A non-linear optimal predictive control of a shunt active power filter

In this paper a nonlinear multiple-input multiple-output (MIMO) predictive control using optimal control approach is applied to control the currents of a three-phase three-wire voltage source inverter used as a shunt active power filter (AF). The nonlinear active filter state-space representation model is elaborated in the synchronous d-q frame rotating at the mains fundamental frequency. This state-space model is seen as two separate subsystems, namely an inner multiple-input multiple-output model with fast dynamics and an outer single-input single-output model with slow dynamics. The proposed nonlinear MIMO predictive control law is applied to the inner loop forcing the currents to track their references that are extracted from the sensed nonlinear load currents by applying the synchronous reference frame method. The outer DC voltage loop uses a proportional-integral compensator and the compensated error is added to the inner loop d-axis current reference. In addition to good tracking behavior, the predictive control guarantees stability and improves robustness. Simulation results demonstrate the expected performance of the shunt active filter.