1. Introduction
The rapid expansion of photovoltaic power generation has fundamentally transformed the global energy landscape, with solar panels increasingly deployed across residential, commercial, and utility-scale installations. However, this growth has introduced significant safety challenges, particularly concerning direct current (DC) arc faults in photovoltaic systems. Unlike alternating current systems where arcs naturally extinguish at zero-crossing points, DC arcs exhibit continuous burning characteristics that pose severe fire risks. The hidden nature of DC arcs—their subtle current signatures and lack of obvious waveform distortion—makes them particularly dangerous in solar panel installations. The sustained high temperatures generated by DC arcs, often exceeding 3000 degrees Celsius, can rapidly degrade solar panel materials and ignite surrounding combustibles, leading to devastating fires. Statistics from the German photovoltaic industry reveal that among 1.7 million installed solar panels, 430 component-related fires occurred, highlighting the critical need for robust arc detection solutions.
DC arc faults in solar panel systems are categorized into series, parallel, and ground faults. Series arcs typically arise from loose connections or degraded cable insulation, while parallel arcs result from insulation breakdown between conductors of different potentials. The photovoltaic array, operating in the 600-1500V DC range, provides ideal conditions for arc formation and sustained combustion. Under sufficient irradiance, solar panels continuously supply energy to maintain an arc once initiated, creating a dangerous feedback loop. The minimal voltage required to sustain a DC arc is surprisingly low—merely tens of volts—making prevention challenging through conventional means. Traditional protective devices such as circuit breakers and fuses prove inadequate for DC arc detection due to the fundamentally different physical characteristics of DC arcs compared to AC arcs.
Standardization efforts have advanced alongside technological development. The UL1699B standard, established by Underwriters Laboratories and updated in 2018, specifies requirements for DC arc fault detection in photovoltaic systems operating between 80V and 1000V. This standard mandates that arc duration must not exceed 2 seconds or the minimum value of 750 Joules divided by arc power. In China, GB/T31143.4-2014 and T/CEEIA350-2019 provide corresponding technical specifications for arc fault protection devices in distributed photovoltaic systems. These regulatory frameworks underscore the urgency of developing accurate, reliable arc detection methodologies specifically tailored for solar panel applications.
2. Data Acquisition and Feature Engineering
2.1 Experimental Platform Construction
To systematically investigate DC arc characteristics in solar panel systems, we constructed a comprehensive experimental platform aligned with UL1699B Class A standards. The platform comprised a programmable DC photovoltaic simulator capable of delivering 0-1500V continuously variable output, a high-precision arc generation device with programmable electrode gap control, a DC electronic load module, and a high-speed data acquisition system. The arc generation device featured copper and carbon rod electrodes configured in a point-contact arrangement, with the copper electrode mounted on a precisely controlled slider mechanism that regulated electrode separation distance.
Data acquisition employed high-accuracy Hall effect current sensors deployed at the input terminals of the photovoltaic DC-DC system. The sampling frequency was set to 500 kHz, strictly following the Nyquist sampling theorem, ensuring complete capture of arc characteristic frequency components. Frequency domain analysis of experimental data revealed that DC arc high-frequency components predominantly reside in the 50-200 kHz band, necessitating this high sampling rate. A dual-buffer strategy was implemented in the data acquisition software to support sustained high-speed sampling without data loss. Before each experiment, electrode contact surfaces were meticulously polished with sandpaper to eliminate oxidation layers and carbon deposits from previous tests, ensuring consistent arc initiation behavior and data reproducibility.
| Component | Specification | Purpose |
|---|---|---|
| Photovoltaic Simulator | 0-1500V programmable | Simulate solar panel output characteristics |
| Arc Generation Device | 0.1-5cm adjustable gap | Generate controlled arc faults |
| Current Sensor | Hall effect, 500kHz bandwidth | High-frequency current measurement |
| Data Acquisition System | 500kHz sampling rate | Capture transient arc signatures |
| Electronic Load | R, L, C configurable | Simulate different load conditions |
2.2 Time-Domain Feature Extraction
Analysis of the collected data revealed distinct time-domain signatures between normal operation and arc fault conditions in solar panel systems. The normal current waveform exhibited stable fluctuations around 3100-3350 units, while arc current demonstrated random variations accompanied by sudden spikes reaching 3600 units—a 14% increase from baseline. Through systematic multi-condition testing, we identified six fundamental time-domain features that comprehensively characterize DC arc behavior. These features were selected based on their physical interpretability and ability to distinguish arc signatures under diverse operating conditions, including variations in load type, current level, and environmental noise.
The arithmetic mean (\(\bar{x}\)) serves as a first-order statistical descriptor reflecting the DC component of the signal. Under arc fault conditions, the nonlinear impedance characteristics of the arc channel induce persistent deviations in the current mean value. The standard deviation (\(\sigma\)) quantifies signal dispersion and captures the non-stationary fluctuations characteristic of arc plasma instabilities. Peak-to-peak value (\(V_{pp}\)) detects extreme transient excursions in the signal, effectively identifying the microsecond-scale current spikes associated with arc breakdown events. These spikes typically exceed normal operating variations by a factor of two or more. The root mean square (RMS) value provides a measure of signal energy, with its quadratic emphasis amplifying high-frequency components that distinguish arc signatures from background noise. Variance (\(\sigma^2\)) offers complementary information about signal dispersion while providing natural immunity to periodic interference sources such as switching harmonics. Finally, we introduce an adapted zero-crossing rate (ZCR) specifically designed for DC systems, which counts signal crossings around a dynamic sliding-window mean rather than an absolute zero reference, effectively quantifying the high-frequency oscillations characteristic of plasma dynamics in solar panel arcs.
$$\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$$
$$\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i – \mu)^2}$$
$$V_{pp} = \max_{1 \leq i \leq n}\{x_i\} – \min_{1 \leq i \leq n}\{x_i\}$$
$$X_{rms} = \sqrt{\frac{1}{n}\sum_{i=1}^{n} x_i^2}$$
$$\sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i – \mu)^2$$
The composite feature set demonstrates several synergistic advantages for DC arc detection in solar panel systems. First, it provides comprehensive coverage of arc physical mechanisms: mean values track overall current shifts indicating sustained arc activity; standard deviation and variance quantify fluctuation intensity; peak-to-peak values capture extreme transient events; RMS values reflect energy dissipation patterns; and zero-crossing rate characterizes high-frequency plasma oscillations. Second, the multi-dimensional approach exhibits enhanced noise immunity through dynamic baseline tracking and complementary frequency selectivity. Third, all features are computed in the time domain avoiding computationally intensive transforms, facilitating potential deployment on resource-constrained embedded platforms for real-time solar panel monitoring.
| Time-Domain Feature | Formula | Physical Significance | Arc Discrimination Capability |
|---|---|---|---|
| Mean | \(\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i\) | DC component/steady-state level | Detects sustained arc-induced current offset |
| Standard Deviation | \(\sigma = \sqrt{\frac{1}{N}\sum(x_i-\mu)^2}\) | Signal dispersion | Quantifies arc plasma instability |
| Variance | \(\sigma^2 = \frac{1}{N}\sum(x_i-\mu)^2\) | Fluctuation energy | Captures arc-induced turbulence |
| Peak-to-Peak | \(V_{pp} = \max\{x_i\} – \min\{x_i\}\) | Extreme excursion range | Detects breakdown transient spikes |
| RMS | \(X_{rms} = \sqrt{\frac{1}{n}\sum x_i^2}\) | Signal energy | Amplifies high-frequency components |
| Zero-Crossing Rate | \(ZCR = \frac{1}{T}\sum \mathbb{I}(x_i \text{ crosses } \bar{x})\) | High-frequency oscillation frequency | Quantifies plasma oscillation characteristics |
2.3 Dataset Construction and Normalization
Following feature extraction, we constructed a comprehensive dataset spanning multiple operational scenarios. The dataset incorporated measurements from 10A and 11A operating currents under resistive, capacitive, and inductive load conditions, comprising both normal and arc fault states. Data collection involved 11 repetitive trials per condition, each lasting 2.1 seconds at 500 kHz sampling rate, yielding a total of 44 data records containing 46.2 million raw data points. Each record was processed to compute the six time-domain features, generating feature vectors labeled with binary classification targets where 1 represented arc fault conditions and 0 represented normal operation.
Min-Max normalization was applied to the feature vectors to eliminate dimensional disparities across the six features. This normalization method maps values to the [0,1] interval through the transformation:
$$x_{norm} = \frac{x – \min(x)}{\max(x) – \min(x)}$$
The selection of Min-Max normalization over Z-score standardization was driven by several considerations: Min-Max preserves the original distribution shape while eliminating scale differences; it resists abnormal value interference due to its dependence only on extreme values; its computational simplicity suits real-time embedded implementations; and it provides natural adaptive baseline drift compensation through dynamic maximum/minimum updates. This normalization approach ensures stable model training across varying solar panel system scales and operating conditions, enhancing the transferability of the developed detection models.
| Data Category | Total Samples | Training Set | Test Set |
|---|---|---|---|
| 10A Normal Operation | 11,550,000 | 9,240,000 | 2,310,000 |
| 10A Arc Fault | 11,550,000 | 9,240,000 | 2,310,000 |
| 11A Normal Operation | 11,550,000 | 9,240,000 | 2,310,000 |
| 11A Arc Fault | 11,550,000 | 9,240,000 | 2,310,000 |
3. LSTM-Based Arc Detection Method
3.1 Recurrent Neural Network Limitations
Traditional recurrent neural networks (RNNs) provide a natural foundation for sequential electrical signal analysis due to their recursive computation architecture. However, standard RNNs suffer from fundamental limitations when applied to DC arc detection in solar panel systems. Their hidden state computation follows \(h_t = \tanh(W_h h_{t-1} + W_x x_t + b_h)\), which theoretically can retain information across arbitrary sequence lengths. In practice, the vanishing gradient problem severely constrains the effective memory horizon, preventing RNNs from capturing the long-range temporal dependencies inherent in arc dynamics. During backpropagation, the continuous multiplication of gradient terms through time leads to exponential decay or explosion, making training unstable and limiting the networks capability to learn patterns spanning more than a few time steps. This deficiency proves particularly problematic for solar panel arc detection, where events such as arc reignition may occur milliseconds after initial breakdown, requiring models to maintain relevant information across extended time scales while distinguishing from benign transients like maximum power point tracking (MPPT) adjustments.
3.2 Long Short-Term Memory Architecture for Arc Detection
To overcome these RNN limitations, we implemented a Long Short-Term Memory (LSTM) network specifically designed for DC arc fault detection in solar panels. LSTM networks, introduced by Hochreiter and Schmidhuber, incorporate a memory cell controlled by three gating mechanisms that regulate information flow, effectively addressing the vanishing gradient challenge. The forgetting gate determines which information from previous cell states should be discarded, the input gate controls which new information should be stored, and the output gate regulates information output to the hidden state. The mathematical formulation of the LSTM cell operations is given by:
$$f_t = \sigma(W_f \cdot [h_{t-1}, x_t] + b_f)$$
$$i_t = \sigma(W_i \cdot [h_{t-1}, x_t] + b_i)$$
$$\tilde{C}_t = \tanh(W_C \cdot [h_{t-1}, x_t] + b_C)$$
$$o_t = \sigma(W_o \cdot [h_{t-1}, x_t] + b_o)$$
$$C_t = f_t \odot C_{t-1} + i_t \odot \tilde{C}_t$$
$$h_t = o_t \odot \tanh(C_t)$$
In the context of solar panel arc detection, these gating mechanisms align naturally with the physical processes governing arc behavior. The forgetting gate activation should appropriately decrease during arc extinguishing phases when thermal inertia diminishes, prompting the model to discard outdated historical states and respond rapidly to arc interruption. Conversely, during arc reignition when current suddenly surges due to insulation breakdown, the input gate activation should increase significantly to capture this critical new information. The output gate then regulates how accumulated internal state information contributes to external observable predictions, corresponding to the release of abrupt signals when arc energy accumulates to critical thresholds.
3.3 Model Architecture Design
We designed a specialized LSTM architecture with parameters optimized through grid search experimentation. The model accepts six-dimensional input features corresponding to the time-domain statistics extracted from solar panel current measurements. The network architecture comprises an input layer receiving sequences of 50 time steps (representing 50 ms windows), two LSTM layers with 128 hidden units each, a dropout layer operating at 0.3 rate for regularization, and a fully connected output layer with sigmoid activation for binary classification. The sliding window segmentation employed a window length of 500 ms with step size equal to half the window duration, preserving temporal continuity while eliminating redundancy. The complete model configuration is summarized in the following table:
| Layer Parameter | Configuration | Selection Rationale |
|---|---|---|
| Input Dimension | 6 | Corresponding to six time-domain features |
| Sequence Length | 50 | 50 ms temporal window |
| Hidden Layers | 2 | Balances capacity vs. gradient stability |
| Hidden Units | 128 | Optimal through grid search |
| Dropout Rate | 0.3 | Prevents overfitting while preserving capacity |
| Learning Rate | 0.001 | Stable convergence |
| Batch Size | 32 | Computational efficiency and stability |
| Loss Function | Weighted Cross-Entropy | Handles class imbalance |
| Optimizer | AdamW | Decoupled weight decay improves generalization |
A dual-condition early stopping mechanism was implemented to balance training efficiency and model performance. The primary stopping criterion triggered termination when validation loss failed to decrease for 2 consecutive epochs, employing weighted moving average smoothing to avoid spurious fluctuations. The auxiliary criterion considered model convergence attained when the F1 score range across 5 epochs remained below 0.5%. If only the auxiliary condition triggered, training continued for one additional epoch to confirm stability.
3.4 Performance Comparison: LSTM vs. RNN
We conducted systematic comparisons between the LSTM-based detection model and a traditional RNN baseline. The RNN baseline employed a four-layer stacked architecture with 64 hidden units per layer, 300 ms time steps covering the complete arc development cycle, 0.01 learning rate, 0.2 dropout, and stochastic gradient descent optimization. The LSTM model significantly outperformed the RNN across all evaluation metrics, achieving 98.8% accuracy versus 98.1%, as detailed in the comprehensive comparison below.
| Evaluation Metric | RNN Baseline | LSTM Model | Relative Improvement |
|---|---|---|---|
| Accuracy | 98.1% | 98.8% | 0.7% |
| Precision | 98.34% | 98.76% | 0.42% |
| Recall | 97.87% | 98.84% | 0.97% |
| F1 Score | 98.1% | 98.8% | 0.7% |
Confusion matrix analysis of the LSTM model revealed balanced classification performance with 4,917 true negatives, 4,893 true positives, 83 false alarms, and 107 missed detections among 10,000 validation samples. The misclassification pattern demonstrated acceptable symmetry, with slightly higher missed detections (FN > FP). The LSTM model successfully suppressed switching noise and MPPT transients that typically generate false positives in threshold-based methods. The arc extinction and reignition cycles, which manifest as complex non-stationary sequences, were effectively modeled by the LSTM gating mechanisms, enabling accurate discrimination between benign transients and genuine arc events in solar panel systems.
4. Physics-Informed Neural Network for Arc Detection
4.1 Mayr Arc Model Integration
While LSTM networks demonstrated excellent performance in solar panel arc detection, their black-box nature limits interpretability and trust for safety-critical applications. To address this limitation, we proposed a Physics-Informed Neural Network (PINN) approach that embeds the Mayr arc equation as a physical constraint within the LSTM framework. The Mayr model, originally developed for low-current arc analysis, is particularly suitable for DC arc detection in solar panels due to its dynamic energy balance formulation:
$$\frac{dg}{dt} = \frac{1}{\tau}\left(\frac{P}{g} – g\right)$$
where \(g\) represents arc conductance, \(\tau\) denotes the arc time constant, and \(P\) is the instantaneous arc power given by \(P = i \cdot u\). The first term \(P/g\) represents energy input enhancing conductance, while \(-g\) accounts for energy dissipation through cooling and radiation. This comprehensive model accurately captures the complex energy dynamics governing DC arc behavior in solar panel systems, making it an ideal physical constraint for guiding neural network training.
The selection of the Mayr model over alternatives such as the Cassie model was based on fundamental physical considerations relevant to solar panel systems. The Mayr equation naturally accommodates small-current arcs, which are characteristic of early-stage faults or series arcs in photovoltaic installations. DC arcs lack natural zero-crossing points and continuously receive energy input from solar panels under illumination, creating a sustained combustion state precisely described by the Mayr dynamic equilibrium. The models internal adaptive nonlinearity enables accurate prediction of arc maintenance or extinction critical conditions. In contrast, the Cassie model assumes thermal equilibrium where input power completely converts to heat dissipation, neglecting transient energy accumulation crucial for fast dynamic processes.
4.2 Physics-Embedded Neural Network Architecture
The integration of the Mayr equation into the LSTM architecture creates a unique physics-guided deep learning framework. This integration assigns physical meaning to each LSTM gating mechanism, establishing a systematic mapping between neural network operations and arc physical processes. The input gate, which controls how new information (arc power increments) updates the cell state, corresponds to the energy input enhancement effect on conductance in the Mayr equation. The forgetting gate, governing retention of historical states (accumulated energy), aligns with conductance decay due to heat dissipation. The cell state corresponds to arc conductance itself, while the output gate managing the mapping from cell state to hidden state (observable voltage features) corresponds to the physical voltage-conductance relationship.
This physical mechanism mapping enables explicit embedding of the Mayr equation as a differential constraint within the network. The training process enforces learning that respects arc energy conservation laws while maintaining high detection accuracy. The loss function incorporates both data-driven and physics-based components:
$$\mathcal{L} = \mathcal{L}_{data} + \lambda \cdot \mathcal{L}_{physics}$$
where \(\mathcal{L}_{data}\) represents the weighted binary cross-entropy between predicted and actual labels, and \(\mathcal{L}_{physics}\) quantifies the residual error of the Mayr equation evaluated at each time step. The balance coefficient \(\lambda = 0.7\) was optimized through systematic experimentation to achieve optimal performance across diverse operating conditions.
4.3 Performance Evaluation and Comparative Analysis
The PINN model achieved exceptional performance in solar panel arc detection, with an accuracy of 99.6% significantly outperforming both the LSTM baseline and conventional detection approaches. Comprehensive evaluation metrics are presented in the comparative analysis below:
| Evaluation Metric | LSTM Baseline | PINN Model | Relative Improvement |
|---|---|---|---|
| Accuracy | 98.8% | 99.6% | 0.8% |
| Precision | 98.76% | 99.64% | 0.88% |
| Recall | 98.84% | 99.56% | 0.72% |
| F1 Score | 98.8% | 99.6% | 0.8% |
The superiority of the PINN approach becomes evident through detailed error analysis. Among 10,000 validation samples, the PINN model produced only 18 false alarms and 22 missed detections, representing reductions of 62.1% and 71.0% respectively compared to the LSTM baseline. The physics-informed training effectively constrained the model optimization space toward physically consistent solutions, enhancing detection accuracy while providing explicit physical interpretability through the Mayr equation integration. The model successfully captures the subtle differences between arc transition phases—initiation, steady-state burning, and extinction—that data-driven models often struggle to distinguish due to similar spectral characteristics.
The PINN approach offers three fundamental advantages. First, it provides physically consistent feature learning through the Mayr equation constraint, enforcing energy conservation principles during training. Second, it enhances dynamic process modeling, accurately capturing arc initiation and extinction critical points that challenge pure data-driven approaches. Third, it delivers interpretable feature extraction by mapping LSTM internal states directly to physical quantities: cell state represents conductance, output gate probability correlates with arc breakdown risk, and forgetting gate activity mirrors heat dissipation dynamics.
4.4 Model Compression and Hardware Deployment
Addressing the computational demands of the PINN model for practical solar panel deployment, we developed a comprehensive lightweight solution incorporating knowledge distillation and hardware acceleration. The teacher-student distillation framework employed a 5-layer Mayr-LSTM teacher model (1.2M parameters) with 256 hidden units, transferring physical knowledge to a lightweight Temporal Convolutional Network (TCN) student model (0.18M parameters) using depthwise separable convolutions. The teacher model achieved 99.6% accuracy, while the distilled student model attained 98.7% accuracy, representing only a 0.9% accuracy loss while achieving an 85% parameter reduction.
The knowledge distillation incorporated two key components. First, a physical knowledge transfer loss aligning conductance derivatives between teacher and student models:
$$\mathcal{L}_{phy} = \sum_{t=1}^{T} \left\|\frac{dg^{tea}}{dt} – \frac{dg^{stu}}{dt}\right\|^2 + \lambda \|P_{loss}^{tea} – P_{loss}^{stu}\|_1$$
Second, an attention transfer loss propagating the teachers attention patterns regarding arc transient features to the student model, implemented as normalized attention matrix alignment. The student model after distillation demonstrated significant improvement in weak arc recognition rate, increasing from 94.3% to 97.5%, while reducing physical consistency error by 25%.
| Model Configuration | Accuracy | Parameters | Physical Error |
|---|---|---|---|
| Teacher Model (Mayr-LSTM) | 99.6% | 1.2M | 0.015 |
| Student Model (TCN) | 98.1% | 0.8M | 0.028 |
| Distilled Student Model | 98.7% | 0.8M | 0.021 |
Deployment optimization targeted the TI TMS320F28388D digital signal processor platform. Mixed-precision quantization compressed convolutional layer weights from 32-bit floating-point to 8-bit integers representing negligible accuracy degradation, while physics constraint calculations retained FP16 precision for differential equation solving accuracy. The quantization reduced model size from 0.23MB to 0.11MB representing a 52% compression ratio. Memory access optimization employed the DSPs 256KB SARAM cache for input features and cyclic block techniques dividing time-series data into 50ms sub-blocks, reducing cache miss rate by 37%. Vector CRC instructions accelerated convolution operations on the C28x core, achieving real-time detection capability with 200 MHz operational frequency and supporting 600-1500V system voltage boundaries.
5. Conclusion and Future Directions
This research has systematically addressed the critical challenge of DC arc fault detection in solar panel systems through an integrated approach combining experimental characterization, advanced signal processing, and physics-informed deep learning. The key findings and contributions of this work include the successful development of a comprehensive experimental platform enabling controlled arc fault generation and high-fidelity data acquisition, the formulation of a six-dimensional time-domain feature set providing comprehensive arc characterization with physical interpretability, and the development of a physics-informed neural network that integrates the Mayr arc equation with LSTM architecture achieving 99.6% detection accuracy. The proposed approach significantly outperforms traditional threshold-based methods, which exhibit approximately 61.3% detection success rates with fixed thresholds and 76.8% with adaptive thresholds, and conventional machine learning approaches.
Furthermore, we demonstrated the feasibility of deploying such advanced detection models on embedded hardware platforms through knowledge distillation and optimization techniques. The physics-informed approach provides explicit interpretability, breaking through the traditional black-box limitation of deep learning models. The successful integration of physical laws with data-driven learning establishes a new paradigm for fault detection that combines the pattern recognition capabilities of neural networks with the rigor of physical principles.
Future research directions include developing few-shot learning mechanisms for novel solar panel types using meta-learning approaches to achieve zero-shot generalization on unseen configurations, establishing comprehensive health assessment systems that integrate arc characteristics with degradation indicators to enable predictive maintenance across solar panel installations. Additionally, exploring deployment across diverse photovoltaic scenarios including residential rooftop installations, utility-scale ground-mounted plants, and floating solar farms presents opportunities for reducing inspection frequency and operational costs. The continued evolution of this technology will contribute to enhanced safety and reliability of solar panel systems, addressing the critical challenge of arc fault prevention in the rapidly expanding photovoltaic industry.