Taking a Vienna rectifier as the research object, the power mathematical model based on a switching function is established according to its working principle. A sliding mode variable structure control algorithm based on the reaching law is examined in order to address the issues of the slow response speed and inadequate anti-interference of classical PI control in the face of abrupt changes in the DC-side load. In response to the sluggish convergence rate and inadequate chattering suppression of classical integer order sliding mode control, a fractional order exponential reaching law sliding mode, direct power control approach with rapid convergence is developed. The fractional calculus is introduced into the sliding mode control, and the dynamic performance and convergence speed of the control system are improved by increasing the degree of freedom of the fractional calculus operator. The method of including a balance factor in the zero-sequence component is employed to address the issue of the midpoint potential equilibrium in the Vienna rectifier. Ultimately, the suggested control is evaluated against classical PI control through simulation analysis and experimental validation. The findings indicate that the proposed technique exhibits rapid convergence, reduced control duration, and enhanced robustness, hence augmenting its resistance to interference.