Torque estimator using MPPT method for wind turbines

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 2, April 2020, pp. 1208~1219
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i2.pp1208-1219  1208
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
Torque estimator using MPPT method for wind turbines
Youssef Baala, Seddik Bri
Materials and Instrumentation (MIM), High School of Technology, Moulay Ismail University, Morocco
Article Info ABSTRACT
Article history:
Received Sep 29, 2018
Revised Oct 15, 2019
Accepted Oct 25, 2019
In this work, we presents a control scheme of the interface of a grid
connected Variable Speed Wind Energy Generation System based on Doubly
Fed Induction Generator (DFIG). The vectorial strategy for oriented stator
flux GADA has been developed To extract the maximum power MPPT from
the wind turbine. It uses a second order sliding mode controller and Kalman
observer, using the super twisting algorithm. The simulation describes
the effectiveness of the control strategy adopted.For a step and random
profiles of the wind speed, reveals better tracking and perfect convergence of
electromagnetic torque and concellation of reactive power to the stator.
This control limits the mechanical stress on the tansmission shaft, improves
the quality of the currents generated on the grid and optimizes the efficiency
of the conversion chain.
Keywords:
Doubly fed induction generator
(DFIG)
Kalman
MPPT
Second order sliding mode
control
Wind turbine
Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Youssef Baala,
Materials and Instrumentation (MIN), High School of Technology,
Moulay Ismail University,
Route Agouray High School of Technology, Meknès - Morocco.
Email: ysfbaala@gmail.com
1. INTRODUCTION
When it is desired to obtain efficient transient regimes (short response time, limited overrun, etc.)
and robustness with respect to external disturbances in order to control the asynchronous machine, the control
scheme based on the "transient" or "Dynamic"of the machine is the vector control of the machine [1, 2].
This type of control makes it possible to have a faster response dynamics and a better accuracy of the torque
control. Furthermore, PID family controllers rely on a state model with constant coefficients where system
parameters are assumed to be accurately known, which is no longer the case for the asynchronous machine
where some of its variables Are inaccessible to the direct measurements (rotor flux) and its parameters
(in particular the time constant) are affected by the thermal effect and saturation, thus leading to limited
performance.For this, the use of non-linear ordering techniques was timely and justified. Indeed, the control
technique with variable structures (CSV), known for its simplicity, speed and robustness with regard to
external perturbations and parametric variations, was widely adopted and showed its effectiveness in many
applications. Our contribution was based on nonlinear control techniques aimed at optimizing the control of
GADA [3-5]. We will start by modeling the wind turbine and its transmission chain then model the observer
of the torque and the controller MPPT then a model of the machine DFIG followed by the model of the high
controller sliding mode.
2. RESEARCH METHOD
2.1. Modeling the part mechanics
The maximum energy that can be collected by a wind turbine can not in any case exceed 59% of
the theoretical kinetic energy of the mass of air passing through it.Currently 60 to 70% of this power can be
exploited by the most sophisticated gears. This is the problem addressed by designers who aim to develop

Int J Elec & Comp Eng ISSN: 2088-8708 
Torque estimator using MPPT method for wind turbines (Youssef Baala)
1209
robust and reliable MPPT algorithms for maximum power point monitoring in order to optimize energy
efficiency. The wind turbine is composed of a turbine with its own parameters defining its potential to
capture the energy of the moving air mass [6-8]. A judicious choice of the control strategies of
the conversion chain makes it possible to obtain a system with a minimum cost and energy efficient enough,
regardless of the intermittence of the wind and the variation of the load.We opted first for a model of
the mechanical part (turbine and speed multiplier), and this for the 1.5 MW wind turbine, commonly used in
current wind systems. Figure 1 summarizes the basic elements of the mechanical part of a wind energy
conversion chain [9]. Figure 2 shows the structure of the production of energy around a DFIG.
Figure 1. Basic elements of the mechanical part of a
transmission chain
Figure 2. Control strategy
2.1.1. Modeling the wind turbine
The aerodynamic power of the wind is expressed as a function of the air density ρ, the blade radius
Rpâle, the wind speed Vvent and the power coefficient Cp by relation 1 [10].
Paero =
1
2
. Cp(β, λ). ρ. π. Rp2
. Vvent3
(1)
The efficiency of the turbine, called the power coefficient Cp, is specific to each wing Figure 3.
It depends on the angle of setting of the pales β and the specific ratio of the velocities λ. If Ωt is the rotor
speed, the velocity specific ratio λ is defined as :
λ =
Ωt .Rpale
Vvent
(2)
Figure 3. Limits of the power factor for different technologies
The power coefficient Cp (λ, β) for different values of the calibration angle β of a wind turbine of
1.5 MW with three pales is approximated by relation 3 [11].
Cp(β, λ) = c1. (
c2
λi
− c3. β − c4) e−
c5
λi + c6. λ (3)
1
λi
=
1
λ−0.08 β
−
0.035
β3+1
(4)

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 10, No. 2, April 2020 : 1208 - 1219
1210
The six coefficients c1.c6 depend on the turbine studied as show in Table 1. In the case of the E-40 turbine,
proposed by the German manufacturer ENERCON, these coefficients are [12-13].
Table 1. Coefficients of the E-40 turbine
c1 c2 c3 c4 c5 c6
0 .5176 116 0.4 5 21 0.0068
Figure 4 shows the variations of the power coefficient Cp as a function of the ratio specific
velocity λ, parameterized as a function of the setting angle β. These curves have a maximum for a wedge
angle β = 0. In the following, the wedge angle of the pales will be fixed at a zero value (β = 0). The wind
speed can then be expressed by the relation:
Vvent =
Ωt .Rpale
λ
(5)
For each wind speed Vvent there corresponds an optimal value of the speed of the rotor Ωopt.
Figure 4. Variation of the Cpas a function of the reduced speed λ for different values of β
When the specific ratio of speeds λ is fixed at its optimum value. The power point optimal is characterized
by: (β = 0 °; λopt = 8.1; Cpmax= 0.48). Under these conditions, the maximum aerodynamic power produced
is expressed by [14-15].
Paero =
1
2
. Cpmax.ρ. S. Vvent3
(6)
It corresponds an aerodynamic torque:
Taero =
Paero
Ωt
=
1
2
. Cp(λ, β) . ρ. S.
V3vent
Ωt
(7)
Figure 5 shows the optimum mechanical power, recovered by the turbine, as a function of the angular speed
of the rotor.
Figure 5. Variation of mechanical power as a function of turbinerotation Ωt

1211
The optimum mechanical power Popt is given by [16]:
Popt =
1
2
. ρ. π. Rpale5
. V
Cpmax
λopt3 Ωt3
= Kopt. Ωt3
(8)
Kopt =
1
2
ρ. π. Rpale5
. V
Cpmax
λopt3 (9)
2.1.2. Modeling the mechanical shaft
The speed of the turbine is much less than the speed of the generator. Therefore, in one conventional
wind energy conversion system, the mechanical transmission by means of a speed multiplier whose main role
is to adapt the speed of rotation of the turbine to that of the generator. The multiplier thus connects the shaft
of the turbine to the shaft of the generator. The two-mass model for the drive of Figure 6 is widely used [17].
Figure 6. Mechanical coupling (turbine, multiplier, generator)
Considering the coefficients of friction (Kt, Kg) and damping (Bt, Bg), we obtain the following
equations:
Jt. Ωṫ = Ta − Kt. Ωt − Bt. θt − Tls (10)
Jg. Ωm = Ths − Kg. Ωm − Bg. θm − Teṁ (11)
we obtain:
Jt
Ng
Ωm =̇ Ta −
Kt
Ng
Ωm −
Bt
Ng
θm −
Tls
Ng
Jg Ωṁ = Ths − Kg. Ωm − Bg.θm − Tem (12)
With: Ng =
Ωm
Ωt
=
Tls
Ths
(13)
The fundamental relationship of the dynamics of rotating masses brought back to the generator shaft
is written:
J. Ωṁ = Tm − K. Ωm − B. θm − Tem (14)
If one neglects the rigidity, the expression of the dynamics of the turbine becomes:
J. Ωṁ = Tm − K. Ωm − Tem (15)
The model of the turbine developed under matlab simulink is represented by Figure 7.

 ISSN: 2088-8708
1212
Figure 7. Wind-turbine model
2.2. Design of the MPPT control
2.2.1. Mechanical torque observer
The MPPT control ensures the convergence of mechanical torque to its optimal value in a finite
time [18]. The KALMAN observer is then used to estimate the value of the mechanical torque with state
variables x1 and x2 representing the speed of the rotor Ωr and the image of the mechanical torque Tm.
x1 = Ωr ; x2 =
Tm
J
(16)
The expression of the dynamic of the turbine become:
x1̇ = x2 −
Tem
J
−
f.x1
J
; x2̇ = f(t) (17)
We can rewrite this subsystem in matrix form:
Ẋ = A. X + B. Tem ;Y = C. X (18)
With: X=(x1 x2)T
A=(
−f
J
1
0 0
) B=(
−1
J
0
) and C=(1 0) (19)
The observer is based on the following state transformation:
{
Ẋ̂ = A. X̂ + B. Tem + H. (y − C. X̂)
H = (h1 h2)T
̇
ŷ = C. X̂
(20)
The resulting estimation error is then written:
X̃ = X − X̂ (21)
The dynamic of the errors is governed by the following:
X̃̇ = Ẋ − X̂̇ = (A − H. C). X̃ (22)
AO = A - H . C, is chosen so that it is a Hurwitz matrix by appropriate choice of vector H,
X̃̇ = Ẋ − X̂̇ is sure to converge exponentially to 0. The dynamics of the estimated states is expressed by [19]:
x1̂̇ = x2̂ −
Tem
J
−
f.x1̂
J
+ h1. x1̃ ;x2̂̇ = h2. x1 (23)

1213
2.2.2. MPPT controller design
The control must force the value of the mechanical torque Tm to follow the optimum value Top in
order that the tracking error is canceled [20].
eT = Topt − T̂m ;Tm̂ = J. x2̂ (24)
The equation of the dynamics of the turbine makes it possible to write the equations of the dynamics of
the tracking error as follows:
eṪ = Topṫ − Tm̂̇ eṪ = 2. kopt.
Ωr
J
. (Tm̂ − Tem − f. Ωr) − Tm̂̇ (25)
In order to stabilize the system, taking as the Lyapunov function candidate:
V =
1
2
. eT2
+
1
2
. X̃T
PX̃ (26)
Where P is a positive matrix such as:
A0T
P + P A0 = −I2 (27)
The dynamic of the Lyapunov function is:
V̇ = eṪ eT −
1
2
X̃T
X̃ (28)
The actual reference of the Tem∗
electromagnetic torque is made with the choice:
eT = −d. eT (29)
If d is a positive synthetic constant, the control law is chosen as follows:
V = −d. eT2
−
1
2
X̃T
X̃ < 0 (30)
We deduce the control law backstepping of controller:
Tem∗
= Tm̂ − f. Ωr +
J
2.Kopt.Ωr
(d. eT − Tm̂̇ ) (31)
The model of the Kalman observer designed under matlab simulink is represented by Figure 8.
Figure 8. Kalman observer
2.3. Modeling of the DFIG
The electrical equations of the DFIG can be written as follows [21]:
{
vsd = Rs. isd +
dΦsd
dt
− ωs. Φsq and vsq = Rs. isq +
dΦsq
dt
+ ωs. Φsd
vrd = Rr. ird +
dΦrd
dt
− ωr. Φrq and vrq = Rr. irq +
dΦrq
dt
+ ωr. Φrd
(32)

 ISSN: 2088-8708
1214
{
Φsd = Ls. isd + Lm.ird and Φsq = Ls. isq + Lm.irq
Φrd = Lr. ird + Lm.isd and Φrq = Lr. irq + Lm.isq
(33)
Ls,Lr and Lm :stator,rotor and magnetizing inductances and σ : leakage coefficient σ = 1 −
Lm2
Ls.Lr
ωr=ωs-p.Ωr :pulsation of rotor currents and p: number of pole pairs of DFIG.
The stator, rotor active and reactive powers are defined by:
{
Ps = vsd. isd + vsq. isq Qs = vsq. isd − vsd. isq
Pr = vrd. ird + vrq. irq Qr = vrq. ird − vrd. irq
(34)
The electromagnetic torque is defined as:
Tem = p. Lm. (ird. isq − irq. isd) (35)
By setting the quadratic component of the stator flux to the null value and assuming that
the resistance of the stator winding Rs is neglected, the voltage equations and the flux equations of the stator
windings can be simplified in steady state as: Φsd = Φs ; Φsq = 0 and vsd = 0 (Rs = 0)
{
isq =
−lm
ls
. irq isd = (Φs − lm. ird).
1
ls
Φrq = lr. σ. irq Φrd = lr. σ. ird +
lm
ls
. Φs
vrd = Rr. ird + lr. σ.
dird
dt
− lr. ωr. σ. irq
vrq = Rr. irq + lr. σ.
dirq
dt
− lr. ωr. σ. ird + Φs.
lm.ωr
ls
(36)
The stator active and reactive powers are obtained:
Ps = −Us.
lm
ls
. irq Where Us=√3 .Vs (37)
Qs = Us. (
Φs
ls
−
lm.ird
ls
) (38)
Tem = −p.
lm
ls
. Φs. irq (39)
Pr = g. Pem = g. Cem. Ωr (40)
The model of DFIG designed under matlab simulink is represented by Figure 9 (refer appendix).
2.4. High order sliding mode controller
This section shows the design of the proposed high-order sliding mode controller based on
the super-twisting algorithm [22]. The second order sliding mode algorithm synthesizes ad is continuous
control, which makes the surface and its derivative null with continuous control, therefore reducing
chattering and avoiding strong mechanical efforts while preserving classical sliding mode advantages.
To ensure the DFIG electromagnetic torque and reactive stator power convergence, the d-q rotor currents
references are defined:
irq∗
= −Tem∗
.
ls
p.M.Φsd
And ird∗
=
Φsd
M
− Q∗
.
ls
M.Us
(41)
Two sliding functions Sq and Sd are defined by:
Sq̇ =
1
lr.σ
(vrq − Rr. irq − Lr. ωr. σ. ird −
M.ωr
ls
. Φsd) −
dirq∗
dt
(42a)
Sḋ =
1
lr.σ
(vrd − Rr. ird + Lr. ωr. σ. irq) −
dird∗
dt
(42b)

1215
By introducing two terms G1 and G2, such as [23]:
G1 =
1
lr.σ
(−Rr. irq − Lr. ωr. σ. ird −
M.ωr
ls
. Φsd) −
dirq∗
dt
And G2 =
1
lr.σ
(−Rr. ird + Lr. ωr. σ. irq) −
dird∗
dt
(43)
The second derivatives of the slip functions are then given by:
Sq̈ =
1
lr.σ
. vrq̇ + G1̇ and Sd̈ =
1
lr.σ
. vrḋ + G2̇ (44)
The second order sliding mode controller is based on the super twisting algorithm (ST) which was introduced
by Levant as follows [24]:
vrq = u&1 + 𝑢2 and vrd = w1 + w2 (45)
The parameters α and θ are chosen to ensure convergence in finite time [24]-[25]:
{αi >
μi
lr.σ
θi ≥
4.μi.(αi+μi)
lr2.σ2.(αi−μi)
|Gi|̇ < 𝜇𝑖 𝑖 = 1,2 (46)
The terms of the equivalent control laws are defined by canceling the terms of the dynamics of the slip
functions Sq̇ and Sḋ :
Vrdeq = Rr. ird − lr. ωr. σ. irq + lr. σ.
dird∗
dt
and Vrqeq = Rr. irq + lr. ωr. σ. ird + Φsd.
M.ωr
ls
+ lr. σ.
dirq∗
dt
(47)
The second ordre sliding mode model designed under matlab simulink is represented by Figure 10 (refer
appendix).
3. RESULTS AND ANALYSIS
The performances of the controller have been validated by means of simulation in MATLAB/
Simulink environment. The table summarizes the parameters of the controlled system Table 2. For this
simulation, one of tow profiles of the wind speed is applied to the input of the turbine: step or random as
shown in Figure 11. The Figure 12 shows the stator voltage is sinusoidal with maximum value 980V which
corresponds to the output voltage of efficient 690V. The Figure 13 shows the current flow rate of the GADA
on the three-phase to the grid. For an step turbine speed profile, the maximum current passes from 200A for
a wind speed of 7 m/s to 800A for a wind speed of 14 m/s. other is done at the moment 25s is done quickly
and lasts 0.01s.For an random turbine speed profile, the maximum current stator output is constant worth
800A. The Figure 14 shows the speed of the GADA. For a step turbine speed profile, the speed of the GADA
goes from 700 rpm and slightly exceeds 1500rpm at the moment 25s following the wind scale. This variation
corresponds to the range of speeds allowed by the GADA. For a random turbine speed profile, the speed of
the rotor follows the variation of the speed of the tubine between 1000 rpm and 1600 rpm.
Table 2. System parameters
Turbine KALMAN Back stepping
Second order
Sliding Mode
Power
(MW)
Number
of blades
Ρ
Blade
longer
Multiple
rapport
h1 h2 D α1 α2
1.5 3 1.225 Kg/m3 32.25m 60 2500 25000 10-4 350 0.75
GADA Grid
Second order
Sliding Mode
Pn Rs Rr Ls Lr M J F V θ1 θ2
1.5Mw 12mΩ 21mΩ 13.7mH 13.6mH
13.5
mH
0.175
Kg.m2
0.0024
N/rad/s2
690-50Hz 0.5 0.06

 ISSN: 2088-8708
1216
Figure 11. Variation of wind speed
Figure 12. Stator voltage
Figure 13. Stator current
Figure 14. Rotor speed
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-1000
-800
-600
-400
-200
0
200
400
600
800
1000
Stator voltage
t(s)
Vs1(V)

1217
In Figure 15 we show a perfect continuation of the electromagnetic torque at its reference delivered
by the observer block of Kalman for step speed profile. We note the convergence of the electromagnetic
torque Tem to wards the optional reference torque Topt. Figure 16 shows the variation of stator active power
P and stator reactive power Q to the grid. Note the variation of the power Ps produced by the DFIG to
the network according to the maximum point of the wind while garanteissant a unit cosφ by asservissement
which guarantees the cancellation of the reactive power. We obtain a sinusoidal three-phase current output
with minimal distortion.The stator reactive power Q is kept zero to guarantee a unit power factor cosφ = 1.
The spectral representation of the stator current shows that this command does not introduce harmonic
pollution to the grid with a harmonic distortion rate of 0.06%.
Figure 15. Electromagnetic torque
Figure 16. Stator active and reactive powers
4. CONCLUSION
To develop a command for the wind turbine generators it’s necessary to use a linearization
approach. However, due to conditions of stochastic operation, and inevitable uncertainties inherent in
the system, such control strategies are pay at the price of a system with poor performance and decreased
reliability. Hence, the use of a strategy of non-linear and robust control for taking into accounts these
problems. The strategy developed and presented in this article; to know first to define the reference torque by
a kalman observer combined with a command by sliding mode then in a second time to order the dual mode
asynchronous generator by one mode sliding order 2, meets the assigned objectives. Indeed, she is robust
thereby increasing reliability, it improves the energy efficiency, and with the little chatter she generates,
it limits the mechanical stress on the tree of transmission.
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 ISSN: 2088-8708
1218
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APPENDIX
Figure 9. DFIG model
Figure 10. Second ordre sliding mode model

Torque estimator using MPPT method for wind turbines

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