As modern power systems continue to evolve, accurate power load forecasting remains a critical issue in energy management. The phase space reconstruction method can effectively retain the inner chaotic property of power load from a system dynamics perspective and thus is a promising knowledge-based preprocessing method for short-term forecasting. In order to fully utilize the capability of PSR method to model the non-stationary characteristics within power load, and to solve the problem of the difficulty in applying traditional PSR prediction methods to form a general multi-step forecasting scheme, this study proposes a novel multi-step forecasting approach by delicately integrating the PSR with neural networks to establish an end-to-end learning system. Firstly, the useful features in the phase trajectory are discussed in detail. Through mathematical derivation, the equivalent characterization of the PSR and another time series preprocessing method, patch segmentation, is demonstrated for the first time. Based on this knowledge, an image-based modeling perspective is introduced. Subsequently, a novel deep learning model, namely PSR-GALIEN, is designed, in which the Transformer Encoder and 2D-CNN are employed for the extraction of the global and local patterns in the image, and a MLP-based predictor is used for the efficient correlation modeling. Then, extensive experiments are conducted on five real-world benchmark datasets to verify the effectiveness of the PSR-GALIEN. The results show that, compared with six state-of-the-art deep learning models, the forecasting performance of PSR-GALIEN consistently surpasses these baselines, achieving superior accuracy in both intra-day and day-ahead forecasting scenarios. At the same time, the attributions of its forecasting results can be explained through the visualization-based method, which significantly increases the interpretability.