Optimal Configuration of Virtual Inertia and Fast Frequency Response in Low-Inertia Power Systems

To address the declining system inertia levels and the associated frequency security challenges arising from the increasing penetration of renewable generation, this study proposes a coordinated configuration of virtual inertia (VI) and fast frequency response (FFR) resources in low-inertia power systems. An improved system frequency response (SFR) model is established by incorporating synchronous inertia response (SIR), primary frequency response (PFR) and FFR. Through the improved model, analytical expressions for the rate of change in frequency (RoCoF) and the frequency nadir are derived as functions of each decision variable. These expressions reveal a decoupled mechanism in which each frequency security constraint drives the configuration of a specific resource type. A coordinated optimization model is then formulated to minimize total ancillary service cost subject to these frequency security constraints. Systematic case studies under multiple scenarios validate the proposed model and reveal that VI and FFR requirements increase monotonically with rising renewable penetration, with Hv=2.89 s and α=0.19 at 70% penetration. FFR is further shown to offer significantly greater cost effectiveness for nadir improvement than VI. These results provide quantitative guidance for the optimal configuration of both resource types under varying system conditions.