Abstract: With the continuous extension of the power supply radius of distribution networks and the large-scale integration of distributed generators at the terminals, the problem of terminal voltage deviation in radial branch lines has become increasingly prominent. Traditional reactive power-dominated voltage regulation methods struggle to balance voltage quality and operational economy. To address this issue, this paper proposes a voltage compensation scheme targeting minimum current injection. By establishing a terminal voltage drop model and combining phasor geometric analysis, the optimal amplitude and phase relationship of the compensation current is derived. On this basis, the distribution static synchronous compensator connected at the terminal is selected, and a minimum current optimization control strategy is constructed. Simulation results based on the IEEE 33-bus distribution network show that this method can effectively reduce the demand for compensation current while ensuring qualified voltage, thus improving the efficiency and economy of terminal voltage regulation in distribution networks.