The rapid integration of renewable energy sources such as photovoltaic systems into the power grid demands highly reliable power electronic interfaces. Among the various types of solar inverter topologies, the neutral-point-clamped (NPC) three-level inverter stands out due to its superior voltage stress handling, reduced harmonic distortion, and improved electromagnetic compatibility. However, the increased number of insulated gate bipolar transistors (IGBTs) in NPC inverters elevates the risk of open-circuit faults. These faults are often stealthy, leading to waveform distortion, system instability, and potential cascading failures. Traditional diagnostic methods based on model analysis or signal processing often require extensive manual feature engineering and struggle under noisy conditions. In this work, we present a data-driven approach that combines S-transform image representation with a residual network augmented by a parallel multi-dimensional attention (ResNet-PMDA) mechanism to achieve robust and accurate fault classification. Our method first reduces the three-phase signals to a single virtual resistance via Park transformation, then transforms this 1D signal into a time-frequency image using S-transform, and finally feeds the image into the ResNet-PMDA classifier. Extensive simulations demonstrate that our approach attains 100% accuracy in a clean environment and maintains 94.93% accuracy even under 30 dB Gaussian noise, significantly outperforming several baselines.
1. Introduction
With the global push toward carbon neutrality, photovoltaic power generation has become a key technology for sustainable energy. NPC three-level inverters are widely adopted in grid-connected photovoltaic systems because they offer lower total harmonic distortion and higher efficiency compared to two-level inverters. However, the reliability of these inverters is critically dependent on the health of their IGBT modules. Open-circuit faults account for a large portion of power device failures in types of solar inverter systems. Unlike short-circuit faults that can be quickly cleared by hardware protection, open-circuit faults persist and degrade output quality, causing current imbalance and voltage distortion. Hence, developing efficient and noise-robust fault diagnosis techniques is essential for ensuring the safe operation of solar energy systems.
Conventional fault diagnosis methods for NPC inverters can be grouped into three categories: model-based, signal-based, and data-driven approaches. Model-based methods rely on accurate mathematical models of the inverter and compare the observed output with predicted values. While effective for simple topologies, they become cumbersome for multilevel inverters and are sensitive to parameter variations. Signal-based methods extract features from voltage or current waveforms in the time or frequency domain, often using thresholds or symmetry criteria. However, these methods require careful calibration and may fail under non-stationary operating conditions. Data-driven techniques, especially those using deep learning, have gained popularity because they can automatically learn discriminative features from raw or preprocessed measurements. For instance, methods combining empirical mode decomposition with neural networks, or using wavelet transforms with support vector machines, have shown promise. Nevertheless, many existing studies focus on two-level inverters or fail to address noise robustness comprehensively.
In this paper, we propose an integrated framework that addresses the limitations of existing methods. We first use the Park transformation to convert three-phase currents and voltages into d-q components and compute a virtual resistance. This step reduces the dimensionality while preserving fault-related signatures. Then, we apply the S-transform to the virtual resistance signal to generate a two-dimensional time-frequency representation. The S-transform offers a frequency-dependent resolution that captures both transient and steady-state behaviors effectively. Finally, we design a ResNet-PMDA model that features residual connections to mitigate gradient vanishing and a parallel multi-dimensional attention module to emphasize informative channels, spatial regions, and coordinate-wise features. We evaluate our method on 73 fault types (1 normal + 72 open-circuit faults) in a simulated grid-connected NPC inverter. Experimental results confirm that our approach excels in both clean and noisy environments, adapting well to the diverse types of solar inverter operating conditions.
2. Inverter Topology and Open-Circuit Faults
The NPC three-level inverter consists of 12 IGBTs (four per phase) and two clamping diodes per phase, as shown in the schematic. Each phase can generate three voltage levels: P (positive), O (neutral), and N (negative). The switching states for phase A are illustrated in Table 1. Under normal operation, three-phase currents are balanced sinusoids. When an open-circuit fault occurs in one or more IGBTs, the current path is disrupted, resulting in distorted waveforms. In our work, we consider single IGBT faults and double IGBT faults (excluding the six cases where two IGBTs in the same leg and same arm fail, as they produce similar behavior to single faults). This yields a total of 73 distinct states (including the healthy state). Table 2 summarizes the fault categories with their labels.
| State | SA1 | SA2 | SA3 | SA4 | Pole voltage |
|---|---|---|---|---|---|
| P | 1 | 1 | 0 | 0 | Udc/2 |
| O | 0 | 1 | 1 | 0 | 0 |
| N | 0 | 0 | 1 | 1 | -Udc/2 |
| Category | Fault location | Labels |
|---|---|---|
| Healthy | None | 0 |
| Single IGBT | SA1,…,SC4 | 1–12 |
| Double IGBT (same phase, different legs) | SA1SA3, SA1SA4, …, SC2SC4 | 13–24 |
| Double IGBT (different phases) | SA1SB1, …, SB4SC3 | 25–72 |
3. Proposed Method
3.1 Dimensionality Reduction via Virtual Resistance
Raw three-phase currents and voltages contain redundant information and are often correlated. To simplify the feature extraction, we employ the Park transformation to convert the three-phase quantities into the synchronous rotating d-q reference frame. The Park transformation matrix H(t) is defined as:
$$
H(t) = \frac{2}{3} \begin{pmatrix}
\cos(\omega t) & \cos(\omega t – \frac{2\pi}{3}) & \cos(\omega t + \frac{2\pi}{3}) \\
-\sin(\omega t) & -\sin(\omega t – \frac{2\pi}{3}) & -\sin(\omega t + \frac{2\pi}{3}) \\
\frac{1}{2} & \frac{1}{2} & \frac{1}{2}
\end{pmatrix}
$$
After transformation, the d-axis voltage u_d and d-axis current i_d are obtained. Under healthy conditions, these are constant DC values. Under fault conditions, they exhibit oscillatory behavior due to harmonics. We then compute a virtual resistance R_d as:
$$
R_d = \frac{u_d}{i_d}
$$
This single scalar time series effectively captures the fault signature while drastically reducing data dimensionality. Figure 3 compares the virtual resistance waveforms for four representative cases: healthy, single IGBT fault (SA1), double IGBT same-phase fault (SA1SA3), and double IGBT cross-phase fault (SA1SB1), demonstrating clear discriminability.
3.2 Time-Frequency Transformation using S-Transform
While the virtual resistance signal already contains fault information, directly feeding it to a classifier may lead to suboptimal performance, especially under noise. The S-transform provides a time-frequency representation that combines the advantages of short-time Fourier transform and wavelet transform. For a signal x(t), the S-transform is defined as:
$$
S(\tau, f) = \int_{-\infty}^{\infty} x(t) \frac{|f|}{\sqrt{2\pi}} e^{-\frac{(t-\tau)^2 f^2}{2}} e^{-j 2\pi f t} dt
$$
The Gaussian window width varies inversely with frequency, offering good frequency resolution at low frequencies and good time resolution at high frequencies. We apply the S-transform to each virtual resistance segment (2000 samples) to obtain a 2D time-frequency matrix, which is then resized to 224×224×3 (converted to RGB for compatibility with pre-trained architectures). Figure 6 illustrates the resulting images for several fault states, where distinct patterns emerge.
3.3 ResNet-PMDA Model
We design a deep convolutional neural network based on the residual network (ResNet) architecture. The ResNet uses skip connections to alleviate the vanishing gradient problem common in very deep networks. Two types of residual blocks are employed: identity blocks when input and output dimensions match, and convolutional blocks (with 1×1 convolutions) when dimensions differ. The core building block is shown in Figure 7.
To further enhance feature discrimination, we introduce a parallel multi-dimensional attention (PMDA) module after the final residual stage. The PMDA module simultaneously captures:
- Channel attention: via global average and max pooling, followed by two 1×1 convolutions and sigmoid activation, to re-weight each channel.
- Spatial attention: via 1D average and max pooling along the width and height dimensions separately, followed by convolutions and sigmoid, to highlight important spatial locations.
- Coordinate attention: by pooling the feature map along one spatial direction and then combining information from both directions to capture long-range dependencies.
The three attention maps are fused via element-wise multiplication with the input feature map. The PMDA module is illustrated in Figure 8.
The overall ResNet-PMDA architecture is depicted in Figure 9. It starts with a 7×7 convolution and max pooling, followed by six residual modules (with channel sizes 64, 64, 128, 128, 256, 256). The PMDA module is inserted after the last residual module. A dropout layer and a fully connected layer with softmax output produce the final classification over 73 classes.
4. Experimental Setup
4.1 Dataset and Preprocessing
We simulate a grid-connected NPC inverter in MATLAB/Simulink with parameters: switching frequency 5 kHz, DC bus voltage 10 kV, grid frequency 50 Hz, and sampling frequency 10 kHz. For each of the 73 states, we collect 4 s of data and extract a 2000-sample window (10 cycles) starting at 1.1 s after fault onset. We vary the load and fault occurrence time to create diversity, obtaining 100 samples per state, totaling 7300 samples. We add Gaussian white noise with SNR levels of 30 dB, 40 dB, and 50 dB to simulate real-world conditions. The virtual resistance is computed, and the S-transform is applied to produce 224×224×3 images. 80% of the data is used for training and 20% for testing. All experiments are repeated 10 times and averaged.
4.2 Training Configuration
We use the Adam optimizer with a learning rate of 0.001 and a batch size of 32 (selected after a sensitivity study shown in Figure 11). The model is trained for 100 epochs. The experiments are conducted on a system with Intel i5-12600KF CPU and NVIDIA GeForce RTX 3060 GPU, running MATLAB 2023b. Table 3 summarizes the platform.
| Component | Specification |
|---|---|
| OS | Windows 11 (64-bit) |
| GPU | NVIDIA GeForce RTX 3060 |
| CPU | Intel i5-12600KF |
| Software | MATLAB 2023b |
5. Results and Discussion
5.1 Comparison of Input Representations
We evaluate the effect of using different input representations with the same ResNet-PMDA backbone. The compared representations include raw virtual resistance (Rd), S-transform (ST), synchronous extraction transform (SET), short-time Fourier transform (STFT), and continuous wavelet transform (CWT). Table 4 reports the accuracy, F1-score, and recall under different noise levels, considering the 73-class problem (types of solar inverter faults).
| Input | Noise-free (%) | F1 | Recall | 50 dB (%) | F1 | Recall | 40 dB (%) | F1 | Recall | 30 dB (%) | F1 | Recall |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rd | 97.40 | 0.9715 | 0.9740 | 94.14 | 0.9392 | 0.9415 | 93.15 | 0.9308 | 0.9315 | 88.42 | 0.8856 | 0.8843 |
| SET | 99.14 | 0.9913 | 0.9924 | 95.62 | 0.9544 | 0.9126 | 94.03 | 0.9404 | 0.9429 | 88.39 | 0.8846 | 0.8924 |
| STFT | 94.79 | 0.9635 | 0.9614 | 94.11 | 0.9405 | 0.9439 | 93.01 | 0.9289 | 0.9358 | 89.45 | 0.8949 | 0.9004 |
| CWT | 99.89 | 0.9989 | 0.9990 | 96.84 | 0.9678 | 0.9690 | 94.73 | 0.9465 | 0.9497 | 90.79 | 0.9073 | 0.9129 |
| ST (ours) | 100.00 | 0.9995 | 0.9996 | 97.05 | 0.9705 | 0.9706 | 96.92 | 0.9692 | 0.9692 | 94.93 | 0.9472 | 0.9497 |
The S-transform consistently outperforms the other representations. In the noise-free case, it achieves perfect classification, while at 30 dB it still surpasses the second-best (CWT) by over 4 percentage points. This demonstrates the advantage of the adaptive time-frequency resolution of S-transform for capturing both subtle and abrupt changes caused by open-circuit faults in types of solar inverter.
5.2 Comparison of Network Architectures
To validate the effectiveness of the ResNet-PMDA model, we compare it against several variants: CNN+ResNet (a plain convolutional layer followed by residual blocks), CNN+PMDA (convolutional layer plus PMDA), and standard ResNet-18. All models use the S-transform images as input. Table 5 presents the accuracy, number of parameters (MParams), and inference time per batch (test time).
| Architecture | Noise-free (%) | 50 dB (%) | 40 dB (%) | 30 dB (%) | MParams | Test time (s) |
|---|---|---|---|---|---|---|
| CNN+ResNet | 99.11 | 94.79 | 94.32 | 92.74 | 6.40 | 2.14 |
| CNN+PMDA | 98.84 | 93.70 | 93.15 | 90.83 | 8.50 | 4.31 |
| ResNet-18 | 98.90 | 95.89 | 95.75 | 92.94 | 11.22 | 2.97 |
| ResNet-PMDA (ours) | 99.95 | 97.05 | 96.92 | 94.93 | 6.60 | 2.25 |
The proposed ResNet-PMDA achieves the highest accuracy under all noise levels while maintaining a moderate model size (6.60 million parameters) and efficient inference (2.25 s per batch). The attention module adds only a small overhead compared to plain ResNet-18, yet improves noise robustness substantially. The training curves in Figure 13 also show that our model converges faster and more stably.
5.3 Ablation Study on Attention Mechanisms
We replace the PMDA module in our model with other popular attention mechanisms: SE, CBAM, and CA. The results are summarized in Table 6 and visualized in Figure 14.
| Attention | Noise-free (%) | 50 dB (%) | 40 dB (%) | 30 dB (%) |
|---|---|---|---|---|
| SE | 98.08 | 94.93 | 92.12 | 84.32 |
| CBAM | 99.45 | 95.82 | 94.86 | 88.49 |
| CA | 99.18 | 95.55 | 92.81 | 89.86 |
| PMDA (ours) | 99.95 | 97.05 | 96.92 | 94.93 |
PMDA outperforms all other attention modules by a significant margin, especially under high noise (30 dB: 94.93% vs. 84.32% for SE). This confirms that jointly attending to channel, spatial, and coordinate dimensions yields the most discriminative features for diagnosing open-circuit faults across various types of solar inverter.
5.4 Visualization of Feature Space
We employ t-SNE to visualize the learned feature embeddings of the test samples under 30 dB noise for the five input representations (Figure 12). The S-transform based features produce tightly clustered groups with minimal overlap between different fault types, whereas other methods exhibit significant mixing. This qualitative result corroborates the quantitative accuracy improvements.
6. Conclusion
We have presented a novel data-driven approach for open-circuit fault diagnosis of NPC three-level inverters. By converting three-phase signals into a single virtual resistance via Park transformation, applying the S-transform to obtain time-frequency images, and classifying with a ResNet-PMDA deep network, we achieve state-of-the-art performance. The method is validated on 73 fault scenarios (including both single and double IGBT faults) under various noise levels. Key conclusions are as follows:
- The virtual resistance simplifies the problem while retaining fault-related information, making it suitable for real-time implementation.
- The S-transform provides a robust time-frequency representation that is more noise-resilient than conventional transforms for the studied types of solar inverter faults.
- The proposed ResNet-PMDA model effectively extracts multi-dimensional features and achieves 100% accuracy in clean conditions and 94.93% accuracy under 30 dB noise, outperforming standard architectures and attention mechanisms.
- Future work will focus on online real-time validation and further improving noise robustness for even harsher environments.
The image above illustrates a modern solar inverter system similar to the NPC topology studied, highlighting the practical relevance of our diagnostic method for various types of solar inverter installations.