Control issues of a Permanent Magnet Generator variable-speed Wind Turbine
A. Haniotis, S. Papathanassiou, A. Kladas* and M. Papadopoulos
Electric Power Division
Department of Electrical & Computer Engineering
National Technical University of Athens
9, Iroon Polytechneiou Street, 15780 Athens, Greece
(*) Tel: (+3)-010-7723765, fax: (+3)-010-7723593, email: kladasel@central.ntua.gr
Voltage Source Diode
ABSTRACT: In this paper a prototype of the electrical part of a
Inverter Rectifier
variable speed wind turbine is considered, equipped with a
permanent magnet synchronous generator. The modeling of the
generator and power electronics interface is checked with
SG
measurements realized in the prototype under both steady state and
dynamic conditions. Measurements as well as control functions are
performed by using a microprocessor. The outcome of the
simulation and experimental work are actually utilized in the
development of a 25 kW wind turbine, in the frame of a research
Fig. 1. Subsystems of the electrical part of a typical permanent magnet
project.
generator variable speed wind turbine system
Keywords: dynamic response, microprocessor based control,
microprocessor [15].
permanent magnet, synchronous generator, wind turbine.
The outcome of the simulation and experimental work are
actually utilized in the development of a low cost 25 kW wind
I. INTRODUCTION turbine, in the frame of a research project funded by the
Greek Secretariat for Research and Technology.
The control of wind turbine systems is a complicated task due
to the stochastic nature of available energy by the wind.
II. SUBSYSTEMS AND MODELING
Moreover often conflicting requirements are involved, such as
the low cost and reduced stresses [14], on the one hand, and
The basic components of a variable speed wind turbine
the good output power quality and dynamic characteristics on
system are shown in Fig. 1. In this figure, it may be noted that
the other [9],[10]. In this paper variable speed wind turbines
there is no gearbox to increase the speed of the generator
are considered, equipped with permanent magnet generators
rotor. This is due to the machine multiple pole structure, in
[7],[8]. The examined wind turbines are multi-polar in order
order to achieve reasonable electrical frequencies for low
to avoid switch-gears, exhibiting the well-known weight and
rotor speed. In the case considered 100 poles are needed (100
reliability problems [6].
rpm) for the 25 kW sized machine while 24 poles (400rpm)
In order to achieve variable speed operation, a power
were adopted for the prototype.
electronics converter stage is necessary to connect the
The static converter shown in Fig. 1 consists of an
generator to the grid [1],[2]. The system analysis in such
uncontrolled 3-phase diode rectifier, a DC/DC boost
cases involves models for the generator [3],[4],[5], the static
converter, a 3-phase PWM voltage source inverter and
converter [2],[12] and the grid [9].
possibly a step-up transformer.
In this paper a 2 kW prototype of the electrical part of such a
variable speed wind turbine is considered, equipped with a 24
A. Aerodynamic part and control reference
pole permanent magnet synchronous generator. The modeling
of the generator and power electronics interface is presented
Aerodynamic analysis of the wind turbine blades provided the
and checked with measurements realized in the prototype,
characteristics shown in Fig.2. The continuous curves show
both in the steady state and in dynamic conditions.
variations of the rotor torque with rotor speed, for a given
Measurements as well as control functions are performed by a
wind speed.
The dotted line is the proposed reference for the control
system and can be divided into three main parts associated to
different control operations: the leftmost part, with low
inclination, corresponds to the maximum power points for
every wind speed. The median part, with high inclination,
prevents the turbine from over-speed, thus protecting it by
using the stall effect. The rightmost part corresponds to the
situation that the machine cannot deliver more torque, so an
external braking system is needed for shutting down the
system. Obviously, the control action should avoid such a
situation, that is why the paper is devoted to the
implementation of the first two parts of the reference.
Simulated characteristic
Experimental results
400
350
300
250
200
y = -15.12x + 356.76
150
100
50
0
0 2 4 6 8 10 12
I (A)
dc
Fig. 3. I-V characteristics of the rectified output of the synchronous
permanent magnet generator
Rotor speed (rpm)
V
PARAMETERS:
Fig. 2. Aerodynamic part torque-speed characteristics for different wind RL 200�
speeds and proposed control reference
V1 R1 L1
The characteristics shown in Fig. 2 are static corresponding to
FILE=phase1.txt
19.134mH
2.872�
the steady state of the aerodynamic part. The wind speed is
V2 R2 L2
{RL}
RL
FILE=phase2.txt
practically never steady. In fact, it is quite variable,
19.134mH
2.872�
V3 R3 L3
depending on the wind characteristics of the specific place.
FILE=phase3.txt
19.134mH
2.872�
So it is very important both in the design and implementation
of the control system to consider the dynamic behavior.
B. Electrical part
Fig. 4. Three phase equivalent circuit used in all simulations of the
The actual configuration used in the laboratory did not
permanent magnet synchronous generator
include the shown in Fig. 1. In our case the generator s
inductance was used for voltage boosting and filtering.
are shown in figures 6a and 7a, respectively.
Moreover, the voltage source inverter and the grid have been
While the simulated current is in very good agreement with
represented by a convenient resistive load controlled by a
the measured one by using this model, the voltage is not
chopper.
represented properly. This implies that fundamental
The rectified output of the generator prototype is quite similar
component model cannot be very accurate in voltage
to the ones of a direct current machine. This is shown in
prediction as it neglects the higher harmonics .
Fig. 3 comparing the theoretical prediction of such a
Higher harmonics model is in very good agreement with the
characteristic by using finite element simulation [8]. This
measured waveforms for both phase current (figure 6b) and
form of behavior involves simple calculations for
voltage (figure 7b). In these figures, even the spikes due to
representation of the boost converter.
diode recovery are efficiently represented.
The generator model used in the electric circuit analysis
At high load conditions the current has less higher harmonic
considered sinusoidal electromotive forces. This provides
content but the voltage is even more distorted.
acceptable accuracy for the generator representation while
necessitating reduced calculation means [7].
To ensure accuracy, a three phase equivalent circuit has been
used together with a rectifier and a resistive load, and both
measured and simulated waveforms have been compared. The
circuit illustrated in Fig. 4 allowed for both fundamental and
higher harmonics analysis.
The case of low load condition has been simulated and the
computed results by the different models are compared to
measurements. The measured time variations of the phase
current and voltage are shown in figures 6c and 7c,
respectively. Both current and voltage waveforms are
distorted due to the reactive power effect of the rectifier.
The simulated results by the fundamental component model
Fig. 5. Reduction of fundamental electromotive force to match rms electrical
values in fundamental component model
for the phase current and voltage in the machine in this case
-
-
-
+
+
+
dc
V
(V)
Rotor Torque (kN" m)
Low load
No load
a a
Low load
No load
b
b
c
c
Fig. 7: Phase voltage of the permanent magnet synchronous
Fig. 6: Phase current of the permanent magnet synchronous machine at
machine at low load conditions
low load conditions
a: simulated by the fundamental component model
a: simulated by the fundamental component model
b: simulated by the higher harmonics model
b: simulated by the higher harmonics model
c: measured
c: measured
Higher harmonics model provides simulated waveforms,
C. Mechanical part
which are almost identical to the measured ones.
Furthermore, this model needs no adjustment of
In the case of the simpler representation of the mechanical
electromotive force s amplitude to represent efficiently rms
part by a concentrated mass with moment of inertia J rotating
values, and can be easily used for lower machine speeds.
at angular velocity �r, the governing equation is:
On the contrary the results in fundamental analysis showed
the need for reduction of electromotive force to match rms
2 d�r
�ł �ł
Tm - Te = J (1)
�ł �ł
electrical values. Fig. 5 shows the amount of reduction in full
P dt
�ł łł
speed operation.
VC = I2RL/D2
Tm-Te �
Tm + 1 I2 "VC/"I2 = (RL/D2) [1-exp(-tD2/RLC)] VC
"VC/"D2 = -(RLI2/D22) [1-exp(-tD2/RLC)]
Js
Low - pass
Te -
filter with
� < 500źs
D2 (25%)
(PWM2)
Constant of
comparison
�ref
1
Ł K2(VC-VC") VC"
T s +1
f
Fig. 10. Schematic diagram of capacitor voltage -loading control
subsystem
�-ń
The power drawn from the generator charges the filtering
Fig. 8. Speed control system block diagram
capacitors. The voltage control loop takes care of monitoring
the accumulated power in the capacitors to the load.
where P is the number of poles, Tm is the mechanical torque
As the capacitors are charged, their voltage increases. This PI
on the shaft and Te the electromagnetic torque
controller shown in Fig. 10 filters the measurement and
In order to obtain a control without oscillations, a low-pass
compares the result with a pre-defined constant. Then
filter must be included in the rotor speed feedback path of the
capacitors are discharged through the load adjusted by a
control, as shown in Fig. 8. Its purpose is to attenuate speed
PWM controlled IGBT.
oscillations, which otherwise would be reflected on the
The program consists of two branches as shown in Fig. 11:
generator torque, degrading the output power quality and
the main program and automatic control. In the main program
contributing to the variability of the mechanical torques. Thus
the user may review measurements and alter state variables
a convenient selection of Tf is very important [7].
[15]. By pressing the  C key on the PC keyboard one may
start the automatic control, where the two aforementioned
III. CONTROL SYSTEM AND MEASUREMENTS
loops cooperate and monitoring is disabled due to speed
problems. Special care is taken at extreme circumstances, i.e.
After constructing the circuits and predicting the electrical
in case of an over-voltage condition.
behavior, a control program is needed to evaluate the data
measured and act as necessary to bring the system to the
desired working point [11]. In our case two loops are
working: A current control loop associating the reference
BEGIN
torque-speed characteristic to a convenient generator current -
speed characteristic as shown in Fig. 9 has been introduced.
Moreover a voltage - loading control loop has been adopted
illustrated in Fig. 10.
The current control loop draws monitors the electrical power
 C
from the generator in order to achieve the correct
AUTOMATIC MAIN
combination of power and electrical frequency corresponding
CONTROL PROGRAM
 R
to the optimum operation of the aerodynamic part (reference
in Fig. 2). It is a PI controller with a low pass filter and a non-
linear reference.
VC
I1 = E(f)/R + (D1-1)VC/RG
G
"I1/"VC = (D1-1)/RG [1-exp(-tR/L)]
G
f I
1
"I /"E(f) = 1/R [1-exp(-tR/L)]
1 G G
"I1/"D1 = VC/RG [1-exp(-tR/L)]
G
PERIOD
COUNTER
D1
(PWM1)
Control reference Ł
Current -- speed
Fig. 11. Flow chart of microprocessor program
Low pass
filter
I1"
K (I ")
1 1-I
1 � =9250źs IV. RESULTS AND DISCUSSION
(95%)
The experimental set-up comprises the permanent magnet
synchronous generator prototype consisted of 24 poles,
illustrated in Fig. 12. The shaft torque is controlled by using a
Fig. 9. Schematic diagram of synchronous generator
dc machine torque-meter simulating the aerodynamic part of
current -speed control subsystem
the wind- turbine. The maximum rotating speed adopted for
8
7
6
3500 2 4 6 8 10 12 14 16
340
330
20 2 4 6 8 10 12 14 16
1.5
1
20 2 4 6 8 10 12 14 16
1.5
1
8000 2 4 6 8 10 12 14 16
600
400
0 2 4 6 8 10 12 14 16
time(s)
Fig. 14. Simulated electromechanical time response for step up wind
speed variation
Vw are shown in Fig. 14. This figure shows that the time
Fig. 12. Experimental set-up showing the 2 kW permanent magnet
constant involved is approximately 2 seconds, which is in
synchronous machine prototype.
good agreement with the time responses of the measured
the experiments was 400 rpm. This system enables also
capacitor voltage and generator current for a step increase in
dynamic analysis by applying convenient torque steps through
rotor torque, given in Fig. 15.
appropriate control of the four quadrant converter supplying
The agreement between simulated and measured time
the dc torque-meter.
responses can be observed in Figs. 16 and 17 showing the
Fig. 13 shows the capacitor voltage (Channel 1 - 550V) and
same results in case of step down wind speed variation.
generator rectified current ripples (Channel 2 - 5A) at steady
state. This figure illustrates the very good steady state
V. CONCLUSION
characteristics of the system.
The dynamic behavior of the system is of equally great
The design, construction and testing of a control system for
importance. The simulated time responses for the rotor
synchronous permanent magnet generator wind turbines has
angular velocity �m, mechanical torque Tm, electrical Torque
been presented. This system ensures produced power
Te and generated power Pe, in case of a step up in wind speed
optimization as well as overspeed protection in case of high
Channel 1 wind speeds. Its performance has been checked by means of a
T=3.5kgm and f=64Hz
2 kW experimental set-up. The proposed system provides
Channel 2
excellent steady state characteristics and adequate time
6
response to step torque variations.
5
T:1.5kgm->1.87kgm Channel 1
and f:41Hz->56Hz Channel 2
4
3,5
3
3
2,5
2
2
1
1,5
1
0
0 0,01 0,02 0,03 0,04 0,05
0,5
-1
0
Time (s)
0 5 10 15
-0,5
Time (s)
Fig. 13. Measured steady state system ripples (capacitor voltage and
Fig. 15. Measured system time response for step up torque (capacitor
generator current for 3.5 kg.m torque and 64Hz frequency)
voltage and generator current time variations)
w
V
(m/s)
m
� (rad/s)
m
e
T (kg" m)
T (kg" m)
e
P (W)
9 T:2.55kgm->2.05kgm
Channel 1
and f:61Hz->59Hz
Channel 2
8
3
7
3600 2 4 6 8 10 12 14 16
2,5
350
2
340
1,5
30 2 4 6 8 10 12 14 16
1
2
0,5
1
0
2.50 2 4 6 8 10 12 14 16
0 5 10 15
-0,5
2
Time (s)
1.5
10000 2 4 6 8 10 12 14 16
Fig. 17. Measured system time response for step down torque (capacitor
voltage and generator current time variations)
800
[11] Automatic Control Systems", B. C. Kuo, 7th Edition, Prentice
600
Hall International Editions.
0 2 4 6 8 10 12 14 16
[12]  Implementation of wind-turbine controllers , D. J. Leith,
time(s)
W. E. Leithead, Int. Journal on Control, Vol. 66, no 3, 1997,
Fig. 16. Simulated electromechanical time response for step down wind
pp. 349-380.
speed variation
[13]  Design and performance evaluation of a fuzzy-logic-based
variable-speed wind generation system , M. G. Simoes, B. K. Bose,
VI. AKNOWLEDGEMENT R. J. Spiegel, IEEE Trans. on Industry Applications, Vol. 33, no 4,
1997, pp. 956-965.
The authors express their gratitude to the General Secretariat for Research [14]  Dynamic Behavior of Variable Speed Wind Turbines under
and Technology of Greece for co-financing this work under SYN Grant Stochastic Wind , S. Papathanassiou, M. Papadopoulos, IEEE
No 96SYN24.
Trans. on Energy Conversion, Vol. 14, No. 4, Dec. 1999, pp. 1617-
1623.
VII. REFERENCES [15] MICROCHIP: Complete PIC18C Reference Manual, 2001.
[1]  Motion control with permanent magnet AC machines , T. M.
VIII. BIOGRAPHIES
Jahns, IEEE Proceedings, Vol. 82, No 8, 1994, pp. 1241-1252.
[2] Power Electronics-Converters, Applications and Design, N. Mohan,
Antonios E. Chaniotis (e-mail: achan@cc.ece.ntua.gr) was born in
T. M. Undeland, W. P. Robbins, Wiley, 1995.
Greece, in 1976. He received the Diploma in Electrical and Computer
[3]  Modeling and experimental verification of the performance of a
Engineering from the National Technical University of Athens in 2001
skew mounted permanent magnet brushless dc motor drive with where he follows post-graduate studies. His research interests include
parameters computed from 3D-FE magnetic field solutions , microprocessor based power control systems as well as analysis of
M.A. Alhamadi, N. A. Demerdash, IEEE Trans. on Energy generating units by renewable energy sources.
Conversion, Vol. 9, no 1, 1994, pp. 26-35.
Stavros A. Papathanassiou (e-mail: st@power.ece.ntua.gr) was born in
[4] Marchand C., Ren Z., Razek, A.,  Torque optimization of a buried
Thesprotiko, Greece, in 1968. He received the Diploma in Electrical
permanent magnet synchronous machine by geometric modification
Engineering from the National Technical University of Athens (NTUA),
using FEM , EMF 94 International Conference, Leuven, Belgium,
Greece, in 1991 and the Ph.D. degree in 1997 from the same University.
1994, pp. 53-56.
His research mainly deals with electric machines and drives, wind turbine
[5]  Optimization procedure of surface permanent magnet synchronous
modeling and control and the analysis of autonomous power systems with
motors , T. Higuchi, J. Oyama, E. Yamada, E. Chiricozzi,
large wind penetration.
F. Parasiliti, M. Villani, IEEE Trans. on Magnetics, Vol. 33, no 2,
Antonios G. Kladas (e-mail: kladasel@central.ntua.gr) was born in
1997, pp. 1943-6.
Greece, in 1959. He received the Diploma in Electrical Engineering from
[6] Kladas A., Papadopoulos M., Tegopoulos J.,  Multipole permanent
the Aristotle University of Thessaloniki, Greece in 1982 and the DEA and
magnet generator design for gearless wind power applications ,
Ph.D. degrees in 1983 and 1987 respectively from the University of Pierre
ICEM 98, Istanbul, Turkey, 1998, pp. 2055-9.
and Marie Curie (Paris 6), France. He served as Associate Assistant in the
[7] Aliprantis D., Papathanassiou S., Papadopoulos M., Kladas A.,
University of Pierre and Marie Curie from 1984-1989. During the period
"Modeling and control of a variable-speed wind turbine equipped
1991-1996 he joined the Public Power Corporation of Greece, where he
with permanent magnet synchronous generator", ICEM'2000,
was engaged in the System Studies Department. Since 1996 he joined the
Helsinki, Finland, August 2000, pp. 558-562.
Department of Electrical and Computer Engineering of the National
[8]  Neural Network Approach compared to Sensitivity Analysis based
Technical University of Athens, where he is now Associate Professor. His
on Finite Element Technique for Optimization of Permanent
research interests include transformer and electric machine modeling and
Magnet Generators , G. Tsekouras , S. Kiartzis , A. Kladas,
design as well as analysis of generating units by renewable energy sources
J. Tegopoulos, IEEE Trans. on Magnetics, Vol. 37, no 5/1, 2001,
and industrial drives.
pp. 3618-3621.
Michael P. Papadopoulos (e-mail: mpapad@power.ece.ntua.gr) was
[9] Grid Integration of Wind Energy Conversion Systems, S. Heier,
born in Ioannina, Greece, in 1932. He received the Diploma in Electrical
Wiley, 1998.
and Mechanical Engineering in 1956 and the Ph.D. degree in 1974 from
[10]  Damping of power-angle oscillations of a permanent magnet
the National Technical University of Athens (NTUA), Greece. In 1956 he
synchronous generator with particular reference to wind power
joined the Public Power Corporation of Greece, where he was engaged in
applications , A. J. G. Westlake, J. R. Burnby, E. Spooner, IEE
the planning, design, operation and control of rural and urban distribution
Proceedings - Electric Power Applications, Vol. 143, No 3, 1996,
networks, as well as in the utilisation of electric energy. He is currently
pp. 269-280.
Em. Professor in NTUA and member of the Regulatory Authority for
Energy of Greece.
w
V
(m/s)
m
� (rad/s)
m
T (kg" m)
e
T (kg" m)
e
P (W)


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