Prediction of monthly average global solar radiation based on statistical distribution of clearness index

Abstract

In this paper, probability distribution of clearness index is proposed for the prediction of global solar radiation. First, the clearness index is obtained from the past data of global solar radiation, then, the parameters of the appropriate distribution that best fit the clearness index are determined. The global solar radiation is thereafter predicted from the clearness index using inverse transformation of the cumulative distribution function. To validate the proposed method, eight years global solar radiation data (2000–2007) of Ibadan, Nigeria are used to determine the parameters of appropriate probability distribution for clearness index. The calculated parameters are then used to predict the future monthly average global solar radiation for the following year (2008). The predicted values are compared with the measured values using four statistical tests: the Root Mean Square Error (RMSE), MAE (Mean Absolute Error), MAPE (Mean Absolute Percentage Error) and the coefficient of determination (R2). The proposed method is also compared to the existing regression models. The results show that logistic distribution provides the best fit for clearness index of Ibadan and the proposed method is effective in predicting the monthly average global solar radiation with overall RMSE of 0.383 MJ/m2/day, MAE of 0.295 MJ/m2/day, MAPE of 2% and R2 of 0.967.