Power synchronization control of grid-connected voltage source converters (VSC) in high-voltage direct-current (HVDC) transmission is applied as a credible method. However, the non-minimum-phase phenomena in the dynamic models of this system developed through the space-vector approach imposes a significant limitation on the stability margin of the VSC-HVDC converters. This restriction is more pronounced in valtage fault conditions and frequency oscillations. In this paper, a new PID design based on power-synchronization law along with a new approach to power-frequency swing equation has been designed. This new control method has the features of a virtual synchronous machine and is equipped with a highpass filter that robustifies the control operation during severe voltage and frequency instabilities in weak-grid conditions. A thorough analytical explanation of the proposed method along with performance evaluations in Hardware-in-the-loop environment demonstrate the efficacy of the operation and its simple implementation.