Spectral characterization of controllability and observability for frequency regulation dynamics

We give a full characterization using spectral graph theory of the controllability and observability of the swing and power flow dynamics in frequency regulation. In particular, we show that the controllability/observability of the system depends on two orthogonal conditions: 1) intrinsic structure of the system graph 2) algebraic coverage of buses with controllable loads/sensors. Condition 1) encodes information on graph symmetry and is shown to hold for almost all practical systems. Condition 2) captures how buses interact with each other through the network and can be verified using the eigenvectors of the graph Laplacian matrix. Based on this framework, the optimal placement of controllable loads and sensors in the network can be formulated as a set cover problem. We demonstrate how our results identify the critical buses in real systems by performing simulation in the IEEE 39-bus New England interconnection test system. We show that for this testbed, a single well chosen bus is capable of providing full controllability/observability.