A novel time-varying parameters structural adaptive Hausdorff fractional discrete grey model and its application in renewable energy production and consumption prediction

The role of energy is essential in driving human development and achieving economic and social progress. It's crucial to make precise predictions about how traditional and new energy sources will be used in the future, as this information can help a country create effective energy strategies and make adjustments to its energy structure accordingly. Considering the common presence of volatility, nonlinearity and periodicity in long-term energy data series, this paper proposes a novel time-varying parameters adaptive discrete grey prediction model FHATDGM (1,1) based on Hausdorff fractional derivative. This model further explores the possible periodic features in the system, in order to more comprehensively and accurately describe the development trend of the time series. In addition, the Grey Wolf Optimization algorithm (GWO) is selected to optimize the parameters of the model. Then, for the robustness of the results obtained by introducing intelligent optimization algorithm, this paper uses the method of combining Monte Carlo simulation and probability density analysis to test, indicating that the proposed model has better stability and accuracy compared with the existing six models. Finally, three actual cases of China's solar power generation, United States hydroelectric power generation and China's consumption of coal are predicted. The results show that the FHATDGM (1,1) has the highest fitting and forecasting accuracy. The reduction in prediction error compared to the other six models ranged from 1.46 % to 37.49 %.