3. Slow Coherency and Aggregation

This chapter presents the theory and analysis of slow coherency and aggregation. The main idea is that slow coherency arises from interarea modes, that is, groups of machines swinging together against each other at oscillatory frequencies slower than the local modes of the machines in the same coherent group swinging against each other. We show analytically that this phenomenon can be attributed to the coherent areas being weakly coupled, either because of higher impedance transmission lines, heavily loaded transmission lines, or fewer connections between the coherent areas compared to the connections within a coherent area. These system properties allow the use of singular perturbations to display the time-scale separation of the interarea modes and local modes, resulting in eigenvector-based algorithms to identify coherent machines. In addition, the singular perturbations technique has the capability to provide correction terms for improving reduced-order models in capturing the slow coherent dynamics.