A Bi-Sliding Mode PI Control of DC-Link Voltage of Three-Phase Three-Wire Shunt Active Power Filter

A novel bi-sliding mode PI control (bi-SMPIC) of the dc-link voltage of a three-phase three-wire shunt active power filter (APF) is proposed in this article. One SMPIC having an improved reaching law function in the reaching phase can make the speed of the state variables reaching the sliding surface approach zero. The other SMPIC possessing an improved reaching law function with a boundary layer in the sliding phase can render the state variables asymptotically stable at the origin of the sliding surface. Thus, the proposed bi-SMPIC can effectively reduce system chattering. Moreover, it is proven that the system has reachability and asymptotic stability. Further, a formula for determining the PI control parameters is obtained. From the formula, the proposed bi-SMPIC can have ideal control effects in both the reaching phase and the sliding phase. Finally, the high control performance of the bi-SMPIC is confirmed by both experimental and simulation results.