Michael Graham - Wind Energy Handbook

Publicly funded monitoring programmes have enabled much to be learned about the environmental impacts of offshore wind farms, and some of these findings are reported in a new section on environmental monitoring. Finally, the section on power collection and transmission has been updated to describe the use of modular multi‐level convertors for HVdc transmission.

A large number of individuals have assisted the authors in a variety of ways in the preparation of this work. In particular, however, we would like to thank David Infield for providing some of the content of Chapter 4, David Quarton for scrutinising and commenting on Chapter 5, Mark Hancock, Martin Ansell, and Colin Anderson for supplying information and guidance on blade material properties reported in Chapter 7, and Ray Hicks for insights into gear design. Thanks are also due to Roger Haines and Steve Gilkes for illuminating discussions on yaw drive design and braking philosophy, respectively, and to James Shawler for assistance and discussions about Chapter 3.

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

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

Extracts from British Standards reproduced with the permission of the British Standards Institution under licence number 2001/SK0281. Complete Standards are available from BSI Customer Services (Tel +44 (0) 20 8996 9001).

The second edition benefited greatly from the continuing help and support provided by many who had assisted in the first edition. However, the authors are also grateful to the many individuals not involved in the first edition who provided advice and expertise for the second, especially in relation to the new offshore chapter. In particular the authors wish to acknowledge the contribution of Rose King to the discussion of offshore electric systems, based on her PhD thesis, and of Tim Camp to the discussion of offshore support structure loading. Thanks are also due to Bieshoy Awad for the drawings of electrical generator systems, Rebecca Barthelmie and Wolfgang Schlez for advice on offshore wake effects, Joe Phillips for his contribution to the offshore wind resource, Sven Eric Thor for provision of insights and illustrations from the Lillgrund wind farm, Marc Seidel for information on jacket structures, Jan Wienke for discussion of breaking wave loads, and Ben Hendricks for his input on turbine costs in relation to size.

In addition, several individuals took on the onerous task of scrutinising sections of the draft text. The authors are particularly grateful to Tim Camp for examining the sections on design loading, on‐ and offshore, Colin Morgan for providing useful comments on the sections dealing with support structures, and Graeme McCann for vetting sections on the extrapolation of extreme loads from simulations and monopile fatigue analysis in the frequency domain. Nevertheless, responsibility for any errors remains with the authors. (In this connection, thanks are due to those who have pointed out errors in the first edition.)

Tony Burton would also like to record his thanks to Martin Kuhn and Wim Bierbooms for providing copies of their PhD theses – entitled, respectively, ‘Dynamics and Design Optimisation of Offshore Wind Energy Conversion Systems’ and ‘Constrained Stochastic Simulation of Wind Gusts for Wind Turbine Design’ – both of which proved invaluable in the preparation of this work.

The authors would like to acknowledge the assistance provided by the many colleagues and individuals in the wider wind energy community who have shared their knowledge and expertise. Of these, a number have been particularly generous with their time and warrant special mention here.

The revised and expanded section on blade design necessitated the gathering of much new material. In this context, Tony Burton would like to thank Mark Hancock for sharing his insights into the practicalities of blade design, Daniel Samborsky for shedding light on the lessons from laminate fatigue testing, and Tomas Vronsky for hosting an informative visit to the Vestas blade testing facility on the Isle of Wight.

The new section on monopile geotechnical design focuses on the more sophisticated design methods made possible by the PISA joint industry research project. Tony Burton would like to thank two lead participants in the project, Byron Byrne and Guy Houlsby of Oxford University, for hosting a tutorial on the project findings, and their research student, Toby Balaam, for his part in arranging it.

Tony Burton would also like to record his gratitude to those who have taken on the chore of reviewing parts of the text. Amongst these are Mark Hancock, Daniel Samborsky, and Samuel Scott, who have reviewed different parts of the blade design section; Byron Byrne, who checked the section on monopile geotechnical design; and James Nicholls and Kevin Drake, who critiqued the floating support structures section. However, responsibility for any errors in these sections remains with the author.

Nick Jenkins would like to express his thanks to Alan Harris of ReSoft for his advice and the use of images from the Windfarm design tool. He would also like to acknowledge and thank Prof. Janaka Ekanayake of Peradeniya University for his contributions to and scrutiny of Chapter 11.

A workspace free from interruptions and distractions is vital for any author. Tony Burton would like to thank former colleague Richard Stonor for providing a quiet and congenial place of work in his home, until evacuation was mandated by Covid‐19 guidelines in March 2020.

We have made extensive use of publications by NREL, Sandia Laboratories, Montana State University, DNV GL, and Danish Technical University and record our thanks to these organisations for making documents available to us free of charge and sanctioning the reproduction of some of the material therein. Thanks are also due to Georgios Deskos (Imperial College London and now at National Renewable Energy Laboratory, CO. USA) for the cover design taken from his numerical simulation of flow through a wind farm.

Note: This list is not exhaustive and omits many symbols that are unique to particular chapters

aaxial flow induction factor; ab at blade azimuthally averagedaflange projection beyond bolt centrea′tangential flow induction factor; a′b at blade ′azimuthally averaged tangential flow induction factor at the blade tipatwo‐dimensional lift curve slope, (dC1/dα)a1constant defining magnitude of structural dampingA, ADrotor swept areaA∞, Awupstream and downstream streamtube cross‐sectional areasAcCharnock's constantbface width of gear teeth; eccentricity of bolt to tower wall in bolted flange joint; wake widthbrunbiased estimator of βrBnumber of bladescblade chord; Weibull scale parameter; dispersion of distribution; flat plate half width; half of cylinder immersed widthc*half of cylinder immersed width at time t* damping coefficient per unit lengthcigeneralised damping coefficient with respect to the ith modeCdecay constant; wave celerity, L/T; constrained wave crest elevationC(v), C(k)Theodorsen's function, where v or k is the reduced frequency: C(v) = F(v) + iG(v)Cdsectional drag coefficientCDdrag coefficient in Morison's equationCDSsteady flow drag coefficient in Morison's equationCfsectional force coefficient (i.e. Cd or C1 as appropriate)C1, CLsectional lift coefficientCMinertia coefficient in Morison's equation; moment coefficient ( Section 4.6) coefficient of a Kinner pressure distributionCNnormal force coefficient ( Section 4.6)Cppressure coefficientCPpower coefficient or coefficient of performanceCQtorque coefficientCTthrust coefficient; total cost of wind turbineCTBtotal cost of baseline wind turbineCxcoefficient of sectional blade element force normal to the rotor planeCycoefficient of sectional blade element force parallel to the rotor planeC(Δr, n)coherence – i.e. normalised cross‐spectrum – for wind speed fluctuations at points separated by distance s measured in the across wind directionCjk(n)coherence – i.e. normalised cross‐spectrum – for longitudinal wind speed fluctuations at points j and kdstreamwise distance between vortex sheets in a wake; water depth; floating support structure draftd1pitch diameter of pinion geardPLpitch diameter of planet gearDdrag force; tower diameter; rotor diameter; flexural rigidity of plate; constrained wave trough elevationEenergy capture, i.e. energy generated by turbine over defined time period; modulus of elasticityE1longitudinal elastic modulus of uniaxial composite plyE2transverse elastic modulus of uniaxial composite plyE{}time averaged value of expression within brackets expected value of significant wave height conditional on a hub‐height mean wind speed ftip‐loss factor; Coriolis parameter; wave frequency; source intensityf( )probability density functionf1(t)support structure first mode hub displacementfj(t)blade tip displacement in jth modefin(t)blade tip displacement in ith mode at the end of the nth timestepfJ(t)blade j first mode tip displacementfpwave frequency corresponding to peak spectral densityfT(t)hub displacement for tower first modeFforce; force per unit lengthFxload in x (downwind) directionFYload in y directionFtforce between gear teeth at right angles to the line joining the gear centresF(μ)flow expansion function determining the radial distribution of the radial component of induced velocity normal to the wake axisF( )cumulative probability distribution functionF(x|Uk)cumulative probability distribution function for variable x conditional on U = Ukgacceleration due to gravity; vortex sheet strength; peak factor, defined as the number of standard deviations of a variable to be added to the mean to obtain the extreme value in a particular exposure period, for zero up‐crossing frequency, vgpeak factor as above, but for zero up‐crossing frequency nGgeostrophic wind speed; shear modulus; gearbox ratioG12shear modulus of composite plyG(f)transfer function divided by dynamic magnification ratioG(t)t second gust factorhheight of atmospheric boundary layer; duration of timestep; thickness of thin‐walled panel; maximum height of single gear tooth contact above critical root section; height of centre of buoyancy above centre of gravity for a spar buoyh(ψ)root vortex influence functionHhub height; wave height; hub height above mean sea levelH11 year extreme wave heightH5050 year extreme wave heightHjkelements of transformational matrix, H, used in wind simulationHi(n)complex frequency response function for the ith modeH(f)frequency‐dependent transfer functionHssignificant wave heightHs11 year extreme significant wave height based on 3 hour reference periodHs5050 year extreme significant wave height based on 3 hour reference periodHBbreaking wave heightIturbulence intensity; second moment of area; moment of inertia; electrical current (shown in bold when complex)Iambient turbulence intensityI+added turbulence intensityI++added turbulence intensity above hub heightIbblade inertia about rootIrinertia of rotor about horizontal axis in its planeIrefreference turbulence intensity, defined as expected value of hub‐height turbulence intensity at reference mean wind speed of 15 m/sIulongitudinal turbulence intensityIvlateral turbulence intensityIwvertical turbulence intensityIwaketotal wake turbulence intensityi, j kshape parameter for Weibull function; shape parameter for GEV distribution; integer; reduced frequency, (ωc/2W); wave number, 2π/L; surface roughness; turbulence energy ( Section 4.7.3)kigeneralised stiffness with respect to the ith mode, defined as Kconstant on right hand side of Bernouilli equationKCKeulegan–Carpenter numberKPpower coefficient based on tip speedKSMBsize reduction factor accounting for the lack of correlation of wind fluctuations over structural element or elementsKSx(n1)size reduction factor accounting for the lack of correlation of wind fluctuations at resonant frequency over structural element or elementsKv()modified Bessel function of the second kind and order vK(χ)function determining the induced velocity normal to the plane of a yawed rotorLlength scale for turbulence (subscripts and superscripts according to context); lift force; wave length integral length scale for the along‐wind turbulence component, u, measured in the longitudinal direction, xmmass per unit length; integer; depth below seabed of effective monopole fixity; inverse slope of log‐log plot of S‐N curvemaadded mass per unit span of blademigeneralised mass with respect to the ith modemT1generalised mass of tower, nacelle, and rotor with respect to tower first modeMmoment; integer; tower top mass; mass of floating structure mean bending momentMpeak quasi‐static mudline momentM1(t)fluctuating cantilever root bending moment due to excitation of first modeMTteeter momentMXblade in‐plane moment (i.e. moment causing bending in plane of rotation); tower side‐to‐side momentMYblade out‐of‐plane moment (i.e. moment causing bending out‐of‐plane of rotation); tower fore–aft momentMZblade torsional moment; tower torsional momentMYSlow‐speed shaft moment about rotating axis perpendicular to axis of blade 1MZSlow‐speed shaft moment about rotating axis parallel to axis of blade 1MYNmoment exerted by low‐speed shaft on nacelle about (horizontal) y axisMZNmoment exerted by low‐speed shaft on nacelle about (vertical) z axisnfrequency (Hz); number of fatigue loading cycles; integer; distance measured normal to a surfacenzero up‐crossing frequency of quasi‐static responsen1frequency (Hz) of first mode of vibrationNnumber of timesteps per revolution; integer; design fatigue life in number of cycles for a given constant stress rangeN(r)centrifugal forceN(S)number of fatigue cycles to failure at stress level Spstatic pressurep()probability density functionPaerodynamic power; electrical real (active) power associated Legendre polynomial of the first kindq(r, t)fluctuating aerodynamic lift per unit lengthQrotor torque; electrical reactive powerQaaerodynamic torque rate of heat flow mean aerodynamic lift per unit lengthQDdynamic factor defined as ratio of extreme moment to gust quasi‐static momentQgload torque at generatorQLloss torque associated Legendre polynomial of the second kindQ1(t)generalised load, defined in relation to a cantilever blade by Eq. (A5.13)rradius of blade element or point on blade; correlation coefficient between power and wind speed; radius of tubular tower; radius of monopiler′radius of point on blader1, r2radii of points on blade or bladesRblade tip radius; ratio of minimum to maximum stress in fatigue load cycle; electrical resistanceReReynolds numberRu(n)normalised power spectral density, n.Su(n)/ , of longitudinal wind speed fluctuations, u, at a fixed pointsdistance inboard from the blade tip; distance along the blade chord from the leading edge; separation between two points; Laplace operator; slip of induction machine; spacing of columns of a semi‐submersibles1separation between two points measured in the along‐wind directionSwing area; autogyro disc area; fatigue stress range; surface area S(apparent) electrical power (bold indicates a complex quantity)S()uncertainty or error bandSjk(n)cross‐spectrum of longitudinal wind speed fluctuations, u, at points j and k (single‐sided)SM(n)single‐sided power spectrum of bending momentSQ1(n)single‐sided power spectrum of generalised loadSu(n)single‐sided power spectrum of longitudinal wind speed fluctuations, u, at a fixed point single‐sided power spectrum of longitudinal wind speed fluctuations, u, as seen by a point on a rotating blade (also known as rotationally sampled spectrum) cross‐spectrum of longitudinal wind speed fluctuations, u, as seen by points at radii r1 and r2 on a rotating blade or rotor (single‐sided)Sv(n)single‐sided power spectrum of lateral wind speed fluctuations, v, at a fixed pointSw(n)single‐sided power spectrum of vertical wind speed fluctuations, w, at a fixed pointSηη (n)single‐sided power spectrum of sea surface elevationttime; gear tooth thickness at critical root section; tower wall thickness; monopole wall thickness; thickness of aerofoil section (maximum)Trotor thrust; duration of discrete gust; wind speed averaging period; wave period for regular waves; time stepTcmean period between wave crestsTppeak wave period, 1/fpTzmean zero crossing wave periodufluctuating component of wind speed in the x direction; induced velocity in upstream direction (as in Figure 4.5); perturbation velocity in x direction (downstream, as in Figure 4.11); in‐plane plate deflection in x direction; gear ratio; water particle velocity in x directionu*friction velocity in boundary layerU∞free‐stream velocityUfree‐stream velocityU, U(t)instantaneous wind speed in the along‐wind direction mean component of wind speed in the along‐wind direction – typically taken over a period of 10 min or 1 hUaveannual average wind speed at hub heightUDstreamwise velocity at the rotor discUiturbine lower cut‐in wind speedUWstreamwise velocity in the far wakeUe1extreme 3 s gust wind speed with 1 year return periodUe50extreme 3 s gust wind speed with 50 year return periodUturbine upper cut‐out wind speedUrturbine rated wind speed, defined as the wind speed at which the turbine's rated power is reachedUrefreference wind speed defined as 10 min mean wind speed at hub height with 50 year return periodU1strain energy of plate flexureU2in‐plane strain energyvfluctuating component of wind speed in the y direction; induced velocity in y direction; in‐plane plate deflection in y directionVairspeed of an autogyro; streamwise velocity at rotor disc, U∞(l – a) ( Section 7.1.15); voltage (shown in bold when complex)VArreactive power volt‐amperes‐reactiveV(t)instantaneous lateral wind speedVAapparent power electrical volt‐amperesVffibre volume fraction in composite materialwfluctuating component of wind speed in the z direction; induced velocity in z direction; out‐of‐plane plate deflection; weighting factor; water particle velocity in z directionw(r)blade shell skin thickness ( Section 6.4.2)Wwind velocity relative to a point on rotating blade; electrical power lossxdownwind coordinate – fixed and rotating axis systems; horizontal co‐ordinate in the direction of wave propagation; downwind displacementx(t)stochastic component of a variablexnlength of near wake regionxmode of distribution 1first mode component of steady tip displacementXelectrical inductive reactanceXncoefficient of nth term in Dean's stream functionylateral coordinate with respect to vertical axis (starboard positive) – fixed axis systemylateral coordinate with respect to blade axis – rotating axis systemylateral displacement; reduced variate of distribution; height above seabedzvertical coordinate (upwards positive) – fixed axis system; height above ground datum; height above water level; delay operatorzradial coordinate along blade axis – rotating axis systemzground roughness lengthz1number of teeth on pinion gearz(t)periodic component of a variableZsection modulus; externally applied load on flanged joint Zelectrical impedance (bold indicates a complex quantity)