In the contemporary energy landscape, the proliferation of solar power generation represents a cornerstone of sustainable development strategies. The reliable and efficient operation of these systems is paramount, with the on grid inverter serving as the critical interface responsible for converting direct current from photovoltaic panels into grid-compliant alternating current. The health and functionality of this on grid inverter directly influence the overall performance, safety, and economic return of the entire photovoltaic installation. Among the various potential failure modes of the power semiconductor switches within the inverter, the single-switch open-circuit fault presents a particularly insidious challenge. Unlike catastrophic short-circuit faults which trigger immediate protective shutdowns, a single open-circuit fault often allows the system to continue operating in a degraded state. This persistent operation under fault conditions can lead to increased stress on remaining components, unbalanced output, elevated total harmonic distortion injected into the grid, and ultimately, secondary failures or a complete system breakdown. Therefore, the development of fast, accurate, and reliable diagnostic methods for such faults is an essential research direction for enhancing the reliability and maintainability of grid-connected photovoltaic systems.
This article presents a detailed, two-stage methodological framework for diagnosing single insulated-gate bipolar transistor open-circuit faults in three-phase, two-level voltage source on grid inverters. The proposed approach synergistically combines the speed of blind source separation for initial fault detection with the precision of machine learning for fault localization. The core innovation lies in the sequential application of these techniques: first, the Fast Independent Component Analysis algorithm is employed to decompose the three-phase output currents into their constituent independent components, providing a rapid and definitive binary indicator of whether a single-switch fault has occurred. Following a positive detection, a comprehensive set of time-domain and frequency-domain features is extracted from the transformed rotating current. These features then serve as the input to a trained Linear Discriminant Analysis classifier, which accurately identifies the specific faulty switch among the six possibilities. The entire diagnostic process, from raw current measurement to specific fault identification, is elaborated upon, with supporting simulation evidence validating the high accuracy and robustness of the method.
1. Operational Analysis of the On Grid Inverter Under Single-Switch Open-Circuit Fault
The topology under consideration is the standard three-phase, two-level voltage source on grid inverter, which comprises six active switches (typically IGBTs with anti-parallel diodes). Each phase leg consists of an upper and a lower switch. A fault in switch VT1 (the upper switch of phase A) is analyzed as a representative case to elucidate the fault mechanism. The current path for phase current \(I_a\) under normal and faulty conditions for VT1 is dictated by the switching states.
Under normal operation, when the upper switch VT1 is commanded ON (state S1=1) and the lower switch VT2 is OFF (S2=0), the phase current \(I_a\) flows positively from the DC link through VT1 to the grid. Conversely, when S1=0 and S2=1, the negative \(I_a\) flows back through the freewheeling diode VD2. The critical scenario occurs when S1=1 and S2=0 under normal command, but VT1 has failed open. In this state, the intended path through VT1 is broken. Consequently, the positive current cannot be established. Instead, the phase current is forced to flow through the only available low-impedance path, which is the freewheeling diode VD2 of the lower switch, effectively clamping the phase output to the negative DC rail. This results in a characteristic distortion of the phase A current waveform: the positive half-cycle is entirely missing. The current control loop, which regulates the three-phase currents, is disrupted. To maintain the power transfer and satisfy the control loop’s objectives (often based on dq-axis currents), the controller drives the remaining healthy phases (B and C) harder, leading to an increase in the magnitude of currents \(I_b\) and \(I_c\). This asymmetric operation generates significant negative-sequence currents and harmonics. The waveform distortion pattern is analogous for faults in other switches; the faulted phase will exhibit a missing half-cycle (positive for an upper switch fault, negative for a lower switch fault), while the magnitudes of the currents in the non-faulted phases increase.
2. Diagnostic Framework: Detection and Localization
2.1 Fault Detection via Fast Independent Component Analysis
The three-phase output currents of a faulty on grid inverter represent a mixture of underlying source signals. Under a single open-circuit fault, these source signals can be conceptually considered as a half-wave rectified sinusoid (from the faulted phase), two near-sinusoidal signals with amplified magnitude (from the healthy phases), and inherent system noise. Blind Source Separation techniques aim to recover these original source signals from their observed mixtures without prior knowledge of the mixing process, making them ideal for this fault detection task.
FastICA was chosen for its computational efficiency and robust convergence properties compared to other algorithms like Informax. The FastICA algorithm finds the independent components by maximizing the non-Gaussianity of the estimated sources, using a fixed-point iteration scheme for speed. The mathematical model is:
Let \(\mathbf{s}(t) = [s_1(t), s_2(t), …, s_n(t)]^T\) be the vector of \(n\) unknown independent source signals.
Let \(\mathbf{x}(t) = [x_1(t), x_2(t), …, x_m(t)]^T\) be the vector of \(m\) observed mixed signals (the three-phase currents).
The mixing process is linear and instantaneous: \(\mathbf{x}(t) = \mathbf{A}\mathbf{s}(t)\), where \(\mathbf{A}\) is an unknown \(m \times n\) mixing matrix.
The goal is to find a demixing matrix \(\mathbf{W}\) such that \(\mathbf{y}(t) = \mathbf{W}\mathbf{x}(t)\) provides an estimate \(\mathbf{y}(t)\) of the source signals \(\mathbf{s}(t)\).
The FastICA algorithm for a single unit (finding one independent component) involves the following steps, which are iterated for all components:
- Centering: Remove the mean from the observed data \(\mathbf{x}\) to make it zero-mean.
- Whitening: Transform the observed vector \(\mathbf{x}\) linearly so that its components become uncorrelated and their variances equal unity. This is done via Principal Component Analysis: \(\mathbf{z} = \mathbf{D}^{-1/2}\mathbf{E}^T\mathbf{x}\), where \(\mathbf{E}\) is the matrix of eigenvectors of the covariance matrix \(E\{\mathbf{x}\mathbf{x}^T\}\) and \(\mathbf{D}\) is the diagonal matrix of its eigenvalues.
- Initialization: Choose an initial random weight vector \(\mathbf{w}\).
- Iteration: Update the weight vector using a fixed-point iteration. A common form is:
$$ \mathbf{w}^+ = E\{\mathbf{z}g(\mathbf{w}^T\mathbf{z})\} – E\{g'(\mathbf{w}^T\mathbf{z})\}\mathbf{w} $$
where \(g\) is a non-quadratic function, e.g., \(g(u)=\tanh(a_1 u)\) or \(g(u)=u^3\). - Normalization: \(\mathbf{w} = \mathbf{w}^+ / \|\mathbf{w}^+\|\).
- Convergence: Repeat steps 4 and 5 until \(\mathbf{w}\) converges.
When applied to the three-phase current signals from a faulty on grid inverter, FastICA efficiently separates them into distinct independent components. A successful separation yielding one component resembling a half-wave rectified sinusoid and another resembling an amplified sinusoid provides a clear, data-driven signature of a single-switch open-circuit fault. This detection is fast and operates directly on the measured currents, requiring no detailed model of the on grid inverter.
2.2 Feature Extraction from the Rotating Current
Once a fault is detected, the next step is to pinpoint the exact faulty switch. For this, we move from the three-phase stationary frame (abc) to a two-phase rotating reference frame (dq). The dq-transformation, synchronized to the grid voltage phase, is applied to the three-phase currents. Under balanced, normal conditions, the d-axis current \(I_d\) corresponds to the active power component and is a steady DC value. The q-axis current \(I_q\) corresponds to the reactive power component. Under an asymmetric fault like a single open-circuit, these rotating currents, particularly \(I_d\), exhibit distinct harmonic oscillations and waveform distortions. Analyzing \(I_d\) provides a consolidated, single-channel signal rich in fault-specific information. A comprehensive set of features is extracted from this \(I_d\) signal over a fundamental cycle post-fault.
The extracted features are categorized into two domains:
Time-Domain Features: These are calculated directly from the signal samples \(x_i\) of \(I_d\).
| Feature Category | Formula | Description |
|---|---|---|
| Maximum | $$\max(x_i)$$ | Peak value of the waveform. |
| Minimum | $$\min(x_i)$$ | Minimum value of the waveform. |
| Mean | $$\bar{x} = \frac{1}{N}\sum_{i=1}^{N} x_i$$ | Average value. |
| Root Mean Square (RMS) | $$X_{rms} = \sqrt{\frac{1}{N}\sum_{i=1}^{N} x_i^2}$$ | Measure of the signal’s power. |
| Variance | $$\sigma^2 = \frac{1}{N}\sum_{i=1}^{N} (x_i – \bar{x})^2$$ | Dispersion around the mean. |
| Kurtosis | $$K = \frac{\frac{1}{N}\sum_{i=1}^{N} (x_i – \bar{x})^4}{\sigma^4}$$ | Indicates the “tailedness” of the distribution. |
| Shape Factor | $$S_f = \frac{X_{rms}}{|\bar{x}|}$$ | Ratio of RMS to absolute average (for non-zero mean). |
| Crest Factor | $$C_f = \frac{\max(|x_i|)}{X_{rms}}$$ | Ratio of peak to RMS. |
| Impulse Factor | $$I_f = \frac{\max(|x_i|)}{|\bar{x}|}$$ | Ratio of peak to absolute average. |
| Margin Factor | $$M_f = \frac{\max(|x_i|)}{X_r}$$ where \(X_r = (\frac{1}{N}\sum \sqrt{|x_i|})^2\) | Related to signal peaks. |
| Clearance Factor | $$CL_f = \frac{\max(|x_i|)}{X_{r}}$$ | Similar to Margin Factor. |
Frequency-Domain Features: These are derived from the power spectral density \(P(f)\) of \(I_d\), obtained via a Fast Fourier Transform.
| Feature | Formula | Description |
|---|---|---|
| Frequency Center (FC) | $$FC = \frac{\sum_{k} f_k P(f_k)}{\sum_{k} P(f_k)}$$ | Weighted average frequency. |
| Root Mean Square Frequency (RMSF) | $$RMSF = \sqrt{\frac{\sum_{k} f_k^2 P(f_k)}{\sum_{k} P(f_k)}}$$ | Second moment of the spectrum. |
| Mean Square Frequency (MSF) | $$MSF = \frac{\sum_{k} f_k^2 P(f_k)}{\sum_{k} P(f_k)} = (RMSF)^2$$ | |
| Frequency Standard Deviation (FSD) | $$FSD = \sqrt{\frac{\sum_{k} (f_k – FC)^2 P(f_k)}{\sum_{k} P(f_k)}}$$ | Spread of the spectrum. |
This results in a 24-dimensional feature vector (11 time-domain + 4 frequency-domain features, though exact count may vary based on implementation) for each sample of the on grid inverter’s operating state.
2.3 Fault Localization with Linear Discriminant Analysis
With the multi-dimensional feature vectors extracted for different fault states, the problem of identifying the specific faulty switch becomes a multi-class classification task. We have seven classes: Normal operation, and faults in VT1 through VT6. Linear Discriminant Analysis is a classical, yet powerful, supervised dimensionality reduction and classification technique well-suited for this purpose. Its goal is to find a linear combination of features that best separates the classes by maximizing the ratio of between-class variance to within-class variance in the projected space.
Mathematically, let \(\mathbf{x}_i\) be our feature vector for sample \(i\). We have \(K\) classes. LDA seeks projection vectors \(\mathbf{w}\) that maximize the Fisher criterion \(J(\mathbf{w})\):
$$ J(\mathbf{w}) = \frac{\mathbf{w}^T \mathbf{S}_B \mathbf{w}}{\mathbf{w}^T \mathbf{S}_W \mathbf{w}} $$
where:
\(\mathbf{S}_B\) is the between-class scatter matrix:
$$ \mathbf{S}_B = \sum_{k=1}^{K} N_k (\boldsymbol{\mu}_k – \boldsymbol{\mu})(\boldsymbol{\mu}_k – \boldsymbol{\mu})^T $$
\(\mathbf{S}_W\) is the within-class scatter matrix:
$$ \mathbf{S}_W = \sum_{k=1}^{K} \sum_{\mathbf{x}_i \in C_k} (\mathbf{x}_i – \boldsymbol{\mu}_k)(\mathbf{x}_i – \boldsymbol{\mu}_k)^T $$
Here, \(N_k\) is the number of samples in class \(k\), \(\boldsymbol{\mu}_k\) is the mean vector of class \(k\), and \(\boldsymbol{\mu}\) is the overall mean vector.
The optimal projection matrix \(\mathbf{W}\) is formed by the eigenvectors corresponding to the largest eigenvalues of \(\mathbf{S}_W^{-1} \mathbf{S}_B\) (for \(K\) classes, at most \(K-1\) projections are meaningful). Classification of a new sample \(\mathbf{x}\) is then performed by projecting it onto this new subspace: \(\mathbf{z} = \mathbf{W}^T \mathbf{x}\), and assigning it to the class \(k\) whose mean projection \(\mathbf{W}^T \boldsymbol{\mu}_k\) is closest (e.g., using Euclidean or Mahalanobis distance). LDA provides a clear, linear decision boundary and is computationally efficient, making it ideal for real-time implementation in the diagnostic system of an on grid inverter.
3. Integrated Diagnostic Workflow and Validation
The complete diagnostic procedure for the on grid inverter is systematic and automated. The workflow is as follows:
1. Continuously sample the three-phase output currents \(I_a, I_b, I_c\) from the on grid inverter.
2. Apply the FastICA algorithm to the most recent cycle of data.
3. Analyze the separated independent components. If a component resembling a half-wave sinusoid is clearly identified, trigger a “Fault Detected” flag. If all components resemble full sinusoids (with possible noise), the system is “Normal”.
4. Upon fault detection, calculate the dq-transformation to obtain the rotating current \(I_d\).
5. Extract the comprehensive 24-dimensional feature vector from \(I_d\).
6. Feed the feature vector into the pre-trained LDA classification model.
7. The model outputs the identified state: Normal, VT1 fault, VT2 fault, …, or VT6 fault.
3.1 Simulation Model and Fault Injection
A detailed simulation model of a 100 kW grid-connected photovoltaic system was built to validate the method. The system includes a PV array model, a DC-DC boost converter stage raising the voltage to 800 V DC, and the central three-phase two-level on grid inverter connected to a 380 V (line-line), 50 Hz grid via an LCL filter. A fault injection block was implemented to force an open-circuit condition on any specified IGBT at a predefined simulation time (e.g., 0.02 seconds).
3.2 Fault Detection Results
With VT1 forced open at t=0.02s, the three-phase currents exhibited the expected distortion: phase A current lost its positive half-cycle, while phases B and C currents increased in magnitude while remaining roughly sinusoidal. These three current signals were mixed with a low level of Gaussian noise to simulate realistic measurements. FastICA processing of this noisy mixture successfully separated three primary independent components: one matching the half-wave pattern, one matching the amplified sine wave, and one containing the noise. This unambiguous result confirms the capability of FastICA to serve as a robust fault detector for the on grid inverter.
3.3 Fault Localization Performance
For the localization stage, a dataset was created by simulating the on grid inverter under all seven states (Normal + 6 fault types). For each state, 40 independent runs were performed with slight variations in operating point (e.g., solar irradiance) and noise realization. From each run, the \(I_d\) feature vector (24 features) was extracted, creating a data matrix of size \(280 \times 24\). This dataset was used to train and test the LDA classifier. To rigorously evaluate performance and avoid overfitting, k-fold cross-validation was employed. The model’s accuracy was compared against other common classifiers: Linear Support Vector Machine and Quadratic Support Vector Machine.
The diagnostic accuracy results are summarized below:
| Cross-Validation Proportion (%) | Diagnostic Accuracy (%) – LDA | Diagnostic Accuracy (%) – LSVM | Diagnostic Accuracy (%) – QSVM |
|---|---|---|---|
| 0 (Resubstitution) | 99.6 | 91.4 | 94.6 |
| 5 | 98.9 | 95.0 | 98.4 |
| 10 | 98.9 | 94.3 | 96.4 |
| 15 | 99.3 | 94.3 | 97.5 |
| 20 | 99.3 | 94.6 | 97.5 |
| 25 | 98.9 | 94.3 | 97.1 |
| 30 | 99.6 | 94.6 | 97.5 |
| 35 | 99.6 | 94.3 | 97.5 |
The Area Under the Receiver Operating Characteristic Curve (AUC) for each class under a 10% cross-validation setting was also calculated. An AUC of 1.0 represents perfect separability.
| On Grid Inverter State | AUC Value (LDA Model) |
|---|---|
| Normal | 1.00 |
| VT1 Fault | 1.00 |
| VT2 Fault | 1.00 |
| VT3 Fault | 1.00 |
| VT4 Fault | 1.00 |
| VT5 Fault | 1.00 |
| VT6 Fault | 1.00 |
The results demonstrate that the proposed LDA-based classifier, operating on the engineered features from the on grid inverter’s rotating current, consistently achieves superior accuracy (above 98.9% across all validation splits) compared to the SVM variants. The perfect AUC scores indicate excellent class separability in the projected feature space.
4. Conclusion
This article has presented a comprehensive and effective two-stage methodology for diagnosing single-switch open-circuit faults in three-phase on grid inverters, which are central to photovoltaic power systems. The method addresses the critical need for early detection of this subtle yet damaging fault mode. The first stage leverages the computational speed and blind processing nature of the FastICA algorithm to perform an initial, model-free detection by separating the characteristic half-wave and sinusoidal components from the three-phase output currents. This provides a rapid and reliable fault alarm. The second stage employs a targeted machine learning approach for precise fault localization. By extracting a rich set of time-domain and frequency-domain features from the d-axis rotating current—a signal highly sensitive to asymmetric imbalances—and using a Linear Discriminant Analysis classifier, the specific faulty switch among the six can be identified with high accuracy (exceeding 98.9%). The integration of blind source separation for detection and machine learning for classification creates a robust diagnostic framework that enhances the reliability and predictive maintenance capabilities of grid-connected photovoltaic systems. The method’s performance, validated through detailed simulation, confirms its potential as a valuable tool for ensuring the operational integrity of the critical on grid inverter component.