Authors:  María Martínez-Barbeito [1], Damià Gomila [1] , Pere Colet [1] , Julian Fritzsch [2,3], Phillippe
Jacquod [2,3]
1 Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes
Balears, Palma de Mallorca, Spain
2 Department of Quantum Matter Physics, University of Geneva, CH-1211 Geneva, Switzerland
3 University of Applied Sciences of Western Switzerland HES-SO, CH-1950 Sion, Switzerland

Abstract:
The urgent need to reduce CO2 emissions requires the gradual phase-out of fosil fuel power plants, increasing
the amount of generation from renewable sources such as sun and wind which are subject to weather variability
and geographical constraints. However areas with high solar irradiation or persistent wind are often located far
from major consumption centers. This spatial mismatch leads to significant long-distance power flows and
increases stress on transmission networks. This is particularly relevant for large networks formed by the
addition of smaller ones, such as the continental Europe synchronous area, which are not specifically designed
for large inter-area flows. Here we discuss a general methodology for identifying critical lines in the
long-distance transmission of power across large electric grids [1]. For large power imbalances such as those
generated by high penetration of variable renewable energy sources, the network gets destabilized and loses
synchrony. As flows increase, we identify two different instability scenarios. In the first one, specific sets
of lines reach their maximal load simultaneously, causing the grid to split into two desynchronized zones. In
the second, more generic, instabilities occur well after one or several phase differences exceed π/2. Thus line
capacity limits are not the immediate cause of the instability, rather it emerges from grid topology
constraints. The mechanism behind is a pair of complex eigenvalues, associated to a Jacobian eigenvector with
nonzero components on nodes with generation, that become real (Belayakov-Devaney transition) and move apart,
triggering a saddle-node bifurcation when one of them becomes zero. To push the system beyond this limit, we
have proposed a mathematical trick converting certain lines to DC. The critical lines identified in this way
match those that triggered the separation of the synchronous grid of continental Europe in two instances in
2021. We further discuss how the modes of the system provide information on which areas are more susceptible to
lose synchrony with each other. In particular we find that, for a very broad range of scenarios, Pyrenees and
Balkans are particularly vulnerable areas.