Low-Effort $H_{\infty}$ Control for Z-Source Inverter Under Unbalanced Loads

In this work, a robust controller based on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> is designed for stabilization of a Z-source inverter under unbalanced loads. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> is developed in such a way that reduces oscillations and overshoot of voltage in the capacitor while minimizing the control effort signals. All of these are obtained in the limited control effort signal to be practically implementable. A third-order small-signal model has been used to design the controller. Since weighting functions are essential in designing an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> controller, the details of the defined weighting functions to achieve the optimal performance are fully described. The performance of the controller has been evaluated under uncertain load as well as the three-phase unbalanced loads. The results of simulations illustrate an excellent performance of the designed controller under severe conditions of uncertainties.