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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003
Modeling and Control of a Wind Turbine Driven
Doubly Fed Induction Generator
Arantxa Tapia, Gerardo Tapia, J. Xabier Ostolaza, and José Ramón Sáenz
Abstract—This paper presents the simulation results of a
grid-connected wind driven doubly fed induction machine (DFIM)
together with some real machine performance results. The modeling of the machine considers operating conditions below and
above synchronous speed, which are actually achieved by means
of a double-sided PWM converter joining the machine rotor to the
grid. In order to decouple the active and reactive powers generated
by the machine, stator-flux-oriented vector control is applied. The
wind generator mathematical model developed in this paper is
used to show how such a control strategy offers the possibility of
controlling the power factor of the energy to be generated.
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I. NOMENCLATURE
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Manuscript received February 5, 2001; revised December 4, 2001. This work
was supported by the electric generation company IBERDROLA S.A.
A. Tapia, G. Tapia, and J. X. Ostolaza are with the Systems Engineering
and Control Department, University of the Basque Country, Donostia-San Sebastián, 20011, Spain (e-mail: isptaota@sp.ehu.es).
J. R. Sáenz is with the Electrical Engineering Department, University of the
Basque Country, Bilbao, 48013, Spain (e-mail: iepsaruj@bi.ehu.es).
Digital Object Identifier 10.1109/TEC.2003.811727
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Index Terms—Doubly fed induction machine, power converter,
power factor, vector control, wind power generation.
Stator side power factor.
Wind turbine net power factor.
Grid frequency.
Stator magnetising current space phasor
modulus.
Direct- and quadrature-axis stator magnetising current components respectively,
expressed in the stationary reference
frame.
Rotor current space phasor modulus.
Direct- and quadrature-axis rotor current
components respectively, expressed in the
stationary reference frame.
Direct- and quadrature-axis rotor current
components respectively, expressed in the
stator-flux-oriented reference frame.
Reference values of the rotor current
and
components, respectively.
Direct- and quadrature-axis rotor current
components respectively, expressed in the
rotor natural reference frame.
Direct- and quadrature-axis stator current
components respectively, expressed in the
stationary reference frame.
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Direct- and quadrature-axis stator current
components respectively, expressed in the
stator-flux-oriented reference frame.
Inner loop vector controller PI compensator parameters.
Outer control-loop PI compensator parameters.
Magnetizing inductance.
Rotor and stator inductances, respectively.
Rotor transient inductance.
Wind turbine net active and reactive
powers. Sum of the stator and rotor side
active and reactive powers, respectively.
Rotor side active and reactive powers, respectively.
Stator side active power actual and reference values, respectively.
Stator side reactive power actual and reference values, respectively.
Stator and rotor phase winding resistances,
respectively.
Direct- and quadrature-axis rotor decoupling voltage components, respectively, expressed in the stator-flux-oriented reference frame.
Direct- and quadrature-axis rotor voltage
components, respectively, expressed in the
stator-flux-oriented reference frame.
Direct- and quadrature-axis rotor voltage
components respectively, expressed in the
rotor natural reference frame.
Stator voltage space phasor modulus.
Direct- and quadrature-axis stator voltage
components, respectively, expressed in the
stationary reference frame.
Rotor electrical angle.
Phase angle of stator flux-linkage space
phasor with respect to the direct-axis of the
stationary reference frame.
Rotor electrical speed.
Angular slip frequency.
II. INTRODUCTION
W
IND energy is one of the most important and promising
sources of renewable energy all over the world, mainly
because it is considered to be nonpolluting and economically
viable. At the same time, there has been a rapid development of
related wind turbine technology [1]–[3].
0885-8969/03$17.00 © 2003 IEEE
TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR
Nevertheless, this kind of electric power generation usually
causes problems in the electrical system it is connected to, because of the lack or scarcity of control on the produced active
and reactive powers. Several designs and arrangements have
been implemented so as to cope with this difficulty [4]–[8].
As far as variable-speed generation is concerned, it is necessary to produce constant-frequency electric power from a variable-speed source [1], [3], [4], [9]. This can be achieved by
means of synchronous generators, provided that a static frequency converter is used to interface the machine to the grid.
An alternative approach consists in using a wound-rotor induction generator fed with variable frequency rotor voltage. This
allows fixed-frequency electric power to be extracted from the
generator stator. Consequently, the use of doubly fed induction
machines is receiving increasing attention for wind generation
purposes [6], [7], [10], [11]. One of the main advantages of
these generators is that, if rotor current is governed applying
stator-flux-oriented vector control—carried out using commercial double-sided PWM inverters, decoupled control of stator
side active and reactive powers results.
The ability to generate electricity with power factors different
—would reduce the costs of introducing adto one—
ditional capacitors for reactive power regulation, and would be
especially advantageous for both producers and distributors in
charge of transmission systems.
This paper aims to show the techniques followed to control a
DFIM power factor. Several significant simulation results, obtained after modeling both the generator and its overall control
system in MATLAB/SIMULINK, validated with real machine
performance results are also presented.
III. WIND TURBINE MODEL
Several models for power production capability of wind turbines have been developed and can be found throughout the bib, capliography [4], [7], [9], [12]. The mechanical power
tured by a wind turbine, depends on its power coefficient
given for a wind velocity and can be represented by
(1)
where and correspond to the air density and the radius of
the turbine propeller, respectively.
The power coefficient can be described as the portion of mechanical power extracted from the total power available from
power coefthe wind, and it is unique for each turbine. This
ficient is generally defined as a function of the tip-speed-ratio
which, in turn, is given by
(2)
where represents the rotational speed of the wind turbine.
Fig. 1 shows a typical relationship between the power coefficient and the tip-speed-ratio. It should be noted that there
. Thus, it can be
is a value of to ensure a maximum of
stated that, for a specified wind velocity, there is a turbine rotational speed value that allows capturing the maximum mechanical power attainable from the wind, and this is, precisely, the
turbine speed to be followed.
Fig. 1.
195
Typical power coefficient versus tip-speed-ratio curve.
Fig. 2. DFIM configuration.
The method followed in this paper in order to reach the optimum tip-speed-ratio at each wind velocity consists in, based
on the generator rotor speed, estimating and, therefore, trying
to achieve the optimum active power to be generated by means
of the rotor current stator-flux-oriented vector control.
power coeffiSpecifically, assuming that the optimum
tip-speed-ratio values for
cient and, as a result, the optimum
the particular wind turbine employed are properly identified, the
which is made
stator side active power reference value
is established starting from the turbine anequal to
gular speed through (1) and (2).
This operation principle is only effective below the rated wind
speed, where the available wind power does not exceed the rated
capacity of the generator. However, above the rated wind speed
pitch regulation is applied so as to limit the attainable wind
power, hence leaving the optimal power coefficient operation.
IV. DOUBLY FED INDUCTION GENERATOR ELECTRICAL MODEL
The basic configuration of a DFIM is sketched in Fig. 2. The
most significant feature of this kind of wound-rotor machine is
that it has to be fed from both stator and rotor side.
Normally, the stator is directly connected to the grid and the
rotor is interfaced through a variable frequency power converter.
In order to cover a wide operation range from subsynchronous
to supersynchronous speeds, the power converter placed on the
rotor side has to be able to operate with power flowing in both
directions. This is achieved by means of a back-to-back PWM
inverter configuration. The operating principle of a DFIM can be
analyzed using the classic theory of rotating fields and the wellmodel, as well as both three-to-two and two-toknown
three axes transformations.
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003
TABLE I
DFIG ELECTRIC PARAMETERS
system outputs. As a result, the state equations implemented in
MATLAB are the following:
Fig. 3. Stator and rotor side reference frames for the “Quadrature-Phase
Slip-Ring” model.
In order to deal with the machine dynamic behavior in the
most realistic possible way, both stator and rotor variables are
referred to their corresponding natural reference frames in the
developed model. In other words, the stator side current and
voltage components are referred to a stationary reference frame,
while the rotor side current and voltage components are referred
to a reference frame rotating at rotor electrical speed, —see
Fig. 3. The machine electrical model expressed in such reference frames is referred to as the “Quadrature-Phase Slip-Ring”
model [8].
When aiming to express the induction machine electrical
model in the above-mentioned reference frames, it is first
necessary to perform the Clarke’s transformation from the
current and voltage system, through
three-phase to the
the equations given in the Appendix.
In this way, taking the general three-phase model of the
electric machine dynamic performance as starting point, the
“Quadrature-Phase Slip-Ring” model for the DFIM might be
expressed through the following matrix equation See equation
represents the
(3) at the bottom of the page. where
Laplace differential operator.
The roles of current and voltage components in (3) need
to be interchanged so as to treat voltages as independent
variables—system inputs—and currents as dependent variables—system outputs, as corresponds to a voltage doubly
fed induction generator (DFIG). On top of this, each of the
equations included in (3) is rewritten according to a nonlinear
state equation, in order to achieve expressions whose structure
is compatible with that of S-function-type C-MEX files. The
,
, and
—correspond to
states to be considered— ,
(4)
(5)
(6)
(7)
where all inductances are assumed to remain constant.
In order to obtain the electric parameters needed to completely define the dynamic model of a four-pole 660–kW
wound-rotor induction generator, different experimental tests
were performed in a test-bed placed in the origin factory. From
those standard tests, the parameter values referred to a 20 C
ambient temperature, collected in Table I, were obtained.
(3)
TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR
197
Therefore, the parameters defined for the dynamic model are
computed as follows:
mH
mH
mH
(8)
V. THERMAL STUDY
Since the main objective of this research work consists in
designing a controller so as to let the DFIG work with different
power factors, the operating limits of the machine in regard to
active and reactive powers need to be accounted for.
One of the main aspects to be considered when trying to
govern the reactive power generated or absorbed by a DFIG, is
directly related to the temperature—heat—reached on the rotor
side because of the high rotor currents the back-to-back PWM
converter may drive. Such currents may cause damage to the
insulation of the rotor windings, hence reducing the machine
life span. As a result, while the working temperature increases,
the amount of heat that can be removed out from the machine
diminishes and, consequently, the value of the highest current
that is allowed to be driven into or out of the DFIG rotor also
decreases.
In order to obtain an analytical expression relating the stator
side active and reactive powers with the rotor side current maximum value, the following expressions are considered [8]:
(9)
Fig. 4. Generator P –Q limits for several operating temperatures.
capability, several limit – curves, shown in Fig. 4, have been
derived from the DFIM heating test by considering different operating temperatures—30, 50, and 60 C, exactly—, which lead
to different values of the maximum permissible rotor current.
The solid curve at the top of Fig. 4, which has been derived by
considering that the bidirectional PWM is able to handle currents up to 400 A, reflects the limitation imposed just by this
rotor side converter. It has also to be stated that it can feed the
DFIG rotor with instantaneous voltages up to 380 V. Generated
active and reactive powers are considered to be positive.
Consequently, considering the induction generator operating
limits provided in the – curves above, a control strategy has
to be designed in order to govern separately the active and reactive powers interchanged with the grid through the stator. This
can be achieved by implementing a stator-flux-oriented vector
control algorithm on the rotor side, which requires the determination of both the stator flux-linkage space phasor position and
rotor electric angle at each moment.
VI. CONTROL SCHEME
(10)
Based on (9) and (10), the equation for
given next is derived
–
load curves
(11)
corresponds to the rotor current maxwhere
imum value. According to (11), the radius and eccentricity of
any load curve can be easily computed as
and
, respectively.
As already mentioned, the limitation curve given in (11) is
directly related to the rotor side current maximum value. Therefore, as the ambient temperature increases, the radius of the
, the highest current that is
semicircle becomes smaller since
allowed to flow through the DFIG rotor, decreases. On the other
hand, the eccentricity inherent to – load curves is caused by
the inductive nature of induction machines.
Based on (11), and considering the restrictions imposed by
rotor slip-rings and brushes, as well as those due to converter
The DFIM control structure shown in Fig. 5 contains two
cascaded control-loops. The outer one governs both the stator
side active and reactive powers, so that the power factor setpoint value demanded by the electric energy distribution company is complied with as accurately as possible. Simultaneously,
it would be convenient to employ profitably the whole active
power generation capability provided by the wind at each moment, from the income-yield capacity point of view.
On the other hand, the inner control-loop task consists in conand quadratrolling independently the rotor current direct
components expressed according to the reference frame
ture
fixed to the stator flux-linkage space phasor. In order to implement this inner control-loop, the stator-flux-oriented vector control method based on two identical PI controllers is used.
It has to be pointed out that Tustin’s trapezoidal method
[13] has been used to discretise the PI controllers in both inner
and outer control-loop algorithms. Consequently, a hybrid
model containing a continuous induction machine and discrete
controllers has been developed in MATLAB/SIMULINK using
S-function type C-MEX files. Furthermore, as the controllers
used are PI type, anti wind-up algorithms have also been
implemented so as to prevent converter saturation.
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003
Fig. 5. Overall control structure for the DFIM.
Particularly, if the control signals originally computed in the
inner or outer loops exceed the bidirectional converter capability, they are limited in such a way that priority is given to
active power set-point achievement, rather than attempting to
ensure the reactive power reference value demanded.
A. Vector Control Implementation
As stated in (9) and (10), when governing a stator-flux-oriented vector-controlled generator, it can be proved that variations in rotor current real and imaginary components— ,
—are directly reflected on their corresponding stator current
components— , —provided that they are all referred to the
reference frame fixed to the stator flux-linkage space phasor [8].
and
are used to control the stator reactive and
Therefore,
active powers, respectively.
Thus, the steps followed to model and implement this vector
control algorithm are described below and can also be identified
in Fig. 5.
1) Three-to-two phase Clarke’s transformation of measured
stator and rotor side currents in their corresponding natural reference frames.
2) Estimation of the stator flux-linkage space phasor angular position with respect to the stationary direct axis.
Since the rotor side current components need first to be
changed from their natural axes to the stationary reference frame, it is necessary to measure the rotor angle. The
equations to be followed are given next
3) Expression of the rotor current space phasor in the reference frame fixed to the stator flux-linkage space phasor,
so as to compare its
and
components with their
and
set-point values. Based
corresponding
on the errors in both current components, the voltage
and
components to be applied to the rotor side are generated by means of two identical PI controllers, as shown
below
(13)
For this particular case, both PI controllers in (13) have
been tuned applying the pole assignment method, in an
attempt to reach a critically damped inner loop response
with a 40-ms settling time. Furthermore, inclusion of parameter allows placing independently not only the inner
loop poles, but also the unique zero inherent to the PI controller. Particularly, if is made equal to zero, the PI conand, as a result, its influtroller zero is placed at
ence on the closed-loop time response is cancelled out.
4) In order to improve the decoupling between and axes,
and
decoupling voltage components given
the
and
, respectively
below are added to
(14)
,
, and
. The resultant voltages in both
and
.
axes will be referred to as
where
(12)
TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR
Fig. 6. Three-phase voltages applied to the rotor.
Fig. 7.
Fig. 8.
Time response of the rotor current i
199
component.
Fig. 9. Generated active power performance.
Rotor three-phase currents.
5) Expression of
and
according to the rotor natural
reference frame as follows:
(15)
and
6) Clarke’s inverse transformation of rotor voltage
components from two-to-three phases.
It is worth pointing out that replacing the voltage-controlled
back-to-back PWM sketched in the control scheme proposed in
Fig. 5 with a current-controlled rotor converter, this inner control-loop—PI controllers and computation of decoupling voltages—could be avoided. Actually, it would be sufficient to apply
the reference frame change and the two-to-three phase transformation, given in steps 5. and 6. respectively, to current compoand
provided by the outer loop, in order to
nents
generate the three-phase current signals to be demanded to the
rotor converter.
Some results obtained when simulating the described model
are provided in Figs. 6–12. These results correspond to a test
carried out according to Table II, in which, keeping wind condim/s and
kg/m —, six changes
tions constant—
Fig. 10.
Time response of the rotor current i
component.
in rotor current
and
reference values were performed.
First, two changes affected both components simultaneously,
while last four involved only one of them.
Figs. 6 and 7 show the three-phase voltages applied to the
rotor side through the converter and the resulting rotor threephase currents. On the other hand, the correlation existing beand
components and the stator
tween the rotor current
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003
Fig. 11.
ergy is employed not only to generate electric power, but also
to produce rotational mechanical energy, which is associated to
rotor speed. Therefore, since the wind power provided to the turbine remains constant during this test, generated active power
increases and decreases, shown in Fig. 9, give rise to rotor decelerations and accelerations, respectively.
In addition, Figs. 9 and 12 prove that, below the synchronous
speed, the rotor side
power flows from the grid to the DFIG,
whereas, at supersynchronous speeds, it flows in the opposite
direction. This slip power management, which is closely related
to slip frequency control, allows to generate electric energy at
synchronous frequency permanently, in spite of rotor angular
speed significant variations.
As a result, it can be stated that the implemented vector control algorithm achieves very good decoupling of the stator side
active and reactive powers, thus making it possible to follow
either stator side or net different power factor reference values
just by adding an outer control-loop which performs a relatively
simple control strategy.
Reactive power performance.
B. Outer Control-Loop Design
Fig. 12.
Rotor angular speed time response.
TABLE II
SET-POINT VALUES
FOR i
AND i
CURRENT
DURING THE TEST
COMPONENTS
Once the vector control algorithm has been implemented on
the induction generator, it is required to design the outer loop
control law, which is responsible for providing the power generation process with the desired power factor. The steps followed
by the designed control algorithm are summarized next:
active power to be gen1. Calculation of the optimum
angular speed.
erated from the instantaneous rotor
It should be noticed that, once this outer control-loop has been
active power intercorrectly implemented, the amount of
changed between the grid and the DFIG through its rotor side,
net
turns out to be only a short fraction of the wind turbine
active power. Consequently, the stator side active power does
not differ significantly from .
reactive power to be
2. Computation of the stator side
generated or absorbed, based on the instantaneous active power
set-point obtained in the previous step and the desired
or
,
either stator side or net power factor—
respectively.
If the specification to be complied with corresponds to the
is straightforstator side power factor, the calculation of
ward
(16)
side active and reactive powers, respectively, can be clearly observed in Figs. 8–11, where both generated active and reactive
powers have been assumed to be negative. The time response of
rotor side- as well as wind turbine net active and reactive powers
are also displayed in Figs. 9 and 11, respectively.
At this point, it is convenient to highlight that, even though
wind conditions do not alter during the whole test, the amount of
generated active power can be varied just by modifying the
current component value, provided that the outer control-loop
shown in Fig. 5 is not yet implemented.
Moreover, the machine rotor accelerations and decelerations
current component setobserved in Fig. 12 correspond to
point changes. In fact, it has to be considered that wind en-
net power factor
On the other hand, if a wind turbine
is derived as follows:
is specified as set-point,
(17)
where the rotor side active and reactive powers might be either
measured or estimated as
(18)
TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR
201
As far as the sign of
is concerned, it has necessarily to
be established by considering the nature of the requested power
factor. Accordingly, leading capacitive and lagging inductive
power factors should give rise to reactive power generation and
consumption, respectively. In addition, it is checked whether the
produces an operating point within the limits
resulting
defined by the DFIG – load curve or not. If not, it is limited
according to this restriction.
3. Application of two identical PI compensators to the previously decoupled stator side active and reactive power controland
rotor curloops, in order to generate the reference
rent components to be followed by the inner control-loop—see
Fig. 5—as
Fig. 13.
Generator net power factor time response.
Fig. 14.
Rotor angular speed time response.
Fig. 15.
Rotor current i
(19)
Since, according to (9) and (10), it turns out that signals
and
as well as
and
exhibit contrary signs at any time
[8], it is essential to note that, for this outer loop, the error signals
fed into its PI controllers are obtained by subtracting the setor
—from
point of the variable to be controlled—
or , respectively.
its actual value—
Similarly to the inner loop case, these two PI controllers are
again tuned following the pole assignment method. In particular,
a monotonically increasing time response with no overshooting
and a 70-ms settling time is demanded for the outer control-loop.
The function of factor is equivalent to that satisfied by parameter in the inner loop.
The stator side actual active and reactive powers are measured
by means of a digital power analyzer, so that their corresponding
error signals are fed into the PI controllers given in (19).
During the test, whose simulation results are collected in
Figs. 13–20, in addition to changing the wind turbine net
power factor set-point four times, sudden wind speed variations
were applied in order to evaluate the overall control-system
performance under wind gusts. Nevertheless, since the wind
speed did not exceed its rated value all through the test, no pitch
regulation took place. As shown in Table III, throughout the
first four test stages, the wind speed and the net power factor
set-point were alternatively varied, while in the last two both
variables were simultaneously changed. In addition, the DFIG
net power factor was kept lagging during these last two stages.
Fig. 13 shows the fast wind generator response to DFIG net
power factor set-point changes. It should also be noted that,
once the outer control-loop is put into operation, only wind
speed changes can cause the generated active power to vary,
, depends
since rotor angular velocity, which establishes
on wind speed. Thus, the overall control-system designed allows
the generator to work properly either under subsynchronous or
supersynchronous conditions, as shown in Fig. 14.
and
rotor curOnce again, the relationship between the
rent components and the stator side active and reactive powers
component time response.
becomes evident in Figs. 15–18, where generated active and reactive powers have been taken as negative. As stated before,
Fig. 16 reveals that, provided that the outer control-loop works
properly, the DFIG net and stator side active powers turn out to
be very similar. Finally, the three-phase rotor voltages and currents corresponding to this test are also displayed in Figs. 19 and
20, respectively.
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003
Fig. 16.
Generated active power performance.
Fig. 17.
Rotor current i
component time response.
Fig. 19.
Rotor three-phase voltages.
Fig. 20.
Rotor three-phase currents.
TABLE III
NET POWER FACTOR SET-POINT AND WIND SPEED VALUES DURING THE TEST
Fig. 18.
Reactive power performance.
VII. COMPARISON BETWEEN REAL AND SIMULATED RESULTS
In order to validate the wind generator model performance
when the designed control law for stator active and reactive
power decoupling is applied, some graphs comparing real and
simulation results are presented.
Figs. 21 and 22 show the dynamic behavior of a real 660-kW
generator working in a wind farm when, generating 300 kW as
,
a result of the wind speed at the moment with a
sudden stator side power factor set-point changes take place. In
both cases, this new set-point corresponds to a
power factor, leading in Fig. 21, and lagging in Fig. 22. Generated active and reactive powers are considered to be positive.
Since wind conditions remain constant during the whole test, it
can be seen that generated stator active power does not change,
while stator side reactive power varies rapidly so as to track the
power factor new set-point.
On the other hand, the simulated dynamic performance of the
wind generator model described throughout this paper is shown
TAPIA et al.: MODELING AND CONTROL OF A WIND TURBINE DRIVEN DOUBLY FED INDUCTION GENERATOR
Fig. 21.
case.
203
Dynamic performance of a real wind generator. Leading power factor
Fig. 24. Simulated dynamic performance of the wind generator model.
Lagging power factor case.
Fig. 22.
case.
Dynamic performance of a real wind generator. Lagging power factor
paper, correspond strictly to those of a real doubly fed induction generator working in a wind farm.
Even if working conditions and, consequently, the optimum
of active power to be generated vary because of changes in wind
speed, the designed control laws are capable of keeping track of
the desired power factor in the wind generator. Nevertheless,
it is worth pointing out that the above-mentioned curve, which
provides the optimum active power to be generated for each
wind speed, could be optimized and tested using the developed
wind generator model.
Since the simulation results obtained so far are really satisfactory, it would be especially interesting to build a wind farm
model based on the wind generator model described in this
paper, so as to design and analyze possible power factor control
laws for the overall wind farm system.
APPENDIX
Any three-phase stator or rotor electrical magnitude can be
expressed according to its natural reference frame—stationary,
if it is a stator side quantity, and rotating at rotor electrical speed
if it is a rotor side quantity—direct, quadrature, and zerosequence components as follows:
Fig. 23. Simulated dynamic performance of the wind generator model.
Leading power factor case.
(20)
in Figs. 23 and 24. The simulation reproduces the real test conditions so that, for a constant wind speed, a sudden change in the
stator side power factor set-point is introduced, thus varying its
to a leading—Fig. 23—or lagreference value from
. Since simulation results obging—Fig. 24—
tained in these and other diverse tests are completely according
to the wind generator real behavior, the reliability of the developed model is proved.
where represents the stator or rotor side voltage, current or
flux-linkage. Equation (20) is referred to as Clarke’s transformation. Similarly, the Clarke’s inverse transformation from
to three-phase quantities can be carried out just by applying the matrix equation given next
VIII. CONCLUSION
The simulation results obtained when running the wind generator and its overall control-system model presented in this
(21)
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 18, NO. 2, JUNE 2003
ACKNOWLEDGMENT
We would especially like to thank R. Criado and J. Soto from
the electric generation company IBERDROLA for their helpful
comments. The authors are also grateful to the induction generator manufacturing company, INDAR, and the control systems
company, INGETEAM, for their contribution in providing the
electric machine characteristics and all the test results needed
for this research work; special thanks to G. Rivas, J. Garde, and
J. Mayor.
Arantxa Tapia was born in San Sebastián, Spain, on September 24, 1963. She
received the electrical engineering degree from the School of Industry Engineers, University of Navarra, Spain, in 1987. She received the Ph.D. degree in
1992 from the Univeristy of Basque Country.
Currently, she is Full Professor in Control at the University of Basque
Country. She joined the University of the Basque Country in the Systems Engineering and Control Department. She worked for five years in the Electronics
and Control Department in CEIT, a research center in the Basque Country. Her
current research interests include control and monitoring of different processes
as ac machines and different industrial multivariable processes.
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Gerardo Tapia was born in San Sebastián, Spain, on April 22, 1970. He received the electrical engineer degree from the University of Navarra, Spain, in
1995, and the M.Sc. degree in digital systems engineering from Heriot-Watt
University, U.K., in 1996. He received the Ph.D. degree from the University of
the Basque Country Systems Engineering and Control Department, in 2001.
During the first half of 1997, he was an Assistant Researcher with Ikerlan Research Center, Spain. Currently, he is Full Lecturer in control and digital electronics with the University of the Basque Country Systems Engineering and
Control Department. His current research interests include wind power generation and control of electric drives based on vector and direct torque control
schemes.
J. Xabier Ostolaza was born in San Sebastián, Spain, on October 23, 1968. He
received the degree in Electrical Engineering from University of Navarra, Spain,
in 1993. He worked for five years in the Electronics and Control Department of
CEIT Research Centre, until he awarded a Ph.D. in 1998. After that, he joined
the University of the Basque Country in its Systems Engineering and Control
Department, where nowadays he is full lecturer in System Modeling and Control. His current research interests include Frequency-based Robust QFT Control, Distributed Electrical Generation Control and Process Automation.
José Ramón Sáenz was born on January 12, 1954. He received the Ph.D. degree
in electrical engineering from University of Navarra, Spain, in 1980.
Currently, he is Full Professor in the electrical engineering department (University of the Basque Country) and Head of the Department. He leads an appreciable number of research groups and projects in areas such as wind energy,
electric energy systems, deregulated electric markets, and electrical machinery.