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 (<i>RMSE</i>) between the estimated and measured current values of solar cells (referred to as the <i>RMSE</i> _<i>I</i> ). This involves using an analytical expression for current - <i>I</i> as a function of voltage - <i>U</i> (<i>I</i> = <i>f</i> ₁(<i>U</i>)) expressed through the Lambert <i>W</i> function. This paper introduces a new analytical solution for calculating the <i>RMSE</i> between measured and estimated solar cell voltages (referred to as the <i>RMSE</i> _<i>U</i> ). The formula is derived using the <i>g</i>-function or LogWright function, which provides a numerically applicable method for representing the analytical relation between solar cell voltage and current (<i>U</i> = <i>f</i> ₂(<i>I</i>)). Moreover, the paper presents the original formulas for calculating Mean Absolute Error (<i>MAE</i>) and Mean Absolute Percentage Error (<i>MAPE</i>) for solar cell voltages expressed through the <i>g</i>-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 <i>RMSE</i> _<i>U</i> 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 <i>RMSE</i> _<i>U</i> . 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 <i>RMSE</i> expression and algorithm. Additionally, the study confirms the applicability of the g-function in invertible solar cell modeling.