A Lyapunov Approach Based Higher Order Sliding Mode Controller for Grid Connected Shunt Active Compensators with a LCL Filter

A Lyapunov approach based homogeneous higher order SM-Controller (HOSMC) is considered here, for grid connected three phases three wires shunt active filter (SAF) via LCL filter. This nonlinear controller is an alternative solution to overcome phase shift caused by a linear controller and a chattering effect caused by a 1st order sliding mode controller that is supposed to be of relative degree 1. The last fact requires a special sliding variable design that yields asymptotic convergence of the tracking error to zero versus a finite time convergence provided by HOSMC. On the other hand, it is well known that VSI based SAFs compensate for the main types of current perturbations in the electrical power systems, while generate some undesired components caused by switching frequency. In order to avoid the spreading of these components to the grid side, a VSI connected to the grid via a LCL output filter is largely proposed, but for renewable energy systems, where the component to be injected into the grid is only the fundamental. Unfortunately, when the currents to be generated by SAF include both fundamental and harmonics, and for a LCL output filter associated to linear controllers, a phase shift appears, between the identified harmonics current and the injected current, and impacts negatively, harmonic current filtration of the SAF.In this article, a PWM-HOSMC is proposed to operate in a fixed frequency without chattering, preventing a variable switching frequency effects. In addition, this article proposes a solution for the non-robustness drawback, from disturbances point of view, of the used control method. The rapidity, tracking and effectiveness of this proposed controller, within the SAF, are validated by simulations carried out by Matlab, Simulink, Simscape-SimPower System code.