Addressing the issue of low accuracy in predicting short-term power generation and consumption data for the photovoltaic-storage-direct-flexible distribution system using existing time series models, a multi-data prediction model based on grey relation analysis (GRA), ensemble empirical mode decomposition (EEMD), and Informer, namely the GRA/EEMD-Informer is proposed. This model effectively captures the precise long-range correlation coupling between outputs and inputs through grey relation analysis, modal decomposition, combined with a self-attention distillation mechanism. It reduces spatiotemporal complexity and significantly alleviates the limitations of traditional encoding and decoding methods. Using data from a photovoltaic power station, the electricity consumption of typical office building, and an electric vehicle charging station for a certain month as the original data, the model is tested using evaluation metrics such as mean squared error (MSE), mean absolute error (MAE), and root mean squared error (RMSE). Ablation experiments and analyses are conducted, and the results are compared with those of long short-term memory (LSTM), particle swarm optimization-based LSTM (PSO-LSTM), and the transformer time series prediction method. The results indicate that the proposed method exhibits significantly higher fitting accuracy than other prediction methods, verifying the effectiveness and practicality of the GRA/EEMD-Informer algorithm in enhancing prediction capabilities.