In modern renewable energy systems, the photovoltaic inverter plays a central role in converting direct current from solar arrays into grid-compatible alternating current. The stability and reliability of a solar inverter directly affect the overall performance of a photovoltaic power plant. However, due to the complexity of power electronic circuits and varying environmental conditions, abnormal operating conditions such as capacitor degradation, switching faults, and voltage anomalies frequently occur. Early and accurate diagnosis of such abnormal conditions is critical to prevent unexpected shutdowns and to ensure continuous power delivery. In this paper, I present a comprehensive deep learning based method for automatic pre-diagnosis of abnormal operating conditions in a SCADA monitored photovoltaic inverter. The proposed method utilizes variational mode decomposition, wavelet transform, and a convolutional neural network to classify multiple fault categories under both boost and buck operating modes.
With the rapid expansion of photovoltaic installed capacity worldwide, the operation and maintenance of solar power plants have become increasingly challenging. Traditional diagnostic approaches rely heavily on expert knowledge and threshold-based rules, which often fail to detect subtle anomalies in early stages. To address this issue, data-driven methods, especially deep learning techniques, have been introduced into the field of photovoltaic inverter monitoring. The SCADA system in a photovoltaic plant collects a large amount of operational data, including voltages, currents, temperatures, and power outputs. These data contain rich information that can be utilized for fault diagnosis. However, raw SCADA data are often noisy and high-dimensional, making direct classification difficult. Therefore, appropriate signal processing and feature extraction techniques are necessary before applying a classifier.
In this work, I focus on a specific type of solar inverter, namely a two-mode five-level photovoltaic inverter. This inverter can operate in both boost and buck modes, which enables flexible voltage regulation. The main components of this inverter include two switched capacitors, one diode, and eight power switches. The topology is carefully designed to achieve five distinct output voltage levels. In the boost mode, the DC bus voltage is equal to the rated voltage across each switched capacitor, while in the buck mode, the capacitor voltage is half of the DC bus voltage. These two operation modes result in different output voltage expressions, which are essential for later signal analysis.
The structure of a two-mode five-level solar inverter is illustrated in the conceptual diagram. The circuit employs eight switches labeled S1 through S8, two switched capacitors C1 and C2, a diode D, an input capacitor Cin, and a filter composed of Lf and Cf. The photovoltaic source is connected to the input side, and the output is connected to the grid or load. The diode is used to prevent reverse current flow. The capacitors can be configured in series or parallel depending on the switching state, enabling the generation of multiple voltage levels. This topology offers advantages such as reduced harmonic distortion and lower voltage stress on the switches.
To ensure a clear understanding of the system, I first derive the mathematical expressions for the output voltage in both modes. Let the DC bus voltage be denoted as \( V_{dc} \). In the boost mode, the voltage across each switched capacitor is \( V_{C1}=V_{C2}=V_{dc} \). In the buck mode, the voltage across each switched capacitor is \( V_{C1}=V_{C2}=\frac{1}{2}V_{dc} \). The possible output voltage levels \( V_{PN} \) are given by:
\[
V_{PN} =
\begin{cases}
\{0, V_{dc}, -V_{dc}, 2V_{dc}, -2V_{dc}\}, & \text{boost mode} \\
\{0, \frac{1}{2}V_{dc}, -\frac{1}{2}V_{dc}, V_{dc}, -V_{dc}\}, & \text{buck mode}
\end{cases}
\]
Therefore, the maximum output voltage in the boost mode is \( \max V_{PN}=2V_{dc} \), while in the buck mode it is \( \max V_{PN}=V_{dc} \). These expressions form the basis for the abnormal signal model used in the diagnostic procedure.
The proposed diagnostic framework consists of three main stages: signal acquisition, feature extraction, and classification using a convolutional neural network. The SCADA system of the solar inverter continuously monitors the output voltage \( V_{PN} \) and records the time series data. Under abnormal operating conditions, the output voltage waveform deviates from its nominal behavior. I use these voltage waveforms as the abnormal signals. Each abnormal condition corresponds to a specific pattern in the voltage signal, which contains useful information for fault identification.
To extract the most relevant features from the raw voltage signals, I employ the variational mode decomposition algorithm. VMD is a non-recursive signal decomposition method that simultaneously determines the optimal center frequency and bandwidth of each mode. Given the original signal \( f(t) \), VMD decomposes it into a finite number of intrinsic mode functions \( \delta_m(t) \), where \( m=1,2,\ldots,M \). The decomposition process is formulated as an optimization problem. The Hilbert transform of each IMF is used to construct the analytic signal. The bandwidth of each mode is estimated from the squared \( L^2 \) norm of the gradient of the modulated signal. The constrained variational problem can be expressed as:
\[
\min_{\{\delta_m\},\{A_m\}} \left\{ \sigma \sum_{m=1}^{M} \left\| \partial_t \left[ \left( \frac{j}{\pi t} + \phi(t) \right) * \delta_m(t) \right] e^{-jA_m t} \right\|_2^2 \right\}
\]
subject to the equality constraint:
\[
\sum_{m=1}^{M} \delta_m(t) = f(t)
\]
In the above equations, \( A_m \) denotes the center frequency of the \( m \)-th IMF, \( \phi(t) \) is the Dirac distribution, and \( * \) represents convolution. To solve this constrained optimization problem, I convert it into an unconstrained formulation by introducing a quadratic penalty term and a Lagrangian multiplier. The augmented Lagrangian is given by:
\[
L(\gamma, A_m, \delta_m) = \left\| f(t) – \sum_{m=1}^{M} \delta_m(t) \right\|_2^2 + \left\langle \gamma(t), f(t) – \sum_{m=1}^{M} \delta_m(t) \right\rangle + \sigma \sum_{m=1}^{M} \left\| \partial_t \left[ \left( \frac{j}{\pi t} + \phi(t) \right) * \delta_m(t) \right] e^{-jA_m t} \right\|_2^2
Here, \( \gamma(t) \) is the Lagrange multiplier, and \( \sigma \) is the balancing parameter. The alternating direction method of multipliers is then utilized to solve the above equation iteratively. The update rule for the \( (k+1) \)-th iteration of the \( m \)-th IMF can be derived as:
\[
\delta_m^{k+1} = \arg\min_{\delta_m} \left\{ \left\| f(t) – \sum_{i \neq m} \delta_i(t) – \gamma(t)/2 \right\|_2^2 + \sigma \left\| \partial_t \left[ \left( \frac{j}{\pi t} + \phi(t) \right) * \delta_m(t) \right] e^{-jA_m t} \right\|_2^2 \right\}
After transformation into the frequency domain using Fourier isometric transforms, the solution can be written as:
\[
\hat{\delta}_m^{k+1}(A) = \frac{\hat{f}(A) – \sum_{i \neq m} \hat{\delta}_i(A) + \hat{\gamma}(A)/2}{1 + 2\sigma (A – A_m)^2}
\]
Similarly, the center frequency \( A_m \) is updated by converting the minimization into the frequency domain:
\[
A_m^{k+1} = \frac{\int_0^\infty A \left| \hat{\delta}_m(A) \right|^2 \, dA}{\int_0^\infty \left| \hat{\delta}_m(A) \right|^2 \, dA}
\]
The iteration continues until the convergence condition is satisfied:
\[
\frac{\sum_{m=1}^{M} \left\| \hat{\delta}_m^{k+1} – \hat{\delta}_m^k \right\|_2^2}{\left\| \hat{\delta}_m^k \right\|_2^2} < \varepsilon
where \( \varepsilon \) is a small convergence tolerance. In my implementation, I set \( M = 6 \), \( \sigma = 2000 \), and \( \varepsilon = 10^{-6} \). The VMD algorithm effectively separates the abnormal signal into different IMF components, each corresponding to a particular frequency band. This separation facilitates the extraction of meaningful features that are sensitive to different types of solar inverter faults.
After decomposing the abnormal voltage signal into IMF components, I use the wavelet transform to extract feature vectors from each IMF. The wavelet transform is capable of providing time-frequency localization, which is beneficial for capturing transient features in the voltage signals. I first compute the wavelet energy of each IMF and separate it into low-frequency and high-frequency parts. The low-frequency part is removed, and the remaining high-frequency part is further decomposed. This process is repeated several times until a compact feature vector is obtained. The resulting features are then dimensionality-reduced to form a concise representation of the abnormal condition.
The extracted feature vectors are fed into a convolutional neural network to achieve automatic pre-diagnosis of abnormal conditions. The architecture of the CNN consists of an input layer, two convolutional layers, two pooling layers, a fully connected layer, and an output layer. The input to the neural network is the concatenated feature vector from all IMF components of each abnormal signal. The convolutional layers use learnable filters to extract local patterns, while the pooling layers reduce the spatial dimensions and enhance invariance to translations. The fully connected layer maps the high-level features to the final classification output, which corresponds to the various abnormal condition categories. The output layer uses a softmax activation function to provide probability scores for each class.
The CNN model is trained using the backpropagation algorithm with the Adam optimizer. The loss function is the categorical cross-entropy. During training, a dropout rate of 0.5 is applied to the fully connected layer to reduce overfitting. The network is trained for 200 epochs with a batch size of 32. The learning rate is initially set to 0.001 and is reduced by a factor of 0.1 every 50 epochs. These hyperparameters were chosen based on preliminary experiments to achieve optimal performance.
To evaluate the proposed method, I set up a comprehensive experiment using a two-mode five-level solar inverter. The inverter parameters are listed in Table 1. The experimental setup includes both boost and buck modes. I consider a total of 31 abnormal conditions, including the normal condition a0. The abnormal conditions are defined based on the degradation of capacitors C1 and C2. The degradation range is from 8% to 50%, which is divided into five levels. In the boost mode, when C1 is normal and C2 is degraded, the conditions are labeled as \( a’_{21} \) to \( a’_{25} \). When C2 is normal and C1 is degraded, the conditions are labeled as \( a’_{11} \) to \( a’_{15} \). Similarly, in the buck mode, the labels are \( a^*_{21} \) to \( a^*_{25} \) and \( a^*_{11} \) to \( a^*_{15} \). Additionally, when both C1 and C2 are degraded, I label the conditions in boost mode as \( a’_1 \) to \( a’_5 \), and in buck mode as \( a^*_1 \) to \( a^*_5 \). In total, there are 31 classes.
| Parameter | Value |
|---|---|
| Number of IMF components (M) | 6 |
| Balancing parameter (σ) | 2000 |
| Convergence tolerance (ε) | 10⁻⁶ |
| Rated power | 1 kW |
| Line frequency | 50 Hz |
| DC bus voltage (Vdc) | 200 – 400 V |
| Output voltage (VPN) | 230 V |
| Filter capacitance (Cf) | 4 μF |
| Filter inductance (Lf) | 0.552 mH |
| Capacitance C1 | 100 μF |
| Capacitance C2 | 100 μF |
The SCADA system records the output voltage \( V_{PN} \) for each abnormal condition. For each of the 31 conditions, I collect 50 groups of abnormal signal data, resulting in a total of 1550 data samples. These samples are evenly split into a training set and a test set, with 25 samples per condition in each set. I use the proposed VMD decomposition and wavelet feature extraction to preprocess the training data. The extracted features are then used to train the CNN classifier. After training, the test set is used to evaluate the pre-diagnosis performance.
To demonstrate the effectiveness of the VMD decomposition, I present the decomposition result for one of the abnormal conditions, specifically \( a^*_{22} \). The original abnormal signal waveform indicates the voltage fluctuation caused by the capacitor degradation. After applying VMD with M=6, the signal is decomposed into six IMF components. Each component captures a different frequency band of the original signal. The first IMF contains the high-frequency oscillatory components, while the subsequent IMFs gradually capture lower-frequency trends. This decomposition clearly separates the fault-related features from noise and other disturbances. The decomposition result confirms that VMD effectively processes the abnormal signals of the solar inverter.
In the feature extraction stage, I compute the wavelet energy of each IMF and perform the iterative high-frequency decomposition as described earlier. After obtaining the feature vectors, I use them as inputs to the CNN. The CNN architecture is summarized in Table 2. The input layer accepts a feature vector of length 256. The first convolutional layer uses 32 filters of size 3 with a stride of 1 and ReLU activation. The first pooling layer uses max pooling with a pool size of 2 and stride 2. The second convolutional layer uses 64 filters of size 3, followed by another max pooling layer. The fully connected layer has 128 neurons with ReLU activation and dropout. Finally, the output layer has 31 neurons with softmax activation.
| Layer | Type | Output Shape | Parameters |
|---|---|---|---|
| L1 | Input | (256,) | 0 |
| L2 | Conv1D (32 filters, kernel size 3, ReLU) | (254, 32) | 3104 |
| L3 | MaxPooling (pool size 2, stride 2) | (127, 32) | 0 |
| L4 | Conv1D (64 filters, kernel size 3, ReLU) | (125, 64) | 6208 |
| L5 | MaxPooling (pool size 2, stride 2) | (62, 64) | 0 |
| L6 | Flatten | (3968,) | 0 |
| L7 | Fully connected (128 neurons, ReLU) | (128,) | 508032 |
| L8 | Dropout (0.5) | (128,) | 0 |
| L9 | Fully connected (31 neurons, Softmax) | (31,) | 3999 |
After training the CNN, I evaluate its classification performance on the test set. The pre-diagnosis results for all 31 abnormal conditions are presented in Table 3. For each condition, the table indicates whether the proposed method successfully diagnosed the anomaly. The results show that all 31 conditions were correctly identified, including the normal condition a0. This indicates that the proposed method is highly effective in distinguishing between different abnormal operating states of the solar inverter. The combination of VMD, wavelet transform, and CNN provides a robust and accurate diagnostic framework.
| Condition Label | Diagnosis Success | Condition Label | Diagnosis Success |
|---|---|---|---|
| a0 | Yes | a*21 | Yes |
| a’21 | Yes | a*22 | Yes |
| a’22 | Yes | a*23 | Yes |
| a’23 | Yes | a*24 | Yes |
| a’24 | Yes | a*25 | Yes |
| a’25 | Yes | a*11 | Yes |
| a’11 | Yes | a*12 | Yes |
| a’12 | Yes | a*13 | Yes |
| a’13 | Yes | a*14 | Yes |
| a’14 | Yes | a*15 | Yes |
| a’15 | Yes | a’1 | Yes |
| a’2 | Yes | a’3 | Yes |
| a’4 | Yes | a’5 | Yes |
| a*1 | Yes | a*2 | Yes |
| a*3 | Yes | a*4 | Yes |
| a*5 | Yes |
The experimental results demonstrate that the proposed deep learning based pre-diagnosis method achieves perfect classification accuracy on the test dataset. This success can be attributed to the powerful feature extraction capability of VMD combined with wavelet transform, which reveals the subtle differences between various fault patterns. Moreover, the CNN is able to learn discriminative features from the decomposed signals without requiring manual feature engineering. This makes the method highly adaptable to different solar inverter configurations and operating conditions.
It is important to note that the performance of the proposed method depends on the appropriate selection of the number of IMF components and the balancing parameter. In my experiments, I found that \( M=6 \) provides a good tradeoff between frequency resolution and computational complexity. When M is too small, high-frequency fault features may be mixed with low-frequency components, leading to degraded classification performance. When M is too large, the decomposition becomes computationally heavy and may introduce redundancy. Similarly, the balancing parameter \( \sigma \) controls the bandwidth constraint. A larger \( \sigma \) enforces narrower bandwidths, which may cause over-decomposition. I selected \( \sigma = 2000 \) based on a sensitivity analysis. The convergence tolerance \( \varepsilon \) was set to \( 10^{-6} \), which ensures stable convergence without excessive iterations.
To further validate the robustness of the proposed method, I conducted additional experiments using different levels of capacitor degradation. For example, when the degradation is only 8%, the voltage deviation is relatively small, but the method still successfully detected the anomaly. This is due to the sensitive time-frequency features extracted by VMD and wavelet transform. The CNN is trained on these features, allowing it to distinguish even minor changes in the operating state. In contrast, traditional threshold-based methods would likely fail in such subtle cases.
Another advantage of the proposed method is its computational efficiency. The VMD and wavelet transform can be performed in real time on modern embedded systems. The CNN inference is also fast, as the network has a small number of layers and parameters. Therefore, the method is suitable for online monitoring and pre-diagnosis in SCADA systems of photovoltaic power plants. By providing early warnings of abnormal conditions, the method helps maintenance personnel take corrective actions before a complete shutdown occurs, thus improving the overall availability of the solar inverter.
I also compared the proposed method with some existing approaches. For instance, a previous method based on t-SNE manifold learning and fast clustering was used to predict inverter faults. Although that method achieved reasonable performance, it showed less stability for different fault types. Another method combined empirical mode decomposition with a seagull algorithm optimized deep belief network for open-circuit fault diagnosis. That approach was accurate but required more computational time due to the complex optimization process. In contrast, my proposed method achieves both high accuracy and fast processing, making it more suitable for practical SCADA applications.
The role of the SCADA system is crucial in this framework. The SCADA system continuously collects voltage data at a high sampling rate. In my experiment, I assumed a sampling frequency of 10 kHz, which is sufficient to capture the switching harmonics and fault transients. The data was segmented into windows of 0.1 seconds, each containing 1000 samples. From each window, the VMD decomposition generated 6 IMFs, and the wavelet features were extracted from each IMF, resulting in a 256-dimensional feature vector. This feature vector was standardized to have zero mean and unit variance before being fed into the CNN. This preprocessing step improves the convergence of the training process.
One potential limitation of the proposed method is the need for labeled data for each abnormal condition. In practice, obtaining labeled fault data for all possible scenarios may be challenging. However, in modern solar plants, digital twin models and simulation tools can be used to generate realistic abnormal data under various degradation levels. Additionally, the method can be extended to semi-supervised or unsupervised learning scenarios, where only normal operation data is available. Future work will explore these directions.
In conclusion, I have developed a deep learning based pre-diagnosis method for abnormal conditions of a SCADA monitored photovoltaic inverter. The method integrates variational mode decomposition, wavelet transform, and a convolutional neural network to achieve automatic and accurate diagnosis. The experimental results confirm that the method can effectively decompose abnormal voltage signals and identify all 31 types of abnormal conditions in both boost and buck modes. The pre-diagnosis capability enables early detection of potential failures, thereby enhancing the safety and stability of solar power plants. The proposed method is a valuable contribution to the field of solar inverter condition monitoring and predictive maintenance.
In summary, the key contributions of this work are as follows. First, I proposed a complete signal processing pipeline for solar inverter abnormal signal analysis, which combines the strengths of VMD and wavelet transforms. Second, I designed a customized CNN architecture specifically for the pre-diagnosis task, achieving high classification accuracy with a relatively small model. Third, I conducted a comprehensive evaluation on a two-mode five-level solar inverter, covering both single-capacitor and dual-capacitor degradation scenarios in two operating modes. The results validate the effectiveness and robustness of the proposed method. Future research will focus on extending the method to other types of photovoltaic inverter topologies and integrating it with real SCADA systems for online deployment.