Short-term electricity load forecasting is crucial for maintaining the stable operation of power systems and effective planning in electricity markets. Accurate load forecasting requires precise modeling of complex patterns, including the spatial relationships between sequences and the temporal changes within sequences. To address this, we propose a spatial-temporal dynamic graph Transformer (SDGT) model. This model consists of spatial-temporal dynamic graph modeling (SDGM) and multi-scale Transformer modeling (MSTM). The SDGM component generates dynamic graph structures in a data-driven manner, using graph convolutional networks (GCN) to identify and model potential relationships between time series. The MSTM component utilizes multiple detected cycles in time series to segment the sequences into patches of varying sizes and employs a Transformer to extract features at different scales within the sequences. By combining both approaches, the model captures both spatial dependencies between sequences and the temporal variations within sequences, leading to more accurate load fore casting. Experiments on two publicly available load datasets demonstrate that our model outperforms a range of state-of-the-art Transformer and MLP-based models.