Solving multi-period OPF with transmission interface constraints via physics-informed spatiotemporal graph convolutional networks

• Proposing PI-STGCN for MPOPF with explicit transmission interface limits; • Capturing spatiotemporal dependencies via graph convolution and GRU; • A physics-informed training strategy to guide the data-driven solution toward feasible solutions; • Achieving high accuracy and reduced violations across different power system scales. With the widespread deployment of renewable energy sources (RES) and energy storage systems, multi-period optimal power flow (MPOPF) has become a key analytical tool for coordinating short-term and long-term power system operations over a predefined time horizon. High RES penetration, however, tends to induce transmission congestion across inter-regional transmission interfaces. Incorporating transmission interface constraints into MPOPF remains challenging due to the substantial computational complexity introduced by inter-temporal coupling and the spatial interdependence of transmission interfaces. To address these challenges, this paper proposes a physics-informed spatiotemporal graph convolutional neural network (PI-STGCN) for solving MPOPF with explicit transmission interface constraints. The proposed PI-STGCN architecture integrates three key components. First, a dual-path graph convolutional module with transmission interface embedding captures spatial dependencies among grid buses. Second, a gated recurrent unit (GRU) models temporal dynamics across consecutive operating periods. Third, a physics-informed loss function incorporates branch flow limits and transmission interface flow limits as soft constraints to enhance solution feasibility. Extensive experiments on modified IEEE 30-bus, 118-bus, and 300-bus systems with high RES penetration demonstrate that PI-STGCN consistently outperforms state-of-the-art baselines in predictive accuracy, constraint satisfaction, and generalization capability. In particular, on the IEEE 300-bus system, it achieves an overall prediction accuracy of 98.11% and reduces the maximum violation magnitude by 48.7% compared with the best competing approach. Moreover, PI-STGCN exhibits strong data efficiency. By using only 60% of the training data, MAPEs of 1.27% for the IEEE 30-bus system and 1.88% for the IEEE 118-bus system are achieved, outperforming baseline approaches training on the full dataset.