Fitting generalized lambda distribution to solar radiation in Colombo, Sri Lanka

Abstract

There is a need to look at the country’s potential to develop solar power as a key power resource. As increasing the importance of solar radiation it is essential to identify a proper statistical distribution, to get an idea about the availability of solar radiation .The daily solar radiation data (MJ/m2) collected by the Meteorological department from 1997 to 2007 at a station in Colombo at latitude 6 54 30’ and longitude 79 51 30’ were used for the analysis. The daily solar radiation for monthly periods in Colombo tends to have a non-normal distribution and hence there is a need to identify a distribution which will cover different curve shapes. Thus, this study aims at fitting the Generalized Lambda Distribution (GLD) to daily solar radiation for each month. The parameters were estimated using the maximum likelihood method. The quality of the fits were assessed using histograms, qqplots, and resample KS (Kolmogorov-Smirnov) test. The fitted distribution was compared with the distributions in the literature namely the Weibull, Logistic, Normal and Lognormal using root mean square error. The above mentioned goodness of fit test and the plots show that the GLD fits the data well. When compared with the distributions in the literature GLD has the minimum root mean square error. All the months tends to have negatively skewed distributions. The daily solar radiation totals from February to September show strong negative skewness and almost same distribution pattern. Further the months January, October, November and December show the least skewness. The mean solar radiation for the period 1997 to 2007 is 16 MJ/m2. By taking16 MJ/m2 as the threshold value probabilities were calculated above this value. The chance that the daily solar radiation above 16 MJ/m2 is more than 87% for the months from February to September and for the rest of the months there is no chance of having solar radiation above this value. Since three fourths of the months have solar radiation more than 87% of the average value, a substantial potential exists in the city of Colombo for harnessing solar energy.