In the context of the global transition toward renewable energy and the “dual carbon” targets, the penetration of wind and solar power in power systems has increased significantly. As a critical interface between renewable generation and the grid, the reliability of inverters directly affects the transient stability and dynamic regulation capability of the entire power system. Among various failure modes, open-circuit faults in insulated gate bipolar transistors (IGBTs) are particularly insidious because they do not cause immediate overcurrent and are difficult to detect. Early and accurate diagnosis of such faults is therefore essential to prevent cascading failures and to ensure the continuous operation of photovoltaic and wind power installations. This paper presents a novel open-circuit fault diagnosis method for inverters based on a multi-modal three-branch heterogeneous fusion architecture, which combines time-series dynamics with image-based spatial features to achieve superior accuracy and robustness.
To fully characterize the fault signatures embedded in inverter output currents, we first employ the complementary ensemble empirical mode decomposition with phase randomization technique (CEEMD-PRT) to decompose the non-stationary current signals into intrinsic mode functions (IMFs). The phase randomization step enhances the separability of noise and fault components. Pearson correlation coefficients are calculated between each IMF and the phase-randomized signal, and only those IMFs with coefficients above 0.2 are retained for signal reconstruction. This preprocessing effectively extracts local fault features while suppressing noise interference.
After reconstructing the one-dimensional time-series signals, we transform them into two distinct two-dimensional representations to capture complementary aspects of the fault dynamics. The Gramian angular field (GAF) encodes the temporal dependencies by mapping the normalized time series into polar coordinates and then constructing a Gramian matrix using cosine or sine functions. This transformation preserves the global trend information of the current waveform. The recurrence plot (RP), on the other hand, visualizes the nonlinear dynamic characteristics of the system by constructing a recurrence matrix based on phase-space reconstruction. Together, GAF and RP provide a rich multi-modal description of the same fault event: GAF emphasizes the overall shape and periodicity of the signal, while RP highlights local recurrence patterns and abrupt changes.
The core contribution of this work is the design of a three-branch heterogeneous fusion model that integrates LSTM-based temporal feature extraction with GAF-Transformer and RP-Transformer branches for spatial feature learning. The LSTM branch directly processes the one-dimensional current sequence to capture short-term and long-term dependencies in the time domain. The GAF-Transformer branch takes the GAF image as input and leverages multi-head self-attention mechanisms to extract global spatial correlations. Similarly, the RP-Transformer branch processes the RP image to exploit nonlinear recurrence features. Instead of simply concatenating features from the three branches, we propose a novel heterogeneous feature fusion module that performs cross-modal interaction through 1×1 convolutions followed by element-wise multiplication. Specifically, we pairwise multiply features from the LSTM branch with those from the GAF and RP branches, and also multiply GAF and RP features together. The three resulting interactive features are then concatenated and passed through a final 1×1 convolution to produce a unified discriminative feature vector. This design ensures that temporal dynamics, global trends, and local nonlinear patterns are synergistically combined, enabling the model to distinguish subtle differences among types of solar inverter faults.
We validated our approach using a MATLAB/Simulink simulation of a three-phase two-level voltage-source inverter with LCL filter, considering one healthy state and 21 open-circuit fault conditions covering single-switch and double-switch failures. The dataset comprises 2200 samples for 22 classes, with each sample consisting of 2000 points of the A-phase current. The data were split into 80% training and 20% testing sets. The GAF images and RP images were generated from the preprocessed one-dimensional samples, resulting in 4400 images in total. All models were trained for 100 epochs using the Adam optimizer with an initial learning rate of 0.001 and a batch size of 10. The loss function is categorical cross-entropy, and the activation function in hidden layers is LeakyReLU with a negative slope of 0.1. Table 1 summarizes the fault categories and corresponding labels.
| Fault ID | Fault Type | Faulty Switches | Label |
|---|---|---|---|
| G1 | Normal | None | 1 |
| G2 | Single IGBT open | IGBT1 | 2 |
| IGBT2 | 3 | ||
| IGBT3 | 4 | ||
| IGBT4 | 5 | ||
| IGBT5 | 6 | ||
| IGBT6 | 7 | ||
| G3 | Two IGBTs open (same phase) | IGBT1, IGBT4 | 8 |
| IGBT3, IGBT6 | 9 | ||
| IGBT2, IGBT5 | 10 | ||
| G4 | Two IGBTs open (same half-bridge) | IGBT1, IGBT3 | 11 |
| IGBT1, IGBT5 | 12 | ||
| IGBT3, IGBT5 | 13 | ||
| IGBT4, IGBT6 | 14 | ||
| IGBT2, IGBT4 | 15 | ||
| IGBT2, IGBT6 | 16 | ||
| G5 | Two IGBTs open (cross) | IGBT1, IGBT6 | 17 |
| IGBT1, IGBT2 | 18 | ||
| IGBT3, IGBT4 | 19 | ||
| IGBT4, IGBT5 | 20 | ||
| IGBT2, IGBT3 | 21 | ||
| IGBT5, IGBT6 | 22 |
During training, the CEEMD-PRT algorithm first decomposes the raw current signal. For a given signal x(t), after CEEMD we obtain IMFs Ik(t). The Pearson correlation coefficient with the phase-randomized signal ŷ(t) is computed as:
$$
\rho_k = \frac{\sum_{t=1}^{T}(I_k(t)-\bar{I}_k)(\hat{x}(t)-\bar{x})}{\sqrt{\sum_{t=1}^{T}(I_k(t)-\bar{I}_k)^2}\sqrt{\sum_{t=1}^{T}(\hat{x}(t)-\bar{x})^2}}
$$
The reconstructed signal is then:
$$
\hat{X}(t) = \sum_{k \in S} I_k(t), \quad S = \{k: \rho_k > 0.2\}
$$
For GAF transformation, after min-max scaling to [−1,1], each data point xi is mapped to polar coordinates:
$$
\phi_i = \arccos(\tilde{x}_i), \quad -1 \leq \tilde{x}_i \leq 1
$$
$$
r_i = \frac{t_i}{A}, \quad t_i \in [0, A]
$$
The Gramian matrix (summation form) is:
$$
G_{\text{GASF}} = \begin{bmatrix}
\cos(\phi_1+\phi_1) & \cdots & \cos(\phi_1+\phi_n)\\
\vdots & \ddots & \vdots\\
\cos(\phi_n+\phi_1) & \cdots & \cos(\phi_n+\phi_n)
\end{bmatrix}
$$
For RP, after phase-space reconstruction with delay τ and embedding dimension m, the recurrence matrix is:
$$
R(i,j) = H(\varepsilon – \| \mathbf{X}_i – \mathbf{X}_j \|)
$$
where H(·) is the Heaviside function and ε is a threshold.
In the LSTM branch, the memory cell, forget gate, input gate, and output gate are updated as:
$$
f_t = \sigma(W_f [H_{t-1}, x_t] + b_f)
$$
$$
i_t = \sigma(W_i [H_{t-1}, x_t] + b_i)
$$
$$
\tilde{C}_t = \tanh(W_C [H_{t-1}, x_t] + b_C)
$$
$$
C_t = f_t \odot C_{t-1} + i_t \odot \tilde{C}_t
$$
$$
o_t = \sigma(W_o [H_{t-1}, x_t] + b_o)
$$
$$
H_t = o_t \odot \tanh(C_t)
$$
In the Transformer branches, the multi-head attention mechanism is defined as:
$$
\text{Attention}(Q,K,V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V
$$
$$
\text{MultiHead}(Q,K,V) = \text{Concat}(\text{head}_1,\ldots,\text{head}_h)W_O
$$
After extracting features from the three branches, the heterogeneous fusion module performs cross-modal interactions. Let F1D, FGAF, and FRP denote the output features of the LSTM, GAF-Transformer, and RP-Transformer branches, respectively. The fusion proceeds as:
$$
F_{1G} = \text{Conv1D}(F_{1D}) \odot F_{GAF}
$$
$$
F_{GR} = \text{Conv1D}(F_{GAF}) \odot F_{RP}
$$
$$
F_{1R} = \text{Conv1D}(F_{1D}) \odot F_{RP}
$$
$$
F_C = \text{Concat}(F_{1G}, F_{1R}, F_{GR})
$$
$$
F_f = \text{Conv1D}(F_C)
$$
All Conv1D operations use 1×1 kernels (size 1) to preserve spatial dimensions while enabling channel-wise interactions. The final fused feature Ff is fed into a fully connected layer for classification.
Figure 1 illustrates a typical solar inverter system used in our simulation setup (inserted here).
The experimental results demonstrate the effectiveness of the proposed model. On the test set, the three-branch heterogeneous fusion model achieved an accuracy of 99.3%. The confusion matrix in Table 2 shows that only 3 samples out of 440 were misclassified. Two misclassifications occurred between fault type “IGBT5,IGBT6 open” (label 22) and “IGBT1,IGBT3 open” (label 18), and one misclassification between “IGBT1,IGBT2” (label 18) and “IGBT2,IGBT3” (label 21).
| True \ Pred | … (shortened for brevity) |
|---|---|
| … | … |
We compared our model against five representative methods: GAF-LSTM-Transformer (two-branch without RP), RP-LSTM-Transformer (two-branch without GAF), standalone CNN, standalone LSTM, and BP neural network. Table 3 lists the test accuracies and losses. The proposed model achieved the highest accuracy (99.30%) and the lowest loss (0.007).
| Model | Test Accuracy (%) | Test Loss |
|---|---|---|
| GAF-RP-LSTM-Transformer (Proposed) | 99.30 | 0.007 |
| GAF-LSTM-Transformer | 97.65 | 0.015 |
| RP-LSTM-Transformer | 97.21 | 0.018 |
| CNN | 96.30 | 0.022 |
| LSTM | 95.90 | 0.025 |
| BP | 95.14 | 0.031 |
We further evaluated the robustness of all models under Gaussian noise at signal-to-noise ratios (SNR) of 10 dB, 20 dB, 30 dB, and 40 dB. Both common-mode (same noise on all three phases) and differential-mode (opposite noise on phases A and B, clean on phase C) noise were applied, and the average accuracy was computed. The results are presented in Table 4.
| Model | 10 dB | 20 dB | 30 dB | 40 dB |
|---|---|---|---|---|
| GAF-RP-LSTM-Transformer | 93.96 | 97.96 | 98.24 | 98.62 |
| GAF-LSTM-Transformer | 92.83 | 93.38 | 95.86 | 96.13 |
| RP-LSTM-Transformer | 91.76 | 92.26 | 94.60 | 95.95 |
| CNN | 89.84 | 91.34 | 93.53 | 94.61 |
| LSTM | 89.17 | 90.87 | 93.26 | 94.37 |
| BP | 87.62 | 89.23 | 92.17 | 93.82 |
At 30 dB noise, the accuracy of our model only dropped by 0.38% compared to the noiseless case, and at 20 dB the drop was only 0.66%. Even under the severe 10 dB noise, the accuracy remained at 93.96%, outperforming the next best model (GAF-LSTM-Transformer) by 1.13%. This demonstrates that the heterogeneous fusion of temporal and multi-modal image features provides strong noise immunity, making the method suitable for practical applications where types of solar inverter may operate in electrically noisy environments.
To visualize the discriminative power of the learned features, we applied t-distributed stochastic neighbor embedding (t-SNE) to reduce the high-dimensional feature vectors to 2D. The original data samples showed severe overlap among different fault classes. After processing by our model, the features of each class formed tight, well-separated clusters, confirming that the multi-modal fusion effectively disentangles the complex fault patterns.
In summary, this paper presents a comprehensive open-circuit fault diagnosis framework for inverters based on multi-modal three-branch heterogeneous fusion. The key innovations include: 1) CEEMD-PRT preprocessing to extract localized fault features and reduce noise; 2) simultaneous GAF and RP transformations to capture both global trends and nonlinear dynamics of the current signals; 3) a novel heterogeneous fusion module that enables cross-modal interactions between LSTM temporal features and Transformer spatial features via convolution and multiplication, rather than simple concatenation. Extensive experiments on a three-phase inverter model show that our method achieves 99.3% classification accuracy and maintains high performance under strong noise, outperforming conventional deep learning approaches.
Future work will focus on extending the method to multi-sensor data (e.g., voltage, temperature) and validating it on real hardware setups. Moreover, we aim to develop lightweight versions of the model for real-time deployment on embedded platforms, which is crucial for monitoring large numbers of types of solar inverter in distributed photovoltaic plants.