Complex-Based Controller for a Three-Phase Inverter With an LCL Filter Connected to Unbalanced Grids

A new controller for a grid-connected inverter with an LCL filter is proposed in this paper. The system is described by its complex representation, and the controller is designed using the complex root locus method. The complex representation allows a considerable reduction in the order of the system, simplifying the design task and making it possible to use advanced techniques, such as the complex root locus. The new complex controller adds an extra degree of freedom that makes it possible to move the poles of the systems and to improve the stability and speed of response compared with the conventional controls. This paper includes a detailed discussion of the effect of the gains of the controller on the root locus. The proposal is validated with simulation and experimental results.