Mathematical models to forecast temporal variations of power law shape parameters of a PV module working in real weather conditions: Prediction of maximum power and comparison with single-diode model

Abstract

In this study, an innovative approach has been proposed to generate real time current–voltage characteristics and forecast peak power of photovoltaic (PV) modules working outdoors beneath real meteorological conditions. Power-Law Model (PLM) including four unknown parameters, two PV metrics (ISC, VOC), and two profile parameters (γ, m), has been used for fast, accurate and reliable modelling of PV modules. Explicit expressions giving γ and m parameters as functions of cardinal point coordinates (IMPP,VMPP, ISC and VOC) have been established. A daily monitoring of PV quantities, throughout one reference day, has been used to derive novel mathematical models of γ and m depending on module temperature and solar irradiance. To describe PV module behavior under changing meteorological conditions during an arbitrary day, mathematical models have been called to reproduce dynamical values of PLM shape parameters γ and m. Reliability of the approach has been assessed by comparing current–voltage characteristics and maximum power coming from PLM and Single-Diode Model (SDM) to experimental data of twenty-two PV modules measured at NREL. Comparison also reveals that I-V characteristics generated and predicted separately by PLM and SDM parameters are very close. In some cases, I-V characteristics generated by PLM parameters are more accurate. Furthermore, NRMSE values for generated and predicted I-V characteristics for all kinds of PV modules evaluated for different working conditions do not exceed 4% for both PLM and SDM, and determination coefficient values for long-term prediction of maximum power are close to one and annual average value is greater than 0,95.