Control and Stability Analysis of Grid-Connected Inverters in an Unbalanced and Distorted Weak Grid Using MDSOGI Based Selective Virtual Impedance

Increasing the penetration of grid-connected inverters and integration of single-phase microgrids (MG) and unbalanced loads into three-phase MGs result in power quality issues such as voltage harmonics and unbalance at the point of common coupling (PCC) under nonideal grid conditions. The grid impedance also increases in a weak grid and influences the system's stability. This paper proposes a novel PCC voltage feed-forward control method using selective virtual impedance loops (SVIL) based on multiple dual second-order generalized integrators (MDSOGI) for unbalanced MGs in distorted weak grids. The comprehensive development of the proposed SVIL including virtual positive/negative-sequence impedance (VPI/VNI) loops at the fundamental frequency and a virtual variable harmonic impedance (VVHI) loop at harmonic frequencies is presented. VPI and VVHI improve low-order voltage harmonics while VNI regulates the unbalanced voltage at the PCC terminal. In addition, the system stability with the proposed control is evaluated. The effectiveness of the proposed approach is validated using control hardware-in-the-loop (CHIL) for an unbalanced MG in distorted and weak grid, demonstrating improved power quality and better performance compared to existing methods.