A cyber-physical framework for estimating inertia distribution in power systems

The growing of renewable energy integration in the power systems requires precise inertia estimation to ensure the overall stability. Current data-driven methods exhibit physical inconsistency and limited mode interpretability. To address these challenges, this paper proposes a cyber-physical framework that combines physical laws with a model for data-driven mode extraction. First, an inertia distribution model incorporating a nonlinear correction term is developed to enhance nonlinear parameter identification accuracy. Then, a physics-informed dynamic mode decomposition (PIDMD) is proposed, integrating physical laws to improve inertia behavior tracking capability while enabling inertia distribution interpretation through a modal mapping. Finally, evaluations of the proposed framework on a modified IEEE 39-bus test system demonstrate a 6.3% improvement in inertia estimation accuracy, and achieving a normalized error of 0.4%. Field validations using phasor measurement units successfully capture multi-frequency oscillations at 0.1 Hz, 0.31 Hz and 0.08 Hz. These results clearly show the important causal relationships between oscillatory modes and the distribution of inertia in renewable-dominated power systems.