13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
IMD-123
Modeling and Control of Variable Speed Wind Turbine Equipped with PMSG
D.I. Stroe∗
Aalborg University
Aalborg, Denmark
A.I. Stan†
Aalborg University
Aalborg, Denmark
I. Visa‡
Transilvania University
Brasov, Romania
Abstract— The Variable Speed Wind Turbine (VSWT)
configuration is the dominant wind turbine topology available at this moment on the market. Moreover, the Permanent Magnet Synchronous Generator (PMSG) offers better
performance than other generators because of its higher
efficiency and of less maintenance since they don’t have
rotor current. Therefore, in this paper the modeling and
control of a 2 MW VSWT equipped with PMSG is presented. As control strategy for the generator side converter the Direct Torque Control method was chosen. All
the components of the wind turbine except the DC-link and
the grid-side converter are developed and implemented in
MATLAB/Simulink. In order to analyze the behavior of the
wind turbine system and to validate the developed control
system, a study case is carried out.
I. Stroe§
Transilvania University
Brasov, Romania
speed wind turbine concept with full-scale frequency converter has an increasing market share. The most common generators used in this topology, the doubly fed induction generators (DFIGs) and permanent magnet synchronous generators (PMSGs), allow the extraction of maximum power from a large wind speed interval, for an optimum tip-speed ratio.
The PMSG has some valuable advantages over the DFIG
such as: better efficiency, easier controllability, no need for
reactive magnetizing current and they are smaller in size.
The paper focuses on a large scale 2 MW variable speed
wind turbine, using a surface mounted PMSG, together
with a full scale power converter, consisting of a back-toback voltage source converter and a DC link capacitor, together allowing a bidirectional power flow in the system
and fully decoupled control between the generator side and
the grid side converters. The presented topology is subjected to a number of control schemes: pitch angle control
for limiting the output power above rated values, generator
control for maintaining the desired rotor speed and grid side
inverter control for active, reactive power flow control, and
constant DC link control. One of the most used generator
control strategies was implemented: Direct Torque Control
with Space Vector Modulation (DTC-SVM). The grid side
inverter modeling and control was not considered in this
paper.
Keywords: VSWT, PMSG, DTC-SVM, modeling, control
I. Introduction
Nowadays, the extraction of power from the wind on a
large scale became a recognized industry.
The pace in which it developed is remarkable, it holds
great potential showing that in the future will become the
undisputed number one choice form of renewable source
of energy. The powerful force that pushes this clean technology upward is simple economics. The conventional fossil fuel technology is mature and the costs for installations
in this field are predictable. Moreover the non-renewable
nature of fossil-fuels along with the increasing energy demands in the world will only make the prices go higher.
This factor called scarcity, which describes all traditional
energy sources does not apply for renewable. Wind power
is abundant and there will be always zero cost of the wind.
The technology here is still improving, much of research
being conducted in grid connecting wind farms for producing more electricity for lower prices.
According to [1], the wind energy sector continued its
market growth in the European Union at an increased rate
of 23% compared to year 2008 installations, reaching by
the end of 2009, a total installed capacity of 75 GW.
Because of the rapid development of power electronic
devices and thus decreasing equipment costs, the variable
II. System and Model Description
Throughout this section the modeling of the wind turbine system equipped with PSMG is presented. However,
because the focus of this paper is the control of the generator side converter, only the components of the wind turbine system until the DC-link are modeled. Fig. 1 presents
the variable speed wind turbine with full-rating power converter concept which was considered for modeling.
Rotor
PCC
PMSG
Transformer
Wind
G
Drive
Train
External
grid
Generator Side
Converter
Grid Side
Converter
∗ dis@et.aau.dk
† astan@student.aau.dk
Fig. 1. Variable speed wind turbine equipped with PMSG
‡ visaion@unitbv.ro
§ stroei@unitbv.ro
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13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
= 0.4721. As the wind speed increases, so does ωr , but the
tip-speed-ratio is kept constant at λopt . Region II is governed by the policy: fixed pitch-variable torque. In Region
III, which starts from rated wind speed Vrated , the rated
power is reached, therefore it must be kept constant as wind
is still increasing. The cut-out wind speed value (here considered 25 m/s) ends the third region, and forces the wind
turbine to shut down for avoiding damage at rotor and generator. Region III is governed by the policy: constant rotor
speed-constant torque- variable pitch.
However, the problem with large wind turbine is that the
rated shaft speed is reached before the rated wind speed. As
presented in [4], the tip speed constraint consists of speed
control at the turbine shaft at the transition between Region
II and Region III of turbine operation. Thus, in the developed wind turbine rotor model, the rotor shaft speed was
compared with the rated value ωrated , at every wind speed
between cut-in and rated wind speed. Therefore between
Region II and Region III a new region called Region II1/2
was attached. In Region II the blade pitch was kept fixed at
0 degrees to maintain the power coefficient at Cp max [3].
The rotor shaft speed was increased as the wind speed was
increasing. After rated rotor speed was reached, the blade
tip speed also reached its maximum value, therefore it was
be kept at this level. This state represents the beginning
of Region II1/2. As the wind speed was further increased
towards rated value, the rotor shaft speed was maintained
constant, so the only thing that was decreased had been the
tip speed ratio [3]. Implementing this algorithm, the power
profile of the considered wind turbine showing the different
regions encompassing all speeds of operation is presented
in Fig. 4.
A. Wind Turbine Rotor
The wind turbine rotor is designed to extract maximum
power from the wind and this value can be calculated as:
Pwt =
1
ρπR2 Vw3 Cp
2
IMD-123
(1)
Where, ρ represents the air density, R represents the blade
radius, Vw represents the wind speed and Cp represents the
power coefficient. The power coefficient Cp can have a
maximum value of 0.593, but in reality, the aerodynamics
of the rotor are not perfect and typical values for Cp are
between 0.4 - 0.5 [2]. Fig. 2 shows the power profile for
a typical large wind turbine compared with total available
power based on wind speeds.
Fig. 2. Power profile for a large wind turbine [3]
The Cp (λ, β) characteristic of the considered wind turbine when the pitch angle is varied towards ”feathering” is
shown in Fig. 3. The maximum power coefficient for the
modeled wind turbine is Cp max = 0.4721 when β = 0◦ .
β=0
β=4
β=8
β = 12
Region I
Region
II
β = 16
Region
II1/2
Region III
β = 20
Fig. 4. Mechanical power as function of wind speed
Fig. 3. Family of Cp curves as function of tip-speed-ration and pitch angle
As presented in Fig. 2 the power profile of the considered
wind turbine can be divided in three regions. The behavior
of the WTS in this three regions is presemted in detail in the
next paragraphs. Thus, Region I represents the lowest wind
speeds under the cut-in wind speed 3:5 m/s. In this region
the wind turbine will not start. In the rotor model, this condition will attribute zero values to mechanical power Pmec
and rotor speed ωr . Next comes Region II, in which the turbine starts operating, following the maximum power point
of operation, maintaining the power coefficient at Cp max
Cp vs. wind speed
X: 3.6
Y: 0.4721
0.5
Cp
0.4
0.3
Rated wind
speed
0.2
X: 15
Y: 0.2069
0.1
Region I
0
0
Region II
5
Region II1/2
10
Region III
15
Wind speed [m/s]
20
25
Fig. 5. Cp curve as function of wind speed
2
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13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
From Fig. 5, it can be observed that even though the
rated wind speed is not reached, values of Cp are starting to
decrease from Cp max in Region II1/2, for maintaining the
maximum tip speed constraint.
D. Converter Model
Nowadays the back-to-back Voltage Source Converter
(VSC) is the most used converter topology in the wind turbine industry. Both converters can operate in rectifier or
inverter mode, and thus a bidirectional power flow can be
achieved. In the developed model, the generator side converter works as a rectifier, being able to control the torque
and speed, while the grid side converter works as an inverter keeping the voltage constant in the DC-link [6], [5].
The equivalent circuit of the VSC connected at the output
terminals of a PMSG is presented in Fig. 6.
B. Drive Train Model
As presented in [5] and [6], the drive train model can be
modeled as a simple kinematic converter for direct torque
to torque conversion. Thus, the drive train can be expressed
as a second order system:
G(s) =
Kωn2
s2 + 2ζωn s + ωn2
IMD-123
(2)
IDC
PMSG
Where, ζ represents the damping ration, ωn represents the
natural frequency and K represents the gearbox ratio. The
model of the drive train was developed using (3) and (4)
where, Tem represents the electromagnetic torque and ωm
represents the mechanical speed.
Tem = G(s) · Twt
(3)
ωm = kgear · ωwt
(4)
Twt, Ωwt
disd
− ωe Lq isq
dt
Ia
Sb
Sc
A
Ib
N
VDC
B
Ic
C
Fig. 6. Star-connected PMSG with VSC [6]
In order to introduce the mathematical model of the VSC,
three switching variables Sa, Sb and Sc must be introduced.
Each of these switching variables is associated with a phase
of the inverter and can take only two values, either 1 or 0.
Thus, the switching variable Sk (k = 1, 2, 3) is defined to
take the value 1 if the ”upper” switch of the leg is on and
the ”lower” switch of the same leg is off. Furthermore, if
the ”upper” switch is off and the ”lower” switch is on the
switching variable Sk will assume the value 0.
According to [8] for the connection presented in Fig. 6
the applied voltages at the machine terminals, uan , ubn and
ucn and the DC-link current IDC may be found as:





uan
2 −1 −1
S1
V
 ubn  = DC  −1 2 −1   S2 
(9)
3
u
−1 −1 2
S
C. PMSG Model
The model of the PMSG was developed in the dq synchronous reference frame, where the q-axis is 90◦ phase
shifted ahead of the d-axis with respect to the direction of
rotation [7].
In order to simplify the system, the generator was assumed to be a PMSG with surface-mounted magnets. Thus,
the model of the PMSG in the dq synchronous reference
frame is given by the voltage equations (5) and (6), the
torque equation (7) and the mechanical equation (8).
usd = Rs isd + Ld
Sa
(5)
3
cn
usq
disq
= Rs isq + Lq
+ ωe ψP M + ωe Ld isd
dt
Tem =
(6)
IDC =
3
npp ψP M isq
2
(7)
dωm
dt
(8)
Tem − TL = J

S1
S2
S3

ia
 ib 
ic
(10)
III. DTC-SVM of PMSG
PMSG control methods can be divided into scalar and
vector control. The general classification of the variable
frequency control is presented in Fig.7 [6].
The scalar control methods are based on a valid relation
in steady state, where only the magnitude and frequency
of voltage, currents and flux linkage space vectors are controlled. On the other hand, vector control is based on a relation valid for dynamic states and not only the magnitude
and frequency, but also the position of the voltage, current
and flux space vectors are controlled [5]. Among these vector control methods, one of the most popular strategy used
Where, usd , usq represent the direct and quadrature components of the stator voltages, isd , isq represent the direct and
quadrature components of the stator currents, Ld , Lq represent the direct and quadrature components of the stator
inductances Rs represents the stator resistance, ωm represents the mechanical speed of the rotor, ωe represents the
electrical speed of the rotor, ψP M - represents the permanent magnet flux linkage, Tem - represents the electromagnetical torque, npp represents the number of the pole pairs.
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13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
alytical methods and the SISOtool package provided by
MATLAB/Simulink. The detailed procedure of tuning
these PI controllers is presented in [6].
Variable Frequency Control
Scalar based controllers
IMD-123
Vector based controllers
Field Oriented Control
(FOC)
V/Hz Control
PM (rotor)
Flux Oriented
(RFOC)
IV. Simulation Results
In order to analyze the behavior of the developed wind
turbine system (plant and control) when changes in the
wind speed occur, the next study case was performed. Thus,
the positive step in the wind speed (from 15 m/s to 16 m/s)
shown in Fig. A was considered at the input of the system
Direct Torque Control
(DTC)
Stator Flux
Oriented
(SFOC)
Direct Torque
Control with Space
Vector Modulation
(DTC-SVM)
Circular flux
trajectory
Wind Profile
16.2
Fig. 7. Classification of PMSG control methods [6]
16
for controlling PMSGs is the Direct Torque Control with
Space Vector Modulation (DTC-SVM).
The Direct Torque Control (DTC) strategy was proposed
in the mid 80’s by Takahashi and Noguchi [9]. The name
DTC comes from the fact that, based on the torque and
flux errors it is possible to control the inverter states without using inner current control loops [10], [11], citeABB.
There are two main alternatives to implement the DTCSVM strategy: using a cascade structure or using a parallel
structure. In this paper, the second alternative was used and
block scheme of the DTC-SVM with parallel control structure is shown in Fig. 8.
Wind Speed [m/s]
15.8
15.6
15.4
15.2
15
14.8
4
4.2
4.4
4.6
4.8
5
Time [s]
5.2
5.4
5.6
5.8
6
Fig. 9. Positive step in the wind speed used as input in the WPS
Based on the wind speed presented in Fig. 9, the response of the system is shown in Fig. 10.
VDC
eѰs
Ωm*
eΩ
-
PI
eT
Tem*
-
PI
Usd*
PI
Usq*
Reference and Measured Speed
Usα*
1.01
SA
Space
SB
Vector
Usβ* Modulation SC
PWM
Inverter
1.006
1.004
Generator
Model
Tem
d/dt
Reference speed
Measured speed
1.008
θѰs
|Ѱ s |
Ωm
Reference
Voltage
Vector
Calculation
Speed [p.u.]
|Ѱs* |
Is
γm
encoder
PMSG
1.002
1
0.998
0.996
0.994
0.992
Fig. 8. Block scheme of DTC-SVM with parallel structure [5]
0.99
4.5
5
5.5
6
6.5
7
7.5
8
Time [s]
In order to obtain the flux error eψs which represents the
input of the flux PI controller, the reference value of the
stator flux |ψs∗ | is compared with the estimated value of the
stator flux |ψs | which is obtained from the generator model.
The same principle is followed-up in the case of the torque
∗
PI controller, where the torque reference value Tem
is compared with the estimated value Tem . Thus, the torque error
eT is obtained [6].
Furthermore, delivering eψs and eT at the input of the PI
controllers, the reference voltage components in dq refer∗
∗
ence frame, Usd
and Usq
, are obtained. These voltage signals are transformed to stationary αβ reference frame using
∗
the stator flux angle eθs . These new obtain voltages, Usα
∗
and Usβ , are delivered to the space vector modulator and
thus the switching signals Sa , Sb and Sc used to control the
PWM converter are obtained [6].
The tuning of the PI controllers was realized using an-
Fig. 10. Reference and measured speed at a positive unit step change in
the wind speed
As it can be observed, initially (for simulation time
smaller than 5 seconds) the reference speed as well as the
measured speeds have the value 1 p.u.. This fact is due to
the value of wind speed which initially is set to 15 [m/s],
wind speed for which the rotor speed had already reached
its rated value. The positive step in the wind occurs at simulation time equal to 5 seconds and this will determine a
small ripple in the measured speed. The overshoot produced by the change in the wind speed is very small and the
system stabilizes in a short time, reaching again 1 p.u. value
after approximately 4 seconds. The settling of the system
is influenced by the value of the total moment of inertia of
the wind turbine system. Thus the bigger the moment of
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13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
Mechanical and Electrical Power
inertia is, the longer it will take the system to stabilize and
vice versa.
In Fig. 11 the load (mechanical) torque from the wind
turbine rotor and the electromagnetic torque are plotted.
The Load Torque is the wind turbine torque obtained at the
output of the drive train and transferred to the PMSG, while
the Electromagnetic Torque is obtained from the generator.
It can be observed that when the change in the wind speed
occurs the mechanical torque changes as a consequence of
higher mechanical power delivered by the rotor. The electromagnetic torque has an identical shape with the mechanical torque. As the mechanical speed of the PMSG is kept
almost unchanged, the most part of the mechanical power
is converted into electrical power. During the wind speed
change the mechanical and electromagnetic torques reach
values above 1 [p.u.]. This torque rise is due to the fact
that the pitch mechanism needs some time to respond and
limit the power. After the pitch mechanism has limited the
power, the mechanical and electromagnetic torques return
to their rated value.
1.35
Power [p.u.]
1.25
1.2
1.15
1.1
1.05
1
0.95
4.5
5
5.5
6
Time [s]
6.5
7
7.5
Fig. 12. Mechanical and electrical power at a positive unit step change in
the wind speed
discussed. The wind turbine rotor model has been presented
in detail and the maximum power point tracking was implemented. The generator was modeled in the dq synchronous
reference frame as a PMSG equipped with surface-mounted
magnets.
The DTC-SVM control structure was implemented in the
dq synchronous reference frame. The developed WTS behaved well at step changes in the wind speed when the generator side converter was controlled using the DTC-SVM
strategy
Load and Electromagnetic Torque
Load torque
Electromagnetic Torque
1.2
Torque [p.u.]
Mechanical power
Electrical power
1.3
1.3
1.25
IMD-123
1.15
References
1.1
[1]
[2]
EWEA, “Wind in power - 2009 european statistics,” February 2010.
F. Bianchi, H. Battista, and R. Mantz, Wind Turbine Control Systems.
Principles, Modelling and Gain Scheduling Design. Springer-Verlag
London Limited, 2007.
[3] A. I. Stan, D. I. Stroe, T. Stanciu, and L. Shuai, “Variable speed wind
turbine equipped with synnchronous generator,” Master’s thesis, Institute of Energy Technology, Aalborg, Denmark, June 2009.
[4] C. Bottasso and A. Croce, “Power curve tracking with tip speed constraint using lqr regulators,” tech. rep., Politecnico di Milano, Milano, Italy, March 2009.
[5] C. Busca, A. I. Stan, T. Stanciu, and D. I. Stroe, “Control of permanent magnet synchronous generator for large wind turbines,” Proceedings of IEEE-ISIE2010, pp. 3871–3876, 2010.
[6] C. Busca, A. I. Stan, T. Stanciu, and D. I. Stroe, “Control of permanent magnet synchronous generator for large wind turbines,” Master’s thesis, Departament of Energy Technology, Aalborg University,
Denmark, December 2009.
[7] M. Ying, G. Li, M. Zhou, and C. Zhao, “Modeling of the wind turbine with a permanent magnet synchronous generator for integration,” IEEE, pp. 1–6, 2007. ISBN 1-4244-1298-6.
[8] F. Iov, A. Hansen, P. Sorensen, and F. Blaabjerg, “Wind turbine
blockset in matlab/simulink,” tech. rep., Aalborg University and
RISO, March 2004.
[9] L. Takahashi and T. Noguchi, “New quick-response and highefficiency control strategy of an induction motor,” IAS, pp. 495–502,
1985.
[10] G. Buja and M. Kazmierkowski, “Direct torque control of pwm inverter - fed ac motors - a survey,” IEEE Transactions of Industrial
Electronics, vol. 51, pp. 744–757, August 2004.
[11] D. Swierczynski, Direct Torque Control with Space Vector Modulation (DTC-SVM) of Inverter-Fed Permanent Magnet Synchronous
Motor Drive. PhD thesis, Institute of Control and Industrial Electronics, Warszaw University of Technology, 2005.
1.05
1
0.95
4.5
5
5.5
6
Time [s]
6.5
7
7.5
Fig. 11. Load and mechanical torque at a positive unit step change in the
wind speed
In Fig. 12 the mechanical and electrical power in the
wind turbine system are presented. The offset between
the mechanical power (measured at the output of the drive
train) and the electrical power obtained using the DTCSVM method is due to the efficiency of the combined generator and drive train system. The sudden change in the power
which may be observed in Fig. D is due to the change in the
wind speed. At the beginning of the simulation the electrical power is equal to 1 p.u. because the value of the wind is
equal to 15 m/s which represent the rated wind speed. After
the positive step change in the wind occurs, the mechanical
and electrical power increases. Due to the pitch controller,
which keeps the output power constant in the interval between the rated wind speed (15 [m/s]) and the cut-out wind
speed (25 [m/s]), the power returns to its rated value in a
relatively short time.
V. Conclusions
The modeling of a variable speed wind turbine equipped
with a permanent magnet synchronous generator has been
5