Cascading Failures in AC Electricity Grids

TL;DR

This paper simulates cascading failures in AC power grids, revealing how failure probabilities follow power laws and depend on grid topology, placement of generators and consumers, and failure thresholds, with implications for grid robustness.

Contribution

It introduces a dynamic AC model for simulating cascading failures and analyzes the impact of topology and component placement on failure propagation.

Findings

Failure probabilities follow power-law decay with system size.

Large generator and consumer clusters are more vulnerable.

Failure probability decay varies from power law to exponential depending on thresholds.

Abstract

Sudden failure of a single transmission element in a power grid can induce a domino effect of cascading failures, which can lead to the isolation of a large number of consumers or even to the failure of the entire grid. Here we present results of the simulation of cascading failures in power grids, using an alternating current (AC) model. We first apply this model to a regular square grid topology. For a random placement of consumers and generators on the grid, the probability to find more than a certain number of unsupplied consumers decays as a power law and obeys a scaling law with respect to system size. Varying the transmitted power threshold above which a transmission line fails does not seem to change the power law exponent $q \approx 1.6$. Furthermore, we study the influence of the placement of generators and consumers on the number of affected consumers and demonstrate that large clusters of generators and consumers are especially vulnerable to cascading failures. As a real-world topology we consider the German high-voltage transmission grid. Applying the dynamic AC model and considering a random placement of consumers, we find that the probability to disconnect more than a certain number of consumers depends strongly on the threshold. For large thresholds the decay is clearly exponential, while for small ones the decay is slow, indicating a power law decay.