The characteristics of shunt connected voltage source converter to mitigate voltage sags are theoretically analyzed by means of the superposition principle and equivalent circuit model. The state space models of shunt compensator with LC output filter are established in dq synchronous reference frame. Then the double vector control algorithm with inner loop current controller and outer loop voltage controller is proposed. A realistic simulation model using PSCAD/EMTDC to test the digital dual vector controller is built. Problems of closed-loop control method based on positive SRF are analyzed. A novel closed-loop control method based on double synchronous reference frames is proposed， which uses two groups of double vector controllers， one group in the positive SRF to control the positive-sequence components， and the other one in the negative SRF to control the negative components. The proposed control method can completely compensate both balanced and unbalanced voltage sags without static error.