Assessment of Various Three-Phase PLLs Based on SOGI-QSG for Grid Synchronization Under Unbalanced Grid Conditions

In grid-connected inverter systems, the Phase-Locked Loop (PLL) is fundamental for achieving and maintaining precise synchronization between the inverter and the electrical grid. Developing an efficient and robust PLL is essential to ensure reliable operation, particularly in the presence of abnormal grid conditions. Among the existing synchronization methods, the Synchronous Reference Frame-based PLL (SRF-PLL) is widely adopted due to its robust performance; however, it suffers from degraded accuracy under unbalanced voltage conditions. To address this limitation, the Second-Order Generalized Integrator-Quadrature Signal Generator (SOGI-QSG) was proposed in previous studies as an alternative approach. Despite its advantages, the SOGI-PLL exhibits weak filtering capability for lower-order harmonics and remains sensitive to DC offset, both of which can affect synchronization quality. As a result, numerous advanced PLLs based on SOGI-QSG have been proposed in the literature to address SOGI-QSG limitations by enhancing DC offset rejection, filtering capability, and dynamic response. This article provides a comprehensive assessment of various three-phase PLLs based on SOGI-QSG under unbalanced grid conditions, focusing on peak-to-peak frequency error, filtering performance, and DC offset rejection. The operational principles and mathematical models of each technique are discussed, and their performances are validated using MATLAB/Simulink (R2025b). The results show that the SRF-PLL exhibits oscillatory behavior under unbalanced conditions, whereas the PLLs based on SOGI-QSG demonstrate stable synchronization with different trade-offs between filtering strength and dynamic response. Therefore, the selection of the appropriate PLLs based on SOGI-QSG depends on the priorities of the specific application.