Equivalent DQ Sequence-Domain Model of Unbalanced Three-Phase Passive Elements for Power Converter Controllers

Equivalent
$dq0$
models of three-phase passive impedances are widely used for the design of three-phase inverter and rectifier controllers in the synchronous frame. However, these equivalent models assume that the impedance in each phase are the same, which is not always applicable. The fact that the impedance in each phase is different, generates second order harmonic content in the
$dq0$
components, which hinders the advantages of the
$dq0$
transformation. To avoid the second harmonic in these scenarios, it is possible to use the Fortescue's theorem to represent any asymmetrical set of three-phase signals as a linear combination of three symmetrical sequences. In the literature, only a few works have attempted to derive the equivalent model of unbalanced three-phase passive elements in the sequence domain, and none is able to account for the interaction between the zero sequence and the positive and negative sequences. This work presents the derivation of the equivalent
$dq$
sequence-domain model of unbalanced three-phase passive elements both analytically and with an intuitive graphical approach. Experimental results are shown to validate the proposed models.