Estimation of global radiation using Clear - Sky model at selected sites in Kenya

Abstract

World energy demand has been outstripping supply since the 1973 Arab/OPEC oil crisis. This has led to a wide interest in, and development of, renewable and sustainable energy including solar energy. Solar radiation data is an important input parameter in the design and implementation of solar energy systems. Only a few scattered meteorological stations in Kenya measure solar radiation on a continuous basis. The use of models to estimate this parameter can alleviate the problem. A clear sky model can be easily obtained from measured global solar radiation on a horizontal surface situate on Earth’s surface. Using solar radiation and duration of sunshine data from 11 Kenyan meteorological stations, this study tested seven Angstrom - Prescott type regression models for their suitability to estimate clearness index for clear skies ) ( c K . The Angstrom - Prescott type models were obtained by regressing sunshine duration against clearness index and obtaining curves of best fit. Linear, quadratic, exponential, power and logarithmic fits were obtained. Model performance was measured using goodness of fit statistics including Pearson correlation coefficient (r), coefficient of determination (R 2 ), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Students - t - statistic, and the t- test. Out of the 11 stations considered data from Dagoretti, Eldoret, J K Airport, and Voi meteorological stations showed high R 2 values and these were used to produce modified Angstrom - Prescott models whose long - term, short - term, and overall per formances were measured using MBE, RMSE, and t - statistic respectively. For each of the four stations with high R 2 values 10 pairs of equations, one each for c K presented. These 20 equations are recommended for use in estimating clear - sk y clearness indices at the four stations (and in the immediate neighbourhood) using measured fraction of duration of sunshine as the only input. The correlation coefficients for each model were determined and these were found to be site dependent. For exa mple the correlation coefficients for the linear model of the Angstrom type for Dagoretti and Eldoret were 0.316, 0.706 and 0.421, 0.650 respectively while those for the quadratic model for the same two stations were respectively 0.348, 0.579, 0.118 and 0 .264, 1.175, - 0.426. A number of recommendations on the use of these models are given.