Dq-Frame Impedance Modeling of Three-Phase Grid-Tied Voltage Source Converters Equipped with Advanced PLLs

With the increased prevalence of power converters in power systems, especially three-phase voltage source converters (VSCs), the stability analysis of power electronics-based power systems has received much attention recently. To this end, different impedance models, such as the dq-domain, sequence-domain, and phasor-domain impedance models among others, have been developed for three-phase VSCs in recent years. A common trend in all these impedance models, which have no noticeable practical advantage compared to each other, is considering a standard synchronous reference frame phase-locked loop (SRF-PLL) for the synchronization of the VSC with the power grid. The standard SRF-PLL, however, has a limited filtering ability and, therefore, may not be very practical in most applications. To deal with this shortcoming of the SRF-PLL, a great number of advanced three-phase PLLs have been proposed in the literature. These advanced PLLs may have different feedback/feedforward loops and filters in their structures, which make including their dynamics in the available impedance models complicated. Bridging this gap in research is the objective of this article. To this end, it is demonstrated that advanced three-phase PLLs have an alternative representation, which can be easily obtained and included in the available dq-frame impedance model. Several case studies are presented to verify this idea.