Finite-time Correlations Boost Large Voltage-Angle Fluctuations in Electric Power Grids

TL;DR

This paper studies how finite-time correlated noise from renewable energy sources influences large voltage-angle fluctuations in power grids, revealing that non-Gaussian disturbances persist over large scales when noise correlation times are long.

Contribution

It demonstrates that non-Gaussian fluctuations in power input propagate globally in power grids when their correlation time exceeds system time scales, providing new insights into grid stability under renewable integration.

Findings

Non-Gaussian noise propagates over the entire network with long correlation times.

Rapidly fluctuating noise loses non-Gaussian characteristics over short distances.

Increasing uncorrelated noise sources reduces non-Gaussian effects due to the Berry-Esseen theorem.

Abstract

Decarbonization in the energy sector has been accompanied by an increased penetration of new renewable energy sources in electric power systems. Such sources differ from traditional productions in that, first, they induce larger, undispatchable fluctuations in power generation and second, they lack inertia. Therefore, substituting new renewables for traditional generation induces stronger and more frequent disturbances and modifies the way disturbances propagate across AC electric power grids. Recent measurements have indeed reported long, non-Gaussian tails in the distribution of local grid-frequency data. Large frequency deviations may induce grid instabilities, leading in worst-case scenarios to cascading failures and large-scale blackouts. In this manuscript, we investigate how correlated noise disturbances, characterized by the cumulants of their distribution, propagate through meshed, high-voltage power grids. We show that for a single source of fluctuations, non-Gaussianities in the form of finite skewness and positive kurtosis of the noise distribution propagate over the entire network when the noise correlation time is larger than the network's intrinsic time scales, but that they vanish over short distances if the noise fluctuates rapidly. We furthermore show that a Berry-Esseen theorem leads to the vanishing of non-Gaussianities as the number of uncorrelated noise sources increases. Our results show that the persistence of non-Gaussian fluctuations of feed-in power have a global impact on power-grid dynamics when they fluctuate over time scales larger than the intrinsic time scales of the system, which, we argue, is the relevant regime in real power grids. Our predictions are corroborated by numerical simulations on realistic models of power grids.