Set-based Predictive Control of a Grid-tied Inverter with LCL filter Under Variable Grid Inductance Conditions

This paper presents a set-based model predictive control algorithm for controlling a grid-connected converter with an LCL filter. Taking into account uncertainties in the grid impedance the system is modeled using a polytopic linear parameter varying system framework. A robust stabilizing state feedback gain is computed together with a robust positively invariant terminal set. Starting from the terminal set, a family of inner ellipsoidal approximations of control invariant sets is computed off-line. Online an optimization problem is solved subject to a set-membership constraint on the first state. In that way, the model predictive controller is used to steer the states of the system to the terminal set in a finite time.