A Multi-Objective PQI-Based Adaptive Virtual Impedance Strategy for Harmonic and Voltage Unbalance Mitigation in Renewable-Rich Hybrid Microgrids

The increasing penetration of converter-interfaced renewable energy sources poses significant challenges to power quality in modern microgrids, especially under nonlinear and unbalanced load conditions. Conventional virtual-impedance strategies can improve converter-grid interaction; however, the use of fixed parameters or adaptation based on a single electrical variable may provide limited performance under dynamically changing power-quality conditions. This article proposes a multi-objective power-quality-index-based adaptive virtual impedance (PQI-AVI) strategy for grid-connected hybrid microgrids with high renewable-energy penetration. The supervisory PQI combines normalized voltage total harmonic distortion (THDv), the voltage unbalance factor (VUF), and voltage-magnitude deviation to continuously adjust the virtual resistance and reactance. To prevent excessive impedance adaptation, the setpoint generated by the PQI is further constrained by a grid-strength-dependent stability limit derived from a small-signal analysis that includes pulse-width modulation (PWM) delay dynamics. The proposed strategy is evaluated in MATLAB-Simulink® using a modified IEEE 14-bus hybrid microgrid with an aggregate operating demand of 10 MW under nonlinear and unbalanced load conditions. Compared with the uncompensated condition, the proposed controller reduces THDv from 7.84% to 2.11%, THDi from 15.8% to 4.8%, and VUF from 2.50% to 0.80%, while simultaneously improving the power factor from 0.86 to 0.97. The stability analysis further demonstrates that the admissible virtual-impedance adaptation depends on grid strength when PWM dynamics are explicitly considered. These results show that the proposed stability-constrained PQI-AVI framework enables coordinated power-quality improvement while restricting the virtual-impedance command to the numerically identified small-signal stable adaptation region for the grid-strength conditions considered.