Improved MIMO modelling and enhanced transient performance of phase locked loop during grid fault

In a grid-connected power converter, synchronizing with ac grid voltage is often realized by a phase-locked loop (PLL). A single input single output linear model of PLL with the phase angle of the point of common coupling (PCC) voltage as input and the estimated phase angle as the output is generally used in the PLL analysis and design. However, an undesirable coupling between the magnitude and phase of the input voltage is present when a filtering stage is incorporated before the control loop, which cannot be captured by a SISO model, and could result in a large disturbance in the PLL estimated phase during grid faults}. To overcome this deficiency in SISO PLL modeling, this paper proposes a generalized multi-input multi-output linear model that captures the complete PLL dynamics during symmetrical faults for a PLL equipped with any prefilter. The proposed model captures this undesirable coupling between the magnitude and phase of the input voltage. Furthermore, a compensation method that decouples the magnitude dynamics of the input voltage from the phase dynamics is proposed in this paper. The proposed compensation improves the PLL's phase tracking performance by ensuring that the prefiltered PLL acts only on the PCC voltage phase changes.