Identifying the Largest RoCoF and Its Implications

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 predominantly rely on aggregated frequency models which are tractable in optimization problems. These models, however, do 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 an aggregated frequency model, particularly in systems characterized by unevenly distributed inertia. To bridge this gap, in this paper, the post-contingency nodal RoCoF model is first derived on the basis of augmented direct current power flow equations and the intrinsic nature that (virtual) synchronous generators will keep their rotor angles constant immediately after a disturbance. Then, the maximal initial RoCoF is mathematically proven to be at one of buses with inertia. This finding together with the nodal RoCoF model contribute to the establishment of the optimal nodal inertia dispatch method in a convex and concise form. The effectiveness of our finding and the proposed nodal inertia dispatch method are further verified by simulation results of two typical interconnected power systems under different scenarios.