This paper investigates dq-reference-frame (dq-RF) self and cross-coupling output impedances of the islanded voltage source converter (VSC), by considering the controller impacts. The dq-RF impedances for the closed-loop system are designed to exhibit the desired resistive, inductive, or capacitive characteristics, and are employed in the power control of VSC. The effects of these impedances and connecting lines impedances on the power control of islanded parallel connected VSCs, for different impedance characteristics, are also studied. It is shown in this paper that the unbalanced impedance significantly affects the performance and power control of these parallel converters. Besides, virtual impedance based active and reactive power control of the parallel converters in the dq-RF, for resistive, inductive, and capacitive cases, are designed and implemented. The numerical and experimental results verify the analysis presented in this paper about the dq-output impedance and the virtual impedance based power sharing control.
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