Solar inverters are critical components in photovoltaic systems, converting direct current from solar panels into alternating current for grid integration. The insulated gate bipolar transistor (IGBT) is a key power switching device in solar inverters due to its high voltage and current tolerance. However, IGBT wiring faults, caused by factors like poor soldering, aging connections, or environmental stress, can lead to parasitic resistances that gradually worsen over time. These faults are often subtle and difficult to detect early, potentially escalating into severe structural failures that increase maintenance costs and safety risks. Traditional diagnostic methods for solar inverters, such as those based on current analysis, suffer from slow detection speeds, low recognition rates, and susceptibility to external interference. In this study, we propose a novel approach that combines a voltage mean-based feature extraction strategy with an improved lion swarm optimization (ILSO) algorithm to optimize the kernel extreme learning machine (KELM) for efficient IGBT wiring fault diagnosis in solar inverters. Our method simplifies feature extraction by leveraging Concordia-transformed voltage signals and enhances diagnostic accuracy and speed through advanced machine learning techniques.
The increasing adoption of solar energy has highlighted the importance of reliable solar inverter operation. IGBTs, being prone to faults in harsh environments like deserts and high-altitude regions, account for approximately 70% of power electronic device failures in solar inverters. Common structural faults include short circuits, open circuits, and intermittent misfires, but wiring faults—characterized by parasitic resistances at connection points—are often overlooked. These resistances, typically ranging from 6.1 to 50 Ω, can cause gradual performance degradation without triggering protection mechanisms. Existing diagnostic techniques for solar inverters, such as current vector trajectory analysis or wavelet-based methods, are slow and inefficient. Voltage-based approaches offer faster detection but often involve complex feature extraction processes. To address these limitations, we focus on developing a robust diagnostic framework that ensures rapid and accurate fault identification for solar inverters, ultimately enhancing system reliability and reducing downtime.
In this paper, we first analyze the fault mechanisms of IGBT wiring faults in a Z-source solar inverter, a topology known for its buck-boost capabilities and suitability for fluctuating DC-link voltages. We categorize faults into single-IGBT and dual-IGBT types, encompassing 22 distinct fault states. By simulating these states under varying parasitic resistances, we collect three-phase voltage signals and apply Concordia transformation to compress the data into two-dimensional vectors. The mean values of these vectors serve as effective fault features, reducing dimensionality and improving separability. Next, we employ an ILSO algorithm, enhanced with Sine chaotic mapping for better global optimization, to tune the KELM model’s parameters. The optimized ILSO-KELM model is then validated through extensive simulations, demonstrating superior performance in terms of diagnostic accuracy and computational efficiency compared to conventional methods like SVM, ELM, and PSO-KELM. Our contributions include a simplified feature extraction process and a high-performance diagnostic model tailored for solar inverter applications.
Fault Mechanism Analysis in Solar Inverters
Solar inverters, particularly Z-source inverters, are designed to handle wide voltage fluctuations in renewable energy systems. The Z-source topology, as illustrated in the provided figure, includes a Z-network, IGBTs, and diodes, enabling voltage boost without additional converters. IGBT wiring faults are modeled by introducing parasitic resistances in series with the device terminals, representing connection issues. Under normal conditions, stray resistances range from 0 to 6 Ω, while fault conditions involve resistances from 6.1 to 50 Ω. These faults can occur in single IGBTs or multiple IGBTs, though simultaneous faults in more than two devices are rare. We define 22 fault states, including normal operation (F0), single-IGBT faults (F1–F6), and dual-IGBT faults categorized into Type I (F7–F12), Type II (F13–F18), and Type III (F19–F21). Each state is simulated with 60 different resistance values, resulting in 1,320 samples of three-phase voltage signals for analysis.
The simulation parameters for the Z-source solar inverter model are set as follows: photovoltaic array DC voltage $U_d = 400$ V, grid frequency of 50 Hz, filter inductance $L_f = 50$ μH, capacitance $L_C = 10$ mF, Z-network inductance $L_1 = L_2 = 1$ mH, and capacitance $C_1 = C_2 = 3,300$ μF. Three-phase voltage signals $U_a$, $U_b$, and $U_c$ are captured under each fault state. For instance, in fault F19 (dual-IGBT Type III), the voltage waveforms exhibit distortion compared to normal operation, but visual differentiation between faults is challenging. This underscores the need for advanced feature extraction techniques to isolate fault characteristics effectively in solar inverters.
Table 1 summarizes the fault types and their corresponding codes, providing a clear reference for diagnosis. Single-IGBT faults affect individual switches (S1–S6), while dual-IGBT faults involve combinations such as same-phase opposite arms (Type III) or different phases (Types I and II). The parasitic resistance values are randomly selected within the specified ranges to mimic real-world scenarios, ensuring the robustness of our diagnostic approach for solar inverters.
| Fault Type | Fault Code | Faulty Devices | Wiring Resistance (Ω) |
|---|---|---|---|
| Normal | F0 | — | 0–6 |
| Single IGBT | F1 | S1 | 6.1–50 |
| F2 | S2 | 6.1–50 | |
| F3 | S3 | 6.1–50 | |
| F4 | S4 | 6.1–50 | |
| F5 | S5 | 6.1–50 | |
| F6 | S6 | 6.1–50 | |
| Dual IGBT Type I | F7 | S1, S2 | 6.1–50 |
| F8 | S1, S3 | 6.1–50 | |
| F9 | S2, S3 | 6.1–50 | |
| F10 | S4, S5 | 6.1–50 | |
| F11 | S4, S6 | 6.1–50 | |
| F12 | S5, S6 | 6.1–50 | |
| Dual IGBT Type II | F13 | S1, S5 | 6.1–50 |
| F14 | S1, S6 | 6.1–50 | |
| F15 | S2, S4 | 6.1–50 | |
| F16 | S2, S6 | 6.1–50 | |
| F17 | S3, S4 | 6.1–50 | |
| F18 | S3, S5 | 6.1–50 | |
| Dual IGBT Type III | F19 | S1, S4 | 6.1–50 |
| F20 | S2, S5 | 6.1–50 | |
| F21 | S3, S6 | 6.1–50 |
Feature Extraction Based on Voltage Mean for Solar Inverters
Feature extraction is a crucial step in fault diagnosis for solar inverters, as it directly impacts the efficiency and accuracy of the diagnostic model. We propose a voltage mean-based approach that leverages the Concordia transformation to compress three-phase voltage signals into two-dimensional features. The Concordia transformation, also known as the Clarke transformation, converts the three-phase voltages $U_a$, $U_b$, and $U_c$ into two-phase components $U_\alpha$ and $U_\beta$ in the α-β plane, reducing data dimensionality while preserving essential fault information. The transformation equations are given by:
$$ U_\alpha = \frac{2}{3} \left( U_a – \frac{1}{2} U_b – \frac{1}{2} U_c \right), $$
$$ U_\beta = \frac{2}{3} \left( \frac{\sqrt{3}}{2} U_b – \frac{\sqrt{3}}{2} U_c \right). $$
Under normal operating conditions, the trajectory of $U_\alpha$ and $U_\beta$ forms a nearly perfect circle centered at the origin. However, when IGBT wiring faults occur, this trajectory becomes distorted and irregular. To quantify these changes, we compute the mean values of $U_\alpha$ and $U_\beta$ over a sampling period $N$:
$$ \bar{U}_\alpha = \frac{1}{N} \sum_{n=1}^{N} U_\alpha(n), $$
$$ \bar{U}_\beta = \frac{1}{N} \sum_{n=1}^{N} U_\beta(n), $$
where $N$ is the number of sampling points. The mean values $\bar{U}_\alpha$ and $\bar{U}_\beta$ form a two-dimensional feature vector that effectively characterizes the fault state. In normal operation, this vector lies close to the origin, but it deviates significantly under fault conditions, with the deviation magnitude correlating with the severity of the wiring resistance.
We analyze the distribution of these mean values across different fault types for solar inverters. For single-IGBT faults, the vectors align along specific axes: F1 and F4 along the $U_\alpha$ axis, F2 and F5 along rotated directions, and F3 and F6 along other orientations. As the wiring resistance increases, the points move farther from the origin. Dual-IGBT faults exhibit more complex patterns: Type I faults distribute into six sectors, Type II faults also occupy distinct sectors, and Type III faults align along axes similar to single faults but with different magnitudes. Although two-dimensional scatter plots show separability, overlapping regions exist, necessitating advanced classification models for precise diagnosis in solar inverters.
To illustrate, we generate scatter plots for each fault type using 20 resistance values per fault. The global scatter plot reveals that while most faults are distinguishable, some overlaps occur, particularly between dual-IGBT types and single-IGBT faults. This highlights the importance of combining this feature extraction method with a powerful classifier like KELM to achieve high diagnostic accuracy for solar inverters. The voltage mean approach simplifies the feature set to just two dimensions, significantly reducing computational complexity compared to traditional methods that use high-dimensional time-domain or frequency-domain features.
Diagnosis Model Using ILSO-Optimized KELM for Solar Inverters
The kernel extreme learning machine (KELM) is a variant of the extreme learning machine (ELM) that incorporates kernel functions to enhance generalization and stability. Unlike standard ELM, which uses random hidden layer weights, KELM employs a kernel matrix to implicitly map inputs to a high-dimensional feature space, improving performance for non-linear problems like fault diagnosis in solar inverters. Given a training dataset $D = \{ (\mathbf{x}_i, \mathbf{t}_i) | i = 1, 2, \dots, N \}$, where $\mathbf{x}_i$ is the input feature vector (e.g., $[\bar{U}_\alpha, \bar{U}_\beta]$) and $\mathbf{t}_i$ is the target output, the KELM model aims to minimize the output error. The output of a single-hidden-layer neural network is expressed as:
$$ \mathbf{y}_i = \sum_{j=1}^{K} \boldsymbol{\beta}_j g(\mathbf{x}_i \mathbf{w}_j + b_j), $$
where $g(\cdot)$ is the activation function, $b_j$ is the bias of the $j$-th hidden node, $\mathbf{w}_j$ and $\boldsymbol{\beta}_j$ are weight vectors, and $K$ is the number of hidden nodes. For zero error approximation, $\sum_{i=1}^{N} \| \mathbf{y}_i – \mathbf{t}_i \| = 0$, leading to the matrix equation $\mathbf{H} \boldsymbol{\beta} = \mathbf{T}$, where $\mathbf{H}$ is the hidden layer output matrix. The solution for the output weights $\boldsymbol{\beta}^*$ is given by:
$$ \boldsymbol{\beta}^* = \mathbf{H}^+ \mathbf{T} = \mathbf{H}^T \left( \mathbf{H} \mathbf{H}^T \right)^{-1} \mathbf{T}, $$
where $\mathbf{H}^+$ is the Moore-Penrose generalized inverse. To improve robustness, KELM replaces $\mathbf{H} \mathbf{H}^T$ with a kernel matrix $\Omega_{\text{ELM}}$, where each element is defined by a kernel function $K(\mathbf{x}_i, \mathbf{x}_j)$. Using the radial basis function (RBF) kernel:
$$ K(\mathbf{x}_i, \mathbf{x}_j) = \exp \left( -\frac{\| \mathbf{x}_i – \mathbf{x}_j \|^2}{2\sigma^2} \right), $$
the KELM output becomes:
$$ \mathbf{y}(\mathbf{x}) = \mathbf{h}(\mathbf{x}) \mathbf{H}^T \left( \frac{\mathbf{I}}{C} + \mathbf{H} \mathbf{H}^T \right)^{-1} \mathbf{T} = \begin{bmatrix} K(\mathbf{x}, \mathbf{x}_1) \\ \vdots \\ K(\mathbf{x}, \mathbf{x}_N) \end{bmatrix}^T \left( \frac{\mathbf{I}}{C} + \Omega_{\text{ELM}} \right)^{-1} \mathbf{T}, $$
where $C$ is a regularization parameter that controls the trade-off between training error and model complexity, and $\mathbf{I}$ is an identity matrix. The performance of KELM depends heavily on the selection of $\sigma$ and $C$, which we optimize using an improved lion swarm algorithm (ILSO).
The lion swarm algorithm (LSO) is a metaheuristic optimization technique inspired by the social behavior of lions. It consists of three groups: the lion king, lionesses, and cubs, each updating their positions differently to explore the search space. However, standard LSO tends to converge prematurely and lacks diversity in later stages. To address this, we enhance LSO with Sine chaotic mapping for population initialization, which improves global search capability. The Sine chaotic map is defined as:
$$ x_{i_0+1} = \delta \sin(\pi x_{i_0}), $$
where $i_0$ is the iteration index, $x_{i_0}$ is the chaotic variable, and $\delta$ is a control parameter set to 1. This map generates chaotic sequences that are used to initialize the lion positions, ensuring better coverage of the solution space for solar inverter fault diagnosis.
The ILSO process involves the following steps for optimizing KELM parameters $\sigma$ and $C$:
- Initialize the lion population using Sine chaotic mapping, with $M$ lions in a $D$-dimensional space (here, $D=2$ for $\sigma$ and $C$). The number of adult lions is $m = \lambda M$, where $\lambda \in (0,1)$ is a proportion factor.
- Evaluate the fitness of each lion, defined as the diagnostic accuracy of the KELM model on training data.
- Update positions:
- Lion king: Moves locally around the best position $g^k$ at iteration $k$: $$ \mathbf{x}_i^{k+1} = g^k \left( 1 + \eta \| \mathbf{p}_i^k – g^k \| \right), $$ where $\eta \sim N(0,1)$ is a random number, and $\mathbf{p}_i^k$ is the historical best position of lion $i$.
- Lionesses: Collaborate with a randomly chosen partner $c$: $$ \mathbf{x}_i^{k+1} = \frac{ \mathbf{p}_i^k + \mathbf{p}_c^k }{2} (1 + \lambda \eta), $$ where $\lambda = \text{step} \cdot \exp(-30 f / F)$, $\text{step} = 0.1 \times (h – l)$, $f$ is the current iteration, $F$ is the maximum iterations, and $h$ and $l$ are bounds for $\sigma$ and $C$.
- Cubs: Follow the lion king or lionesses based on a probability $q$:
$$ \mathbf{x}_i^{k+1} = \begin{cases}
\frac{g^k + \mathbf{p}_i^k}{2} (1 + \beta \eta), & q \leq \frac{1}{3}, \\
\frac{\mathbf{p}_m^k + \mathbf{p}_i^k}{2} (1 + \beta \eta), & \frac{1}{3} < q \leq \frac{2}{3}, \\
\frac{\mathbf{d}^k + \mathbf{p}_i^k}{2} (1 + \beta \eta), & \frac{2}{3} < q \leq 1,
\end{cases} $$
where $\beta = \text{step} \cdot (F – f)/F$, $\mathbf{p}_m^k$ is a randomly selected lioness’s historical best, and $\mathbf{d}^k = h + l – g^k$ represents a driven-away position.
- Update historical best positions and the global best $g^k$.
- Repeat until convergence or maximum iterations are reached.
The optimal parameters $\sigma^*$ and $C^*$ obtained from ILSO are used to train the final KELM model for solar inverter fault diagnosis.
The overall diagnostic workflow for solar inverters is as follows:
- Collect three-phase voltage signals $U_a$, $U_b$, $U_c$ from the solar inverter under various operating conditions.
- Apply Concordia transformation to obtain $U_\alpha$ and $U_\beta$, then compute their mean values $\bar{U}_\alpha$ and $\bar{U}_\beta$ to form feature vectors.
- Split the dataset into training and testing sets (e.g., 40 samples per fault for training, 20 for testing).
- Use ILSO to optimize KELM parameters $\sigma$ and $C$ on the training set.
- Train the KELM model with optimized parameters and evaluate its performance on the test set.
This approach ensures efficient and accurate fault classification for solar inverters, handling both single and dual IGBT wiring faults effectively.
Validation and Comparative Analysis for Solar Inverters
To validate our proposed method, we conduct simulations using the Z-source solar inverter model in MATLAB/Simulink. We generate 1,320 samples of three-phase voltage signals across 22 fault states, each with 60 resistance values. The feature vectors $[\bar{U}_\alpha, \bar{U}_\beta]$ are extracted and divided into training and testing sets. We compare the ILSO-KELM model against several established methods: support vector machine (SVM), extreme learning machine (ELM), KELM without optimization, particle swarm optimization-based KELM (PSO-KELM), and standard LSO-KELM. Each model is evaluated based on diagnostic accuracy, training time, and testing time, with results averaged over 10 runs to ensure reliability.
The convergence behavior of the optimization algorithms is illustrated in Figure 6, where ILSO-KELM achieves faster convergence and higher accuracy compared to LSO-KELM and PSO-KELM. For instance, ILSO-KELM reaches near-optimal fitness within 20 iterations, while PSO-KELM requires more than 50 iterations. This demonstrates the effectiveness of Sine chaotic mapping in enhancing global search for solar inverter applications.
Table 2 presents the average diagnostic accuracy and computational times for each method. ILSO-KELM achieves the highest accuracy of 98.4%, significantly outperforming SVM (73.7%), ELM (80.5%), KELM (85.9%), PSO-KELM (89.1%), and LSO-KELM (93.0%). Moreover, ILSO-KELM has the shortest training time (0.0237 seconds) and testing time (0.0108 seconds), making it suitable for real-time fault diagnosis in solar inverters. The confusion matrix for ILSO-KELM shows minimal misclassifications, with most faults correctly identified, including challenging dual-IGBT types.
| Model | Diagnostic Accuracy (%) | Training Time (s) | Testing Time (s) |
|---|---|---|---|
| SVM | 73.7 | 2.7138 | 1.1781 |
| ELM | 80.5 | 1.2703 | 0.7729 |
| KELM | 85.9 | 1.4927 | 0.4871 |
| PSO-KELM | 89.1 | 0.7614 | 0.2937 |
| LSO-KELM | 93.0 | 0.2971 | 0.1011 |
| ILSO-KELM | 98.4 | 0.0237 | 0.0108 |
The superior performance of ILSO-KELM can be attributed to several factors. First, the voltage mean feature extraction reduces data dimensionality, focusing on the most relevant fault characteristics for solar inverters. Second, the ILSO algorithm effectively tunes KELM parameters, avoiding local optima and ensuring robust generalization. Third, the KELM model itself offers fast learning and high accuracy due to its kernel-based approach. In contrast, SVM and ELM struggle with non-linearities and overfitting, while PSO-KELM and LSO-KELM exhibit slower convergence and lower accuracy. These results confirm that our method is well-suited for diagnosing IGBT wiring faults in solar inverters, providing a balance of speed and precision.
Additionally, we analyze the impact of feature dimensionality on diagnostic performance. Methods that use high-dimensional features, such as those based on wavelet transforms or time-domain statistics, often require more computational resources and longer training times. By contrast, our two-dimensional feature vector enables rapid processing without sacrificing accuracy. This is particularly advantageous for large-scale solar inverter systems where real-time monitoring is essential. The ILSO-KELM model can be deployed in embedded systems for online fault detection, enhancing the reliability and maintenance efficiency of solar inverters.
Conclusion
In this study, we have developed a comprehensive fault diagnosis method for IGBT wiring faults in solar inverters, addressing the limitations of existing approaches in terms of speed and accuracy. By leveraging voltage mean values derived from Concordia-transformed three-phase signals, we extract low-dimensional feature vectors that encapsulate essential fault information. This simplification streamlines the diagnostic process for solar inverters, reducing computational overhead while maintaining high discriminative power. The integration of an improved lion swarm algorithm with kernel extreme learning machine (ILSO-KELM) further enhances performance by optimizing model parameters effectively, resulting in faster convergence and superior fault recognition rates.
Our experimental results, based on a Z-source solar inverter model, demonstrate that the proposed method achieves an average diagnostic accuracy of 98.4%, outperforming traditional techniques like SVM, ELM, and PSO-KELM. The ILSO-KELM model also exhibits remarkable efficiency, with training and testing times of 0.0237 seconds and 0.0108 seconds, respectively, making it suitable for real-time applications in solar inverters. The method successfully handles both single and dual IGBT wiring faults, covering a wide range of fault scenarios with minimal misclassification.
Future work could explore the extension of this approach to other types of solar inverter faults, such as capacitor degradation or sensor failures, and investigate its applicability in grid-connected systems with multiple inverters. Additionally, incorporating adaptive feature selection or deep learning elements may further improve robustness. Overall, our contributions provide a practical and efficient solution for enhancing the reliability and safety of solar inverters, supporting the growing adoption of solar energy worldwide.