The transition of traditional power systems towards new power systems dominated by renewable energy sources has placed grid-tied inverters at the very core of modern energy conversion. As the critical interface connecting distributed generation sources like photovoltaics and wind turbines to the main grid, the operational health and reliability of these grid-tied inverters directly impact the overall stability and security of the power network. Within the inverter’s power stage, the insulated-gate bipolar transistor (IGBT) switch tubes are among the most vulnerable components due to their exposure to significant electrical and thermal stresses during continuous high-frequency switching operations. Failures in these switches can lead to catastrophic system downtime and potentially trigger cascading failures. Therefore, the development of advanced, real-time health monitoring and predictive diagnostic methods for inverter switch tubes is of paramount importance for ensuring the resilience of the future grid.
Conventional fault diagnosis for grid-tied inverters has predominantly focused on identifying hard faults, such as open-circuit or short-circuit failures in the IGBTs. These methods, while effective for post-failure isolation, represent a reactive approach. By the time a hard fault is detected and diagnosed, the inverter has already ceased normal operation, potentially causing power loss and affecting system performance. A more proactive strategy involves the early detection of parameteric soft defects—incipient anomalies that precede catastrophic hard failures. These soft defects manifest as gradual degradations in the switch tube’s characteristics, such as an increase in on-state resistance ($R_{on}$), a decrease in off-state resistance ($R_{off}$), or changes in switching timing due to parasitic capacitance variations. Although an inverter with such defects might continue to function, its efficiency decreases, thermal stress increases, and the risk of an imminent hard fault rises significantly. Diagnosing these subtle, early-stage anomalies from the inverter’s output waveforms presents a significant challenge due to the small magnitude of signal distortions and the presence of system noise.
To address this challenge, we propose a novel data-driven health diagnosis framework for grid-tied inverter switch tubes. Our method leverages the synergistic combination of Gramian Angular Field (GAF) transformation and a parallel Convolutional Neural Network (CNN) architecture. The core innovation lies in transforming time-series voltage and current signals into two distinct types of two-dimensional diagnostic images that encapsulate temporal correlations. These images are then processed in parallel by a deep learning model to achieve highly accurate and robust classification of various switch tube defect states. This approach enables predictive maintenance by identifying problematic switches before they fail completely, thereby enhancing the operational reliability of grid-tied inverters in renewable energy systems.
Methodology: From Time-Series to Diagnostic Images
The proposed health monitoring framework consists of several key stages: data acquisition and feature construction, image encoding via GAF, and parallel deep learning-based classification. The overall pipeline is designed to be efficient and suitable for potential real-time implementation.
1. Signal Acquisition and Virtual Resistance Feature
In a practical setting, the three-phase output voltages ($u_a, u_b, u_c$) and currents ($i_a, i_b, i_c$) of the grid-tied inverter are the most readily available measurements. To construct a sensitive feature that amplifies the signatures of switch tube defects while mitigating the influence of grid-side impedance, we define a “virtual resistance” parameter. For each sampling instant, the virtual resistance $R^*_k$ for phase $x$ is calculated as:
$$ R^*_x[k] = \frac{E – u_x[k]}{i_x[k]} $$
where $E$ is a constant virtual electromotive force, typically set slightly above the nominal voltage (e.g., $E = 1.1U_N$), and $u_x[k]$ and $i_x[k]$ are the sampled voltage and current at time step $k$. This transformation projects the coupled voltage-current dynamics onto a single, more discriminative one-dimensional time-series sequence $X = \{R^*[1], R^*[2], …, R^*[n]\}$, where $n$ is the sequence length. The data from all three phases are concatenated to form a comprehensive sample.
2. Gramian Angular Field (GAF) Image Encoding
The GAF technique provides a powerful means to encode the temporal structure of a one-dimensional time series into a two-dimensional image, preserving temporal dependencies in a visually recognizable and machine-learnable format. The transformation involves three main steps applied to the virtual resistance sequence $X$.
Step 1: Normalization. The time series $X$ is scaled to the range $[-1, 1]$ to ensure consistency and facilitate the subsequent polar transformation.
$$ \tilde{x}_i = \frac{(x_i – \max(X)) + (x_i – \min(X))}{\max(X) – \min(X)} $$
where $\tilde{X} = \{\tilde{x}_1, \tilde{x}_2, …, \tilde{x}_n\}$ is the normalized series.
Step 2: Polar Coordinate Transformation. Each normalized value $\tilde{x}_i$ is mapped to the polar coordinate system. The value itself is encoded as the cosine of the angle $\phi_i$, and the time stamp is encoded as the radius $r_i$.
$$ \phi_i = \arccos(\tilde{x}_i), \quad \tilde{x}_i \in [-1,1] $$
$$ r_i = \frac{t_i}{N} $$
where $t_i$ is the time index and $N$ is a constant scaling factor. This mapping is bijective and preserves the absolute temporal order of the data points.
Step 3: Gramian Field Calculation. The temporal correlation between different time points is captured by computing the trigonometric sum/difference between their corresponding angles. This generates two distinct types of Gramian matrices, which serve as our diagnostic images.
- Gramian Angular Summation Field (GASF): This image represents correlations based on the cosine of the sum of angles.
$$ \text{GASF}_{ij} = \cos(\phi_i + \phi_j) $$
The full GASF matrix is:
$$ G_{\text{GASF}} = \begin{bmatrix}
\cos(\phi_1+\phi_1) & \cdots & \cos(\phi_1+\phi_n) \\
\vdots & \ddots & \vdots \\
\cos(\phi_n+\phi_1) & \cdots & \cos(\phi_n+\phi_n)
\end{bmatrix} $$ - Gramian Angular Difference Field (GADF): This image represents correlations based on the sine of the difference of angles.
$$ \text{GADF}_{ij} = \sin(\phi_i – \phi_j) $$
The full GADF matrix is:
$$ G_{\text{GADF}} = \begin{bmatrix}
\sin(\phi_1-\phi_1) & \cdots & \sin(\phi_1-\phi_n) \\
\vdots & \ddots & \vdots \\
\sin(\phi_n-\phi_1) & \cdots & \sin(\phi_n-\phi_n)
\end{bmatrix} $$
A critical advantage of using both GASF and GADF is their inherent robustness to common types of measurement noise. For additive noise causing phase shifts $\Delta \phi_i$ and $\Delta \phi_j$, the transformations exhibit natural cancellation properties. For common-mode noise ($\Delta \phi_i = \Delta \phi_j$), the difference in GADF cancels it out ($\sin((\phi_i+\Delta)-(\phi_j+\Delta)) = \sin(\phi_i-\phi_j)$). For differential-mode noise ($\Delta \phi_i = -\Delta \phi_j$), the sum in GASF cancels it out ($\cos((\phi_i+\Delta)+(\phi_j-\Delta)) = \cos(\phi_i+\phi_j)$). This property significantly enhances the diagnostic model’s robustness in real-world, noisy environments.
3. Parallel Convolutional Neural Network Architecture
Convolutional Neural Networks are exceptionally well-suited for learning hierarchical spatial features from image data. To fully exploit the complementary information contained in the GASF and GADF images, we designed a dual-channel parallel CNN architecture.
The GASF and GADF images generated from the same virtual resistance sequence are fed into two separate but identical CNN channels. Each channel performs feature extraction independently through a series of convolutional and pooling layers. The convolutional layers apply filters to detect local patterns, while the pooling layers downsample the feature maps to achieve translation invariance and reduce computational complexity. After passing through several such layers, the high-level features from each channel are flattened into one-dimensional vectors.
These two feature vectors are then concatenated into a single, comprehensive feature vector. This fused vector is passed through one or more fully connected (dense) layers, which integrate the features from both channels to learn complex non-linear relationships. Finally, a Softmax classifier outputs a probability distribution over all possible health states of the grid-tied inverter switch tubes. The architecture of the proposed parallel CNN is summarized in the table below.
| Layer Type | Channel 1 (GASF Input) | Channel 2 (GADF Input) | Output Shape (per Channel) |
|---|---|---|---|
| Input | 64×64×1 Image | 64×64×1 Image | – |
| Conv2D + ReLU | 32 filters (3×3) | 32 filters (3×3) | 64×64×32 |
| MaxPooling2D | Pool size (2×2) | Pool size (2×2) | 32×32×32 |
| Conv2D + ReLU | 64 filters (3×3) | 64 filters (3×3) | 32×32×64 |
| MaxPooling2D | Pool size (2×2) | Pool size (2×2) | 16×16×64 |
| Flatten | – | – | 16384 |
| Feature Fusion (Concatenate) | 32768 | ||
| Dense + ReLU | 128 neurons | 128 | |
| Dense + Softmax | 21 neurons (for 21 classes) | 21 | |
Experimental Setup and Data Generation
To validate the proposed method, a detailed simulation model of a three-phase two-level grid-tied inverter was developed in a specialized electromagnetic transient (EMT) simulation platform. The system parameters, representative of a medium-scale photovoltaic installation, are listed below.
| Parameter | Symbol | Value |
|---|---|---|
| DC Link Voltage | $V_{dc}$ | 700 V |
| Grid Voltage (L-L, RMS) | $U_g$ | 380 V |
| Grid Frequency | $f$ | 50 Hz |
| Filter Inductance | $L_f$ | 3 mH |
| Filter Resistance | $R_f$ | 0.1 Ω |
| Switching Frequency | $f_{sw}$ | 5 kHz |
| Sampling Frequency | $f_s$ | 1 kHz |
Switch tube defects were simulated by altering the parameters of the IGBT/diode models. We considered three fundamental types of parametric soft defects for a single switch tube (e.g., VT1 in the inverter bridge):
- On-State Resistance Increase ($R_{on}$ Defect): Modeled by adding a series resistance with the IGBT, significantly higher than its nominal value.
- Off-State Resistance Decrease ($R_{off}$ Defect): Modeled by adding a shunt resistance across the IGBT, significantly lower than its nominal blocking resistance.
- Switching Delay / Capacitance Change (C Defect): Modeled by adding a shunt capacitance across the IGBT, altering its switching transients.
For a comprehensive diagnosis, the health states of all six IGBTs in the three-phase grid-tied inverter must be considered. This includes individual defects in any of the six switches (3 defect types × 6 switches = 18 states) and selected multiple-defect scenarios (e.g., simultaneous defects in two switches, adding 3 more states), leading to a total of 21 distinct health condition classes, including the normal healthy state. For each class, 300 simulation runs were performed with randomized defect severity levels and starting times within the cycle, resulting in a total dataset of 6,300 virtual resistance time-series samples. Each 0.2s sample (200 points per phase, 600 points total) was transformed into a pair of 64×64 pixel GASF and GADF images.
| Defect Category | Affected Switch(s) | Parameter Change | Number of Classes |
|---|---|---|---|
| Single-Tube On-State Defect | VT1, VT2, VT3, VT4, VT5, VT6 | $R_{on}$ increased 10-100x | 6 |
| Single-Tube Off-State Defect | VT1, VT2, VT3, VT4, VT5, VT6 | $R_{off}$ decreased to 0.01-0.1x | 6 |
| Single-Tube Delay/Capacitance Defect | VT1, VT2, VT3, VT4, VT5, VT6 | Shunt Capacitance added (10-20x nominal) | 6 |
| Double-Tube Defect (Example) | (VT1, VT3), (VT1, VT4), (VT2, VT5) | Combination of the above | 3 |
| Normal State | None | All parameters nominal | 1 |
| Total Health Condition Classes | 21 | ||
Results and Comparative Analysis
The dataset of 12,600 images (GASF + GADF pairs) was randomly split into training (70%), validation (10%), and testing (20%) sets. The proposed parallel CNN model was trained using the Adam optimizer with an initial learning rate of 0.001 and a batch size of 256. The cross-entropy loss function was minimized over 150 training epochs.
1. Performance of the Proposed Model
The training and validation accuracy/loss curves demonstrated effective convergence. The final model achieved a test set accuracy of 95.16% in correctly classifying the 21 health states of the grid-tied inverter switch tubes. The average inference time per sample was approximately 7.83 ms, which is well within the requirements for real-time or near-real-time monitoring applications. The high accuracy, despite the subtle nature of the parametric defects, validates the effectiveness of the GAF transformation in encoding discriminative temporal features and the parallel CNN’s capability to learn from them.
2. Ablation and Comparative Study
To rigorously evaluate the contribution of each component in our proposed framework, we compared its performance against several alternative deep learning models using the same dataset. The results are summarized in the table below.
| Model Architecture | Key Characteristics | Final Test Accuracy | Remarks |
|---|---|---|---|
| Proposed GAF + Parallel CNN | Uses both GASF & GADF images in parallel channels. | 95.16% | Highest accuracy, robust feature fusion. |
| Single-Channel GASF-CNN | Uses only GASF images as input. | 92.40% | Lower than proposed model, loses complementary info from GADF. |
| Single-Channel GADF-CNN | Uses only GADF images as input. | 93.85% | Closest to proposed model but still slightly inferior. |
| Multi-Layer Perceptron (MLP) | Operates directly on flattened time-series data. | 87.40% | Lowest accuracy; fails to capture temporal correlations. |
| Recurrent Neural Network (RNN) | Processes sequential data directly. | ~91.0% | Struggles with long sequences; prone to gradient issues. |
| Long Short-Term Memory (LSTM) | Advanced RNN designed for long-term dependencies. | ~91.5% | Better than RNN but computationally heavier and less stable in validation. |
| Gated Recurrent Unit (GRU) | Simpler variant of LSTM. | ~91.8% | Similar to LSTM, faster training but accuracy plateaus. |
The comparison clearly shows that the proposed model outperforms all alternatives. The single-channel CNNs confirm that both GASF and GADF contain valuable information, and their fusion yields the best result. The inferior performance of MLP, RNN, LSTM, and GRU highlights the advantage of first converting the time-series into an image-based spatial representation that is inherently more suitable for CNN-based feature extraction, especially for the subtle patterns caused by incipient defects in a grid-tied inverter.
3. Robustness Analysis Under Noise
The real-world operation of a grid-tied inverter involves measurement noise from sensors and electromagnetic interference. To assess the practical viability of our model, we injected additive white Gaussian noise (AWGN) at different signal-to-noise ratios (SNR) into the test set current signals. We evaluated two common noise modes: Common-Mode Noise (same noise added to all three phases) and Differential-Mode Noise (opposite noise added to two phases). The average diagnostic accuracy across these noise modes is presented below.
| Model | Noise-Free | 40 dB SNR | 30 dB SNR | 20 dB SNR |
|---|---|---|---|---|
| Proposed Model | 95.16% | 94.80% | 94.62% | 94.30% |
| Single-Channel GADF-CNN | 93.85% | 94.46% | 94.02% | 92.75% |
| Single-Channel GASF-CNN | 92.40% | 93.40% | 92.80% | 91.28% |
| GRU | ~91.8% | 94.29% | 93.20% | 91.80% |
| LSTM | ~91.5% | 93.88% | 92.45% | 90.64% |
| RNN | ~91.0% | 94.20% | 94.15% | 89.15% |
| MLP | 87.40% | 93.05% | 91.88% | 89.86% |
The results demonstrate the exceptional robustness of the proposed method. Even under a strong 20 dB noise condition, the accuracy drop is minimal (less than 1%). This robustness can be attributed to the inherent noise-cancellation properties of the GAF transformations (GASF against differential-mode, GADF against common-mode noise) and the powerful feature learning of the parallel CNN. In contrast, other models, particularly RNN and MLP, exhibit significantly larger performance degradation under high noise levels. This confirms that the GAF-CNN approach is not only accurate but also reliable for health monitoring of grid-tied inverters in practical, noisy industrial settings.
Discussion and Outlook
The proposed framework presents a significant step towards predictive maintenance for power electronic systems. By successfully diagnosing parametric soft defects in grid-tied inverter switch tubes, it shifts the paradigm from reactive fault handling to proactive health management. The use of GAF transformation is a key enabler, as it allows the utilization of powerful image-based deep learning techniques on time-series data without requiring high-frequency sampling or complex manual feature engineering (like wavelet or VMD transforms). The low sampling rate (1 kHz) used in this study is readily achievable with standard industrial monitoring equipment, enhancing the method’s practical applicability.
The parallel CNN architecture effectively leverages the dual-perspective provided by GASF and GADF images. While GADF alone showed strong performance, the fusion of both channels consistently yielded the highest accuracy and robustness, indicating that the sum and difference correlations capture non-redundant information about the state of the grid-tied inverter.
However, certain limitations and future research directions are acknowledged. The current study focuses on defects that cause relatively pronounced changes in switch tube parameters (e.g., an order-of-magnitude change). Detecting earlier, more subtle degradation stages remains a challenge. Furthermore, the model was trained and validated on simulated data. While simulation provides a controlled environment for generating a comprehensive fault library, the final step towards deployment requires validation and potential fine-tuning using real-world data from operational grid-tied inverters experiencing natural aging.
Future work will explore several avenues to enhance this methodology:
- Multi-Modal Data Fusion: Incorporating additional sensory data, such as heat sink temperature, case vibration, or electromagnetic emissions, could provide complementary physical evidence of degradation, enabling even earlier and more confident diagnosis.
- Lightweight Model Design: Optimizing the CNN architecture for edge deployment on embedded devices within the inverter controller would facilitate truly decentralized, real-time health monitoring.
- Lifetime Prognostics: Extending the framework from classification (identifying the present defect) to regression (estimating the remaining useful life of a switch tube) would represent the ultimate goal of predictive maintenance for critical components in renewable energy systems.
Conclusion
This article presented a novel, data-driven health diagnosis method for switch tubes in grid-tied inverters, a critical component for renewable energy integration. The method centers on transforming easily measurable three-phase voltage and current signals into a discriminative virtual resistance time-series, which is then encoded into two-dimensional Gramian Angular Summation Field (GASF) and Gramian Angular Difference Field (GADF) images. These images preserve the temporal correlation structure of the signals in a format ideal for convolutional neural networks. A dedicated parallel CNN architecture processes both image types simultaneously, fusing their features to achieve a highly accurate classification of various switch tube parametric soft defects, such as increased on-resistance, decreased off-resistance, and switching delay anomalies.
Extensive simulation-based experiments demonstrated that the proposed GAF and parallel CNN model achieves a superior diagnosis accuracy of 95.16%, outperforming several alternative deep learning models including single-channel CNNs, RNNs, LSTMs, and GRUs. Crucially, the method exhibits remarkable robustness against common-mode and differential-mode measurement noise, a essential characteristic for field deployment. By enabling the early detection of incipient switch tube failures, this approach facilitates predictive maintenance strategies. This can significantly reduce unplanned downtime, prevent catastrophic failures, and improve the overall operational reliability and lifespan of grid-tied inverters, thereby contributing to the stability and security of the evolving power grid.