In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.

1. Research Article
Real time simulation of nonlinear generalized predictive control
for wind energy conversion system with nonlinear observer
Kamel Ouari a
, Toufik Rekioua a,n
, Mohand Ouhrouche b
a
Laboratory LTII, University of Bejaia, Algeria
b
Laboratory LICOME, University of Quebec at Chicoutimi, Canada
a r t i c l e i n f o
Article history:
Received 21 February 2011
Received in revised form
16 December 2012
Accepted 8 August 2013
Available online 7 September 2013
Keywords:
Nonlinear generalized predictive control
(NGPC)
Doubly-fed induction generator (DFIG)
DFIG-based wind turbine
Real-time simulation
a b s t r a c t
In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques
must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control
(NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-
based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop
that provides the torque reference. In order to enhance the robustness of the controller, a disturbance
observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation.
Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.
& 2013 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Recently, many new wind farms have employed wind turbines
based on doubly-fed induction generator (DFIG) [1], due to their
full power control capability, variable speed operation, low con-
verter cost and reduced power loss [2,3]. However, DFIG constitu-
tes a challenging control problem, because of its fast dynamics,
and being a highly coupled and nonlinear multi-variable system.
The field-oriented vector control using cascaded PI controllers
is widely used, in DFIG-based wind turbines, for reasons of
simplicity and applicability [4]. However, PI-type control methods
are not effective when the system to be controlled is characterized
by strong nonlinearity and external disturbances. To overcome
these drawbacks, various approaches have been proposed to
replace PI-type controllers. Some examples are the H1 control
theory, neural networks and sliding mode control [5-7].
On the other hand, model predictive control (MPC) is now
regarded as one of the most robust control strategies because of its
advantages, such as insensitivity to parameter variations, external
disturbance rejection and fast dynamic responses [8]. Therefore, it
has been applied in the industry as a promising form of advanced
control [9].
Several control strategies using linear and nonlinear MPC have
been proposed in the technical literature [10,15]. In [10] Chen et al.
have designed a nonlinear predictive control law for multi-
variable nonlinear systems based on Taylor series expansion,
where the same relative degree of multi-input and multi-output
system is considered. In [11,12], the principle of the MPC is
combined with the well-known direct torque control (DTC) and
applied to an induction motor (IM) for a fast torque response.
Hedjar et al. [13] have proposed a cascaded NGPC based on Taylor
series expansion for an IM. However, in these studies, the load
torque is considered as a known disturbance.
MPC techniques have also been proposed for DFIG-based wind
turbines. In [14], the GPC has been used to control the pitch angle
of windmill blades in order to reduce power fluctuations. Multi-
variable control strategy based on MPC techniques has been
proposed for wind turbines based on DFIG in [15]. A predictive
current control (PCC) strategy for doubly fed induction generators
has been treated in [16]. Nevertheless, all these methods achieve a
high performance only when the external disturbance (aerody-
namic torque) is known.
In order to provide powerful abilities in handling system
disturbances and improving robustness, the nonlinear generalized
predictive control must be combined with a disturbance observer
[17,18]. For improvement, in this paper, the aerodynamic torque
observer is integrated into the control law in order to enhance the
robustness of the controller. The combination of this observer with
NGPC works as a nonlinear controller.
In this paper, the performance index proposed in [18] is
considered to improve the performances of the DFIG-based wind
turbine under unknown disturbance and parameter variations.
To this end a cascaded NGPC and stator-field-oriented control
are investigated. In addition, an aerodynamic torque observer,
defined from predictive control, is integrated into the control law.
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/isatrans
ISA Transactions
0019-0578/$ - see front matter & 2013 ISA. Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.isatra.2013.08.004
n
Corresponding author. Tel./fax: þ213 34205090.
E-mail addresses: Ouari.Kamel@ymail.com (K. Ouari),
to_reki@yahoo.fr, t_rekioua@yahoo.fr (T. Rekioua),
Mohand_ouhrouche@uqac.ca (M. Ouhrouche).
ISA Transactions 53 (2014) 76–84

2. In Section 2, the dynamic model of wind energy conversion system
is exposed. In Section 3, mathematical formulation of NGPC for
nonlinear system is presented. The proposed controller is applied
to the DFIG in Section 4. The design of the disturbance observer
and real time simulation results are given in Sections 5 and 6,
respectively. Finally, Section 7 concludes the paper.
2. Mathematical model of WECS
The DFIG-based wind turbine is shown in Fig. 1. It consists of a
three blade wind turbine rotor coupled to a doubly-fed induction
generator through a gearbox. The two pulse width modulated
voltage source converters are connected back to back between the
rotor terminals and the utility grid via a common DC link.
2.1. Wind turbine model
The aerodynamic power extracted from the wind can be
expressed as
Pt ¼
1
2
ρaπR2
Cpðλ; βÞv3
ð1Þ
where v is the wind speed, ρa is the air density, R is the rotor radius
and Cp is the power coefficient that depends on both, pitch angle β
and tip speed ratio λ. The coefficient Cp is specific for each wind
turbine. The tip speed ratio is defined as:
λ ¼
ΩtR
ν
ð2Þ
Ωt is the turbine speed.
A typical relationship between Cp and λ is shown in Fig. 2 [19].
At the point λopt, Cp¼Cp-max, the maximum power can be extracted.
To this end, the turbine should always operate at λopt.
Neglecting the transmission losses, the torque and speed of the
wind turbine, referred to the generator side of the gearbox, are
given by
Tr ¼
Tt
G
Ωt ¼
Ωr
G
ð3Þ
where G is the gear ratio, Ωr is the generator speed, Tr and Tt are,
respectively, the generator torque and aerodynamic torque.
Substituting Eq. (3) in Eqs. (1) and (2), the rotor speed and
electrical grid power references are
ΩrÀref ¼
λopt G
R v
PgridÀref ¼ 1
2ηρaπ2
CpÀ maxv3
8
<
:
ð4Þ
where η is the system (wind turbineþDFIG) efficiency and ρa is the
air density.
Nomenclature
Pt Aerodynamic power (W)
ρa Air density (kg m3
)
v wind speed
R Rotor turbine radius (m)
Cp Power coefficient
Cp-max Maximal power coefficient
β Blades pitch angle
λ Tip-speed ratio
λopt Optimal tip-speed ratio
Tt Aerodynamic torque (N M)
Tr Generator torque (N m)
Ωt Turbine speed rad/s
Ωr Generator speed (rad/s)
Ωr-ref Reference generator speed
G Gear ratio
η WECS efficiency
Pgrid-ref Reference grid Active power (W)
η System (wind turbineþDFIG) efficiency.
Rs, Rr Per-phase stator and rotor resistances,
Ls, Lr Stator, rotor self inductances
M Mutual inductance
P Number of pole pairs
J Moment of inertia
fr Coefficient of friction.
ωs, ωr Stator and rotor angular velocities (rd/s)
s Generator slip
s Dispersion ratio
x State vector
u Control output
Tr Disturbance
f(x),h(x) Functions assumed to be continuously differentiable
gu(x), gT(x) continuous functions of x
ℑ Finite horizon cost function
Tp Predictive time
ρi Relative degree of the output i
Wind
Blades
Grid side Converter
Grid
DFIG
Gearbox
LC
Filter
Rotor side Converter
Fig. 1. System configuration.
K. Ouari et al. / ISA Transactions 53 (2014) 76–84 77

3. 2.2. DFIG model
The DFIG model can be described, according to [20], in an
arbitrary (d–q) reference frame, as follows
Vds ¼ RsIds þ d
dt
ψdsÀωsψqs
Vqs ¼ RsIqs þ d
dt
ψqs þωsψds
Vdr ¼ RrIdr þ d
dt
ψdrÀðωsÀωrÞψqr
Vqr ¼ RrIqr þ d
dt
ψqr þðωsÀωrÞψdr
8
>>>>><
>>>>>:
ð5Þ
with:
ψds ¼ LsIds þMIdr
ψqs ¼ LsIqs þMIqr
ψdr ¼ LrIdr þMIds
ψqr ¼ LrIqr þMIqs
8
>>>><
>>>>:
ð6Þ
ωr ¼ P Ωr ð7Þ
The notations are defined as follows:
Vds, Vqs, Vdr, Vqr Two-phase stator and rotor voltages,
Ids, Iqs, Idr, Iqr Two-phase stator and rotor currents,
Rs, Rr Per-phase stator and rotor resistances,
ψds, ψqs, ψdr, ψqr Two-phase stator and rotor fluxes,
ωs, ωr Stator and rotor angular velocities,
P Number of pole pairs,
Ls, Lr Stator and rotor inductances,
M Magnetizing inductance.
The electrical model is completed by the mechanical equation
given below
J
d
dt
Ωr ¼ TemÀTrÀf rΩr ð8Þ
where J and fr are, respectively, the moment of inertia and the
coefficient of friction.
The electromagnetic torque Tem is written as a function of stator
fluxes and rotor currents
Tem ¼ P
M
Ls
ðψqsIdrÀψdsIqrÞ ð9Þ
If the stator flux is linked to the d-axis of the frame [21,22] we
have
ψds ¼ ψs ψqs ¼ 0 ð10Þ
Then, by using Eqs. (9) and (10), the electromagnetic torque
will only depend on the q-axis rotor current
Tem ¼ P
MVs
ωsLs
Iqr ð11Þ
As shown in Fig. 3, if the per phase stator resistance is negle-
cted, the stator voltage vector is consequently in quadrature
advance compared to the stator flux vector [23]. So, the stator
voltages are:
Vds ¼ 0 Vqs ¼ Vs ¼ ωsψs ð12Þ
By substituting Eqs. (10) and (12) in Eqs. (5) and (6), the rotor
voltages, the stator active and reactive power are expressed
according to the rotor currents as
Vdr ¼ RrIdr þsLr
d
dt
IdrÀsLrsωsIqr
Vqr ¼ RrIqr þsLr
d
dt
Iqr þs sωsIdr þsMVs
Ls
8
<
:
ð13Þ
Ps ¼ ÀMVs
Ls
Iqr
Qs ¼ Vs
2
ωsLs
ÀMVs
Ls
Idr
8
<
:
ð14Þ
with:
s ¼ 1À
M
LrLs
; s ¼
ωsÀωr
ωs
s is the generator slip
3. Mathematical formulation of NGPC
The nonlinear generalized predictive control proposed by Chen
et al. [17], is briefly described in this section. We consider a
nonlinear system of the form:
_xðtÞ ¼ f ðxÞþguðxÞuðtÞþgT ðxÞTrðtÞ
y ¼ hðxÞ
(
ð15Þ
where xAℜn
is the state space vector, uAℜm
is the control input
and Tr Aℜ is the external disturbance. The function f(x) and h(x)
are assumed to be continuously differentiable a sufficient number
of times. Vector function gu(x) and gT(x) are continuous functions
of x. The problem consists in elaborating a control law u(t) such
that the output y(tþτ) can optimally track a desired reference yr
(tþτ) in presence of the disturbance Tr. The predictive control will
be optimal if the finite horizon cost function ℑ is minimized
ℑ ¼
1
2
Z Tp
0
½yðtþτÞÀyrðtþτÞŠT
½yðtþτÞÀyrðtþτÞŠdτ ð16Þ
Tp is the predictive time
To solve the nonlinear optimization problem (16), the predicted
output y(tþτ) and the predicted reference yr(tþτ) are approximated
by Taylor series expansion:
yiðtþτÞ ¼ hiðxÞþ ∑
ρi
k ¼ 1
τk
k!
Lk
f hiðxÞþ
τρi
ρi!
LguL
ðρiÀ1Þ
f
hiðxÞuðtÞ ð17Þ
where Lk
f hi, denote the kth order Lie derivative of hi and ρi is the
relative degree of the output yi.
Fig. 2. Typical power coefficient.
Fig. 3. Voltage and flux vectors settings.
K. Ouari et al. / ISA Transactions 53 (2014) 76–8478

4. The Lie derivative of function hi(x) along a vector field f(x)¼
(f1(x)…….. fn(x)) is denoted by
Lf hiðxÞ ¼ ∂hiðxÞ
∂x f ðxÞ
Lk
f hiðxÞ ¼ Lf ðLkÀ1
f hiðxÞÞ
Lgu
Lf hiðxÞ ¼
∂Lf hiðxÞ
∂x guðxÞ
LgT
Lf hiðxÞ ¼
∂Lf hiðxÞ
∂x gT ðxÞ
8
>>>>>><
>>>>>>:
ð18Þ
The necessary condition for the optimal control is given by
dℑ
du
¼ 0 ð19Þ
4. Cascaded nonlinear generalized predictive controller
As DFIG is characterized by two-time scales modes; i.e. elec-
trical (fast) and mechanical (slow) modes, a cascaded structure is
adopted for the design of the controller, see Fig. 4. The inner loop
is used to regulate the d-axis rotor current and the electromag-
netic torque, whereas the outer loop is employed for the speed
trajectory tracking.
4.1. Inner control loop
The aim of this inner loop is to regulate the d-axis rotor current
and the electromagnetic torque by acting on the rotor armature
voltage. The compact form of Eq. (13) can be written as follows:
_xðtÞ ¼ f ðxÞþguðxÞuðtÞ
y ¼ hðxÞ
(
ð20Þ
with:
x ¼ ðIdr IqrÞT
; u ¼ ðVdr VqrÞT
; y ¼ ðTem IdrÞT
The state vector x is composed of the d-axis and q-axis
component of the armature rotor currents. The input vector u is
made of the d-axis and q-axis components of the armature rotor
voltage. The output vector y consists of the electromagnetic torque
and the d-axis rotor current, while vector function f(x) and gu(x)
are defined as:
f ðxÞ ¼
À Rr
sLr
Idr þsωsIqr
À Rr
sLr
IqrÀsωsIdr þsMVs
sLr Ls
0
@
1
A; guðxÞ ¼
1
sLr
0
0 1
sLr
0
@
1
A
The outputs to be controlled in the inner loop are defined as
follows:
y1 ¼ h1ðxÞ ¼ Tem ¼ PMVs
ωsLs
Iqr
y2 ¼ h2ðxÞ ¼ Idr
(
ð21Þ
For the outputs y1 and y2, their relative degrees ρ1 and ρ2 are
equal to 1, as the first derivative reveals the input.
The resulting NGPC applied to the system (20) is given by
uðtÞ ¼ ÀGuðxÞÀ1
∑
1
i ¼ 0
Ki½Li
f hðxÞÀy½iŠ
r ðtÞŠ ð22Þ
with:
K0 ¼
3
2Tp1
0
0 3
2Tp1
0
@
1
A; K1 ¼
1 0
0 1
; GuðxÞ ¼
PMVs
ωsLs
1
sLr
0
0 1
sLr
0
@
1
A;
hðxÞ ¼
Tem
Idr
!
; yr ¼
TemÀref
IdrÀref
!
y½iŠ
r ðtÞ denotes the ith
derivative of yrðtÞ and Tp1 is the prediction
time of the inner loop.
4.2. Outer control loop
The speed controller in the outer loop is obtained by consider-
ing the mechanical dynamics of the DFIG. From Eq. (8), it follows
that the mechanical equation can be expressed as:
_xðtÞ ¼ f ðxÞþguðxÞuðtÞþgT ðxÞTrðtÞ
y ¼ hðxÞ
(
ð23Þ
where x and u are, respectively, the rotor speed Ωr and the
electromagnetic torque Tem. Tr is the aerodynamic torque and the
output y is the rotor speed. The vector function f(x), gu(x) and gT(x)
are given by:
f ðxÞ ¼ Àf r
J Ωr
guðxÞ ¼ 1
J
gT ðxÞ ¼ À1
J
8
:
ð24Þ
The relative degree ρ of the output y is equal to 1. Then, we
shall have the optimal control input as
uðtÞ ¼ ÀGuðxÞÀ1
∑
1
i ¼ 0
kiðLi
f hðxÞÀy½iŠ
r ðtÞÞþGT ðxÞTrðtÞ
#
ð25Þ
with
k0 ¼
3
2Tp2
; k1 ¼ 1; hðxÞ ¼ Ωr; yr ¼ ΩrÀref
GuðxÞ ¼
∂hðxÞ
∂x
guðxÞ ¼
1
J
; GT ðxÞ ¼
∂hðxÞ
∂x
gT ðxÞ ¼ À
1
J
Tp2 is the prediction time of the outer loop.
5. Nonlinear disturbance observer
In this work, the aerodynamic torque is considered as an
unknown disturbance, so the use of an observer is necessary to
Fig. 4. Cascaded control configuration.
K. Ouari et al. / ISA Transactions 53 (2014) 76–84 79

5. estimate it. Thus, the optimal control (25) becomes:
uðtÞ ¼ ÀGuðxÞÀ1
∑
1
i ¼ 0
kiðLi
f hðxÞÀy½iŠ
r ðtÞÞþGT ðxÞ^TrðtÞ
#
ð26Þ
^Tr is the estimated aerodynamic torque.
The nonlinear disturbance observer is developed in the same
spirit as Chen et al. [17]. An initial disturbance observer is given by
_^TrðtÞ ¼ ÀψðxÞgT ðxÞ^TrðtÞþψðxÞ½_xðtÞÀf ðxÞÀguðxÞuðtÞŠ ð27Þ
where ψ(x) is the gain to be designed to ensure the stability of the
observer. It is chosen as follows:
ψðxÞ ¼ ϕ0
∂hðxÞ
∂x
ð28Þ
with is constant.
From Eq. (23), it follows that:
gT ðxÞTrðtÞ ¼ _xðtÞÀf ðxÞÀguðxÞuðtÞ ð29Þ
Since there is no information about the derivative of the
disturbance, we assume that
_Tr ¼ 0 ð30Þ
Substituting Eqs. (29) and (30) in Eq. (27), the observer error is
described as
_εT ðtÞþψðxÞgT ðxÞεT ðtÞ ¼ 0 ð31Þ
where the observer error is: εT ¼ TrðtÞÀ^TrðtÞ
From Eq. (31), it can be shown that the observer is exponen-
tially stable by choosing:
ψðxÞgT ðxÞ40 ð32Þ
Using the Lie derivative (18) and Eq. (28), we get:
ψðxÞgT ðxÞ ¼ ϕ0GT ðxÞ
ψðxÞ_xðtÞ ¼ ϕ0 _yðtÞ
ψðxÞf ðxÞ ¼ ϕ0Lf hðxÞ
ψðxÞguðxÞ ¼ ϕ0GuðxÞ
8
:
ð33Þ
Substituting Eqs. (26) and (33) in Eq. (27), we obtain
_^TrðtÞ ¼ Àϕ0ðk1 _εyðtÞþk0εyðtÞÞ ð34Þ
where: εy ¼ yrðtÞÀyðtÞ is the speed tracking error.
Integrating Eq. (34), the estimated disturbance is calculated as
follows:
_^TrðtÞ ¼ Àϕ0 k1εyðtÞþk0
Z t
0
εyðτÞdτ
þTrð0Þ ð35Þ
with:
Trð0Þ ¼ ^Trð0Þþϕ0εyð0Þ
If the initial value of the estimated disturbance ^Trð0Þ is taken as
^Trð0Þ ¼ Àϕ0εyð0Þ ð36Þ
Then, the estimated disturbance will be as follows:
^TrðtÞ ¼ Àϕ0 k1εyðtÞþk0
Z t
0
εyðτÞdτ
ð37Þ
Substituting Eq. (37) in Eq. (26), the control law becomes
uðtÞ ¼ kpεyðtÞþkdðyrðtÞÀLf hðxÞÞþki
Z t
0
εyðτÞdτ ð38Þ
where kp, ki and kd are the proportional, integral and derivative
gains, respectively.
kp ¼
3J
2Tp2
Àϕ0; kd ¼ J; ki ¼ À
3ϕ0
2Tp2
Fig. 5. Block diagram of the proposed NGPC for DFIG-based wind turbine.
K. Ouari et al. / ISA Transactions 53 (2014) 76–8480

6. 6. Real time simulation results
To evaluate the proposed controller performance, the drive system
given in Fig. 5 is implemented first in Matlab/Simulink in block
diagram format. This Simulink model is then opened and compiled
with RT-Lab software package. The main system parameters are listed
in Tables 1 and 2. The predictive time of the inner loop Tp1 and the
outer loop Tp2 are set to 0.5 ms and 8 ms, respectively. The stability of
the aerodynamic torque observer is guaranteed by choosing the value
of ϕ0 equal to À3.
6.1. Tracking performance under unknown aerodynamic torque
In this simulation, the robustness of the proposed control law,
against the aerodynamic torque variations, is tested. The d-axis rotor
current reference is calculated to maintain at null value the reactive
power flow to the grid. The rotor speed and electrical grid power
references are given in the Eq. (4). In order to limit the control effort,
the reference speed signal is passed through a second order linear
Table 1
Doubly fed induction machine parameters.
Parameter Value
Power 1.5 MW
Voltage 690 V
Frequency 50 Hz
Rs 0.021 Ω
Ls ¼Lr s 0.0137 H
Jg 500 Kg m2
P 2
M 0.0135 H
f 0.0071
Table 2
Wind turbine parameters.
Parameter Value
Turbine diameter 60 m
Number of blades 3
Hub height 85 m
R 36.5 m
Gear box 90
0 2 4 6 8 10 12 14 16 18
9
10
11
12
13
14
15
Time (s)
windspeed(m/s)
Fig. 6. Wind speed profile.
0 2 4 6 8 10 12 14 16 18
4
6
8
10
12
Time(s)
Aerodynamictorque(kNm)
Actual torque
Estimed l torque
Fig. 7. Actual and estimated aerodynamic torque.
0 2 4 6 8 10 12 14 16 18
-0.2
-0.1
0
0.1
0.2
Time(s)
Slip
Fig. 8. DFIG slip.
0 2 4 6 8 10 12 14 16 18
120
140
160
180
Time(s)
Rotorspeed(rad/s)
Actual speed
Reference speed
Fig. 9. Rotor speed trajectory tracking response.
0 2 4 6 8 10 12 14 16 18
-0.02
-0.01
0
0.01
0.02
0.03
Time (s)
Speederror(rad/s)
Fig. 10. Speed tracking error response.
Electromagnetique
torque(kNm)
Actual torque
Torque reference
0 2 4 6 8 10 12 14 16 18
4
6
8
10
12
Time (s)
Fig. 11. Electromagnetic torque trajectory tracking.
K. Ouari et al. / ISA Transactions 53 (2014) 76–84 81

7. filter given by
FðsÞ ¼
w2
n
s2 þ2ξwnsþw2
n
ð39Þ
Where wn¼5 ζ¼1.2
The wind speed profile used in the simulation is illustrated in
Fig. 6. As seen in Fig. 7, the disturbance observer gives a good
estimate of the aerodynamic torque. The speed and electromag-
netic torque tracking performances are satisfactory achieved as
shown, in Figs. 9–11. The stator and rotor active power are plotted
in Fig. 12. The sense of drainage depends on the sign of the DFIG
slip (Fig. 8). Fig. 13 shows that the grid reactive power is
maintained at zero value contributing to compensate the grid
power factor. The rotor voltage and current at sub-synchronous,
synchronous and hyper-synchronous modes are plotted in Fig. 14.
6.2. Tracking performance under DFIG's parameter variations
As NGPC is a model-based approach, the accuracy of the DFIG
parameters may influence the drive. The parameter variations intro-
duced in the DFIG model are set to the following values: 25% in the
rotor resistance at t¼4 s and 25% in the moment of inertia at t¼10 s.
These variations are not taken into account in the controller. From
Fig. 15, we demonstrate that the grid active power tracks perfectly its
reference aiming to maximize the conversion efficiency. The reference
tracking is not affected by the parameter variations.
6.3. Performance evaluation under predictive time change
This test is performed to evaluate the performance of the
controller under predictive time change. To this end, only the
predictive time of the outer loop Tp2 is decreased from 20 ms to
5 ms. As shown in Figs. 16 and 17, a smaller predictive time results
in a fast disturbance rejection to the detriment of the control effort
Tem which is limited by the speed filter.
6.4. Performance evaluation under observer gain change
For this case, only the observer gain ϕ0 is increased from À1 to
À8. As shown in Figs. 18 and 19, a large gain ϕ0 results in a fast
disturbance rejection at the expense of the control effort Tem
which is limited by the speed filter.
The observer sensitivity to the gain ϕ0 is also investigated in
this test. Fig. 20 shows the observer error for ϕ0 equals to À1 and
À8. These results show clearly that ^TrðtÞ converges quickly to TrðtÞ
for high values of the observer gain ϕ0.
7. Conclusion
A cascaded NGPC for a DFIG-based wind turbine has been
presented in this paper. The control law is derived from optimization
0 2 4 6 8 10 12 14 16 18
-2
-1.5
-1
-0.5
0
0.5
Time(s)
Statorandrotor
activepower(Mw)
Rotor active power
Stator active power
Fig. 12. Stator and rotor active power.
0 2 4 6 8 10 12 14 16 18
-0.2
-0.1
0
0.1
0.2
Time (s)
Gridreactive
power(MVAR)
Actual power
Reference power
Fig. 13. Grid reactive power trajectory tracking.
0 2 4 6 8 10 12 14 16 18
-3
-2
-1
0
1
2
3
Time(s)
Rotorvoltage(0.1kv)
androtorcurrent(kA)
Rotor voltage
Rotor current
Fig. 14. Rotor Voltage and current.
0 2 4 6 8 10 12 14 16 18
-2.5
-2
-1.5
-1
-0.5
Time(s)
Gridactive
power(Mw)
Actual grid active power
Grid active power reference
Fig. 15. Grid active power trajectory tracking under DFIG's parameter variations.
0 2 4 6 8 10 12 14 16 18
-0.04
-0.02
0
0.02
0.04
Time (s)
Speederror(rad/s)
0 2 4 6 8 10 12 14 16 18
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Time (s)
Speederror(rad/s)
Fig. 16. Speed tracking error under predictive time change: (a) for Tp2¼20 ms and (b) for Tp2 ¼5 ms.
K. Ouari et al. / ISA Transactions 53 (2014) 76–8482

8. of an objective function that considers the control effort and the
difference between the predicted outputs and the specific references.
To ensure robustness against aerodynamic torque and parameter
variations, a disturbance observer is designed and integrated into
the control law. Furthermore, in order to limit the control effort, the
reference speed signal is passed through a second order linear filter.
The dynamic real time simulation shows that the grid active
power tracks perfectly its reference aiming to maximize the
conversion efficiency and the grid reactive power is maintained
at zero value contributing to compensate the grid power factor.
This justifies the efficiency and the reliability of the NGPC with an
aerodynamic torque observer.
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0 2 4 6 8 10 12 14 16 18
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Time (s)
Electromagnetic
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Electromagnetic
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