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 RMSEI). This involves using an analytical expression for current - I as a function of voltage - U (I = f1(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 RMSEU). 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 = f2(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 RMSEU 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 RMSEU. 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.