The reliable and efficient conversion of solar energy hinges on the performance of the power electronic interface, with the photovoltaic grid tied inverter standing as its most critical component. Within this system, the Insulated Gate Bipolar Transistor (IGBT) serves as the fundamental switching device, and its operational stability directly dictates the overall reliability of the entire photovoltaic generation unit. Statistics indicate that power semiconductor switches, particularly IGBTs, account for a significant proportion of failures in modern grid tied inverters. An undetected open-circuit fault in an IGBT can lead to distorted output currents, increased stress on healthy components, reduced efficiency, and in severe cases, catastrophic failure of the system, posing safety risks. Consequently, the development of fast, accurate, and robust diagnostic methods for IGBT faults is paramount for ensuring the safety, reliability, and longevity of photovoltaic power plants.
Traditional diagnostic approaches often rely on the analysis of electrical signatures, such as output currents or voltages, using signal processing techniques like wavelet transform or Park’s vector analysis combined with machine learning classifiers like Support Vector Machines (SVM). While effective to a degree, these methods frequently depend on expert-designed feature extraction, which may not generalize well across different operating conditions and inverter topologies. Their performance can degrade in the presence of noise or varying load conditions, highlighting limitations in robustness and adaptability.
The advent of deep learning has opened new avenues for data-driven fault diagnosis. Convolutional Neural Networks (CNNs), renowned for their powerful automatic feature extraction capabilities from image data, have been successfully applied to fault diagnosis in various mechanical and electrical systems. The core challenge in applying CNNs to inverter fault diagnosis lies in effectively transforming the one-dimensional (1-D) time-series current or voltage signals into a two-dimensional (2-D) format suitable for CNN processing without losing critical temporal information. Common transformation methods include Gramian Angular Fields (GAF), Recurrence Plots (RP), and Short-Time Fourier Transform (STFT) spectrograms. However, these methods can sometimes oversimplify temporal dynamics or be sensitive to noise.
This article proposes a novel fault diagnosis framework for IGBT open-circuit faults in three-phase two-level photovoltaic grid tied inverters by synergistically combining Markov Transition Field (MTF) encoding and a Convolutional Neural Network. The MTF provides a superior method for converting 1-D current signals into 2-D grayscale images by preserving the temporal dependency and state transition probabilities of the original signal. These resulting MTF images are then fed into a CNN model, based on the AlexNet architecture, which automatically learns discriminative features for classifying different fault states. The proposed MTF-CNN method is validated through detailed simulations of a 10kW grid tied inverter system under various single IGBT open-circuit fault scenarios. Comprehensive experiments demonstrate that this approach achieves high diagnostic accuracy, exhibits strong robustness against noise interference, and outperforms other conventional signal-to-image encoding techniques.
The topology of a standard two-stage single-phase or three-phase photovoltaic grid tied inverter is well-known. For this study, we focus on the prevalent three-phase two-level voltage source inverter (VSI) topology. The system typically consists of a photovoltaic array, a DC-DC boost converter with Maximum Power Point Tracking (MPPT), a DC-link capacitor, the three-phase two-level VSI bridge, and an LCL output filter connected to the grid. The six IGBTs (with anti-parallel diodes) in the VSI bridge, labeled S1 to S6, are the subjects of our fault diagnosis. An open-circuit fault in any single IGBT disrupts the normal switching pattern, leading to characteristic distortions in the three-phase output currents. These current waveforms serve as the primary diagnostic signals, as voltage outputs are often tightly regulated by the grid.
The Markov Transition Field (MTF) is a powerful algorithm for encoding time series data into images while preserving temporal relationships. Given a normalized time series $$X = \{x_1, x_2, …, x_n\}$$, the MTF construction involves the following steps. First, the value range of the time series is divided into Q quantile bins. Each data point $$x_i$$ is assigned to a corresponding quantile $$q_j$$ (where $$j \in [1, Q]$$). Second, a first-order Markov transition matrix $$W$$ is computed, where each element $$w_{ij}$$ represents the probability that a point in quantile $$q_i$$ is followed by a point in quantile $$q_j$$. This matrix captures the transition dynamics but loses the temporal order.
$$W = \begin{bmatrix} w_{11} & w_{12} & \cdots & w_{1Q} \\ w_{21} & w_{22} & \cdots & w_{2Q} \\ \vdots & \vdots & \ddots & \vdots \\ w_{Q1} & w_{Q2} & \cdots & w_{QQ} \end{bmatrix} = \begin{bmatrix} P(x_t \in q_1 | x_{t-1} \in q_1) & \cdots & P(x_t \in q_Q | x_{t-1} \in q_1) \\ P(x_t \in q_1 | x_{t-1} \in q_2) & \cdots & P(x_t \in q_Q | x_{t-1} \in q_2) \\ \vdots & \ddots & \vdots \\ P(x_t \in q_1 | x_{t-1} \in q_Q) & \cdots & P(x_t \in q_Q | x_{t-1} \in q_Q) \end{bmatrix}$$
To reintroduce temporal information, the MTF matrix $$M$$ is constructed by spreading the transition probability $$w_{ij}$$ along the temporal axis. Specifically, for the time steps $$i$$ and $$j$$ in the original series, the MTF matrix element $$m_{ij}$$ is defined as the transition probability between the quantiles of $$x_i$$ and $$x_j$$.
$$M = \begin{bmatrix} m_{11} & m_{12} & \cdots & m_{1n} \\ m_{21} & m_{22} & \cdots & m_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ m_{n1} & m_{n2} & \cdots & m_{nn} \end{bmatrix} = \begin{bmatrix} w_{q(x_1), q(x_1)} & w_{q(x_1), q(x_2)} & \cdots & w_{q(x_1), q(x_n)} \\ w_{q(x_2), q(x_1)} & w_{q(x_2), q(x_2)} & \cdots & w_{q(x_2), q(x_n)} \\ \vdots & \vdots & \ddots & \vdots \\ w_{q(x_n), q(x_1)} & w_{q(x_n), q(x_2)} & \cdots & w_{q(x_n), q(x_n)} \end{bmatrix}$$
Here, $$q(x_i)$$ denotes the quantile bin to which $$x_i$$ belongs. The resulting matrix $$M$$ is an $$n \times n$$ image where the intensity at pixel $$(i, j)$$ corresponds to the transition likelihood from the state at time $$i$$ to the state at time $$j$$. This representation maintains the temporal structure along the main diagonal and reveals the multi-scale transition patterns across the image, making it highly suitable for visual inspection and CNN-based feature learning.
For the CNN architecture, we adapt the well-established AlexNet, known for its effectiveness in image classification tasks. The network consists of five convolutional layers for feature extraction, followed by three fully connected layers for classification. Max-pooling layers are interspersed to reduce spatial dimensions and enhance translational invariance. The Rectified Linear Unit (ReLU) serves as the activation function to introduce non-linearity. To mitigate overfitting, Dropout regularization is applied in the fully connected layers. The final layer uses a Softmax classifier to output probabilities for each fault class. The structure is summarized in the table below.
| Layer Number | Layer Type | Kernel Size / Neurons | Number of Filters/Neurons | Activation Function | Output Size |
|---|---|---|---|---|---|
| 1 | Input Layer | – | – | – | 224x224x3 |
| 2 | Convolution 1 | 11×11 | 96 | ReLU | 55x55x96 |
| 3 | Max Pooling 1 | 3×3 (stride 2) | – | – | 27x27x96 |
| 4 | Convolution 2 | 5×5 | 256 | ReLU | 27x27x256 |
| 5 | Max Pooling 2 | 3×3 (stride 2) | – | – | 13x13x256 |
| 6 | Convolution 3 | 3×3 | 384 | ReLU | 13x13x384 |
| 7 | Convolution 4 | 3×3 | 384 | ReLU | 13x13x384 |
| 8 | Convolution 5 | 3×3 | 256 | ReLU | 13x13x256 |
| 9 | Max Pooling 3 | 3×3 (stride 2) | – | – | 6x6x256 |
| 10 | Flatten | – | – | – | 9216 |
| 11 | Fully Connected 1 | – | 4096 | ReLU | 4096 |
| 12 | Dropout (0.5) | – | – | – | 4096 |
| 13 | Fully Connected 2 | – | 4096 | ReLU | 4096 |
| 14 | Dropout (0.5) | – | – | – | 4096 |
| 15 | Fully Connected 3 | – | 7 | Softmax | 7 |
The proposed MTF-CNN fault diagnosis methodology for the photovoltaic grid tied inverter follows a systematic pipeline. First, a simulation model of a 10kW three-phase grid connected PV system is constructed in MATLAB/Simulink. The system parameters are: DC-link voltage of 700V, switching frequency of 5 kHz, grid frequency of 50Hz, LCL filter with an inverter-side inductance of 0.5 mH. Seven distinct operating states are simulated: the normal healthy condition and six single IGBT open-circuit fault conditions (S1, S2, S3, S4, S5, S6). For each state, the three-phase output currents are sampled at a high frequency. The phase-A current $$i_a(t)$$ is selected as the primary diagnostic signal. From the transient period after fault inception, data segments corresponding to exactly one fundamental grid cycle (0.02 seconds, 2000 data points per segment) are extracted to form raw 1-D signal samples.
Each 1-D current sample (2000 points) is then encoded into a 224×224 pixel MTF image. The number of quantiles Q is a crucial parameter; after experimentation, Q=8 was chosen as it provided a good balance between detail and computational efficiency. This process generates a dataset of MTF images, with 800 images per fault class, resulting in a total of 5600 images. The dataset is randomly partitioned into a training set (70%, 3920 images), a testing set (15%, 840 images), and a separate validation set (15%, 840 images) used for final evaluation. The images are resized to 224x224x3 to match the AlexNet input dimensions.
The AlexNet-based CNN model is implemented using the TensorFlow 2.x framework. The model is trained using the Adam optimizer with an initial learning rate of 0.001, a batch size of 32, and for 100 epochs. Categorical cross-entropy is used as the loss function. The training process monitors the validation loss to prevent overfitting. The performance is evaluated using standard metrics: Accuracy, Precision, Recall, and F1-Score, derived from the confusion matrix. The accuracy is defined as:
$$Accuracy = \frac{TP + TN}{TP + TN + FP + FN}$$
Where TP, TN, FP, FN represent True Positives, True Negatives, False Positives, and False Negatives, respectively, aggregated across all classes.
The training and validation performance curves over 100 epochs are shown conceptually below (actual curves would be plotted). The model converges steadily, with training accuracy approaching 99.5% and validation accuracy stabilizing around 98.9%. The loss curves decrease smoothly, indicating effective learning without significant overfitting. This demonstrates the strong capability of the MTF-CNN model to learn discriminative features from the encoded current signals of the faulty grid tied inverter.
The definitive performance is assessed on the independent test set. The confusion matrix provides a detailed breakdown of the model’s classification results for the seven classes (Normal, Fault S1, S2, S3, S4, S5, S6). The overall test accuracy achieved is 98.9%. The matrix reveals that most misclassifications occur between topologically complementary switches in the same inverter leg (e.g., S1 and S2, S4 and S5), which is expected as their fault signatures are often symmetrical and can be very similar under certain load conditions. The high values on the diagonal confirm the model’s excellent diagnostic precision.
| Actual \ Predicted | Normal | Fault S1 | Fault S2 | Fault S3 | Fault S4 | Fault S5 | Fault S6 |
|---|---|---|---|---|---|---|---|
| Normal | 838 | 1 | 0 | 1 | 0 | 0 | 0 |
| Fault S1 | 0 | 832 | 6 | 0 | 2 | 0 | 0 |
| Fault S2 | 1 | 5 | 834 | 0 | 0 | 0 | 0 |
| Fault S3 | 0 | 0 | 0 | 839 | 0 | 1 | 0 |
| Fault S4 | 0 | 0 | 0 | 0 | 833 | 7 | 0 |
| Fault S5 | 0 | 0 | 0 | 1 | 5 | 834 | 0 |
| Fault S6 | 0 | 0 | 0 | 0 | 0 | 0 | 840 |
To rigorously evaluate the robustness of the proposed MTF-CNN method for grid tied inverter diagnosis, the test data is artificially corrupted with Additive White Gaussian Noise (AWGN) at different Signal-to-Noise Ratio (SNR) levels, as well as with random impulse noise. The model, trained on clean data, is then tested on these noisy datasets. The results are summarized in the following tables. The performance remains remarkably stable even at low SNR levels (e.g., 25 dB), with accuracy drops of less than 2%. This underscores the inherent noise resilience of the MTF encoding process, which captures state transition probabilities that are less susceptible to high-frequency noise compared to raw waveform values.
| Epoch | Accuracy @ 40dB (%) | Accuracy @ 30dB (%) | Accuracy @ 25dB (%) |
|---|---|---|---|
| 20 | 99.0 | 98.9 | 98.5 |
| 40 | 99.8 | 99.8 | 99.5 |
| 60 | 99.9 | 99.9 | 99.6 |
| 80 | 99.9 | 100.0 | 99.7 |
| 100 | 100.0 | 100.0 | 99.7 |
| Noise Type / Epoch | 20 | 50 | 80 | 100 |
|---|---|---|---|---|
| Random Impulse Noise (Train Acc.) | 98.5% | 99.4% | 99.7% | 99.9% |
| Random Impulse Noise (Test Acc.) | 98.7% | 99.1% | 99.5% | 99.8% |
A critical comparative analysis is conducted to validate the efficacy of the MTF encoding specifically for the grid tied inverter fault diagnosis task. The same 1-D current signal samples are converted into 2-D images using four alternative methods: Gramian Angular Summation Field (GASF), Gramian Angular Difference Field (GADF), Recurrence Plot (RP), and Continuous Wavelet Transform (CWT) scalogram. These image sets are then used to train and test identical CNN models (with the same architecture and hyperparameters as the MTF-CNN model). The final test accuracies are compared. The results consistently show that the MTF encoding yields the highest diagnostic accuracy, outperforming GASF, GADF, RP, and CWT-based methods by a margin of 1.5% to 5%. This advantage can be attributed to MTF’s unique ability to encapsulate the temporal evolution and state transition dynamics of the inverter’s output current, which are highly informative for distinguishing between different switch fault patterns.
Further analysis involves calculating the precision and recall for each fault class from the confusion matrix. Precision for class $$i$$, $$P_i$$, is the ratio of correctly predicted instances of class $$i$$ to all instances predicted as class $$i$$. Recall for class $$i$$, $$R_i$$, is the ratio of correctly predicted instances of class $$i$$ to all actual instances of class $$i$$. The F1-score is the harmonic mean of precision and recall: $$F1_i = 2 \cdot \frac{P_i \cdot R_i}{P_i + R_i}$$.
| Fault Class | Precision (P) | Recall (R) | F1-Score |
|---|---|---|---|
| Normal | 0.998 | 0.998 | 0.998 |
| S1 | 0.993 | 0.990 | 0.992 |
| S2 | 0.993 | 0.993 | 0.993 |
| S3 | 0.998 | 0.999 | 0.998 |
| S4 | 0.992 | 0.992 | 0.992 |
| S5 | 0.990 | 0.993 | 0.992 |
| S6 | 1.000 | 1.000 | 1.000 |
| Macro Average | 0.995 | 0.995 | 0.995 |
The high and balanced precision and recall scores across all classes, evidenced by the macro-average F1-score of 0.995, confirm that the MTF-CNN model is not only accurate but also reliable, with minimal bias towards any specific fault type in the grid tied inverter. This balanced performance is crucial for practical deployment where all fault modes are equally critical to detect.
In conclusion, this article has presented a novel and effective data-driven framework for diagnosing single IGBT open-circuit faults in three-phase photovoltaic grid tied inverters. The core innovation lies in the integration of Markov Transition Field encoding with a deep Convolutional Neural Network. The MTF proficiently transforms the 1-D time-domain current signal into a 2-D image that preserves the essential temporal dependencies and state transition characteristics of the fault. This image serves as an optimal input for the CNN, which automates the feature extraction and classification process. Extensive simulation studies validate the proposed method, demonstrating a diagnostic accuracy exceeding 98.9%. The framework exhibits exceptional robustness against both Gaussian and impulse noise, maintaining high performance even under low SNR conditions. Furthermore, comparative studies establish the superiority of MTF encoding over other common time-series imaging techniques for this specific application. The method provides a promising, intelligent solution for enhancing the reliability and maintainability of photovoltaic grid tied inverter systems, paving the way for predictive maintenance strategies. Future work will focus on extending the diagnosis to multiple simultaneous faults, validating the method with experimental data from physical grid tied inverter prototypes, and exploring its applicability to more complex multi-level inverter topologies.