As high-order nonlinear large-scale systems, wind farms composed of multiple wind turbines (WTs) need to adopt active power control (APC) to track the power set points, rather than the maximum power points. In this paper, the proportional distribution strategy is utilized to specify the power set point according to the available output power of each WT based on the ultra-short-term wind speed prediction. Then, we convert the APC problem into the rotor speed tracking control problem, and a robust adaptive fault-tolerant control approach based on the barrier Lyapunov function is developed to track the desired power signal of each WT with guaranteed transient performance and robustness to actuator faults. The effectiveness and the merit of the proposed approach are validated by applying it to the APC of a wind farm.