Broadly speaking, none of these early prototypes spawned commercial designs and the quest for large turbines slowed after the 1980s. The introduction of market incentives, initially in California, US, and later in Denmark and elsewhere, led to the construction of many thousands of machines that are quite small by today’s standards — 50-100kW, with a 15 to 20-metre diameter. But over the years, a process of what might be termed technical evolution has taken place, bringing a steady growth in size and output. Several commercial types of wind turbines now have ratings in excess of 3MW and rotor diameters of up to 80 metres; machines for the offshore market have outputs up to 6MW and diameters up to 126 metres.
The issue of the most economical size of wind turbine has been debated for many years. As the market has evolved, the preferred size has gradually increased. The average rating of turbines installed in Germany in 1992 was 180kW. By 2008 it had reached just under 2MW, which is an increase of more than ten times. And wind turbine size is likely to continue to grow.
Tall and efficient
It is fairly easy to explain the enthusiasm for large turbines. First, they are more productive. In Germany in 2009, a 2.3MW turbine, delivering 1,337kWh per square metre of rotor area was the most productive machine (Windpower Monthly WindStats, Spring 2010). Out of the 85 wind turbines that delivered more than 1,000kWh per square metre, only nine were rated at less than 1MW. The improved energy yield of the larger wind turbines is partly because it is more efficient and partly because the rotor is located higher from the ground — and intercepts higher velocity winds. A 1980s 25-metre-diameter turbine with a 25-metre hub height might be exposed to a mean wind speed of 5.5 metres per second, but a multi-megawatt machine with a hub height of 100 metres would be exposed to a speed of around 6.7 metres per second. That extra speed corresponds to around 40% greater yield.Click here for PDF version
The improvements in efficiency account for another 10-15% and include the aerodynamic performance of the rotor, the mechanical efficiency of the gearbox and the overall conversion efficiency of the electrical generator.
The other major reason why large turbines have turned out to be commercially attractive is that they allow economies of scale in foundation materials, in operations and maintenance, and in infrastructure on the site, such as access roads. Put together, these savings can outweigh the higher costs of, say, a 5MW machine over a 3MW machine. Offshore, these advantages become even more significant.
For many years, conventional wisdom suggested that electricity production from wind turbines increased in proportion with the square of the rotor diameter, but that the weight increased in line with the cube of the diameter. As cost tends to be related to weight, it was believed, therefore, that increased costs would eventually outstrip the increased value of the electricity produced — and wind turbine sizes would settle at an optimum level.
While there is an element of sound reasoning behind that maxim, it has not been borne out in practice. Energy production does in fact increase faster than the square of rotor diameter — because the larger wind turbine is exposed to higher wind speeds at greater heights — and experience shows that rotor weights do not increase in line with the cube of the diameter (see graph below). The figure also shows how rated power increases with rotor diameter.
Several manufacturers and research groups are actively involved in the development of 10MW turbines, with rotor diameters of around 160 metres — roughly consistent with the data in the graph below. Extrapolation of this trend suggests that a 200-metre diameter rotor might have blades that weigh just over 160 tonnes with an output power of around 14MW. Rotors of this size are now being researched.
The other reason why it is believed there will eventually be a size limit to horizontal-axis wind turbines is that the stresses around the root of the larger and heavier blade will eventually become critical. When this happens, the strengthened blade weight increases in such a way that a 10% size increase leads to a 61% weight increase, rapidly making them unmanageable. However, there is little sign of this happening yet. Most of the discussions relating to size limits tend to focus on the difficulties of transporting very large components rather than any inherent design problem.
The graph below shows the available data on the weight of complete wind turbines in relation to the diameter of the rotor and suggests that perhaps the critical component might be the weight of the towers, rather than the blades. The graph shows that the total weights of the two largest machines appear to be on a more steeply rising curve than the others, which may be due to the need to prevent buckling of the tower. As the tower is basically a simple structure, however, the additional costs may be modest.
Beyond 200 metres
In order to establish where the turbine size limit is, it is necessary to look at the factors that influence blade construction. Blade design is affected by a number of forces — those that fluctuate and contribute to fatigue stresses, and those that are steady. The thrust on the rotor blades, for example, is key in informing blade geometry, together with the force exerted on the blades when they are subjected to extreme gusts. By comparison, the stresses associated with bending of the blades under their own weight are generally quite modest, but they depend on the strength-to-weight ratio of the blade material and do increase with size.
Eventually, however, the stresses induced by gravity start to dominate and, beyond this point, blade weights increase rapidly due to the increasing thickness that is needed to ensure that stresses are limited to safe levels. As any size limit is likely to be fairly close to this critical diameter, indicative estimates can be derived for a range of blade materials (see chart, right). This suggests that the diameter limit for an ordinary structural steel blade may be about 100 metres, rising to more than 200 metres with glass-reinforced plastic and to nearly 800 metres with carbon-fibre-reinforced plastic. The extensive use of carbon fibre may account for manufacturers’ lack of concern about size limits. Vestas speculates that 20 years from now, giant floating 20MW wind turbines with rotors 250 metres in diameter could be a common sight across the world’s deep ocean waters.