With the increasing adoption of renewable energy sources, solar power has emerged as a critical component in the global energy mix due to its sustainability and minimal environmental impact. Solar inverters, which convert direct current from photovoltaic panels into alternating current for grid integration, are essential for efficient energy conversion. However, these solar inverters are prone to open-circuit faults, which can lead to significant operational failures and economic losses if not diagnosed promptly. Traditional fault diagnosis methods, such as model-based approaches and signal analysis, often rely on complex mathematical models or additional sampling circuits, making them less adaptable to dynamic system changes. In contrast, data-driven techniques leverage raw signals directly, offering a more flexible solution. This paper proposes a novel fault diagnosis framework that combines Gramian Angular Field (GAF) encoding with an improved Residual Network (ResNet) to enhance the detection and classification of open-circuit faults in solar inverters. By transforming one-dimensional current signals into two-dimensional images, the method preserves temporal dependencies and enables deep learning models to capture both spatial and temporal features effectively. The integration of Squeeze-and-Excitation (SE) attention mechanisms, Swish activation functions, and the Ranger optimizer further optimizes the ResNet architecture, improving feature extraction and diagnostic accuracy. Experimental results demonstrate that this approach achieves high precision and rapid diagnosis, making it suitable for real-time applications in solar energy systems.
The core of the proposed method lies in the transformation of time-series data into visual representations using GAF encoding. For a given time series \( X = \{x_1, x_2, \cdots, x_n\} \), normalization is first applied to scale the data between -1 and 1:
$$ \tilde{x}_i = \frac{[x_i – \max(X)] + [x_i – \min(X)]}{\max(X) – \min(X)} $$
where \( \tilde{x}_i \) represents the normalized value at time \( i \). This step ensures that the data is suitable for polar coordinate transformation. The normalized series is then converted into polar coordinates by calculating the angle and radius:
$$ \phi = \arccos(\tilde{x}_i), \quad -1 \leq \tilde{x}_i \leq 1 $$
$$ r = \frac{t_i}{N}, \quad t_i \in \mathbb{N} $$
Here, \( \phi \) denotes the angular value, \( r \) is the radial value, \( t_i \) is the time stamp, and \( N \) is a constant factor that adjusts the radial span. This transformation maps the time series onto a unit circle, where temporal relationships are preserved through angular positions. Two variants of GAF encoding are employed: Gramian Angular Summation Field (GASF) and Gramian Angular Difference Field (GADF). The GASF matrix is defined as:
$$ G_{\text{GASF}} = \begin{bmatrix} \cos(\phi_1 + \phi_1) & \cdots & \cos(\phi_1 + \phi_n) \\ \vdots & \ddots & \vdots \\ \cos(\phi_n + \phi_1) & \cdots & \cos(\phi_n + \phi_n) \end{bmatrix} $$
Similarly, the GADF matrix is given by:
$$ G_{\text{GADF}} = \begin{bmatrix} \sin(\phi_1 – \phi_1) & \cdots & \sin(\phi_1 – \phi_n) \\ \vdots & \ddots & \vdots \\ \sin(\phi_n – \phi_1) & \cdots & \sin(\phi_n – \phi_n) \end{bmatrix} $$
These matrices encode the temporal correlations into 2D images, where each pixel represents a specific relationship between time points. For instance, a sinusoidal current signal from a solar inverter can be visualized as distinct patterns in the GAF images, highlighting fault characteristics that are difficult to discern in the original 1D form. The dual-channel approach, combining both GASF and GADF, provides complementary information, enhancing the feature richness for subsequent deep learning processing.
To process these 2D representations, an improved ResNet architecture is utilized. Traditional Convolutional Neural Networks (CNNs) suffer from degradation issues as network depth increases, leading to vanishing gradients and overfitting. ResNet addresses this through residual blocks, which incorporate skip connections to facilitate gradient flow. The basic residual block computes the output as \( y = F(x) + x \), where \( F(x) \) is the transformation applied by convolutional layers and \( x \) is the input. This allows the network to learn residual functions, easing the training of deep architectures. For solar inverter fault diagnosis, ResNet50 is selected as the base model due to its balance between depth and computational efficiency. It consists of five stages: an initial convolutional layer for input preprocessing, followed by four stages of bottleneck layers comprising convolutional and identity blocks. The overall structure includes convolutional layers, batch normalization, activation functions, and pooling layers, culminating in a fully connected layer for classification.
However, the standard ResNet does not prioritize feature channels, which can limit its performance in capturing critical fault indicators. To overcome this, Squeeze-and-Excitation (SE) modules are integrated into the residual blocks. The SE mechanism enhances channel-wise feature responses by modeling interdependencies between channels. Specifically, it performs global average pooling to squeeze spatial information into a channel descriptor:
$$ z_c = F_{\text{sq}}(u_c) = \frac{1}{H \times W} \sum_{i=1}^{H} \sum_{j=1}^{W} u_c(i, j) $$
where \( u_c \) is the feature map of channel \( c \), and \( H \) and \( W \) are its dimensions. This is followed by excitation through two fully connected layers with a Sigmoid activation:
$$ s_c = F_{\text{ex}}(z, W) = \sigma(W_2 \delta(W_1 z)) $$
Here, \( \sigma \) denotes the Sigmoid function, \( \delta \) is the ReLU activation, and \( W_1 \) and \( W_2 \) are weights of the fully connected layers. The resulting weights \( s_c \) are used to recalibrate the original features:
$$ \tilde{u}_c = F_{\text{scale}}(u_c, s_c) = s_c \cdot u_c $$
This process emphasizes informative features and suppresses less relevant ones, improving the network’s ability to discriminate between different fault types in solar inverters. Additionally, the ReLU activation function in the residual blocks is replaced with the Swish function to mitigate issues like neuron saturation. Swish is defined as:
$$ f(x) = \frac{x}{1 + e^{-\beta x}} $$
where \( \beta \) is a learnable parameter. Swish provides smoother gradients and better performance in deep networks compared to ReLU. Furthermore, the Ranger optimizer, which combines Rectified Adam (RAdam) and Lookahead, is employed to stabilize training and accelerate convergence. These enhancements collectively enable the SE-ResNet model to delve deeper into image features, capturing both local and global patterns associated with open-circuit faults in solar inverters.
The fault diagnosis process is divided into offline training and online diagnosis phases. In the offline stage, a simulation model of a solar inverter is developed to generate fault data. Open-circuit faults are categorized into single-switch faults (e.g., T1, T2), same-side bridge faults (e.g., T1 T4), same-phase bridge faults (e.g., T1 T3), and cross-bridge faults (e.g., T1 T2), totaling 21 fault types. For each fault, three-phase output current signals are sampled at 25 kHz, and 50 samples per fault are collected, resulting in a dataset of 1050 samples. The data is split into training and testing sets, and GAF encoding is applied to convert 1D signals into 2D images. The training set is used to optimize the SE-ResNet model, while the testing set evaluates its performance. The model is trained for 100 epochs with a learning rate of 0.001, and the best-performing model is saved for online use.
In the online phase, real-time current signals from solar inverters are acquired and transformed into GAF images. These images are fed into the pre-trained SE-ResNet model, which outputs the fault classification. This approach allows for rapid diagnosis within a single current cycle, making it suitable for practical applications. The dual-channel GAF encoding ensures that temporal features are retained, while the improved ResNet architecture provides robust feature extraction and classification.
To validate the effectiveness of the proposed method, extensive experiments are conducted. The dataset includes both simulated and experimental data from a solar inverter setup. The simulation model replicates various fault conditions, and the experimental platform uses a DC power supply to emulate photovoltaic arrays, with a DSP-based control system for signal acquisition. The following table compares the diagnostic accuracy of different GAF encoding methods using the SE-ResNet model:
| Encoding Method | Single-Switch Faults (%) | Same-Side Bridge Faults (%) | Same-Phase Bridge Faults (%) | Cross-Bridge Faults (%) |
|---|---|---|---|---|
| GADF | 94.7 | 95.4 | 97.1 | 95.4 |
| GASF | 95.1 | 96.7 | 94.4 | 97.9 |
| GADF-GASF | 98.9 | 99.2 | 99.3 | 99.5 |
The results indicate that the dual-channel encoding outperforms individual methods, achieving an average accuracy of over 99% across all fault categories. This is attributed to the complementary information provided by GASF and GADF, which enhances feature representation. Additionally, the training and testing accuracy curves show that the dual-channel approach converges faster and with lower loss, demonstrating its stability and efficiency.
To further analyze the feature extraction capabilities, t-Distributed Stochastic Neighbor Embedding (t-SNE) is used to visualize high-dimensional features in a 2D space. The following table summarizes the performance of different models on experimental data:
| Model | Training Accuracy (%) | Testing Accuracy (%) | Diagnosis Time (ms) |
|---|---|---|---|
| VGG16 | 76.73 | 77.32 | 1.23 |
| GoogLeNet | 86.26 | 85.19 | 0.46 |
| ResNet50 | 90.74 | 88.51 | 0.84 |
| SE-ResNet50 | 99.12 | 99.41 | 0.18 |
The SE-ResNet model achieves the highest accuracy and the shortest diagnosis time, highlighting its superiority for solar inverter fault diagnosis. The visualization results confirm that SE-ResNet produces well-separated clusters for different fault types, whereas other models show overlapping and dispersed features. This underscores the importance of the SE attention mechanism and architectural improvements in distinguishing subtle fault patterns.
In conclusion, the integration of GAF encoding and enhanced SE-ResNet provides a robust solution for open-circuit fault diagnosis in solar inverters. The method effectively transforms 1D current signals into informative 2D images, preserving temporal correlations and enabling deep learning models to capture critical features. The improvements in ResNet, including SE modules, Swish activation, and Ranger optimization, address limitations of traditional CNNs, resulting in higher accuracy and faster diagnosis. Experimental validation on both simulated and real-world data demonstrates the method’s efficacy, with an accuracy of 99.41% and a diagnosis time of 0.18 ms. This approach offers significant potential for enhancing the reliability and efficiency of solar energy systems, contributing to the broader adoption of renewable energy sources. Future work will focus on extending this framework to other types of faults and integrating it with edge computing for real-time deployment in solar inverters.