Voltage root mean square error calculation for solar cell parameter estimation: A novel g-function approach

The existing research on estimating solar cell parameters mainly focuses on minimizing the Root-Mean-Square Error (RMSE) between the estimated and measured current values of solar cells (referred to as the RMSE ). This involves using an analytical expression for current - I as a function of voltage - U (I = f ₁(U)) expressed through the Lambert W function. This paper introduces a new analytical solution for calculating the RMSE between measured and estimated solar cell voltages (referred to as the RMSE ). The formula is derived using the g-function or LogWright function, which provides a numerically applicable method for representing the analytical relation between solar cell voltage and current (U = f ₂(I)). Moreover, the paper presents the original formulas for calculating Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) for solar cell voltages expressed through the g-function. The paper also compares various published approaches and examines two well-known solar cells/modules, namely the RTC France solar cell and the SOLAREX MSX-60 PV solar module, in terms of the RMSE and single-diode solar cell models. Additionally, a novel metaheuristic algorithm, known as the Chaotic Walrus Optimization Algorithm (Chaotic-WaOA), is proposed for solar cell parameter estimation. This algorithm is applied to both mentioned solar cells to determine their parameters in terms of minimal RMSE . In order to verify the proposed research, experimental observations were conducted on a 60Wp monocrystalline solar module installed at the Faculty of Sciences and Mathematics in Niš, Serbia. This was done using a specialized PV-KLA apparatus under different outdoor conditions. The research was also verified with a Cadmium telluride solar module (CdTe75638) and a multi-crystalline silicon solar module (mSi0188). The investigation results demonstrate the accuracy, applicability, and numerical feasibility of the proposed RMSE expression and algorithm. Additionally, the study confirms the applicability of the g-function in invertible solar cell modeling.