AckermannTh. (ed) Wind Power in Power Systems
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24.4.6 Protection systems and relays
The protection scheme of wind turbines is based on measurements of various quan-
tities, such as voltage, current and rotor speed, including possible measuring delays
and the various relay limits. If these limits are exceeded more than a permissible period
of times they will cause the relay to initiate protective action. Examples of such
protective action are disconnection or preventive rapid power reduction, the second
action being similar to the so-called fast valving process in thermal power plants.
Obviously, such protection system action may have a significant impact on the out-
come of any simulation.
24.5 Per Unit Systems and Data for the Mechanical System
Per unit systems (p.u. systems) are commonly and traditionally used in many power
system simulation programs. Therefore, one is bound to encounter p.u. systems sooner
or later when working with simulation programs for electrical power systems.
Experience sh ows that the questions relating to p.u. systems and data interpretation,
especially for the mechanical part of the system, are a source of many serious misunder-
standings, problems and errors [e.g. when an (electrical) engineer must convert manu-
facturer (mechanical) information into vali d data in a simulation program]. For that
reason we will describe this in more detail here, even though it, theoretically, seems to be
basic knowledge. This way, we hope to raise awareness of this issue in order to avoid or
at least reduce p.u. related problems.
At first glance, the p.u. concept may be rather confusing. However, it is nothing more
than a definition of a new set of – conveniently and carefully chosen – basic measuring
units for the physical quantities that are under consideration. That means that, for
example, instead of measuring the power from a wind turbine in watts, kilowatts or
megawatts the power may be measured as the percentage of the rated power from the
wind turbine. In fact, the power can be measured as the percentage of any other constant
power that is suitable to be used for a comparison in a given context. Likewise, all
voltages at the same voltage level as the wind turbine generator can be measured as the
percentage of the nominal voltage of the wind turbine. These basic ‘measuring units’ are
the base values of the p.u. system.
Once the most fundamental base values for electrical quantities such as power and
voltage have been chosen, it is possible to derive base values for other electrical
quantities such as current, resistance and reactance on each voltage level in the system.
Power is an invariant quantity at all voltage levels so it is only possible to choose one
base value for power. For voltage, it is possible and necessary to define a base value for
each voltage level in the system.
It is assumed that the reader is sufficiently familiar with the p.u. concept in electrical
systems that there is no need to go into further detail. For more information, see standard
text books that provide an introduction to the p.u. concept (e.g. Kundur, 1994).
Now, if the p.u. system is to be extended to the rotating mechanical syst em, it becomes
necessary to define additional base values for angular speed and angle. The de finition of
these base values is in many cases not stated clearly, but they are nevertheless defined
implicitly, otherw ise the p.u. syst em would not be consistent. Using these two additional
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base values it is possible to derive consistent base values for other relevant quantities,
such as torque (T
base
) and shaft stiffness (k
base
), which can be defined as:
T
base
¼
P
base
!
base
; ð24:10Þ
k
base
¼
T
base
base
¼
P
base
!
base
base
; ð24:11Þ
Where the subscript ‘base’ indicates the base value of the quantity concerned. Note that
the base values for angular speed (!
base
) and angle (
base
), and consequently all other
derived base values, so far must be assumed to be in electrical radians (i.e. they are
referred to the electrical system). However, if the mechanical system rotates at a
different (typically lower) speed as a result of generator pole pairs an d/or a mechanical
gear system, supplementary base values must be defined accordingly. This definition of
new base values for each ‘speed level’ corresponds to the fact that for each voltage level a
separate voltage base value is chosen.
The most commonly used definition of base electrical angular rotational speed refers
to synchronous operation; that is, 314.16 rad/s in 50 Hz systems, and 376.99 rad/s in
60 Hz systems.
The base angle, however, is not traditionally defined as a base value. However, we
have found that it makes the p.u. concept easier to understand and more consistent.
The introduction of a separate base angle also makes it possible to extend the p.u.
system to all parts (or ‘speed levels’) of the mechanical syst em in a logical way that is
consistent with the definition of separate base voltages at separate voltage levels. Since
base angles are traditionally not explicitly defined, base angles have instead been
defined implicitly (i.e. because of a lack of actual choice rather than as a deliberate
choice). Consequently, shaft stiffness, for instance, is often specified in p.u. per
electrical radian (el. rad) instead of in ‘true’ p.u. – and one electrical radian is therefore
the most commonly used (implicit) definition of base angle. It follows from this that
the resulting p.u. value for shaft stiffness, for example, will be exactly the same whether
it is specified as p.u./el.rad or as ‘true’ p.u. with a base angle of 1 el. rad. It would be
just as possible to choose an other base angle value, such as 2 el. rads (corresponding
to one electrical revolution). From various perspectives, this base value might be even
more justified.
We have not had the opportunity to work in detail with models of Type D wind
turbines. In this type of wind turbines, the generator electrical system is decoupled from
the rest of the electrical system through full-load converters. Therefore the p.u. system
presented above may not be suitable for that type of wind turbi ne. It will at least be
necessary to consider carefully the definitions of base angular speed and base angle in
the g enerator system, which – from an electrical perspective – is an island system.
A suitable choice of base electrical angular speed would probably refer to the nominal
operation of the wind turbine. That means that the suitable value of base electrical
angular speed would depend on the nominal turbine rotational speed [and thereby on
the turbine radius; see Equation (24.8)] and on the number of pole pairs, n
PP
, of the
generator. If there is a gearbox, the gear ratio, n
gear
, has also to be included. Usually,
Type D wind turbines do not have a gearbox, though.
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As for inertia of the rotating parts (i.e. of the wind turbine rotor and generator
rotor), these are typically specified in SI units such as J, GD
2
or similar traditionally
used definitions. In p.u. systems, the inertia time constant, H, is generally us ed. H is
defined as:
H ¼
J!
base
2
2P
base
: ð24:12Þ
Strictly speaking, H is not a p.u. value. Unlike real p.u. values, which by the very
definition of p.u. systems are without physical unit, the inertia time constant is measured
in seconds. However, it is a convenient and, for historical reasons, commonly acknow-
ledged quantity.
Because of the various ways to specify inertia, it is very important to be absolutely
clear about which definition the manufacturers are applying; otherwise, data may be
misinterpreted, which would lead to erroneous simulation results.
Table 24.1 lists the typical range of physical values for the necessary mechanical data
of a wind turbine in the 2 MW range with a gearbox in the shaft system and with a grid-
connected generator (i.e. of Type A, B or C). It also includes an example of a dataset,
which will be used to illustrate the application of the p.u. system.
In order to convert these values into p.u., the necessary base values must be defined.
The power base value is:
P
base
¼ 2MW:
In the following, the indices el., HS and LS denote, respectively; the electrical system,
the system at the high-speed side of the gearbox (i.e. with the generator rotor) and the
system at the low-speed side of the gearbox (i.e. with the turbine rotor).
Assuming a 50 Hz system, the electrical base angular speed and base angle, !
base, el:
and
base, el:
, respectively, become:
!
base; el:
¼ 314:16 rad= s ðcorresponding to 50 HzÞ;
base; el:
¼ 1:0 rad ðtraditional choiceÞ;
RPM
nom; el:
¼ 3000:
Table 24.1 Typical mechanical data: physical values
Quantity Typical range Example value
Generator rotor intertia, J
gen
(kg m
2
) 65–130 121.5
Wind turbine inertia, J
turb
(10
6
kg m
2
) 3–9 6.41
High-speed shaft stiffness, K
HS
(kNm/rad) 50–100 92.2
Low-speed shaft stiffness, K
LS
(MNm/rad) 80–160 145.5
Number of pole pairs, n
pp
22
Gear ratio, n
gear
90–95 93.75
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The corresponding base values in the HS and the LS system become:
!
base; HS
¼
!
base; el:
n
pp
¼
314:16
2
rad=s ¼ 157:1 rad = s;
base; HS
¼
base; el:
n
pp
¼
1:0
2
rad ¼ 0:5 rad;
RPM
nom; HS
¼
RPM
nom; el:
n
pp
¼
3000
2
¼ 1500:
and
!
base; LS
¼
!
base; el:
n
pp
n
gear
¼
314:16 rad=s
2 93:75
¼ 1:676 rad=s;
base; LS
¼
base; el:
n
pp
n
gear
¼
1:0 rad
2 93:75
¼ 0:00533 rad;
RPM
nom; LS
¼
RPM
nom; el:
n
pp
n
gear
¼
3000
2 93:75
¼ 16:
Using the angular speed base values, the inertia time constants can be calculated as
follows:
H
gen
¼
J
gen
ð!
base; HS
Þ
2
2P
base
¼ 0:75 s;
H
turb
¼
J
turb
ð!
base; LS
Þ
2
2P
base
¼ 4:5s;
Where J
gen
and J
turb
are the generat or rotor intertia and wind turbine inertia, respec-
tively. The base values for shaft stiffness are calculated equally easily:
k
base; el:
¼
P
base
!
base;el:
base;el:
¼ 6366 kNm=rad;
k
base; HS
¼
P
base
!
base; HS
base; HS
¼ 25:46 kNm=rad;
k
base; LS
¼
P
base
!
base; LS
base; LS
¼ 223:8 MNm=rad;
thus making it possible to calculate the p.u. shaft stiffnesses:
k
HS
¼
k
HS
k
base; HS
¼ 3:62;
k
LS
¼
k
LS
k
base; LS
¼ 0:65:
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The use of base angle and base angular speed in this p.u. system automatically ensures
that all quantities are referred to the electrical side with n
pp
and n
gear
raised to the correct
power exponent.
As indicated in Section 24.4.2, the inertia of the tooth wheels in the gearbox is often
ignored. In that case, the total p.u. shaft stiffness k
tot
can be calculated as a ‘parallel
connection’ of the two shaft stiffnesses:
k
tot
¼ k
HS
jjk
LS
¼
1
k
HS
þ
1
k
LS
1
¼ 0:55:
It is recognised that the stiffness of the low-speed shaft – when measured in p.u. – is so
much smaller than that of the high-speed shaft that the low-speed shaft effectively
determines the total shaft stiffness. This is the case in spite of the fact that the low-
speed shaft stiffness – when measured in physical units (Nm/rad) – is more than a factor
1000 higher than the value of the high-speed shaft. Because of the gearbox, the physical
values of the shaft stiffnesses are simply not co mparable, but the use of the p.u. system
neutralise this. Hence the p.u. shaft stiffnesses become directly comparable.
The calculated p.u. data are organised in Table 24.2. Although the typical physical
values of the mechanical data in Table 24.1 are representative only for wind turbines in
the 2 MW range, the p.u. values of the mechanical data will be representative for wind
turbines of a much wider power range, reaching from below 1 MW up to 4 or 5 MW and
maybe even wider (see also the chapter on ‘scaling wind turbines and rules for similarity’
in Gasch and Twele, 2002).
The range of typical values is, of course, quite wide. However, there is a tendency that
data for active-stall-controlled wind turbines are at the upper end of the range, whereas
those for pitch-controlled wind turbines are at the lower end of the range.
In some cases, the manufacturer supplies the torsional eigenfrequencies of the shaft instead
of shaft stiffnesses. If the inertias are known, it is possible to calculate the shaft stiffness from
these data, provided it is absolutely clear which eigenfrequencies have been specified.
From Equations (25.8) in Section 25.5.4, and setting the external electrical and
mechanical torques, T
e
and T
wr
, respectively, in these equations to zero, the eigenoscil-
lations of the drive train can be determined. The eigenfrequency of a so-called free–free
shaft system, f
free–free
, is then straightforwardly given by:
2 f
freefree
¼ !
base; el:
k
tot
2
1
H
turb
þ
1
H
gen
1=2
: ð24:13 Þ
Table 24.2 Typical mechanical data – p.u. values
Quantity Typical range Example value
Generator rotor inertia constant, H
gen
(s) 0.4–0.8 0.75
Wind turbine inertia constant, H
turb
(s) 2.0–6.0 4.5
High-speed shaft stiffness, k
HS
(p.u.) 2.0–4.0 3.62
Low-speed shaft stiffness, k
LS
(p.u.) 0.35–0.7 0.65
Total shaft stiffness, k
tot
(p.u.) 0.3–0.6 0.55
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Similarly, it can be shown that the eigenfrequency of a free–fixed shaft system is:
2 f
freefree
¼ !
base; el:
k
LS
2
1
H
turb
1=2
: ð24:14Þ
In this case, the use of the LS shaft stiffness, k
LS
, indicates that the system is assumed to
be fixed at the gearbox, as opposed to the use of k
tot
in Equation (24.13), which indicates
that the entire drive train is assumed to take part in the free–free eigenoscillation.
Knowing the eigenfrequencies and the inertia time constants and using Equations
(24.14) and (24.15), it is trivial to determine the p.u. shaft stiffnesses. Note that both the
free–free and the free–fixed eigenfrequencies often are referred to merely as eigenfre-
quency. Therefore, such frequencies have to be interpreted correctly, making sure
exactly which parts of the mechanical construction are actually included in the eigen-
oscillation under consideration.
24.6 Different Types of Simulation and Requirements for Accuracy
When performing computer simulations the available simulation software, the inherent
models available in the software and the available data for these models may for obvious
reasons often be used without any special considerations by some users. However, in all
simulation work it is a given fact that the simulation type, the model accuracy and the
data accuracy all may have a significant impact on the outcome of the investigations.
24.6.1 Simulation work and required modelling accuracy
In addition to the purpose of the simulations, it is also necessary to be aware of the
individual parts of the total system model and to identify the parts that are most important
with respect to the investigations in question. There must be a reasonable balance between
the accuracy of all models in the simulated system, that is, of individual component models
as well as a possible external system model. There has to be a level of proportionality,
which means that the minimum acceptable accuracy of a model must increase with the
significance that the specific model has to the phenomena under consideration.
In this context, it is important to keep in mind that accuracy of a model representa-
tion of a component is achieved through a combination of the accuracy of the compon-
ent model itself and the accuracy of the model data. The accuracy of the component
model refers to the validity of the model and the physical level of detail in the model,
whereas the accuracy of the model data refers to the quality of the parameter measuring
or estimation methods. Likew ise, the accuracy of the total system model depends on the
accuracy of the models of the individual components in the system.
Ultimately, the total quality of any simulation result depends on the least accurate
model representation of the most significant components in the total system model. The
consequence of all this is that the development of very accurate models can be justified
only if it is also possible to obtain data with a corresponding accuracy. Likewise, it is
only justifiable to apply very accurat e model representations (i.e. model and data) of
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components if the model representation of other components that have a similar or
higher significance to the simulation results has an equally high accuracy.
However, high-accuracy models and/or high-accuracy data for any model representa-
tions of comp onents can be used whenever it is convenient and justified for other
reasons, for instance in order to avoid constructing and verifying equival ents, or to
produce models that are more realistic and therefore more trustworthy and intuitively
understandable for the users.
24.6.2 Different types of simulation
As previously stated, computer simulations can be used to investigate many different
phenomena. Therefore, requirements regardi ng simulation programs, the necessary
level of detail in the models and the model data may differ substa ntially depending on
what is to be investigated. Depending on the objective of the simulation, there is a large
number of different software programs available that are each specially tailored for
specific types of investigation.
In the following, the overall purpose of different types of simulations is briefly
discussed, and for each different type of simulation the req uired level of accuracy of
the various parts of the wind turbine model is briefly evaluated. We will also mention
typical programs used for these types of simulations.
We would like to stress that the programs mentioned here are those programs we have
become familiar with during our work. That does not mean in any way that other
programs that are not mentioned here will be of inferior value.
24.6.2.1 Electromagnetic transients
Electromagnetic transients are simulated using special electromagnetic transients pro-
grams (EMTPs) such as Alternative Transient Pro gram (ATP), the DCG/EPRI EMTP,
EMTDC
TM
, and Simpow
TM
.
(2)
These program s include an exact phase representation
of all electrical components, often with the possibility to include a complex representa-
tion of saturation, travelling wave propagation and short—circuit arcs, for instance.
Simulations are, in general, performed in the time domain, and the imme diate simula-
tion output are the instantaneous values of voltages, currents and quantities derived
therefrom.
EMTP simulations are used to determine fault currents for all types of faults,
symmetrical as well as nonsymmetrical. Overvoltages in connection with switching
surges, lightning surges as wel l as ferro-resonance in larger networks, for example, can
also be determined, which is useful for coordinating the insulation. The exact functions
of power electronics [e.g. high-voltage direct-cur rent (HVDC) links, static VAR com-
pensators (SVCs), STATCOMs, and voltage source converters (VSCs)] can also be
simulated with use of such programs.
(2)
ATP and DCG/EPRI EMTDC
TM
is a trademark of Manitoba HVDC Research Centre Inc.; Simpow
TM
is a registered trademark of STRI AB.
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The general level of detail in EMTP programs requires a reasonable wind turbine
model in such programs to include the significant electrical components [i.e. the gen-
erator, possible power electronics (including basic controls), possible surge arresters and
possible static reactive compensation]. Other parts of the construction may be neglected
or considered to be constant. This could be, for instance, the incoming wind, the
incoming mechanical power, the secondary parts of the control system and, in some
cases, the mechanical shaft system.
24.6.2.2 Dynamic stability and dynamic stabi lity simulations
Transient and voltage stability are normally evaluated with use of special transient
stability programs (TSPs), such as PSS/E
TM
(Power System Simulator for Engineers),
Simpow
TM
, CYMSTAB, PowerFactory, and Netomac
TM
.
(3)
In general, these programs
have a pha sor representation of all electrical components. In some of these TSPs, only
the positive sequence is represented, whereas other TSPs also include a representation of
the negative and zero sequences. Simulations are, in general, performed in the time
domain, and the immediate simulation output are the root mean square (RMS) values
of voltages, currents and quantities derived therefrom.
TSP simulations are used to evaluate the dynamic stability of larger networks. The
terms ‘dynamic stabi lity’ and ‘transient stability’ are often used interchangeably for the
same aspect of power system stability phenomena. The conceptual definition of ‘trans-
ient stability’ is outlined in Kundur (1994, pages 17–27), among others, and associated
with ‘the ability of the power system to maintain synchronism when subjected to a
severe transient disturbance’. The term ‘voltage stability’ is also in accordance with the
definition in Kundur (1994, page 27), and others, as ‘the ability of a power system to
maintain steady acceptable voltages at all buses in the system under normal operati ng
conditions and after being subjected to a disturbance’. Neither of these stability terms
should be confused with actual electromagnetic ‘transient phenomena’ such as lightning
and switching transients. Such transients are characterised by significantly lower time
constants (mi croseconds) and, consequently, EMTP simulations should be used to
analyse these phenomena (see Section 24.6.2.1). Therefore, the terms ‘dynamic analysis’
and ‘dynamic stability analysis’ are commonly associated with the ability of the power
system to maintain both the transient and the voltage stability. Bruntt, Havsager and
Knudsen (1999) and Noroozian, Knudsen and Bruntt (2000), among others, give
examples of wind power related dy namic stability investigations.
The general level of detail in such programs requires a reasonable wind turbine model
in such programs to include the major electrical components: that is the generator,
possible power electronics (including basic controls), possible static reactive compensa-
tion, main control systems and protection systems that may be activated and come into
operation during simulated events, ‘soft’ mechanical shaft systems and the incoming
mechanical power from the turbine rotor. Only very few other parts, (e.g. the incoming
wind) may be neglected or considered constant. Chapter 25 and Slootweg, Polinder and
(3)
PSS/E
TM
is a trademark of PTI; PowerFactory Netomac
TM
is a registered trademark of Siemens.
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Kling (2002) give examples of wind turbine models, that have been implemented in
TSPs. The examples also include the most significant typical data for the generator drive
and the turbine rotor.
As shown in Section 24.3.2, the incoming mechanical power from the turbine rotor
can be represented in many different ways with more or less detailed representations.
However, a constant power representation is not adequate if the model must be able to
represent a preventive rapid power reduction or similar actions resulting from adherence
to the grid code, for instance. It remains to be determined whether a simple or an
accurate static C
P
approximation is sufficient or whether the exact aerodynamic model
with representations of aerodynamic transition processes is required. Strictly speaking,
the effects demonstrated in the verification of the aerodynamic rotor model in Section
27.2.3 show only that the more exact representation does include a short-lasting torque
pulse. However, it is not known whether this torque pulse may significantly alter the
final results of any overall transient stability study or whether it can be neglected
without any significant consequences for the final results.
24.6.2.3 Small signal stability
Small signal stability is associated with the ability of a system – usually a large system,
such as an entire interconnected AC power system – to return to a stable point of
operation after a smaller disturbance. In a textbook example of a small signal stability
analysis, the eigenvalues of the system, which are usually complex, and the correspond-
ing eigenvectors are determined. However, since a large system may easily include many
hundreds or even thousands of state variables – not to mention the exact same number
of complex eigenvectors of exactly the same dimension – it is by no means a simple task
to do this with adequate numerical accuracy.
Some dynamic stability programs include in their very nature the necessary model
data for the physical system and the relevant control systems, having built-in modules to
perform eigenvalue analyses. Examples of such models are PSS/E, with the module
LSYSAN (Linear System Analysis), and Simpow. These two programs are compared in
Persson et al. (2003). We also assume that other dynamic stability programs will include
similar linear system analysis modules. For additional references, see, for example,
Paserba (1996), which gives an overview of a number of linear analysis software
packages. There are also special programs for eigenvalue analysis, such as AESOPS
and PacDyn. Bachmann Erlich and Grebe (1999) provide an example of eigenvalue
analysis on the UCTE (Union pour la Coordination du Transpo rt d’Electricite) system
with use of such a specialised eigenvalue analysis software.
If convenient, it is also possible to perform an indirect small signal stability analysis
directly by using a time domain dynamic stability analysis program. Applying a small
disturbance will in most cases excite the predominant eigenoscillations in the system,
and the eigenoscillations will then be visible in many output variables such as voltages,
currents, rotor speeds, and so on. A postprocessing, where the frequency and the
damping of the various swing modes in a selected section of the postdisturbance output
curves are calculated, will then give a goo d indication of the eigenvalues that were
excited by the disturbance. This is an easy way to get an initial idea of a system or to
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confirm results obtained through eigenvalue analyses. This is addressed in Bachmann
Erlich and Grebe (1999).
Hitherto, wind turbines have not been taken into account in connection with small
signal stability investigations because of the nature of wind power production, which
traditionally has been dispersed in the power system, and because of the size of the
individual wind turbines, which are several orders of magnitude smaller than centralised
power plants and even more orders of magnitude smaller than the total interconnected
power system. However, the size of individual wind turbines and entire wind farms on
land as well as offshore is increasing, resulting in a higher wind power penetration.
In addition, the controllability of modern wind turbines is being improved. This feature is
becoming increasingly important because of the increasingly demanding grid codes.
Therefore, wind power will increasingly be included in small signal stability investigations.
The general level of detail in small signal stability programs requires a reasonable
wind turbine model in such programs to include the components that may contribute to
and have an impact on the eigenoscillations of the system (i.e. linearised representations
of the shaft system, the control system, the generator and possible power electronics).
Other parts of the construction may be neglected or considered constant, such as, the
incoming wind and all discrete actions performed by the control and protection system.
24.6.2.4 Aerodynamic modelling and mechanical dimensioning
The design of a wind turbine involves many decisio ns regarding mechanical construc-
tion and aerodynamic design. In this process, the wind turbine itself is at the very centre
of investigations. The strength and shaping of the blades, the dimensioning of the shafts
and gear, the strength of the tower and even the tower foundation – especially for
offshore wind turbines – have to be considered carefully when designing a wind turbi ne.
As we have not been working with these aspects of wind turbine development, the
following are rather general statements.
There are many CAD-like simulation tools that can handle mechanical constructions,
on the one hand, and other tools that can deal with aerodynamic propert ies, on the
other hand. However, in the design phase of a wi nd turbine, the mechanical and the
aerodynamic properties must be regarded as a whole. Consequently, there is a need for
specialised simulation tools that can deal with both aspects at the same time. One such
tool is FLEX4, which can represent blade deflection, as well as the torsional twist of the
shaft system and the tower. A newer version, FLEX5, can also cope with the deflections
of the tower and the foundation (Christensen et al., 2001).
A reasonable wind turbine model in such programs has to include the major mechan-
ical and aerodynamic components of the wind turbine [i.e. the blades, the pitch servo
system (if pitching changes are to be evaluated), the shaft system (including gearbox),
the generator (as a minimum representation, there must be a decelerating torque), the
tower and, in some cases, the foundation]. Also, the emergency disc brake can be
included if the mechanical impact of an emergency shutdown on the turbine is to be
evaluated. Finally, as the most significant external factor influencing a wind turbine is
the wind itself, it must be represented in a realistic way such as by measured wind series,
preferably with frequent wind gusts.
550 The Modelling of Wind Turbines