Automated Multi-Timescale Coordination in Smart Grids via Graph Neural Network-Embedded DAE-Constrained Optimization

Abstract

Coordination schemes for large-scale power systems often fail to accurately capture dynamic processes, thereby compromising physical feasibility. This paper proposes a graph neural network-embedded differential algebraic equation constrained optimization framework (GNN-DAE-COF) that integrates physical constraints into distributed optimization. We encode DAE constraints directly into message-passing mechanisms, enabling parallelization while preserving feasibility. A differentiable implementation of Pontryagin’s maximum principle (PMP) leverages automatic differentiation for efficient gradient computation, eliminating numerical discretization. An adaptive multi-timescale attention mechanism automatically coordinates fast, medium, and slow dynamics through learned weights, achieving hierarchical optimization without manual separation. Projection layers enforce the affine power-balance and the convex voltage/frequency limits exactly for any weights; the remaining nonlinear AC feasibility is recovered by a convex relaxation whose residual is driven below tolerance. On the IEEE 118-bus system, the gap stays at or below 0.42% across the three scenarios; across system sizes from 39 to 2383 buses, it stays at or below 0.78%. At 100% loading, the gap rises to 1.24% with a 95% convergence rate, and an ablation study shows that the projection, PMP, attention, and ADMM-coordination modules each control a separate performance axis. Note to Practitioners—As renewable energy sources like wind and solar increase their share of generation, their inherent variability makes this coordination problem increasingly urgent. Current optimization methods either run too slowly for real-time decisions or produce solutions that violate physical operating limits during actual implementation. Our approach embeds the fundamental physics of power systems directly into a graph neural network architecture. This design ensures that every solution the system produces automatically satisfies physical constraints, eliminating the post-processing corrections that plague current methods. The framework learns to automatically identify and coordinate different timescale dynamics without requiring operators to manually tune separation thresholds. Testing on the IEEE 118-bus system demonstrates strong, feasible results across all three scenarios. The method maintains a 95% convergence rate under high-stress conditions where current approaches frequently fail. Future development will extend the approach to handle probabilistic constraints and coordinate multiple interconnected control areas.