Revisiting the Synchronous Reference Frame Phase-Locked Loop from a System Theory Point of View

The synchronous reference frame phase-locked loop (SRF-PLL) is analyzed using classical system theory. The internal model principle explains why a proportional-integral controller is used. The stability of the SRF-PLL is proven for control parameters larger than zero and a formula for designing its parameters is derived achieving the aperiodic limit case. The stability of the SRF-PLL is further illustrated by means of phase-portraits and simulations.