DC Line 1 contains only 235 samples per fault type. Such a small sample size is representative of real-world conditions where fault events are rare. Without augmentation, the CNN model achieved a diagnosis accuracy of 99.57%, with three misclassified instances. The accuracy can be improved to 99.94% with the increase in test samples after GAN and WGAN enhancement methods, but there are still two misclassified samples. After applying WGAN-GP-based augmentation, the accuracy improved to 100%, as shown in Table 8. This validates that the proposed method can effectively improve diagnostic accuracy under limited-sample conditions.

To measure the end-to-end delay of fault diagnosis, the average diagnostic duration (t) for a single fault sample is obtained by processing the identification time (T) of all generated samples (with the quantity being N). The fault diagnosis duration of DC Line 1 is shown in Table 8. It can be found that the WGAN-GP augmentation method also achieves good results in terms of diagnostic duration, which is attributed to the more obvious fault features after data augmentation, leading to a certain improvement in diagnostic performance.

From the table, it can be observed that the fault diagnosis accuracy on the test set augmented by WGAN-GP reaches 100%. Based on the fault diagnosis effect, it is known that the samples generated by the WGAN-GP network can fit the fault scenarios of AC/DC hybrid transmission system lines. The generated samples obtained through the generator network model have both high similarity to the original fault samples and appropriate differences. Therefore, the fault diagnosis effect has been improved after dataset expansion, which largely indicates that the data augmentation method of the WGAN-GP network plays a key role, and provides an important solution for how to efficiently improve the diagnostic capability of deep learning models in scenarios with limited sample data.

5. Conclusions

Tackling the challenge of limited fault samples in the fault diagnosis of real-world AC/DC hybrid transmission system lines, this paper proposes a method for data augmentation of fault samples based on WGAN-GP. Firstly, a discriminator and generator network model suitable for fault sample data is constructed. Then, new samples highly similar to the original fault samples are generated using the WGAN-GP network. Finally, the application effect of the generated samples is verified through a fault diagnosis network. The case study verifies the following conclusions:

(1) This paper introduces gradient penalty constraints into the WGAN network model, which effectively enhances the training stability of both the discriminator and the generator. By comparing the iterative change curves of the discriminator loss functions of WGAN and WGAN-GP, it is concluded that WGAN-GP can quickly reach a convergence state and has higher stability.

(2) The quality of the generated samples is evaluated by feeding them into the CNN fault diagnosis model for testing and analysis. The generated samples based on the WGAN-GP network can highly simulate the original real samples. Through the t-SNE dimensionality reduction visualization analysis of the generated samples and real samples, it is concluded that the generator constructed in this paper can ensure that the generated samples have diverse characteristics different from the real samples.

(3) The samples generated by the WGAN-GP network are merged with the original dataset to form a new sample set and input into the fault diagnosis network for inspection. Compared with the original sample set, the expanded sample set has improved fault diagnosis effect, indicating that the proposed method can achieve better sample augmentation effect and improve the fault diagnosis performance of the network.

Although the proposed method is validated using a three-terminal AC/DC hybrid transmission system, the approach itself is data-driven and does not rely on system-specific structural assumptions. As such, it can be generalized to other AC/DC hybrid configurations, provided that sufficient representative training data are available. Future work will focus on validating the method across different topologies and expanding its applicability to real-world measured fault records.