Interval Prediction Method for Solar Radiation Based on Kernel Density Estimation and Machine Learning

Precise global solar radiation (GSR) data are indispensable to the design, planning, operation, and management of solar radiation utilization equipment. Some examples prove that the uncertainty of the prediction of solar radiation provides more value than deterministic ones in the management of power systems. This study appraises the potential of random forest (RF), V-support vector regression (V-SVR), and a resilient backpropagation artiï¬ cial neural network (Rprop-ANN) for daily global solar radiation (DGSR) point prediction from average relative humidity (RHU), daily average temperature (AT), and daily sunshine duration (SD). To acquire more accurate predictions of DGSR and examine the influence of historical DGSR on the performance of point prediction models, two different model inputs are considered: (1) three meteorological variables and (2) the lags of DGSR and three meteorological variables. Then, two interval prediction methods are developed by introducing the KDE to out-of-bag (OOB), introducing kernel density estimation (KDE) to split conformal (SC) based on the three machine learning models. The two methods for interval prediction are denoted as OOB-KDE and SC-KDE. The mean absolute error (MAE), mean relative error (MRE), and Kendall rank correlation (Kendall) are used to assess the point prediction models. The performance of interval prediction methods is evaluated by the prediction interval coverage probability (PICP), prediction interval normalized average width (PINAW), and coverage width criteria (CWC). The following conclusions are drawn from this study. First, the V-SVR model performs best with the lowest mean absolute error (MAE) of 0.016 and mean relative error (MRE) of 0.001. Second, the lags of DGSR improve the prediction accuracy by about 30%. Third, the OOB-KDE and SC-KDE methods improved the quality of the prediction interval (PI). OOB-KDE improved CWC by 81%, and SC-KDE improved CWC by 99.99%. Fourth, the best interval prediction result is obtained using the SC-KDE method using the V-SVR model. The average difference between its PICP and prediction interval nominal coverage (PINC) is only 3% of the PINC, and its PINAW is less than 0.007.