<p>Renewable energy is believed to be one of the most low-carbon energy sources. Accurate forecasts of renewable energy generation can help the government make correct energy decisions. However, the sequence of renewable energy generation is irregular, nonlinear, and complex. And the existing techniques has problems such as being too linear or requiring a large amount of modeling data. Therefore, a new method is needed to solve these problems. A novel fractional grey model with Bessel function of the first kind as the grey input is proposed, and the discrete convolution solution is utilized to make the model viable in operation. The introduction of Bessel function of the first kind and fractional accumulation makes the model more adaptable and stable, and has better nonlinear fitting ability. The Salp Swarm Algorithm is used to determine the optimal nonlinear parameters of the proposed model. Compared with the existing 15 models in 5 developed countries in Europe and North America, the minimum forecasting MAPE of the proposed model just reaches 0.58%, which is better than all comparison models. Since the model performs well in actual situations, it has high potential in accurately forecasting renewable energy generation. Hence, it can be considered as a reliable forecasting tool in the future.</p>