Impact analysis of initial conditions on numerical methods for PV system modeling

Accurate modeling of photovoltaic (PV) systems is essential for performance evaluation, optimization, and seamless integration into power networks. Numerical methods such as fzero and fsolve are commonly employed to solve the implicit Single-Diode Model (SDM), which involves nonlinear equations. The performance and reliability of these iterative methods are highly sensitive to the choice of initial conditions; poorly chosen values can lead to divergence, convergence to incorrect solutions, or complete solver failure. This study presents a comparative analysis of fzero and fsolve under varying initial conditions, both with fixed load resistance and varying loads. Additionally, the analysis extends to scenarios where the PV system is integrated with boost and flyback converters, enabling a system-level evaluation. The impact of initialization on iteration count and computational efficiency is assessed, and the accuracy of both methods is verified through comparison under well-defined conditions. Furthermore, the results demonstrate that for a PV system with converter and load, stable and accurate PV curves are obtained across all resistance values when a small initial condition of the order 10⁻⁶ is used. In contrast, larger initial values lead to solver divergence or oscillations, particularly in flyback converters, which exhibit greater sensitivity than boost converters. Additionally, the choice of solver affects robustness, with fzero and fsolve showing different convergence behavior under the same conditions. Simulations using lower initial values also show reduced iteration count and faster computation time, enhancing numerical efficiency. By addressing the challenges associated with initialization, this work offers valuable insights into enhancing the robustness and applicability of numerical methods for real-world PV system simulations.