Optimising Large Scale Turbine Farms

Tremendous progress has been made in tidal current power generation with the a 1.2MW turbine now operating  in Strangford Lough, Ireland (right) .  These "underwater wind turbines" generate power from strong tidal currents through narrow channels.  Hundreds of turbines in large tidal farms will be needed to make a significant contribution.  Tidal power research at Otago focuses on understanding  the efficiency of large scale turbine farms and estimating the size of  resource from a given number of turbines. Research relates to the  fluid dynamic efficiency of large farms and how to optimise the arrangement and tuning of large farms in high flow channels.

The Energetics of Large Tidal Turbine Arrays

Vennell, R.,  in press, Renewable Energy (2012) pre print

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 \sqrt{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. Energy losses due to drag on turbine support structure can be significant in multi-row farms, altering their performance and limiting farm size.

Realizing the Potential of Tidal Currents and the Efficiency of Turbine Farms in a Channel

Vennell, R.,  Renewable Energy,  in press (2012) pre print

Tidal turbines in strong flows have the potential to produce significant power. However, not all of this potential can be realized when gaps between turbines are required to allow navigation along a channel. A review of recent works is used to estimate the scale of farm required to realize a significant fraction of a channel's potential. These works provide the first physically coherent approach to estimating the maximum power output from a given number of turbines in a channel. The fraction of the potential realisable from a number of turbines, a farm's fluid dynamic efficiency, is constrained by how much of the channel's cross-section the turbines are permitted to occupy and an environmentally acceptable flow speed reduction. Farm efficiency increases as optimally tuned turbines are added to its cross-section, while output per turbine increases in tidal straits and decreases in shallow channels. Adding rows of optimally tuned turbines also increases farm efficiency, but with a diminishing return on additional rows. The diminishing return and flow reduction are strongly influenced by how much of the cross-section can be occupied and the dynamical balance of the undisturbed channel. Estimates for two example channels show that realizing much of the MWatt potential of shallow channels may well be possible with existing turbines. However unless high blockage ratios are possible, it will be more difficult to realize the proportionately larger potential of tidal straits until larger turbines with a lower optimum operating velocity are developed.

Estimating the Power Potential of Tidal Currents and the Impact of Power Extraction on Flow Speeds

Vennell, R.,Renewable Energy, 36, 3558-3565, doi:10.1016/j.renene.2011.05.011 (2011) pre print

A simple method for estimating the potential of currents in tidal channels to produce power is presented. The method only requires measurement of the peak tidal volume transport through the channel without turbines, along with a bottom drag coefficient and the channel’s dimensions. A recent existing method for estimating potential requires measurements of the undisturbed transport as well as water levels at both ends of the channel to give the head loss. The adaption of the existing method presented here exploits analytic solutions for the transport and optimal farm drag coefficient and does not require measurement of the head loss. The equations presented allow both the channel’s potential and the flow reduction due to power extraction to be estimated using a calculator. Thus the presented method has much of the ease of use of the older KE flux method, but is more reliable as it includes retardation of the flow by the turbines. The presented method can be used for the initial assessment of channels to determine whether the additional measurements required to use the existing method are warranted. It can also be used where the headloss in the channel is too small to measure reliably. The presented equations enable the maximum power available to be simply traded off against environmentally acceptable flow speed reduction. The presented method is applied to two example channels. Cook Strait NZ has an estimated potential of 15 GW, while the entrance channel to Kaipara Harbour has a potential between 110 MW and 240 MW.

Tuning Tidal Turbines In-Concert to Maximise Farm Efficiency

Vennell, R., Journal of Fluid Mechanics, 671, 587–604, doi:10.1017/S0022112010006191 (2011) pre print

Tuning is essential to maximise the output of turbines extracting power from tidal currents. To realise a large fraction of a narrow channel's potential, rows of turbines not only have to be tuned for a particular tidal channel, they must also be tuned in the presence of all the other rows, ie ``tuned in-concert''. The necessity for in-concert tuning to maximise farm efficiency occurs because the tuning of any one row affects a channel's total drag coefficient and hence the flow through all other rows. Surprisingly in several circumstances the optimal in-concert tunings are the same or almost the same for all rows. Firstly, in both constricted and unconstricted channels, rows with the same turbine density have the same optimal tuning. Secondly turbine rows in channels with a quasi-steady dynamical balance typically have almost the same optimal in-concert tunings, irrespective of their turbine density or any channel constrictions. Channel constrictions, occupying a large fraction of the cross-section or adding more rows of turbines also make optimal tunings more uniform between rows. Adding turbines to a cross-section increases a farm's efficiency. However, in a law of diminishing returns for quasi-steady channels, turbine efficiency (the output per turbine) decreases as turbines are added to a cross section. In contrast for inertial channels with only moderate constrictions turbine efficiency increases as turbines are added to a cross-section.

Tuning Turbines in a Tidal Channel

As tidal turbine farms grow they interact with the larger scale flow along a channel by increasing the channel's drag coefficient. This interaction limits a channel's potential to produce power. The tuning of the flow through the turbines and the density of turbines in a channel's cross-section also interacts with the larger scale flow, via the drag coefficient, to determine the power available for production. To maximse the power available with the fewest turbines farms must occupy the largest fraction of a channel's cross-section permitted by navigational and environmental constraints. Maximising power available with these necessarily densely packed farms requires turbines to be tuned for a particular channel and turbine density. The optimal through-flow tuning fraction varies from near 1/3 for small farms occupying a small fraction of the cross-section, to near 1 for large farms occupying most of the cross-section. Consequently tunings are higher than the optimal through-flow tuning of 1/3 for an isolated turbine from classic turbine theory. Large optimally tuned farms can realise most of channel's potential. Optimal tunings are dependant on the number of turbines per row, the number of rows, as well as channel geometry, background bottom friction coefficient and the tidal forcing.