  Cascade failures in power grids occur when the failure of one component or
subsystem causes a chain reaction of failures in other components or
subsystems, ultimately leading to a widespread blackout or outage. Controlling
cascade failures on power grids is important for many reasons like economic
impact, national security, public safety and even rippled effects like
troubling transportation systems. Monitoring the networks on node level has
been suggested by many, either controlling all nodes of a network or by
subsets. This study identifies sensitive graph elements of the weighted
European power-grids (from 2016, 2022) by two different methods. Bridges are
determined between communities and "weak" nodes are selected by the lowest
local synchronization of the swing equation. In the latter case we add bypasses
of the same number as the bridges at weak nodes, and we compare the
synchronization, cascade failure behavior by the dynamical improvement with the
purely topological changes. The results are also compared if bridges are
removed from networks, which results in a case similar to islanding, and with
the addition of links at randomly selected places. Bypassing was found to
improve synchronization the best, while the average cascade sizes are the
lowest with bridge additions. However, for very large or small global couplings
these network changes do not help, they seem to be useful near the
synchronization transition region, where self-organization drives the
power-grid. Thus, we provide a demonstration for the Braess' Paradox on
continent-sized power grid simulations and uncover the limitations of this
phenomenon. We also determine the cascade size distributions and justify the
power-law tails near the transition point on these grids.

Physics and Society;Disordered Systems and Neural Networks;Statistical Mechanics;Adaptation and Self-Organizing Systems