Large-Signal Synchronisation Analysis of Phase-Locked Loop-Based Reactive Current Injection Under Weak Grids

Abstract

In this paper, a large-signal synchronisation analysis method based on saddle point characteristics is proposed to discuss the stability of the phase-locked loop (PLL)-based reactive current injection system. Firstly, the large-signal model of the PLL-based reactive current injection is established. An equilibrium point analysis shows that the PLL-based reactive current injection has an infinite number of stable points and saddle points. Then, based on the characteristic that trajectories converging to saddle points form the boundaries of convergence regions for stable points, the large-signal stability analysis of the PLL-based reactive current injection is obtained. It is concluded that the PLL-based reactive current injection has infinite convergence regions. Each convergence region has one stable point, and the position of the stable point is relevant to the grid voltage amplitude and reactive current reference. When the states of the reactive current injection system lie within a convergence region, the final states will converge to the stable point of this region. In addition, the shapes and sizes of the convergence regions are strongly influenced by the grid voltage amplitude and the reactive current reference. When the grid voltage amplitude drops or the reactive current reference increases, the size of the convergence regions reduces. In particular, when the grid voltage amplitude and/or reactive current reference changes largely, the sizes of the convergence regions decrease significantly. In this case, the system states at the original stable point will fall outside the new convergence region, and the PLL-based reactive current injection will lose its synchronisation stability. The effectiveness of the proposed theoretical analyses is verified by simulations.