According to the Global Wind Energy Council, in early 2016 there were 314,000 wind turbines worldwide with a total installed capacity of 433 GW. "With an increasing number of installed turbines eventually – especially in windy regions – wind farms will increase in size," Patrick Volker of the Technical University of Denmark told environmentalresearchweb. "This is obvious in the plans in the North Sea, where wind-farm clusters will eventually merge to bigger wind farms. It is now important to better understand the wake losses inside wind farms."

The North Sea is currently the largest contributor to offshore wind energy worldwide. Its Dogger Bank area is under consideration for extensive wind-farm development. The 15,000 square km region could support a cluster of nine medium-sized wind farms, each 35 km apart, according to Volker and colleagues. For a wind farm with an intermediate turbine spacing, this would result in an annual energy production of around 68 TWh, more than one-fifth of UK electricity consumption in 2014.

To come up with their results, Volker and colleagues modelled the wind-speed conditions at small (5 km × 5 km), medium (18.5 km square), large (170 km x 170 km) and very large (338 km × 338 km) wind farms with turbines in square arrays with spacings of 420 m, 560 m or 840 m. They assumed the turbines were Vestas V80s, which have a nominal output of 2 MW, a 70 m high hub, an 80 m rotor diameter and produce electricity for wind speeds of 4–25 m/s. The turbines were modelled as drag devices, with the drag increasing for wind speeds up to around 12 m/s. At higher speeds the power production is at the rated power level and the turbine pitches its blades to reduce drag.

The largest offshore wind farm to date is the London array off the south-east of the UK, which has 175 3.6 MW turbines covering 100 square km – smaller than the study’s definition of medium size.

The team chose three locations for their model farms – one onshore with moderate winds (median wind speed 7.4 m/s), similar to the Great Plains in the US, and two offshore, one with strong winds (9.1 m/s) to represent the North Sea, and one with very strong winds (13.1 m/s) like the Strait of Magellan, Gulf of Suez and Somalian Indian Ocean, which have substantial potential for wind energy.

"To make as efficient as possible use of wind energy, we should consider the local wind and surface conditions when constructing wind farms," said Volker. "In offshore regions with very high wind speeds, small wind farms are extremely efficient, but also very large wind farms with a wide (around 10 rotor diameter) turbine spacing would remain efficient electricity generators."

This means that small wind farms are appropriate for compact areas of high wind such as the Gulf of Suez or Kenya’s Lake Turkana, whilst very large wind farms would suit larger high-wind-speed regions.

As wind farms grow larger, they could become less productive because of decreasing wind speeds resulting from successive turbine wakes. The wake from each turbine can extend for hundreds of rotor diameters downstream. Balancing this drop in wind speed is an influx of momentum from turbulent air from above. As a result of these two opposing factors – one acting to decrease and one to increase wind speeds – after the wind has travelled a certain distance into the interior of the wind farm and interacted with a number of turbines it may reach an equilibrium speed.

Because the influx of momentum from above depends on how turbulent the air is surrounding the wind farm, as well as on wind speed, wind farms behave differently onshore to offshore. On land the surface roughness is relatively high and creates more turbulence compared to the ocean, where the surface roughness is lower but varies with wind speed. So onshore the factor acting to restore wind speed after interaction with a turbine may be higher. Turbine spacing and wind speed also affect the balance of the opposing factors.

As a result of all these interactions, offshore, the team’s model showed, clusters of smaller wind farms are generally preferable to larger farms, unless the winds are very strong. Onshore very large wind farms are an option even for regions with moderate winds, although such farms will have a lower power density than offshore.

If there were no turbine wakes, the power density of the wind farm, known as the reference power density, would increase with wind speed and narrower turbine spacings. For an onshore very large wind farm with moderate winds, the researchers found that the actual power density, which includes wake effects, is limited to around 1 W per square metre. In these wind conditions a farm will reach this limit when the turbines are closer together than the intermediate spacing of 560 m. At that point, reducing the turbine spacing further would not increase the actual power density.

Previously, based on analysis of hypothetical wind farms in the Great Plains area of the US, scientists had thought that all very large wind farms might be limited to a power density of 1 W per square metre. But Volker and colleagues discovered that very large wind farms offshore may reach power densities some 3.5 times higher.

"For onshore regions with moderate winds our results agree with those from previous research," said Volker. "However, in regions with very strong winds the power density of a very large wind farm could exceed even 3.5W per square metre, because the wind speed deep inside the wind farm remains high due to the large turbulent influx of momentum from above the wind farm and the fact that the turbine's drag decreases at higher wind speeds."

In a very-high-wind-speed offshore site, the annual 1 TWh produced by a small wind farm – with 81 × 2MW turbines – would be 40% higher than that of the Danish offshore wind farm Horns Rev I. A very large wind farm at the same extremely windy site, with 161,604 × 2MW turbines, would produce 1.7 PWh each year, enough to supply more than 7% of global electricity consumption.

"In offshore regions with slightly lower, but still good, winds, the turbulence levels over the smooth water are not high enough to compensate the turbine drag," said Volker, "for this reason very large wind farms become less efficient electricity generators. Instead, in these conditions almost all turbines in smaller wind farms (25–342 square km) benefit from the good wind conditions."

Onshore in moderate winds, such as on the Great Plains, very large wind farms with a wider turbine spacing are more efficient then smaller wind farms with turbines close together. "In these onshore regions mixing is caused by the high roughness guaranteeing that turbines deep inside the wind farm remain efficient as long as the turbine spacing is wide," said Volker. "One very large wind farm would produce around 690 TWh annually, which is nearly 17% of the total US electrical consumption."

Volker says there are many interesting problems remaining, such as finding the best use of space for wind farms in a specific region to maximize efficiency and "given that wind farms are optimized to reduce internal wake losses, especially in the North Sea, what are the consequences to neighbouring wind farms, considering that the wake behind the wind farm could become more pronounced?"

Volker and colleagues reported their findings in Environmental Research Letters (ERL).

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