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Modeling and Control of Grid Connected Variable Speed
PMSG Based Wind Energy System
Ankit Kumar Singh
Electrical Engineering Department, NIT Hamirpur,Hamirpur,
Himachal Pradesh-177005, India
E-mail: ankitee04@gmail.com
Ram Krisham
Electrical Engineering Department, NIT Hamirpur,Hamirpur,
Himachal Pradesh-177005, India
E-mail: ramkrishan6388@gmail.com
Yograj Sood
Electrical Engineering Department, NIT Hamirpur,Hamirpur,
Himachal Pradesh-177005, India
E-mail: yrsood@gmail.com
Abstract
In recent years, The advancement of power electronic technology, novel control strategies and new circuit
topologies, the grid connected small wind turbine industry is primarily dominated by the permanent magnet
synchronous generators (PMSG) have increasingly drawn interests to wind turbine manufactures. This paper
presents modeling and control strategy for the grid connected PMSG-based wind turbine systems, where PMSG is
used as a variable speed generator. The two mass drive train models is established for coupling the wind turbine and
generator , pitch angle control at high wind speed, an LC filter is used at both side of grid side converter for desired
power quality. The control scheme is developed for grid side converter to get regulated voltage at grid side. The
simulation model is tested in MATLAB/SIMULINK environment.
Keywords: Drive train, grid side converter (or inverter), LC filter, PMSG, wind turbine.
1. Introduction
There are various types of wind power systems, some of
which are connected to power system grid and some
independent of the power grid. Many wind power
sources have been installed in isolated islands and
remote villages. However, since these wind power
systems are highly dependent on the wind, it is
necessary to link them with the power grid so that they
can continuously provide electric power to customers,
which is a big incentive for both customers and utility
companies[1][2].
In the recent years, wind energy conversion
systems have become a focal point in the research of
renewable energy sources. This is in no small part due
to the rapid advances in the size of wind generators as
well as the development of power electronics and their
applicability in wind energy extraction. For isolated
settlements located far from a utility grid, one practical
approach to self-sufficient power generation involves
using a wind turbine with battery storage to create a
stand-alone system [3]. The use of permanent magnet
machines has become attractive for use in wind turbines
because now days the available permanent magnet
materials have high coercive field strength and
temperature resistance, and are price competitive. In
addition, the required power electronic converters for
output power control have undergone a major evolution.
Conference on Advances in Communication and Control Systems 2013 (CAC2S 2013)
© 2013. The authors - Published by Atlantis Press
134
Ankit Kumar Singh, Ram Krishan, Y R sood
Modern, high performance PWM converter provides
desired power factor and low harmonics distortion in
system
2. Wind Turbine Model
The wind turbine converts energy of wind flow into
mechanical energy. The turbine shaft drives the
generator rotor through drive train. The mechanical
power output from the wind turbine is
3
1
m p w
2
P AC V
(1)
Where ρ is the air density, A is the sweep area of
the turbine blades, Vw is wind speed, Cp is the
Aerodynamic power coefficient which is a function of
the pitch angle β and the tip speed ratio λ. Since and A
are constant parameters, the wind turbine can produce
maximum power under a certain wind speed only when
the turbine operates at the maximum Cp. A generic
equation is used to express Cp. This equation, based on
the turbine characteristics of, is given by
C5
2i
i
C
p 1 3 4 6
C ( , ) C ( C C )e C
(2)
With
3
i
1 1 0.035
0.08 1
(3)
is blade pitch angle, and
is defined by
m
m
w
R
V
(4)
In (4),
m
is the turbine angular velocity and R is
the turbine radius. In small wind turbine generation
systems,
is rarely changed.
Where
1 2 3 4 5
c 0.5716,c 116,c 0.4,c 5,c 21
and
6
c 0.0068
fig. 1 shows the
p
C
curve described by
(2) for different pitch angle of
.The maximum value
of
Cp
(
Cpmax
=0.48) is achieved
=0 degree and for
=8.1.This particular value of
is defined as nominal
value (λnom).
3. PMSG Modeling
Permanent magnet have been extensively used to
replace the excitation winding in synchronous machines
with the well-known advantages of simple rotor design
without field windings, slip-rings and excitation system.
Hence, avoiding heat dissipation in the rotor winding
and providing higher overall efficiency. Recently the
PMSG is gaining lot of attention for WECS due to
compact size, higher power density, reduced losses,
high reliability and robustness. Moreover there is a need
of low speed gearless generator, especially for off-shore
wind applications, where the geared doubly fed
induction generator or induction generator will require
regular maintenance due to tearing-wearing in brushes
and gear box. Both the brushes and gear box can be
eliminated from WECS by using directly coupled low
speed generators. Further, the elimination of gear box
can increase the efficiency of wind turbine by 10%
[4][5]. The low speed PMSG requires:
a. Higher number of poles to get suitable
frequency at low speed and
b. Big rotor diameter for the high wind turbine
torque.
In case of asynchronous generators having large
no. of poles, the magnetizing current is very high due to
their low magnetizing reactance. Hence, for low speed
operation, PMSG with large number of poles are highly
beneficial. The dynamic model of PMSG can be
represented in rotating reference frame with the help of
following equations.
q
q s q q r d d r m
di
V R i L L i
dt
(5)
d
d s d d r q q
di
V R i L L i
dt
(6)
The expression for electromagnetic torque in the
rotor can be written as
e d q q d m q
3P
T L L i i i
22
(7)
Fig. 1. Cp-λ curve.
135
PMSG Based Wind Energy System Paper
In case of cylindrical rotor, the
d
L
≈
q
L
and hence
the above equation reduces to
e m q
3P
Ti
22
(8)
4. Drive Train Model
Drive train as the mechanical system of a wind turbine
consists turbine, generator and gear box. The major
sources of inertia of this system lie in the turbine and
generator. The tooth wheels of the gearbox contribute
only a relatively small fraction. For this reason, the
inertia of the gear is often neglected and only the
transformation ratio of the gear system is included, but
in this modeling gear ratio is taken to unity. Thus, drive
train is modeled as a two mass model, with a connecting
shaft, and with all inertia and shaft elements as indicated
in fig. 2.
The dynamic equations of drive train written on the
generator side are
tur
tur tur s s s tur gen
d
2H T K D
dt
(9)
gen
gen s s gen s tur gen
d
2H K T D
dt
(10)
s
tur gen
d
dt
(11)
Where
tur
T
- Wind turbine torque
gen
T
- Generator torque
tur
H
-Wind turbine moment of inertia constant
gen
H
- Generator rotor moment of inertia
constant
tur
- Wind turbine speed
gen
- Generator speed
s
K
-Shaft stiffness
s
D
- Damping coefficient.
5. Pitch angle Control
The pitch angle controller is active only in high wind
speeds, normally. In such circumstances, the rotor speed
can no longer be controlled by increasing the generated
power, as this would lead to overloading the generator
and/or the converter. Therefore the blade pitch angle is
changed in order to limit the aerodynamic efficiency of
the rotor. This prevents the rotor speed becoming too
high. Unbalance power between output and wind energy
input will increase the rotor speed of the generator. The
pitch angle should be changed, to balance the electrical
and mechanical power. After the fault, pitch angle will
be change back to normal operation. Pitch angle
controller model is shown as fig. 3. PI controller is used
for pitch angle controller. The output of PI controller is
the speed of pitch angle, it always limited up to 5°/s for
normal operation. In this model, the actuator and
mechanical system is equivalent to an inertial link. It
should be taken into account that the pitch angle cannot
be changed immediately, because of the size of the rotor
blades.
6. Power Electronics Interface
The power electronic plays an important role in the
wind energy conversion systems. As the wind turbine
operates at variable speed according to available wind
velocity, the voltage generated is of variable magnitude
and frequency. Therefore the power generated is needed
to be processed before feeding it to grid or isolated
network. Several types of power electronic interfaces
have been investigated for variable speed wind turbines
[6][7]. The proposed system consists of two back to
back converters decoupled by a dc-link. Generator side
converter is uncontrolled rectifier. The grid side
converter has been realized by using six IGBT switches
Fig. 2. Two mass drive train model
PI Angle
limit
Rate
limiter
Maximum
rotor speed
rotor speed
angle change
speed
Pitch
angle
1
s
+
Fig. 3. Pitch Angle Controller Model
136
Ankit Kumar Singh, Ram Krishan, Y R sood
for each converter. Since PMSG is connected to grid
through AC/DC/AC system, only active power of
PMSG can be transferred to grid and exchange of
reactive power cannot take place due to presence of dc-
link. To make the dc link voltage ripple free a LC filter
is connected after AC/DC Rectifier. The control scheme
is developed for grid side converter.
7. Control of grid side converter
The control of grid side converter is to regulate the
output voltage of dc/ac converter shown in fig. 4. The
LC filter output voltage is measured and transformed
into d-q variable and compared with reference voltage
which is taken as one p.u. whole of the control scheme
for grid side converter is developed through d-q
transformation technique.
Simulink diagram of voltage regulator is shown in
fig. 5. The six-pulses to dc/ac converter is given through
discrete PWM generator. PWM generator takes the
input from output of the d-q to abc conversion block.
PWM converter has capability to absorb and deliver the
reactive power for the requirement of voltage
regulation.LC filter along with grid side PWM
converter regulate the voltage of grid side with low
harmonic distortion. Frequency of PWM generator is
taken between 5 to 10Kz.
Fig. 4. Block diagram of grid connected PMSG based wind turbine system
Fig. 5. Simulink diagram of voltage control for grid side converter
137
PMSG Based Wind Energy System Paper
8. Simulation results
The system described above was simulated using matlab
Simulink environment. Wind speed profile is in stepped
form. Although real wind does not occur with such
abrupt slopes, a series of steps is a standard testing
signal which permits a clear interpretation of the system
behavior Fig. 6 shows rotor speed and pitch angle
control. Pitch angle control comes into picture at higher
wind speed, when the generator speed increases above
base speed due to increase of wind speed.
Fig. 7. (a) and (b) shows instantaneous output
voltage and current of PMSG. Fig. 7 (c) and (d) shows
phase to phase rms value of voltage and current of
PMSG. The output power of PMSG is shown in figure
(e). The maximum power output of wind turbine at base
speed is 0.8 times of nominal mechanical power of
turbine, which is shown in fig. 8.
Fig. 9. (a) and (b) shows rectifier voltage and
inverter output voltage respectively . The THD in
inverter output voltage around 64%, which contain a
large number of harmonics. A LC filters after inverter
output is connected to suppress the harmonics. Filter
output voltage contain only 1.4% THD value, which is
shown in fig. 9 (c).
9. Conclusion
This paper has proposed modeling and control of grid
connected wind energy system using Matlab/Simulink.
The modeled system including all subsystems is
Fig. 7. (a) Instantaneous output voltage of PMSG.(b)
instantaneous output current of PMSG(c) rms output voltage of
PMSG.(d) rms output current of PMSG and (e) generator output
power
Fig. 6. (a) rotor speed of generator in p.u. (b) rotor speed of
generator in rad/s and (c) pitch angle.
Fig. 8. p.u. turbine output power versues turbine speed
138
Ankit Kumar Singh, Ram Krishan, Y R sood
characterized and analyzed for validation. In the
modeling of drive train neglecting the gear ratio and it
reduces the losses in the system. Pitch angle control has
precisely implemented to control mechanical power
generated by the turbine. Control algorithm for grid side
converter along with LC filter is developed to regulate
the voltage at grid side with desired power quality.
Table 1. Parameters of PMSG
Table 2. Parameters of Turbine
10. References
1. R. Mukund, “Wind and Solar Power Systems,” CRC
Press, USA, 1999.
2. A. Murdoch, R. S. Barton, J. R. Winkelman, and S. H.
Javid, “Control Design and Performance Analysis of a 6
MW wind Turbine Generator,” IEEE Transactions on
Power Apparatus and Systems, vol. 102, no. 5,pp.1340-
1347, May 1983.
3. S. R. Hadian-Amrei and H. Iranmanseh, “Novel direct
power control for compensating voltage unbalance and
load fluctuations in PWM rectifiers”, ACSE Journal, vol.
6, no. 4, Dec., 2006; pp. 39-45.
4. Westlake A. J. G., Bumby J.R., Spooner E., „„damping
the power-angle oscillations of a permanent magnet
synchronous generator with particular reference to wind
turbine applications,‟‟. IEE Proceedings, Electr. Power
Appl., vol 143, No 3, May, 1996.
5. Binder A., Schneider T., „„Permanent Magnet
Synchronous Generators for Regenerative Energy
Conversion-- A survey,‟‟ European Conference on
Power Electronics and Applications, EPE 2005, 11-14
Sept., Dresden, Germany, 2005.
6. J. Morren and S. W. de Hann, „„Ride through of wind
turbines with doubly-fed induction generator during a
voltage dip,‟‟ IEEE Trans. Energy Convers., vol. 20, no.
2, pp. 435--441, Jun. 2005.
7. M. Fatu, C. Lascu, G. D. Andreescu, R. Teodorescu, F.
Blaabjerg, I. Boldea, “Voltage Sags Ride-Through of
Motion Sensorless Controlled PMSG for Wind
Turbines,” IEEE 42nd IAS Annual Meeting Conference,
pp.171-178, Sept. 2007.
8. M.T. Iqbal., “Modeling and simulation of a small wind
turbine,” in Proc. Newfoundland Electrical and
Computer Engineering Conf., St. John‟s, Canada, 2003,
pp. 1-4.
9. Z. Chen, J. M. Guerrero, and F. Blaabjerg, “A Review of
the State of the Art of Power Electronics for Wind
Turbines,” IEEE Transactions on Power Electronics, vol.
24, no. 8, pp. 1859-1875, Aug. 2009.
10. Md. Arifujjaman, M.T. Iqbal, and J. E. Quaicoe,
“Performance comparison of grid connected small wind
energy conversion systems,” Wind Engineering, vol. 33,
no. 1, pp. 1-18, July 2009.
Fig. 9. (a) Rectified dc voltage .(b) inverter output voltage and
(c) filter output voltage
Parameters
Values
Rated power of generator
8.5 kw
Grid voltage and frequency
575V,60Hz
Load at grid side
6.8 kw
Base speed
152.5 rad/s
Ld stator d-axis inductance
0.0082H
Lq stator q-axis inductance
0.0082H
Permanent magnet flux
0.482Wb
Number of pole pairs
5
Parameters
Values
ρ air density
1.08kg/m2
Base wind speed
12m/s
Inertia constant(p.u.)
4
139