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In a grid-connected power converter, synchronizing with ac grid voltage is often realized by a phaselocked loop (PLL). A single input single output (SISO) 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 (MIMO) 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. A vital application of the proposed compensation method for PLL is during a grid fault case, wherein the converters are expected to contribute to the fault current, which requires an accurate measurement of the PCC voltage phase. The compensation method's effectiveness is demonstrated using power hardware in the loop simulation of a hardware voltage source converter interfaced to a distribution system simulated in real-time.

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