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.

中文翻译：

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存在不平衡时使用 LTI 和 LTP 建模的 DDSRF-PLL 稳定性分析指南


在本文中，通过分析推导出存在电压不平衡情况下 DDSRF-PLL 的两种不同实现的线性时不变 (LTI) 和线性时间周期 (LTP) 模型。通过时域仿真、频率扫描和稳定性分析来研究模型的准确性。在此基础上，提出了根据电网电压不平衡程度正确选择 LTI 和 LTP 模型以进行 DDSRF-PLL 稳定性评估的指南。此外，据透露，根据 DDSRF-PLL 的实现，正序电压也可能导致 LTP 动态，即使不平衡度较低，也会导致 LTI 模型不准确。