Optimal and Systematic Design of Current Controller for Grid-Connected Inverters

A design approach for grid-connected inverter controllers for distributed and renewable energy system applications is proposed, where a high number of controller gains can be designed optimally in a fairly systematic way. The linear quadratic regulator problem is first modified to accommodate sinusoidal signal tracking through a meaningful state-space transformation. The cost function is modified to explicitly include the tracking error, so that its weights are designed in a transparent and systematic way. The proposed technique is applied to the well-known control structure comprising the fundamental and harmonic resonant controllers. Second, the control structure is rearranged to reject the distortions from both the grid voltage and the reference signal, and the proposed design technique is applied to this new structure. It is shown that the desired features of active damping for $LCL$ filters and robust performance against system uncertainties, harmonics, and disturbances are achieved. Third, the controller and the systematic design procedure are extended for inverters with $LLCL$ filters. Proposed control structures are designed and simulated and then implemented on a digital signal processor. Results confirm features of the method and its ability to address control system challenges in high power density and efficient inverter applications.