Cyber Network Design for Secondary Frequency Regulation: A Spectral Approach

We present a preliminary theoretical framework based on spectral graph theory that captures how the cyber topology of a distributed secondary frequency control scheme impacts the stability, optimality, and transient performance of our power system as a cyber-physical network. We show that a collection of polynomials defined in terms of the cyber and physical Laplacian eigenvalues encode information on the interplay between cyber and physical networks. It is demonstrated that to understand the impact of adding cyber connectivity, one should separate the low-damping and high-damping regimes. Although adding cyber connectivity always improves the performance for high-damping systems, it is not the case for low-damping scenarios. Based on the theoretical study, we discuss how a good cyber network should be designed. Our empirical study shows that for practical systems, the number of communication channels that is needed to achieve near-optimal performance is usually less than twice the number of buses.