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Network Robustness

The ongoing Energy Transition in many regions of the world creates changes in the patterns of consumption and production, and of power flows on the electrical network. Understanding the stability characteristics of the electrical distribution and transport networks is then of major importance nowadays to ensure a secure supply of electricity.

We also measure robustness of a synchronous operating point against perturbations numerically and analytically [Del17b,Tyl18]. Each synchronous state has a basin of attraction and we establish a method to estimate the size of these basins. To evaluate robustness, we use performance measures which quantify the excursion from the synchronous state due to external perturbations. By averaging the perturbations over the network we obtain new topological indices that can be used to compare the robustness of different networks [Tyl18]. These indices are generalization of the Kirchhoff index and are linked to the distribution of the resistance distances of the network.