On Small-Signal Modelling of Advanced Phase-Locked Loops for Three-phase Grid-connected Applications

In grid applications, phase-locked loops (PLLs) are built using the synchronous reference frame phase-locked loop (SRF-PLL), which is a standard structure. As the standard SRF-PLL has a limited disturbance (harmonic, interharmonic, dc offset and grid voltage imbalance) filtering capability, often additional filters are included within its control loops or before its input. When an in-loop filter is used in the SRF-PLL structure, its linear modeling, which is required for dynamics and stability studies, is quite straightforward. It is, however, not the case when additional filters are included before the SRF-PLL input, because these filters are often of a high order and interact with the SRF-PLL through a feedback loop. To tackle this difficulty, a simple modeling approach with a general theme is presented in this paper.