Forecasting China’s renewable energy consumption using a novel dynamic fractional-order discrete grey multi-power model

Accurately predicting renewable energy consumption is crucial for sustainable social and economic development, especially in China during its energy transition. This research introduces a novel dynamic fractional-order discrete grey multi-power model (DFDGMM(1,1,N)) to enable accurate forecasting of renewable energy consumption in China. The proposed method introduces a fractional-order accumulation operator and three power exponents that not only ensure the priority of new information, but also accurately capture the nonlinear traits of system data. It also incorporates a dynamic time delay function to account for the time lag between energy and economic development, enhancing the model's flexibility. Additionally, the study combines the whale optimization algorithm and the double-error idea to optimal parameter search. The proposed model is versatile and can be simplified into 14 other grey models. The case study demonstrates the model's impressive predictive accuracy, with a fitting error of 4.02% and a test error of 0.89%. The model is then employed to forecast renewable energy consumption in China, predicting a rapid annual growth rate of 17.25% from 2022 to 2030. Overall, this article successfully constructs a dynamic prediction model in theory and scientifically provides valuable data support for the nation's energy development planning in practice.