A New Optimal Current Controller for a Three-Phase Shunt Active Power Filter Based on Karush–Kuhn–Tucker Conditions

This paper presents an algorithm for finding the optimal control for a current controller that operates as a part of a control system of a shunt active power filter. The algorithm is based upon the Karush–Kuhn–Tucker conditions for finding an optimal value where control signal is limited and constraints create a cube. The explicit solution of the Karush–Kuhn–Tucker problem is presented and simplified calculations are given to lower calculation complexity. The presented Karush–Kuhn–Tucker algorithm is compared with a classical PI controller. It is given the algorithm for finding the optimal parameters of the PI controller and the behavior of the PI controller is compared with the presented algorithm. Attention has been paid to the saturation of controllers in commutation states of load currents, which has a negative impact on the final performance of the controllers and the controlled shunt active power filter. The paper also presents the software and hardware platforms applied to run the presented algorithms in real-time. For both controllers, the shunt active power filter response is shown using real experimental results. The results of the experiments prove better behavior regarding the presented algorithm, especially in the case of commutative load currents, where the output signals from other controllers become saturated.