The energetics of large tidal turbine arrays

The components of the energy lost by currents flowing along tidal channels with large turbine arrays provide insights about developing farms to generate electricity from tidal streams. The performance and economics of a farm are profoundly affected by where a farm lies on the curve of the total power lost by the flow in relation to its peak at a total drag coefficient of 2. Farms in shallow channels lie well above the peak, where a falling ceiling in the total power lost leads to a diminishing return on optimally tuned turbines. Farms in large tidal straits lie well below the peak. They grow initially in the context of a rapidly rising ceiling in the total power lost and may benefit from an increasing return on turbines added to the cross-section, a power production per turbine well above that of the first turbine installed and have turbines which may exceed the Betz limit. Surprisingly farms in tidal straits have proportionately higher mixing losses behind the turbines, thus the benefits are not due to a higher turbine conversion efficiency as the blockage ratio increases. There is an optimal number of rows for a farm, however a harsh diminishing return on new rows near this optimum will result in farms being significantly smaller than the optimum size. Energy losses due to drag on turbine support structure can be significant in multi-row farms, altering their performance and limiting farm size.

► Turbines in large tidal straits may exceed the Betz limit on efficiency as they fill the channel’s cross-section.
► The efficiency of turbines in shallow channels falls below the Betz limit as they fill the cross-section.
► Maximizing the power production of large farms is not the same as maximizing the conversion efficiency of the turbines.
► The power produced by each turbine decreases as rows are added to a farm.
► The fraction of total power lost by the flow which is lost to bottom friction deceases as a farm expands.