An Instantaneous Power Theory Extension for Unbalanced Low Voltage Ride Through Compensation

In voltage source inverter (VSI)-based distributed generation (DG) systems, the control of the active and reactive power during an unbalanced low voltage ride through (LVRT) is generally implemented through a current injection strategy based on the standard instantaneous power theory (IPT). However, IPT inherently introduces oscillations in active and reactive power caused by unbalanced grid voltages. To address this limitation, a per-phase IPT is proposed, which enables independent control of both active and reactive power in each of the ABC phases. This is achieved by expanding the conventional <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha \beta$</tex> transformation to a per-phase basis, in contrast to the standard theory that operates on a combined three-phase basis and lacks per-phase flexibility. Based on that, a suitable instantaneous per-phase current injection reference is generated, serving the required power for normal and LVRT conditions. The simulation results validate the feasibility of the proposed IPT extension and its effectiveness in eliminating the oscillations during LVRT compensation.