The low energy conversion efficiency of the vanadium redox flow battery (VRB) system poses a challenge to its practical applications in grid systems. The low efficiency is mainly due to the considerable overpotentials and parasitic losses in the VRB cells when supplying highly dynamic charging and discharging power for grid regulation. Apart from material and structural advancements, improvements in operating strategies are equally essential for achieving the expected high-performance VRB system, although an optimized solution has not been fully exploited in the existing studies. In this paper, a two-stage control strategy is thus developed based on a proposed and experimental validated multi-physics multi-time-scale electro-thermo-hydraulic VRB model. Specifically, in the first stage, the optimal flow rate of the VRB is obtained based on online optimization to reduce parasitic loss and enhance instantaneous system efficiency, and the result serves as the set point of a feedback flow rate controller. In the second stage, dual time scales are specifically considered. And the current and flow rate controllers are designed to meet the highly varying power demands for grid-connected applications. The effectiveness of the proposed control strategy is verified under a scenario to smooth wind power generation. Comparative studies show that compared to the prevailing approaches, higher efficiency can be achieved in tracking the theoretical optimal power profiles for online battery control.