Computational Complexity Analysis of Arc Fault Detection Algorithms for Photovoltaic Systems

Photovoltaic (PV) systems are increasingly prevalent, but they introduce the risk of arc faults, which can lead to dangerous fires. Arc Fault Detection (AFD) algorithms are crucial for mitigating this danger. Although there are several AFD algorithms, their computational complexity can significantly impact real-time performance, especially on resource-limited embedded systems. In that sense, this work analyzes the computational complexity of three representative AFD algorithms based on: Fast Fourier Transform (FFT), Principal Component Analysis (PCA), and Variational Mode Decomposition (VMD). Big-O notation is a common tool for complexity analysis, but it often overlooks constant factors that become significant for small input sizes typical in AFD. We demonstrate these limitations by comparing Big-O estimates with the actual execution times of the three algorithms. The results highlight substantial discrepancies, particularly for VMD, which has the highest complexity. To address this, we propose a refined complexity analysis that incorporates low order terms. This approach provides more accurate execution time estimates, crucial for selecting appropriate AFD algorithms for embedded hardware with limited processing power.