A mode-in-state contribution factor based on Koopman operator and its application to power system analysis

TL;DR

This paper introduces a novel mode-in-state contribution factor based on Koopman operator spectral analysis, enabling nonlinear power system analysis beyond linear approximations.

Contribution

It develops a new contribution factor leveraging Koopman eigenfunctions to quantify mode and state variable contributions in nonlinear systems.

Findings

Effective in large-signal simulations of power systems

Quantifies mode contributions beyond linear regimes

Applicable to interconnected AC/DC power systems

Abstract

This paper proposes a mode-in-state contribution factor for a class of nonlinear dynamical systems by utilizing spectral properties of the Koopman operator and sensitivity analysis. Using eigenfunctions of the Koopman operator for a target nonlinear system, we show that the relative contribution between modes and state variables can be quantified beyond a linear regime, where the nonlinearity of the system is taken into consideration. The proposed contribution factor is applied to the numerical analysis of large-signal simulations for an interconnected AC/multi-terminal DC power system.