For resource characterization of tidal channels, sophisticated tidal turbine models that capture the relevant physical effects are necessary. For large turbines with diameters in the order of the water depth, one relevant physical effect is the interaction of the water surface with the turbine stream tube. This effect is often neglected in literature, which leads to an overprediction of the extractable energy and thus, of the tidal potential. In this paper the upper limit for power extraction from a quasistationary open-channel flow by a regular turbine array is derived using an experimentally validated actuator disc theory which takes the streamtube deformation due to surface effects into account. Since the disturbance of each turbine propagates both downstream and upstream, the turbines in an array influence each other as well as the turbine field influences the flow state of the whole tidal system. Thus, the optimal operating strategy (distribution of the entire power generation on the individual turbines) differs from the simple approach of a maximum power control in each turbine and is calculated to derive the resulting maximum possible coefficient of performance for a given tidal system and array design. The results are compared to the results obtained with other common actuator disc models for hydrokinetic turbines. It is shown, that for high blockages and high energy extraction per turbine the predicted energy extraction differs. In some cases, even flow conditions with physically impossible results that conflict with conservation laws occur.