A novel discrete multivariable grey model with seasonal time-lag effect for clean energy generation forecasting

Accurate prediction of clean energy generation is essential for optimizing the energy structure and ensuring supply stability. This study proposes an enhanced seasonal grey forecasting framework to address the challenges posed by strong seasonality and time-lag effects in clean energy data. Specifically, we integrate seasonal dummy variables and lagged background values, and extend the model from integer to fractional orders to better capture periodic patterns and time-lag effects. Hyperparameters such as the fractional accumulation order and time power index are calibrated using the Grey Wolf Optimizer, and its performance is evaluated through comparisons with other algorithms under identical iteration settings. The proposed model is evaluated using three distinct clean energy datasets, China's quarterly solar energy with sustained growth, China's quarterly nuclear energy with relative stability and American monthly nuclear energy with high volatility. Compared with seven benchmark models, the proposed model achieves lower mean absolute percent error scores on the test sets of 2.494 %, 3.229 % and 1.667 %. Robustness analysis and sensitivity analysis further confirm that the proposed model offers a reliable and adaptive forecasting framework suited to the volatile seasonal characteristics of clean energy generation.