The numerical calculation of single-diode solar-cell modelling parameters

The accurate simulation of a photovoltaic solar cell requires the precise determination of modelling parameters specific to the device under study. For the case of the single diode model, five parameters must be determined; Iph, I0, Rs, Rsh, and n. Generally speaking these values may be calculated either by analytical or numerical methods. Although analytical approaches are simple and fast to carry out, the assumptions and simplifications they introduce in order to deal with the non-linear characteristics of a solar cell may result in modelling inaccuracies. In this study a new approach is presented to calculate all five parameter values numerically minimising assumptions and simplifications. The method proposed is based on solving the single diode current-voltage equation expressed using the Lambert W-function at five experimentally obtained points along the current-voltage curve. To solve the system of non-linear equations, the multi-dimensional variant of the Newton-Raphson method is applied. All necessary first order partial differential equations are provided in closed form. Experimental validation of the proposed method revealed an improvement in modelling accuracy over one commonly used analytical approach. Furthermore, using TRNSYS software to simulate the annual energy output we show that modelling photovoltaic systems with small variations in solar cell parameters can result in non-trivial variations in annual energy output highlighting the importance of their calculation.