Systematic Design of a DLQR Applied to Grid-Forming Converters

This article proposes a systematic state-space procedure to design an optimal discrete-time linear quadratic regulator applied to grid-forming converters. A comprehensive mathematical modeling of a voltage-sourced converter with an LC output filter is performed and a systematic way of including digital resonant compensators is addressed. The choice of weights is based on the minimization of selected transfer functions infinity norm, as well as on the stability margin and bandwidth. The effects of weighting on closed-loop transfer functions shape are analyzed and important points are discussed in order to establish a methodical way of choosing the weighting matrices. Experimental results are presented to validate the design and to demonstrate the system effectiveness with high loading and highly nonlinear balanced and unbalanced loads.