[论文解读] Coupled and decoupled impedance models compared in power electronics systems

Atle Rygg, Marta Molinas+2 more|arXiv (Cornell University)|Oct 17, 2016

Microgrid Control and Optimization参考文献 7被引用 3

一句话总结

本文比较了电力电子系统中的耦合（矩阵）与解耦阻抗模型，引入了镜像频率耦合（MFC）概念以评估精度。定义了解耦与半解耦模型，并提出使用范数ε量化耦合误差，结论为序列域中的解耦模型在精度上几乎等同于半解耦模型，但复杂度显著降低。

ABSTRACT

This paper provides a comparative analysis of impedance models for power electronic converters and systems for the purpose of stability investigations. Such models can be divided into either decoupled models or matrix models. A decoupled impedance model is highly appealing since the Single-Input-Single-Output (SISO) structure makes the analysis and result interpretation very simple. On the other hand, matrix impedance models are more accurate, and in some cases necessary. Previous works have applied various approximations to obtain decoupled models, and both the dq- and sequence domains have been used. This paper introduces the terms decoupled and semi-decoupled impedance models in order to have a clear classification of the available approximations. The accuracy of 4 decoupled impedance models are discussed based on the concept of Mirror Frequency Coupling (MFC). By definition the decoupled models based on sequence domain impedances will be exact for systems without MFC. In the general case, they are expected to be more accurate than the decoupled dq-impedance models. The paper defines a norm $ε$ to measure the degree of coupling in the impedance matrices. This norm equals the error in the eigenvalue loci between the matrix and semi-decoupled models. This can also be viewed as the error in the semi-decoupled Nyquist plot. An example case study consisting of a grid-connected VSC with current controller and PLL is used to compare the different methods. It is found that decoupled and semi-decoupled models in the dq-domain are only applicable in grids with very low X/R-ratio. Furthermore, it is concluded that the decoupled model in the sequence domain gives close to equal results as the semi-decoupled model.

研究动机与目标

• 系统分类并比较电力电子系统中的解耦、半解耦与精确阻抗模型。
• 解决现有文献中关于解耦与半解耦模型定义不明确的问题。
• 引入定量度量ε，以评估阻抗模型中解耦近似带来的误差。
• 在不同电网条件下（特别是X/R比）评估不同阻抗建模方法的精度。
• 为稳定性分析提供在何时使用解耦、半解耦或精确矩阵模型的实际建议。

提出的方法

• 定义三种模型类型：解耦（最初忽略耦合）、半解耦（捕捉完整耦合但最终分析中忽略）和精确（完整2×2矩阵模型）。
• 引入范数ε以量化半解耦模型与精确模型之间的误差，定义为特征值轨迹或奈奎斯特图的偏差。
• 应用改进的序列域变换，通过酉变换矩阵A_Z将dq域阻抗矩阵与序列域矩阵关联。
• 以采用电流控制与PLL的并网VSC为案例研究，比较不同电网X/R比下各模型的性能。
• 在dq域与序列域中注入扰动信号，从仿真中提取阻抗矩阵。
• 使用特征值轨迹与奈奎斯特图分析稳定性，以比较不同建模方法的精度。

实验结果

研究问题

• RQ1 在电力电子系统中，dq域中的解耦与半解耦阻抗模型与精确矩阵模型相比，精度如何？
• RQ2 镜像频率耦合（MFC）在dq域中如何降低解耦模型的精度？
• RQ3 在何种电网条件下，dq域中的解耦模型仍有效，何时会失效？
• RQ4 选择阻抗域（dq vs. 序列）如何影响解耦建模的精度与实用性？
• RQ5 范数ε能否可靠预测何时需要使用矩阵模型以实现准确的稳定性分析？

主要发现

• dq域中的解耦与半解耦模型仅在X/R比极低的电网中（例如X/R ≈ 0.1）保持准确，对典型感性电网则失效。
• 序列域中的解耦模型在精度上与半解耦模型几乎完全一致，经由特征值轨迹与奈奎斯特图比较验证。
• 范数ε能有效量化解耦带来的误差，值越高表示耦合效应越强，需采用矩阵模型。
• 对于无镜像频率耦合（MFC）的系统，解耦序列域模型在定义上即为精确模型。
• 半解耦模型在精度上并未显著优于解耦模型，但其测量或仿真过程复杂度显著更高。
• 本文建议优先采用序列域中的解耦模型，而非半解耦或dq域模型，因其在精度与简洁性之间达到更优平衡。