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.

中文翻译：

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配备高级 PLL 的三相并网电压源转换器的 DQ 帧阻抗建模

随着电力系统中电力转换器的日益普及，尤其是三相电压源转换器（VSC），基于电力电子的电力系统的稳定性分析最近受到了广泛关注。为此，近年来针对三相 VSC 开发了不同的阻抗模型，例如 dq 域、序列域和相量域阻抗模型等。所有这些阻抗模型的一个共同趋势是考虑使用标准同步参考系锁相环 (SRF-PLL) 来实现 VSC 与电网的同步，这些模型相互之间没有明显的实际优势。然而，标准 SRF-PLL 的滤波能力有限，因此在大多数应用中可能不太实用。为了解决 SRF-PLL 的这个缺点，文献中提出了大量先进的三相 PLL。这些高级 PLL 在其结构中可能具有不同的反馈/前馈环路和滤波器，这使得在可用阻抗模型中包含它们的动态变得复杂。弥合这一研究差距是本文的目标。为此，证明了先进的三相 PLL 具有替代表示，可以轻松获得并包含在可用的 dq 帧阻抗模型中。提供了几个案例研究来验证这个想法。弥合这一研究差距是本文的目标。为此，证明了先进的三相 PLL 具有替代表示，可以轻松获得并包含在可用的 dq 帧阻抗模型中。提供了几个案例研究来验证这个想法。弥合这一研究差距是本文的目标。为此，证明了先进的三相 PLL 具有替代表示，可以轻松获得并包含在可用的 dq 帧阻抗模型中。提供了几个案例研究来验证这个想法。