Physics-Informed Dynamic State Estimation For Current Transformers Using Graph Neural Networks

Current transformers (CTs) are essential for protection and measurement, but core saturation during transients can severely distort the secondary current and degrade signal fidelity. This paper presents a dynamic state-estimation pipeline for CT saturation correction using COMTRADE measurements generated in WinIGS-T, a time-domain power-system simulation environment for producing high-fidelity electromagnetic transient data. Integration methods (Forward Euler, Trapezoidal, Quadratic, and Backward Euler) and iterative solvers (Gauss--Newton and Levenberg--Marquardt) are evaluated across multiple SNR conditions, together with a graph neural network (GNN) warm-start strategy. The results reveal clear trade-offs: Forward Euler achieves the lowest average runtime, Levenberg--Marquardt attains the best final residual accuracy, and a hybrid GN->LM strategy provides the strongest convergence robustness. The GNN also improves initialization quality, yielding an average state-distance gain of 25% and an average initial-objective gain of 38% relative to cold-start GN. With better initialization alignment, the warm-started GN process also achieves a positive average iteration-count improvement of 4.55%. These findings show that the GNN provides a robust, physics-consistent prior that improves early optimization conditions and supports faster practical convergence in noisy CT state-estimation settings.