On the definition of the power coefficient of tidal current turbines and efficiency of tidal current turbine farms

During the last decade, the development of tidal current industries has experienced a rapid growth. Many devices are being prototyped. For various purposes, investors, industries, government and academics are looking to identify the best device in terms of of cost of energy and performance. However, it is difficult to compare the cost of energy of new devices directly because of uncertainties in the operational and capital costs. It may however be possible to compare the power output of different devices by standardizing the definition of power coefficients. In this paper, we derive a formula to quantify the power coefficient of different devices. Specifically, this formula covers ducted devices, and it suggests that the duct shape should be considered. We also propose a procedure to quantify the efficiency of a tidal current turbine farm by using the power output of the farm where no hydrodynamic interaction exists between turbines, which normalizes a given farm's power output. We also show that the maximum efficiency of a farm can be obtained when the hydrodynamic interaction exists.