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

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 worstcase 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.

Rare desynchronization events in power grids: On data implementation and dimensional reductions

“…To consider a more interesting situation in which the overload is not along an edge to a leaf node, we repeat in Figs. 11 and The analysis of [5] finds that appropriate values for 1/α are 2-5 minutes; to consider the higher end of this range, we consider 1/α = 300 s in Fig. 11(b) and find that the same results hold as for 1/α = 100 s in Fig.…”

“…6 this will be manifest in the results for the average time to desynchronization. A further discussion comparing M i and γ i to the timescale of the noise is given in [5], where it is argued that typical timescales of fluctuations are so long (1/α = 100 − 300s) that the impact of M and γ on the propagation of non-Gaussian disturbances can typically be neglected. The results of [5] are for typical fluctuations; our results are derived for rare large fluctuations, thus complementing their results.…”

“…The first 8 cumulants of these distributions are shown in Table 1. The authors of [5] explicitly analyze the time correlations p(t)p(t ) p(t) 2 for the wind and solar data of [17] and find that correlations typically decay on a timescale of 2 − 5 minutes. Accordingly, we here set 1/α = 100 s, and also consider 1/α = 300 s in Sec.…”

“…When strong fluctuations in the production propagate through the grid, non-Gaussian tails in the distribution of local grid-frequency data have been observed, which themselves may induce large-scale blackouts in the worst case. Here the authors of [5] focused on the role of time correlations in the fluctuations. According to their results, noise disturbances with finite skewness and positive kurtosis propagate through the entire grid when the noise correlation time is larger than the network's intrinsic time scales.…”

Layered complex networks as fluctuation amplifiers

“…Extension of this work should consider the latter fact into more details, as well as different interlayer coupling functions. Also, investigating moments higher than the second [27] or including inertia for the dynamical agents to potentially uncover resonances in case of time-dependent inter-layer coupling [28] represent two research avenues of interest.…”