This paper demonstrates how the range of stable power transfer in weak grids with voltage source converters (VSCs) can be extended by modifying the grid synchronisation mechanism of a conventional synchronous reference frame phase locked loop (PLL). By introducing an impedance-conditioning term in the PLL, the VSC control system can be virtually synchronised to a stronger point in the grid to counteract the instability effects caused by high grid impedance. To verify the effectiveness of the proposed approach, the maximum static power transfer capability and the small-signal stability range of a system with a VSC HVDC terminal connected to a weak grid are calculated from an analytical model with different levels of impedance-conditioning in the PLL. Such calculations are presented for two different configurations of the VSC control system, showing how both the static power transfer capability and the small-signal stability range can be significantly improved. The validity of the stability assessment is verified by time-domain simulations in the Matlab/Simulink environment.