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This paper provides a comparative analysis of impedance models for powerelectronic converters and systems for the purpose of stability investigations.Such models can be divided into either decoupled models or matrix models. Adecoupled impedance model is highly appealing since theSingle-Input-Single-Output (SISO) structure makes the analysis and resultinterpretation very simple. On the other hand, matrix impedance models are moreaccurate, and in some cases necessary. Previous works have applied variousapproximations to obtain decoupled models, and both the dq- and sequencedomains have been used. This paper introduces the terms decoupled andsemi-decoupled impedance models in order to have a clear classification of theavailable approximations.  The accuracy of 4 decoupled impedance models are discussed based on theconcept of Mirror Frequency Coupling (MFC). By definition the decoupled modelsbased on sequence domain impedances will be exact for systems without MFC. Inthe general case, they are expected to be more accurate than the decoupleddq-impedance models. The paper defines a norm $\epsilon$ to measure the degreeof coupling in the impedance matrices. This norm equals the error in theeigenvalue loci between the matrix and semi-decoupled models. This can also beviewed as the error in the semi-decoupled Nyquist plot.  An example case study consisting of a grid-connected VSC with currentcontroller and PLL is used to compare the different methods. It is found thatdecoupled and semi-decoupled models in the dq-domain are only applicable ingrids with very low X/R-ratio. Furthermore, it is concluded that the decoupledmodel in the sequence domain gives close to equal results as the semi-decoupledmodel.

Coupled and decoupled impedance models compared in power electronics systems