Optimization of four-diode equivalent circuit models for solar cells: Analytical formulation and performance enhancement

The ongoing evolution of power systems and the growing penetration of photovoltaic (PV) technologies necessitate the development of solar cell models that are both highly accurate and computationally efficient. This work presents two novel Four-Diode Model (FDM) equivalent circuits—PEC1 and PEC2—that offer closed-form current–voltage (I–V) characteristics derived analytically via the Lambert W function. By eliminating the need for iterative solvers, these models enhance numerical stability and significantly reduce computational burden, making them well-suited for large-scale and real-time applications. Extensive validation was performed on several benchmark PV modules, including KC200GT, PHOTOWATT-PWP 201, and mSi0188, under varying environmental conditions. For the PHOTOWATT PWP 201 solar panel, the proposed models achieved up to a 29 % reduction in root-mean-square error (RMSE) compared to the most accurate method reported in the literature. In addition, the models were experimentally verified using a laboratory-scale ET 250 photovoltaic training system, further confirming their precision and applicability under real-world operating scenarios. Across all tested modules and conditions, the models demonstrated strong agreement with measured data, exhibiting robustness, adaptability, and generalization capabilities. The combination of analytical solvability, low complexity, and broad applicability renders the proposed FDM models particularly advantageous for integration into PV simulation software, energy management systems, and smart grid optimization environments, where modeling speed and precision are critical. These attributes highlight the models’ relevance for both academic research and industrial deployment.