Modeling of uncertainty of solar irradiance forecasts on numerical weather predictions with the estimation of multiple confidence intervals

One-day-ahead solar forecasting by numerical weather prediction is expected to be an effective tool to improve the operation of an electrical system that integrates a large amount of solar power generation. The purpose of this study is to develop a new empirical method to model the prediction uncertainty of the solar irradiance forecast on numerical weather prediction. The proposed method comprises of four steps. First, predicted and measured solar irradiances are transformed into Gaussian random variables using data observed in a modeling window in the near past. Second, a multivariate normal joint distribution model is estimated using data in the same window. Next, a distribution of irradiance of the next day conditional on one-day-ahead forecast is derived. Finally, multiple confidence intervals both temporally and spatially are estimated by using the conditional distribution. A solution to select an appropriate length for the modeling window is presented. The multivariate normality assumption is checked by evaluating the joint hit rate of the estimated multiple confidence intervals numerically.