Learning the Frequency Dynamics of the Power System Using Higher-order Dynamic Mode Decomposition

TL;DR

This work tackles the challenge of learning power-system frequency dynamics under high renewable penetration, where nonlinear effects render linear models inadequate. It introduces higher-order Dynamic Mode Decomposition (HODMD) with delayed embedding to learn spatio-temporal frequency dynamics from data without assuming predefined features, enabling robust predictions in high-dimensional systems. The approach yields clear local and global oscillation modes and demonstrates superior predictive accuracy compared with LANDO and SINDy on IEEE 14-bus and WECC test systems, even in the presence of noise. The findings have practical implications for stability assessment and modal analysis in future grids, where data-driven, model-free learning of nonlinear dynamics is essential.

Abstract

The increasing penetration of renewable energy sources, characterised by low inertia and intermittent disturbances, presents substantial challenges to power system stability. As critical indicators of system stability, frequency dynamics and associated oscillatory phenomena have attracted significant research attention. While existing studies predominantly employ linearized models, our findings demonstrate that linear approximations exhibit considerable errors when predicting frequency oscillation dynamics across multiple time scales, thus necessitating the incorporation of nonlinear characteristics. This paper proposes a data-driven approach based on higher-order dynamical mode decomposition (HODMD) for learning frequency dynamics. The proposed method offers distinct advantages over alternative nonlinear methods, including no prior knowledge required, adaptability to high-dimensional systems, and robust performance. Furthermore, HODMD demonstrates superior capability in capturing system-wide spatio-temporal modes, successfully identifying modal behaviour that remains undetectable through standard Dynamic Mode Decomposition techniques. The efficacy of the proposed methodology is validated through comprehensive case studies on both IEEE 14-bus and WECC systems.

Figures (10)

• Figure 1: Comparison of different order d (IEEE 14-bus system).
• Figure 2: Comparison of different order d (WECC system).
• Figure 3: Performance on tes data ($d=8$ for IEEE 14-bus system).
• Figure 4: Performance on test data ($d=15$ for WECC system).
• Figure 5: RRMES with noisy data: (a) IEEE 14-bus system; (b) WECC system.