A Hybrid LQR–PI Control Strategy with Virtual Impedance for Next-Generation Inverter-Based Microgrids: Enhanced Dynamic Stability and Power Quality

Advanced control strategies for inverter-based distributed energy resources (DERs) are essential to ensure stable, reliable, and high-quality operation of modern islanded microgrids (MGs) as renewable energy penetration increases. This paper proposes a hybrid optimal control framework that combines a Linear Quadratic Regulator (LQR) with a Proportional–Integral (PI) controller and integrates droop control with a virtual impedance technique to improve the dynamic performance, power-sharing capability, and power quality of inverter-based MGs. The PI controller regulates the inverter current, while the LQR provides optimal state feedback to improve transient response and disturbance rejection. Primary droop control enables decentralized active and reactive power sharing, whereas secondary control restores voltage and frequency to their nominal values following load disturbances. Furthermore, the virtual impedance technique mitigates the adverse effects of line impedance mismatches and improves power-sharing accuracy among distributed generators. The proposed control strategy was validated through MATLAB/Simulink simulations that accounted for dynamic load variations. Compared with a conventional PI controller, the proposed hybrid LQR–PI approach reduced the frequency settling time from 0.5 s to 0.2 s, decreased the voltage recovery time from 0.5 s to 0.25 s, and achieved reduced voltage and current total harmonic distortion (THD) compared with the conventional PI control, despite the higher control energy. The optimal state feedback provided by the LQR contributed to improved transient performance, while the virtual impedance technique enhanced system robustness and maintained accurate power sharing under uncertain operating conditions. The obtained results demonstrate that the proposed control framework provides an effective and computationally efficient solution for next-generation inverter control in islanded MGs, offering enhanced dynamic stability, improved power quality, and reliable operation of renewable-energy-based distributed power systems.