A variable-frequency critical-soft-switching (VF-CSS) model predictive control method is developed combining with a modified nonisolated inverter to improve the efficiency. A two-level control structure is developed, including 1) the central-level grid-side inductor current control and zero-sequence voltage control; and 2) the local-level per-phase power module control of VF-CSS model predictive controller with state estimator. Two VF-CSS controllers are proposed, including variable-continuous-frequency critical-soft-switching controller and variable-discrete-frequency critical-soft-switching, to achieve critical soft-switching operation for high efficiency. The combination of MPC and VF-CSS guarantees a complete critical soft-switching operation at full period range of varying frequency and especially during transient. The state estimator provides sampling noise rejection and accurate switch-side inductor current estimations for MPC and VF-CSS. Also, with the help of state estimator, the current sensor cost is reduced by 50%. Meanwhile, the estimator contributes to a more accurate switch-side inductor current reading for MPC implementation with variable continuous frequency controller, especially when the critical soft switching requires huge inductor current ripple. With the proposed control strategies and topology, medium-frequency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$>$</tex-math></inline-formula> 200 kHz, 45 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> H) and high-frequency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$>$</tex-math></inline-formula> 1 MHz, 4.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> H) test benches are validated experimentally. The efficiency is above 99% at a rated power of 15 kW. A power density of more than 10.4 kW/L is achieved.
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