Superellipse model: An accurate and easy-to-fit empirical model for photovoltaic panels

Abstract

The accurate representation of the photovoltaic (PV) characteristic curves especially at maximum power point (MPP) are essential for the real-time performance evaluation of PV panels. Over the years, equivalent circuit models which are based on the conversion behavior of PV panels have been the only approach employed in its modeling, simulation, and analysis. However, since the resulting I–V characteristic equation is inherently nonlinear and implicit, the full range enumeration of the PV characteristic curves is usually obtained in a complicated way. Thus, this paper proposes a novel empirical model for modeling and analysis of PV panels. Due to the unique similarities between the geometric shapes of a superellipse and the graphical characteristics of the I–V curve, an explicit mathematical correlation describing the behavior of PV panels can be established. By outlining a step-by-step procedure, the parameter extraction procedures are illustrated. As a result, the straightforward description of the full-range parameter fitting extraction of the I–V curve is greatly simplified. To validate the superiority of the proposed model over the conventional single-diode model, the model accuracy is evaluated according to the IEC EN 50530 standard. The simulation results revealed that irrespective of PV panel specification, cell material, and ambient conditions, the proposed empirical model maintains a low absolute current and power errors within the vicinity of MPP.