Burton T. (et. al.) Wind energy Handbook

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rotational speed; the pitch angle should always return to the optimum setting for

highest efﬁciency. Pitch control regulation is also required in conditions above the

rated wind speed when the rotational speed is kept constant.

4.5 Estimation of Energy Capture

The quantity of energy that can be captured by a wind turbine depends upon the

power versus wind speed characteristic of the turbine and the wind-speed distribu-

tion at the turbine site. The wind-speed distribution at a site can be represented by

the Weibull function: the probability that the wind speed will exceed a value U is

F(U) ¼ e

 U=c

ðÞ

(4:2)

where c, called the scale factor, is a characteristic speed related to the average wind

speed at the site by

c ¼

ˆ 1 þ



(4:3)

(ˆ being the gamma function and k is a shape parameter, see also Section 2.4). Let

U ¼ u a normalized wind speed.

The wind speed distribution density is then the modulus of the derivative of

Equation (4.2) with respect to u:

f (u) ¼ k



k1





(4:4)

i.e., the probability that the wind speed lies between u and u þ u is f(u)u.

Alternatively, Equation (4.4) gives the proportion of time for which the wind speed

u will occur.

The performance curve shown in Figure 4.14 is for a turbine designed with an

optimum tip speed ratio of 7. As an example, assume that the 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 Weibell shape factor k ¼ 1:8 then, from Equation (4.3), the

scale factor c ¼ 6:75 m=s.

Figure 4.15 shows the K

–1=º 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

is 0.22.

The required maximum electrical power of the machine is 500 kW, the transmis-

sion loss is 10 kW, the mean generator efﬁciency is 90 percent 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 percent.

The maximum rotor shaft power (aerodynamic power) is then

ESTIMATION OF ENERGY CAPTURE 185

¼ 500=0:9 þ 10 ¼ 567 kW

The wind speed at which maximum power is developed is 13 m=s, therefore the

rotor swept area must be, assuming an air density of 1:225 kg=m

567 000=(1=2 3 1:225 3 13

3 0:22) ¼ 1:92 3 10

The rotor radius is therefore 24:6m.

0 5 10 15

0.5

0.4

0.3

0.2

0.1

Figure 4.14 C

– º Curve for a Design Tip Speed Ratio of 7

0 0.1 0.2 0.3 0.4 0.5 0.6

0.002

0.004

Figure 4.15 K

–1=º Curve for a Fixed Speed, Stall-regulated Turbine

186

WIND-TURBINE PERFORMANCE

The tip speed of the rotor will be 3:7 3 13 m=s ¼ 48:1m=s and so the rotational

speed will be 48:1=24:6 rad=s ¼ 1:96 rad=s, which is 1:96 3 60=2 rev=min ¼

18:7 rev=min.

The power versus wind-speed curve for the turbine can then be obtained from

Figure 4.15.

Power (electrical) ¼ (K

3 1:225 kg=m

3 (48:1m=s)

3 1:92 3 10

 10 3 1000 W) 3 0:9

Wind speed ¼ 48:1m=s=º

To determine the energy capture of the turbine over a time period T multiply the

power by f (u ) 3 T (Equation 4.4); because f (u) is the proportion of time T spent at

a normalized wind speed u.

f (u)u ¼

T

(4:5)

and

f (u)du ¼ 1(4:6)

Plot power against u and integrate over the operational wind-speed range of the

turbine to give the energy capture.

The operational speed range will be between the cut-in speed and the cut-out

speed. The cut-in speed is determined by the transmission losses and is the wind

speed at which the turbine begins to generate power. The cut-in speed is usually

0 5 10 15 20 25

600

400

200

U (m/s)

(kW)

Figure 4.16 Power versus Wind Speed

ESTIMATION OF ENERGY CAPTURE 187

chosen to be somewhat higher than the zero power speed, in the present case, say

4m=s.

The cut-out speed is chosen to protect the turbine from high loads, usually about

25 m=s.

The energy captured over a time period T (ignoring down time) will be

P(u) f (u)du ¼ E (4:7)

which is the area under the curve of Figure 4.17 times the time period T.

Unfortunately, the integral does not have a closed mathematical form in general

and so a numerical integration is required, such as the trapezoidal rule or, for better

accuracy, Simpson’s rule.

For a time period of 1 year T ¼ 365 3 24 h. Therefore, for the 10 data points

shown in Figure 4.18, the energy capture will be, using the trapezoidal rule,

E ¼ 0:98T

i¼1

iþ1

f (u

iþ1

) þ P

f (u

))

iþ1

 U

)

(4:8)

where

E ¼ 4:5413 3 10

kWh

Even though the upper limit of integration u

¼ 4:17 is greater than highest value

of u shown in Figure 4.18 it is clear that almost no energy is captured between those

speeds.

A turbine which has pitch control would be able to capture more energy but at

the expense of providing the control system and the concomitant reduction in

0 1 2 3 4 5

100

(u)f(u)

Figure 4.17 Energy Capture Curve

188

WIND-TURBINE PERFORMANCE

reliability. A turbine operating at variable speed (constant tip speed ratio) until

maximum power is reached and thence at constant speed, constant power and pitch

control, see Figure 4.19, would capture the maximum possible amount of energy in

a given time.

The annual energy capture would be

E ¼ 4:8138 3 10

kWh

which is a 6 percent increase in energy capture compared with the ﬁxed-speed,

stall-regulated machine. Whether or not the increase in captured energy is econom-

ically worthwhile is a matter for debate.

0 1 2 3 4 5

100

)f(U

)

Figure 4.18 Energy Capture Curve for Numerical Integration

0 5 10 15 20 25

600

400

200

U (m/s)

(kW)

Figure 4.19 Power Curve for Variable Speed Turbine

ESTIMATION OF ENERGY CAPTURE 189

4.6 Wind-turbine Field Testing

4.6.1 Introduction

Wind-turbine ﬁeld testing is undertaken in the main for two different reasons. First,

as part of the development of new designs, manufacturers and researchers under-

take a wide range of measurements to check on the operation of a given machine

and in some instances to validate wind turbine models used in the design process.

The second, and perhaps the most common, reason for testing is to establish the

performance of a given wind turbine for commercial reasons. Because in the second

case the objectives are better deﬁned and since many of the problems are common

to both sorts of tests, there will be a concentration on performance measurement.

Performance measurement is also the area best covered by agreed standards and

recommendations, although some difﬁculties and inconsistencies still remain. It

should be mentioned that testing is also increasingly undertaken, in a commercial

context by the operators, to verify the manufacturer’s performance warranty. Such

tests will tend to follow the agreed performance testing methodology although the

context is often more demanding, involving possibly complex terrain and also the

inﬂuence of adjacent turbines.

There are other specialized tests that are of importance, such as for determining

the acoustic emission characteristics, and the assessment of noise at a given site.

Other areas such as the evaluation of fatigue, including the associated mechanical

loads, and power quality can involve direct measurement.

This section will provide an overview of ﬁeld testing, and in particular will:

• describe the reasons for undertaking ﬁeld testing,

• identify recognized testing procedures,

• examine practical aspects of transducers and data loggers,

• discuss the difﬁculties associated with aerodynamic performance assessment,

and

• look at errors and uncertainty.

4.6.2 Information sources for wind-turbine testing

Wind turbines have increasingly become part of mainstream technology over the

last decade, and this is reﬂected by the attention paid to them by the national and

international standards bodies.

International Electro-technical Commission (IEC)

The IEC is currently developing a range of standards speciﬁcally applicable to wind

turbines. The work is being undertaken in the main by its TC88 Technical Committee,

190 WIND-TURBINE PERFORMANCE

and covers power performance, acoustics, blade testing, mechanical loads and power

quality. Power performance testing is covered by the published IEC standard 61400-

12 (1998). The IEC standard also exists as a British and European Standard BS EN

61400-12:1998. All national standards bodies have a responsibility which extends to

any signiﬁcant technology. Accordingly, national standards committees have been

formed in most countries to cover wind energy technology. In many instances these

merely formalize the national participation in international standards formation, and

tend to adopt acceptable international standards as national standards.

CENELEC

CENELEC is a European committee, concerned with electro-technical matters,

which has established a task force to manage the harmonization of safety and

testing standards in support of various European Union Directives. The task force

is presently assessing the adequacy of evolving IEC standards and may, or may not,

issue its own standards relevant to wind turbines in the future.

International Energy Agency (IEA)

In the early days of wind energy, prior to the involvement of the standards

organizations, the IEA took the lead in drawing up recommendations, or informal

codes of practice. The IEA codes of practice have been highly inﬂuential, and

covered power performance, acoustics, power quality and fatigue.

MEASNET

Most western European countries have established national wind test sites. There

has been a tradition of close co-operation between these sites and, supported by the

European Commission, many useful documents have been developed by ECWETS

(the European Community Wind Energy Test Station). More recently, the MEAS-

NET network for the promotion of quality, common interpretation and mutual

recognition in testing standards, was created.

MEASNET is a European collaboration of experts concerned with establishing

rigorous standards for all measurement procedures related to wind energy. In

particular, they have drawn up draft guidelines for ‘power performance measure-

ment procedure’. Although heavily reliant on the IEC Standard, they are in some

areas more precise.

4.7 Wind-turbine Performance Measurement

In the ﬁnal analysis, wind-turbine performance is concerned with the estimation of

long-term energy production expected on a given site. The wind resource is

WIND-TURBINE PERFORMANCE MEASUREMENT 191

described by the probability distribution (usually annual) of 1 h (sometimes,

10 min) mean wind speeds. To calculate the average energy production for a given

probability distribution of wind speeds a relationship between wind speed and

wind power is needed—this is the power curve of the wind turbine. As dynamic

effects are not of interest for long-term performance, averaging of the measured

wind speed and wind turbine power is carried out which improves the correlation

between them and attenuates the effects of wind turbulence. This is not to say that

site turbulence is irrelevant—a point which will be dealt with later.

It is also important to note the power from the wind turbine which is of relevance

here is the net power, deﬁned as the power available from the wind turbine less

power needed for control, monitoring, display or maintaining operation. In other

words it is the power available to the user and is measured at the point of

connection to the network.

4.7.1 Fie ld testing methodology

Although a few years ago, the International Energy Agency (IEA) recommended

practices for wind turbine testing which were the nearest thing to an agreed

procedure for wind turbine evaluation. Now, as mentioned, an IEC standard is

available: IEC 61400-12: Wind-turbine Generator Systems, Part 12:- Wind-turbine

Power Performance Testing (1998). It is interesting to contrast it with Volume 1 of

the IEA recommendations (1982) and subsequent editions (1990), which deal with

power performance testing. These notes will draw on both the IEC standard, which

forms the basis of European and national standards, and its precursor IEA

documents. It is essential that the IEC standard, and any amendments which may

have been agreed, be obtained before contemplating power performance measure-

ments.

The wind turbine should ideally be located on a site free from obstructions and

local topographic features which could affect the measurements; the IEC standard

speciﬁes relevant criteria. Site calibration is needed for non-ideal sites, and the IEC

document also includes an approach, included as Annex B (designated ‘informa-

tive’ in contrast to the compulsory, ‘normative’ content of the Standard). This is to

facilitate the evaluation of machine performance in situ, within a commercial wind

farm, which is unlikely to conform to the test site requirements. However, MEAS-

NET ﬁnd that this calibration procedure is not rigorous enough, and have recom-

mended an alternative method. Testing should be conducted under ‘natural’

conditions which excludes towing tests, testing while it is raining (or other

precipitation) and when ice accumulates on the turbine, all of which affect wind

turbine performance and should be avoided. If conditions like rain do occur during

the tests the data affected should be appropriately demarcated. Clearly, modiﬁca-

tions or adjustments should not be made to the wind turbine during the period of

data collection.

The test procedure consists of taking a series of measurements of wind speed,

wind direction, atmospheric pressure and temperature, net power and in some

circumstances rotor speed. These measurements should be taken over as wide a

range of wind speeds as possible. All data should be checked for accuracy and

192 WIND-TURBINE PERFORMANCE

consistency and if any of the variables have been found to be misread the sample

should be discarded. Data collected while the anemometer is in the wake of the

wind turbine or in the wake of the anemometer tower, or other obstacle, should also

be discarded.

4.7.2 Wind-speed measurement

Wind speed is the most critical parameter to be measured so considerable emphasis

should be placed on its accuracy. According to the IEA (1982) the anemometer

should have an accuracy of 5 percent or better over the range of relevant wind

speeds and according to the revised IEA recommendation (1990) it should be

accurate to 0:1m=s or less for wind speeds between 4 and 25 m/s. Finally the IEC

have opted to eschew a stated precision, and require instead calibration against a

traceable instrument. The instrument should be calibrated, before and after the test,

so as to establish that its accuracy has been maintained throughout the test

(MEASNET have documented a speciﬁed calibration procedure). To avoid pro-

blems, it is advisable to run in a new anemometer for a period of about 2 months

before use, to allow the bearings to ease. Another characteristic of an anemometer is

its distance constant, which the IEC states, should be 5 m or less. The distance

constant is an indication of the response of the anemometer and is deﬁned as the

length of wind run which must pass the anemometer for its output to reach

(1 1=e) ¼ 0:63 of its ﬁnal value. Large distance constants can give rise to a signiﬁ-

cant over speeding effect because the cup anemometer responds more quickly to

increases in wind speed than decreases, and this is the reason for the 5 m cut off in

the standard. Some believe that, even with a distance constant of 5 m, the instru-

ment should be assessed to evaluate the likely over-speeding error, and a correction

applied if necessary. The IEC allow this as the accuracy can be shown to be

improved.

The wind speed that is measured should be as representative as possible of wind

which would have been present in the plane of the rotor in the absence of the wind

turbine. The desired velocity never exists and so a suitable upstream velocity is

selected instead. The anemometer location is generally chosen so as to minimize

any interference from the wind turbine rotor itself whilst maintaining a reasonable

correlation between the measured wind speed and the output from the wind

turbine. Between 2 and 4 rotor diameters from the wind turbine is stated in the IEC

standard, which recommends 2.5 diameters as the optimum. This compares with

the 2 and 6 diameters recommended by the IEA. If the anemometer were placed

signiﬁcantly nearer than 2 diameters, correction for the velocity deﬁcit caused by

the rotor would have to be made.

Although corrections can in theory be made to take account of wind shear for

anemometers not at hub height, this is discouraged and whenever possible the

wind speed should be measured at the same height (relative to ground level) as

the hub of the wind turbine rotor. The IEC specify a height within 2.5 percent of the

turbine hub height.

As already mentioned, the anemometer must not be located in the wake of the

turbine, or other signiﬁcant obstacles on the site, including of course other wind

WIND-TURBINE PERFORMANCE MEASUREMENT 193

turbines, operating or otherwise. Figure 4.20, taken from the Standard, shows the

allowed location in relation to the turbine being measured, with the exclusion zone

dependent on the distance from the turbine. A precise speciﬁcation exists in the

Standard for the calculation of all other exclusion zones.

Poor location of the anemometer on the tower has recently been identiﬁed as a

potential cause of error and for the ﬁrst time with the IEC standard, precise

guidelines exist. These reﬂect the need to avoid mast wake effects and any signiﬁ-

cant blockage in the vicinity of the instrument. An ideal location is on a vertical tube

clear of the top of the meteorological mast.

To speed up the experimental assessment it is common to use more than one

meteorological mast, arranged so that at least one anemometer is free of any

exclusion zone at any given time.

4.7.3 Wind-direction measurement

The wind direction is monitored so as to eliminate wind-speed data taken in the

excluded zones. The wind vane should be located at the same height as the

anemometer (within 10 percent of the hub height) and in its proximity but not so as

to interfere with the wind-speed measurement. The IEC requires an absolute

accuracy better than 5 degrees for the direction measurement.

4.7.4 Air temperature and pressure measurement

For a given wind velocity the energy in the wind depends on the air density. So as

to be able to correct for changes in air density, the air temperature and pressure

should be measured. At high temperatures it is recommended that relative humid-

Wind

WTGS

2 D

2,5 D

Meteorology mast at 4 D

Distance of meteorology

mast to WTGS between

2 D and 4 D, 2,5 D is

recommended

Disturbed sector due

to wake of WTGS

on meteorology

mast; sector angle

taken from annex A:

103 at 2 D

93 at 2,5 D

74 at 4 D

Maximum measurement sector:

257 at 2 D

267 at 2,5 D

286 at 4 D

Figure 4.20 Anemometer Placement in Relation to Turbine

194

WIND-TURBINE PERFORMANCE