Braess Paradox and Self-Organization in Modern Power Grids

Distributed, renewable energy sources will dominate the dynamics of future electric power grids. Upgrading grids for decentralized sources poses an enormous challenge for its design and stable operation and constitutes a multi-billion Euro business. Bridging the gap between abstract statistical physics and detailed engineering device modeling, we are aiming to understand nonlinear power grid dynamics at an intermediate level using simple but dynamic coarse-scale oscillator models. Substantial results so far include: 1) The addition of new transmission lines may destabilize power grid operation (via Braess' paradox that we identified in oscillator networks). We reveal geometric frustration as the mechanism underlying Braess' paradox in oscillator networks. 2) More and smaller, but distributed power sources may stabilize grid operation due topological decentralization. Our results indicate that coarse-scale modeling of power grids by oscillator networks seems feasible for the study of their self-organized synchronization dynamics.