Global Stability Analysis for Synchronous Reference Frame Phase-Locked Loops

• Published in: IEEE transactions on industrial electronics (1982) 2022-10, Vol.69 (10), p.10182-10191
• Main Authors: Dai, Zhiyong, Li, Guangqi, Fan, Mingdi, Huang, Jin, Yang, Yong, Hang, Wei
• Format: Article
• Language: English
• Subjects: Analytical models; Convergence; Equilibrium; Frequency estimation; Global stability analysis; grid synchronization; large-signal model; Linearization; Phase locked loops; phase-locked loop; Power grids; Power system stability; Saddle points; Signal analysis; Small signal analysis; Stability analysis; synchronous reference frame; Voltage
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2021.3125655

This article analyzes the global stability of synchronous reference frame phase-locked loops (SRF-PLLs) from a large signal viewpoint. First, a large-signal model of SRF-PLL is accurately established, without applying any linearization method. Then, according to the phase portrait and Lyapunov argument, the global performance of SRF-PLL is discussed in the nonlinear frame. Compared with the small-signal analysis methods, the proposed analysis, not relying on the small-signal model and linearization method, provides a global discussion of the SRF-PLL performance. The contributions of this article are as follows. First, it is found that SRF-PLL has infinite equilibrium points, including stable points and saddle points. Second, it provides a way to divide the global region of SRF-PLL into many small regions. In each small region, the SRF-PLL only has one stable equilibrium point. And for any initial states (\tilde{\theta }(t_0),\tilde{\omega }(t_0)) in a small region, all states (\tilde{\theta }(t),\tilde{\omega }(t)),t>t_0 will remain in this small region, and SRF-PLL will converge to the unique stable equilibrium point of this small region. Third, by dividing the global region of SRF-PLL into many small regions, it is found that when the frequency of grids varies largely, the SRF-PLL will converge to a new equilibrium point that is far away from the original equilibrium point. It is the reason why the frequency convergence of SRF-PLL has many oscillations and SRF-PLL has a rather slow dynamic, when the frequency changes largely. The experimental results are provided to verify the proposed global stability analysis of SRF-PLL.