Robust Distribution System State Estimation with Physics-Constrained Heterogeneous Graph Embedding and Cross-Modal Attention

Real-time distribution system state estimation is hampered by limited observability, frequent topology changes, and measurement errors. Neural networks can capture the nonlinear characteristics of power-grid operation through a data-driven approach that possesses important theoretical value and is promising for engineering applications. In that context, we develop a deep learning framework that leverages General Attributed Multiplex Heterogeneous Network Embedding to explicitly encode the multiplex, heterogeneous structure of distribution networks and to support inductive learning that adapts to dynamic topology. A cross-modal attention mechanism further models fine-grained interactions between input measurements and node/edge attributes, enabling the capture of nonlinear correlations essential for accurate state estimation. To ensure physical feasibility, soft power-flow residuals are incorporated into training as a physics-constrained regularization, guiding predictions toward consistency with grid operation. Extensive studies on IEEE/CIGRE 14-, 70-, and 179-bus systems show that the proposed method surpasses conventional weighted least squares and representative neural baselines in accuracy, convergence speed, and computational efficiency while exhibiting strong robustness to measurement noise and topological uncertainty.