Synchronization dynamics on the EU and US power grids

TL;DR

This study models the synchronization dynamics and cascade failures in EU and US power grids using the Kuramoto equation, revealing hysteresis, power-law failure distributions, and effects of feedback mechanisms.

Contribution

It provides analytical and numerical insights into synchronization transitions, cascade failure statistics, and the impact of control strategies on power grid stability.

Findings

Synchronization transition exhibits hysteresis and metastable states.

Cascade failure PDFs follow power-law tails near critical coupling.

Feedback and dissipation influence local synchronization and stability.

Abstract

Dynamical simulation of the cascade failures on the EU and USA high-voltage power grids has been done via solving the second-order Kuramoto equation. We show that synchronization transition happens by increasing the global coupling parameter $K$ with metasatble states depending on the initial conditions so that hysteresis loops occur. We provide analytic results for the time dependence of frequency spread in the large $K$ approximation and by comparing it with numerics of $d=2,3$ lattices, we find agreement in the case of ordered initial conditions. However, different power-law (PL) tails occur, when the fluctuations are strong. After thermalizing the systems we allow a single line cut failure and follow the subsequent overloads with respect to threshold values $T$. The PDFs $p(N_f)$ of the cascade failures exhibit PL tails near the synchronization transition point $K_c$. Near $K_c$ the exponents of the PL-s for the US power grid vary with $T$ as $1.4 \le \tau \le 2.1$, in agreement with the empirical blackout statistics, while on the EU power grid we find somewhat steeper PL-s characterized by $1.4 \le \tau \le 2.4$. Below $K_c$ we find signatures of $T$-dependent PL-s, caused by frustrated synchronization, reminiscent of Griffiths effects. Here we also observe stability growth following the blackout cascades, similar to intentional islanding, but for $K > K_c$ this does not happen. For $T < T_c$, bumps appear in the PDFs with large mean values, known as "dragon king" blackout events. We also analyze the delaying/stabilizing effects of instantaneous feedback or increased dissipation and show how local synchronization behaves on geographic maps.