Yet the term capacity factor has a clear meaning and purpose throughout the power industry (see box). It is a standard measure of expected energy output from a power plant over a given period and therefore an important tool for power system planners.

Here is the fundamental dilemma. The capacity factors applied to wind plant today are of little use and often of great disservice. Yet to be treated as serious suppliers of power, the wind business must use this measure of energy output. A way has to be found of making it more meaningful.

The root of the problem

Wind turbine capacity factors mislead simply because there is no standard way of defining "rated power" for wind turbines -- and capacity factors are calculated from rated power. The rated power of thermal plant is unambiguous -- it is the maximum output of the plant -- and this output is usually maintained for long periods. With wind turbines, the rated output may be the maximum -- or it may be less. What is more, the rated power is only achieved for short periods (about 10-15% of the time). And, as if that did not introduce enough confusion, the average power output from a wind turbine is only about one-third of the rated value.

The root of the problem is the variability of the wind. At what level does a wind turbine designer fix the rated power? The power in the wind varies as the cube of the wind speed and it makes sense, therefore, to try and capture as much of this power as possible. However, the higher the rating, the less time a turbine will generate at maximum output (and the lower the capacity factor). There is no sense in designing machines to convert all the power in the wind at 20 m/s, since the wind blows at this speed for less than 1% of the time. A 25 metre diameter wind turbine could deliver around 1 MW at this wind speed, but the result would be a very costly machine, strengthened to withstand the loads at a power output of 1 MW, but hopelessly uneconomic. Conversely, the lower the rating, the more power will need to be rejected in high winds.

A manufacturer's choice of generator size depends on his assessment of the balance between the costs of higher output -- a larger generator and gearbox plus other items -- and the value to his customers of higher energy production. There is no universal economic optimum rating for a machine of given size.

A hazardous procedure

Since there are these wide disparities in how to rate turbines the use of capacity factors to compare the performance of two different machines is an extremely hazardous procedure. It simply does not follow that the machine with the higher capacity factor will produce more energy -- often the reverse is true. This can be seen in a comparison of the capacity factors and energy production for two 25 m diameter machines -- the HMZ 300 kW and the Vestas 200 kW (Fig. 1). The HMZ machine, clearly, can squeeze more power out of the air on account of its higher rating, but its capacity factors are lower. The reason for the apparent anomaly is quite simple. If the rated output of a machine of given size is increased by, say, 20%, the extra energy gain is much less than this -- around 5%. The energy production (in the numerator) therefore goes up by 5%, the rated power (in the denominator) goes up by 20% and the capacity factor comes down by about 15%, even though the energy production has risen.

The link between turbine rating and annual energy output is seen in comparisons of machines of different sizes. One of the best examples is to compare the world's biggest wind turbine with the most powerful. The biggest was the 100 m Growian machine in Germany, rated at 3 MW. The most powerful was the 78 m Hamilton Standard WTS-4 machine, rated at 4 MW. Since the rating was high for its size, capacity factors for the Hamilton Standard machine were low, but these did not imply that the machine was inefficient.

In today's world of commercial machines those destined for high wind speed sites tend to be given generators with a high rating. The reason for this is that the steady increase in output with increased rating is more pronounced in higher wind speeds (Fig 2). It is simply not worth fitting a machine destined for a low wind speed site with a generator of high rating. The energy production data plotted in Fig 2 has all been taken from manufacturers' published energy figures and gives an insight into why rating philosophies vary. The wide variations in rating philosophy between manufacturers means there is a wide spread when capacity factors are compared with energy outputs. Data from many machines in the Eurowin database illustrate the wide variation (fig 3)

Apart from differences in rating philosophy, the different design options have a bearing on machine ratings and energy productivity (fig 4). Another complication is the existence of pitch controlled, stall controlled and variable speed machines. For each a slightly different relationships between energy and capacity factor may be expected since the output varies:

¥ variable speed machines operate at (nominally) constant efficiency until rated power, beyond which the power is constant.

¥ variable pitch machines operate at fixed speed and variable efficiency up to rated power after which it levels out and becomes constant.

¥ stall regulated machines need to have pitch setting angles adjusted so as to limit the maximum power -- with some possible loss of efficiency both above and below rated power

¥ stall regulation can also be achieved by varying the speed of a rotor, once it has reached rated power.

As the power from stall regulated machines varies continuously with wind speed, the "rated" power is not clearly defined. Most manufacturers do not use the maximum power achieved by the rotor, introducing further complications. Some, with an understanding of the good public relations' to be earned with a high capacity factor, fix the rated power well below the peak and achieve high capacity factors as a result. Apparent improvements in capacity factor can also be achieved by all types of wind turbine through clever selection of the nominal rated power. Others, with an eye on subsidies linked to rated power, fix the rating at peak level, which results in the wind plant having an extremely low capacity factor.

Solving the dilemma

Can capacity factors be re-defined so that a single number becomes both meaningful and useful? One solution would be to abandon the concept of capacity factor altogether and concentrate instead on presenting all energy production data on a basis of annual kilowatt-hours per square metre of rotor swept area (Fig 5). This is a more useful guide to a wind turbine's output and enables comparisons to be made between machines of different size. It is also exact and will continue to be used in specialist studies. But, although it may be scientifically elegant, it lacks the perspective of simplicity. Neither would it fit the standard terminology of the power industry.

The key to unravelling the anomalies is to find a way of defining rated power which makes capacity factors meaningful. It seems that new certification rules for wind turbines, now being developed, are likely to link rated power to the maximum power produced by a rotor -- but this will do nothing to dispel the confusion. The fundamental problem of deriving capacity factor from turbine ratings remains: the higher the rating, the higher the energy output, but the smaller the gains at a given wind speed and the lower the capacity factor. In other words more energy does not necessarily mean a higher capacity factor.

The temptation could be to solve this problem by specifying a standard power rating in watts per square metre of rotor area, known as the specific rated power. Although there are no hard and fast rules, most machines are now designed to reach their maximum output at around 12 m/s and the rated power of the machine divided by the swept area of the rotor usually comes out between 350 and 600 watts m2. But the specific rated power of a wind turbine calculated in this way gives rise to a rather theoretical figure from which it is not easy to calculate a capacity factor.

Possibly the best way forward, one which links simplicity with relevance, would be to adopt a formula similar to that in the German 250 MW programme. Here, the rated power used is defined as the power output from the wind turbine at a specified wind speed. If a wind speed of around 12m/s were used -- close to the level at which most machines reach their rated output -- this would have very little effect on the capacity factor of most pitch-regulated wind turbines (fig 4), but would make them comparable. It would also eliminate the uncertainties over the rating of stall-regulated machines and yield fair numbers for both variable speed and stall-regulated wind designs. It would certainly enable calculation of a far more meaningful capacity factor -- and allow more balanced comparisons to be made between the outputs from machines of widely differing designs. Last, but by no means least, price comparisons between machines -- often made on a $ per kW basis -- would also become meaningful for the first time.

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