To prepare for the future high penetration level of renewable energy sources, the power grid’s technical boundaries/constraints for the correct operation of powerelectronics interfaced devices need to be further examined and defined. This paper investigates the challenge of integrating Voltage Source Converters (VSC) into low inertia power grids, where the system frequency can vary rapidly due to the low kinetic energy buffer available, which used to be provided by the rotational inertia of synchronous generators. The impact of rate of change of frequency (ROCOF) on the PLL dynamics and its subsequent influence on the VSC power stage output is explained. The Bonaire island network is presented as case study. The performance of the VSC is analyzed under a fast ROCOF event, which is triggered by a short circuit fault. A down-scaled experiment is used to validate the Bonaire island network simulation results. It shows that the phase angle error measured by the synchronous-reference frame phase-locked loop (SRF-PLL) is proportional to the slope of the ROCOF and inversely proportional to its controller integral gain constant.