Structural Analysis of Laplacian Spectral Properties in Complex Electric Grids

Motivated by recent interest for power grid architectures, we study the relationship between structural features of electrical transmission networks and the behavior of certain dynamical processes taking place in the network. The spectrum of the Laplacian matrix plays a key role in a wide range of networked dynamical problems, from transient stability analysis to distributed control. Using methods from algebraic graph theory and convex optimization, we study the relationship between structural features of the network and spectral properties of the Laplacian matrix. We illustrate our results by studying the influence of structural properties on the Laplacian eigenvalues of the American (western states), Spanish and French high-voltage transmission networks.