Time-domain Simulation and Stability Analysis of a Photovoltaic Cell Using the Fourth-order Runge-Kutta Method and Lyapunov Stability Analysis
DOI:
https://doi.org/10.12928/biste.v7i2.13233Keywords:
Runge-Kutta Fourth Order, Lyapunov Stability, Photovoltaic Modeling, Single-diode Model, Nonlinear I-V CharacteristicsAbstract
This paper aims to analyze the nonlinear dynamic behavior of a photovoltaic (PV) cell under constant irradiance using numerical simulation and stability analysis. PV systems are inherently nonlinear and time-varying, making accurate dynamic modeling essential for control and performance optimization. Understanding how the system responds over time is critical for designing stable and efficient PV-based energy systems. A single-diode equivalent circuit model is used to represent the PV cell. The fourth-order Runge-Kutta (RK4) method is chosen for time-domain simulation due to its balance between computational efficiency and accuracy. A quadratic Lyapunov function is formulated to assess system stability by observing the sign of its time derivative. Simulation results show that the voltage reaches steady state smoothly with minor overshoot, and the current converges rapidly. The Lyapunov function decreases consistently, confirming asymptotic stability. The system demonstrates a maximum voltage error below 2% and low standard deviation, with consistent return to equilibrium despite changes in initial conditions. In conclusion, the proposed approach effectively characterizes the PV cell’s nonlinear dynamic behavior and confirms system stability under constant irradiance. The effectiveness of combining RK4 integration with Lyapunov analysis for modeling nonlinear PV dynamics ids demonstrated.
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