Abstract
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.