Fig. 1: Spatial distributions of wind and solar power prediction errors and the impacts of different methods and time scales.

a Wind energy. b Solar energy. The larger bubbles indicate the provincial wind and solar energy installations, and the smaller ones indicate the average wind and solar energy generation (8760 h) by province. The provinces are divided into four groups according to the provincial prediction error (average value of 8760 h) and marked with four gradient colors. The thick red line marks the boundaries of the four areas of China, I. North China, II. East China, III. Central China, and IV. Southwest China. Individual provinces are indicated with lighter white lines. MW Megawatt, BJ Beijing, TJ Tianjin, HE Hebei, SX Shanxi, IM Inner Mongolia, LN Liaoning, JL Jilin, HL Heilongjiang, SH Shanghai, JS Jiangsu, ZJ Zhejiang, AH Anhui, FJ Fujian, JX Jiangxi, SD Shandong, HA Henan, HB Hubei, HN Hunan, GD Guangdong, GX Guangxi, HI Hainan, CQ Chongqing, XZ Tibet, SC Sichuan, GZ Guizhou; YN Yunnan, SN Shaanxi, GS Gansu, QH Qinghai, NX Ningxia XJ Xinjiang. c Prediction error distribution across 30 provinces obtained by different methods. The smoothed curve in the left and right parts represents the prediction error density function across 30 provinces of solar and wind energy, respectively. The short black line in the middle of each shape is the median value of the data distribution, which visualizes the central tendency of the data distribution of each method. The algorithm used to fit the density function is Kernel Density Estimation. RF random forest, RNN recurrent neural network, FCNN fully-connected neural network, SVM support vector machine, ARIMA autoregressive integrated moving average. d Nationwide prediction error distribution of each hour based on 2, 6 and 24-h ahead prediction. Each box includes 1917, 638, and 159 samples for solar energy and 4297, 1432, and 358 samples for wind energy. The lower/upper end of each box indicates the minimal/maximal value, and the lower and upper percentiles indicate 25% and 75%, respectively. The short blue line indicates the median, and the blue points show the outliers. There are blank areas for the 2-h and 6-h predictions since these two prediction tasks only contain 2 and 6 time periods, respectively.