Due to the fluctuation characteristics of the wind turbine (WT) production, the design of the control system needs to ensure the stability of the power system at different wind speeds. In this context, a WT-oriented adaptive robust control agent for a static synchronous compensator having additional damper controller (STATCOM-ADC) is proposed in this paper. An artificial neural network based estimator for system identification which can identify the equivalent transfer function of the whole system in real time is used in this paper. Then a Deep Deterministic Policy Gradient (DDPG) algorithm is adopted to train the agent on learning the adaptive robust control strategy for STATCOM-ADC. Compared with other control strategies, the proposed method has modelled self-learning abilities, and the parameter settings provided by the agent for one operation state of the system are still applicable to other states. Simulation results on the actual wind farm located in China Ningxia province show that the proposed method can enhance the stability of the system under different fault conditions and wind speeds.