The three-phase four-wire shunt active power filter(SAPF)with mid-point capacitor can be used to compensate for all harmonics

zero sequence and reactive current of the nonlinear load no matter whether the power system is balanced or unbalanced because of the additional path for zero sequence current compared to three-phase three-wire SAPF. Control of SAPF via the nonlinear passive controller by using its passivity can yield a better compensating effect than the conventional linear and nonlinear controller. And there is no need of detection and treatment of the positive and negative sequence components of all harmonics when the power system is unbalanced. A hybrid passivity-based control(PBC)strategy of mid-point capacitor three-phase four-wire SAPF is proposed. Firstly

according to the Euler-Lagrange mathematical model of the controlled object in the dq0 coordinate system

the passivity of the SAPF is analyzed

and the passive control law of the inner-loop current of SAPF able to make the controlled quantity converge to the expected value is obtained. Secondly

the damping injection method is used to simplify the design of the system

and the new passive control law capable of completely decoupling the compensation current of the inner-loop is obtained as an improvement on the dynamic performance of the system. Thirdly

the outer-loop voltage controller of SAPF based on the 2-order low-pass filter is designed according to the close relation between the total and differential voltage at the DC side and compensating current. Finally

the feasibility and superiority of applying hybrid PBC to SAPF is verified by Simulink software simulation and experiment. Compared with the traditional PI control

the control method proposed in this paper has a faster response speed and better compensation effect.