Power-law distributions of dynamic cascade failures in power-grid models

Abstract

Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here we attempt to describe it using an AC threshold model, with a second-order Kuramoto type equation of motion of the power-flow. We have focused on the exploration of network heterogeneity effects, starting from homogeneous 2D lattices to the US power-grid, possessing identical nodes and links, to a realistic electric power-grid obtained from the Hungarian electrical database. The last one exhibits node dependent parameters, topologically marginally on the verge of robust networks. We show that too weak quenched heterogeneity, coming solely from the probabilistic self-frequencies of nodes (2D lattice) is not sufficient to find power-law distributed cascades. On the other hand too strong heterogeneity destroys the synchronization of the system. We found agreement with the empirically observed power-law failure size distributions on the US grid, as well as on the Hungarian networks near the synchronization transition point. We have also investigated the consequence of replacing the usual Gaussian self-frequencies to exponential distributed ones, describing renewable energy sources. We found a drop in the steady state synchronization averages, but the cascade size distribution both for the US and Hungarian systems remained insensitive and have kept the universal tails, characterized by the exponent $\tau \simeq 1.8$. We have also investigated the effect of an instantaneous feedback mechanism in case of the Hungarian power-grid.

arXiv commentExtended version with minor changes, accepted in Entropy 22 pages, 13 figures

References in corpus (20)

• Synchronization in complex networks
• Analysis of a power grid using the Kuramoto-like model
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Average path length in random networks
• Average path length in uncorrelated random networks with hidden variables
• Dynamically induced cascading failures in power grids
• Short term fluctuations of wind and solar power systems
• Hysteretic transitions in the Kuramoto model with inertia
• The Impact of the Topology on Cascading Failures in Electric Power Grids
• Frustrated hierarchical synchronization and emergent complexity in the human connectome network
• Self-Organized Synchronization and Voltage Stability in Networks of Synchronous Machines
• Entrainment transition in populations of random frequency oscillators
• Enhancing power grid synchronization and stability through time delayed feedback control
• Topological Performance Measures as Surrogates for Physical Flow Models for Risk and Vulnerability Analysis for Electric Power Systems
• Critical synchronization dynamics of the Kuramoto model on connectome and small world graphs
• Heterogeneity effects in power-grid network models
• Synchrony-optimized networks of Kuramoto oscillators with inertia
• Slow, bursty dynamics as the consequence of quenched network topologies
• The effect of noise on the synchronization dynamics of the Kuramoto model on a large human connectome graph
• Load Dependence of Power Outage Statistics

Cited by in corpus (9)

• Synchronization dynamics on the EU and US power grids
• Chimera states in neural networks and power systems
• Synchronization transition of the second-order Kuramoto model on lattices
• Improving power-grid systems via topological changes, or how self-organized criticality can help stability
• Dynamical heterogeneity and universality of power-grids
• Revisiting and modeling power-law distributions in empirical outage data of power systems
• Studying power-grid synchronization with incremental refinement of model heterogeneity
• Sandpile cascades on oscillator networks: the BTW model meets Kuramoto
• The effect of HVDC lines in power-grids via Kuramoto modelling