Wind Energy Handbook pot

3 Aerodynamics of Horizontal-axis Wind Turbines 413.4.3 Relationship between bound circulation and the induced velocity 53 3.5.3 The blade element – momentum BEM theory 613.5.4 Determina

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Library of Congress Cataloguing-in-Publication Data

Handbook of wind energy / Tony Burton [et al.].

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 0 471 48997 2

Typeset in 10/12pt Palatino by Keytec Typesetting Ltd, Bridport, Dorset

Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire

This book is printed on acid-free paper responsibly manufactured from sustainable forestry,

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2.2 Geographical Variation in the Wind Resource 122.3 Long-term Wind-speed Variations 132.4 Annual and Seasonal Variations 142.5 Synoptic and Diurnal Variations 16

2.6.5 Length scales and other parameters 232.6.6 Cross-spectra and coherence functions 26

2.8.1 Extreme winds in standards 312.9 Wind-speed Prediction and Forecasting 33

3 Aerodynamics of Horizontal-axis Wind Turbines 41

3.4.3 Relationship between bound circulation and the induced velocity 53

3.5.3 The blade element – momentum (BEM) theory 613.5.4 Determination of rotor torque and power 643.6 Breakdown of the Momentum Theory 65

3.7.2 Optimal design for variable-speed operation 68

3.7.4 Effects of drag on optimal blade design 753.7.5 Optimal blade design for constant-speed operation 773.8 The Effects of a Discrete Number of Blades 78

3.8.3 Prandtl’s approximation for the tip-loss factor 83

3.8.5 Effect of tip loss on optimum blade design and power 873.8.6 Incorporation of tip-loss for non-optimal operation 913.9 Calculated Results for an Actual Turbine 933.10 The Aerodynamics of a Wind Turbine in Steady Yaw 963.10.1 Momentum theory for a turbine rotor in steady yaw 96

3.10.2 Glauert’s momentum theory for the yawed rotor 993.10.3 Vortex cylinder model of the yawed actuator disc 103

3.10.6 Wake rotation for a turbine rotor in steady yaw 1133.10.7 The blade element theory for a turbine rotor in steady yaw 1153.10.8 The blade element–momentum theory for a rotor in steady yaw 1163.10.9 Calculated values of induced velocity 1203.10.10 Blade forces for a rotor in steady yaw 1213.10.11 Yawing and tilting moments in steady yaw 1223.11 The Method of Acceleration Potential 125

3.11.2 The general pressure distribution theory 1263.11.3 The axi-symmetric pressure distributions 1293.11.4 The anti-symmetric pressure distributions 1333.11.5 The Pitt and Peters model 1363.11.6 The general acceleration potential method 137

Appendix: Lift and Drag of Aerofoils 156

A3.4 Boundary-layer Separation 160A3.5 Laminar and Turbulent Boundary Layers 161A3.6 Definition of Lift and its Relationship to Circulation 163

A3.9 Aerofoil Drag Characteristics 168A3.10 Variation of Aerofoil Characteristics with Reynolds Number 169

4.1.1 The CP
º performance curve 1734.1.2 The effect of solidity on performance 174

4.2 Constant Rotational Speed Operation 177

4.5 Estimation of Energy Capture 185

4.6.2 Information sources for wind-turbine testing 1904.7 Wind-turbine Performance Measurement 1914.7.1 Field testing methodology 192

4.7.3 Wind-direction measurement 1944.7.4 Air temperature and pressure measurement 194

4.10 Aerodynamic Performance Assessment 200

4.11.1 Evaluation of uncertainty 204

4.11.3 Estimating uncertainties 2064.11.4 Combining uncertainties 206

5.4 Extreme Loads 2145.4.1 Non-operational load cases – normal machine state 2145.4.2 Non-operational load cases – machine fault state 2155.4.3 Operational load cases – normal machine state 2155.4.4 Operational load cases – loss of load 2175.4.5 Operational load cases – machine fault states 2185.4.6 Start-up and shut-down cases 218

5.5.1 Synthesis of fatigue load spectrum 218

5.6.1 Lift and drag coefficients 2195.6.2 Critical configuration for different machine types 219

5.7 Blade Loads During Operation 2285.7.1 Deterministic and stochastic load components 2285.7.2 Deterministic aerodynamic loads 228

5.7.4 Deterministic inertia loads 2365.7.5 Stochastic aerodynamic loads – analysis in the frequency domain 2395.7.6 Stochastic aerodynamic loads – analysis in the time domain 249

5.8.10 Wind turbine dynamic analysis codes 282

5.9.1 Methodology for blade fatigue design 2875.9.2 Combination of deterministic and stochastic components 2885.9.3 Fatigue predictions in the frequency domain 290

5.10 Hub and Low-speed Shaft Loading 293

Appendix: Dynamic Response of Stationary Blade in Turbulent Wind 313

A5.2 Frequency Response Function 313

A5.2.2 Frequency response function 314A5.3 Resonant Displacement Response Ignoring Wind Variations along the

A5.3.1 Linearization of wind loading 315A5.3.2 First mode displacement response 315A5.3.3 Background and resonant response 315A5.4 Effect of Ac-Wind Turbulence Distribution on Resonant Displacement

A5.4.1 Formula for normalized co-spectrum 319A5.5 Resonant Root Bending Moment 320A5.6 Root Bending Moment Background response 322

A5.8 Bending Moments at Intermediate Blade Positions 326

6.6.2 Limitation of large excursions 349

6.6.4 Teeter stability on stall-regulated machines 349

6.8.1 Independent braking systems—requirements of standards 3576.8.2 Aerodynamic brake options 3586.8.3 Mechanical brake options 360

6.9 Fixed-speed, Two-speed or Variable-speed Operation 360

7.1.2 Aerodynamic design 3787.1.3 Practical modifications to optimum design 379

7.1.5 Blade materials and properties 3807.1.6 Properties of glass/polyester and glass/epoxy composites 3847.1.7 Properties of wood laminates 389

7.1.10 Design against buckling 413

7.6.6 Low-speed shaft brake design 450

7.9.2 Constraints on first-mode natural frequency 454

8 The Controller 4718.1 Functions of the Wind-turbine Controller 472

8.2 Closed-loop Control: Issues and Objectives 475

8.3 Closed-loop Control: General Techniques 4808.3.1 Control of fixed-speed, pitch-regulated turbines 4808.3.2 Control of variable-speed pitch-regulated turbines 4818.3.3 Pitch control for variable-speed turbines 4848.3.4 Switching between torque and pitch control 4848.3.5 Control of tower vibration 4868.3.6 Control of drive train torsional vibration 4888.3.7 Variable-speed stall regulation 4898.3.8 Control of variable-slip turbines 4908.3.9 Individual pitch control 4928.4 Closed-loop Control: Analytical Design Methods 4938.4.1 Classical design methods 4938.4.2 Gain scheduling for pitch controllers 4988.4.3 Adding more terms to the controller 4988.4.4 Other extensions to classical controllers 5008.4.5 Optimal feedback methods 500

9.1.2 Project feasibility assessment 5149.1.3 The measure–correlate–predict technique 514

9.2.2 Design and mitigation 523

10.4.3 Electrical distribution networks 570

10.4.5 Power flows, slow-voltage variations and network losses 57310.4.6 Connection of embedded wind generation 577

10.5.3 Measurement and assessment of power quality characteristics of

grid-connected wind turbines 589

10.7.5 Impact on the generation system 604

A large number of individuals have assisted the authors in a variety of ways in thepreparation of this work In particular, however, we would like to thank DavidInfield for providing some of the content of Chapter 4, David Quarton for scrutinis-ing and commenting on Chapter 5, Mark Hancock, Martin Ansell and ColinAnderson for supplying information and guidance on blade material propertiesreported in Chapter 7, and Ray Hicks for insights into gear design Thanks are alsodue to Roger Haines and Steve Gilkes for illuminating discussions on yaw drivedesign and braking philosophy, respectively, and to James Shawler for assistanceand discussions about Chapter 3

We have made extensive use of ETSU and Risø publications and record ourthanks to these organisations for making documents available to us free of chargeand sanctioning the reproduction of some of the material therein

While acknowledging the help we have received from the organisations andindividuals referred to above, the responsibility for the work is ours alone, socorrections and/or constructive criticisms would be welcome

Extracts from British Standards reproduced with the permission of the BritishStandards Institution under licence number 2001/SK0281 Complete Standards areavailable from BSI Customer Services (Tel þ44 (0) 20 8996 9001)

List of Symbols

Note: This list is not exhaustive, and omits many symbols that are unique toparticular chapters

a axial flow induction factor

a9 tangential flow induction factor

a9t tangential flow induction factor at the blade tip

a0 two-dimensional lift curve slope, (dC1=dÆ)

a1 constant defining magnitude of structural damping

A, AD rotor swept area

A1, AW upstream and downstream stream-tube cross-sectional areas

b face width of gear teeth

c blade chord; Weibull scale parameter

^

cc damping coefficient per unit length

ci generalized damping coefficient with respect to the ith mode

C decay constant

C(
) Theodorsen’s function, where
is the reduced frequency:

C(
) ¼ F(
) þ iG(
)

Cd sectional drag coefficient

Cf sectional force coefficient (i.e., Cdor C1as appropriate)

C1 sectional lift coefficient

Cmn coefficient of a Kinner pressure distribution

Cp pressure coefficient

CP power coefficient

CQ torque coefficient

CT thrust coefficient; total cost of wind turbine

CTB total cost of baseline wind turbine

Cx coefficient of sectional blade element force normal to the rotor plane

Cy coefficient of sectional blade element force parallel to the rotor planeC(˜r, n) coherence—i.e., normalized cross spectrum – for wind speed

fluctuations at points separated by distance s measured in the acrosswind direction

Cjk(n) coherence—i.e., normalized cross spectrum – for longitudinal wind

speed fluctuations at points j and k

d streamwise distance between vortex sheets in a wake

d1 pitch diameter of pinion gear

dPL pitch diameter of planet gear

D drag force; tower diameter; rotor diameter; flexural rigidity of plate

E energy capture, i.e., energy generated by turbine over defined time

period; modulus of elasticity

Ef g time averaged value of expression within brackets

f tip loss factor; Coriolis parameter

f ( ) probability density function

fj(t) blade tip displacement in jth mode

fin(t) blade tip displacement in ith mode at the end of the nth time step

fJ(t) blade j first mode tip displacement

fT(t) hub displacement for tower first mode

F() function determining the radial distribution of induced velocity

normal to the plane of the rotor

F( ) cumulative probability density function

g vortex sheet strength; peak factor, defined as the number of standard

deviations of a variable to be added to the mean to obtain the extremevalue in a particular exposure period, for zero-up-crossing frequency,

g0 peak factor as above, but for zero upcrossing frequency n0

G geostrophic wind speed; shear modulus; gearbox ratio

G(t) t second gust factor

h height of atmospheric boundary layer; duration of time step; thickness

of thin-walled panel; maximum height of single gear tooth contactabove critical root section

H hub height

Hjk elements of transformational matrix, H, used in wind simulation

Hi(n) complex frequency response function for the ith mode

I turbulence intensity; second moment of area; moment of inertia;

electrical current (shown in bold when complex)

IB blade inertia about root

I0 ambient turbulence intensity

Iþ added turbulence intensity

Iþþ added turbulence intensity above hub height

IR inertia of rotor about horizontal axis in its plane

Iu longitudinal turbulence intensity

Iv lateral turbulence intensity

Iw vertical turbulence intensity

Iwake total wake turbulence intensity

j ffiffiffiffiffiffiffi

1p

k shape parameter for Weibull function; integer; reduced frequency,

(øc=2W)

ki generalized stiffness with respect to the ith mode, defined as miø2

i

KP power coefficient based on tip speed

KSMB size reduction factor accounting for the lack of correlation of wind

fluctuations over structural element or elements

KSx(n1) size reduction factor accounting for the lack of correlation of wind

fluctuations at resonant frequency over structural element or elements

K
( ) modified Bessel function of the second kind and order

K() function determining the induced velocity normal to the plane of a

yawed rotor

L length scale for turbulence (subscripts and superscripts according to

context); lift force

Lx

u integral length scale for the along wind turbulence component, u,

measured in the longitudinal direction, x

m mass per unit length, integer

mi generalized mass with respect to the ith mode

mT1 generalized mass of tower, nacelle and rotor with respect to tower

first mode

M moment; integer

M mean bending moment

MT teeter moment

MX blade in-plane moment (i.e., moment causing bending in plane of

rotation); tower side-to-side moment

MY blade out-of-plane moment (i.e., moment causing bending out of

plane of rotation); tower fore-aft moment

MZ blade torsional moment; tower torsional moment

MYS low-speed shaft moment about rotating axis perpendicular to axis of

blade 1

MZS low-speed shaft moment about rotating axis parallel to axis of blade 1

MY N moment exerted by low-speed shaft on nacelle about (horizontal)

y-axis

MZ N moment exerted by low-speed shaft on nacelle about (vertical) z-axis

n frequency (Hz); number of fatigue loading cycles; integer

n0 zero up-crossing frequency of quasistatic response

n1 frequency (Hz) of 1st mode of vibration

N number of blades; number of time steps per revolution; integer

N(r) centrifugal force

N(S) number of fatigue cycles to failure at stress level S

p static pressure

P aerodynamic power; electrical real (active) power

Pmn( ) associated Legrendre polynomial of the first kind

q(r, t) fluctuating aerodynamic lift per unit length

Q rotor torque; electrical reactive power

Qa aerodynamic torque

_

Q rate of heat flow

Q mean aerodynamic lift per unit length

QD dynamic factor defined as ratio of extreme moment to gust quasistatic

moment

Qg load torque at generator

QL loss torque

Qmn( ) associated Legrendre polynomial of the second kind

Q1(t) generalized load, defined in relation to a cantilever blade by Equation

(A5.13)

r radius of blade element or point on blade; correlation coefficient

between power and wind speed; radius of tubular tower

r9 radius of point on blade

r1, r2 radii of points on blade or blades

R blade tip radius; ratio of minimum to maximum stress in fatigue load

cycle; electrical resistance

Re Reynold’s number

Ru(n) normalized power spectral density, n:Su(n)=2

u, of longitudinal speed fluctuations, u, at a fixed point

wind-s distance inboard from the blade tip; distance along the blade chord

from the leading edge; separation between two points; Laplace

operator; slip of induction machine

s1 separation between two points measured in the along-wind direction

S wing area; autogyro disc area; fatigue stress range

S electrical complex (apparent) power (bold indicates a complex

quantity)

S( ) uncertainty or error band

Sjk(n) cross spectrum of longitudinal wind-speed fluctuations, u, at points j

and k (single sided)

SM(n) single-sided power spectrum of bending moment

SQ1(n) single-sided power spectrum of generalized load

Su(n) single-sided power spectrum of longitudinal wind-speed fluctuations,

u, at a fixed point

S0u(n) single-sided power spectrum of longitudinal wind-speed fluctuations,

u, as seen by a point on a rotating blade (also known as rotationallysampled spectrum)

S0u(r1, r2, n) cross spectrum of longitudinal wind-speed fluctuations, u, as seen by

points at radii r1and r2on a rotating blade or rotor (single sided)

Sv(n) single-sided power spectrum of lateral wind speed fluctuations, v, at a

fixed point

Sw(n) single-sided power spectrum of vertical wind-speed fluctuations, w,

at a fixed point

t time; gear tooth thickness at critical root section; tower wall thickness

T rotor thrust; duration of discrete gust; wind-speed averaging period

u fluctuating component of wind speed in the x-direction; induced

velocity in x-direction; in-plane plate deflection in x-direction; gearratio

u friction velocity in boundary layer

U1 free stream velocity

U, U(t) instantaneous wind speed in the along-wind direction

U mean component of wind speed in the along-wind direction –

typically taken over a period of 10 min or 1 h

Uave annual average wind speed at hub height

Ud streamwise velocity at the rotor disc

Uw streamwise velocity in the far wake

Ue1 extreme 3 s gust wind speed with 1 year return period

Ue50 extreme 3 s gust wind speed with 50 year return period

U0 turbine upper cut-out speed

Ur turbine rated wind speed, defined as the wind speed at which the

turbine’s rated power is reached

Uref reference wind speed defined as 10 min mean wind speed at hub

height with 50 year return period

U1 strain energy of plate flexure

U2 in-plane strain energy

v fluctuating component of wind speed in the y-direction; induced

velocity in y-direction; in-plane plate deflection in y-direction

V airspeed of an autogyro; longitudinal air velocity at rotor disc,

U1(1
a) (Section 7.1.9); voltage (shown in bold when complex)V(t) instantaneous lateral wind speed

VA electrical volt-amperes

Vf fibre volume fraction in composite material

Vt blade tip speed

w fluctuating component of wind speed in the z-direction; induced

velocity in z-direction; out-of-plane plate deflection

W wind velocity relative to a point on rotating blade; electrical power

loss

x downwind co-ordinate – fixed and rotating axis systems; downwind

displacement

x(t) stochastic component of a variable

xn length of near wake region

x1 first-mode component of steady tip displacement

X electrical inductive reactance

y lateral co-ordinate with respect to vertical axis (starboard positive) –

fixed-axis system

y lateral co-ordinate with respect to blade axis – rotating-axis system

y lateral displacement

z vertical co-ordinate (upwards positive) – fixed-axis system

z radial co-ordinate along blade axis – rotating-axis system

Z section modulus

Z electrical impedance (bold indicates a complex quantity)

z0 ground roughness length

z1 number of teeth on pinion gear

z(t) periodic component of a variable

Greek

Æ angle of attack – i.e., angle between air flow incident on the blade and

the blade chord line; wind-shear power law exponent

 inclination of local blade chord to rotor plane (i.e., blade twist plus

pitch angle, if any)

 wake skew angle: angle between the axis of the wake of a yawed rotor

and the axis of rotation of rotor

M1 weighted mass ratio defined in Section 5.8.6

a logarithmic decrement of aerodynamic damping

s logarithmic decrement of structural damping

 logarithmic decrement of combined aerodynamic and structural

damping; width of tower shadow deficit region

3 angle between axis of teeter hinge and the line perpendicular to both

the rotor axis and the low-speed shaft axis

1,2,3 proportion of time in which a variable takes the maximum, mean or

minimum values in a three-level square wave

 flow angle of resultant velocity W to rotor plane

ª yaw angle; Euler’s constant (¼ 0:5772)

ªL load factor

ªmf partial safety factor for material fatigue strength

ªmu partial safety factor for material ultimate strength

ˆ blade circulation; vortex strength

k von Karman’s constant

kL(s) cross-correlation function between velocity components at points in

space a distance s apart, in the direction parallel to the line joiningthem

kT(s) cross-correlation function between velocity components at points in

space a distance s apart, in the direction perpendicular to the linejoining them

ku(r, auto-correlation function for along-wind velocity component at radius

r on stationary rotor

k0

u(r, auto-correlation function for along-wind velocity component as seen

by a point at radius r on a rotating rotor

ºr tangential speed of blade element at radius r divided by wind speed:

local speed ratio

¸ yaw rate

 non-dimensional radial position, r=R; viscosity; coefficient of friction

i(r) mode shape of ith blade mode

i(z) mode shape of ith tower mode

T(z) tower first mode shape

TJ(r) normalized rigid body deflection of blade j resulting from excitation

of tower first mode

z mean value of variable z

ellipsoidal co-ordinate; mean zero up-crossing frequency

Ł wind-speed direction change; random phase angle; cylindrical panel

co-ordinate; brake disc temperature

r air density

r0

u(r1, r2,

components as seen by points (not necessarily on same blade) at radii

r1and r2on a rotating rotor (i.e., k0u(r1, r2, 2u)

 blade solidity; standard deviation; stress

 mean stress

M standard deviation of bending moment

M1 standard deviation of first-mode resonant bending moment, at blade

root for blade resonance, and at tower base for tower resonance

MB standard deviation of quasistatic bending moment (or bending

moment background response)

Mh standard deviation of hub dishing moment

MT standard deviation of teeter moment for rigidly mounted, two-bladed

v standard deviation of wind speed in across-wind direction

w standard deviation of wind speed in vertical direction

x1 standard deviation of first-mode resonant displacement, referred to

blade tip for blade resonance, and to nacelle for tower resonancetime interval; non-dimensional time; shear stress

ı Poisson’s ratio

ø angular frequency (rad=s)

ød demanded generator rotational speed

øi natural frequency of ith mode (rad=s)

øg generator rotational speed

ør induction machine rotor rotational speed

øs induction machine stator field rotational speed

rotational speed of rotor; earth’s rotational speed

damping ratio

ł angle subtended by cylindrical plate panel

łuu(r, r9, n) real part of normalized cross spectrum (see Appendix 1, section A1.4)

B baseline

c compressive

d disc; drag; design

e1 extreme value with return period of 1 year

e50 extreme value with return period of 50 years

max maximum value of variable

min minimum value of variable

n value at end of nth time step

x is perpendicular to the blade axis, and in the plane

passing through the blade and shaft axis – in the downwind direction

y is perpendicular to the blade and shaft axes, to give

a right-hand co-ordinate systemNB: Although shaft is tilt and rotor coning are not shown

on the sketch, the axis definitions given accommodate both these variants

blade) NB: Although shaft tilt and rotor coning are not shown on the sketch, the axisdefinitions given accommodate both these variants

direction

z is perpendicular to the shaft axis and in the

vertical plane passing through the shaft axis

y is perpendicular to the shaft axis and

horizontal to starboard, giving a right-hand co-ordinate system

NB: Although shaft is tilt and rotor coning are notshown on the sketch, the axis definitions given accommodate both these variants

Respect to Hub NB: Although shaft tilt and rotor coning are not shown on the sketch, the axisdefinitions given accommodate both these variants

Golding (1955) and Shepherd and Divone in Spera (1994) provide a fascinatinghistory of early wind turbine development They record the 100 kW 30 m diameterBalaclava wind turbine in the then USSR in 1931 and the Andrea Enfield 100 kW

24 m diameter pneumatic design constructed in the UK in the early 1950s In thisturbine hollow blades, open at the tip, were used to draw air up through the towerwhere another turbine drove the generator In Denmark the 200 kW 24 m diameterGedser machine was built in 1956 while Electricite´ de France tested a 1.1 MW 35 mdiameter turbine in 1963 In Germany, Professor Hutter constructed a number ofinnovative, lightweight turbines in the 1950s and 1960s In spite of these technicaladvances and the enthusiasm, among others, of Golding at the Electrical ResearchAssociation in the UK there was little sustained interest in wind generation untilthe price of oil rose dramatically in 1973

The sudden increase in the price of oil stimulated a number of substantialGovernment-funded programmes of research, development and demonstration Inthe USA this led to the construction of a series of prototype turbines starting withthe 38 m diameter 100 kW Mod-0 in 1975 and culminating in the 97.5 m diameter2.5 MW Mod-5B in 1987 Similar programmes were pursued in the UK, Germany

and Sweden There was considerable uncertainty as to which architecture mightprove most cost-effective and several innovative concepts were investigated at fullscale In Canada, a 4 MW vertical-axis Darrieus wind turbine was constructed andthis concept was also investigated in the 34 m diameter Sandia Vertical Axis TestFacility in the USA In the UK, an alternative vertical-axis design using straightblades to give an ‘H’ type rotor was proposed by Dr Peter Musgrove and a 500 kWprototype constructed In 1981 an innovative horizontal-axis 3 MW wind turbinewas built and tested in the USA This used hydraulic transmission and, as analternative to a yaw drive, the entire structure was orientated into the wind Thebest choice for the number of blades remained unclear for some while and largeturbines were constructed with one, two or three blades.

Much important scientific and engineering information was gained from theseGovernment-funded research programmes and the prototypes generally worked asdesigned However, it has to be recognized that the problems of operating verylarge wind turbines, unmanned and in difficult wind climates were often under-

MICON, www.neg-micon.dk)

estimated and the reliability of the prototypes was not good At the same time asthe multi-megawatt prototypes were being constructed private companies, oftenwith considerable state support, were constructing much smaller, often simpler,turbines for commercial sale In particular the financial support mechanisms inCalifornia in the mid-1980s resulted in the installation of a very large number of

quite small (, 100 kW) wind turbines A number of these designs also suffered

from various problems but, being smaller, they were in general easier to repair andmodify The so-called ‘Danish’ wind turbine concept emerged of a three-bladed,stall-regulated rotor and a fixed-speed, induction machine drive train This decep-tively simple architecture has proved to be remarkably successful and has now beenimplemented on turbines as large as 60 m in diameter and at ratings of 1.5 MW Themachines of Figures 1.1 and 1.2 are examples of this design However, as the sizes

of commercially available turbines now approach that of the large prototypes of the1980s it is interesting to see that the concepts investigated then of variable-speedoperation, full-span control of the blades, and advanced materials are being usedincreasingly by designers Figure 1.3 shows a wind farm of direct-drive, variable-speed wind turbines In this design, the synchronous generator is coupled directly

to the aerodynamic rotor so eliminating the requirement for a gearbox Figure 1.4shows a more conventional, variable-speed wind turbine that uses a gearbox, while

a small wind farm of pitch-regulated wind turbines, where full-span control of theblades is used to regulate power, is shown in Figure 1.5

NEG MICON, www.neg-micon.dk)

The stimulus for the development of wind energy in 1973 was the price of oil andconcern over limited fossil-fuel resources Now, of course, the main driver for use

of wind turbines to generate electrical power is the very low CO2 emissions (overthe entire life cycle of manufacture, installation, operation and de-commissioning)

by permission of Wind Prospect Ltd., www.windprospect.com)

Renew-able Energy Systems Ltd., www.res-ltd.com)

and the potential of wind energy to help limit climate change In 1997 the sion of the European Union published its White Paper (CEU, 1997) calling for 12percent of the gross energy demand of the European Union to be contributed fromrenewables by 2010 Wind energy was identified as having a key role to play in thesupply of renewable energy with an increase in installed wind turbine capacityfrom 2.5 GW in 1995 to 40 GW by 2010 This target is likely to be achievable since atthe time of writing, January 2001, there was some 12 GW of installed wind-turbinecapacity in Europe, 2.5 GW of which was constructed in 2000 compared with only

Commis-300 MW in 1993 The average annual growth rate of the installation of windturbines in Europe from 1993–9 was approximately 40 percent (Zervos, 2000) Thedistribution of wind-turbine capacity is interesting with, in 2000, Germany account-ing for some 45 percent of the European total, and Denmark and Spain each havingapproximately 18 percent There is some 2.5 GW of capacity installed in the USA ofwhich 65 percent is in California although with increasing interest in Texas andsome states of the midwest Many of the California wind farms were originally

permission of Wind Prospect Ltd., www.windprospect.com)

constructed in the 1980s and are now being re-equipped with larger modern windturbines.

Table 1.1 shows the installed wind-power capacity worldwide in January 2001although it is obvious that with such a rapid growth in some countries data of thiskind become out of date very quickly

The reasons development of wind energy in some countries is flourishing while

in others it is not fulfilling the potential that might be anticipated from a simpleconsideration of the wind resource, are complex Important factors include thefinancial-support mechanisms for wind-generated electricity, the process by whichthe local planning authorities give permission for the construction of wind farms,and the perception of the general population particularly with respect to visualimpact In order to overcome the concerns of the rural population over the environ-mental impact of wind farms there is now increasing interest in the development ofsites offshore

The power output, P, from a wind turbine is given by the well-known expression:

Capa-city Throughout the World, January 2001

Location Installed capacity

values are achieved in practice (see Chapter 3) The power coefficient of a rotorvaries with the tip speed ratio (the ratio of rotor tip speed to free wind speed) and isonly a maximum for a unique tip speed ratio Incremental improvements in thepower coefficient are continually being sought by detailed design changes of therotor and, by operating at variable speed, it is possible to maintain the maximumpower coefficient over a range of wind speeds However, these measures will giveonly a modest increase in the power output Major increases in the output powercan only be achieved by increasing the swept area of the rotor or by locating thewind turbines on sites with higher wind speeds.

Hence over the last 10 years there has been a continuous increase in the rotordiameter of commercially available wind turbines from around 30 m to more than

60 m A doubling of the rotor diameter leads to a four-times increase in poweroutput The influence of the wind speed is, of course, more pronounced with adoubling of wind speed leading to an eight-fold increase in power Thus there havebeen considerable efforts to ensure that wind farms are developed in areas of thehighest wind speeds and the turbines optimally located within wind farms Incertain countries very high towers are being used (more than 60–80 m) to takeadvantage of the increase of wind speed with height

In the past a number of studies were undertaken to determine the ‘optimum’ size

of a wind turbine by balancing the complete costs of manufacture, installation andoperation of various sizes of wind turbines against the revenue generated (Molly

et al., 1993) The results indicated a minimum cost of energy would be obtained withwind turbine diameters in the range of 35–60 m, depending on the assumptionsmade However, these estimates would now appear to be rather low and there is noobvious point at which rotor diameters, and hence output power, will be limitedparticularly for offshore wind turbines

All modern electricity-generating wind turbines use the lift force derived from theblades to drive the rotor A high rotational speed of the rotor is desirable in order toreduce the gearbox ratio required and this leads to low solidity rotors (the ratio ofblade area/rotor swept area) The low solidity rotor acts as an effective energyconcentrator and as a result the energy recovery period of a wind turbine, on a goodsite, is less than 1 year, i.e., the energy used to manufacture and install the windturbine is recovered within its first year of operation (Musgrove in Freris, 1990)

The use of wind energy to generate electricity is now well accepted with a largeindustry manufacturing and installing thousands of MWs of new capacity eachyear Although there are exciting new developments, particularly in very largewind turbines, and many challenges remain, there is a considerable body of estab-lished knowledge concerning the science and technology of wind turbines Thisbook is intended to record some of this knowledge and to present it in a formsuitable for use by students (at final year undergraduate or post-graduate level) and

by those involved in the design, manufacture or operation of wind turbines Theoverwhelming majority of wind turbines presently in use are horizontal-axis, land-

based turbines connected to a large electricity network These turbines are thesubject of this book.

Chapter 2 discusses the wind resource Particular reference is made to windturbulence due to its importance in wind-turbine design Chapter 3 sets out the basis

of the aerodynamics of horizontal-axis wind turbines while Chapter 4 discusses theirperformance Any wind-turbine design starts with establishing the design loads andthese are discussed in Chapter 5 Chapter 6 sets out the various design options forhorizontal-axis wind turbines with approaches to the design of some of the importantcomponents examined in Chapter 7 The functions of the wind-turbine controller arediscussed in Chapter 8 and some of the possible analysis techniques described InChapter 9 wind farms and the development of wind-energy projects are reviewedwith particular emphasis on environmental impact Finally, Chapter 10 considershow wind turbines interact with the electrical power system

The book attempts to record well-established knowledge that is relevant to windturbines, which are currently commercially significant Thus, it does not discuss anumber of interesting research topics or where wind-turbine technology is stillevolving rapidly Although they were investigated in considerable detail in the1980s, vertical-axis wind turbines have not proved to be commercially competitiveand are not currently manufactured in significant numbers Hence the particularissues of vertical-axis turbines are not dealt with in this text

There are presently some two billion people in the world without access to mainselectricity and wind turbines, in conjunction with other generators, e.g., dieselengines, may in the future be an effective means of providing some of these peoplewith power However, autonomous power systems are extremely difficult to designand operate reliably, particularly in remote areas of the world and with limitedbudgets A small autonomous AC power system has all the technical challenges of

a large national electricity system but, due to the low inertia of the plant, requires avery fast, sophisticated control system to maintain stable operation Over the last 20years there have been a number of attempts to operate autonomous wind–dieselsystems on islands throughout the world but with only limited success This class

of installation has its own particular problems and again, given the very limitedsize of the market at present, this specialist area is not dealt with

Installation of offshore wind turbines is now commencing The few offshore windfarms already installed are in rather shallow waters and resemble land-based windfarms in many respects using medium sized wind turbines Very large wind farmswith multi-megawatt turbines located in deeper water, many kilometres offshore,are now being planned and these will be constructed over the coming years.However, the technology of offshore wind-energy projects is still evolving at toorapid a pace for inclusion in this text which attempts to present established engin-eering practice

References

CEU, (1997) ‘Energy for the future, renewable sources of energy – White Paper for aCommunity Strategy and Action Plan’ COM (97) 559 final

Freris, L L (ed.), (1990) Wind energy conversion systems Prentice Hall, New York, US.Golding, E W (1955) The generation of electricity from wind power E & F N Spon (reprinted

Zervos, A (2000) ‘European targets, time to be more ambitious?’ Windirections, 18–19.European Wind Energy Association, www.ewea.org

Bibliography

Eggleston, D M and Stoddard, F S., (1987) Wind turbine engineering design Van NostrandRheinhold, New York, USA

Gipe, P., (1995) Wind energy comes of age John Wiley and Sons, New York, USA

Harrison, R., Hau, E and Snel, H., (2000) Large wind turbines, design and economics John Wileyand Sons

Johnson, L., (1985) Wind energy systems Prentice-Hall

Le Gourieres, D., (1982) Wind power plants theory and design Pergamon Press, Oxford, UK.Twiddell, J W and Weir, A D., (1986) Renewable energy sources E & F N Spon

The Wind Resource

The energy available in the wind varies as the cube of the wind speed, so anunderstanding of the characteristics of the wind resource is critical to all aspects ofwind energy exploitation, from the identification of suitable sites and predictions ofthe economic viability of wind farm projects through to the design of wind turbinesthemselves, and understanding their effect on electricity distribution networks andconsumers

From the point of view of wind energy, the most striking characteristic of thewind resource is its variability The wind is highly variable, both geographicallyand temporally Furthermore this variability persists over a very wide range ofscales, both in space and time The importance of this is amplified by the cubicrelationship to available energy

On a large scale, spatial variability describes the fact that there are many differentclimatic regions in the world, some much windier than others These regions arelargely dictated by the latitude, which affects the amount of insolation Within anyone climatic region, there is a great deal of variation on a smaller scale, largelydictated by physical geography – the proportion of land and sea, the size of landmasses, and the presence of mountains or plains for example The type of vegeta-tion may also have a significant influence through its effects on the absorption orreflection of solar radiation, affecting surface temperatures, and on humidity.More locally, the topography has a major effect on the wind climate More wind

is experienced on the tops of hills and mountains than in the lee of high ground or

in sheltered valleys, for instance More locally still, wind velocities are significantlyreduced by obstacles such as trees or buildings

At a given location, temporal variability on a large scale means that the amount

of wind may vary from one year to the next, with even larger scale variations overperiods of decades or more These long-term variations are not well understood,and may make it difficult to make accurate predictions of the economic viability ofparticular wind-farm projects, for instance

On time-scales shorter than a year, seasonal variations are much more able, although there are large variations on shorter time-scales still, which althoughreasonably well understood, are often not very predictable more than a few daysahead These ‘synoptic’ variations are associated with the passage of weathersystems Depending on location, there may also be considerable variations with the

predict-time of day (diurnal variations) which again are usually fairly predictable On thesetime-scales, the predictability of the wind is important for integrating large amounts

of wind power into the electricity network, to allow the other generating plantsupplying the network to be organized appropriately

On still shorter time-scales of minutes down to seconds or less, wind-speedvariations known as turbulence can have a very significant effect on the design andperformance of the individual wind turbines, as well as on the quality of powerdelivered to the network and its effect on consumers

Van der Hoven (1957) constructed a wind-speed spectrum from long- and term records at Brookhaven, New York, showing clear peaks corresponding to thesynoptic, diurnal and turbulent effects referred to above (Figure 2.1) Of particularinterest is the so-called ‘spectral gap’ occurring between the diurnal and turbulentpeaks, showing that the synoptic and diurnal variations can be treated as quitedistinct from the higher-frequency fluctuations of turbulence There is very littleenergy in the spectrum in the region between 2 h and 10 min

Ultimately the winds are driven almost entirely by the sun’s energy, causing ential surface heating The heating is most intense on land masses closer to the equator,and obviously the greatest heating occurs in the daytime, which means that the region

differ-of greatest heating moves around the earth’s surface as it spins on its axis Warm airrises and circulates in the atmosphere to sink back to the surface in cooler areas Theresulting large-scale motion of the air is strongly influenced by coriolis forces due tothe earth’s rotation The result is a large-scale global circulation pattern Certain

identifiable features of this such as the trade winds and the ‘roaring forties’ are wellknown.

The non-uniformity of the earth’s surface, with its pattern of land masses andoceans, ensures that this global circulation pattern is disturbed by smaller-scale vari-ations on continental scales These variations interact in a highly complex and non-linear fashion to produce a somewhat chaotic result, which is at the root of the day-to-day unpredictability of the weather in particular locations Clearly though, under-lying tendencies remain which lead to clear climatic differences between regions.These differences are tempered by more local topographical and thermal effects.Hills and mountains result in local regions of increased wind speed This is partly

a result of altitude – the earth’s boundary layer means that wind speed generallyincreases with height above ground, and hill tops and mountain peaks may ‘project’into the higher wind-speed layers It is also partly a result of the acceleration of thewind flow over and around hills and mountains, and funnelling through passes oralong valleys aligned with the flow Equally, topography may produce areas ofreduced wind speed, such as sheltered valleys, areas in the lee of a mountain ridge

or where the flow patterns result in stagnation points

Thermal effects may also result in considerable local variations Coastal regionsare often windy because of differential heating between land and sea While the sea

is warmer than the land, a local circulation develops in which surface air flows fromthe land to the sea, with warm air rising over the sea and cool air sinking over theland When the land is warmer the pattern reverses The land will heat up and cooldown more rapidly than the sea surface, and so this pattern of land and sea breezestends to reverse over a 24 h cycle These effects were important in the earlydevelopment of wind power in California, where an ocean current brings coldwater to the coast, not far from desert areas which heat up strongly by day Anintervening mountain range funnels the resulting air flow through its passes,generating locally very strong and reliable winds (which are well correlated withpeaks in the local electricity demand caused by air-conditioning loads)

Thermal effects may also be caused by differences in altitude Thus cold air fromhigh mountains can sink down to the plains below, causing quite strong and highlystratified ‘downslope’ winds

The brief general descriptions of wind speed variations in Sections 2.1 to 2.5 areillustrative, and more detailed information can be found in standard meteorologicaltexts Section 9.1.3 describes how the wind regimes at candidate sites can beassessed, while wind forecasting is covered in Section 2.9

Section 2.6 presents a more detailed description of the high-frequency wind tions known as turbulence, which are crucial to the design and operation of windturbines and have a major influence on wind turbine loads Extreme winds are alsoimportant for the survival of wind turbines, and these are described in Section 2.8

There is evidence that the wind speed at any particular location may be subject tovery slow long-term variations Although the availability of accurate historical

records is a limitation, careful analysis by, for example, Palutikoff, Guo andHalliday (1991) has demonstrated clear trends Clearly these may be linked to long-term temperature variations for which there is ample historical evidence There isalso much debate at present about the likely effects of global warming, caused byhuman activity, on climate, and this will undoubtedly affect wind climates in thecoming decades.

Apart from these long-term trends there may be considerable changes in ness at a given location from one year to the next These changes have many causes.They may be coupled to global climate phenomema such as el nin˜o, changes inatmospheric particulates resulting from volcanic eruptions, and sunspot activity, toname a few These changes add significantly to the uncertainty in predicting theenergy output of a wind farm at a particular location during its projected lifetime

While year-to-year variation in annual mean wind speeds remains hard to predict,wind speed variations during the year can be well characterized in terms of aprobability distribution The Weibull distribution has been found to give a goodrepresentation of the variation in hourly mean wind speed over a year at manytypical sites This distribution takes the form

F(U) ¼ exp
U

c

k!

(2:1)

where F(U) is the fraction of time for which the hourly mean wind speed exceeds

U It is characterized by two parameters, a ‘scale parameter’ c and a ‘shapeparameter’ k which describes the variability about the mean c is related to theannual mean wind speed U by the relationship

U ¼ cˆ(1 þ 1=k) (2:2)whereˆ is the complete gamma function This can be derived by consideration ofthe probability density function

U ¼

ð1 0

A special case of the Weibull distribution is the Rayleigh distribution, with k ¼ 2,which is actually a fairly typical value for many locations In this case, the factor