As conventional synchronous generators are replaced by large-scale converter-interfaced renewable-energy sources (RESs), the electric power grid encounters the challenge of low rotational inertia. Consequently, system frequency deviation is exacerbated and system instability may occur when the frequency deviates beyond the acceptable range. To mitigate this effect, this study proposes a virtual inertia control (VIC) strategy based on a fractional-order derivative and controller parameter-tuning method. The tuning method uses the stability boundary locus and provides a stability criterion for identifying the stability region in the parameter space. The controller parameters are then optimized within the identified stability region to suppress frequency deviation and enhance system robustness. The proposed controller and tuning method is applied to a battery energy-storage system (BESS) in a low-inertia power system with the integration of RESs. Time-domain simulations are carried out to verify the stability region and compare the performance of the optimized proposed controller to that of the traditional integral-order controller. The simulation results show that the stability-analysis method is effective and that the fractional-order VIC, tuned with the proposed method, outperforms the traditional method in both frequency-regulation performance and parametric robustness.