Stochastic Modeling of Power-Grid Frequency Fluctuations in Low-Inertia Systems via a Gaussian-Core Potential and Superstatistics

TL;DR

This paper introduces a novel stochastic model combining Gaussian-core potential and superstatistics to accurately capture the complex, evolving frequency fluctuations in low-inertia power grids, especially bimodality and heavy tails.

Contribution

It presents a data-driven, interpretable model that reproduces empirical frequency distribution features and tracks changes in grid inertia over time.

Findings

Model successfully reproduces bimodal frequency distributions and heavy tails.

Central barrier parameter increases as grid inertia decreases from 2020 to 2025.

The superstatistical approach captures autocorrelation decay in frequency data.

Abstract

Power grid frequency stability is fundamental to the secure operation of modern energy systems, yet the growing penetration of renewables and the associated reduction of system inertia have made frequency fluctuations increasingly non-Gaussian and difficult to model. Existing stochastic models based on standard Ornstein--Uhlenbeck-type restoring terms yield a unimodal frequency distribution and therefore fail to reproduce the bimodal structure, central suppression, and heavy tails widely observed in empirical data. Here, we propose a data-driven stochastic process that combines a Gaussian-core potential with superstatistical modeling, assuming slowly fluctuating coefficients for the grid dynamics. The Gaussian-core potential captures the potential barrier that gives rise to the characteristic double-peak structure of frequency distributions. Fitting the model to frequency data resolved at one-second intervals from the Great Britain grid, we find that the central barrier parameter increases substantially from 2020 to 2025 as the grid inertia progressively decreases. To simulate superstatistics, we use an Euler--Maruyama discretization and sample the drift amplitude from a lognormal distribution, thereby successfully reproducing empirical bimodality and heavy tails, as well as the autocorrelation decay. Our results establish a compact and interpretable model for characterizing the evolving complexity of low-inertia grid frequency dynamics.