Global Stability Analysis for Synchronous Reference Frame Phase-Locked Loops

This paper 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 tool, the global stability of SRF-PLL is discussed in the nonlinear frame. Compared with existing methods, the proposed analysis, not relying on small signal model and linearization method, provides a global discussion of SRF-PLL stability. Some novel discoveries are as follow: 1) SRF-PLL has infinite equilibrium points, including stable points and saddle points; 2) Although saddle points are unstable in local regions, there still exists two special lines for each saddle point, and SRF-PLL converges to a certain saddle point when the initial states are on its special lines. 3) These special lines of saddle points divide the global region of SRF-PLL into infinite small regions. A Lyapunov-based discussion proves that SRF-PLL converges to different stable points, when the initial states are in the different small regions. The experiment results have been verified the global stability analysis of SRF-PLL.