Modeling of unbalanced three-phase driving-point impedance with application to control of grid-connected power converters

The dq transformation is widely used in the analysis and control of three-phase symmetrical and balanced systems. The transformation is the real counterpart of the complex transformations derived from the symmetrical component theory. The widespread distributed generation and dynamically connected unbalanced loads in a three-phase system inherently create unbalanced voltages to the point of common coupling. The unbalanced voltages will always be transformed as coupled positive-sequence and negative-sequence components with double-frequency ripples that can be removed by some filtering algorithms in the dq frame. However, a technique for modeling unbalanced three-phase impedance between voltages and currents of same sequences or of opposite sequences is still missing. We propose an effective method for modeling unbalanced three-phase impedance using a decoupled zero-sequence impedance and two interacting positive-sequence and negative-sequence balanced impedances in the dq frame. The proposed method can decompose a system with unbalanced resistance, inductance, or capacitance into a combination of independent reciprocal bases (IRB). Each IRB basis belongs to one of the positive-sequence, negative-sequence, or zero-sequence system components to facilitate further analysis. The effectiveness of this approach is verified with a case study of an unbalanced load and another case study of an unbalanced voltage compensator in a microgrid application.