Understanding the complexity of frequency and phase angle fluctuations in power grids

TL;DR

This study analyzes large-scale high-resolution data of power grid frequency and phase-angle fluctuations in the UK and South Africa, using superstatistical modeling to understand underlying stochastic processes and their impact on grid stability.

Contribution

It introduces an analytical superstatistical model that accurately reproduces complex frequency distributions and phase-angle fluctuations, revealing differences between mature and developing grids.

Findings

The model reproduces multimodal frequency distributions and heavy tails.

Frequency autocorrelation decays are double-exponential and match measurements.

Spatial phase-angle fluctuations are well-characterized by a low-dimensional model.

Abstract

Power grids must modernize to meet climate goals while maintaining reliable and stable operating conditions. Yet progress is hindered by a limited understanding of the stochastic processes underlying grid frequency and phase-angle fluctuations, which are induced by the growing penetration of renewable generation, consumer demand fluctuations, and market trading. This issue is particularly acute in Africa, where grids often face weak investment. Here, we present results from a newly collected, large-scale, high-resolution dataset of grid frequency and phase angles for the United Kingdom and South Africa, comprising close to one billion data points. Using superstatistical modeling, we treat market-driven power fluctuations as a slowly varying parameter driving grid dynamics and incorporate nonlinear frequency control. As a result, we derive an analytical model that reproduces multimodal frequency distributions previously obtained from numerical simulations, as well as heavy-tailed fluctuations and double-exponential frequency autocorrelation decays, all in excellent agreement with experimental measurements. Beyond frequency, we also address the so far largely overlooked problem of characterizing spatial phase-angle fluctuations. By comparing our predictions with measurement data, we demonstrate that a low-dimensional effective grid model accurately fits South African data despite the grid's complexity. We also highlight significant differences between the grids of South Africa and the United Kingdom. Our results clarify how energy markets and control policies shape grid dynamics across countries with contrasting infrastructure maturity.