Hybrid DNN and EnKF framework for dynamic state estimation in power systems

Abstract

As modern power systems evolve, their structural and operational characteristics are becoming increasingly dynamic, complex, and uncertain. Traditional model-driven state estimation (SE) methods face limitations in accuracy and adaptability under nonlinear and time-varying operating conditions. To address these challenges, this paper proposes a deep neural network (DNN)-based dynamic SE framework with physics-constrained and ensemble Kalman filter (EnKF)-guided training. The DNN is first pretrained using labeled measurement–state samples and is then refined through a second-stage offline optimization that jointly incorporates prior-state supervision, EnKF-based covariance-aware correction, and nonlinear AC measurement consistency. After offline training, direct DNN inference is combined with a physics-consistency-based residual gate for selective online adaptation. Simulation studies on the IEEE 118-bus system show that the proposed method achieves an mean absolute error of 0.0100 and an root mean square error of 0.0139, corresponding to reductions of 34.34% and 34.39%, respectively, compared with weighted least squares. Additional tests under impulsive noise and time-varying operating conditions further demonstrate the robustness and adaptability of the proposed framework.