Three-level neutral-point-clamped (3L-NPC) power converters are necessary interfaces to form micro-energy systems. Naturally, designing a suitable control scheme, featuring superior dynamics, strong robustness, and simple structure, is a promising solution to guarantee more efficient operation of converter. This paper proposes a robust high-quality current control strategy for the 3L-NPC power converter in the stationary <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha \beta$</tex-math></inline-formula> frame. A super-twisting algorithm coupled with a Luenberger observer current controller is proposed to deal with the poor sinusoidal current tracking issue due to the existing inductance/grid frequency deviations and the disturbance of the sinusoidal dynamic nature. Additionally, an extended sliding mode disturbance observer based proportional control is built to dramatically enhance voltage regulation performance, in the case of capacitance deviations and unknown dc-loads. Experimental data confirm the effectiveness of the proposed solution outperforms the conventional proportional-resonant/-integral control in terms of accurate tracking current/voltage, anti-disturbance, and grid current total harmonic distortion.