A Complex-Type Voltage Normalization Method for Three-Phase Synchronous Reference Frame Phase-Locked Loop

Voltage normalization is widely used in phase-locked loops (PLLs) to keep their dynamic and stability decoupled from the grid-voltage amplitude. In this article, a complex-type voltage normalization method is proposed for three-phase PLLs. First, the performances of the PLL under the conventional voltage magnitude normalization method and the <inline-formula><tex-math notation="LaTeX">$d$</tex-math></inline-formula>-axis voltage normalization method are reviewed. When large frequency and/or phase jumps occur, the voltage magnitude normalization method has undesirable oscillations, and the <inline-formula><tex-math notation="LaTeX">$d$</tex-math></inline-formula>-axis voltage normalization method exists unexpected stable equilibrium points. To address these, a complex-type voltage normalization method is proposed. Then, the large-signal model of the PLL under the complex-type voltage normalization is established. And the phase-portrait and Lyapunov-based analysis are provided. It is shown that for any large frequency jump and/or phase jump, the PLL with the complex-type voltage normalization still converges to the unique stable point (0,0). Experimental tests are also provided, which show the superior performance of the proposed complex-type voltage normalization method.