Sensorless Vector Control of Induction Machines for Variable

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196
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004
Sensorless Vector Control of Induction Machines for
Variable-Speed Wind Energy Applications
Roberto Cárdenas, Member, IEEE, and Rubén Peña, Member, IEEE
Abstract—A sensorless vector-control strategy for an induction
generator in a grid-connected wind energy conversion system is
presented. The sensorless control system is based on a model reference adaptive system (MRAS) observer to estimate the rotational
speed. In order to tune the MRAS observer and compensate for
the parameter variation and uncertainties, a separate estimation
of the speed is obtained from the rotor slot harmonics using an
algorithm for spectral analysis. This algorithm can track fast
dynamic changes in the rotational speed, with high accuracy.
Two back-to-back pulse-width-modulated (PWM) inverters are
used to interface the induction generator with the grid. The
front-end converter is also vector controlled. The dc link voltage
is regulated using a PI fuzzy controller. The proposed sensorless
control strategy has been experimentally verified on a 2.5-kW
experimental set up with an induction generator driven by a wind
turbine emulator. The emulation of the wind turbine is performed
using a novel strategy that allows the emulation of high-order wind
turbine models, preserving all of the dynamic characteristics. The
experimental results show the high level of performance obtained
with the proposed sensorless vector-control method.
Index Terms—Fuzzy logic, induction generator, induction motor
drives, spectral analysis, wind energy.
NOMENCLATURE
A. General
,
,
,
Air density.
Pitch angle.
Wind turbine blade radius.
Electrical torque.
Inertia and viscous friction.
Wind velocity.
Magnetizing, rotor, stator inductance.
Rotor, stator resistance.
Induction machine leakage coefficient.
DC link voltage.
Rotor flux.
Number of pole pairs.
Induction machine rotational speed.
Turbine rotational speed.
Electrical frequency (in radians per second).
Electrical frequency (in Hertz).
Rotor time constant.
Number of rotor slots.
Forgetting factor.
Manuscript received September 12, 2002. This work was supported in part
by the Chilean Research Council Conicyt under Grant 1000979 and in part by
internal grants from the University of Magallanes.
The authors are with the Electrical and Electronics Engineering Department,
University of Magallanes, Punta Arenas, Chile (e-mail: [email protected]).
Digital Object Identifier 10.1109/TEC.2003.821863
Shaft compliance.
Shaft viscous fiction.
B. Superscripts
Estimated value.
Reference value.
C. Subscripts
Stator fixed coordinates.
Synchronous rotating coordinates.
Rotor or stator quantities.
Turbine or generator quantities.
I. INTRODUCTION
T
HE advantages of cage induction machines are well
known. These machines are relatively inexpensive, robust, and require low maintenance. When induction machines
are operated using vector-control techniques, fast dynamic
response and accurate torque control are obtained [1]. All
of these characteristics are advantageous in variable-speed
wind energy conversion systems (WECS). The control systems for the operation of indirect rotor flux-oriented (IRFO)
vector-controlled induction machines for variable-speed wind
energy applications have already been discussed in [1]–[3]. In
[1], the number of transducers, rating of the power converters
and control schemes suitable to operate cage and doubly fed
induction machines are discussed. In [2] and [3], cage induction
machines are considered and a fuzzy control system is used to
drive the WECS to the point of maximum energy capture for a
given wind velocity. The induction machine is connected to the
utility using back-to-back converters.
In [1]–[3], speed encoders are used to implement the vectorcontrol strategies. The use of this encoder implies additional
wiring, extra cost, extra space, and careful mounting which detracts from the inherent robustness of cage induction machines
[4]–[6].
In this paper, a sensorless control structure based on a direct
rotor flux-oriented (DRFO) vector-control system, for variablespeed wind energy applications, is discussed. A speed estimation, obtained from a model reference adaptive system (MRAS)
[4], is used to control the electrical torque of the induction machine. A V/F control strategy is used in the low-speed region
for starting and driving the WECS set into the speed operating
range. In order to tune the MRAS system and compensate for the
variation of the machine parameters, an estimation of the rotational speed is obtained from the rotor slot harmonics (RSH) [7],
[8]. The spectral analysis method used in this publication can
track the rotational speed not only in steady state but also when
0885-8969/04$20.00 © 2004 IEEE
CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES
Fig. 1.
197
Control system proposed.
the WECS is subjected to fast dynamic changes. To the best of
our knowledge, this is the first publication discussing a sensorless vector-control method, including tuning of the MRAS observer, for a WECS.
The system proposed in this paper is shown in Fig. 1. An
induction generator is driven from an emulated variable-speed
wind turbine. A microprocessor-based system is used to implement the DRFO algorithms, the V/F control strategy, the MRAS
rotational speed observer, the spectral estimation algorithm, the
control of the front-end converter, and the emulation of the wind
turbine. The front-end converter supplies the electrical energy
into the grid. This converter controls the dc link voltage of the
back-to-back configuration using a fuzzy PI controller.
currents and voltages of the induction machine are
The
referred to a reference frame aligned to the rotor flux. These
currents take dc values in steady state. The rotor flux is calculated from the machine voltages and currents (“Voltage model”
in Fig. 1). The – components of the flux are used to calculate
the electrical angle for the vector rotators.
In Sections II–VII, the control system shown in Fig. 1 is discussed. Experimental results obtained from a 2.5-kW prototype
will be presented and fully analyzed.
II. WIND TURBINE MODELING
is the torque coefficient and
where
ratio defined as
is the tip-speed
(2)
The power captured from the wind turbine is obtained as
(3)
is the power coefficient. The value, which
where
maximizes the power coefficient, is the optimal tip-speed ratio
. For the experimental work of this paper, the
curve reported in [12] has been used. This curve is shown in
Fig. 2 for
. The model of a typical variable-speed wind
turbine [11] is shown in Fig. 3.
A. Torque Control of the Induction Generator
In the experimental work presented in this paper, the electrical torque is controlled according to the well-known control
strategy for below rated wind speed (BRWS) operation which,
in steady state, drives the WECS to the point of maximum energy capture [13]
(4)
There are several models appropriate for wind turbines depending on the size, blade radius, nominal power, shaft stiffness,
losses, gear box ratio, etc. [9]–[11]. The mechanical torque produced by the blades is given by
depends on
In (4), the losses have been neglected and
the blade aerodynamics and wind turbine parameters. The electrical torque of the DRFO induction machine is calculated as
(1)
(5)
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004
III. MRAS OBSERVER
A MRAS observer is used to estimate the rotational speed of
the induction machine. This observer is based on two models,
the voltage model and the current model [4]. The voltage model
is used to obtain the rotor flux as
(8)
The rotor flux is also calculated from the stator current, speed
and machine inductances. The flux from the current model is
obtained as
(9)
Fig. 2.
C versus curve (
= 0).
where the 2/3 arises from the 2–3 axes scaling and
is the
torque producing current. Using (4–5) the reference for the
torque current can be obtained as
In the MRAS observer, the flux obtained from (8) is used as
the reference. By adjusting the rotational speed, it is possible
to reduce the error between the reference flux and the flux estimated from (9). The error in – components is usually defined
as
(10)
(6)
For sensorless control, the estimated rotational speed
the MRAS observer is used in (6).
from
B. Wind Turbine Emulation
From Fig. 3, the discrete state equations of the wind turbine
can be obtained as
Equations (8)–(10) are used to implement the MRAS speed
observer. The error calculated using (10) is driven to zero by a
PI controller (see Figs. 1 and 4). The output of this PI controller
used in (6). The implemenis the estimated rotational speed
tation of the MRAS observer is shown in Fig. 4. The voltage
model is used to obtain the rotor flux using a band-pass filter
as a modified integrator to block the dc components of the measured voltages and currents. From the voltage model, the elecis calculated using the – components of the
trical angle
rotor flux. At the bottom of Fig. 4 is the current model and the
estimated speed .
A. Detuning of the Machine Parameters
(7)
where is the sampling time. The mechanical torque on the
blades is calculated from (1) and the electrical torque is calculated using the current [see (5)]. In (7)
, , ,
,
,
and
have been referred to the generator side of the gearbox
and the high-speed part of the shaft is considered very stiff.
A wind turbine emulation method, which preserves all of the
dynamic characteristics of a wind turbine, is obtained by implementing (7) in a microprocessor board [14]. The values of
,
, and
are calculated by the microprocessor in each sampling time. A speed control system, implemented using a dc machine driving the induction machine, is
used to force the generator speed to follow the value of
calculated from (7). With this emulation technique, the induction machine rotates at the same speed as that of a generator
driven by a real wind turbine. Further information about the
wind turbine emulation strategy used in this work can be found
in [14], [15].
The dynamic performance of a MRAS observer has been
studied in [4]–[6] and [16]. Using a small-signal model, it can
be shown that when the machine parameters are correctly estimated and the MRAS speed estimator is implemented using
a relatively large close loop bandwidth, the transfer function
is a first-order low-pass filter [4]. In this case, the
effects of the MRAS observer in the control system dynamics
are negligible. However, a MRAS observer with incorrect parameters can be considered as an encoder with inherent ripple
[5], producing oscillations and even instability. Besides the dynamic effects, incorrect parameters in the MRAS observer lead
to an estimated speed with a steady-state error [5], [6], [16]. The
steady-state speed error may give rise to the following.
1) Reduced Power Capture for BRWS Operation: Because
of steady-state speed error, the control strategy of (6) will not
drive the WECS to the point of maximum power capture. Using
(3), the reduction on the captured power, for BRWS operation
is calculated as
(11)
CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES
199
Fig. 3. Modeling of a typical wind turbine.
the wind velocity for ARWS operation. In [18], a wind speed
observer is proposed for BRWS control, and in [19], a torque
observer is presented for BRWS operation.
Therefore, it is important to have accurate speed estimation
for ARWS/BRWS operation. In Section V, a novel method for
obtaining the speed from the RSH is discussed. This method
can be used to tune the MRAS observer and compensate for
parameter variations
IV. SPEED ESTIMATION USING ROTOR SLOT HARMONICS
Fig. 4. MRAS observer implemented.
where
is the quiescent tip-speed ratio and
is the rotational speed for optimal energy capture. From (11), the reduction in the power captured depends both on the steady speed
error and the variation of the power coefficient in respect to the
tip-speed ratio.
2) Incorrect Pitch Control Operation: Pitch control of the
blades is used to avoid overloading the wind turbine for ARWS
operation as reported in [9] and [10]. The pitch angle is controlled using a rotational speed signal. When the rotational speed
, the torque is controlled
is below a given rotational speed
according to (4) [BRWS operation]. When the rotational speed
, the pitch angle of the blade is controlled to reis above
duce the power capture (ARWS operation).
Because the power capture is a function of the cube of the
wind velocity, incorrect switching between control strategies
may produce overloading or reduced power capture. In [9] and
[10], a hysteresis band of only 2% of the nominal speed is used
to switch between ARWS/BRWS control.
Therefore, an accurate estimation of the rotational speed is
necessary in this application.
3) Incorrect Operation for Other Control Systems: There
are other control schemes which require an accurate rotational
speed signal. For instance in [17], the speed is used to estimate
In a squirrel cage induction machine, the rotor slots produce
airgap permeance waves with a spatial distribution dependent
on the number of slots in the machine [7], [8]. The rotor slots
interact with the magnetizing component of the airgap MMF,
generating harmonics that are dependent on the machine rotational speed. The frequencies of the rotor slot harmonics are defined from the following equation:
(12)
where
is the slip frequency and is an integer. In this
is used. In Fig. 5,
application, only the first-order RSH
the RSH and PWM harmonics obtained experimentally for
600 r/min, 30% of full load are shown.
A. Tracking of the RSH
There are several methods which can be used to estimate the
position of the RSH. The fast Fourier transforms (FFTs) and the
interpolated FFT [20] can yield very accurate speed estimates
but rely on long record lengths and cannot be used to track fast
speed changes. There is also a high computational burden associated with a FFT with good resolution.
In this paper, the RSH are tracked using a recursive maximum
likelihood adaptive tracking filter (RML-ATF) [8], [21]. Based
on the principle of maximum likelihood estimation [21], the
method uses an adaptive notch filter that is adaptively moved
to minimize or eliminate a particular RSH. The filter is realized
by [21]
(13)
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004
Fig. 5. RSH obtained from the experimental rig.
where is the filter input, is the filter output, and
,
are parameters updated recursively. The notch frequency is obtained as
cos
(14)
The bandwidth of the notch filter is related to
as
(15)
Therefore, if
the bandwidth is infinitely narrow. If
is reduced, the bandwidth is increased. The adaptive notch
is tuned to eliminate the largest sinusoidal component in the
is adapted by a
input signal. To achieve this, the parameter
recursive maximum likelihood (RML) algorithm through which
(16)
is minimized. The parameter is the forgetting factor. The full
algorithm implemented in the microprocessor is
(17)
The residual prediction error is given by
(18)
The error covariance
is
(19)
The parameter estimate is
(20)
the prediction error update is obtained solving the difference
equation of (13)
(21)
the forgetting factor
cording to
and the notch width
are updated ac-
(22)
Fig. 6.
Control system proposed for the tracking of the RSH.
where and determine the rate at which the forgetting factor
and the notch width converge toward the final values
,
.A
computer model is used to select the initial values of the forget,
, using experimental line current
ting factor, as well as
data. This model also tests the performance of the RML-ATF algorithm for fast dynamic transients and steady-state operation.
The adaptive RML-AT notch filter is fully explained in [8]
and [21]. This filter is computationally efficient because 13 multiplications, 14 additions, and 1 division are required for iteration. The implementation of the RML-ATF algorithm takes
30 in the experimental rig described in Section VI. The convergence of the filter is also fast because the notch frequency
is established in few iterations, provided the RSH is clearly the
largest signal.
In Fig. 6, the implementation of the proposed RSH tracking
scheme, for the sensorless control system of Fig. 1, is shown.
From the voltage model, the electrical angle and the electrical
frequency
is obtained. A second-order filter, not shown in
A fourth-order
Fig. 6, is used to eliminate the noise from
high-pass filter eliminates the fundamental and the low-order
harmonics from the current.
Because the induction machine used in the experimental prototype has 14 rotor slots per pole pair, from (12), the upper
(considlimit for the position of the first-order RSH is
). The lower limit is obtained assuming operaering
tion at nominal slip and considering that it is unlikely to operate
the machine below 250 r/min (because of the BRWS operating
range of a typical wind turbine, for example, [17]).
Considering the lower limit for the position of the first-order
.
RSH, the cutoff frequency of the high-pass filter is set to
With this cutoff frequency, the fundamental and low-order harmonics are eliminated from the current without attenuating the
RSH tracked by the RML-ATF algorithm.
After the high-pass filter, a band-pass filter is used to isolate
the first-order RSH. The center frequency of this filter is calculated considering the electrical frequency and an estimation of
the slip frequency derived from . The band-pass area of this
filter must be narrow to avoid harmonics produced by the PWM
but wide enough to avoid filtering the tracked RSH when, because of parameter variations, the slip frequency is incorrectly
estimated. Finally, in Fig. 6, the RML-ATF is used to obtain the
CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES
201
frequency of the RSH through a lookup table implementation of
is obtained from (12).
(14). The speed estimation
To obtain a speed estimation with high accuracy and lownoise contents, the forgetting factor and the notch width
must converge to near unity values. However, because of the
narrow bandwidth and reduced weighting given to past values,
the dynamic response of the RML-ATF is rather poor when
and are close to unity values. In order to improve the dynamic
response of the RML-ATF, a slope detector has been included in
the RSH tracking control system. When a transient is detected,
the parameters and are reduced, increasing the notch filter
bandwidth and reducing the weight given to past samples. A
simple algorithm is implemented to reset the forgetting factor
is
and the notch bandwidth to their initial values when
above a given threshold.
B. Tuning of the Parameters Using RSH Tracking
In WECS, the generator is not required to operate at very low
rotational speeds. Therefore, most of the problems related with
the use of a MRAS observer in the low-speed range are avoided
because the fundamental voltage applied to the machine is relatively large and the small voltage drop produced in the stator resistance is negligible. Unless the stator resistance is really overestimated, the stability of the system is not compromised [6].
Therefore, tuning of the stator resistance is not considered in
this work. Also because the induction machine is operating at
fixed flux, tuning of the machine inductances is not necessary.
(or ) is the most
For this application, the parameter
important factor to determine the accuracy of the speed estimate. In order to implement a tuning algorithm, the following
relationship between the real and estimated slip frequencies
is used:
(23)
Assuming that ,
and
are measured or estimated
without error, the following equation is obtained:
(24)
From (24), using
and
yield
(25)
Therefore, it is possible to reduce the speed error to zero by
to zero
correcting the rotor time constant and forcing
[6], [20]. Fig. 1 shows the control system for parameter tuning
obtained from the RSH (i.e.,
).
with the speed
A PI controller is used to regulate the time constant . This
controller processes the error between the speed estimated from
. The output is
which is added
the MRAS observer and
to drive the estimation of the rotor time constant to the
to
correct value.
The tuning algorithm is switched off for fast speed changes
to avoid the relatively large speed errors produced at the output
Fig. 7.
Supply-side converter control schematic.
of the RML-AT filter (in practice, this does not take place very
often because of the large inertia of WECS). Due to the reduced
slip at light load, small errors in the estimated speed may produce a large variation in the estimated rotor time constant [see
(25)]. To avoid this, the tuning algorithm is also switched off
when the current is small.
V. CONTROL OF THE FRONT-END CONVERTER
The aim of the boost-type PWM converter is to regulate
supplying the energy generated from
the dc link voltage
the WECS into the grid. Furthermore, the use of vector-control techniques allows to control the ac currents with high
bandwidth. In this application, the reference frame is oriented
along the supply voltage rotating vector. Therefore, the power
supplied into the grid is controlled using the direct current. The
reactive power is controlled using the quadrature current.
For this application, the system shown in Fig. 7 is proposed
[22] for the control of the front-end converter. A fuzzy logic
controller is used because the transfer function between the dc
link voltage and the current is nonlinear and because the generating condition is unknown and varies with the wind speed in
a wide range.
The fuzzy controller is augmented by a feedforward compensupsation term that relates the current with the current
plied from the WECS or from other generation sources or loads
connected to the dc link capacitors. The feedforward compensation term is calculated from the power balance between the
dc link side and the front-end converter output. The relationship
is
between and
(26)
where
is the grid voltage and arises from the 2–3 axes
scaling. To further discuss the control of the front-end converter
is beyond the scope of this paper and more information can be
found in [22].
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004
Fig. 8. Experimental system.
VI. EXPERIMENTAL RESULTS
A 2.5-kW, 380-V, 50-Hz, four-pole cage induction machine
is utilized in the experimental prototype. The machine parameters are given in the Appendix. Two 5-kW commercial inverters
with a 1-kHz switching frequency are used. The supply-side
converter is connected to the grid via three 12-mH single-phase
inductors. The dc link voltage is regulated to 550 V. A speed encoder of 10 000 ppr is used to calculate the system speed. This
speed is not used in the control algorithms and it is only used
for comparison purposes and the emulation of the wind turbine.
In the machine side, two line currents and two line voltages are
measured. Also, in the front-end converter, two line currents and
two line voltages are measured together with the dc link voltage
and the current . The experimental rig is shown in Fig. 8.
The generator is driven by a speed-controlled dc motor drive
speed is calculated
that emulates a wind turbine. The
in each sampling time from (7) and sent to the dc machine control system which regulates the shaft speed. A lookup table is
characteristic in the microprocessor.
used to store the
Additional lookup tables are used to implement (14), the abc
transformations, the calculation of the electrical angle ,
to
etc.
The control strategies proposed in this paper have been tested
with several wind profiles (obtained from [23]) and similar results have been achieved. Fig. 9 shows a typical wind profile
with a 0.1-s sampling time for the wind velocity. The results in
this section have been obtained using this profile. The performance of the RML-ATF algorithm has been investigated emulating wind turbines of different inertia, friction coefficient, and
compliance. The most challenging test for the RML-ATF algorithm is the emulation of wind turbines with stiff shaft because
in this case the shaft is not absorbing part of the speed fluctuations. For this reason, only the emulation of wind turbines with
stiff shafts is considered in this paper. The torque current is
controlled according to (6).
The response of the MRAS observer and RML-ATF is shown
in Fig. 10 for a wind step between 6 to 9 m/s when a wind tur-
Fig. 9.
Fig. 10.
Wind profile used in the experimental rig.
System response to a wind step between 6 to 9 m/s.
bine of
kgm
is emulated. A wind step
is not very realistic but it is the most drastic change from the
control system point of view. In Fig. 10, the rotor time constant
is correctly estimated and the estimated speeds from the MRAS
observer and RML-ATF algorithm are very good with a negligible tracking e
Fig. 11 shows the performance of the MRAS and RML-ATF
kgm is emulated. In
algorithm when a wind turbine of
this test, the rotor time constant is underestimated by 50% and
the tuning algorithm is off.
The top graphic in Fig. 11 shows the speed obtained from the
encoder, MRAS and RML-ATF for the whole wind profile. The
speed is tracked by the RML-ATF with a negligible error during
CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES
Fig. 11.
Sensorless control using an untuned MRAS observer.
Fig. 12.
Sensorless control using the tuning control system.
the whole wind profile. The MRAS observer tracks the real
speed with a relatively large error. The bottom graphic in Fig. 11
to 60 s). Note that the
shows the speeds during 40 s (
real speed is closely tracked by the estimation obtained from
the RSH.
Fig. 12 shows the performance of the control system when the
tuning algorithm is on. In this case, the MRAS observer and the
RML-ATF are tracking the real speed during the whole wind
profile with very small error. The error between the estimated
speed from the MRAS observer and the real speed from the
encoder is almost negligible.
Fig. 13 shows the speed tracking error corresponding to
Fig. 12. The top graphic in Fig. 13 shows the tracking error
of the RML-ATF algorithm and the bottom graphic shows the
tracking error of the MRAS observer when the tuning of the
rotor time constant is on.
Fig. 13 shows that the error of the RML-ATF algorithm is
r/min with some peaks of up to 7 r/min.
approximately
The corresponding tracking error of the MRAS observer is
203
Fig. 13.
Speed estimation errors.
Fig. 14.
Control system response of the parameter-tuning algorithm.
r/min. The tracking error of the MRAS is smaller than the error
from the RML-ATF because the tuning algorithm has a reduced
bandwidth, which eliminates the fast and noisy variations at the
output of the RML-ATF, and also because the tuning algorithm
is switched off when fast dynamic changes are detected.
Fig. 14 shows the performance of the parameter-tuning algo, the algorithm is activated and the speed from
rithm. In
the MRAS observer is driven to the real speed. After 2 s, the
speed error is negligible. The system is operating with a wind
m/s.
speed of
The performance of the RML-ATF algorithm and MRAS observer for wind turbines of different inertia is shown in Table I.
,
Using the wind profile of Fig. 9, wind turbines of
1.75, and 3 kgm are emulated and the error of the MRAS and
RML-ATF estimations are obtained. Table I shows the average
and the standard deviation of the error
.
value of the error
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Fig. 15.
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 1, MARCH 2004
Control system response of the RML-ATF for several inertia values.
TABLE I
SPEED ERRORS FOR MRAS AND RML-ATF
For all of the wind turbines emulated in this work, the value of
is smaller for the MRAS error than that from the RML-ATF.
As mentioned previously, this is mainly because the small
bandwidth of the parameter-tuning algorithm eliminates the
high-frequency components of the RML-ATF. When the turbine
inertia is increased, the speed tracking errors from the MRAS
observer and RML-ATF algorithm are reduced. For inertia
values higher than 3 kgm the improvement in performance
is negligible. Fig. 15 shows the real speed and the speed
obtained from the RML-ATF algorithm, when the wind profile
is used. Curves a,b,c correspond to inertia values of 0.9 kgm ,
1.75 kgm , and 3 kgm , respectively. The tracking of the
RML-ATF algorithm is very good even for a small inertia of
0.9 kgm .
current of
The top graphic in Fig. 16 shows the
the front-end converter when the wind profile is used
kgm . The bottom graphic of Fig. 16 shows the corresponding dc link voltage. Despite the large and relatively fast
variations in the wind speed with its corresponding variation in
V
the generated power, the dc link voltage varies less than
for the whole wind profile.
Finally, Fig. 17 shows the waveform for the line current ,
and the dc link voltage
for
the equivalent phase voltage
the supply side of the front-end converter when the WECS is
in steady state. The system operates at the optimum tip-speed
ratio with a wind velocity of 8 m/s with the front-end converter
current set to zero for close-to-unity power factor operation.
VII. CONCLUSION
This paper has presented a new sensorless vector-control
strategy for an induction generator in a variable-speed WECS
Fig. 16.
Front-end converter i current and dc link voltage.
Fig. 17.
Voltage and current waveforms for the supply side.
using a MRAS observer to estimate the rotational speed of the
induction generator. In the sensorless system, the application
of a novel RML adaptive tracking filter for the estimation of
the RSH has been discussed. The dynamic performance of
this adaptive filter is very good and can be used to obtain an
accurate estimation of the rotational speed not only in steady
state but also when fast input changes as wind steps are applied
to the WECS.
Using the speed estimated from the RML-ATF algorithm, a
parameter tuning control system has been implemented to improve the accuracy of the MRAS observer. When the tuning
of the rotor time constant is enabled, the MRAS observer can
track the speed of the wind turbine with an error of less than
r/min for the whole speed range. The experimental results
show that the RML-ATF algorithm could be used to tune the
rotor time constant not only during steady state but also during
speed transients.
CÁRDENAS AND PEÑA: SENSORLESS VECTOR CONTROL OF INDUCTION MACHINES
Experimental results have been obtained using a wind turbine
emulator and an induction machine of 2.5 kW. A novel method
for the emulation of high-order wind turbine models has been
implemented. This emulation strategy has been used to emulate
wind turbines with inertias between 0.9 kgm and 3 kgm . Even
with inertias as low as 0.9 kgm , the performance of the proposed sensorless control scheme is very good and the tracking
of the RML-ATF is accurate.
For the control of the front-end converter, an improved control structure is used. An improvement in regulation is achieved
using feedforward mapping of the net dc-link disturbance
current with the direct axis (real power) current component
of the power converter. The experimental results have also
shown the excellent performance achieved with the proposed
front-end converter control strategy.
APPENDIX
1) Induction Machine:
(rated) 1450 r/min, (rated)
1.8 A,
,
,
,
,
,
.
m,
,
2) Wind Turbine Emulation:
2.12,
,
,
Gear-box ratio
kgm , wind turbine emulated using a dc machine of
1500 r/min, 6.5 kW.
REFERENCES
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Roberto Cárdenas (S’95–M’97) was born in Punta Arenas, Chile. He received
the electrical engineering degree from the University of Magallanes, Punta
Arenas, Chile, in 1988, and the M.Sc. and Ph.D. degrees from the University
of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively.
Currently, he is with the Electrical Engineering Department at the University
of Magallanes. From 1989 to 1991, he was a Lecturer at the University of Magallanes. His research interests include control of electrical machines for wind
energy applications and variable-speed drives.
Rubén Peña (S’95–M’97) was born in Coronel, Chile. He received the electrical
engineering degree from the University of Concepcion, Concepcion, Chile, in
1984, and the M.Sc. and Ph.D. degrees from the University of Nottingham, Nottingham, U.K., in 1992 and 1996, respectively.
Currently, he is with the Electrical Engineering Department at the University
of Magallanes, Chile, where he was a Lecturer from 1985 to 1991. His main
research interests are in control of power electronics converters, ac drives, and
renewable energy systems.
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