-
ra
Tr
Cana
Received 10 September 2014Accepted 10 April 2015
Multivariable controlWind turbineDC generator
wiiable control of a wind turbine is designed for investigation
of theoretical concepts and their physicalimplementation. The
control system includes a speed controller and a disturbance
estimator for
wind energy and energy extraction, a maximum power point
tracking algorithm is developed and in-
wer ge
increase in the related education and research [1e4]. Because it
is
whose robustness need to be veried under realistic
operatingconditions [7].
Laboratory experiments in the wind energy area
includinghardware-in-the loop (HIL) and advanced control systems
areimportant for education of future engineers and researchers.
turbine system and extracting mathematical models needed for
thejor requirement in
(WECS) is con-ltage in order town, the optimum3]. Variable
speedh wind speeds, thewith power elec-d prevent the tur-ic control
using
variable pitch blades is usually expensive and complex. It ca
alsocause an unnecessarily high activity of the pitch actuator due
tosmall uctuations of power during the steady state operation
[7].
Control systems implemented in the power electronic
interfacerepresent an efcient means to operate a wind turbine at
themaximum power extraction. The control is not always aimed
atcapturing as much energy as possible. Power generation is
limitedduring high wind speeds or when the load demand in an
isolatedsystem is low. Model based control strategies, such as
feedback,
* Corresponding author. Tel.: 1 9024205712; fax: 1
9024205021.
Contents lists availab
Renewable
els
Renewable Energy 83 (2015) 162e170E-mail address:
[email protected] (A. Merabet).difcult to use a real wind turbine
in laboratory environment, asmall turbine that can be used indoors
is the best tool for imple-mentation and demonstration of control
strategies [5,6]. Windturbine emulators, involving motor-generator
set, variable load,and control system, which operate with the
power-speed charac-teristics of a wind turbine are frequently used
for research andteaching purposes due to their simplicity, low
power, and low costdesign [5]. However, neglecting the real wind
effects represents animportant aw, especially when dealing with
control strategies
design of a model-based control system. One mathe considered
wind energy conversion systemtrolling the generator speed and the
load vomaximize wind energy extraction. As well knoturbine speed is
a function of wind speed [1eWECS are increasingly common.
Typically, at higWECS use aerodynamic control in combinationtronics
to regulate torque, speed, and power, anbine from damage. However,
the aerodynamenergy enjoys signicant interest, which has caused
considerable advanced control by analysing the major components of
a windSpeed controlMaximum power extraction
1. Introduction
In modern power systems, the
pohttp://dx.doi.org/10.1016/j.renene.2015.04.0310960-1481/ 2015
Elsevier Ltd. All rights reserved.turbine laboratory system. A
power electronic interface is based on two DCeDC converters: a
buckconverter for control of the speed and a boost converter
controlling the load voltage. Experimental re-sults demonstrate
effectiveness of the multivariable control system for a wind
turbine providingmaximum power extraction. The experiment can be
recongured for teaching various control conceptsto both
undergraduate and graduate students.
2015 Elsevier Ltd. All rights reserved.
neration based onwind
Developing a control system from the model of the wind
turbine,and its practical realization would bridge the gap between
theoryand practice. It would allow the students to implement
theories ofKeywords: tegrated into the control system. The
multivariable control system is implemented in a small
windAvailable online enhanced robustness of the control system. In
order to provide students with deeper understanding ofMultivariable
control algorithm for laboenergy conversion
A. Merabet a, *, Md.A. Islam a, R. Beguenane b, A.M.a Division
of Engineering, Saint Mary's University, Halifax, NS, B3H 3C3,
Canadab Department of Electrical Engineering, Royal Military
College, Kingston, ON, K7K 7B4,c Department of Electrical
Engineering, University of Nevada, Reno, USA
a r t i c l e i n f o
Article history:
a b s t r a c t
Advanced experimentation
journal homepage: www.tory experiments in wind
zynadlowski c
da
th wind energy conversion systems is described. The real time
multivar-
le at ScienceDirect
Energy
evier .com/locate/renene
-
generator is connected to the load via a power electronic
interface
From the electrical and mechanical Equation (4) of the DC
ma-chine, a linear state-space equation can be derived as
_x Fx g1V g2Tt (5)
where,
x i u T ; F
26664RL
KbL
KiJ
BJ
37775; g1
264
1L
0
375; g2
2640
1J
375
The controlled output is the rotational speed u, the input is
thevoltage V and the disturbance is the turbine torque Tt.
In order to nd a relationship between the output u and theinput
V, the mechanical Equation (4b) is differentiated, using
ble Eallowing control of the shaft speed and load voltage.The
power delivered by the turbine shaft (neglecting losses in
the drive train) is given by
Pt 0:5prCplr2v3w (1)
where r denotes the air density, r is the length of the turbine
blade,vw is the wind speed, and l is the ratio of blade tip speed
to windspeed, that is
l urvw
(2)
where u is the angular velocity of the turbine.The power
coefcient Cp depends on speeds of the turbine and
wind, and its relation to l is shown in Fig. 1. The power
coefcientreaches maximum at a specic optimum value lopt. In order
toextract maximum power fromwind, the turbine speed should be
socontrolled as to maintain l at the optimum level.
In some wind turbines, the optimum tip speed ratio may beunknown
or not well dened and subject to change. Therefore,instant locating
of the maximum Cp during the operation of windturbine is very
important. An MPPT algorithm based on the varia-tion of the
generated power and the shaft speed is proposed, inSection 3.
The torque at the turbine shaft produced by the wind is given
bypredictive, and sliding mode, can be employed for speed control
inWECS. Quality of control strategies depends on the accuracy
ofmathematical model of the system, which is usually not high
[8,9].For accurate speed tracking, the controller must maintain
highperformance when facing parameter variations and
uncertaintiesof the system [10e15].
In this paper, a feedback speed control strategy is
developedfrom the mathematical model of a generator connected to a
windturbine. Information about the turbine and wind speeds is
assumedto be unavailable and their variations will be compensated
using atorque estimator integrated in the controller. Performance
of theproposed controller will be tested under multivariable
controlconditionswith amaximumpower point tracking (MPPT)
algorithmand load voltage control. A Quanser's ve-blade wind
turbine isemployed in an experimental setup equipped with a power
elec-tronic interface. The setup allows to verify efcacy of the
proposedcontrol system and to investigate its behaviour with real
wind [16].
The rest of the paper is organized as follows: In Section 2,
adescription of the experimental system of wind turbine system
isgiven. The proposed feedback control method for speed tracking
isdetailed in Section 3 followed by the robustness and
stabilityanalysis in Section 4. The MPPT algorithm, generating the
speedreference needed for maximum extraction of power from wind,
isdescribed in Section 5. The experimental setup is described in
de-tails in Section 6 and experimental results and their discussion
aregiven in Section 7.
2. Wind turbine experimental system
2.1. Wind turbine
Thewind turbine, manufactured by Quanser Inc., is installed in
awind tunnel. It has ve blades and drives a DC generator through
agearbox of ratio 1:1. The gearbox converts rotation of
thehorizontal-axis turbine to that of the vertical-axis generator.
The
A. Merabet et al. / RenewaTt 0:5prCtr3v2w (3)where Ct Cp/l is
the torque coefcient. Here, the mathematicalmodel of the mechanical
structure of wind turbine system isassumed to be unknown. This
uncertainty is dealt with in theproposed control system.
2.2. DC generator
The armature of the DC generator is modeled as an RLE
circuit,with E representing the back emf (speed voltage). Denoting
thegenerated voltage as V, the electrical and mechanical equations
ofthe generator can be written as
didt
RLi Kb
Lu 1
LV (4a)
dudt
KiJi B
Ju 1
JTt (4b)
where i is the armature current, Kb is the machine constant, u
is therotational speed of the generator, V is the generator
voltage, J is therotor inertia, B is the viscous-friction
coefcient, and Tt is the un-known turbine torque.
3. Feedback control for speed tracking
3.1. Feedback controller development
Fig. 1. Power coefcient of the wind turbine versus tip-speed
ratio.
nergy 83 (2015) 162e170 163Equation (4a), which yields
-
In this work, the development of a robust controller to deal
with
ble EPg2 p0 B k2
1
(14)parameter variations and unknown turbine torque is based on
atorque observer. It is derived from the state space model of the
DCgenerator, the control law, and the speed tracking error of the
windenergy conversion system.
From the model (5), the torque variable is dened as
g2Tt _x Fx g1V (10)Using the torque Equation (10) an observer
can be dened as
_bT t Pg2bT t P _x Fx g1V (11)where P, of size 1 2, is the
observer gain to be determined.
From (7), (10) and (11), it can be found that the error dynamic
ofthe observer is given by
_e _Tt _bT t Pg2Tt bT t (12a)_e Pg2e 0 (12b)
It is exponentially stable if the term Pg2 is a positive
constant.Based on (4), (5) and (6), the observer gain P can be
dened as
P p0Ki
JBJ
k20 1
(13)
where p0 is a positive constant.From (5) and (13), the term Pg2
is given by
2u KiJ
_i BJ
_u 1J
_Tt
KiJ
R
Li Kb
Lu
B
J
Ki
Ji B
Ju
Ki
JLV B
J2Tt (6)
The dynamic of the wind turbine is more sluggish than
theelectric energy conversion system. Therefore, according to [10],
itcan be assumed that
_Tt 0 (7)The objective of the control law is minimization of the
speed
tracking error expressed by the second-order equation
eu k2 _eu k1eu 0 (8)
where, eu u urefThe following control law is proposed
V JLKi
k1u uref
k2
Ki
Ji B
Ju _uref
Ki
J
R
Li Kb
Lu
B
J
Ki
Ji B
Ju
uref
k21JTt BJ2 Tt
(9)
Implementation of this law requires precise knowledge of
pa-rameters of the system and the turbine torque, which is not
easilyavailable in the majority of practical wind energy
systems.
3.2. Robust control based on torque estimation
A. Merabet et al. / Renewa164J Jwhich is positive if the control
gain k2 is such thath dDai Dbu DcV Dd Tt xk2 >BJ
(15)
Thus, the stability of the torque observer is guaranteed.Using
the observed torque bT t , the control law (9) becomes
V JLKi
k1u uref
k2
Ki
Ji B
Ju _uref
Ki
J
R
Li Kb
Lu
B
J
Ki
Ji B
Ju
uref
k21JbT t BJ2 bT t
(16)
If Equations (13), (14) and (16) are substituted in (11), a
newform of the torque observer is produced
_bT t p0k1u uref k2 _u _uref u uref (17)Integrating (17), the
torque observer becomes
bT t p0k1
Z u uref
dt k2
u uref
_u _uref
(18)
The torque observer has a PID structure, which helps the
feed-back controller (9) to enhance its capability of speed
tracking andcompensation of uncertainties resulting from the lack
of detailedknowledge of wind turbine parameters.
4. Robustness and stability analysis
4.1. Robustness analysis
The dynamics of the wind turbine is an uncertain system,
wherethe uncertainties include:
a. Structured (parametric) uncertainties characterized by
adynamical model of the system with parameter variations.
b. Unstructured uncertainties characterized by omitted
quantities,unknown torque, and external disturbances.
The rotor dynamic Equation (6) can be rearranged to
u ai bu cV dTt x (19)
where a KiJRL BJ
; b 1J
KiKbL B
2
J
; c KiJL; d BJ2; and x
represents the effects of the omitted quantities of the
electric/po-wer electronics circuit, load, and any external
disturbance.
Now, the Equation (19) can be modied to include
parameteruncertainties D($) and external disturbance x to
u a Dai b Dbu c DcV d DdTt x (20)Equation (20) is now
reorganized to include all uncertainties in a
common term as
u ai bu cV dTt h (21)
where
1
nergy 83 (2015) 162e170The uncertainties term, h, includes
parametric uncertainty,omitted quantities, and external
disturbances in the system.
-
2 3 2 3
Implementation of (34) has been carried out numerically using
a
ble Ex x1x2x3
4 5 eu_eue
4 5 (27)From (26) and (27), the state space representations
are
8>>>>>>>>>>>>>>:
l1 p0k3
l2 k2
k22 4k1
q2
l3 k2
k22 4k1
q2
(32)
It can be seen that eigenvalues li satisfy the condition Re (li)
< 0.Therefore, x(t) / 0 as t / for all x(0), and the stability
isguaranteed.
5. Maximum power point tracking algorithm
For maximum power extraction, if the wind turbine
character-istics are available, the speed reference prole is
derived from (2)using the optimum tip speed ratio lopt such
that
uref loptvw
r(33)
However, practical implementation of the MPPT algorithmbased on
(33) requires measurement of the wind speed andknowledge of the
wind turbine characteristics. It makes this algo-rithm unreliable
due to inaccuracies of the wind speed determi-nation and aws in
modelling the wind turbine. Here, an MPPTmethod based on the
variation of the generated power P and theturbine-generator speed u
is proposed. The variation of the speedreference uref is given
by
durefdt
a,u,dPdt
(34)
where the generated power is found from measurements of
thevoltage and current at the generator, that is,
P Vi (35)
and a is a constant. Correct choice of awill improve speed
tracking
nergy 83 (2015) 162e170 165discretisation method as fellows
-
uref kDt uref k 1Dt a$ukDt$PkDt Pk 1Dt(36)
where, Dt is the sampling time and k is an integer.
6. Wind turbine experimental setup
The wind turbine experimental setup consists of a ve-bladewind
turbine and a DC generator, as shown in Fig. 2. The gener-ator
provides power to a set of LEDs, which form a variable load.Control
of the turbine speed and of the load voltage is realizedthrough a
power electronic interface between the generator andload. The
interface consists of two DCeDC converters as shown inFig. 3. The
DCeDC buck converter controls the rotational speed ofthe generator
and the DCeDC boost converter controls the loadvoltage. Such a
cascade of two DCeDC converters would beimpractical and in a
commercial system. However, it allows inde-pendent manipulations,
valuable for teaching purposes. A detailed
Voltage and current sensors (VS and CS) are available in
theexperimental setup, as shown in Fig. 3, to provide measurements
ofvoltages of the generator, the buck converter, and the load, as
wellas the generator and load currents. The measurements are
deliv-ered to the computer (PC) through a real-time data
acquisitionboard Q8-USB. The results were analysed using software
packagesQuarc with Matlab/Simulink. Quarc is a rapid control
prototypingtool, which signicantly accelerates the control system
design andimplementation [16].
Test 1: A randomwind speed, shown in Fig. 5, was generated
bychanging the blower speed in order to test the MPPT algorithm
and
P Robust Feedback Speed Control
Blower
+V*_
DC Generator
DC-DC Buck
r Wind Turbine
Tunnel
_ref
i
vw
GG
MPPT
G2 G6G1
A. Merabet et al. / Renewable Energy 83 (2015)
162e170166description of the interface exceeds the scope of this
paper andmore information can be found in Ref. [17].
The variable electronic load, based on LEDs and shown in Fig.
4,consists of six parallel equal banks of two LEDs in each bank
inseries with a resistance. The load banks can be switched
auto-matically ON/OFF from Matlab/Simulink, through the
real-timedata acquisition board Q2-USB [16], by sending a signal to
theMOSFET gates of the banks.
The load side converter control system is used to regulate
thevoltage across the load in order to maintain a proper
functioning ofthe LEDs load. The PI voltage controller produces
signal U* given by
U* kpVL V*L
ki
Z VL V*L
dt (37)
The output of the voltage controller is the ring signal to
bedelivered to the gate of the MOSFET in the DCeDC buck converteras
shown in Fig. 3. Rotational speed is measured by an encodermounted
on DC generator rotor shaft. Voltage and current sensorsare
available to measure the armature current and the generatorand load
voltages. The measurements are calibrated and sent tothe computer
(PC) through a real-time data acquisition board Q8-USB, to be
analysed by using the software package QUARC withMATLAB/Simulink.
QUARC is a powerful rapid control prototypingtool that signicantly
accelerates control system design andimplementation [16].Fig. 2.
Experimental set-up of the wind energy conversion system.The wind
is generated by a DC blower motor. An incrementalencoder mounted on
blower rotor shaft measures the motor speed,which is proportional
to the wind speed. The advantage of theproposed control system is
that it does not require knowledge ofthe wind speed for evaluation
of the turbine torque.
7. Experimental results
Experiments were carried out to validate the proposed
controlstrategy under different scenarios of operation. The choice
of thefeedback controller gains (k1 and k2), the estimator gain
(p0) andthe load controller (kp and ki) were determined by trial
and error toachieve high-quality performance.
VL* DC-DC Boost
Converter
Voltage Control
U*L*_
VLV+
Fig. 3. Multivariable control strategy for the experimental wind
turbine-generatorsystem.Fig. 4. Variable electronic load.
-
ed t
A. Merabet et al. / Renewable Energy 83 (2015) 162e170 167the
rotor speed tracking. The experimental wind turbine systemwas
operating with maximum power extraction, nominal values ofthe
parameters of themodel (4), and xed load (all banks were ON).
Fig. 5. MPPT based speIt can be seen that the speed reference
generated from MPPT andthe rotor speed follow the variation of the
wind speed. Estimationsof the extracted power and torque are
illustrated in Fig. 6. The es-timators enhance the control, which
results in a zero steady-state
Fig. 6. Estimated torque, extracted pospeed error. The voltage
regulation does not affect the speedtracking response.
Test 2: The wind turbine and control system were tested with
a
racking for xed load.variable load, the banks being turned ON at
different time intervalsas shown in Fig. 7. It can be observed in
Fig. 8 that speed trackingand voltage control are accurate in spite
of the varying wind andload. This high performance is attained by
precise torque
wer and load voltage regulation.
-
Fig. 7. Variable load banks.
A. Merabet et al. / Renewable Energy 83 (2015)
162e170168estimation, which allows compensation of external
disturbancesarising from the wind and load variations. The
generated powerand current follow the wind speed, as shown in Fig.
9, proving thatthe turbine extracts themaximumpower fromwind. The
calibratedcontrol input signal shown in Fig. 10 makes the turbine
to operatewithin a safe region.
Test 3: The experimental wind turbine system was tested
withmismatched parameters. The perceived values of generator
pa-
rameters had been increased by 10% and the load was varying
Fig. 8. MPPT based speed tragain. The results of speed tracking
and torque estimation areshown in Fig. 11. The performance is still
satisfactory, demon-strating robustness of the developed
controller.
8. Conclusions
A robust feedback control strategy has been proposed to track
aspeed prole, generated by an MPPT algorithm, to operate a
labo-
ratory wind energy system based on a DC generator.
Information
acking for variable load.
-
Fig. 9. Generated power and current, and load voltage
regulation.
A. Merabet et al. / Renewable Energy 83 (2015) 162e170 169about
the wind turbine and wind speed is not needed in theimplementation
of this strategy, as their effects are compensatedthrough a torque
estimator integrated into the controller. Param-eter, wind, and
load variations, and component omitted in themathematical model,
such as the power electronics interface, do
not signicantly spoil the speed tracking performance.
Fig. 10. Calibrated conStability and robustness of the feedback
controller have beenanalysed, and the developed control
algorithmwas tested in a smallscale laboratory wind turbine system.
The systemwill be used as animportant tool for teaching control
systems theory and training inthe eld of wind energy.trol input
signal.
-
Fig. 11. MPPT based speed tracking for variable l
A. Merabet et al. / Renewable Energy 83 (2015)
162e170170Acknowledgements
This study was partially supported by the Natural Sciences
andEngineering Research Council of Canada (NSERC) under the
Engage
Grant 432302-12.
Appendix
Wind turbine: r 14 cm, r 1.14 kg/m3DC generator: R 3.705U, L 575
mH, Kb 10.575 mV/rpm,
Ki 100.95 mNm/A, B 0.001833, J 165 g/cm2Feedback controller and
torque estimator: k1 3.33 105,
k2 250, p0 0.001.MPPT algorithm: a 0.5.PI voltage controller: Kp
20, Ki 0.5.
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Multivariable control algorithm for laboratory experiments in
wind energy conversion1. Introduction2. Wind turbine experimental
system2.1. Wind turbine2.2. DC generator
3. Feedback control for speed tracking3.1. Feedback controller
development3.2. Robust control based on torque estimation
4. Robustness and stability analysis4.1. Robustness analysis4.2.
Closed loop stability analysis
5. Maximum power point tracking algorithm6. Wind turbine
experimental setup7. Experimental results8.
ConclusionsAcknowledgementsAppendixReferences