Improving power-grid systems via topological changes, or how self-organized criticality can help stability

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. We identify sensitive graph elements of the weighted European power-grids (from 2016, 2022) by two different methods. We determine bridges between communities and point out "weak" nodes 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. We also compare the results on bridge removed networks, similar to islanding, and with the addition of links at randomly selected places. The synchronization improves the best by the bypassing, 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 continental 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.