A Mathematical Model of Threshold Solar Irradiance for Computing the Quality Hours of Sunshine

Abstract

This paper proposes a universal mathematical model to compute the number of annual hours that a particular location receives of at least a certain level of Global Horizontal Irradiance (GHI) and Direct Normal Irradiance (DNI). The proposed mathematical model was statistically validated based on actual measured data of various locations in India. A mathematical model is developed using measured solar irradiance data from fifteen different locations in India, and detailed analysis on the quality of the hours of specific solar irradiance using ground measured data, is rarely attempted by researchers in the past, which makes this study a unique one. Statistical analysis is carried out to validate the proposed model using measured data from ten locations in India as well as from five locations globally. The statistical tools used include the Root mean square error (RMSE), Mean absolute percentage error (MAPE), Mean bias error (MBE) and Nash-Sutcliffe Efficiency (NSME). The proposed model gives a best fit to the prediction of over 90% accuracy. It serves as input to designers and policy makers for sizing and feasibility studies in the field solar energy. A statistical analysis was carried out and the model showed excellent performance for GHI calculations for cities in India and the USA