A two-stage energy flow calculation and analysis method based on hybrid drive for electro-thermal coupling systems

In integrated energy systems (IESs), the high penetration of renewable energy and strong electro-thermal coupling characteristics make it difficult to balance the accuracy and computational efficiency of multi-energy flow analysis in scenarios with initial value sensitivity and repeated calculations. To address these challenges, a two-stage solution framework integrating heterogeneous graph neural network (HGNN) and physical correction mechanisms is proposed in this paper. In the first stage, complex coupling relationships are captured by an HGNN, where a multi-task loss function with physical constraints is utilized to balance data-driven patterns and physical laws. Concurrently, an adaptive attention mechanism is introduced to ensure consistency between attention weights and physical principles. In the second stage, a lightweight physical projection model is used on the initial HGNN solution to rectify predicted values, rapidly eliminating system residuals and guiding the flow results toward feasible solutions that satisfy energy conservation constraints. Simulation results demonstrate that the proposed method significantly outperforms traditional approaches in terms of prediction accuracy for both nodal states and energy flows. It achieves efficient solution computation while substantially improving physical consistency, providing a highly efficient and scalable solution for rapid power flow analysis, topology adaptation, and planning optimization in IES.