Fossil fuel consumption is a major source of greenhouse gas emissions. The Russia–Ukraine conflict has led to energy price volatility. Therefore, affordable energy poses a significant threat. The development of renewable energy to meet consumption demands has attracted researchers’ attention in worldwide. In this study, a novel grey adaptive integrated model is proposed to balance the fitting and generalization abilities for renewable energy generation trends. First, feature selection was performed using the mutual information filter method for influencing factors and the wrapper method. Second, FGM(1,1) was used to mine the data features, and AGMC(1,n) was used to extract multivariate time-series relationships. Finally, an adaptive integrated model with a Gaussian kernel function was proposed in order to assign weights. It balances the results of the two forecasting models to avoid the underfitting/overfitting problem generated by excessive data volatility and the abrupt shift of the influencing factors. The study results have shown that the proposed integrated model solved the underfitting and overfitting problems to a certain degree. Its performance is better than single model. We analyze the forecasting results and propose corresponding suggestions for the government and enterprises separately.