[Objective] This paper proposes a fractional-order sliding mode control (FOSMC) method based on the direct power control structure

to suppress the grid-current distortion and DC voltage fluctuations of the three-phase PWM rectifier under unbalanced grid conditions. [Methods] Firstly

a dynamic model for the direct power control of the three-phase PWM rectifier under unbalanced grid conditions was established in the two-phase stationary coordinate system

eliminating the need for phase-locked loops and current loops

which simplifies the system structure. Based on this model

the control objective under unbalanced conditions was transformed into a power tracking problem by correcting the power references. Subsequently

a FOSMC power controller was constructed for the inner power loop. The introduction of the fractional-order term increased design flexibility

effectively mitigating sliding mode chattering while ensuring rapid and precise tracking of the power references. Furthermore

an extended state observer based on the inverse hyperbolic sine function was designed for the outer DC voltage loop. Leveraging its smooth and continuous characteristics

real-time estimation of DC-side load disturbances was achieved. Finally

by integrating this with the FOSMC law

the voltage outer-loop controller was formulated

guaranteeing robust DC voltage control performance even under load disturbances. [Results] The effectiveness of the proposed FOSMC method was validated by theoretical analysis and test results. [Conclusion] The proposed method achieves rapid and precise power tracking and DC voltage regulation under unbalanced grid conditions

effectively suppressing grid-current distortion and DC voltage fluctuations. It significantly enhances the system’s disturbance rejection capability

providing an effective solution for the high-performance control of three-phase PWM rectifiers in unbalanced grid scenarios.