Analysis of a Complex-Valued Droop Method in AC Microgrids with Complete Steady-State Frequency Compensation Using dq-Decomposition

This paper proposes a novel droop technique for AC microgrids with no frequency deviation in steady-state. This droop implementation replaces the classical $P/f + Q/V$ used for inductive lines or the alternative $P/V + Q/f$ for resistive lines with a $S/V_{dq}$ droop in which the coupling terms that appear when the line is not purely inductive/resistive are considered. The proposed droop departs from the classical approach; instead of calculating P and Q expressions considering voltage polar equation which requires sine and cosine terms, the dq-decomposition is used. This allows to create a droop combining both components of the voltage versus P and Q, without requiring small-signal simplification of the trigonometric functions ($\sin\delta\approx\delta$ and $\cos\delta\approx 1$) and taking into account the coupling terms, so that the designed droop is valid for any R/X value.