DQ transformation development for single-phase systems to compensate harmonic distortion and reactive power

An extension of the DQ transformation for single-phase systems is presented in this work, since the original approach can only be applied to three-phase systems. The theoretical principle of the proposed transformation is presented. Equations about how the fundamental component and the harmonics of the variable of concern are mapped in the dq reference frame are derived. The proposed transformation is evaluated under ideal and real conditions, and with magnitude and/or phase deviations. Besides, an adequate selection of the reference generator scheme to compensate systems with harmonic distortion and reactive power is made, obtaining an optimal selection of all parameters.