A novel seasonal time-varying discrete grey power model and its application in solar power generation forecasting

Purpose Solar power generation exhibits significant time-varying seasonal fluctuations and nonlinear trends, which pose a challenge to existing forecasting techniques. Therefore, this paper proposes a novel grey forecasting framework that integrates seasonal decomposition, nonlinear modeling, and time-varying adaptation, namely the seasonal time-varying discrete grey power model. Design/methodology/approach Firstly, seasonal dummy variables are introduced to separate periodic fluctuations from the trend. Secondly, the seasonal effect is innovatively decomposed into fixed and time-varying components, precisely capturing the temporal evolution patterns across different periods. Concurrently, the double-power index structure quantifies the nonlinear driving effects of both historical values and temporal factors on the current state. The hiking optimization algorithm is employed for hyper-parameter tuning. Findings The new model was validated using datasets from the three major economies of the U.S., India, and China, and compared with six competitive models representing different types. Results show that the new model exhibits superior predictive accuracy. Furthermore, robustness tests across multiple time windows further validate the stability of the model under varying scenarios. Practical implications Forecasts for 2025–2027 indicate sustained growth in solar power generation across all three nations, but the magnitude and patterns of growth exhibit significant differences. The research findings provide a reliable decision support tool for solar power planning and grid dispatch in the global energy transition. Originality/value The new model effectively captures the complex dynamics in solar power generation data by integrating seasonal time trend terms, dummy variables, and power index terms into the discrete grey modeling system.