A Straightforward Approach to Drawing Temperature-Dependent I–V Curves of Solar Cell Models

Abstract

Equivalent circuit models of solar cells are important for understanding the behavior of photovoltaic systems under different weather conditions. They provide an equation F(V,I)=0 that expresses the correspondence between voltage V and current I a cell can deliver. The performance of a cell, and, therefore, the parameters of equation F, depend on the cell’s temperature and on the incoming light’s energy and angle. One would like to simulate and visualize these dependencies in real time. Given a fixed set of parameters, no elementary solution s(V)=I of Equation F(V,I)=0 is known. Hence, circuit simulation systems employ numerical methods to solve this equation and to approximate the circuit’s I–V curve, CIV. In this note, we propose a simpler approach. Instead of expressing I as a function of V, we represent both as elementary functions V(u) and I(u) of a real parameter u. In this way, the I–V curve CIV is obtained as the image of the mapping m(u)=(V(u),I(u)) from a u-interval to the VI-plane. Our approach offers both a precise mathematical description of CIV and an easy way to draw it. This allows us to study the influence of environmental changes on CIV by smooth animations, and yet with rather simple means. In this paper, we consider temperature dependence as an example; changes in irradiance or angle could be incorporated as well. Using formulae suggested in the literature that describe how the parameters in equation F(V,I)=0 depend on temperature, it takes only a few lines of code to generate an interactive worksheet that shows how CIV, the location of the maximum power point MPP and the maximum power change as the circuit’s temperature, is altered on a slider. Such a worksheet and its location will be presented in this paper.