Delocalization of Phase Disturbances and the Stability of AC Electricity Grids

TL;DR

This paper investigates how local phase disturbances in AC power grids spread or localize, affecting grid stability, especially with increased renewable energy sources, and derives conditions for their delocalization or localization.

Contribution

It introduces a novel analysis of phase disturbance propagation in AC grids using nonlinear power balance equations mapped to wave equations, highlighting the impact of grid topology and power distribution.

Findings

Delocalized disturbances increase perturbation lifetime and grid instability.

Localized perturbations decay exponentially fast, enhancing stability.

Grid topology and power distribution critically influence disturbance behavior.

Abstract

The energy transition towards an increased supply of renewable energy raises concerns that existing electricity grids, built to connect few centralized large power plants with consumers, may become more difficult to control and stabilized with a rising number of decentralized small scale generators. Here, we aim to study therefore, how local phase perturbations which may be caused by local power fluctuations, affect the AC grid stability. To this end, we start from nonlinear power balance equations and map them to complex linear wave equations, yielding stationary solutions with phases $\varphi_i$ at generator and consumer sites $i$. Next, we study deviations from these stationary solutions. Starting with an initially localized perturbation, it is found to spread in a periodic grid diffusively throughout the grid. We derive the parametric dependence of diffusion constant $D$. We apply the same solution strategy to general grid topologies and analyse their stability against local perturbations. The perturbation remains either localized or becomes delocalized, depending on grid topology, power capacity and distribution of consumers and generators $P_i$. Delocalization is found to increase the lifetime of perturbations and thereby their influence on grid stability, while localization results in an exponentiallyfast decay of perturbations at all grid sites. These results may therefore lead to new strategies to control the stability of electricity grids.