  The rate of change of frequency (RoCoF) is a critical factor in ensuring
frequency security, particularly in power systems with low inertia. Currently,
most RoCoF security constrained optimal inertia dispatch methods and inertia
market mechanisms predominantly rely on the center of inertia (COI) model. This
model, however, does not account for the disparities in post-contingency
frequency dynamics across different regions of a power system. Specifically,
regional buses can exhibit significantly larger RoCoFs than that predicted by
the system's COI, particularly in systems characterized by unevenly distributed
inertia. In this letter, a post-contingency nodal RoCoF model is established,
and the maximal initial RoCoF is further proven to occur at generator buses
equipped with inertia, rather than at inertia-less load buses. This finding
facilitates the development of the optimal nodal inertia dispatch method and
the nodal inertia market mechanism in a convex and concise form. Our argument
is further verified by the simulation results of the South East Australia power
system under various scenarios.
