Accurate forecasting of energy consumption is critical for addressing challenges in energy allocation, especially as renewable energy plays a pivotal role in the pursuit of carbon neutrality. Renewable energy consumption exhibits distinctive trends and seasonal fluctuations, which calls for more sophisticated modeling approaches to ensure predictive accuracy. This study proposes a hybrid forecasting framework that combines grey system model with Gaussian process-based residual uncertainty analysis and a rolling prediction mechanism. The grey model generates forecasts on segmented subsets of the time series, while Gaussian process regression (GPR) analyzes the residual uncertainty, under the rolling prediction mechanism. Furthermore, the particle swarm optimization (PSO) algorithm is implemented to optimize the nonlinear parameters of the grey system model. The proposed framework is tested on

renewable energy consumption data from both commercial and residential sectors in the United States. Its performance is rigorously evaluated and compared against nine other grey hybrid models across four performance metrics. Results demonstrate that the hybrid model incorporating the fractional-order nonhomogeneous discrete grey model (FNDGM) and GPR (FNDGM-GPR) consistently outperforms the competing models in terms of both forecasting accuracy and generalization capability