Global Stability Analysis for Synchronous Reference Frame Phase-Locked Loops

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