Modeling, Stability, and Design of the Single-Phase SOGI-Based Phase-Locked Loop Considering the Frequency Feedback Loop Effect

For single-phase grid-connected inverters, the second-order generalized integrator-based phase-locked loop (SOGI-PLL) is widely used for good harmonics attenuation and frequency adaptability. However, existing studies usually neglect the frequency feedback loop in the modeling and design process, and thus, the potential instability caused by the frequency feedback loop is not well explained. Besides, the improper design of SOGI-PLL can lead to the inverter instability both under ideal and weak grid conditions. Therefore, by fully considering the coupling of the frequency feedback loop, this article establishes an accurate model for SOGI-PLL. Furthermore, effects of different PLL parameters on behaviors of both the SOGI-PLL itself and the inverter are studied, based on which a graphical method for PLL parameters design is proposed. As proved, the frequency feedback loop can deteriorate the stability and performance of both SOGI-PLL itself and inverter system, especially if rapid transient is expected. The modeling method is also extended to the low-pass filter-SOGI-PLL and the improved parameters design is discussed. Experimental results verify the correctness of the proposed PLL model and the abovementioned analysis results. The proposed model is helpful to deeply reveal the instability mechanism and provides a reference for the PLL design under nonideal grid conditions.