The numerical computation of lumped parameter values using the multi-dimensional Newton-Raphson method for the characterisation of a multi-junction CPV module using the five-parameter approach

•New numerical method to characterise multi-junction photovoltaic system is presented.•Based on the single-diode, five parameter approach.•Newton-Raphson approach applied to solve for all five characterisation parameters.•Method experimentally validated. The mathematical modelling of photovoltaic devices is heavily relied upon due to their highly variable yield while operating under varying environmental conditions. A number of methods currently exist to characterise the non-linear electrical behaviour of these devices, with the single-diode, five-parameter model extensively used. In this study, we examine the use of this model for a triple-junction III–V type solar cell operating under concentrated sunlight. In order to use this method, however, five characterisation parameters must be calculated for the specific device under study. Their calculation is difficult due to the intrinsic non-linear operational characteristics of these devices, as such a number of methods currently exist for this purpose. A new method is presented here based on the examination of the power-voltage data from which a system of five residual equations are derived and solved via the multi-variable Newton-Raphson method. The new approach was validated experimentally by means of both qualitative and quantitative assessment. Results revealed that the proposed method was able to accurately model this device type and when compared to several alternative methods, yield the lowest average root mean square error (RMSE) with a 7–55% improvement offered over the alternative methods investigated. The proposed method will be useful to engineers and scientists who wish to characterise the performance of multi-junction photovoltaic devices using the single-diode, five-parameter model and require a method to extract the values of their characterisation parameters. A limitation with this approach is the computational effort required to solve the system of non-linear residual equations and the need for good initial estimates of the lumped parameters to initiate the search.