Photovoltaic parameter extraction through an adaptive differential evolution algorithm with multiple linear regression

Solar cells play a crucial role in generating clean, renewable energy. Accurate modeling of photovoltaic (PV) systems is essential for their development, and simulating their behaviors requires precise estimation of their parameters. However, many optimization methods exhibit high or unstable root mean square error (RMSE) due to local optima entrapment and parameter interdependence. To address these challenges, we propose MLR-DE, a novel hybrid approach that integrates adaptive differential evolution (DE) with multiple linear regression (MLR). The main innovation is to decompose the PV model into linear coefficients and non-linear functions, the latter being iteratively estimated using DE. By treating nonlinear function outputs as independent variables and known measured currents as dependent variables, linear coefficients are analytically solved through MLR. Additionally, we introduce a data-fusion-based parameter generation scheme to improve DE's reliability by integrating historical crossover rates with estimated crossover rates. We validate MLR-DE through experiments across 11 PV configurations: 3 standard diode models and 8 environmental variants. The results demonstrate MLR-DE's superiority in all tests. It achieves the lowest average RMSE compared to other algorithms, with standard deviations at or below 2e-16. In the Friedman test, MLR-DE ranked first with a score of 1.94, outperforming the second-place (3.72) and last-place (7.58) competitors. The convergence curve shows that MLR-DE achieves convergence in less than 3,000 function evaluations over standard models, with an average convergence time of less than 0.6 s.