Small-Signal Modeling of Three-Phase Synchronous Reference Frame Phase-Locked Loops

Synchronous reference frame (SRF) phase-locked loops (PLLs) represent a commonly used technique for grid synchronization in distributed generation (DG) systems. Since PLLs affect transient dynamics, they are a crucial component for stability studies. In this letter, it is shown that a commonly used small-signal SRF-PLL model can be used for stability analysis in some preconditioned scenarios with a single grid-connected DG unit, but does necessarily require perturbation quantities that are offset free. Otherwise, an incorrect usage may result in unacceptable errors. To overcome this restriction, an improved small-signal PLL model is proposed, which enables to analyze the effects of grid frequency and phase angle changes as well as variations of the input voltage magnitude. Finally, the model accuracy is validated by means of computer simulations.