Two types of conformable fractional grey interval models and their applications in regional electricity consumption prediction

Taking the unbalance development inside a region into consideration, it will be better to express the regional electricity consumption (EC) value as an interval number to preserve more complete information. However, there are rare papers about this interesting topic. For the small amount of EC data, grey interval prediction model is employed in this paper. However, the existing models are almost all integer-order grey interval models and based on area coordinate conversion method. In order to fill this gap, and to obtain more accurate forecasting results, a conformable fractional non-homogenous discrete grey model (CFNDGM(1,1,α)) is proposed, and on the basis of CFNDGM model, two conformable fractional grey interval models are built. One is based on area coordinate conversion method (CFNDGM_AC), and the other is with information decomposition conversion method (CFNDGM_ID). The mathematical relationship of the two types of grey interval models is firstly given in this paper. It indicates that which type of model has better performance depends on the characteristics of original data. To assess the two fractional grey models, annal EC values in southern Jiangsu are taken as an example, and other four grey interval models are taken for comparison. Results show that CFNDGM_ID has the best performance among six models in both simulation and prediction. Then CFNDGM_ID is chosen to predict EC of southern Jiangsu in the next five years. To further improve forecasting accuracy, the optimal fitting size of CFNDGM_ID is selected. Forecasting results show that the EC in southern Jiangsu will increase in the next five years, but at a lower growth rate.