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Representations of AC power systems by frequency dependent impedanceequivalents is an emerging technique in the dynamic analysis of power systemsincluding power electronic converters. The technique has been applied fordecades in DC-power systems, and it was recently adopted to map the impedancesin AC systems. Most of the work on AC systems can be categorized in twoapproaches. One is the analysis of the system in the \textit{dq}-domain,whereas the other applies harmonic linearization in the phase domain throughsymmetric components. Impedance models based on analytical calculations,numerical simulation and experimental studies have been previously developedand verified in both domains independently. The authors of previous studiesdiscuss the advantages and disadvantages of each domain separately, but neithera rigorous comparison nor an attempt to bridge them has been conducted. Thepresent paper attempts to close this gap by deriving the mathematicalformulation that shows the equivalence between the \textit{dq}-domain and thesequence domain impedances. A modified form of the sequence domain impedancematrix is proposed, and with this definition the stability estimates obtainedwith the Generalized Nyquist Criterion (GNC) become equivalent in both domains.The second contribution of the paper is the definition of a \textit{MirrorFrequency Decoupled} (MFD) system. The analysis of MFD systems is less complexthan that of non-MFD systems because the positive and negative sequences aredecoupled. This paper shows that if a system is incorrectly assumed to be MFD,this will lead to an erroneous or ambiguous estimation of the equivalentimpedance.

A modified sequence domain impedance definition and its equivalence to  the dq-domain impedance definition for the stability analysis of AC power  electronic systems