Michael Graham - Wind Energy Handbook

The advantages of the pitching to feather method are that the flow around the blade remains attached, and so well understood, and provides good, positive damping. Feathered blade parking and assisted starting are also available.

Pitching to feather has been the preferred pitch control option mainly because the blade loads can be predicted with more confidence than for stalled blades.

The turbine considered in this section is stall regulated and is run at constant rotational speed. More detail about this method of operation will be discussed in the next section, but the main feature is that there is, theoretically, a unique power output for a given wind speed.

When the turbine was under test, the chosen rotational speed was 44 rpm. Energy output and wind speed were measured over one‐minute time intervals and the average power and wind speed determined. The test was continued until a sufficient range of wind speeds had been covered. The one‐minute average results were then sorted in ‘bins’ 0.5 m/s of wind speed wide, and a fairly smooth power vs wind speed curve was obtained, as shown in Figure 3.60.

The turbine has a diameter of 17 m and would be expected to produce rather more power than shown above if operated at a higher rotational speed.

From the data in Figure 3.60, the C P ‐ λ curve can be derived. The tip speed of the blades is ( 44π)/30 rad/s × 8.5 m = 39.2 m/s , the swept area is 8.5 2. π = 227 m 2, and the air density was measured (from air pressure and temperature readings) at 1.19 kg/m 3 .

Figure 3.60 Power vs wind speed curve from the binned measurements of a three blade stall‐regulated turbine.

Figure 3.61 Comparison of measured and theoretical performance curves.

Therefore,

(3.96)

The mechanical and electrical losses were estimated at 5.62 kW, and this value was used to adjust the theoretical values of C P. The resulting comparison of measured and theoretical results is shown in Figure 3.61.

This comparison looks reasonable and shows that the theory is reliable, but the quality of the theoretical predictions really relies upon the quality of the aerofoil data. The blade and aerofoil design are the same as given in Section 3.11.

Figure 3.62 Measured raw results of a three blade wind turbine.

One last point should be made before classifying the theory as complete: it would be as well to look at the raw, one‐minute average data before it was reduced down by a binning process; this is shown in Figure 3.62. In the post‐stall region, there seems to be a much more complex process taking place than the simple theory predicts, and this could be caused by unsteady aerodynamic effects or a bistable separation condition.

The quantity of energy that can be captured by a wind turbine depends upon the power vs wind speed characteristic of the turbine and the wind speed distribution at the turbine site.

Wind speed distribution is discussed in Section 2.4. The distribution at a given site is described by a probability density function, Eq. (2.3), with parameters specified for the site.

A performance curve is shown in Figure 3.63for a turbine designed with an optimum tip speed ratio of 7. As an example, assume that this turbine is stall regulated and operates at a fixed rotational speed at a site where the average wind speed is 6 m/s and the Weibull shape factor k = 1.8, then, from Eq. (2.2), the scale factor c = 6.75 m/s.

Figure 3.64shows the K P ‐1/λ curve for the turbine: from inspection of that curve the tip speed ratio at which stall (maximum power) occurs is 3.7, and the corresponding C Pis 0.22.

The required maximum electrical power of the machine is 500 kW, the transmission loss is 10 kW, the mean generator efficiency is 90%, and the availability of the turbine (amount of time for which it is available to operate when maintenance and repair time is taken into account) is 98%.

Figure 3.63 C P ‐λ curve for a design tip speed ratio of 7 at 7 m/s.

Figure 3.64 K P ‐1/λ curve for a fixed‐speed, stall‐regulated turbine.

The maximum rotor shaft power (aerodynamic power) is then

(3.97)

The wind speed at which maximum power is developed (where dC P/dλ = 3C P/λ for fixed speed) is 13 m/s, therefore the rotor swept area must be, assuming an air density of 1.225 kg/m 3,

The rotor radius is therefore 24.6 m.

The tip speed of the rotor will be 3.7 × 13 m/s = 48.1 m/s, and so the rotational speed will be

The power vs wind speed curve for the turbine can then be obtained from Figure 3.64.

(3.98)

since wind speed = 48.1 m/s / λ , and these are shown in Figure 3.65.

To determine the energy capture of the turbine over a time period T , the product of the power characteristic P(u) with the probability f(u) is integrated with respect to time over T . This can be converted to an integral with respect to wind speed u over the wind speed range, since f(u) is the proportion of time T spent at wind speed u , and therefore:

(3.99)

with

(3.100)

P(u)f(u) can be plotted against u as in Figure 3.66and then integrated over the operational wind speed range of the turbine to give the total energy capture.