Analytical Decomposition of Nodal Frequency Responses

The frequency responses at different buses following a disturbance differ from that of the center-of-inertia (COI). Buses exhibiting much lower frequency nadirs than the COI nadir may pose stability concerns. In this letter, we demonstrate that nodal frequency responses are composed of global and local components. We propose a natural analytical decomposition method to separate these two components. The decomposition provides an insight into the overlap of angle and frequency dynamics. Based on this decomposition, we also derive an indicator that identifies buses susceptible to frequency stability issues. We believe that our findings are fundamental for deepening the understanding of nodal frequency dynamics, with potential applications in related studies. Our work is supported by both numerical simulations and rigorous theoretical analysis.