energies

Article
Enhanced Performance in PMSG-Based Wind Turbine Systems:
Experimental Validation of Adaptive Backstepping
Control Design
Youness El Mourabit 1 , Hassna Salime 2 , Badre Bossoufi 2, * , Saad Motahhir 3 , Aziz Derouich 4 ,
Saleh Mobayen 5, * and Anton Zhilenkov 6

1 National School of Applied Sciences, Abdelmalek Essaadi University, Tetouan 93000, Morocco;
youness.elmourabit@uae.ac.ma
2 LISTA Laboratory, Faculty of Science Dhar El Mahraz-USMBA, Fez 30000, Morocco;
hassna1salime@gmail.com
3 Engineering, Systems and Applications Laboratory, ENSA, USMBA, Fez 30000, Morocco
4 Industrial Technologies and Services Laboratory, Higher School of Technology, Sidi Mohamed Ben Abdellah
University, Fez 30000, Morocco
5 Graduate School of Intelligent Data Science, National Yunlin University of Science and Technology, 123
University Road, Section 3, Douliou, Yunlin 640301, Taiwan
6 Department of Cyber-Physical Systems, St. Petersburg State Marine Technical University,
190121 Saint-Petersburg, Russia
* Correspondence: badre.bossoufi@usmba.ac.ma (B.B.); mobayens@yuntech.edu.tw (S.M.)

Abstract: Ensuring the quality and stability of the electrical grid is of utmost importance during the
phase of electrical energy production. As wind energy plays an increasingly significant role in a
country’s energy composition, maintaining stability and optimal quality has emerged as a prerequisite
for the generated electricity. This article aims to devise a dynamic nonlinear algorithm that can be
implemented in the wind energy conversion system (WECS) featuring a direct-drive permanent
Citation: Mourabit, Y.E.; Salime, H.; magnet synchronous generator (PMSG). Notably, the adaptive backstepping control relies on the
Bossoufi, B.; Motahhir, S.; Derouich, nonlinear model of the controlled system. It harnesses the principles of the Lyapunov stability theory
A.; Mobayen, S.; Zhilenkov, A. to regulate various parameters and uphold the overall system’s stability. Employing simulation
Enhanced Performance in analysis through the Matlab–Simulink environment, the proposed control strategy is evaluated using
PMSG-Based Wind Turbine Systems: a 1.5 MW wind turbine. The results showcase the robust capability of the suggested control algorithm:
Experimental Validation of Adaptive
it effectively maintains the DC bus voltage and produces high-quality electrical energy with a total
Backstepping Control Design.
harmonic distortion (THD) below 0.38%. Moreover, the algorithm demonstrates added resilience.
Energies 2023, 16, 7481.
The practical viability of the adaptive control algorithm is validated through an experimental study
https://doi.org/10.3390/en16227481
on the dSPACE DS1104 prototyping platform. This study underscores the algorithm’s proficiency in
Academic Editors: Francesco achieving all control objectives under diverse wind scenarios.
Castellani, Davide Astolfi and
Lin Wang Keywords: WECS; PMSG; Adaptive Backstepping Control; Lyapunov theory; THD; dSPACE DS1104
Received: 27 August 2023 prototyping platform
Revised: 13 September 2023
Accepted: 19 September 2023
Published: 7 November 2023
1. Introduction
The growing global emphasis on finding environmentally friendly ways to generate
electricity has become a prominent trend in numerous countries [1]. Indeed, innovative and
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
cleaner approaches for sustainable development are emerging as promising alternatives,
This article is an open access article
with wind power generation [2,3] standing out as one of the frontrunners. This method
distributed under the terms and of producing electrical energy has undergone significant evolution, establishing itself as
conditions of the Creative Commons one of the most lucrative and progressively essential components in contemporary energy
Attribution (CC BY) license (https:// production systems [4].
creativecommons.org/licenses/by/ Significant advancements have been incorporated into wind power generation systems,
4.0/). including innovations such as variable-speed wind energy conversion systems (WECS) [5],

Energies 2023, 16, 7481. https://doi.org/10.3390/en16227481 https://www.mdpi.com/journal/energies

Energies 2023, 16, 7481 2 of 28

which have garnered considerable attention for their numerous advantages [6]. Operating
at variable speeds enables high energy production, necessitating generators capable of
functioning at variable speeds and low rotation values [7]. Permanent magnet synchronous
generators (PMSGs) have emerged as particularly well-suited for such low-speed operations
and, in many instances, eliminate the need for a gearbox due to their high pole count [8].
Nevertheless, the control algorithms governing the operation of static converters play a
pivotal role in enhancing the efficiency and performance of the examined system [9].
The wind power conversion system incorporates a high-pole-count permanent magnet
synchronous generator alongside a back-to-back full-scale converter technology [10]. This
configuration facilitates the controlled injection of wind-generated power into the grid
while also managing energy levels to ensure compliance with IEEE-519 standards [11]. To
address this challenge, numerous research initiatives have developed control algorithms
tailored to oversee the distribution of generated energy to the grid. However, some of these
approaches rely on a linear model of the wind turbine, which can negatively impact the
overall system’s performance. It is crucial to note that wind systems inherently exhibit non-
linear characteristics, and the variability of wind profiles further exacerbates the limitations
of the existing wind system controls.
Other research endeavors employ traditional control techniques to govern the wind
systems [12]. Nevertheless, the dynamic alterations within the machinery and the fluctua-
tions and disruptions from external environmental factors render such control methods
insufficient for maintaining the high performance levels essential for electricity genera-
tion [13]. In this context, the present study aims to implement an adaptive nonlinear control
approach. This methodology is engineered to meet specific criteria while ensuring the
accurate regulation and synchronization of electrical and mechanical parameters, even
when confronted with various internal and external disturbances.

Literature Review
Various control methodologies have been implemented to regulate wind energy con-
version systems. In particular, the conventional vector control, also known as field-oriented
control (FOC), has been extensively studied. Salime, H., et al. [14] attempted to apply
FOC in conjunction with direct power control (DPC) to the PMSG for wind system control.
While this approach has proven effective, especially when applied to the machine-side
converter, it exhibits sensitivity to variations in generator parameters, making it vulnerable
in the overall management of the wind system. DPC is employed to control the grid-side
converter and supply the required power to the distribution network. Despite the qual-
ity of the energy obtained through this approach, variations in parameters and external
environmental disturbances pose significant challenges.
Similarly, El Mourabit, Y., et al. [15] also adopted the vector control technique to
regulate a wind system equipped with a PMSG. They implemented an MPPT control
algorithm using a proportional—integral regulator. The results obtained highlight the
persistence of risks associated with changes in machine parameters in the context of vector
control, introducing uncertainty regarding its effectiveness, especially when variations in
machine parameters coincide with significant fluctuations in wind profiles.
In their study [16], the researchers attempted to control the pitch angle using an
improved proportional–integral regulator. However, due to inherent uncertainties in wind
turbine modeling and wind speed profiles, the development of more effective controllers
has become imperative. Furthermore, the parameters of the PID controller are typically
unknown and require selection by the designer, a task that is neither straightforward
nor optimal. Unfortunately, the overall control system still relies on standard regulators,
resulting in a degradation of the required performance for this type of system.
In their research, conducted by Mohammed, H. Q., et al. [17], a suite of eight proportional–
integral regulators was employed to oversee the dual static rectifier/inverter converters
in a direct-drive permanent magnet synchronous generator (PMSG)-centric wind energy
system. Their objectives included enhancing the system’s capacity to manage low-voltage
Energies 2023, 16, 7481 3 of 28

transitions and achieving optimal maximum power point tracking (MPPT). The results
obtained indicate that the control approach can effectively achieve a satisfactory tracking
performance. However, the conventional control method continues to exhibit shortcomings
in terms of energy quality, mainly due to the presence of ripples and overall average
output quality.
In their study, Zhang et al. [18] presented a direct torque control (DTC) strategy that
incorporates the concept of space-flux vectors within a wind energy system powered by a
permanent magnet synchronous generator (PMSG). The control algorithm employed in this
research utilizes a discrete-time control approach, predicting the stator flux vector solely
based on torque and stator flux data. While the results obtained show promise, a significant
drawback of this control method remains evident in the form of the electromagnetic torque
fluctuations observed during switching events.
In a separate study, Zhang et al. [19] dedicated their efforts to exploring finite control
set model predictive control, commonly abbreviated as FCS-MPC. This control methodol-
ogy was implemented on a direct-drive permanent magnet synchronous generator (PMSG)
used in conjunction with a back-to-back power converter. While this control approach
displayed promising signs, its performance was affected by variations in the system param-
eters. To address this issue, the researchers made enhancements to the control algorithm
by incorporating parameter prediction. This innovation aimed primarily to enhance the
system’s robustness against parameter fluctuations and reduce control variable variations,
thus, improving the overall quality of PMSG generator control in changing conditions.
Osman and Alsokhiry [20] put forward an intriguing proposal by suggesting the
use of nonlinear sliding mode control (SMC) to oversee the energy transfer to the grid
from a wind system centered around a permanent magnet synchronous generator (PMSG).
The primary goal of applying SMC control was to counteract potential disturbances and
ensure the quality of the generated energy within the system. This study employed a
simulation through Matlab/Simulink R2022a to compare the performance of the wind
system regulated by SMC with that of proportional–integral control, especially in scenarios
where grid voltage disruptions were present.
In parallel, other research efforts [21,22] have also harnessed sliding mode control to
complement conventional control methods, highlighting its potential to enhance the man-
agement of wind energy systems. Furthermore, some researchers [23] have ventured into
exploring artificial intelligence (AI) techniques in the field of wind energy. These endeavors
have encompassed areas such as energy yield estimation, optimization of maximum power
extraction from wind systems, wind production planning, and control of wind turbine
pitch angles.
It is worth noting that most of these research studies, including the ones mentioned
and others alike, have operated under the assumption of a comprehensive understand-
ing of the wind system parameters. However, it is important to acknowledge that this
assumption may not always hold true, considering the complexity and inherent variability
of such configurations.
Furthermore, the integration of wind energy into the electrical grid raises various
challenges, particularly those related to network stability and quality. Two examples of
these issues are as follows:
 Fluctuations in wind energy production: One of the primary obstacles in the use of
wind energy is its sensitivity to changing weather conditions. Variations in wind
intensity and direction result in oscillations in wind energy production.
 Integration of wind energy into an existing network: Incorporating wind farms into
an existing electrical grid can pose stability challenges, especially when it comes to
synchronizing electricity supply and demand.
Adaptive backstepping control allows for the rapid adjustment of control parameters
in response to wind variations, contributing to maintaining network stability despite these
fluctuations. Adaptive backstepping control also provides the opportunity to make more
Energies 2023, 16, 7481 4 of 28

precise adjustments in wind energy production to meet the network’s needs, thereby
preserving system stability.
To tackle this issues, the adaptive backstepping control is strategically utilized to
oversee the operations of a wind power generation system that relies on a permanent
magnet synchronous generator (PMSG). By employing this technique, not only is the
production of top-notch electrical energy assured, but the system’s capacity to withstand
an array of disruptions is also fortified. Given the dynamic nature of the wind system,
characterized by shifts in parameters and variations in external environmental factors,
the remarkable outcomes obtained through the implementation of this control approach
are evident.
To practically validate the efficacy of the implemented control strategy and its appli-
cability in real-world installations, the experimental verification is conducted using the
dSPACE DS1104 prototyping platform.
To enhance the readability and coherence of this paper, the structure is organized
as follows:
In the initial segment, we provide a comprehensive introduction and delve into a
thorough literature review encompassing diverse control algorithms employed in wind
systems. Moving forward, Section 2 concentrates on the mathematical modeling intricacies
of the wind conversion system chain, intricately examining both the wind turbine and
the generator employed within the context of this study. Section 3 pivots to the adaptive
control principle, coupled with the simulation of the complete chain. Employing the robust
Matlab/Simulink environment, we meticulously demonstrate the application of the pro-
posed control strategy. Shifting focus to Section 4, we present the culmination of our efforts
through experimental validation conducted on the dSPACE DS1104 prototyping platform,
complemented by the graphical capabilities of the ControlDesk tool. This amalgamation
showcases a spectrum of illustrative graphs contributing to the validation process. Con-
cluding the discourse in Section 5, we engage in a comprehensive discussion and draw
pivotal conclusions derived from the depth of our study.

2. Modeling of Wind Turbine and PMSG

2.1. Modeling of Wind Turbine
The wind turbine’s aerodynamic model can be expressed through the following set of
equations [24]:
1 3

 Paer = 2 ρ.S.Vw

1 3
 PTur = C p (λ, β).Paer = C p . 2 ρ.S.Vw



 R.Ω
 λ = Vw


1 1 0.035 (1)
 λ0 = λ+0.08β − β3 + 1  −21

116
 C p (λ, β) = 0.5176 λ0 − 0.4β − 5 e
λ0 + 0.0068λ





C (λ,β).ρ.S.R 3
TTur = 12 p λ3 Ω2



2.2. PMSG Modeling

The depiction of the permanent magnet synchronous generator under examination
within the rotating reference frame is achieved using the subsequent equations [25]:
The formulation of the stator voltage equations is as follows:
•

Vsd = − Rs .isd − Ψsd − ωe .Ψsq

• (2)
 V = − R .i − Ψ + ω .Ψ
sq s sq sq e sd

The relations describing the stator flux components in terms of the generator currents
are provided by
Ψsd = Ld .isd + Ψ f

(3)
Ψsq = Lq .isq
Energies 2023, 16, 7481 5 of 28

Following transformation and subsequent simplification, the resulting formulations

for the stator voltages are derived as follows:

d(isd )
(

Vsd = − Rs .isd − Ld dt − ωe . Lq .isq
d(isq ) (4)
Vsq = − Rs .isq − Lq dt + ωe .( Ld .isd ) + ωe .Ψ f

Henceforth, the dynamics governing the behavior of the stator currents are derived in
the subsequent manner:

 d(isd ) = −1 Vsd + Rs .isd − ωe . Lq .isq


dt Ld
(5)
 d(isq ) = −1 Vsq + Rs .isq − ωe .( Ld .isd ) − ωe .Ψ f
h i
dt Lq

The computation of the electromagnetic torque is attainable through the subsequent formula:

−3 h i
.p. Ld − Lq .isd .isq + Ψ f .isq


Tem = (6)
2
The electromagnetic torque simplification for a permanent magnet synchronous gen-
erator (PMSG) can be achieved using Equation (7), assuming equal inductances (Ld = Lq )
for a machine with uniform poles. Consequently, the electromagnetic torque becomes a
function reliant on the quadrature stator current component and the rotor’s permanent
magnet flux.
−3
Tem = .p.Ψ f .isq (7)
2
The description of the mechanical equation is encapsulated as follows:

dΩ
TTur − Tem − f c .Ω = J. (8)
dt
The active and reactive powers of the permanent magnet synchronous generator
(PMSG) can be denoted through the ensuing expressions:

.Ω = 32 Vsd .isd + Vsq .isq

  
Pgen = Tem
(9)
Q gen = 32 Vsq .isd − Vsd .isq


3. Adaptive Backstepping Algorithm

3.1. Backstepping Principle
Historically, the concept of a backstepping algorithm gained significant prominence,
particularly during the 1980s and early 1990s. The pioneering work by Feurer in 1978 [26],
coupled with the contributions from V. Kokotovic and Sussmann in 1989 [27], played a
pivotal role in bringing widespread attention to the principles of backstepping control.
Their efforts further built upon the foundational research by Feurer and Tsinias [28]. In the
year 1991, Kannellkapoullos extended the understanding of control strategies rooted in
the backstepping algorithm, providing deeper insights into its application across diverse
nonlinear systems [29,30].
The parameters shaping the design of adaptive backstepping control wield a direct and
profound influence over the regulation performance of the wind turbine systems. These
parameters stand as the linchpin for calibrating how the controller tailors its responses to
variations within the system and perturbations stemming from the environment. Here, we
outline several key parameters that wield the potential to significantly impact the control
efficacy of wind turbine systems:
Energies 2023, 16, 7481 6 of 28

Controller Gains: The gains determine the speed at which the controller responds to errors
and variations.
Update Frequency: The frequency at which the controller is updated can impact the
system’s responsiveness.
Parameter Adaptation: Certain adaptive backstepping controls adjust their parameters
based on system variations over time.
System Constraints: Specific characteristics of the wind turbine system, such as voltage or
speed limits, may require specific parameter adjustments to ensure the control operates
within acceptable limits.

3.1.1. Implementing Backstepping Algorithm for PMSG

The fundamental principle underpinning backstepping control revolves around pre-
cise monitoring of the angular position. In this framework, the rotor’s magnetic flux,
generated by permanent magnets, stays synchronized with the stator’s motion. The pri-
mary objective is to finely regulate the electromagnetic torque produced by the machine.
This task is achieved through meticulous control of its mechanical rotational speed, employ-
ing a strategy commonly termed as torque control. This control technique heavily relies on
the notion of vector control for stator voltages. Consequently, the reference voltages are
applied to the converter positioned on the machine’s side. These reference voltages play a
pivotal role in determining the appropriate control signals to govern the rectifier arms. To
effectively implement this control methodology, it becomes imperative to disentangle the
stator current components denoted as isd and isq . These components operate within the d-q
rotating frame, a concept that closely aligns with the principles of vector control.
Hence, the regulation of electromagnetic torque is executed by overseeing the current
isq , while the management of flux is attained by manipulating the forward current isd .
Building upon Equations (4)–(6) and (8), the system model is explicitly defined as follows:
 d(isd ) Rs Lq 1
dt = − Ld .isd − Ld .ωe .isq − Ld .Vsd



 d(isq ) Rs Ld 1 1
dt = − Lq .isq + Lq .ωe .isd + Lq .ωe .Ψ f − Lq .Vsq


fc
(10)
dΩ 1 1 1
dt = hJ .TTur − J .Tem − J .Ω = i J .TTur




+ 23 . J . Ld − Lq .isd .isq + Ψ f .isq − fJc .Ω
p



3.1.2. Employing Non-Adaptive Backstepping Algorithm on PMSG

Based on Equation (10) and assuming that all parameters of the wind system, in-
cluding the PMSG parameters, are known, the procedure for setting up the non-adaptive
backstepping control can be delineated into three essential phases:
Step 1: Designing the Controller for Mechanical Rotational Speed:
The error in mechanical rotational speed is defined by the following expression:

χ1 = Ωre f − Ω (11)

The dynamics of this error, according to Equations (10) and (11), can be obtained using
the following approach:

• • • • 1 fc 3 ph i
χ1 = Ωre f − Ω = Ωre f − .TTur + .Ω − . . Ld − Lq .isd .isq + Ψ f .isq


(12)
J J 2 J

In the scenario of the machine possessing smooth poles, resulting in (Ld = Lq = Ls ), a no-
table simplification occurs within the expression governing the dynamics of the mechanical
speed error.
• • • • 1 3 p fc
χ1 = Ωre f − Ω = Ωre f − .TTur − . .Ψ f .isq + .Ω (13)
J 2 J J
Energies 2023, 16, 7481 7 of 28

The Lyapunov stability theory is crucial in the backstepping algorithm to ensure the
stability of the wind system. It enables the design of iterative controls while maintaining
the overall system’s stability by employing Lyapunov functions that assess the decrease
in the system’s energy. This approach ensures that the system remains stable despite its
nonlinear complexity and wind variations.
The candidate function for Lyapunov is structured in the subsequent manner:

1 2
γ1 = χ (14)
2 1
Its time derivative is given by
•
 
• • 1 3 p fc
γ1 = χ1 χ1 = χ1 Ωre f − .TTur − . .Ψ f .isq + .Ω (15)
J 2 J J

Derived from the backstepping control design, the direct stator current components,
isd , and the quadratic stator current components, isq , are chosen as virtual inputs. Within the
parlance of backstepping control, these virtual inputs are denoted as stabilizing functions.

 isd_re f = 0
•
 
J fc (16)
 isq_re f = 3 −k1 χ1 − Ωre f + J .TTur − J .Ω
1
2 .p.Ψ f

To establish system stability, a positive constant, denoted as k1 , is carefully chosen.

This choice ensures that the virtual inputs isd_ref and isq_ref maintain the negativity of
the designated Lyapunov function. In such an instance, the evolution of the Lyapunov
function’s dynamics can be described as follows:
•
γ1 = −k1 .χ21 ≤ 0 (17)

Step 2: Formulating the Controller for Stator Current Components:

The errors in current magnitudes are characterized by the subsequent expressions:

χ2 = isq_re f − isq
(18)
χ3 = isd_re f − isd = −isd

The dynamics of the error, in accordance with the system Equations (10), (13) and (18),
are illustrated as follows:
 • p

 χ1 = 32 . J .Ψ f .χ2 − k1 .χ1
• • •• •
  
 χ• 2 = i sq_re f − i sq = 3 J

fc
−k1 .χ1 − Ωre f − J .Ω


2 .p.Ψ f (19)
R L


 + Lqs .isq − Ldq .ωe .isd − L1q .ωe .Ψ f + L1q .Vsq
• • •

 •

L
χ3 = i sd_re f − i sd = − i sd = RL s .isd + Lq .ωe .isq + L1 .Vsd

d d d

Step 3: Designing Actual Control Inputs and Conducting Stability Analysis:

The actual control inputs are embodied by the stator reference voltages. In order to
ascertain these voltages, we embrace a new positive definite Lyapunov candidate function.

1 2 1 2 1 2
γ2 = χ + χ + χ (20)
2 1 2 2 2 3
Energies 2023, 16, 7481 8 of 28

The time derivative of this candidate function is obtained from the system of
Equation (19) as follows:
• • • •
γ2 =γ1 + χ2 χ2 + χ3 χ3 = −k1 .χ21 − k2.χ22 − k3 .χ23
•• fc
•
J Rs
 3 .p.Ψ f . −k1 .χ1 − Ωre f − J .Ω + Lq .isq 
+ χ2 . 2  (21)
− LLdq .ωe .isd − L1q .ωe .Ψ f + L1q .Vsq + k2 .χ2
h i
L
+χ3 . RL s .isd + Lq .ωe .isq + L1 .Vsd + k3 .χ3
d d d

In order to ensure the stability of the current dynamics, we meticulously select positive
constants, denoted as k1 , k2 and k3 . Furthermore, the design of stator reference voltages is
aimed at preserving the negativity of the derivative of the chosen Lyapunov function. To
achieve this goal, the expressions for the reference stator voltages are defined by:

 Vsd_re f = − Rs .isd− Lq .ωe .isq − Ld .k3 .χ3
•• •


J.L f
Vsq_re f = 3 q k1 .χ1 + Ωre f + Jc .Ω (22)

 2 .p.Ψ f
− Rs .isq + Ld .ωe .isd + ωe .Ψ f − Lq .k2 .χ2


Consequently, the evolution of the Lyapunov function’s dynamics becomes

•
γ2 = −k1 .χ21 − k2 .χ22 − k3 .χ23 ≤ 0 (23)

3.1.3. Application of Adaptive Backstepping Algorithm to PMSG

The non-adaptive backstepping algorithm operates under the premise that all system
parameters, including those pertaining to the PMSG, are not only known but also remain
fixed. Nevertheless, this presumption is often untenable. In the real world, parameters
can undergo fluctuations due to factors such as alterations in temperature, influences of
magnetic saturation, and shifts in load torque. As such, it becomes imperative to account
for the non-linearities and uncertainties arising from these unknown parameters during
the design of the controller.
One viable approach to enhance the system’s resilience against parametric variations
and measurement noise involves the integration of estimators, commonly referred to as
observers. This second control algorithm leverages these estimations to better approximate
the genuine system parameters, which encompass those specific to the PMSG.
The precise delineation of the system parameters unfolds as follows:


 σ1 = RS
 σ2 = Ld = Lq = LS



σ3 = J (24)



 σ4 = TTur
J
 f
σ5 = Jc


The parameter configuration represented by system 24 will be substituted with

[σ̂1 σ̂2 σ̂3 σ̂4 σ̂5 ] T (25)

The errors in these parameters are delineated as follows:

= σ̂1 − σ1


 σ1
e

σ2
 e = σ̂2 − σ2
σ3
e = σ̂3 − σ3 (26)
= σ̂4 − σ4

σ
 4

e

σ5
e = σ̂5 − σ5
Energies 2023, 16, 7481 9 of 28

The stabilizing function initially outlined in Equation (16) undergoes a redefinition

as follows: 
 isd_re f = 0
•
 
(27)
 isq_re f = 3 σ̂3
−k1 χ1 − Ωre f + σ̂4 − σ̂5 .Ω
2 .p.Ψ f

The dynamic of the error is reconfigured as follows:

• • p p
χ1 = Ωre f − σ4 + 23 . σ3 .Ψ f .χ2 − 23 . J .Ψ f .isq_re f + σ5 .Ω

•
 (28)
3 p
= 2 . σ3 .Ψ f .χ2 + σ3 −k1 .χ1 − Ωre f + σ̂4 − σ̂5 .Ω + e
σ3
e
σ4 − e
σ5 .Ω − k1 .χ1

• σ̂1 σ1 σ̂2 σ2 1 1
χ2 = σ2 .i − σ2 .isq
e
− σ2 .ωe .isd + σ2 .ω
e
.i − σ2 .ω .Ψ +
σ2 .Vsq
• sq e sd e f
• • •• • •

+ 3 .p.Ψ σ̂3
−k1 .χ1 − Ωre f + σ̂4 − σ̂5 .Ω + σ̂3
3 .p.Ψ −k1 .Ωre f − Ωre f + σ̂4 − σ̂5 .Ω
f f
2 2 (29)
− eσσ33 (k1 − σ̂5 ).isq − (k1 − σ̂5 ).isq − σ̂3
3 .p.Ψ (k1 − σ̂5 )(e
σ4 − e
σ5 )
2 f
σ̂3
+ 3 .p.Ψ (k1 − σ̂5 )(σ̂4 − σ̂5 .Ω)
2 f

• σ̂1 σ σ̂2 σ2 1
.i − 1 .i + ..ωe isq − .ωe isq + .Vsd
e e
χ3 = (30)
σ2 sd σ2 sd σ2 σ2 σ2
The control laws are formulated to achieve stabilization of the dynamic current errors
in the subsequent manner:

Vsd_re f = −σ̂1 .isd − σ̂2 .ωe .isq − σ̂2 .k3 .χ3 (31)

Vsq_re f = −σ̂1 .isq + σ̂2 .ωe .isd + ωe .Ψ f + σ̂2 .k2 .χ2

 • 
•
 
σ̂3
 32 .p.Ψ f − k .χ
1 1 − Ω re f + σ̂ 4 − σ̂5 .Ω 
 
• •• • •
  (32)
−σ̂2 . + 3 σ̂3 Ω Ω
 
− k 1 . re f − re f + σ̂ 4 − σ̂ 5 .Ω 
2 .p.Ψ f
 
 σ̂3

−(k1 − σ̂5 ).isq + 3 .(k1 − σ̂5 )(σ̂4 − σ̂5 .Ω)
2 .p.Ψ f

where in k1 , k2 and k3 represent positive constants.

By substituting the values of the stator voltages defined in Equations (31) and (32) into
Equations (29) and (30), we obtain
•
χ2 = −k2 .χ2 − eσσ12 .isq + eσσ22 .ωe .isd + k2 .χ2 . eσσ22 − eσσ33 (k1 − σ̂5 ).isq
σ̂3
− 3 .p.Ψ (k1 − σ̂5 )(e σ4 − eσ5 )
2  f
• 
•
 
σ̂3
 32 .p.Ψ f − k .χ
1 1 − Ω re f + σ̂4 − σ̂5 .Ω  (33)
• •• • •
   
σ2 
+ σ2  + 3 σ̂3 −k1 .Ωre f − Ωre f + σ̂4 − σ̂5 .Ω
e 

 2 .p.Ψ f

 σ̂3

−(k1 − σ̂5 ).isq + 3 (k1 − σ̂5 )(σ̂4 − σ̂5 .Ω)
2 .p.Ψ f

• σ1 σ2 σ2
χ3 = −k3 .χ3 − .i − .ωe isq − .k3 .χ3
e e e
(34)
σ2 sd σ2 σ2
Energies 2023, 16, 7481 10 of 28

3.1.4. Parameter Adaptation and Analysis of Stability

The concluding stage entails establishing the adaptation laws governing the param-
eters. To accomplish this, a novel Lyapunov function is introduced, characterized by
adaptation gains, as expressed by the following equation:
!
1 2 2 2 σ̂12 σ̂22 σ̂32 σ̂42 σ̂52
γ3 = χ1 + χ2 + χ3 + + + + + (35)
2 σ2 .ň1 σ2 .ň2 σ3 .ň3 ň4 ň5

where ňi (i = 1, 2, 3, 4, 5) correspond to the affirmative adaptation gains.

The temporal derivative of Equation (35) yields
• • • • •
• • • • σ̂1 .σ̂1 σ̂2 .σ̂2 σ̂3 .σ̂3 σ̂4 .σ̂4 σ̂5 .σ̂5
γ3 = χ1 .χ1 + χ2 .χ2 + χ3 .χ3 + σ2 .ň1 + σ2 .ň2 +  σ3 .ň3 + ň4 + ň5
3 .p.Ψ • 
f
= −k1 .χ21 − k2 .χ22 − k3 .χ23 − 2
σ3 .χ .χ
1 2 + σ1 σ̂1
− isd .χ3 − isq .χ2
e
σ2 ň1
 • • 
•
 
 ň2
σ̂2
− χ .ω
3 e sq.i + χ 2 . ( ω .i
e sd − χ .χ
1 2 ) + σ̂3
3 .p.Ψ . − k .χ
1 1 − Ω re f + σ̂ 4 − σ̂5 .Ω
2 f

+ eσσ22  
• •• • •
 (36)
. −k1 .Ωre f − Ωre f + σ̂4 − σ̂5 .Ω − (k1 − σ̂5 ).isq + 3 σ̂3 .(k1 − σ̂5 )(σ̂4 − σ̂5 .Ω)
 σ̂3 
+ 3 .p.Ψ
• 2 f 2 .p.Ψ f
•
  
+ σ3 ň3 + χ1 −k1 .Ω − Ωre f + σ̂4 − σ̂5 .Ω − (k1 − σ̂5 ).isq .χ2
e σ3 σ̂3
•  • 
σ̂4 σ̂3 σ̂5 σ̂3
σ4 ň + χ1 − 3
+e .(k1 − σ̂5 ).χ2 + e σ5 ň − χ1 .Ω + 3 .(k1 − σ̂5 ).χ2 .Ω
4 2 .p.Ψ f 5 .p.Ψ 2 f

The parameters’ adaptation laws are structured in a manner that ensures the derivative of
the Lyapunov candidate function is consistently negative, as depicted below:
•

σ̂1 = −ň1 −isd .χ3 − isq .χ2 (37)
 
χ3 .ωe .isq+ χ2 (−ωe .isd + χ1 χ2 )
• •

k1 .χ1 − Ωre f + σ̂4 − σ̂5 .Ω +
 
 + 3 σ̂3 − 
• 2 .p.Ψ f
 
σ̂2 = −ň2  σ̂  (38)
 
• •• • •

 2 .p.Ψ f −k1 .Ωre f − Ωre f + σ̂4 − σ̂5 .Ω

 3 3 

 
−(k1 − σ̂5 ).isq + 3 σ̂3 (k1 − σ̂5 )(e σ4 − e
σ5 .Ω)
2 .p.Ψ f

• •
   
σ̂3 = −ň3 χ1 −k1 .Ω − Ωre f + σ̂4 − σ̂5 .Ω − (k1 − σ̂5 ).isq .χ2 (39)

" #
• σ̂3
σ̂4 = −ň4 χ1 − 3 (k1 − σ̂5 ).χ2 (40)
2 .p.Ψ f
" #
• σ̂
σ̂5 = −ň5 −χ1 .Ω + 3 3 (k1 − σ̂5 ).χ2 .Ω (41)
2 .p.Ψ f

Ultimately, the evolution of the Lyapunov function’s dynamics can be described as

3
• 2 .p.Ψ f
γ3 = −k1 .χ21 − k2 .χ22 − k3 .χ23 − .χ1 .χ2 ≤ 0 (42)
σ3

The configuration of the adaptive nonlinear backstepping control for PMSG is illus-
trated in Figure 1.
 Ultimately, the evolution of the Lyapunov function’s dynamics can be described as
3
• . p.Ψ f
γ 3 = −k1.χ12 − k2 .χ 22 − k3.χ32 − 2 .χ1.χ 2 ≤ 0 (42)
σ3
Energies 2023, 16, 7481 11 of 28
The configuration of the adaptive nonlinear backstepping control for PMSG is illus-
trated in Figure 1.

Figure 1. Block Diagram of Adaptive Backstepping Control.

Figure 1. Block Diagram of Adaptive Backstepping Control.
3.1.5. Control of the Grid-Side Converter
3.1.5. Control of the Grid-Side Converter
The inverter plays a crucial role as a static converter within the conversion chain,
The inverter plays a crucial role as a static converter within the conversion chain,
simplifying the management of the energy flow injected into the electrical grid. Control of
simplifying the management of the energy flow injected into the electrical grid. Control
the grid-side inverter primarily focuses on two essential parameters [31]: regulating the
of the grid-side inverter primarily focuses on two essential parameters [31]: regulating the
intermediate bus voltage and achieving a unity power factor.
intermediate bus voltage and achieving a unity power factor.
The dynamics of grid currents and the transferred power are depicted within the
The dynamics of grid currents and the transferred power are depicted within the
context of a rotating reference frame, as outlined below:
context of a rotating reference frame, as outlined below:

 d(i gd ) = 1 Vf d − Vgd − R f .i gd + ω g . L f .i gq
h  i

dt Lf
(43)
 d(i gq ) = 1 Vf q − Vgq − R f .i gq − ω g . L f .i gd − ωe .Ψ f
h   i

dt fL

 h i
 Pg = 3 Vgd .i gd + Vgq .i gq
2h i (44)
 Q g = 3 Vgq .i gd − Vgd .i gq
2

As is evident from Equations (43) and (44), it becomes evident that electrical powers
exhibit a direct proportionality with the network’s current components. This observation
paves the way for the design of backstepping control, structured upon the ensuing steps:
The disparities in the magnitudes of grid currents are precisely delineated through the
subsequent expressions:

ξ gq = i gq_re f − i gq
(45)
ξ gd = i gd_re f − i gd
The dynamics inherent in these errors, in accordance with Equation (45), can be
derived as follows: •
 ξ = •i •
gq gq_re f − i gq
(46)
ξ• = •i −
•
i
gd gd_re f gd
Energies 2023, 16, 7481 12 of 28

The Lyapunov candidate function is represented in the subsequent format:

1 2 1
γg = ξ + ξ2 (47)
2 gd 2 gq
Its time derivative is given by

• • •
γ g = ξ gd .ξ gd + ξ gq .ξ gq (48)

By inserting the current dynamics outlined in the system of Equation (43) into the
expression of Equation (48), the resultant expression becomes
• ξ
   
γ g = −k g1 .ξ 2gd − k g2 .ξ 2gq + Lgd Vf d − Vgd − R f .i gd + ω g . L f .i gq + k g1 .L f .ξ gd
f 
ξ
   (49)
+ Lgq Vf q − Vgq − R f .i gq − ω g . L f .i gd − ωe .Ψ f + k g2 .L f .ξ gq
f

For the purpose of establishing system stability in energy injection into the network, it
is imperative to adopt positive values for kg1 and kg2 . Additionally, the reference voltages
administered to the grid-side converter (GSC) should be determined in alignment with the
system described by Equation (50):

Vf d_re f = Vgd + R f .i gd − L f .ω g .i gq − L f .k g1 .ξ gd
(50)
Vgq_re f = Vgq + R f .i gq + L f .ω g .i gd − L f .k g2 .ξ gq

The determination of reference values for the direct and quadrature components of
the grid current is guided by
 igd_ref = 0: This choice ensures the elimination of reactive power, thereby facilitating
the transmission of electrical power to the grid with the power factor of unity.
 igq_ref : The DC bus voltage regulation is pursued to enable the management of the
active power transfer to the electrical grid.
Illustrated in Figure 1 is the layout of the adaptive nonlinear backstepping control
framework for PMSG. Within this diagram, Vsd_ref and Vsq_ref denote the target voltage
references directed towards the static converter on the machine side. Furthermore, Vgd_ref
and Vgq_ref signify the reference voltages employed for the grid static converter.
The values of the current and rotational speed errors are clearly illustrated and men-
tioned in the text through Equations (11) and (18), while the estimated values of the various
parameters are indicated in the text using Equations (24)–(26).

4. Performance Test Using Matlab–Simulink

4.1. Performance Test
The efficacy of the adaptive backstepping control technique in the context of wind
power conversion utilizing a PMSG was substantiated through numerical simulations
carried out within the Matlab/Simulink environment. Appendix A furnishes the specific
parameters pertaining to the wind system, encompassing both the turbine and PMSG
components. A comprehensive array of tests was executed to assess and contrast the per-
formance of the regulation between the conventional proportional–integral (PI) controllers
and the innovative adaptive backstepping control approach.
The comparative evaluation encompasses a spectrum of assessments, including re-
silience against perturbations, accuracy in tracking set-points and susceptibility to exter-
nal disturbances.

4.2. Discussion of Results

Based on the outcomes gleaned from the wind-induced step test, a discernible trend
emerges in the context of electromagnetic torque, power dynamics and rotational speed
adjustments. This test scenario, illustrated in Figure 2a, entails abrupt changes occurring
Energies 2023, 16, 7481 13 of 28

Energies 2023, 16, x FOR PEER REVIEW 17 of 33

at t = 2 s, t = 4 s, t = 6 s and t = 8 s. These fluctuations serve to test the system’s resilience
when confronted with sudden external disturbances.

(a) Step wind speed profile

(b) Mechanical rotation speed (c) Direct stator currents isd

(d) Quadrature stator currents isq (e) Stator currents

(f) Three-phase grid currents (g) Stator voltages

Figure 2. Cont.
Energies 2023, 16, 7481
Energies 2023, 16, x FOR PEER REVIEW
14 of 28
18 of 33

(h) three-phase currents injected and grid voltages (i) Active power transmitted

(j) Reactive power transmitted (k) DC bus voltage

Energies 2023, 16, x FOR PEER REVIEW 19 of 33

(l) Electromagnetic torque (m) Power factor

FFT analysis FFT analysis

Fundamental (50Hz) = 299 , THD= 2.41% Fundamental (50Hz) = 468.6 , THD= 0.38%
10 10

9 9
0.7 0.5
8 8
0.6
7 7 0.4
0.5
6 6 0.3
0.4
5 5
0.3
0.2
4 4
0.2
0.1
3 0.1 3

2 0 2 0
0 5 10 15 20 0 5 10 15 20
1 1

0 0
0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20
Harmonic order Harmonic order

(n) FFT analysis PI controller (o) FFT Analysis backstepping algorithm

Figure 2. Performance Testing for the Adaptive Backstepping Control.
Figure 2. Performance Testing for the Adaptive Backstepping Control.
The mechanical rotational speed exhibits optimal adherence to the reference value,
as showcased in Figure 2b, demonstrating the minimal response time to align with the
specified speed. The adaptive control methodology effectively curtails the static error,
markedly outperforming the traditional PI regulation, as depicted in the same figure.
Energies 2023, 16, 7481 15 of 28

The mechanical rotational speed exhibits optimal adherence to the reference value,
as showcased in Figure 2b, demonstrating the minimal response time to align with the
specified speed. The adaptive control methodology effectively curtails the static error,
markedly outperforming the traditional PI regulation, as depicted in the same figure.
Figure 2c,d portray the waveforms of the direct and quadrature stator currents, isd and
isq , respectively. These results unveil a synchronization of currents with their designated
set-points, characterized by a response time congruent with the system’s dynamics. Ad-
ditionally, Figure 2e captures the three-phase currents generated by the stator windings.
In the magnified view within Figure 2e, the waveforms exhibit a commendable level of
quality. Notably, the frequency of these currents maintains a proportional relationship
with the mechanical rotational speed. This underscores the necessity of integrating static
converters between the PMSG and the grid in variable speed wind turbine technology. This
integration serves to precisely adjust the quantity of electricity transmitted to the grid.
Figure 2f reveals the presentation of three-phase currents injected into the electrical
grid. Evidently, the quality of these currents surpasses that of the stator currents. The
waveform’s periodicity of 20 ms harmoniously aligns with a frequency of 50 Hz, sufficiently
meeting the requirements of the electrical network, as magnified within Figure 2f.
Illustrated in Figure 2g are the phase-to-phase voltages characterizing the three-phase
stator windings. The configuration of the voltage curves directly stems from the switching
of electronic components within the machine-side converter. The figure’s close-up view
demonstrates a phase-to-phase stator voltage boasting an amplitude of 5000 V.
The electric current injected into the grid is an outcome of the active power generation.
The waveform of this current adheres remarkably well to network code prerequisites con-
cerning frequency and quality, as evident in both Figure 2f,h. The alignment of the current
with the mains voltage remains consistently maintained, as indicated by the concurrent
current/voltage graph in Figure 2h. A phase shift nearly approaching zero is discernible,
contributing to an operation characterized by a power factor approaching unity.
Noteworthy is the seamless synchronization between electrical active power and the
evolution of mechanical drive power, exhibiting minimal ripple. This attribute remains
exceptionally acceptable within the adaptive backstepping control framework, especially
when considering the generator’s substantial power rating, approximately 1500 KW, and
its pronounced inertia. As displayed in Figure 2i, this power evolution demonstrates a
remarkable continuation in steady-state, underscored by an improved response time in
dynamic conditions, quantified at 10 ms. The ripples attributed to the adaptive control
remain notably subdued compared to conventional control methodologies, as is visually
represented in the same figure.
The system depicted in Figure 1 is simulated with the objective of delivering zero
reactive power, thereby harnessing clean power generation and achieving the unity power
factor. However, as depicted in Figure 2m, the power factor, though typically near unity,
demonstrates fluctuations that correlate with variations in the active power output. Such
fluctuations in reactive power regulation are expected when active power levels undergo
changes, as depicted in the graph of Figure 2j. Even a minor variation of ∆Qgen = 15Kvar,
observed in the zoomed graph of Figure 2j, induces a slight alteration in the power factor
for both control types, although adaptive control showcases a slight enhancement.
Figure 2k offers insight into the behavior of the intermediate DC bus situated between
the two static converters (rectifier and inverter). This intermediate system effectively
maintains a constant voltage, UDC, at the terminals of the two converters. While there
exists a variation in the intermediate DC voltage attributed to fluctuations in active power
generation, the deviation of ∆UDC = 4V, observed in the zoomed graph of Figure 2k,
remains within acceptable limits, constituting a mere 0.08% deviation with respect to the
nominal voltage value. The minor initial overshoot discernible in the same figure’s zoomed
view, not exceeding 0.26%, alongside the estimated response time of approximately 15 ms,
affirms the exceptional performance exhibited by the DC bus voltage regulator.
Energies 2023, 16, 7481 16 of 28

The electromagnetic torque, depicted in Figure 2l, tracks its reference value with
precision, bearing a comparable absolute value to the generated active power. In terms of
speed and static error management, adaptive control demonstrates commendable results
when juxtaposed with conventional control methodologies, as evidenced by the zoomed
view in Figure 2l.
To offer a more comprehensive perspective on the quality of the energy produced
and supplied to the grid, a spectral analysis of the harmonic content within the injected
current is conducted. Figure 2n,o present the outcomes of this analysis for both classic
and adaptive control approaches, respectively. The total harmonic distortion (THD) of the
current is measured at 2.41% for classic vector control and 0.38% for adaptive backstepping
control, encompassing two operational cycles and up to a maximum frequency of 1000 Hz.
The THD achieved through the adaptive control method remains notably competitive and
aligns completely with the “IEEE-519” standard, which stipulates a THD requirement of
less than 5% for grid-injected currents [11].
A comparative analysis was conducted between the two control algorithms within
the context of this performance test simulation for the wind system powered by a PMSG.
Table 1 provides an overview of the key facets encompassing this comparison.

Table 1. Comparative analysis between FOC and backstepping adaptive controllers.

Controller Type FOC Backstepping

Coordinate transformation Required Required
Torque ripple Medium Low
Currents ripple Medium Low
Reference tracking Medium Better
THD (%) 2.41 0.38
Facility of implementation Simple Complex
Algorithm complexity Low Complex

A subsequent comparative investigation contrasting the outcomes yielded by the

proposed control algorithm with those of other studies is detailed in the subsequent table.
Table 2 additionally offers a comprehensive breakdown of the technical specifications, along
with the distinct advantages and disadvantages associated with each control technique.

Table 2. Performance comparison.

Publication Paper [32] [32] [33] [34] [35] Proposed Algorithm

Technic methods (FOPI) (FFOPI+I) (ADRC) (SMC) RTO-PI (ABC)
DFIG DFIG PMSG
Generator used PMSG PMSG DFIG
(1.5 MW) (4 KW) (1.5 MW)
Overshoot (%) 12 4 21 - 1 0.26
THD (%) 4.5 4 - 3.99 3.21 0.38
Response time (ms) - - 27 549 - 10
Power factor 0.974 0.994 - - 0.978 0.997
Facility of
Simple Moderate–simple Moderate–simple Simple Moderate–high Complex
implementation
Algorithm
Medium Medium Medium Medium Complex Complex
complexity
performance Low Moderate–high Low Low Moderate–high High

In order to make a valid comparison between several studies, it is necessary to have the
same simulation conditions and the same parametric quantities. However, achieving this is
not always feasible, and it would be a challenging endeavor. Nevertheless, by conducting
an indicative comparison based on a few well-defined parameters, we can extract the main
characteristics for each control algorithm and discern the primary advantages of each study.
Table 2 serves as a comprehensive juxtaposition of control algorithm outcomes from a
selection of published studies involving two types of wind generators. Upon scrutinizing
the displayed outcomes, a conspicuous trend emerges: the proposed control algorithm
devised for regulating the wind energy conversion system (WECS) based on the 1.5 MW
Energies 2023, 16, 7481 17 of 28

PMSG consistently yields superior results in comparison to various other control strategies.
This ascendancy is notably evident across multiple fronts, including robustness, speed,
and energy quality. The system’s elevated power factor, coupled with a remarkably low
total harmonic distortion (THD) that remains below 0.38%, unequivocally validates the
efficacy of the chosen approach. This reaffirms that the adaptive backstepping control
methodology stands out as a premier contender in the realm of the wind energy conversion
system (WECS) control.

5. Experimental Validation
5.1. Description of Experimental Platform
The results of this approach were obtained using the dSPACE 1104 board in conjunction
with Matlab–Simulink for processor-in-the-loop (PIL), a commonly employed method for
real-time validation of embedded control systems. Subsequently, the key steps for this
experimental validation are as follows:
 Modeling in Matlab–Simulink: Initially, the control system, including the model of
the wind turbine’s electrical system, as well as the adaptive backstepping controller,
was modeled within the Matlab–Simulink environment. This modeling encompasses
all the equations and components necessary to accurately represent the system.
 Real-time Simulation: In the simulation stage, the authors executed the Simulink
model in real-time mode. This means that the Simulink model operates with strict
temporal synchronization, simulating the real-time behavior of the wind turbine’s
electrical system.
 Interface with the dSPACE 1104 board: The dSPACE 1104 board was utilized to
interface the real-time Simulink model with the physical hardware. The dSPACE board
is capable of reading signals generated by the Simulink model and converting them
into physical signals that can be used to control the real system, such as controllers or
for display on an oscilloscope.
 Real-time Execution: The real-time Simulink model was executed on the dSPACE
1104 board, which acts as a real-time processor. This real-time execution enables
the testing and validation of the adaptive backstepping controller under conditions
closely resembling reality, with signals observed on an oscilloscope.
 Data Collection and Analysis: During real-time execution, the authors collected
data on the system’s behavior, including control signals and some physical signals.
These data were subsequently analyzed to assess the performance of the adaptive
backstepping controller and to compare the results with the research objectives.
The experimental platform was established using the dSPACE DS1104 prototyping
platform, which encompasses the following components [36]:
 DSPACE 1104 kit integrated into a computer.
 DS1104 board connection panel.
 Host PC equipped with the Matlab/Simulink environment and Control-Desk
7.6 software.
 Voltage level adaptation probe.
 Oscilloscope for visualizing various analog signals.
To validate and test the control algorithms, a series of essential steps are considered
necessary. In this current study, validation through a real-time simulation was implemented
to demonstrate the high performance and confirm the algorithm’s effectiveness in a real
installation scenario.
The procedure encompasses the subsequent stages:
 Developing the control system via the Simulink modeling tool.
 Conducting simulations to generate a range of control results.
 Transferring the program as C code to dSPACE using the Real-Time Workbench
(RTW) utility.
 Executing the comprehensive model in real-time via the DS1104 R&D board.
 Energies 2023, 16, x FOR PEER REVIEW 22 of 32

Energies 2023, 16, 7481  Developing the control system via the Simulink modeling tool. 18 of 28
 Conducting simulations to generate a range of control results.
 Transferring the program as C code to dSPACE using the Real-Time Workbench
(RTW) utility.
5.2. dSPACE
 1104 the
Executing Digital Processing
comprehensive System
model in real-time via the DS1104 R&D board.
The processor board, manufactured by the German company dSPACE, is outfitted
5.2. dSPACE 1104 Digital Processing System
with an MPC8240 main processor operating at a clock frequency of 250 MHz [37]. Addi-
The processor board, manufactured by the German company dSPACE, is outfitted
tionally,
witha an
complementary software
MPC8240 main processor knownatasa clock
operating “Control-Desk”
frequency of 250facilitates
MHz [37].the construction of
Addi-
a graphical
tionally,interface, streamlining
a complementary real-time
software known visualization
as “Control-Desk” of diverse
facilitates parameters.
the construction
of a graphical
The interface,
interlinkage streamlining
between real-time visualization
the dSPACE board and of thediverse
windparameters.
energy conversion system,
centered on Thethe
interlinkage
PMSG, between the dSPACE
is succinctly board and
portrayed the wind
in Figure 3. energy conversion sys-
tem, centered on the PMSG, is succinctly portrayed in Figure 3.

Figure 3. Connection diagram of dSPACE with the WECS.

Figure 3. Connection diagram of dSPACE with the WECS.

5.3. Results of Implementing the Adaptive Backstepping Control

Figure 3 presents the overall block diagram of the wind system controlled by the
adaptive control algorithm, managed by the dSPACE prototyping board. The control
signals regulate both converters (rectifier/inverter) simultaneously. Table 3 presents the
parameters utilized for this real-time simulation.

Table 3. Parameters used in simulation.

Parameter Value
DC bus voltage 5000 V
DC Bus Capacitor 20 mF
Filter resistance 0.20 mΩ
Filter inductance 10 mH
Sampling frequency 10 KHz
Grid frequency 50 Hz
 Energies 2023, 16, x FOR PEER REVIEW 23 of 32

Energies 2023, 16, 7481 19 of 28

5.3. Results of Implementing the Adaptive Backstepping Control

InFigure 3 presents
order to the overall
substantiate blockofdiagram
the efficacy of theadaptive
the proposed wind system controlled
control bythrough
algorithm the
adaptive control algorithm, managed by the dSPACE prototyping board. The control
real-time simulation, two comprehensive tests are slated for execution. The primary test sig-
is nals regulate both converters (rectifier/inverter) simultaneously. Table 3 presents the pa-
designed to underscore the control’s robustness amidst a wind profile characterized
rameters utilized for this real-time simulation.
by step changes. The subsequent test is tailored to spotlight the control’s adeptness in
maintaining tracking
Table 3. Parameters usedaccuracy and overall efficiency amid the presence of erratic and
in simulation.
extensively variable wind conditions. The execution of these assessments is facilitated by
the dSPACE DS1104 Parameter
board and the Control-Desk development tool,Value
adept at capturing the
DC bus voltage
diverse array of signals of interest. 5000 V
DC Bus Capacitor 20 mF
5.3.1. PerformanceFilter
Test resistance
for Wind Steps 0.20 mΩ
The first testFilter inductance
involves 10 mH The changes occur
the presence of wind variations in steps.
every 2 s, aimingSampling
to assessfrequency 10 KHz
the algorithm’s performance in response to sudden wind shifts.
The average windGrid frequency
speed 50 Hz about the turbine
is approximately 7 m/s. For further details
model and PMSG parameters, please refer to Table A1 in Appendix A. The outcomes of
this testInare
order to substantiate
summarized below.the efficacy of the proposed adaptive control algorithm
through real-time simulation, two comprehensive tests are slated for execution. The pri-
mary
5.3.2. test is designed
Set-Point TrackingtoTest
underscore the control’s
in Fluctuating Windrobustness amidst a wind profile char-
acterized by step changes. The subsequent test is tailored to spotlight the control’s adept-
The subsequent evaluation involves a second test conducted under the influence
ness in maintaining tracking accuracy and overall efficiency amid the presence of erratic
of fluctuating and exceedingly variable wind conditions, aimed at assessing tracking
and extensively variable wind conditions. The execution of these assessments is facilitated
performance. Throughout this test, a consistent sampling frequency of fe = 10 KHz is
by the dSPACE DS1104 board and the Control-Desk development tool, adept at capturing
upheld. A comprehensive
the diverse overview
array of signals of interest. of the diverse graphical representations obtained
during this evaluation is succinctly depicted in Figure 4.

(a) Step wind speed profile

(b) Mechanical rotation speed (c) Direct stator currents isd

Figure 4. Cont.
Energies 2023, 16, 7481 20 of 28
Energies 2023, 16, x FOR PEER REVIEW 24 of 32

(d) Quadrature stator currents isq (e) Stator currents

(f) Grid currents (g) Stator voltages

(h) Injected currents and grid voltages (i) Active power transmitted to the grid

(j) Reactive power transmitted to the grid (k) DC bus voltage

Figure 4. Cont.
Energies 2023,
Energies 16,16,
2023, 7481
x FOR PEER REVIEW 25 21
of of
3228

(l) Electromagnetic torque (m) Power factor

Figure 4. Performance test for wind in step.
Figure 4. Performance test for wind in step.

5.3.3.Discussion
5.3.3. Discussion of of Experimental Results Results
Analyzingthe
Analyzing theoutcomes
outcomesofofthe theinitial
initialtest
testcharacterized
characterizedbybya astepwise
stepwisewind wind profile,
profile, the
the wind’s
wind’s oscillations
oscillations occurring
occurring every every 2 s within
2 s within a 10 as span,
10 s span, as visualized
as visualized in Figure
in Figure 4a
4a show-
showcasing
casing the chosen
the chosen windwind profile,
profile, revealreveal a distinct
a distinct synchronization
synchronization among
among thethemechanical
mechan-
ical speed,
speed, statorstator
currents currents and generated
and generated activeactive
power. power. Evidently,
Evidently, as illustrated
as illustrated in Figure
in Figure 4b–d,i,
4b–d,i, these results underscore the convergence of these dynamics.
these results underscore the convergence of these dynamics. Remarkably, when scrutiniz- Remarkably, when
scrutinizing
ing the arraythe of array
graphs,of graphs,
the adaptivethe adaptive
controlcontrol
algorithmalgorithm consistently
consistently manifests
manifests el-
elevated
evated performance and noteworthy quality outcomes, demonstrating
performance and noteworthy quality outcomes, demonstrating a definitive edge over the a definitive edge
over the conventional
conventional control methods.
control methods.
Figure 4c,d
Figure 4c,d delineate
delineatethe theregulation
regulation of ofthethe
direct
directandandquadrature
quadrature statorstator
currents, re-
currents,
spectively. These
respectively. Thesegraphical
graphicalrepresentations
representationsaffirm affirmthat
thatthe
thebackstepping
backstepping control
control strategy
strategy
achievesprecise
achieves precise tracking
tracking withwith minimal
minimal oscillations.
oscillations.While Whilethe thethree-phase
three-phasestator statorcurrents
currents
presentedininFigure
presented Figure4e 4eexhibit
exhibitaapseudo-sinusoidal
pseudo-sinusoidalpattern, pattern,their
theiragile
agileresponse
responseto totransient
transi-
ent shifts is evident. Notably, the switching of electronic components
shifts is evident. Notably, the switching of electronic components within the static converter within the static
converter contributes to a pronounced harmonic content.
contributes to a pronounced harmonic content. Additionally, the depicted waveform’s Additionally, the depicted
waveform’s
period alignsperiod
with an aligns with an approximate
approximate duration of 100 duration
ms. of 100 ms.
Figure 4f visually depicts the injected current waveformswithin
Figure 4f visually depicts the injected current waveforms withinthe theelectrical
electricalgrid.
grid.AA
discernible sinusoidal nature characterizes these currents compared
discernible sinusoidal nature characterizes these currents compared to those generated by to those generated by
thesynchronous
the synchronousgenerator.
generator.Notably,
Notably,the the zoomed-in
zoomed-in section
section of of
thethesamesame figure
figure under-
underscores
scores
the the rigorous
rigorous adherence adherence
to the to the grid’s
grid’s periodicity
periodicity and and frequency
frequency requisites,
requisites, maintain- a
maintaining
ing a period
20ms 20ms period
congruent congruent
with thewith the network’s
network’s 50 Hz50frequency.
Hz frequency.
The portrayal of three-phase stator voltages takescenter
The portrayal of three-phase stator voltages takes centerstage
stageininFigure
Figure4g.4g.These
These
voltage profiles assume a rectangular shape due to the electronic switch’s switchinginin
voltage profiles assume a rectangular shape due to the electronic switch’s switching thethe
machine-side converter. The zoomed-in segment of the same
machine-side converter. The zoomed-in segment of the same figure distinctly showcases a figure distinctly showcases
a phase-to-phase
phase-to-phase voltage
voltage reading
reading ofof 5000V.V.
5000
As clearly depicted in the combined graph
As clearly depicted in the combined graphof ofgrid
gridvoltages
voltagesand andinjected
injectedcurrents
currents inin
Figure 4h, a coherent temporal alignment between the three-phase
Figure 4h, a coherent temporal alignment between the three-phase voltages and currents is voltages and currents
is observable,
observable, resulting
resulting in ainphase
a phase shiftshift of zero
of zero andand thereby
thereby ensuring
ensuring operation
operation withwith a
a unity
unity power factor. This synchronization is maintained impeccably,
power factor. This synchronization is maintained impeccably, as indicated by the consistent as indicated by the
consistent
50 Hz frequency50 Hz displayed
frequency in displayed in the zoomed-in
the zoomed-in section of section
Figure 4h.of Figure 4h.
Figure 4i offers insight into the injected active power withinthe
Figure 4i offers insight into the injected active power within thepower
powergrid.grid.With
With thethe
wind speed in flux, the mechanical drive power undergoes
wind speed in flux, the mechanical drive power undergoes near-instantaneous changes, near-instantaneous changes,
consequently impacting
consequently impactingthe theactive
activepowerpower delivered
delivered to the
to grid. Remarkably,
the grid. Remarkably,this synchro-
this syn-
nization between the speed and Figure 4i remains consistently upheld. Noteworthy adept-
chronization between the speed and Figure 4i remains consistently upheld. Noteworthy
ness in tracking the reactive power is evidenced by Figure 4j, wherein the reactive power
adeptness in tracking the reactive power is evidenced by Figure 4j, wherein the reactive
closely follows its null reference while maintaining a low value, evaluated at 20 Kvar. This
power closely follows its null reference while maintaining a low value, evaluated at 20 Kvar.
This precise tracking culminates in the injection of predominantly active power into the
electrical grid. The relatively modest level of reactive power, relative to the active power
Energies 2023, 16, x FOR PEER REVIEW 26 of 32

As clearly depicted in the combined graph of grid voltages and injected currents in
Energies 2023, 16, 7481 Figure 4h, a coherent temporal alignment between the three-phase voltages and currents 22 of 28
is observable, resulting in a phase shift of zero and thereby ensuring operation with a
unity power factor. This synchronization is maintained impeccably, as indicated by the
consistent 50 Hz frequency displayed in the zoomed-in section of Figure 4h.
supplied to the grid, contributes to a power factor nearing unity. Figure 4m charts the
Figure 4i offers insight into the injected active power within the power grid. With the
behavior of the power factor during a step change in wind conditions, demonstrating a
wind speed in flux, the mechanical drive power undergoes near-instantaneous changes,
remarkable value of (cosϕ > 0.99) for the backstepping control.
consequently impacting the active power delivered to the grid. Remarkably, this synchro-
The simulation outcomes unveil the regulatory impact on the DC bus voltage, as is
nization
evident in between
Figure the speed
4i. The and Figure
voltage at the4i remains consistently
inverter’s input closelyupheld.
followsNoteworthy
the referenceadept-
value
ness
set at 5000 V. The regulator’s effectiveness is discernible from the swift signalreactive
in tracking the reactive power is evidenced by Figure 4j, wherein the responsepower
time
closely follows its null reference while maintaining a low value,
and minimal overshooting, confined within +/−2 V, as highlighted in the zoomed section evaluated at 20 Kvar. This
precise
of Figure tracking
4i. Whileculminates in the injection
electromagnetic torque still ofexhibits
predominantly active power
notable ripples, into the
the adaptive elec-
control
trical grid. The relatively modest level of reactive power, relative
strategy showcases an improved performance in electromagnetic torque, as visualized to the active power sup-in
plied to
Figure 4j. the grid, contributes to a power factor nearing unity. Figure 4m charts the behav-
ior ofTurning
the power factor
to the duringofa the
outcomes stepsecond
change in wind
test, whichconditions, demonstrating
involves fluctuating a remark-
wind conditions,
able value of (cosφ > 0.99) for the backstepping control.
as illustrated in Figure 5a, it is unmistakable that all variables align closely with their
The simulation
reference outcomesnoteworthy
values. Particularly unveil the regulatory impact on
is the mechanical the DC
rotation bus voltage,
speed’s precisionas in
is
evident in Figure 4i. The voltage at the inverter’s input closely
tracking its reference value, a trait prominently pronounced in the regulation achievedfollows the reference value
set at 5000
through theV.adaptive
The regulator’s effectiveness
control, as evidenced in is Figure
discernible
5b. from the swift signal response
time and
In another scenario, the distinct patterns of the as
minimal overshooting, confined within +/−2V, highlighted
currents in theby
generated zoomed sec-
the stator
tion of Figure
windings 4i.synchronous
of the While electromagnetic
generator adopt torqueastill exhibits notableshape.
pseudo-sinusoidal ripples, the adaptive
These patterns
control
exhibit strategy
varying showcases
periods that an correspond
improved performance
to fluctuations in electromagnetic
in wind speed,torque, as visu-
as depicted in
alized
Figurein5c.Figure 4j.
The approximate period of the three-phase stator currents measures around
Turning
100 ms. to the outcomes
In contrast, the shapesofofthe thesecond test, which
three-phase involves
currents injectedfluctuating windadopt
into the grid condi-a
tions, as illustrated
more sinusoidal in Figure
form, 5a, it istounmistakable
conforming the requirements that all variables
of the IEEE-519 align closely with
standard. their
Figure 5d
reference
illustratesvalues. Particularly
the waveforms noteworthy
of the currents injectedis the into
mechanical rotation
the electrical speed’s
network, withprecision
a focusedin
tracking its reference value,
section underscoring a trait prominently
the high-quality waveformpronounced
and confirming in thea regulation achieved
consistent period of
20 ms. the adaptive control, as evidenced in Figure 5.2.
through

(a) Wind speed profile

(b) Mechanical rotation speed (c) Stator currents

Figure 5. Cont.
Energies 2023, 16, 7481
x FOR PEER REVIEW 2723of
of 32
28

(d) Grid currents (e) Stator voltages

(f) Injected currents and grid voltages (g) Active power transmitted

(h) Reactive power transmitted (i) DC bus voltage

(j) Electromagnetic torque (k) Power factor

Figure 5. Set-point tracking test in fluctuating wind.

Figure 5. Set-point tracking test in fluctuating wind.
In another scenario, the distinct patterns of the currents generated by the stator wind-
Similarly, during this second test, the characteristic rectangular shape of the phase-
ings of the synchronous generator adopt a pseudo-sinusoidal shape. These patterns ex-
to-phase voltages at the stator winding terminals, set at 5000 V, remains conspicuous, as
hibit varying
showcased inperiods thatFurthermore,
Figure 5e. correspond to fluctuations
Figure in wind
5f presents speed, as depicted
the temporally in Figure
aligned shapes of
5c. The approximate period of the three-phase stator currents measures around 100 ms. In
Energies 2023, 16, 7481 24 of 28

the three currents injected into the grid alongside their corresponding grid voltages. The
minimal phase discrepancy between the current and voltage waveforms contributes to a
power factor approaching unity. This phenomenon is even more pronounced in Figure 5k,
which illustrates the measured power factors for both the vector control and backstepping
algorithms. As is evident in Figure 5k, the adaptive control attains a power factor of cosϕ
' 0.995, surpassing the vector control’s cosϕ ' 0.973.
The precision of active power adherence to its mechanical reference is effectively
showcased in Figure 5g. A closer examination of this power behavior, displayed within the
same figure, reaffirms the adaptive control’s capability in maintaining precise active power
regulation. In contrast, the reactive power remains nearly perfectly regulated towards its
zero reference. The marginal variation of reactive power within approximately ± 20Kvar,
as observed in Figure 5h for a 1500 KW synchronous generator, consistently upholds a
high power factor. The adaptive control approach consistently outperforms in terms of
regulation finesse and efficiency, a trend mirrored in the reactive power regulation as well.
The regulation of the DC bus voltage, a pivotal factor in determining the reference
current needed for calculating transmitted active power to the grid, is visualized in Figure 5i.
The efficacy of this regulation becomes evident when examining the zoomed-in segment of
Figure 5i, where a mere ± 1V voltage variation is observed in comparison to the reference
voltage of 5000 V.

5.3.4. Visualization of Analog Signals

The sampling of analog signals is greatly facilitated by the connection panel of the
dSPACE DS1104 card. This panel allows the connection of up to eight output analog
signal channels equipped with digital-to-analog converters (DAC). In order to convinc-
ingly demonstrate the card’s compatibility with external components, we measured and
Energies 2023, 16, x FOR PEER REVIEW
displayed the switching signals, as well as certain signals involving the injection of29voltage
of 32
and phase current, using a digital oscilloscope, as illustrated in Figure 6.

Controller board ControlDesk & Simulink on Controller board

DS1104 R&D computer DS1104 R&D
ControlDesk & Simulink
Oscilloscope
on computer

Oscilloscope

Connection panel

Connection panel

Figure 6.
Figure 6. Digital
Digital Oscilloscope
Oscilloscope Integration
Integration with
with dSPACE
dSPACEController
ControllerBoard.
Board.

6. Conclusions
The objective of this figure is to provide a visual representation of the experiment,
highlighting the equipment
In this study, used
an adaptive withinalgorithm
nonlinear the context of the
based onprocessor-in-the-loop (PIL)
the Lyapunov theory for theto
validate
control of wind energy conversion systems is introduced. The results obtained highlight 6
the proposed control algorithm in this work. It should be noted that Figure
features a referenceadvantages
several significant digital oscilloscope:
in terms ofthe “EZ, Digital
robustness and Oscilloscope
precision whenDSdealing
1250C.”with
This
instrument enabledchallenges.
various regulatory the visualization of various signals while adjusting the adaptive gains
of theThe
RTIalgorithm
Toolbox in Matlab/Simulink
was for in
initially simulated a more in-depth analysis.
the Matlab/Simulink environment and sub-
sequently validated through experimental implementation on the dSPACE DS1104 proto-
typing platform. The results of these tests, which included variations in external wind
conditions, clearly demonstrate the effectiveness of the adaptive backstepping control al-
gorithm. It has proven capable of reducing overshoots, mitigating fluctuations, and im-
proving response times across different parameter sets.
The notable improvements to the wind energy conversion system, based on perma-
Energies 2023, 16, 7481 25 of 28

6. Conclusions
In this study, an adaptive nonlinear algorithm based on the Lyapunov theory for the
control of wind energy conversion systems is introduced. The results obtained highlight
several significant advantages in terms of robustness and precision when dealing with
various regulatory challenges.
The algorithm was initially simulated in the Matlab/Simulink environment and sub-
sequently validated through experimental implementation on the dSPACE DS1104 pro-
totyping platform. The results of these tests, which included variations in external wind
conditions, clearly demonstrate the effectiveness of the adaptive backstepping control
algorithm. It has proven capable of reducing overshoots, mitigating fluctuations, and
improving response times across different parameter sets.
The notable improvements to the wind energy conversion system, based on permanent
magnet synchronous generators (PMSG), can be briefly summarized as follows:
 An exceptionally low total harmonic distortion (THD) of the injected grid currents,
approximately 0.38%.
 A significant reduction in the overshooting of electrical quantities.
 Decreased magnitude ripples compared to the classic vector controller.
 The conclusive validation of the simulation results in Matlab/Simulink compared to
the experimental data, facilitated by the ControlDesk tool.
 The ensuring of the operation with a unity power factor, achieved through the effective
regulation of both active and reactive power injected into the electrical grid.
 Ultimately, the demonstration of the robustness of adaptive control in terms of tracking
and regulation across various parameter sets.
To further advance this research, the authors and members of the laboratory team
have identified the following future prospects:
 The development of a comprehensive test bench that integrates the PMSG, power
converters, wind emulator and the dSPACE DS1104 prototyping board to validate the
adaptive backstepping control algorithm.
 The development of an advanced simulation model that incorporates the aforemen-
tioned variables, particularly during three-phase faults and scenarios of asymmetric
faults, in accordance with the current electrical grid codes.

Author Contributions: Conceptualization, Y.E.M., H.S., B.B. and S.M. (Saad Motahhir); methodology,
Y.E.M.; software, Y.E.M. and H.S.; validation, Y.E.M. and B.B.; formal analysis, Y.E.M.; investiga-
tion, Y.E.M., H.S. and B.B; resources. Y.E.M., H.S. and B.B.; data curation. Y.E.M., H.S. and B.B.
writing—original draft preparation, Y.E.M., H.S. and B.B.; writing—review and editing, Y.E.M., H.S.,
B.B.; A.D., S.M. (Saad Motahhir), S.M. (Saleh Mobayen) and A.Z.; visualization, Y.E.M., H.S., B.B.;
A.D., S.M. (Saad Motahhir), S.M. (Saleh Mobayen) and A.Z.; supervision, Y.E.M., H.S. and B.B.;
project administration, B.B., Y.E.M. and S.M. (Saad Motahhir); funding acquisition, B.B., S.M. (Saleh
Mobayen) and A.Z. All authors have read and agreed to the published version of the manuscript.
Funding: The research is partially funded by the Ministry of Science and Higher Education of
the Russian Federation as part of the World-class Research Center program: Advanced Digital
Technologies (contract N◦ : 075-15-2022-312 dated 20 April 2022).
Data Availability Statement: The datasets used and/or analyzed during the current study are
available from the corresponding author on reasonable request.
Conflicts of Interest: The authors declare no conflict of interest.
Energies 2023, 16, 7481 26 of 28

Appendix A
Table A1. PMSG and wind turbine parameters.

Generator and Wind Turbine

Parameters Symbol Values
Power generator Pn 1.5 MW
Pole number p 72
Stator resistance Rs 6.25 mΩ
d axis inductance Ld 4.229 mH
q axis inductance Lq 4.229 mH
Generator rotor flux ψf 11.1464 Wb
Radius of the turbine blade R 50 m
Turbine and generator
J 10,000 N.m
Moment
Viscous friction fc 0.015 N.m.s/rad
Specific density of air ρ 1.22 kg/m3

Nomenclature

Vw Wind speed (m/s)

Ω Turbine/machine rotational speed (rad/s)
J Turbine/machine total moment of inertia (Nm)
fc Friction forces (N m s/rad)
Paer Air power (W)
PTur Turbine power captured (W)
ρ Air density (Kg/m3 )
S Turbine rotor surface (m2 )
Cp Power coefficient (-)
λ Tip speed ration (-)
β Pitch angle (◦ )
R Turbine blade radius (m)
Tem Generator electromagnetic torque (Nm)
TTur Turbine torque (Nm)
Pgen Active generator power (W)
Q gen Reactive generator power (Var)
p Number of pole pairs (-)
Vs,dq Direct/quadrature stator voltage (V)
is,dq Direct/quadrature stator current (A)
Rs Stator resistance (Ω)
Ls,dq Stator cyclic inductors in the d-q plane (H)
Ψf Rotor flux amplitude (Wb)
Ψs,dq Direct/quadrature stator flux amplitude (Wb)
UC DC link voltage (V)
γi Lyapunov’s candidate function (-)
χi Variable machine error (-)
ξ gi Variable grid error (-)
ki Positive constant (-)
σi System parameter (-)
ňi Positive adaptation gain (-)
i g,abc Three-phase current at the inverter output (A)
Vg,abc Three-phase grid voltages (V)
Rf Filter resistance (Ω)
Lf Filter inductance (H)
Pg Active power injected into the grid (W)
Qg Reactive power injected into the grid (Var)
cos ϕ Power factor (-)
f
Grid frequency (Hz)
Si,abc Inverter arm switching states (-)
Energies 2023, 16, 7481 27 of 28

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