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To provide automatic generation control (AGC) service, wind farms (WFs) are required to control their operation dynamically to track the time-varying power reference. Wake effects impose significant aerodynamic interactions among turbines, which remarkably influence the WF dynamic power production. The nonlinear and high-dimensional nature of dynamic wake model, however, brings extremely high computation complexity and obscure the design of WF controllers. This paper overcomes the control difficulty brought by the dynamic wake model by proposing a novel control-oriented reduced order WF model and a deep-learning-aided model predictive control (MPC) method. Leveraging recent advances in computational fluid dynamics (CFD) to provide high-fidelity data that simulates WF dynamic wake flows, two novel deep neural network (DNN) architectures are specially designed to learn a dynamic WF reduced-order model (ROM) that can capture the dominant flow dynamics. Then, a novel MPC framework is constructed that explicitly incorporates the obtained WF ROM to coordinate different turbines while considering dynamic wake interactions. The proposed WF ROM and the control method are evaluated in a widely-accepted high-dimensional dynamic WF simulator whose accuracy has been validated by realistic measurement data. A 9-turbine WF case and a larger 25-turbine WF case are studied. By reducing WF model states by many orders of magnitude, the computational burden of the control method is reduced greatly. Besides, through the proposed method, the range of AGC signals that can be tracked by the WF in the dynamic operation is extended compared with the existing greedy controller.