A Multivariable Controller in Synchronous Frame Integrating Phase-Locked Loop to Enhance Performance of Three-Phase Grid-Connected Inverters in Weak Grids

This article presents a new current controller in the synchronous reference frame and its associated design for enhancing the performance of three-phase grid-connected inverters, especially against weak-grid conditions. The existing controllers do not perform strongly during high-impedance grid conditions and lead to oscillations and instability issues due to the interactions between the synchronization and control units. The proposed controller addresses this issue by 1) deriving a linear model of the three-phase phase-locked loop (PLL), 2) integrating the PLL model into the current controller design, 3) using a multivariable control design for multi-input multi-output systems, and 4) designing the controller gains using optimal linear quadratic theory. The proposed controller has superior performance over a substantially wider range of weak-grid conditions compared to conventional controllers. Extensive simulation and experimental results are presented in order to validate and reveal the desirable performance of the proposed controller.