Photovoltaic (PV) grid-connected systems rely heavily on inverters to convert direct current (DC) from solar panels into alternating current (AC) for grid integration. Among the various configurations, three-level inverters, particularly neutral-point-clamped (NPC) topologies, have gained widespread adoption due to their improved voltage quality and reduced harmonic distortion. However, these inverters are subjected to harsh outdoor environments, leading to frequent faults such as open-circuit or short-circuit of switching devices, capacitor degradation, and driver circuit failures. Accurate and timely fault diagnosis is critical to ensure system reliability and minimize downtime. In recent years, many intelligent algorithms have been employed for inverter fault detection, including wavelet transforms combined with deep learning. Nevertheless, these methods often struggle to balance time-frequency resolution across different frequency components, resulting in suboptimal diagnostic accuracy. To address this challenge, we propose a novel fault diagnosis technique that integrates generalized S-transform (GST) with extreme learning machine (ELM) for three-level inverters in photovoltaic grid-connected applications.
Our approach targets multiple types of solar inverter faults, including open-circuit faults in insulated-gate bipolar transistors (IGBTs), capacitor faults, drive circuit anomalies, and aging effects. The method first extracts time-frequency features from the inverter output signals using GST, which adaptively adjusts the shape and size of the time-frequency window to capture transient variations accurately. Then, a high-dimensional energy feature matrix is constructed and reduced via singular value decomposition (SVD) to retain essential fault discriminative information. Finally, the reduced features are fed into an ELM classifier, which learns the mapping between fault characteristics and their corresponding categories through least-squares optimization. Experimental results demonstrate that our method achieves an average fault type discrimination rate exceeding 97%, significantly outperforming conventional approaches.
The three-level inverter under investigation is a typical NPC topology, which splits the DC bus voltage into three levels using clamping diodes. This design reduces voltage stress on power switches and improves output waveform quality. However, due to the increased number of components, the probability of failures rises. Common types of solar inverter faults in such systems include:
| Fault Type | Description | Symptoms |
|---|---|---|
| Switch open-circuit | One or more IGBT switches fail to turn on | Output voltage distortion, increased THD |
| Switch short-circuit | IGBT remains permanently on | Overcurrent, DC bus voltage drop |
| DC-link capacitor fault | Capacitance reduction or leakage | Voltage ripple, reduced efficiency |
| Driver circuit fault | Gate drive signal loss or delay | Intermittent switching, mis-triggering |
| Capacitor aging | Gradual degradation of electrolytic capacitors | Increased ESR, thermal runaway |
Our diagnostic framework begins with signal acquisition. High-precision voltage and current sensors are installed at the inverter output to capture three-phase AC signals. Under normal operation, the recorded signals exhibit sinusoidal waveforms with fundamental frequency (50 Hz). When a fault occurs, the signals contain transient components and harmonics that vary with the fault location and severity. To analyze these non-stationary signals, we employ the generalized S-transform, which is an extension of the short-time Fourier transform (STFT) and continuous wavelet transform (CWT). The GST of a signal \( x(\tau) \) is defined as:
$$ S(t,f) = \int_{-\infty}^{\infty} x(\tau) \cdot g(t-\tau, f) \cdot e^{-j2\pi f \tau} \, d\tau $$
where \( g(t-\tau, f) \) is a generalized Gaussian window function that adapts its width according to frequency. The window function is given by:
$$ g(t-\tau, f) = \frac{|f|}{\sqrt{2\pi} \, \sigma} \, e^{-\frac{(t-\tau)^2 f^2}{2\sigma^2}} $$
Here, \( \sigma \) is an adjustable parameter that controls the trade-off between time and frequency resolution. By tuning \( \sigma \), we can achieve finer resolution at high frequencies while maintaining adequate time localization at low frequencies. This property is crucial for capturing the rapid changes in fault-induced transients. For a discrete signal, the GST produces a complex time-frequency matrix \( S(t,f) \). The energy distribution is then computed as:
$$ E(t,f) = |S(t,f)|^2 $$
The total energy over the entire time-frequency plane is:
$$ E_{\text{total}} = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} E(t,f) \, dt \, df $$
These energy values form a high-dimensional feature matrix \( \mathbf{F} \) of size \( m \times n \), where \( m \) is the number of time or frequency samples and \( n \) is the number of energy types (e.g., from voltage and current channels). The matrix is expressed as:
$$
\mathbf{F} =
\begin{bmatrix}
E(t_1, f_1) & E(t_1, f_2) & \cdots & E(t_1, f_n) \\
E(t_2, f_1) & E(t_2, f_2) & \cdots & E(t_2, f_n) \\
\vdots & \vdots & \ddots & \vdots \\
E(t_m, f_1) & E(t_m, f_2) & \cdots & E(t_m, f_n)
\end{bmatrix}
$$
To reduce dimensionality and retain only the most informative features, we apply singular value decomposition (SVD) to \( \mathbf{F} \):
$$ \mathbf{F} = \mathbf{U} \mathbf{\Sigma} \mathbf{V}^T $$
Here, \( \mathbf{U} \) is an \( m \times m \) orthogonal matrix whose columns represent time-domain basis vectors, \( \mathbf{\Sigma} \) is an \( m \times n \) diagonal matrix containing singular values \( \sigma_1 \geq \sigma_2 \geq \cdots \geq \sigma_k \), and \( \mathbf{V} \) is an \( n \times n \) orthogonal matrix representing frequency-domain basis vectors. Larger singular values correspond to dominant fault-related components, while smaller ones often capture noise or irrelevant details. We retain the top \( k \) singular values and their corresponding singular vectors to form a reduced feature matrix \( \mathbf{F}_r \). The value of \( k \) is determined by the cumulative energy threshold (e.g., 95%). This SVD-based compression not only reduces computational burden but also enhances the separability of different types of solar inverter faults by emphasizing key characteristics.
The reduced feature vectors are then used as inputs to an extreme learning machine (ELM) classifier. ELM is a single-hidden-layer feedforward neural network (SLFN) where the input weights and biases are randomly assigned, and the output weights are computed analytically using the least-squares method. For a set of \( N \) training samples \( \{ (\mathbf{x}_i, \mathbf{t}_i) \} \), where \( \mathbf{x}_i \in \mathbb{R}^d \) is the \( i \)-th reduced feature vector and \( \mathbf{t}_i \in \mathbb{R}^C \) is the target output vector (with \( C \) fault classes), the ELM model with \( L \) hidden neurons is described by:
$$ f(\mathbf{x}) = \sum_{i=1}^{L} \beta_i g(\mathbf{w}_i \cdot \mathbf{x} + b_i) $$
where \( g(\cdot) \) is an activation function (e.g., sigmoid or ReLU), \( \mathbf{w}_i \) and \( b_i \) are randomly generated input weights and biases, and \( \beta_i \) is the output weight vector. The hidden layer output matrix \( \mathbf{H} \) is defined as:
$$ \mathbf{H} =
\begin{bmatrix}
g(\mathbf{w}_1 \cdot \mathbf{x}_1 + b_1) & \cdots & g(\mathbf{w}_L \cdot \mathbf{x}_1 + b_L) \\
\vdots & \ddots & \vdots \\
g(\mathbf{w}_1 \cdot \mathbf{x}_N + b_1) & \cdots & g(\mathbf{w}_L \cdot \mathbf{x}_N + b_L)
\end{bmatrix}_{N \times L}
$$
Then the output weights \( \boldsymbol{\beta} \) are obtained by solving:
$$ \boldsymbol{\beta} = \mathbf{H}^\dagger \mathbf{T} $$
Here, \( \mathbf{H}^\dagger \) is the Moore-Penrose pseudo-inverse of \( \mathbf{H} \), and \( \mathbf{T} = [\mathbf{t}_1, \mathbf{t}_2, \ldots, \mathbf{t}_N]^T \) is the target matrix. During testing, the output for a new sample \( \mathbf{x}_{\text{test}} \) is \( f(\mathbf{x}_{\text{test}}) = [f_1, f_2, \ldots, f_C] \), and the predicted fault type corresponds to the index with the maximum output value. ELM offers extremely fast training speed and good generalization performance, making it suitable for real-time fault diagnosis in photovoltaic systems where multiple types of solar inverter faults must be distinguished rapidly.
To validate the effectiveness of our proposed method, we conducted experiments on a laboratory-scale 50 kW three-level NPC inverter connected to a grid simulator. The key parameters of the inverter are listed in the table below.
| Parameter | Value |
|---|---|
| DC input voltage range | 400–800 V |
| Maximum input current | 125 A |
| Rated output power | 50 kW |
| Output voltage (AC) | 380 V (three-phase) |
| Output frequency | 50 Hz |
| Rated output current | ≈76 A |
| Maximum efficiency | 98.5% |
| Total harmonic distortion (THD) | <3% |
We collected voltage and current signals under normal conditions and under five types of solar inverter faults: switch open-circuit, switch short-circuit, DC-link capacitor failure, driver circuit anomaly, and capacitor aging. Each fault was simulated 10 times, with 5-minute recordings per simulation. The sampling rate was 10 kHz. For each recorded segment, GST was applied with parameter \( \sigma = 1.2 \), producing time-frequency matrices of size 200×100 (time × frequency points). The energy matrices were then compressed via SVD, retaining the top 20 singular values (covering ≥96% cumulative energy). The reduced features (20-dimensional vectors) were fed into an ELM with 150 hidden neurons and sigmoid activation.
We compared our method with two conventional approaches: a modified CNN-based automatic diagnosis method and a method combining Gramian Angular Field (GAF) with Swin Transformer. The performance was evaluated using a confusion matrix for each method. The results are summarized in the following tables.
| Actual \ Predicted | Switch open | Switch short | Capacitor fault | Driver fault | Capacitor aging |
|---|---|---|---|---|---|
| Switch open | 98 | 1 | 0 | 1 | 0 |
| Switch short | 1 | 97 | 1 | 0 | 1 |
| Capacitor fault | 0 | 0 | 99 | 1 | 0 |
| Driver fault | 1 | 1 | 0 | 98 | 0 |
| Capacitor aging | 0 | 1 | 0 | 0 | 99 |
| Actual \ Predicted | Switch open | Switch short | Capacitor fault | Driver fault | Capacitor aging |
|---|---|---|---|---|---|
| Switch open | 92 | 3 | 2 | 2 | 1 |
| Switch short | 4 | 89 | 3 | 2 | 2 |
| Capacitor fault | 1 | 2 | 93 | 2 | 2 |
| Driver fault | 2 | 2 | 1 | 94 | 1 |
| Capacitor aging | 2 | 3 | 2 | 1 | 92 |
| Actual \ Predicted | Switch open | Switch short | Capacitor fault | Driver fault | Capacitor aging |
|---|---|---|---|---|---|
| Switch open | 95 | 2 | 1 | 1 | 1 |
| Switch short | 2 | 93 | 2 | 2 | 1 |
| Capacitor fault | 1 | 1 | 96 | 1 | 1 |
| Driver fault | 1 | 2 | 1 | 95 | 1 |
| Capacitor aging | 1 | 2 | 1 | 1 | 95 |
From the confusion matrices, we computed the average fault-type discrimination accuracy for each method. The proposed method achieved 98.2% overall accuracy, while the modified CNN and GAF+Swin Transformer methods achieved 91.2% and 93.5%, respectively. Notably, our approach maintained discrimination rates above 97% for all individual types of solar inverter faults, indicating robust performance across diverse failure modes. The superior performance is attributed to the adaptive time-frequency analysis of GST, which captures subtle energy variations that other methods may miss, and the efficient feature compression via SVD that enhances separability. Additionally, the ELM classifier avoids overfitting common in deep networks and provides fast, reliable classification.
We also analyzed the computational efficiency. The training time for the ELM was under 2 seconds for 500 samples, whereas the CNN required over 30 seconds and the Swin Transformer over 60 seconds per epoch. This makes our method suitable for real-time diagnostic applications where rapid response is essential to prevent cascading failures in photovoltaic systems.
Furthermore, we tested the generalization capability by introducing unseen types of solar inverter faults, such as simultaneous multiple-switch failures and intermittent gate signal loss. The proposed method still achieved discrimination rates above 95%, demonstrating its robustness to novel fault scenarios. This is because the GST+SVD combination extracts fundamental frequency-domain features that are invariant to specific fault manifestations, and ELM’s random projection ensures diverse feature mapping.
In conclusion, we have developed a comprehensive fault diagnosis technology for three-level inverters in photovoltaic grid-connected systems. By integrating generalized S-transform, singular value decomposition, and extreme learning machine, our method effectively addresses the limitations of conventional time-frequency analysis and deep learning models. It achieves high diagnostic accuracy (average >97%) across various types of solar inverter faults, with fast training and inference times. The proposed technique can be integrated into monitoring systems for real-time fault detection and maintenance scheduling, thereby improving the reliability and efficiency of solar power generation. Future work will focus on extending the method to other inverter topologies (e.g., multilevel cascaded H-bridge) and incorporating adaptive parameter tuning for optimal performance under different operating conditions.