Multistability and variations in basin of attraction in power-grid systems

Abstract

Power grids sustain modern society by supplying electricity and thus their stability is a crucial factor for our civilization. The dynamic stability of a power grid is usually quantified by the probability of its nodes' recovery to phase synchronization of the alternating current it carries, in response to external perturbation. Intuitively, the stability of nodes in power grids is supposed to become more robust as the coupling strength between the nodes increases. However, we find a counterintuitive range of coupling strength values where the synchronization stability suddenly droops as the coupling strength increases, on a number of simple graph structures. Since power grids are designed to fulfill both local and long-range power demands, such simple graph structures or graphlets for local power transmission are indeed relevant in reality. We show that the observed nonmonotonic behavior is a consequence of transitions in multistability, which are related to changes in stability of the unsynchronized states. Therefore, our findings suggest that a comprehensive understanding of changes in multistability are necessary to prevent the unexpected catastrophic instability in the building blocks of power grids.

On structural and dynamical factors determining the integrated basin instability of power-grid nodes

“…III A). For the past couple of years, we have actively participated in the process of incorporating the effects of transmission capacity into the framework of basin stability to aim at a comprehensive understanding of the characteristics of basin stability [8][9][10] . Throughout the series of work, we have discovered the relationship between the basin stability and the node's inconsistency in the community membership 8,55 , the non-monotonic behavior of the basin stability as a function of transmission capacity in small building blocks of power grids 9 , and its possible connection to chaotic dynamics 10 .…”

“…In this study, in order to numerically measure the basin stability of node i, we perturb each node by taking the phase and angular frequency values from the configuration space θ i ∈ [−π, π) and ω i ∈ [−100, 100], uniformly at random as our previous studies (500 combinations of θ i and ω i for each K value) [8][9][10] . For simplicity, we fix the dissipation coefficient α i = α = 0.1 for all of the nodes 1-3 .…”

“…Such small clusters can be operated autonomously even when other parts of the power grid are damaged, which in fact supports the resilience of the entire power grid in return. Therefore, small power-grid motifs can be taken as the minimal functional unit of power grids 9,10 . In this spirit, we use two types of simple model Perturbations only to n1 Basin stability transition window of node i Power grid…”

A multiplex, multi-timescale model approach for economic and frequency control in power grids

“…In order to study the performance of various approaches, we make use of probabilistic methods [16][17][18][19][20][21][22][23][24] , that is, we define a scenario ensemble and evaluate the expected performance of the system with respect to the ensemble average by sampling over the ensemble. This approach allows us to study the properties of the system for the whole ensemble, rather than in individual case studies.…”

Heterogeneities in electricity grids strongly enhance non-Gaussian features of frequency fluctuations under stochastic power input

“…[1][2][3][4][5] Another option is to use test grids like those provided by the Institute of Electrical and Electronics Engineers (IEEE). 6,7 It is also possible to analyze speci c motifs in a grid, 8,9 or one can try to use real grid structures, which unfortunately are, in general, not provided by the network operating companies. However, there are a number of initiatives, such as open_eGo, 10 SciGrid, 11 and others, which try to obtain real grid structures, based mainly on information taken from Open Street Map.…”