In this work, we propose a control framework for farms consisting of ocean current turbines (OCT). The ocean current turbine systems used in this farm are tethered to the ground of the ocean, and their depth can be adjusted online based on the maximum ocean current power available. To maximize the average power generated by the farm, the ocean current turbine wake interactions must be taken into account, and also each turbine in the farm should achieve these changes in the position reference with minimum control energy. Considering additional limitations such as keeping the tethering cables away from each other and avoiding collisions between the turbines, an advanced optimization framework is developed to achieve the maximum power generation in a specified region. Tracking of the reference trajectories by the ocean current turbine systems is achieved by model predictive control (MPC). A case study is presented to highlight the significant estimated improvement in the average energy generated by the farm using the proposed framework and control methodology.