Graph-Theoretic Analysis of Power Systems

We present an overview of the applications of graph theory in power system modeling, dynamics, coherency, and control. We first study synchronization of generator dynamics using both nonlinear and small-signal representations of classical structure-preserving models of power systems in light of their network structure and the weights associated with the nodes and edges of the network graph. We overview important necessary and sufficient conditions for both phase and frequency synchronization. We highlight the role of graph structure in coherency properties, and introduce the idea of generator and bus aggregation whereby dynamic equivalent models of large power grids can be developed while retaining the concept of a ‘bus’ in the network graph of the equivalent model. We also discuss several new results on graph sparsification for designing distributed controllers for power flow oscillation damping.