Wind Speed Sensorless Maximum Power Point
Tracking Control of Variable Speed Wind Energy
Conversion Systems
J. S. Thongam1, Member IEEE, P. Bouchard1, H. Ezzaidi2, Member IEEE and M. Ouhrouche2, Member IEEE
1
Department of Renewable Energy Systems, STAS Inc., 1846 Outarde, Chicoutimi, QC, Canada, G7K1H1
Department of Applied Sciences, University of Quebec at Chicoutimi, Chicoutimi, QC, Canada, G7H2B1
thongam.js@stas.com
2
Abstract-A maximum power point tracking (MPPT)
controller for variable speed wind energy conversion system
(WECS) is proposed. The proposed method, without requiring
the knowledge of wind speed, air density or turbine parameters,
generates at its output the optimum speed command for speed
control loop of rotor flux oriented vector controlled machine side
converter control system using only the instantaneous active
power as its input. The optimum speed commands which enable
the WECS to track peak power points are generated in
accordance with the variation of the active power output due to
the change in the command speed generated by the controller.
The concept is analyzed in a direct drive variable speed
permanent magnet synchronous generator (PMSG) WECS with
back-to-back IGBT frequency converter. Vector control of the
grid side converter is realized in the grid voltage vector reference
frame.
Simulation is carried out in order to verify the
performance of the proposed controller.
Keywords-Wind energy conversion system, permanent magnet
synchronous generator, wind speed sensorless, maximum power
point tracking control.
I.
INTRODUCTION
Wind is an abundant source of energy that will never run
out. It is also the world’s fastest growing energy source which
is available free, and once the wind turbine generator is
installed, the running cost is very small consisting only of
routine maintenance and repairs. Therefore, wind generation
systems are attracting great attention all over the world. In
recent years, fixed speed wind energy conversion systems, due
to poor energy capture, stress in mechanical parts and poor
power quality have given way to variable speed systems.
These systems have reduced mechanical stress and
aerodynamic noise, and can be controlled in order to enable the
turbine to operate at its maximum power coefficient over a
wide range of wind speeds, obtaining a larger energy capture
from the wind [1]-[4].
Wind power, even though abundant, varies continually as
wind speed changes throughout the day. Maximum power
which a wind turbine can deliver at a certain wind speed
depends upon certain optimum value of speed at which the
shaft rotates. Extracting maximum possible power from the
available wind power is of utmost importance, because, only
then we can have efficient use of equipment and available
978-1-4244-4252-2/09/$25.00 ©2009 IEEE
energy source; therefore, MPPT control is an active research
area [5-20].
Wind speed sensor normally used in conventional WECS
[5]-[6] for implementing MPPT control algorithm reduces the
reliability of the WECS in addition to inaccuracies in
measuring the wind speed. Therefore, some MPPT control
methods estimate the wind speed; however, many of them
require the knowledge of air density and mechanical
parameters of the WECS [7]-[11]. Such methods, requiring
turbine generator characteristics result in custom-design
software tailored for individual wind turbines. Air density, on
the other hand, depends upon climatic conditions and may vary
considerably over various seasons. Therefore, a lot of research
efforts are focused on developing wind speed sensorless MPPT
controller which does not require the knowledge of air density
and turbine mechanical parameters [12]-[18].
In [12], MPPT control is achieved using stator frequency
derivative and power mapping technique. The maximum
power curves for power mapping are established by running
several simulations or offline experiments at various wind
speeds. In [13], [14] simple hill-climb search type algorithms
are proposed in for tracking peak power point. Hill-climb
search type algorithm proposed in [15] for tracking the peak
power point uses the principle of search-remember-reuse
process. The method uses memory for storing maximum
power points obtained during training process which are used
later for tracking peak power points. Optimum power search
algorithm is proposed in [16] which uses the fact that
dPo/dω=0 at peak power point. The algorithm dynamically
modifies the speed command in accordance with the magnitude
and direction of change of active power. In [17], [18] fuzzy
logic based MPPT controllers are proposed. The MPPT
controllers proposed in these works generate optimum speed
command for the speed control loop of the machine side
converter control system enabling optimal power tracking.
In this paper, a simple wind speed sensorless MPPT
controller for variable speed WECS is proposed. The proposed
method of tracking maximum power point does not require the
knowledge of turbine parameters or air density in addition to
not requiring the knowledge of wind speed. The algorithm
requires only the instantaneous active power as its input and
generates at its output the optimum reference speed for the
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vector controlled machine side converter control system in
order to enable the system to track maximum power point.
Performance of the proposed controller is verified by
simulation; work for complete experimental verification of the
proposed method is underway.
III. THE PMSG MODEL
The dynamic model of the surface mounted PMSG in
magnetic flux reference frame is
vsd = − Rs isd − Ls disd / dt + ω Ls isq
II. WIND TURBINE
vsq = − Rs isq − Ls disq / dt − ω Ls isd + ωφr .
The torque produced by a wind turbine is given by
3
Tm = 0.5πρC p (λ ) R2vw
/ ωr
(2)
In order to compute CP, a look up table of turbine power
coefficient as a function of tip speed ratio and pitch can be
effectively used without much loss of accuracy [19].
Alternatively, CP can also be calculated as shown in [20] using
the relation
C p = 0.5176[116 / λi − 0.4 β − 5]e −21/ λi + 0.006795λi
(3)
where λi = [1/(λ + 0.08β ) − 0.035 /( β 3 + 1)]−1 . The dynamic
equations of the wind turbine is given as
d ω / dt = (1 / J ) ⎡⎣Tm − TL − Fω ⎤⎦
(4)
where ω is the turbine-generator angular speed, J is the
moment of inertia and F is the viscous friction coefficient.
Fig. 1 shows the power coefficient C p as a function of tip
speed ratio λ . The power coefficient and hence the power is
maximum at a certain value of tip speed ratio called optimum
tip speed ratio λopt . In order to have maximum possible power,
the turbine should always operate at λopt . This is possible by
controlling the rotational speed of the turbine so that it always
rotates at the optimum speed of rotation.
Fig. 1 Power coefficient vs. tip speed ratio.
(6)
The electromagnetic torque is given by
(1)
where R is the turbine radius, v w is the wind speed, ω is the
turbine angular speed. The tip speed ratio is given by
λ = ω r R / vw .
(5)
T = (3 / 2) pφr isq .
(7)
IV. THE CONTROL SYSTEM
A.
Machine Side Converter Control
A vector control approach is used where control is
exercised on the rotor flux reference frame. The block
schematic of the machine side converter control system is
shown in Fig. 2. The proposed MPPT controller generates ω * ,
the reference speed which when set as the command speed for
the speed control loop of the machine side converter control
system, maximum power points will be tracked by the WECS.
The details of the controller will be discussed in the next
section. The required d-q components of the machine side
converter voltage vector are derived from two PI controllers:
one of them controls the d-axis component of the current and
the other, the q-axis component. For fast dynamic control
capability COMPd and COMPq are added to the direct and
quadrature axis current regulator outputs respectively to form
command d and q voltage [21]. Space vector PWM generates
the switching pulses for the converter power devices.
B.
Maximum Power Point Tracking Control
The power that can be extracted from a turbine at a certain
wind speed is maximum at a certain optimum speed of rotation
of the rotor. The MPPT controller computes this optimum
speed using information on magnitude and direction of change
in power output due to the change in command speed. The
flow chart in Fig. 3 shows how the proposed MPPT controller
is executed. The operation of the controller is explained
below:
The active power Po(k) is measured, and if the difference
between its values at present and previous sampling instants
ΔPo(k) is within a specified lower and upper power limits PL
and PM respectively then, no action is taken; however, if the
difference is outside the this range then certain control action is
taken. The control action taken depends upon the magnitude
and direction of change in the active power due to the change
in command speed.
• If the power in the present sampling instant is
0 either due to
found to be increased i.e. ∆
an increase in command speed or command speed
remaining unchanged in the previous sampling
instant i.e. Δω* ( k − 1) ≥ 0 then, the command speed
is incremented.
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COMPd = Ls ω isq
*
isd
COMPq = − Ls ω isd + ωφr
Po
MPPT
CONTROLLER
_
+
+
COMPd
*
isq
ω* +
v*sd1 + v*sd
+
_
v*sq1
+
_
_
dq
v*sβ
S
V
P
W
M
GENERATOR
SIDE
CONVERTER
+
isd isq
ω
+
v*sq
αβ
v*sα
COMPq
isa , isb
dq ← αβ ← abc
1/s
PMSG
Fig. 2 Block diagram of the machine side converter controller.
MPPT Control
Set initial values of power and command speed
Read power
Δ ω * ( k − 1) = ω * ( k − 1) − ω * ( k − 2 )
Δ Po ( k ) = Po ( k ) − Po ( k − 1)
Yes
No
∆
Yes
Yes
Δ ω * ( k − 1) ≥ 0
Δ ω * ( k ) =| Δ P ( k ) | * C
ω * ( k ) = ω * ( k − 1)
∆
0
No Yes
No
Δ ω * ( k − 1) ≥ 0
No
Δ ω * ( k ) = − | Δ P ( k ) | *C
i.e. ∆
1
0 then, the command speed is
decremented.
• Further, if the power in the present sampling
0
instant is found to be decreased i.e. ∆
either due to a constant or increased command
speed in the previous sampling instant i.e.
then, the command speed is
Δω* ( k − 1) ≥ 0
decremented.
• And, if the power in the present sampling instant
0 due to a
is found to be decreased i.e. ∆
decrease in command speed in the previous
sampling instant i.e. ∆
1
0 then, the
command speed is incremented.
The magnitude of change, if any, in the command speed in
a control cycle is decided by the product of magnitude of
power error ΔPo ( k ) and C, whose values are determined by the
speed of the wind. During the maximum power point tracking
control process this product decreases slowly and finally equal
to zero at the peak power point.
In order to have good tracking capability at both high and
low wind speeds the value of C should change with the change
in the speed of the wind. The value of C should vary with
variation in wind speed, however, as the wind speed is not
measured, the value of command rotor speed is used to set its
value. As the change in power with the variation in speed is
lower at low speed, the value of C used at low speed is larger
and its value decreases as speed increases. In this work, its
values are determined by running several simulations with
different values and choosing the ones which show best results.
C. Grid Side Converter Control
The grid side converter is vector controlled in grid voltage
reference frame. In grid voltage vector reference frame the
dynamic model of the grid connection is given by
ω * ( k ) = ω * ( k − 1) + Δ ω * ( k )
Fig. 3 Flow chart of MPPT controller.
•
If the power in present sampling instant is found to
be increased i.e. ∆
due to reduction in
command speed in the previous sampling instant
vd = vid − Rid − Ldid / dt + ω Liq
(13)
vq = viq − Riq − Ldiq / dt − ω Lid
(14)
where L and R are the grid inductance and resistance,
respectively, vid and viq are the inverter voltage components.
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θg
id
*
Vdc
id*
+
_
Vdc
iq*
+
ia , ib
dq ← αβ ← abc
_
vd*1
+
vd*
+
iq
+
vab , vbc
ANGLE
COMPUTATION
COMPgd
_
vq*1 +
vq*
θg
αβ
dq
vα*
v*β
S
V
P
W
M
GRID SIDE
CONVERTER
+
COMPgq
_
+
Fig. 4 Grid side converter control scheme.
With the reference frame oriented along the supply voltage, the
grid voltage vector is
v = vd + j 0
(15)
Then the active and reactive power may be expressed as
P = (3 / 2 )vd id
(16)
Q = (3 / 2)vd iq .
(17)
The block diagram of the grid side converter control scheme
is shown in Fig. 4. Active and reactive power control is
achieved by controlling direct and quadrature current
components respectively. Two control loops are used to control
the active and reactive power. An outer dc voltage control loop
is used to set the d-axis current reference for active power
control. This assures that all the power coming from the
rectifier is instantaneously transferred to the grid by the
inverter. The second channel controls the reactive power by
setting a q-axis current reference to a current control loop
similar to the previous one. The current controllers provide a
voltage reference for the inverter that is compensated by
adding rotational emf compensation terms
COMPgd = ω Liq + ed
(18)
COMPgq = −ω Lid .
(19)
V. SIMULATION RESULTS
Simulation is carried out in order to verify the effectiveness of
the proposed method. The block diagram of the direct drive
PMSG WECS incorporating the proposed algorithm
used for simulation is shown in Fig. 5. The details of the
WECS used in this work are given in Appendix.
The values of C as mentioned above are determined by
running several simulations using different values and
selecting the ones which give best results. In this work, C used
in implementing the control algorithm are computed by
performing linear interpolation of 1.1 at 0 rad/s, 0.9 at 10 rad/s,
0.6 at 20 rad/s, 0.32 at 30 rad/s 0.26 at 40 rad/s, 0.25 at 50 rad/s
and 0.24 at 55 rad/s.
During the simulation, the d axis command current of the
machine side converter control system is set to zero; whereas,
for the grid side converter control system, the q axis command
current is set to zero. Simulation is carried out for two speed
profiles applied to the WECS incorporating the proposed
MPPT controller. First, a rectangular speed profile with a
maximum of 9 m/s and a minimum of 7 m/s is applied to the
WECS. The wind speed, rotor speed, power coefficient and
active power output are shown in Fig. 6. Then, a real wind
speed profile is applied to the WECS. The wind speed, rotor
speed, power coefficient and active power for this case are
shown in Fig. 7. It is observed from the results of simulation
that the proposed control algorithm has good capability of
idc
+
Vdc _
FROM
TURBINE
ic
MPPT
CONTROLLER
vb
vc
ω
SVPWM
SVPWM
ω*
isa ,isb
eab,bc
Vdc
ω
Po
ia
ib
ic
va
i
*
Vdc
VECTOR
CONTROL
Fig. 5 PMSG wind energy conversion system.
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VECTOR
CONTROL
ia ,b
ea
eb
ec
APPENDIX
1) Permanent magnet synchronous generator:
Pr =1.1 kW
Rs = 8.39 Ω
Ls = 0.08483 H
nr = 500 rpm
2) Wind turbine:
Pm =1.32 kW
vw = 10 m/s
R = 1.26 m
λopt = 6.597
Cpm = 0.48
J = 1.5 kg.m2
Fig. 6 Operation under step wind speed profile.
3) Supply:
v =240 V
L =0.005 H
Vdc = 400 V
Fig. 6 Operation the WECS under step wind speed profile.
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Fig. 7 Operation of the WECS under real wind speed profile.
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[9]
VI. CONCLUSION
A wind speed sensorless MPPT controller for variable
speed WECS was proposed. The method proposed in this
work does not require the knowledge of wind speed, air density
or turbine parameters.
The algorithm uses only the
instantaneous active power to generate at its output, the
optimum reference speed for the speed control loop of the
machine side converter controller enabling it to track the
peak power points. Results show good tracking capability
under both dynamic and steady state conditions. The method
proposed in this work is applicable to other types of WECS as
well.
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[13]
[14]
ACKNOWLEDGMENT
This work is partly supported by Natural Sciences and
Engineering Research Council (NSERC) of Canada.
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