Nonlinear control of grid-connected wind energy conversion system without mechanical variables measurements

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 12, No. 2, June 2021, pp. 1139∼1149
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v12.i2.pp1139-1149 r 1139
Nonlinear control of grid-connected wind energy conversion
system without mechanical variables measurements
Karim Noussi1
, Abdelmajid Abouloifa2
, Hanane Katir3
, Ibtissam Lachkar4
, Fouad Giri5
1,2,3
TI Lab, Faculty of Sciences Ben M’sick, University Hassan II, Casablanca, Morocco.
4
ESE Lab, ENSEM of Casablanca, University Hassan II, Casablanca, Morocco.
5
NORMANDIE UNIV, UNICAEN, ENSICAEN, LAC, 14000 Caen, France.
Article Info
Article history:
Received Aug 28, 2020
Revised Mar 31, 2021
Accepted Apr 17, 2021
Keywords:
AC/DC/AC converter
Doubly fed induction
generator
High gain observer
Sliding mode control
Wind energy conversion
system
ABSTRACT
This article addresses the problem of controlling an overall wind energy conversion
system (WECS) formed by a wind turbine connected to the grid via a doubly fed in-
duction generator (DFIG) and an AC/DC/AC converter. The main control objectives
are fourfold: (i) designing an output feedback speed controller that makes the DFIG
rotate at the optimal value delivered by the MPPT strategy, (ii) controlling the stator
reactive power so as to be null, (iii) guaranteeing the DC-link voltage in the grid side
converter to be at a given constant value, (iv) ensuring a unitary power factor. A high
gain observer is synthesized, in order to provide estimated values of the mechanical
variables. To achieve the control objectives, a sliding mode controller involving the
mechanical observer is designed. The performance of the system configuration based
on the 2MW-DFIG with the proposed controller is evaluated by a numerical simu-
lation under a realistic wind profile using MATLAB/SIMULINK/SimPowerSystems
environment.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Karim Noussi
TI Lab, Faculty of Sciences Ben M’sick,
University Hassan II of Casablanca,
BP 7955 Casablanca, Morocco.
Email: karim.noussi2@gmail.com
1. INTRODUCTION
Energy is a major factor in the growth of industrial production. Renewable energies mainly wind
and solar are becoming the most supported solutions; as a result of less abundant fossil fuels, greenhouse gas
effect and high population growth [1]. On the other side, wind power is a globally available solution unlike
solar power due to its limitation to specific regions. Wind energy conversion systems are the fastest expanding
technology and the key components to clean and save energy [2]. Among all variable-speed wind turbine
designs, two commercial leading technologies are introduced in extensive scale; wind turbine based DFIG and
synchronous generator (SG). Indeed, DFIG technology has overtaken other ones because of its cost, robustness,
reliability and small power converters requirements [3], [4].
In this work, we are concerned with the control of the whole wind energy conversion system formed
by a wind turbine connected to the grid via a DFIG, a back-to-back converter and three phase RL filter. The
back-to-back converter includes two identical two-level voltage source converters; a rotor side converter (RSC)
and a grid side converter (GSC), linked by a capacitor. The converter consists of six insulated gate bipolar
transistors (IGBT) with anti-parallel diodes to allow the flow of current in both directions [5], [6]. To get full
Journal homepage: http://ijpeds.iaescore.com

1140 r ISSN: 2088-8694
benefits from the DFIG machine, different control techniques are employed for the synthesis of the DFIG wind
turbine system such as the field-oriented control used to decouple and regulate the torque and the stator reactive
power with classical PI-regulator, proposed in [7], [8]. DTC/DPC strategies are employed to control the WECS
powers in [9], a fuzzy logic controller is designed for power capture optimization in [10]. To optimize power
production of DFIG, a host of research works controlled the discussed system using nonlinear control strategies
such as the backstepping approach designed in [11], feedback linearization technique presented in [12], and
flatness-based approach used in [13]. However, in these works, the mechanical torque and the generator speed
are considered as measurable variables which is inappropriate in industrial solutions for electric drive systems
as long as one seeks to eliminate the mechanical sensors because they increase the maintenance costs and
reduce the system reliability, thus affecting the overall wind turbine system stability. In [14], authors proposed
a sensorless backstepping control technique for the DFIG. Nevertheless, only the generator speed is estimated
whereas the mechanical torque is assumed to be measurable. In this paper a high gain observer is synthesized,
in order to provide online estimation of the mechanical torque and the generator speed, only the electrical
variables are assumed to be as measurable quantities.
This article presents a sliding mode controller design in order to control the power converters associ-
ated with the generator which are the key components to handle the energy between the wind turbine and the
electrical grid. The RSC aims at regulating the generator speed to track the optimal reference provided by the
MPPT block, the speed controller is designed based on the mechanical observer, and regulate the stator reactive
power so as to be null. The GSC aims at guaranteeing that the DC-link is maintained at a given constant value
and ensuring a unitary power factor by keeping the grid side reactive power at zero.
The remaining sections of the paper are organized as follows: In Section 2, the whole wind energy
conversion system mathematical model is presented, followed by the sliding mode controller design described
in details for the proposed system in Section 3. The high gain observer is introduced in Section 4. The
simulation results are discussed in Section 5. Lastly, conclusions and future scopes are drawn in Section 6.
DFIG
RSC GSC
Grid
Gear box
3
Rg, Lg
3
3
3
Figure 1. Wind energy conversion system topology
2. SYSTEM MODELLING
The complete system scheme is depicted in Figure 1. According to [5], [15], the mathematical model
in state space form in d-q reference frame of the DFIG connected to the back-to-back converter can be summa-
rized by the following differential equations:
ẋ1 =
µ
J
x2 −
fv
J
x1 −
1
J
Cg (1)
ẋ2 =
1
σLr

x4
2
uq − Rrx2 − ωrσLrx3 − ωr
LmVs
ωsLs

(2)
ẋ3 =
1
σLr
x4
2
ud − Rrx3 + ωrσLrx2

(3)
ẋ4 =
1
Cdc

−
3
2
Vs
x4
x5 + irdc

(4)
ẋ5 =
1
Lg
x4
2
vq − Rgx5 − Vs − ωsLgx6

(5)
Int J Pow Elec Dri Syst, Vol. 12, No. 2, June 2021 : 1139 – 1149

Int J Pow Elec Dri Syst ISSN: 2088-8694 r 1141
ẋ6 =
1
Lg
x4
2
vd − Rgx6 + ωsLgx5

(6)
where [x1, x2, x3, x4, x5, x6] = [Ωm, irq, ird, vdc, igq, igd] denotes the state vector. ud, uq, vd and vq are the
back-to-back converter control inputs in d-q reference frame. Ωm, Cg, p, J and fv are the DFIG mechanical
rotational speed, mechanical torque, the number of pole pairs, the rotor inertia and the friction coefficient,
respectively. (with Ωt = Ωm/N and Ct = Cg.N, N is the gear box gain. Since the shaft rotor coupling
involves a gearbox). ωs, ωm and ωr denote the stator flux synchronous speed, the angular rotor speed and
the rotor angular frequency, respectively, (with ωr = ωs − ωm). ird, igd are the rotor and filter direct current
components. irq, igq are the rotor and filter quadrature current components. Vs is the magnetizing amplitude.
Rs, Rr and Rg designate the stator, rotor and filter resistor, respectively. Ls, Lr, Lm and Lg indicate the
stator, rotor, mutual and filter inductance, respectively. Cdc is the DC-link capacitor, irdc represents the current
flowing through the RSC. µ = (−3pLmVs)/(2Lsωs) designates the electromagnetic torque constant and
σ = 1 − L2
m/(LsLr) is Blondel’s dispersion coefficient.
3. CONTROLLER DESIGN
3.1. Rotor side converter controller
The RSC employs the sliding mode control technique to transfer the available electrical power from
the DFIG stator to the utility grid. The electrical power is generated via the mechanical power produced by the
wind turbine rotor. The controller involves two control loops: the first one is the speed control loop that aims
at regulating the generator speed to track the optimal reference provided by the MPPT block. The second one
is the stator reactive power control loop which is intended to control the stator reactive power so as to be null
[16]-[18].
3.1.1. Generator speed control loop:
Define the following second order sliding mode surface [19], [20]:
Sω(x, Cg) = ė1 + δ1e1 (7)
where e1 = x1 − x∗
1 denotes the tracking error between the generator speed and its optimal value, and δ1 is
the positive parameter design.
It follows from (1) that the error e1 undergoes the following equation:
ė1 = −
fv
J
x1 +
µ
J
x2 −
1
J
Cg − ẋ∗
1 (8)
Based on (1), (2), (7) and (8), the time derivative of the sliding surface is given by:
Ṡω = z1 (x, Cg, t) +
µx4
2σJLr
uq (9)
where,
z1 (x, Cg, t) =

δ1 −
fv
J

−
fv
J
x1 +
µ
J
x2 −
1
J
Cg

−
µ
σJLr

Rrx2 + ωrσLrx3 + ωr
LmVs
ωsLs

−
1
J
Ċg − ẍ∗
1 − δ1ẋ∗
1 (10)
By setting the dynamics of the sliding surface to zero, one can obtain the equivalent control law which ensures
the attractiveness and invariance of the sliding surface Sω:
uq,eq = −
2σJLr
µx4
z1 (x, Cg, t) (11)
Let us consider the positive Lyapunov function candidate:
W1 =
1
2
S2
ω (12)
Nonlinear control of grid-connected wind energy conversion system ... (Karim Noussi)

1142 r ISSN: 2088-8694
Differentiating (12), yields:
Ẇ1 = Sω

z1 (x, Cg, t) +
µx4
2σJLr
uq

(13)
By substituting (11) in (13), one gets:
Ẇ1 =
µx4
2σJLr
Sωuq,n (14)
The following discrete control law will be chosen to guarantee the dynamics of the candidate Lyapunov func-
tion to be negative:
uq,n = −
2σJLr
µx4
kωsgn (Sω) (15)
where kω is the controller parameter to be designed.
Then, the generator speed global control law is given by:
uq = −
2σJLr
µx4
(z1 (x, Cg, t) + kωsgn (Sω)) (16)
3.1.2. Stator reactive power control loop:
To design a controller for the stator reactive power exchanged with the grid, the sliding surface is
defined as follows:
SQ(x) = e2 = Qs − Q∗
s (17)
where the reactive power equation is given by [5]:
Qs = −
3
2
LmVs
Ls

x3 −
Vs
ωsLm

(18)
Using equations (3), (17) and (18), the sliding surface SQ undergoes the differential equation:
ṠQ = −
3
2
LmVs
σLsLr
x4
2

− Q̇∗
s (19)
with ṠQ = 0, the equivalent control law ud,eq can be expressed by:
ud,eq =
2
x4
(Rrx3 − ωrσLrx2) −
4
3
σLsLr
LmVsx4
Q̇∗
s (20)
Considering the following candidate Lyapunov function:
W2 =
1
2
S2
Q ⇒ Ẇ2 = SQṠQ (21)
It follows from (19) that:
Ẇ2 = SQ

−
3
2
LmVs
σLsLr
x4
2

− Q̇∗
s

(22)
Replacing (20) in (22), one gets:
Ẇ2 = −
3
4
LmVsx4
σLsLr
SQud,n (23)
The following discrete control law will be constructed which ensures the negativity of the derivative of the
candidate Lyapunov function W2:
ud,n =
4
3
σLsLr
LmVsx4
kQsgn (SQ) (24)
where kQ is the controller parameter to be designed.
Consequently, the final control law for the stator reactive power is given by:
ud =
2
x4
(Rrx3 − ωrσLrx2) +
4
3
σLsLr
LmVsx4

kQsgn (SQ) − Q̇∗
s

(25)

3.2. Grid side converter controller
The GSC also employs the sliding mode control technique, in order to exchange with the grid only
the active power extracted or injected by the RSC from the rotor, which is indirectly controlled through the
DC-link regulator [21], [22]. To this end, the GSC controller involves two control loops. DC-link and d-axis
current control loops. On one hand, the DC-link control loop aims at regulating the DC-link voltage at a given
constant value which is equal to the converter nominal voltage to avoid the damage of the RSC. On the other
hand, the d-axis control loop is used to force the reactive power to be null, thus ensuring a unitary power factor
by maintaining the direct current at its reference value that is equal to zero.
3.2.1. DC-link voltage control loop:
Let us define the DC-link voltage tracking error between the actual voltage and its reference as:
e3 = x4 − x∗
4 (26)
Using (4), the dynamics of the error e3 are written as:
ė3 = ẋ4 − ẋ∗
4 =
1
Cdc

−
3
2
Vs
x4
x5 + irdc

− ẋ∗
4 (27)
Taking into account the tracking error (26) and its dynamics (27), the considered sliding surface is defined:
Sv(x) = ė3 + δ2e3 (28)
where δ2 is the positive parameter design.
It follows from (5), (27) and (28) that the time derivative of the sliding surface Sv has the next form:
Ṡv = z2 (x, t) −
3
4
Vs
LgCdc
vq (29)
where
z2 (x, t) =
1
Cdc

i̇rdc +
3
2
Vs
x4Lg
(Rgx5 + Vs + ωsLgx6)

+

δ2
Cdc
+
3
2
Vs
C2
dcLgx2
4

irdc −
3
2
Vs
x4
x5

− ẍ∗
4 − δ2ẋ∗
4 (30)
In order to find out the equivalent control law that ensures the attractiveness and invariance of the sliding
surface, we set the dynamics of the sliding surface Sv to zero.
vq,eq =
4
3
LgCdc
Vs
z2 (x, t) (31)
The Lyapunov function candidate can be defined as W3 = 1
2 S2
v and in order to make its derivative negative,
the following discrete control law will be constructed:
vq,n =
4
3
LgCdc
Vs
kvsgn (Sv) (32)
where kv is the controller parameter.
In view of (31) and (32), the global control law for the DC-link voltage is given by:
vq =
4
3
LgCdc
Vs
(z2 (x, t) + kvsgn (Sv)) (33)

1144 r ISSN: 2088-8694
3.2.2. D-axis current control loop:
To control the grid side d-axis current x6, we proceed in the same way as for the earlier control
loops. Based on the alignment discussed in [5], one can calculate the reference of the d-axis current such as
x∗
6 = (2Q∗
g)/(3Vs), where Q∗
g is the grid side reactive power reference.
Let us consider the sliding surface Sid(x) = e4 = x6 − x∗
6. Using (6) the derivative of the sliding surface with
respect to time is given by:
Ṡid = ė4 =
1
Lg
x4
2

− ẋ∗
6 (34)
Setting the sliding surface Ṡid = 0, one obtains the equivalent control law as:
vd,eq =
2
x4
(Rgx6 − ωsLgx5) +
2Lg
x4
ẋ∗
6 (35)
In order to get the discrete control law, the chosen Lyapunov function is defined as W4 = 1
2 S2
id. Using (34),
the dynamics of the Lyapunov candidate are expressed as:
Ẇ4 = Sid

1
Lg
x4
2

− ẋ∗
6

(36)
It can easily be checked that the discrete control law vd,n =
−2Lg
x4
kidsgn (Sid) guarantees the negativity of
Ẇ4, where kid is the controller parameter.
Therefore, the global control law for d-axis control loop is written as:
vd =
2
x4
(Rgx6 − ωsLgx5) +
2Lg
x4
(ẋ∗
6 − kidsgn (Sid)) (37)
Remark: The chattering phenomenon can occur by using the signum function sgn(.). In this paper, we suggest
modifying the control laws by means of using a sigmoid tanh(.) function instead of sgn(.) in order to avoid
bringing in the vibration and nonlinearity into control signals during the reaching mode.
4. HIGH GAIN OBSERVER
In this section, a mechanical observer is employed to get online estimation of the mechanical torque
and the generator speed so as to decrease the number of sensors that reduce the reliability of the system. Since
the DFIG’s dynamic behavior belongs to a class of relatively fast systems, the high gain observer is among the
most suitable choices in the problem of state estimation. This choice is motivated by the fact that the observer
structure involves an explicit correction gain [23]. To this end, a high gain state observer will be designed. Due
to the fact that the position of the rotor is considered to be unknown because it needs a mechanical sensor, the
d-q frame cannot take place as it needs the rotor position information. Thus, the compact form of the DFIG
model in the α-β reference frame, is constructed as in (38) and (39).
ẇ = A w + g (w, i, u) + δ (t) (38)
y = C w = w1 (39)
where w = w1 w2 w3
T
= Tem Ωm TG
T
is the state space vector, y is the output vector,
A =


0 f1 (iαβ) 0
0 0 − 1
J
0 0 0

, g (w, i, u) =


f2 (iαβ, uαβ)
1
J w1 − fv
J w2
0

, δ (t) = 0 0 ε (t)
T
, C = 1 0 0

.
with w1 = (3/4)pLmiT
αβT0iαβ, iαβ = isα isβ irα irβ
T
, uαβ = usα usβ urα urβ
T
,
f1 (iαβ) = (3p2
Lm)/(2σLsLr)iT
αβT0F1iαβ, f2 (iαβ, uαβ) = (3pLm)/(2σLsLr)iT
αβT0 (F2uαβ + F3iαβ),
F1 =

−L2
mJ2 −LrLmJ2
LsLmJ2 LsLrJ2

, F2 =

LrI2 LmI2
−LmI2 LsI2

, F3 =

−RsLrI2 RrLmI2
RsLmI2 −RrLsI2

,

T0 =

O2 J2
−J2 O2

, I2 =

1 0
0 1

, J2 =

0 −1
1 0

, O2 =

0 0
0 0

.
And ε (t) is a bounded function. Then, the state observer of systems (33) is designed as follows [24]:
˙
ŵ = A ŵ + g (ŵ, i, u) − Γ−1
(i) ∆−1
θ KC (ŵ − w) (40)
where Γ(i) = diag 1 f1 (iαβ) − 1
J f1 (iαβ)

and ∆θ = diag 1 1
θ
1
θ2

, θ is a constant positive gain.
The gain matrix K is selected so that the matrix Ā − KC

is Hurwitz, with Ā = Γ−1
AΓ, which implies that
P Ā − K C

+ Ā − K C
T
P = −I3, P ∈ R3
.
The high gain observer stability can be proved using the Lyapunov stability theorem and by considering the
quadratic Lyapunov function candidate: W0 = εT
P ε, where ε = Γ (i) ∆θw̃ and w̃ = ŵ − w [24].
5. SIMULATION RESULTS
The focus in this work is made on the design of an output feedback controller that is carried out
using the nonlinear model of the entire wind energy conversion chain adopted. The proposed controller is
developed based on the sliding mode technique and using a high gain observer. This latter is employed to
estimate the generator speed and the mechanical torque, which improve the WECS performance and reliability
via eliminating the mechanical sensors. In this study, we are interested in the control of the back-to-back
converter, i.e., RSC and GSC, taking into account the IGBT switching devices which are considered ideal
in several works. In addition, our main concern in this paper is directed to both RSC and GSC making our
study complete in comparison to other works that focus only on one of the two converters. Actually, the
power transfer through the back-to-back converter can affect and disturb the global power injected into the
utility grid. The model of the 2-MW DFIG-based WECS connected to the electrical network, employing the
proposed output-feedback controller which was discussed in the previous sections and described by Figure 2 is
performed using MATLAB/SIMULINK/SimPowerSystems environment.
Rotor Side
6 6
controller
Grid side
controller
dq abc dq
abc
High gain observer
Vsabc isabc
PWM PWM
Qs
*
*
3 3
*
vdc
Qg
igd
*
3/2.Vs
abc
dq
MPPT
udq
vdq
m
irdc igdc
DFIG
RSC GSC
Grid
Gear box
3
Rg, Lg
3
3
3
igq
igabc
V
m
Qs
Cg
^
^
vdc
vdc
*
+
_
+
_
+
_
+
_
Figure 2. Schematic representation of the proposed wind energy conversion system with the controller design
The system parameters are given as follows:
Wind turbine parameters: N = 100, R = 42m, ρ = 1.1225Kg.m3
. DFIG and filter parameters: Vn/Un =
400/690V , f = 50Hz, Pn = 2MW, Rs/Rr = 2.6mΩ/2.9mΩ, Ls/Lr = 2.6mH/2.6mH, Lm = 2.5mH,
Rg = 0.02mΩ, Lg = 0.4mH, C = 80mF. Observer and controller parameters: K = [25, 8, 33]T
, θ = 90,
kω = 250, kQ = 300, kv = 120, kid = 150, δ1 = 100, δ2 = 100.
To demonstrate the validity of the output feedback controller, simulation results are obtained in the presence of
a realistic wind speed profile with an average wind speed of 9 m/s characterized by a 4% turbulence intensity
over the time interval [0 100 s], as shown in Figure 3 (a), to further prove the efficiency of the proposed
controller. Figures 3 (b)-(c), illustrate the generator speed and the mechanical torque of the DFIG and highlight
the output feedback control loop convergence. Particularly, Figure 3 (b) shows the time-variations of the
generator speed reference delivered by the MPPT block, together with the measured generator speed and its

1146 r ISSN: 2088-8694
estimated value. As it can be noticed, the estimated value first matches the measured generator speed and
both track the reference effectively so as to meet the control objectives. Also, Figure 3 (c) displays that the
mechanical torque value provided by the high gain observer meets the measured mechanical torque which
demonstrates the efficiency of the mechanical observer. Figure 3 (d) proves that the stator reactive power
converges to the suggested reference which implies that only the active power is exchanged with the grid on
the stator-grid connection. This keeps the currents sinusoidal and in opposite phase with the grid voltages, as
shown in Figure 3 (g), complying with the PFC requirements. Figure 3 (e) verifies that the DC-link voltage is
maintained at its recommended level, which guarantees the appropriate operation of the converter on the grid
side. Figure 3 (f) shows the convergence of the grid side d-axis current which ensures that the reactive power
exchanged with the electrical network on the rotor-grid connection is zero, thus proving the achievement of
the GSC objectives. Figure 3 (g) represents one phase of the network voltage and current. The latter depends
on the variation of the generated active power which fluctuates according to the wind velocity. Figure 3 (h)
illustrates the mechanical power extracted by the wind turbine blades and the electrical power exchanged with
the utility grid.
(a) (b)
(c) (d)
(e) (f)
(g) (h)
Figure 3. Wind energy conversion system estimation and convergence
The observer is synthesized using the DFIG model in the stationary reference frame (α-β frame)
where the rotor position is not used for the observer modelling and implementation in order to increase the
reliability of the system. The estimated value of the generator speed and mechanical torque are used as inputs

of the sliding mode controller that aims at improving the performance of the conversion chain so as to meet the
control objectives. The used controller ensures the system to converge faster than other regulators [7], [8], [10].
In addition, it allows the system to work without the presence of sensors, minimizing the cost and complexity
of the overall structure, unlike other works that must lean on the signals provided by the sensors to achieve
their control objectives [15], [25]. Another added-value of the present study relies on extracting the maximum
available power given by the wind turbine blades. It is worth mentioning that the reactive power ripples shown
in Figure 3 (d) according to the proposed design are much smaller than those shown in [10], [16]. In fact, the
ripples in active and reactive powers have an influence on the current injected into the electrical grid and on the
stress on the turbine shaft. This can lead to the destruction of the wind turbine.
6. CONCLUSION
In this article, a sliding mode controller is designed for the complete WECS constituted by a wind
turbine connected to the grid via a DFIG and a back-to-back converter. The advantage of the proposed design
is that it eliminates the requirement of mechanical sensors using a high gain observer, which improves the
efficiency of the controlled system. It has been illustrated by a numerical simulation that the performance of
the WECS based on the sensorless-sliding mode controller, under realistic wind profile, is better compared to
other controllers and it can be concluded that the control objectives are efficiently achieved. We look forward
to continuing this study in our next papers, first, by developing a novel MPPT strategy to improve the power
extraction without the need of using an anemometer sensor for wind speed measurement, and then, by testing
the control laws in real-time simulations in order to validate the system’s performance.
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BIOGRAPHIES OF AUTHORS
Karim Noussi received his Master’s degree in information processing in 2017 from the Faculty of
Science Ben M’sick, Hassan II University. Since 2017, he has been preparing his Ph.D. in the field of
automatic, renewable energy and electrical machines at University Hassan II, Casablanca, Morocco.
The main topics of his research are in the field of robust and advanced control methods of AC drives
associated with power electronic converters for wind power generation.
Abdelmajid Abouloifa received the Aggregation of Electrical Engineering from Normal High
School, Rabat, Morocco, in 1999, and Ph.D. degree in control engineering from the University of
Caen Basse-Normandie, Caen, France and from Mohammed V University, Rabat, Morocco in 2008.
He is currently Professor at the Faculty of Sciences Ben M’sick, University Hassan II, Casablanca,
Morocco. His research interests include high frequency power converter topologies, power-factor-
correction techniques, power supplies, and nonlinear control.

Hanane Katir received her Master’s degree in information processing from the Faculty of Sciences
Ben M’Sick, University Hassan II, Casablanca, Morocco, in 2017. Since 2017, she has been prepar-
ing her Ph.D. in the field of automatic, renewable energies and multilevel converters in the Faculty
of Sciences Ben M’sick, University Hassan II, Casablanca, Morocco. Her research interests include
the nonlinear control of Cascaded H-Bridge Multilevel Converters, Grid-connected systems, Unin-
terruptable Power Supplies, and renewable energies.
Ibtissam Lachkar received the graduate degree from the Normal High School of Technical Educa-
tion, Rabat, Morocco, in 1995 and her degree of high depth studies from the Mohammedia School
of Engineers, Rabat, in 2005. She received her Ph.D. from Mohammedia School of Engineers. Cur-
rently, she is an Assistant Professor at National School of Electricity and Mechanic.
Fouad Giri received his PhD in automatic control from the Institute National Polytechnique of
Grenoble, France, in 1988. He is Professor at the University of Caen basse-Normandie, Caen, France.
His research interests include nonlinear system identification, nonlinear, adaptive and constrained
control, and the application of identification and control theory to power converters and electric ma-
chines.

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