Wind turbine generators (WTG) can participate in system frequency regulation via virtual inertial controllers (VIC). In the presence of frequency disturbances, VIC temporarily regulates the WTG power output forcing it to release/absorb kinetic energy into/from the grid. With increasing penetration of WTGs in power systems, grid operators require these generators to provide frequency regulation services; however, kinetic energy release/absorption can destabilize WTGs. Hence, to address these issues, a new large-perturbation nonlinear WTG model is proposed in this paper, based on the WTG internal response that is used to tune typical VICs. Novel worst case and optimal VIC tuning approaches are also proposed and discussed based on the developed WTG nonlinear model. Several simulations are presented to test and validate the proposed model and VIC tuning techniques, demonstrating their adequate performance and advantages.