Non-local cascade failures and synchronization dynamics on power grids

Dynamical simulation of the cascade failures on the EU, USA and Hungarian [1] 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 metastable 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 [2], 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(Nf ) of the cascade failures
exhibit PL tails near the synchronization transition point Kc. Below Kc we find signatures of T -
dependent PL-s, caused by frustrated synchronization, reminiscent of Griffiths effects [3]. Here
we also observe stability growth following blackout cascades, similar to intentional islanding,
but for K > Kc this does not happen. For T < Tc , 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. We demonstrate the occurrence of non-local cascade failure events at the
weak points of the networks.

[1] G. Ódor and B. Hartmann, Entropy 22 (2020) 666.
[2] G. Ódor and S. Deng, Entropy 25 (2023) 164.
[3] G. Ódor, S. Deng, B. Hartmann and J. Kelling, Phys. Rev. E 106 (2022) 034311.