Robust Power Control of Three-Phase Grid-Connected Inverter

This paper proposes using Linear Matrix Inequality (LMI) for robust controller design in a three-phase grid-connected inverter (GCI). The controller, applied to a three-phase dc-ac inverter, integrates state feedback and error correction within the dq-rotational frame to eliminate offset errors. An LMI-based optimization minimizes settling time despite uncertainties in the L-filter (expressed as resistance and inductance variations). Sinusoidal pulse width modulation (SPWM) with insulated gate bipolar transistors (IGBTs) is used for switching. A phase-locked loop determines the grid voltage angle. MATLAB computes optimal gains from the GCI model, Microsoft Visual Studio is the programming tool, and PSIM simulation verifies control algorithm effectiveness. This robust control approach ensures a consistent, regulated grid power supply while enhancing GCI performance in output response, stability, and robustness.