This article discusses the mathematical relationship between the grid-voltage-modulated-direct-power-control (GVM-DPC) and the vector-current-control (VCC) for three-phase voltage-source-converters (VSCs). It reveals that the GVM-DPC is equivalent to the VCC at the steady-state, yet presents a superior transient performance by removing the need of phase-locked loop (PLL). That means the GVM-DPC solves the disadvantage of conventional DPC such as poor steady-state performance. Moreover, the GVM-DPC will reduce the computational burden in comparison with the VCC due to the absence of Park transformation and PLL. Consequently, we can expect that the GVM-DPC method has a good capability of plug-and-play for the VSC. Finally, the experiment results match the theoretical expectations closely.