Guidelines for Stability Analysis of the DDSRF-PLL Using LTI and LTP Modelling in the Presence of Imbalance

In this article, the Linear Time Invariant (LTI) and Linear Time Periodic (LTP) models of two different implementations of the DDSRF-PLL in the presence of voltage imbalance are derived analytically. The accuracy of the models is investigated with time domain simulations, frequency scans, and stability analysis. On top of this, a guideline for properly choosing between LTI and LTP models for stability assessment of the DDSRF-PLL according to the degree of grid voltage imbalance is proposed. Furthermore, it is revealed that, depending on the DDSRF-PLL implementation, the positive-sequence voltage might also cause LTP dynamics, rendering the LTI model inaccurate even when the imbalance is low.