适用于一般坐标系的电力电子变换器阻抗(导纳)稳定性模型

Impedance(Admittance) Stability Modeling for AC Power Electronic Converters Applicable to General Coordinate Frames

电力电子变换器的谐波稳定性通常采用频域阻抗或导纳建模方法进行分析。目前已有学者建立了电压源变换器在几种坐标系中的阻抗模型,但各模型是相对独立的。另有学者注意到了dq坐标系和PN以及αβ复坐标系中阻抗模型存在的部分等价关系,但其研究中坐标变换是基于常数矩阵或者部分推导不够完备,无法适用于更一般的坐标系。系统地推导了dq坐标系和“12”空间向量坐标系中变换器的导纳模型,并定量揭示了锁相环在低频段引入负电阻性的机理。在此基础上,针对常用的时域坐标变换,包括Park、Clark、Lyon和顾氏变换等,得到了其频域关系并阐明了dq、fb、“12”等坐标系中阻抗模型的转换关系和等价性。由此建立了适用于一般静止和旋转坐标变换的阻抗模型,完善了现有的电力电子阻抗稳定性建模理论体系,并导出了αβ实坐标系中镜像频率耦合的4维导纳矩阵。通过频率扫描法和理论推导的对照分析验证了该一般阻抗模型的有效性。

Frequency-domain impedance or admittance model is widely used for the harmonic stability analysis of the power electronic converters.Some researchers have independently developed some impedance models of the voltage-source converter in different coordinate frames,without showing their explicit relations.Other researchers have revealed partially the equivalence of the impedance models in the dq,PN and αβ coordinate frames recently,but this conclusions cannot be directly applied to the general coordinates because the transformation matrixes adopted by these researchers are constant ones or some erroneous derivations are found in these works.This paper systematically derives the overall admittance matrix models in the dq and "12" space vector reference frames and quantitively reveals the mechanism of negative conductance in the low-frequency ranges due to the phase-locked loop.Further,the frequency-domain relations of the commonly-used time-domain transformations,including Park,Clark,Lyon and Gu’s transformations,are developed,based upon which the equivalences of the impedance models in the dq,fb,“12” coordinate frames are revealed.An impedance model in general coordinate frames is established,significantly improving the existing theory of the impedance stability modeling for the power electronic converters.A mirror-frequency-coupled 4-dimension admittance matrix in the αβ real coordinate frame is thus built for the first time.The effectiveness of the general model is verified by comparing the admittance models obtained from the theoretical derivation and the frequency-scan measurement.