In this paper, a unified framework to study small- and large-signal frequency response based on the notion of center-of-gravity (COG)-based dynamic equivalents is presented. The method combines the ability of COG equivalents to capture short-term system response with that of unsupervised probabilistic learning techniques to extract the (slow) dominant oscillation patterns associated with observational data. First, a reduced-order representation is obtained in which the overall system dynamics is represented by the interaction of geographical or coherent areas with a virtual COG at which the total system power equations are at balance. Then, a small-signal representation is derived from which key linear relationships between the frequency of the local centers of inertia (COIs) and the COG are determined. Next, the physical properties of the model are studied, and alternative procedures to compute COG equivalents are explored. Finally, the effectiveness of the developed models is demonstrated through applications to two sample systems, thereby verifying their accuracy.
