Closed-Forms Solution for Simplified PV Modeling and Voltage Evaluation Including Irradiation and Temperature Dependence

Abstract

This paper presents a closed-form relation among voltage, current and power of PV cells. The methodology applied consists in a selective use of Taylor series with the purpose of obtaining a solvable analytical equation that presents similar results to the traditional numerical solution. This simplified solution enables an easier but precise evaluation of the PV voltage generated under specific conditions of temperature and solar radiance. The main benefit of this set of equations is the creation of a tool set that allows a precise evaluation of the yearly voltage profile based in PV datasheet and solar plant location. The expected yearly voltage profile provides valuable information in order to set the inverter voltage operation design in an optimal fashion for maximum yield benefits. These results may provide information valuable to compare and decide whether to install an inverter with or without a DC booster. The technique proposed in this work is validated by comparing the results of the set of equations derived with the traditional numerical solution and the PV manufactured values.