Nonlinear Modal Decoupling of Multi-Oscillator Systems with Applications to Power Systems

TL;DR

This paper introduces a nonlinear modal decoupling method for multi-oscillator systems like power grids, enabling easier analysis of individual modes and better understanding of system stability and dynamics.

Contribution

The paper presents a novel nonlinear modal decoupling approach that constructs decoupled oscillators with desired nonlinearities, improving analysis over traditional normal form methods.

Findings

Decoupled oscillators retain most of the original system's modal nonlinearities.

NMD offers a larger validity region than normal form.

Non-SMIB decoupled oscillators better preserve original dynamics.

Abstract

Many natural and manmade dynamical systems that are modeled as large nonlinear multi-oscillator systems like power systems are hard to analyze. For such a system, we propose a nonlinear modal decoupling (NMD) approach inversely constructing as many decoupled nonlinear oscillators as the system oscillation modes so that individual decoupled oscillators can easily be analyzed to infer dynamics and stability of the original system. The NMD follows a similar idea to the normal form except that we eliminate inter-modal terms but allow intra-modal terms of desired nonlinearities in decoupled systems, so decoupled systems can flexibly be shaped into desired forms of nonlinear oscillators. The NMD is then applied to power systems towards two types of nonlinear oscillators, i.e. the single-machine-infinite-bus (SMIB) systems and a proposed non-SMIB oscillator. Numerical studies on a 3-machine 9-bus system and New England 10-machine 39-bus system show that (i) decoupled oscillators keep a majority of the original system modal nonlinearities and the NMD provides a bigger validity region than the normal form, and (ii) decoupled non-SMIB oscillators may keep more authentic dynamics of the original system than decoupled SMIB systems.