New analytical expressions of output current for multi-exponential model of PV solar cells and modules based on Taylor series expansion
Mhammed Zaimi, Khadija El Ainaoui, El Mahdi Assaid
Abstract
The current–voltage (I-V) characteristic equation of single-diode or multi-diode models describing photovoltaic (PV) solar cells or modules is traditionally based on exponential functions, which poses challenges in analytical handling. To tackle this issue, a novel approach employing Taylor series expansion to derive explicit analytical expressions of output current in cases of Single-Diode Model (SDM) and, unprecedentedly, for Multi-Diode Models (MDM) including Double-Diode Model (DDM), Three-Diode Model (TDM), and Four-Diode Model (FDM) is proposed. These derived expressions, referred to as Taylor Series Expressions of Current (TSEC), are exclusively formulated as functions of voltage drop between solar device leads and model physical parameters, allowing for precise representation of I-V data of PV solar cells and modules. Moreover, the proposed expressions can be effectively combined with the Statistical Nonlinear Fitting (SNF) technique to extract physical parameters for all models. To assess the accuracy of proposed analytical expressions, generated values of current are compared to current values obtained via Exact Numerical Solution (ENS). Extracted model physical parameters are benchmarked against parameter values reported in the literature. The evaluation is achieved for RTC France Si PV cell and PhotoWatt-PWP201 PV module. The results demonstrate a significant improvement in precision when utilizing TSEC, as indicated by reduced values of error indicators such as Absolute Error (AE) and Root Mean Square Error (RMSE). The achieved enhancement highlights the fact that TSEC are opportune expressions for an efficient search of model parameters and accurate generation of I-V data for single and multi-exponential models of PV solar cells or modules.