A conformable fractional unbiased grey model with a flexible structure and it’s application in hydroelectricity consumption prediction

Accurate forecasting results of hydropower consumption will help the energy sectors to make plans for sustainable development. Due to the obvious complex and nonlinear characteristics in hydropower consumption, a conformable fractional grey model with a flexible structure is developed in this paper. The flexible structure will enhance the grey model’s ability to forecast the data with nonlinear and complex features. Specifically, the structure of the novel model is flexible, which is selected on the basis of raw data automatically while avoiding overfitting. To further improve the forecasting accuracy, the conformable fractional operators are considered to reveal the historical evolution in the raw data. And the unbiased parameters are derived to avoid the inherent conversion errors in the traditional grey model. For validation,the novel model is compared with six grey models in three practical examples. The comparative models include five grey models with fixed structures and the latest fractional grey model with a variable structure. The results show that the novel model has the highest accuracy in the three examples. Then, based on the data from 2004 to 2020, the novel model is applied to forecast China’s hydropower consumption from 2021 to 2023. The results show an upward trend in the next three years, reaching 3307.65 TWh in 2023. However, the annual growth rate will drop to 0.29% in 2023.