  Representations of AC power systems by frequency dependent impedance
equivalents is an emerging technique in the dynamic analysis of power systems
including power electronic converters. The technique has been applied for
decades in DC-power systems, and it was recently adopted to map the impedances
in AC systems. Most of the work on AC systems can be categorized in two
approaches. One is the analysis of the system in the \textit{dq}-domain,
whereas the other applies harmonic linearization in the phase domain through
symmetric components. Impedance models based on analytical calculations,
numerical simulation and experimental studies have been previously developed
and verified in both domains independently. The authors of previous studies
discuss the advantages and disadvantages of each domain separately, but neither
a rigorous comparison nor an attempt to bridge them has been conducted. The
present paper attempts to close this gap by deriving the mathematical
formulation that shows the equivalence between the \textit{dq}-domain and the
sequence domain impedances. A modified form of the sequence domain impedance
matrix is proposed, and with this definition the stability estimates obtained
with the Generalized Nyquist Criterion (GNC) become equivalent in both domains.
The second contribution of the paper is the definition of a \textit{Mirror
Frequency Decoupled} (MFD) system. The analysis of MFD systems is less complex
than that of non-MFD systems because the positive and negative sequences are
decoupled. This paper shows that if a system is incorrectly assumed to be MFD,
this will lead to an erroneous or ambiguous estimation of the equivalent
impedance.
