  With more inverter-based resources (IBRs), our power systems have lower
frequency nadirs following N-1 contingencies, and undesired under-frequency
load shedding (UFLS) can occur. To address this challenge, IBRs can be
programmed to provide at least three types of fast frequency response (FFR),
e.g., step response, proportional response (P/f droop response), and derivative
response (synthetic inertia). However, these heterogeneous FFR challenge the
study of power system frequency dynamics. Thus, this paper develops an
analytical frequency nadir prediction method that allows for the consideration
of all three potential forms of FFR provided by IBRs. The proposed method
provides fast and accurate frequency nadir estimation after N-1 generation
tripping contingencies. Our method is grounded on the closed-form solution for
the frequency nadir, which is solved from the second-order system frequency
response model considering the governor dynamics and three types of FFR. The
simulation results in the IEEE 39-bus system with different types of FFR
demonstrate that the proposed method provides an accurate and fast prediction
of the frequency nadir under various disturbances.
