1
Maximum Power Point Tracking of
Permanent Magnet Synchronous Generator
Wind Systems using Matrix Converters
G.P.C. Fernandes, MSc Student, IST; S.F. Pinto, Member, IEEE and J.F. Silva, Senior Member, IEEE

Abstract—The aim of this work is to propose the use of
matrix converters for wind generators equipped with
Permanent Magnet Synchronous Generators (PMSG),
replacing the typical AC/DC/AC power converters.
To extract the maximum available power from the wind,
the Matrix Converter is controlled using the Space Vector
representation combined with the Sliding Mode control
technique, so that the converter supplies the generator
with the required currents to provide the tracking of the
established reference variables.
The Maximum Power Point Tracking is achieved using
two different approaches: the speed control and the torque
control. In order to evaluate their performances, both
control approaches were tested.
The proposed wind generation system has been developed
and tested using MATLAB/SIMULINK and it was possible
to determine that the Matrix Converter is a valid
alternative to the AC/DC/AC converter and combined with
adequate input filters it is possible to extract the maximum
power from the wind with a nearly unitary power factor in
the grid connection.
with a power electronics converter connected between the
generator and the network. The AC/AC power converter is a
rectifier-inverter pair structure with an intermediate DC-link
with capacitor banks, which result in increased losses, total
weight, size and costs of the equipment, as well as in
decreased lifetime. [3]
Due to these disadvantages, Matrix Converters have
become an alternative solution to the standard power
converter. Matrix Converters are single stage AC/AC
bidirectional power converters capable of establishing a
desired output frequency and voltage and nearly unitary power
factor at the input. Matrix Converters have a simple topology,
composed exclusively by semiconductors and with nearly no
energy storage components. [4] [5]
Generator
G
PMSG
Matrix Converter AC/AC
Input Filter
Ii
Vi
Index Terms— Wind Energy; Matrix Converter; Space
Vector Modulation; Sliding Mode Control; Maximum
Power Point Tracking; Torque Control; Speed Control;
Permanent Magnet Synchronous Generator; Space Vector
Modulation.
I. INTRODUCTION
N
wind power is one of the most promising
renewable energies. In 1998 wind power worldwide
capacity was around 10 GW and in the year 2012 it reached a
record of 250 GW. [1] [2]
Modern wind turbines are equipped with a generator that
might be a Variable-Speed Synchronous Generator or a
Double-Fed Induction Generator. Both solutions are equipped
OWADAYS
G.Fernandes is with the Instituto Superior Técnico, Technical University
of Lisbon, Lisbon, Portugal (e-mail: guilhermepcfernandes@ist.utl.pt).
S.F. Pinto is with the Instituto Superior Técnico, Technical University of
Lisbon, Lisbon, Portugal (e-mail: soniafp@ist.utl.pt).
J.F.Silva is with the Instituto Superior Técnico, Technical University of
Lisbon, Lisbon, Portugal (e-mail: Fernando.alves@ist.utl.pt).
Lf
Rf
Io
Cf
Grid
Vo
Figure 1 – Proposed wind generation system
The main goal of this work is to control the input and output
currents of a Matrix Converter connected to a permanent
magnet synchronous generator using Space Vector
Modulation combined with the Sliding Mode Control
technique. In addition two different turbine control approaches
will be studied and compared: the Speed Control and the
Torque Control. Both methods are used to extract the
maximum power from the wind.
II. MAXIMUM POWER POINT TRACKING
The wind turbine should be controlled in order to extract the
maximum available wind power. There are two possible
control methods to achieve this goal, the Maximum Power
Point Tracking control (MPPT) and the Pitch Angle control.
The MPPT approach sets the pitch angle to zero and is applied
when the wind speed is between the cut-in speed and nominal
speed of the wind generator. The application of this control
strategy can be made by controlling the generator torque or the
generator speed. Both methods are described and compared in
this paper.
2
A. Wind Turbine Model
The electric power that is extracted from the wind is given
by (1), where
is the power coefficient of the wind power,
is the air density [
,
the area swept by the rotor
blades [
and the wind speed[m/s] [6]:
(1)
depends on the pitch angle
which can be obtained by:
and on the tip-speed ratio ,
The reference torque establishes the currents that will be
applied to the PMSG stator so that the generator speed can
track its reference torque.
The sizing of C(s) compensator has to be done by admitting
that the open-loop chain is of second order with two real poles
at
and
without any poles at the complex plan
origin. Any second-order system can be described by the
transfer function represented in (10):
(10)
(2)
(3)
In order to minimize the effect of the
disturbance and to
guarantee fast response times and zero tracking error to the
step response, a PI controller is used as C(s) [7]:
(11)
Finally:
(4)
The closed-loop transfer function of the system is described by
(11):
The torque obtained from the wind turbine rotor is obtained
by:
(12)
(5)
To cancel the effect of the low frequency pole
B. Speed Controller
The purpose of the speed control strategy is to extract the
maximum power from wind by establishing an optimal speed
and controlling the speed around this value. In order to obtain
the optimal speed value, it is required to determine the
maximum available mechanical power supplied by the wind
turbine [7]:
(6)
(7)
,
is
given by (12):
(13)
From (10) and (12):
(14)
(15)
C. Torque Controller
Replacing (8) in (6), it possible to determine the maximum
power extracted from the wind. From (5), the maximum
torque is given by (16).
(16)
(8)
The generator speed reference is given by (9), where G is the
wind turbine gearbox ratio.
The Matrix Converter reference currents are established from
the reference torque (16) in order to extract the maximum
power from the wind.
(9)
III. PERMANENT MAGNET SYNCHRONOUS
GENERATOR
The model of the speed controller is presented in figure 2.
Figure 2 – Speed Controller.
The proposed wind generation system solution is equipped
with a permanent magnet synchronous generator (Fig. 3)
3
d
(24)
b
id
ib
If
is the same as the reference torque,
will be the
reference current to the Matrix Converter current controller.
ic
c
ia
iq
IV. MATRIX CONVERTER
q
a
Figure 3 – Machine dynamics in both abc and dq frames.
The PMSG can be represented in a bi-phase frame where the d
axis is aligned with the machine rotor position and in
quadrature with the q axis [8] [9].
A. Model Equations
The voltages applied to the stator windings are given by (17)
and (18) [6].
(17)
A. Matrix Converter Model
The three-phase Matrix Converter has the following model:
iA
VA
VAB
S11
S21
S31
S12
S22
S32
S13
S23
S33
iB
VCA
VB
VBC
iC
VC
(18)
ia
The relation between the stator currents and the stator fluxes is
given by (19) and (20).
va
ib
vab
vb
ic
vbc
vc
vca
Figure 4 – Matrix Converter Model
(19)
(20)
The electromagnetic torque of the generator is given by (21).
(21)
B. Rotor Flux Oriented Control
The Rotor Flux Oriented Control approach is used to control
the generator currents. The dq frame is attached to the linkage
flux
. From this it is possible to establish a linear relation
between the electromagnetic torque and the
current [8] [9].
(22)
The
is set to zero, and as a result the linkage flux is the
same as the permanent magnet flux [10]:
(23)
As a result:
The model of the converter is composed by nine
bidirectional switches disposed as a matrix as it can be seen in
figure 4. The purpose of this topology is to connect any output
phase to any input phase. This power converter allows the
connection of a voltage source to a current source, which
means that the input voltages and output currents are known
and it is required to determine the output voltages and input
currents using an adequate modulation process [4].
The power switches
can be represented using two
possible logical states, ON if
or OFF if
.
(25)
(26)
However at any moment there can only be one switch ON at
each line of the matrix, therefore the Matrix Converter has 27
possible states to represent the input currents and output
voltages.
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B. Space Vector Modulation
The application of the Concordia Transformation to the 27
switching states of the power converter allows the
representation of the input currents and output voltages as
vectors, which is an advantage to the control process [4].
C. Sliding Mode Control
The Sliding Mode Control technique combined with the Space
Vector Modulation process is used to control the Matrix
Converter currents.
The matrix converter semiconductors are switched at high
frequency in order to ensure the reference currents are
followed by applying the adequate space vectors [4].
The Sliding Mode Control method will be used to control
both the input and output current of the Matrix Converter.
No reactive power implies that the reference input current
must be set to zero
(31)
The input current controller also has a sliding surface defined
by (32).
(32)
The sliding surface also has to verify the stability condition
(33).
(33)
The input current controller defines a criterion that allows to
choose which of the two available space vectors is the most
adequate to apply.
D. Output Current Control
The sliding surfaces of the output current controller are
represented in (27). The reference currents are obtained from
the PMSG controller [7].
(27)
and
should be greater than zero but limited by the
switching frequency.
To assure that the system slides along the defined surfaces it is
required that they verify the stability conditions (28)
(28)
Based on equations (27) and (28), the Space Vector selection
criterion is:
Space Vector Choice
Value of
Vector that increases
value
Vector that decreases
value
Vector that does not change
+1
-1
0
Value of
+1
-1
Space Vector Choice
Vector that increases
Vector that decreases
The right choice of space vectors guarantees that the
controlled variables track their references.
V. SIMULATION PARAMETERS
In this section the simulation parameters are presented.
The proposed system was tested in MATLAB/SIMULINK
platform.
A. Turbine parameters
The simulation was based on the Siemens turbine model
SWT-1.3-113.
2.3
690
Blade
Length [m]
55
Gear Box
ratio
77
B. Permanent Magnet Synchronous Generator parameters
This technique has, in each instant, two different vectors to
apply in order to control the output current.
E. Input Power Factor Control
To control the input current of the Matrix Converter and the
to obtain a nearly unitary power factor it is required that the
reactive power is zero [7].
The reactive power is obtained by (29).
(29)
(30)
4
2
0.09
0.09
0.05
100
707.1068
0.04
0.865
C. Speed Controller parameters
1
1
2000
50000
25
5
D. Wind Speed Chart
As can be seen from figure 7, the speed reference established
by the controller is tracked by the generator.
Figure 8 represents the electromagnetic torque obtained in the
speed control case.
Figure 5 – Wind Speed Chart.
The wind chart (Fig. 5) was obtained based on average
measurements of wind speed and it will be very useful to test
the proposed system controllers. Due to hardware limitations
the simulation had to be reduced to thirty seconds and the
inertia was also reduced in order to obtain scaled results.
VI. SIMULATION RESULTS
In this section some simulation results are presented and
analyzed.
Figure 8 – Generator torque tracking the reference (speed control
case).
The electromagnetic torque produced by the generator can
track the torque reference established by the speed controller.
As can be seen from figures 5 and 8, when the winds speeds
are low, the torque is continuous and tracks the reference.
However when there are sudden changes in wind speed the
torque has some discontinuities that will result in high current
values.
Figure 9 represents the electromagnetic torque obtained in the
torque control case.
Figure 6 – Speed comparison of Torque Control and Speed Control.
As expected, the speed controller is much faster than the
torque controller. The speed controller allows the generator to
track every wind speed variation. The torque controller
considers that the generator is always rotating at its optimal
speed and as can be seen in figure 6 it is a serious limitation
when the wind speed changes fast.
Figure 9 – Generator torque tracking the reference (torque control
case).
The electromagnetic torque produced by the generator can
track the reference torque established by the torque control. As
can be seen, the electromagnetic torque obtained in this case
has lower values than with the speed control.
Figure 10 represents the electric power generated using both
approaches.
Figure 7 – Generator speed tracking the reference.
The speed controller is provided with a PI feature so it can
track the wind speed variations with adequate response times.
6
allows a nearly unitary power factor in the network
connection.
REFERENCES
Figure 10 – Electric power in both approaches.
It is possible to verify that the speed controller is able to
extract more power from the wind than the torque controller
when the wind speed is between 4 and 7 [m/s]. This result is
clearly a consequence of the PI feature absence in the torque
control case. The torque controller presumes the generator
speed is at its optimal value and defines a torque reference to
the generator controller. However, as can be seen from figure
6 when the wind speed values are low, the generator speed in
the torque control case is much higher than the optimal speed.
As a result it produces less power than the speed control
approach.
VII. CONCLUSIONS
Both Maximum Power Point Tracking techniques were tested
and produced different results. As we’ve seen in chapter VI
The speed controller extracts more power from wind than the
alternative method because the torque controller does not
perform well when wind speed values are near the cut-in
speed limit. This fact is due to the absence of PI feature in the
torque control case. However the electromagnetic torque
produced by the generator in the speed control case has
discontinuities when wind speed values vary fast, and it
reaches very high torque values when the wind speed is close
to the nominal speed of the wind generator. These high values
of torque result in overcurrents which is undesirable to the
power network. In spite of extracting less power from the
wind, the electromagnetic torque produced in the torque
control case has lower values of torque and it is continuous
and much more stable than the speed control case, which is
better for the power network.
From these facts one might conclude that the torque control
approach is the best solution when the wind speed is close to
the wind generator nominal speed value, because it extracts
the same amount of power as the speed control case. When
wind speeds are closer to the wind generator cut-in speed, the
best solution is to control the generator speed, because this
type of controller extracts more power .
Furthermore it was possible to verify that the Matrix
Converter is solid alternative to conventional AC/DC/AC
converters when it is controlled by the Sliding Mode Control
technique combined with Space Vector Modulation, as it
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