A Model for the Estimation of Global Solar Radiation Using Fuzzy Random Variables

Abstract

In this paper, the concept of fuzzy random variables is applied for the estimation of global solar radiation on a surface at ground level. The cloudiness index is defined as the fraction of extraterrestrial radiation that reaches the earth's surface when the sky above the location of interest is obscured by the cloud cover. The cloud cover at the location of interest during the jth time interval of a day is assumed to follow the fuzzy random phenomenon. The cloudiness index, therefore, is considered as a fuzzy random variable that accounts for the cloud cover at the location of interest during the jth time interval of a day. This variable is assumed to depend on four other fuzzy random variables that, respectively, account for the cloud cover corresponding to the 1) type of cloud group, 2) climatic region, 3) season with most of the precipitation, and 4) type of precipitation at the location of interest during the jth time interval. The method is applied to estimate the monthly mean daily global solar irradiation for four different locations corresponding to four different climatic regions in India. The mean hourly global solar irradiation for the months of January and July and the global solar irradiance on a horizontal surface at Delhi for two typical days are also estimated. The deviations of simulated values with respect to the corresponding observed values are calculated using the mean biased error and root-mean-square error statistical parameters characteristic of long-term and short-term predictive values of the deviations, respectively. For the short-term and long-term performances, the simulated values exhibit maximum deviations of 0.532% and 1.86%, respectively, from the corresponding observed values of monthly mean daily global irradiation at Calcutta. The maximum deviations are 3.204% and 5.845%, respectively, for monthly mean hourly global irradiation at Delhi in January.