Dead-time is the most important disturbance in a voltage-source inverter's operation. It introduces low-order harmonics at the inverter's output voltage. To compensate for the dead-time effects in three-phase grid-tied inverters, this paper proposes a Linear Quadratic Gaussian (LQG) multivariable control approach. The LQG multivariable control is known as a robust control approach while provides a high band-width for the closed-loop system. Therefore, it promises significant attenuations in the dead-time introduced harmonics. To achieve a high performance, we run the three-phase grid-tied inverter in the current-controlled mode. Based on the nominal multivariable model derived for the three-phase grid-tied inverter in a synchronous reference frame, the LQG controller is composed such that the closed-loop system exhibits robust stability while attenuates disturbances significantly. The dead-time introduced harmonics produce disturbances in the synchronous reference frame with the highest frequencies. This is the reason for considering the dead-time as the most important disturbance in an inverter's operation. For an experimental set-up manufactured for the three-phase grid-tied inverter, we developed a detailed model in MATLAB/Simulink. It is employed for the performance verifications of designed LQG controller. Extensive results are presented for different important scenarios, based on which, the excellent performance of proposed approach is proven. In fact, by employing the proposed approach, the dead-time introduced harmonics are significantly attenuated such that a Total Harmonics Distortions (THD) of about 5% is achieved for the injected currents to grid which meets the IEEE 1547 standard.
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