![TABLE I VALUES OFROUGHNESSLENGTHz FORVARIOUS LANDSCAPETYPES[9], [10]](/figures/table-i-values-ofroughnesslengthz-forvarious-landscapetypes-2u42t4ef.webp)
144 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 1, FEBRUARY 2003
General Model for Representing Variable Speed Wind
Turbines in Power System Dynamics Simulations
J. G. Slootweg, Member, IEEE, S. W. H. de Haan, Member, IEEE, H. Polinder, Member, IEEE, and
W. L. Kling, Member, IEEE
Abstract—A tendency to erect ever more wind turbines can be
observed in order to reduce the environmental consequences of
electric power generation. As a result of this, in the near future,
wind turbines may start to influence the behavior of electric power
systems by interacting with conventional generation and loads.
Therefore, wind turbine models that can be integrated into power
system simulation software are needed.
In this contribution, a model that can be used to represent all
types of variable speed wind turbines in power system dynamics
simulations is presented. First, the modeling approach is com-
mented upon and models of the subsystems of which a variable
speed wind turbine consists are discussed. Then, some results
obtained after incorporation of the model in PSS/E, a widely
used power system dynamics simulation software package, are
presented and compared with measurements.
Index Terms—Grid integration, modeling, power system dy-
namics, PSS/E, simulation, variable speed wind turbine.
I. INTRODUCTION
A
S A RESULT of increasing environmental concern, the
impact of conventional electricity generation on the envi-
ronment is being minimized and efforts are made to generate
electricity from renewable sources. The main advantages of
electricity generation from renewable sources are the absence
of harmful emissions and the infinite availability of the prime
mover that is converted into electricity. One way of generating
electricity from renewable sources is to use wind turbines that
convert the energy contained in flowing air into electricity.
Up to this moment, the amount of wind power integrated into
large-scale electric power systems only covers a small part of
the total power system load. The rest of the power system load
is for the largest part covered by conventional thermal, nuclear,
and hydropower plants.
Wind turbines mostly do not take part in voltage and fre-
quency control and if a disturbance occurs, the wind turbines are
disconnected and reconnected when normal operation has been
resumed. Thus, notwithstanding the presence of wind turbines,
frequency and voltage are maintained by controlling the large
power plants as would have been the case without any wind tur-
bines present.
This is possible, as long as wind power penetration is still low.
However, a tendency to increase the amount of electricity gen-
Manuscript received April 26, 2001; revised May 17, 2002. This work was
supported by the Dutch Organization for Scientific Research (NWO).
The authors are with Faculty of Information Technology and Systems,
Delft University of Technology, 2600 GA Delft, The Netherlands (e-mail:
j.g.slootweg@its.tudelft.nl).
Digital Object Identifier 10.1109/TPWRS.2002.807113
erated from wind can be observed. Therefore, the penetration of
wind turbines in electric power systems will increase and they
may begin to influence overall power system behavior, making
it impossible to run a power system by only controlling con-
ventional large-scale power plants. It is therefore important to
study the behavior of wind turbines in an electric power system
and their interaction with other generation equipment and with
loads.
In this paper, a general model for representation of variable-
speed wind turbines in power system dynamics simulations is
presented. The model has been developed to facilitate the inves-
tigation of the impact of large amounts of wind turbines on the
behavior of an electric power system. Power systems simulation
software is used to study this subject. Therefore, the level of de-
tail of the model derived here is similar to the level of detail of
models of other generation equipment in power systems simula-
tion software. This enables the integration of the model in these
programs as is shown by simulation results.
The paper is organized as follows. First, the modeling ap-
proach is commented upon and models of the subsystems of
which a variable speed consists are discussed. Then, simula-
tion results obtained after integration of the derived variable-
speed wind turbine model in the power system dynamics simu-
lation software package PSS/E are presented and compared with
measurements.
II. M
ODEL REQUIREMENTS
The goal of the work is to develop a general model to rep-
resent the two most important actual variable-speed wind tur-
bine concepts in powersystemdynamicssimulations.Inthe first
concept, variable-speed operation is enabled through the use of
a doubly fed induction generator with a back-to-back voltage
source converter feeding the rotor winding. In the second con-
cept, a direct drive synchronous generator is used, which is grid
coupled through a diode rectifier and voltage source converter
or through a back-to-back voltage source converter. The derived
model can also be used to represent the variable-speed wind tur-
bine concept of a squirrel cage induction generator, grid cou-
pled through a back-to-back voltage source converter, which is,
however, not used very much in practice and will therefore not
be paid further attention to. Detailed descriptions of these con-
cepts can be found in textbooks on wind energy, for example,
[1].
Keeping in mind that our goal is to derive a model that can be
used in power system dynamics simulations, it should be pos-
sible to easily integrate the developed model into power system
0885-8950/03$17.00 © 2003 IEEE
SLOOTWEG et al.: VARIABLE SPEED WIND TURBINES IN POWER SYSTEM DYNAMICS SIMULATIONS 145
dynamics simulation software packages. To make this possible
indeed, anumberof requirements havetobe posed on the model,
namely
• The wind turbine model should have a level of detail sim-
ilar to the models of the other system components (i.e.,
only the subsystems that determine the behavior in the
frequency range of interest should be incorporated in the
model).
• The wind turbine model should be characterized by a min-
imum number of parameters.
• Integration of the wind turbine model should not lead to
the need for a smaller simulation time step.
• The wind turbine model should only contain fundamental
harmonic components of current and voltage, because
transients and harmonics are not taken into account in
power system dynamics simulations.
The last requirement leads to a decrease in computation time,
because the number of differential equations is substantially re-
duced and because a larger time step can be used due to the
neglect of small time constants [2], [3].
III. S
UBSYSTEM MODELS
A. Subsystems
In this section, the various subsystems of a variable-speed
wind turbine will be modeled, namely
• wind speed model for generating a wind speed signal that
can be applied to the rotor;
• rotor model for converting the kinetic energy contained in
the wind into mechanical power that can be applied to the
generator;
• model of the generator and the converter, converting me-
chanical power into electric power and determining the
rotor speed;
• rotor speed controller for deriving a power set point from
the rotor speed versus generator power control character-
istic, based on the actual rotor speed;
• pitch angle controller for changing the blade pitch above
nominal wind speed preventing the rotor speed from be-
coming too high;
• voltage controller for keeping the terminal voltage near its
reference value;
• protection system for limiting the converter current and
for switching off the wind turbine when terminal voltage
or grid frequency deviation exceed a specified value for a
given time.
In Fig. 1, the above subsystems and the way they are connected
is depicted.
B. Wind Speed Model
The wind speed model consists of a source that generates a
wind speed signal to be applied to the wind turbine. The wind
speed signal consists of four components, namely the mean
wind speed; a wind speed ramp, which is a steady increase in
the mean wind speed; a wind gust; and turbulence. The eventual
wind speed to be applied to the wind turbine is the sum of these
four components [4], [5].
Fig. 1. Subsystems of which the variable speed wind turbine model consists
and their interactions.
TABLE I
V
ALUES OF ROUGHNESS LENGTH
z
FOR VARIOUS LANDSCAPE TYPES [9], [10]
Below the nominal wind speed, the initial wind speed is com-
puted from the power delivered by the wind turbine, as set in the
load flow used to initialize the dynamic simulation. Above the
nominal wind speed, an initial mean wind speed value has to be
given, because abovethe nominal wind speed, there is no unique
relation between wind speed and generated power [6].
The wind speed ramp is characterized by three parameters,
namely:
• amplitude of the wind speed ramp
[m/s];
• starting time of the wind speed ramp
[s];
• end time of the wind speed ramp
[s].
The wind speed gust is characterized by three parameters as
well, namely
• amplitude of the wind speed gust
[m/s];
• starting time of the wind speed gust
[s];
• end time of the wind speed gust
[s].
The wind gust is modeled using the following equation [4], [5]:
(1)
where
is the duration of the gust [s], which equals .
The turbulence has been modeled as a stationary process,
using the following equation for the turbulence spectral density
[7]:
(2)
where
is the frequency [Hz]; is the height at which the wind
speed signal is of interest [m], which normally equals the height
of the wind turbine shaft;
is the mean wind speed [m/s]; is
the turbulence length scale [m] which equals
if is less
146 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 1, FEBRUARY 2003
than 30 m and 600 if is more than 30 m; and is the roughness
length [m].
The roughness length depends on the structure of the land-
scape surrounding the wind turbine. In Table I, the values of
for variouslandscape types are given.Through the parameter ,
the dependence of the turbulence intensity on the landscape in
which the studied wind turbine is erected is taken into account.
In power system dynamics simulations, a signal in the time
domain instead of in the frequency domain is needed. The
method used here to derive a time-domain signal from a power
spectral density is described in [8] and used in [4] and [5].
The wind turbine model offers the possibility to change the
values of all characteristics of the wind speed signal to be ap-
plied, apart from the starting value of the mean wind speed when
the wind turbine delivers less than nominal power. This value is
calculated on the basis of the power generated by the wind tur-
bine in the initial load flow.
C. Modeling of the Rotor
The wind turbine rotor, that extracts the energy from the wind
and converts it into mechanical power is a complex aerodynamic
system. For state-of-the-art modeling of the rotor, blade element
theory must be used [1]. Modeling the rotor using blade element
theory has, however, a number of drawbacks.
• Instead of only one wind speed signal, an array of wind
speed signals has to be applied.
• Detailed information about the rotor geometry should be
available.
• Computations become complicated and lengthy.
To solve these problems, a simplified way of modeling the wind
turbine rotor is normally used when the electrical behavior of the
system is the main point of interest. An algebraic relation be-
tween wind speed and mechanical power extracted is assumed,
which is described by the following equation:
(3)
where
is the power extracted from the wind [W]; is the
air density [kg/m
]; is the performance coefficient or power
coefficient;
is the tip speed ratio; is the ratio between
blade tip speed
[m/s] and wind speed at hub height upstream
the rotor
[m/s] ; is the pitch angle of rotor blades [deg]; and
is the area covered by the rotor [m ].
Numerical approximations have been developed to calculate
for given values of and [1], [4], [5]. Here, the following
approximation is used:
(4)
with
(5)
It is not considered necessary to develop different approxima-
tions for the
of various wind turbine types. The differ-
ences between the curves of wind turbine types are very small
and can be neglected in dynamics simulations, although they are
Fig. 2. Power curve of two commercial wind turbines (dotted) and numerical
approximation (solid).
very important in other cases (e.g., when calculating the energy
yield). In Fig. 2, the power curves of two commercial wind tur-
bines are given, together with the general numerical approxima-
tion described by (4) and (5). The coefficientsin (4) and (5) have
been determined using a numerical optimization minimizing the
error between the power curve following from the equations and
the one from obtained from manufacturer documentation.
The rotor is modeled as a lumped mass and the shaft dynamics
are neglected. It should be noted that this is only allowed when
variablespeed wind turbines are studied. In constant speed wind
turbines, including a dynamic shaft model is very important, es-
pecially for flicker studies and transient stability investigations
[11]. However, it has been shown experimentally that in variable
speed wind turbines, the shaft properties are hardly reflected at
the grid connection due to the decoupling effect of the power
electronic converter [12], [13].
D. Modeling of the Generator/Converter
The combination of generator and converter is the main dif-
ference between the two most important actual variable speed
wind turbine concepts. In the first concept, the decoupling
of the grid frequency and the mechanical rotor frequency is
implemented by using a doubly fed induction generator with
a back-to-back voltage source converter feeding the rotor. In
the second concept, it is implemented by fully decoupling
the synchronous direct drive generator from the grid using a
back-to-back voltage source converter or a combination of a
diode rectifier coupled to the generator stator winding and a
voltage source converter coupled to the grid. The synchronous
generator can be excited using a rotor winding or permanent
magnets [1].
The goal of the research presented in this paper is to develop
a general model by which all variable speed wind turbine con-
cepts can be represented. Although the way in which variable
speed capability is realized differs among the various concepts,
the differences in the behavior with respect to grid interaction
are small. This can be explained by noticing that the power elec-
tronic converter decouples electrical and mechanical behavior
of the wind turbine on the time frame that is of interest in power
system dynamics studies. This conclusion is based on the fol-
lowing reasoning and supported by both theoretical and empir-
ical evidence [14]–[17].
The voltage equations of both a doubly fed induction gener-
ator and a synchronous generator can be found in [2] and will not
SLOOTWEG et al.: VARIABLE SPEED WIND TURBINES IN POWER SYSTEM DYNAMICS SIMULATIONS 147
be reproduced here. First, the terms in the stator voltage
equations of the doubly fed induction generator are neglected.
This is routinely done in power system dynamics simulations
for synchronous and asynchronous machines [2], [3].
Further, theoretical considerations and experiments lead to
the conclusion that in both concepts, the current controllers on
the power electronic converters act very fast. As a result, a new
current reference value can be met within 10 ms or less. Ten
milliseconds is the normal time step in power system dynamics
simulations. Thus, it can be concluded that the current will reach
its new value within one time step. This makes it possible to
model the power electronics converter as a controlled current
source instead of a controlled voltage source and to neglect the
terms in the rotor voltage equations of the doubly fed
induction generator and in the stator and rotor voltage equations
of the direct drive synchronous generator.
These assumptions are only valid when
• the machine parameters are known;
• the controllers operate in their linear region;
• vector modulation is used;
• the terminal voltage approximately equals the nominal
value.
The first two conditions have to be met by the wind turbine man-
ufacturer and are assumed to be fulfilled here. The third assump-
tion is met, because the control of the converter used in vari-
able-speed wind turbines is nearly always based on vector mod-
ulation [1]. The last assumption is not met during grid faults.
However, when a fault occurs, a variable speed wind turbine
is quickly disconnected to protect the power electronic con-
verter. Further, the response of the power electronic converter
to a voltage drop is characterized by very-high-frequency phe-
nomena that cannot be studied using normal power system dy-
namics simulation software. Therefore, a low-frequency repre-
sentation of the behavior of the converter during faults must be
incorporated in the model, such as is done for HVDC converters
[18]. The appropriateness of this approach is beyond the scope
of this paper.
As a result of the simplifications shown, an algebraic rela-
tion results between the
-component of the rotor current in the
doubly fed induction generator and stator currents of the direct
drive generator on one side and the electromechanical torque
on the other. This means that generator torque set points can
be reached instantaneously by injecting the appropriate rotor or
stator currents. Therefore, it is not necessary to drag along the
equations describing the two generator types. Instead, the gen-
erator can be modeled as a torque source, which immediately
generates an amount of torque equal to the set point generated
by the controller.
The only resulting differential equation associated with the
generator and the converter that remains after this simplifica-
tions is the equation of motion
(6)
In (6),
is frequency [per unit]; is the torque [per unit]; and
is the inertia constant of the rotating mass [s]. The indices
and are mechanical and electrical, respectively. The value of
Fig. 3. Optimal (solid) and implemented (dotted) rotor speed versus power
characteristic of an example variable-speed wind turbine.
is normally in the range of three to four and can be calculated
from the moment of inertia of the rotating mass [2].
E. Modeling of the Rotor Speed Controller
The speed controller of the wind turbine model operates as
follows:
• With a sample frequency
[hertz], the actual rotor speed
is measured. From this value, a set point for generator real
powerisderivedusingthe control characteristic. The value
of
is in the order of 20 Hz.
• From this value, a set point for the generated power is
derived using the control characteristic.
• Taking into account the actual generator speed, a torque
set point is derived from the power set point.
• As a result of the generator modeling approach described
before, this torque set point is realized immediately.
To acquire a set point for generated real power, a rotor speed
versus generator power characteristic is used. In most cases,
the rotor speed is controlled in such a way that optimal energy
capture is achieved. It is also possible to develop a rotor speed
versus power characteristic that serves other goals, such as noise
minimization.
The solid line in Fig. 3 depicts the rotor speed versus power
characteristic that leads to optimal energy capture. At low wind
speeds, the rotor speed is kept at its minimum by adjusting the
generator torque. At medium wind speeds, the rotor speed varies
proportional to the wind speed, and thus, with the cubic root of
the power, according to (3). When the rotor speed reaches its
maximum value, generator torque is kept at its maximum [19].
Controlling the power according to this speed versus power
characteristic, however, causes some problems.
• The desired power is not uniquely defined at nominal and
minimal rotor speed.
• If the rotor speed decreases from slightly above nominal
speed to slightly below nominal speed or from slightly
above minimal speed to slightly below minimal speed, the
change in generated power is very large.
To solve these problems, a control characteristic similar to the
one that leads to optimal energy capture is used here. This con-
trol characteristic is depicted by the dashed line in Fig. 3. The
points at which the implemented control characteristic deviates
from the control characteristic leading to optimal energycapture
can be adjusted in the wind turbine model. If these points lie near
the minimal and nominal rotor speed, the maximum amount of
148 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 1, FEBRUARY 2003
energy is extracted from the wind over a wide range of wind
speeds, but rotor speed changes near the minimum and nom-
inal rotor speed result in large powerfluctuations. If these points
lie further from the minimal and nominal rotor speed, the wind
speed range in which energy capture is maximal is narrowed,but
the power fluctuations near minimal and nominal rotor speed are
smaller.
F. Modeling of the Pitch Angle Controller
The pitch angle controller is only active in high wind speeds.
In those circumstances, the rotor speed can no longer be con-
trolled by increasing the generated power, as this would lead to
overloading the generator and/or the converter. To prevent the
rotor speed from becoming too high, which would result in me-
chanical damage, the blade pitch angle is changed in order to
reduce
.
Using (4) and (5), the pitch angle needed to limit the power
extracted from the wind to the nominal power of the wind tur-
bine can be calculated for each wind speed. From these equa-
tions, it can be concluded that the optimal pitch angle equals
zero below the nominal wind speed and from the nominal wind
speed on increases steadily with increasing wind speed. This ob-
servation greatly facilitates pitch control.
Furthermore, it should be taken into account that the pitch
angle cannot change immediately, but only at a finite rate, which
may be quite low due to the size of the rotor blades of modern
wind turbines and the desire to save money on the blade drives.
The maximum rate of change of the pitch angle is in the order
from 3 to 10
/s, depending on the size of the wind turbine. Fur-
ther, because the blade pitch angle can only change slowly, the
pitch angle controller works with a sample frequency
, which
is in the order of 1 to 3 Hz. In Fig. 4, the pitch angle controller
is depicted. The model offers the possibility to specify all pa-
rameters depicted in Fig. 4. In the simulations, the maximum
rate of change of the pitch angle and
equal 3 /s and 2 Hz,
respectively.
Note that using this controller type, the rotor speed is allowed
to exceed its nominal value by up to 20%, depending on
.
However, a proportional controller is used, because
• a slight overspeeding of the rotor above its nominal value
can be allowed and poses no problems for the wind turbine
construction [19];
• the system is never in steady state due to the varying
wind speed, so that the advantage of an integral controller,
which can achievezerosteady state error, is not applicable.
G. Modeling of the Voltage Controller
The voltage controller is based on the notion that to in-
crease the terminal voltage, more reactive power should be
generated, and to decrease the terminal voltage, less reactive
power should be generated by the wind turbine. As already
stated before, variable-speed wind turbine concepts enable full
reactive-power control, by changing the reactive component of
the grid current. In the first concept, this done by changing the
direct component of the rotor current and in the second concept
by changing the reactive component of the converter current at
the grid side. Although the reactive power is thus controlled in
Fig. 4. Pitch angle controller model.
Fig. 5. Voltage controller model.
different ways, simulations have shown that the resulting grid
interaction is very similar [20].
The voltage controller model used here is depicted in Fig. 5.
The model offers the possibility to change all parameters. Note
that the voltage controller can be used to operate the wind tur-
bine at unity power factor by setting
equal to 0. In the simu-
lations presented below,
= 50 and = 0.5 s. The value for
may seem quite high, but this can be explained by noticing
that the voltage controller determines the reactive power. The
current control loop, whose reference is derived from the re-
active-power set point, reaches a set point very quickly as dis-
cussed before. Therefore, in the simulations, the reactive power
is assumed to be the model’s output instead of the current. The
optimal value of
is dependent on the grid characteristics.
H. Modeling of the Protection System
The protection system consists of three parts:
• a converter current limiter;
• a part that switches off the wind turbine when the terminal
voltage deviates more than a specified amount from its
nominal value during a specified time interval;
• a part that switches off the wind turbine when the grid
frequency deviates more than a specified amount from its
nominal value during a specified time interval.
The converter current must be limited to protect the semicon-
ductor switches in the power electronic converter. For the same
reason, the wind turbine must be switched off when the terminal
voltage deviates more than a specified amount from its nominal
value.Frequency changes are not a problem for the wind turbine
itself. However, a large frequency deviation is an indicator that
there exists some problem, islanding for example, which may
make it desirable to disconnect the wind turbines or change the
control strategy.
The converter current limiter boundaries are specified by
giving the maximum amount of reactive power that the wind
turbine can generate in per unit. From this value and the nom-
inal active power, the nominal current is calculated for nominal
terminal voltage. This way of specifying the current limits is
considered more user friendly than specifying the current limits
directly. It is also possible to specify an overloading percentage
and a time during which the converter can be overloaded [21].