According to the characteristic that DC voltage dynamics is much slower than the current dynamics, we firstly view the DCvoltage as a constant, and then simplify the model of Active Power Filter (APF) only including two simple control loops so that thecurrent control loop can be decoupled into two independent current equations. To deal with the robustness of the current control loop,asymptotic rate is employed to design slide mode function, a simplified slide mode model of three-phase active power filters is derived,and its stability is proved. Because fluctuation in the DC voltage results mainly from energy exchange between the AC and DC sides ofAPF, a formula is deduced to control the DC voltage in order to keep its stability, the objective of which is to compensate the modelerror resulted from the simplified model of APF. Simulation results show that the proposed method can not only guarantee the systemstability, but also the robustness when sudden changes of the load happen.