Dynamic State Estimation for Smart Grid Energy Management Using Second-Order Hybrid Extended Kalman Filter and Neural Networks

Accurate state estimation is a critical component of modern smart grid energy management, particularly as renewable energy sources, distributed generation, and dynamic load patterns introduce increasing nonlinearities and uncertainties into power systems. Traditional Kalman filtering methods, while effective for linear systems, often struggle with the complex, nonlinear dynamics prevalent in contemporary energy networks. This paper proposes a novel hybrid framework that integrates a Second-Order Hybrid Extended Kalman Filter (SO-HEKF) with an Artificial Neural Network (ANN) to enhance state estimation accuracy, robustness, and real-time adaptability.

Unlike conventional first-order EKF approaches, the SO-HEKF incorporates second-order corrections and point-based modification techniques to reduce linearization errors, while the ANN component provides adaptive, data-driven learning capabilities to handle system uncertainties and changing operating conditions. The proposed framework is evaluated across three practical energy management scenarios: renewable energy integration, load forecasting, and demand response optimization. Comprehensive simulations using IEEE 118-bus system data and NREL renewable generation profiles demonstrate that the hybrid SO-HEKF+ANN approach achieves up to 16.7% improvement in estimation accuracy compared to standalone EKF and IEKF methods.

The framework also exhibits enhanced noise robustness (97.3% estimation stability), reduced mean absolute error (0.017–0.019 p.u.), and reliable real-time performance with an average iteration time of 0.28 seconds per simulation second. Sensitivity analyses confirm the framework's resilience under varying renewable penetration rates (±20–60%), storage capacity changes, and forecast uncertainties. Comparative evaluations against benchmark methods including traditional PI control, Model Predictive Control (MPC), and deep learning-based estimators show consistent superiority in grid stability, load shifting efficiency, and renewable utilization.

The results highlight the practical potential of the proposed hybrid architecture for real-time energy management in smart grids, microgrids, and renewable-integrated distribution systems. Future research directions include hardware-in-the-loop validation, cyber-resilience enhancements, and scalability to large-scale national grids.