Artículo Académico / Academic Paper
Recibido: 29-10-2020, Aprobado tras revisión: 23-07-2021
Forma sugerida de citación: Muñoz E.; Ayala E.; Pozo N. (2021). “Fuzzy PI Control Strategy to Doubly Fed Induction Wind
Turbine for Power Maximization in Presence of Disturbances”. Revista Técnica "energía". No. 18, Issue I, Pp. 1-10
ISSN On-line: 2602-8492 - ISSN Impreso: 1390-5074
© 2021 Operador Nacional de Electricidad, CENACE
Fuzzy PI Control Strategy to Doubly Fed Induction Wind Turbine for Power
Maximization in Presence of Disturbances
Estrategia de Control Fuzzy PI en una Turbina Eólica con Generador de
Inducción Doblemente Alimentado para Maximizar la Extracción de Potencia
en Presencia de Perturbaciones
E. Muñoz
1
E. Ayala
1
N. Pozo
1
1
Universidad Politécnica Salesiana, Calle Vieja 12-30 and Elia Liut Ave., Cuenca - Ecuador
Mechatronics Engineering Department
E-mail: emunozp2@est.ups.edu.ec; eayala@ups.edu.ec; apozoa@est.ups.edu.ec
Abstract
This proposal implements a speed control system
based on the Fuzzy logic technique supported by a
Proportional Integrator (PI) control, in a Doubly
Fed Induction Generator (DFIG) wind turbine
model for the Maximum Power Point Tracking
(MPPT) in situations of mechanical disturbances.
This control strategy starts from the analysis of the
mechanical and electrical components of the
generator and the turbine to estimate the
electromagnetic torque and the reference current,
seeing the behavior of the wind turbine reflected in
an improvement of the Power Coefficient C
p
.
The validation of this control strategy was carried
out with the analysis of the extracted power and the
response of the C
p
under ideal operating conditions
with the incorporation of white noise to the system
representing alterations in the mechanism. The
software FAST and Matlab-Simulink have been
used for the representation of the 9 MW wind
turbine. The Fuzzy method has been implemented
for MPPT control demonstrating adequate
performance despite the presence of external
disturbances. The simulation displays adequate
results due to the control flexible configuration,
adjusting to variations in the existing operating
conditions.
Keywords Wind turbine, DFIG, power coefficient,
MPPT, Fuzzy, and disturbances.
Resumen
En esta propuesta se implementa un sistema de
control de velocidad basado en la técnica de lógica
Fuzzy apoyada en un control Proporcional
Integrador (PI), en un modelo de turbina eólica
doblemente alimentada (DFIG) para el seguimiento
del punto de máxima potencia (MPPT), en
situaciones de perturbaciones mecánicas. Esta
estrategia de control parte del análisis de las
componentes mecánicas y eléctricas del generador y
la turbina para la estimación del torque
electromagnético y la corriente de referencia,
viéndose el comportamiento del aerogenerador
reflejado en una mejora del coeficiente de potencia
(C
p
).
La validación de esta estrategia de control se llevó a
cabo con el análisis de la potencia extraída y la
respuesta del C
p
en condiciones ideales de
funcionamiento y con la incorporación de ruido
blanco al sistema representando alteraciones en el
mecanismo, haciendo uso del software de simulación
FAST y Matlab-Simulink para la representación de
la turbina eólica. Con el uso del método Fuzzy, el
controlador demuestra un buen rendimiento a pesar
de la presencia de perturbaciones externas debido a
la flexibilidad de la configuración del control,
ajustándose a los cambios de las condiciones de
operación existentes.
Palabras Clave Aerogenerador, DFIG, coeficiente
de potencia, MPPT, Fuzzy, y perturbaciones.
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Edición No. 18, Issue I, Julio 2021
1. INTRODUCTION
The production of energy based on renewable sources
such as wind energy, is a subject of continuous study due
to the benefits they provide to daily activities. The
increase in demand in its generation, as indicated in [1],
[2], demonstrates a reality of the energy need, and
together with the possibility of adaptation in the
environment, wind energy makes possible the
development of new technologies and increasingly
effective control techniques for the extraction of power
from the air in models of different scale adapted to
environmental conditions. In this context, the recurring
control methodologies immersed in different aspects of
the wind turbine systems, contribute to its correct
operation.
One of these strategies, such as the MPPT, allows the
regulation of the optimum operating speed of the turbine
[3]. This principle is widely used for its importance in
optimizing the extraction of power provided by the wind,
which, measured in terms of C
p
, is an indicator of the
performance of the wind turbine. In this research, the
control strategy is intended to find its optimal C
p
value
and modify the command for the power electronic
converter, demonstrating the effectiveness of the
technique in power generation including disturbances.
According to the literature [4], [5], [6], and [7], a
variety of methodologies based on the MPPT principle in
order to extract the maximum power, are developed, such
as: Indirect Speed Control (ISC), Tip Speed Ratio (TSR),
Artificial Neural Network (ANN), Power Signal
Feedback (PSF), Hill Climb Searching (HCS), Optimal
Torque (OT), and Fuzzy-based controllers. These
controllers are widely discussed in wind turbines for
different generator configurations. These techniques use
often DFIG electric machines. This is because of the
advantages they offer about quality and efficient energy
production, low installation costs, and operability in a
more flexible range of speeds [2], [8].
In this research, the MPPT technique is developed
with the use of a Fuzzy controller, which operates based
on the mechanical and electrical characteristics of the
wind turbine, forming a direct speed control (DSC)
model, supported by a PI in the stage of estimating the
current component on the rotor side, i
qr
. The principle of
operation consists of estimating the optimum
electromagnetic torque and consequently the extracted
power, regulating the speed of the turbine, and in this
way, making it possible to reach and maintain its ideal
C
p
operating value around it, reacting to changes in the
input wind speed and mechanical disturbances that may
affect the system. The use of analysis and simulation
software for the correct modeling of the wind turbine was
necessary, for which, FAST from NREL [9], where the
turbine dynamics is estimated, and Matlab-Simulink [10]
where the electrical machine is represented and the
controller is implemented, they are coupled, working
together to validate the results in consideration of more
precise and detailed parameters and characteristics of the
model. With this approach, the responses of the system
dynamics are obtained, validating the strategy based on
the correct behavior of the variables involved, evidencing
the robustness of the control.
The development of this study points out important
aspects that support the method and the working model,
such as in section 2, where the aerodynamic principle that
governs the operation of the wind turbine is explained,
and in section 3 that contextualizes the mechanical
representation based on a powertrain concept. In section
4 the model is complemented with the description of the
electrical part regarding the DFIG generator. In section 5
the effect of disturbances in the system is analyzed and
the MPPT control method is introduced, coupled with the
characteristics of the 9 MW wind turbine model.
Subsequently, the results obtained in section 6 are
presented, with the incorporation of the control
technique, analyzing the viability of the proposal.
2. WIND GENERATOR AERODYNAMICS
The conversion of wind energy goes through a set of
stages from the incidence of the wind on the blades to the
generation of electrical energy. In Fig. 1 the generic
model of a horizontal axis wind turbine with its different
parts is shown.
Figure 1: Generic model of the structure of a wind turbine
The first step of this conversion involves the capture
of energy through the rotating mechanical elements of the
turbine, causing a change in pressure, as seen in Fig. 2,
between the incoming air and the area immediately
behind the blades. The air flows through the turbine
sweep area, resulting in a decrease in pressure due to
energy transformation [11], [12], [13]. During this
process, elements intervene that affect the amount of
power that can be extracted from the air by the turbine,
such is the case of the length of the blades R in (m), the
wind speed
in (m/s), the air density ρ in (kg/m
3
) in the
turbine installation area, the rotational speed of the
turbine
t
in (rad/s) and the angle of rotation of the
blades β in (deg). With these characteristics, the
Blade
2
Muñoz et al. / Fuzzy PI Control Strategy Applied to a DFIG Wind Turbine for MPPT in Presence of Disturbances
mechanical power P in (Watt) produced in the rotor can
be calculated according to the equation (1):
(1)
where, C
p
indicates the value of the power coefficient and
λ is the TSR factor, calculated according to the equation
(2), which indicates the existing speed ratio at the end of
the blades and the speed of the captured wind that causes
the movement.
t
(2)
The following conversion stages occur in the mechanical
gearbox arrangement and finally in the electric generator,
which are detailed in later chapters.
Figure 2: Actuator disc model
2.1. Operating Zones of a Wind Turbine
In consideration of the magnitude of the wind speed
that intercepts the turbine, the operating mode of the wind
turbine differs. In this context, the operational speed
range is delimited, on the one hand, by the cut-in wind
speed from which the wind turbine produces power and,
on the other hand, by the cut-out wind speed, which
establishes the limit of maximum operating speed to
protect the entire system [14]. In this way, as shown in
Fig. 3, the working zones of the wind turbine are
determined, which correspond to the stop zone, zone of
maximum power extraction, and pitch angle control
region [6], [15].
Figure 2: Operation zones of a wind turbine
It is important to establish the operating zone on
which the system works, which in the case of the present
research is the extraction region of maximum power,
where the optimum C
p
is reached through the control of
the rotor speed.
2.2. Power Coefficient Representation
The power coefficient is a non-linear factor delimited
by Betz's law in approximately 0,59, that establishes the
condition of effectiveness in the conversion of wind
energy by the wind turbine, which is found in the
function of β and of the TSR in equation (2) [15], [16]:
β % performance
(2)
Each wind turbine has its own C
p
curve, defined
according to its physical characteristics, which contribute
to the operation of the turbine within specific operating
parameters, and it is expressed mathematically via
equation (3) [13], [17]:
β
β
β
β
(3)
where c
1
…c
8
are the coefficients that establish the
particularities of the wind turbine C
p
. This mathematical
expression can be graphically represented by a C
p
vs TSR
curve, Fig. 4, in which, at different parameters, the
influence of the TSR on the estimation of the C
p
is
appreciated in greater detail, which in turn always
depends on the wind speed and pitch angle input signal.
Figure 3: C
p
vs TSR curves
2.3. Optimal Operating Parameters in Power
Extraction
Introducing the analysis in zone 2 of operation, the
maximum possible power to be extracted in the
respective range of wind speeds requires that the wind
Wind Speed
Cut-in
Cut-out
Generator Power
Maximum Power
Extraction Region
Pitch control
Region
Stop Zone
Power curve
Vw_rated
m_max
m_min
P rated
Stop Zone
0
3 6 9 12 15 18 21
lambda
0.1
0.2
0.3
0.4
0.5
Cp
24 27
= 0°
= 1°
= 3°
= 5°
= 7°
3
Edición No. 18, Issue I, Julio 2021
turbine works with the optimal parameters of TSR λ
opt
and the orientation of the pitch angle β
opt
, responding,
consequently, to the scope of an ideal torque T
ideal
dependent on the rotor speed ω
r
, for which, the maximum
possible value of the power coefficient C
p.max
is required;
all this observation is represented by the following
equations [13], [18]:
(4)
(5)
3. MECHANICAL REPRESENTATION OF THE
WIND GENERATOR
Once the wind energy is captured, movement is
generated in the turbine, which must be transmitted to the
generator. This link stage is the powertrain, a
fundamental part of the structure of the wind turbine that
allows the conversion of speed and torque from the
turbine as an effect of the impact of the wind on the
blades, towards the generator, allowing its rotation and
generation of electrical energy.
Figure 4: Representation of the mechanical model of the turbine
and generator link
The modeling of this section can be simplified in a
description of the type of two-mass structure, Fig. 5,
according to the equations (6), (7), and (8), providing
considerable precision in the analysis, coupled to the
turbine by the Low Shaft Speed (LSS) and to the
generator through the High Shaft Speed (HSS),
maintaining a certain gearbox ratio N
, in equation (9),
for the correct conversion of the mechanical variables
involved [19], [20]:
t
t
(6)
g
(7)
(8)
g
t
(9)
where the inertias J
and J
of the rotor and the generator,
directly influence the dynamics of the system, reflected
in the rotation speed of the turbine and the generator
t
and
g
. The compensation for this behavior depends on
the torques involved in the low and high-speed parts T
ls
and T
hs
respectively, and on the torques of the turbine T
t
and the electromagnetic torque of the electrical machine
T
em
, as well as the damping and stiffness coefficients, B
and C, that can be finally negligible.
From the equations (6), (7), (8), and (9), a global
expression is calculated that represents the mechanical
model of the wind turbine in equation (11):
(11)
When the expression (11) is obtained, the connections
of the turbine with the generator and the transmission of
movement are defined, being useful for the development
of a control by integrating the mechanical and electrical
parts.
4. ELECTRICAL DESCRIPTION OF THE DFIG
To complete the energy conversion process, the
electrical machine is essential. In this investigation, a
DFIG generator model is used.
A notable feature of the DFIG is its dual connection.
On the one hand, the stator is directly linked to the
electrical grid, while the rotor is linked through an
intermediate system, the back-to-back power converter,
with which the conversion zones are identified in rotor
side (RSC) and grid side conversion (GSC), giving the
flexibility to operate within a speed range further from
synchronous speed, by approximately 30%, in addition
to facilitating power control active and reactive with the
use of currents
and
detailed in equations (12) to
(20) [1], [2]. With this configuration of the DFIG, and
using the Park transform in the d-q framework, the
classical equations that govern its operation are extracted
[21]:
(10)
(11)
(12)
(15)
where the fluxes in the stator and rotor are expressed as:
(13)
(14)
(15)
(16)
considering the relationships:
(20)
Where each element is referred to the respective d-q
frame, being ν
ds
, ν
qs
, ν
dr
and ν
qr
voltages; i
ds
, i
qs
, i
dr
and
i
qr
currents, and Φ
ds
, Φ
qs
, Φ
dr
and Φ
qr
the fluxes, both on
the stator and rotor side. In the same way, R
s
and R
r
are
the stator and rotor resistances, L
s
and L
are the stator
w
t
T
t
w
m
T
em
J
t
T
m
C
tm
B
tm
B
t
B
m
N
tg
4
Muñoz et al. / Fuzzy PI Control Strategy Applied to a DFIG Wind Turbine for MPPT in Presence of Disturbances
and rotor inductances, L
l
and L
l
are the leakage
inductances, and M is the mutual inductance.
5. DISTURBANCE AND CONTROL DYNAMIC
RESPONSE
There are several causes that lead to the presence of
disturbances that are introduced in the model of the wind
turbine. The noise could affect the entire system because
of the dynamics of different components. This
perturbance could affect energy production. These
disturbances, as mentioned in [22], and [23], can be the
result of the tower shadow effect when the blades cross
in front of the tower, or by wind shear, caused by a non-
uniform entry of wind in magnitude and position. In
addition, in [24] refers to the effect of wind speed
turbulence that generates vibrations in the gearbox
system.
All these variations affect the performance of the
wind turbine and therefore the maximum power
extraction is compromised. Due to this problem, it is
necessary that the used controllers remain robust enough
to cope with these effects.
5.1. Fuzzy-PI MPPT Controller Design
Due to the existence of various subsystems in a wind
turbine and the complexity of operation that each one of
them involves in its modeling and that of the whole, in
addition to the inevitable presence of disturbances of
different nature, previously analyzed, the ideal behavior
during the process energy conversion is affected. With
this situation, the general operation of the wind turbine
presents a non-linear dynamic that negatively influences
its control. Given this reality, the Fuzzy technique is
implemented, being a viable option, as indicated in [25],
by managing with greater precision the non-linearity of
the system and the inaccuracy of the variables due to
constant changes in them.
The DSC Fuzzy technique that is implemented in this
study operates based on the measurement of the
mechanical and electrical parameters of the wind turbine
and making use of the equations (4), (5), (9), and (11)(11)
to obtain an ideal speed reference of generator operation
ω
g
.
Figure 5: Fuzzification surface of the controller
From the speed reference, it enters the Fuzzy
controller its error E
ωg
signal and returns an alteration
factor of
. The controller follows an estimation
process based on the linguistic terms used: HNV (High
Negative Variation), INV (Intermediate Negative
Variation), MNV (Minimal Negative Variation), N (Null
Variation), MPV (Minimal Positive Variation), IPV
(Intermediate Positive Variation) and HPV (High
Positive Variation), and the control rules reflected in the
conversion curve in Fig. 6, making use of Generalized
Bell-type membership functions.
With this fuzzy logic reference, the effective speed
and torque ratio necessary to follow the optimum
is
established. From the
found, a power signal is
calculated, which enters a classic PI controller to
determine the current reference
with which the torque
indicated by the control can be established in the
machine. The integration of the entire process is
presented in Fig. 7.
Figure 6: Controller implementation scheme with disturbance reference
Mechanical
Disturbances
+
Torque-speed dependence
Kideal
5
Edición No. 18, Issue I, Julio 2021
6. ANALYSIS OF RESULTS
The validation of the control strategy was carried out
in a wind turbine model detailed in Table 1, with the
application of a disturbance signal of the white noise
type, as a reference to alterations in the mechanical
subsystem of the wind turbine. This condition was
carried out in order to test the robustness of the controller
and the response of the system to alterations in the ideal
operating conditions that are actually present. The
disturbances in question are reflected from the rotor
speed input signal as a direct measurement mechanical
variable at the control input.
Table 1: Wind Turbine Parameters with DFIG
Element
Numeric Value
Nominal Power,
9
Nominal Voltage,
575
Mutual inductance,
2,9
Rotor resisance,
0,005
Rotor inductance,
0,156
Stator resistance,
0,00706
Stator inductance,
0,171
Frequency,
60
Turbine speed,
1800
Pole pairs,
3
Power Coefficient,
0,45
Turbine radius,
45
Gearbox ratio,
66
Air density,
1,225
In addition, two types of wind speed input were
considered, both a stepped incremental signal and a
realistic signal with sudden alterations in its magnitude.
In this way, it is possible to verify the response of the
wind turbine, mainly affected only by mechanical
disturbances, as well as by the presence of disturbances
caused by constant variations in the wind.
6.1. System Response with Steps Wind Speed
The first analyzed case of study involves sudden
changes in wind speed, Fig. 8, established as sudden
increases and additions of linear variations.
Figure 7: Stepped wind speed
The robustness of the system with the application
mainly of the Fuzzy controller is measured by detecting
the power extraction capacity around the optimal
operating values. The response of the model without the
influence of external noise in the system is compared
with the response when introducing a signal from
mechanical disturbances in Fig. 9. The incoming
disturbance reflects mechanical disturbances due to
various factors in general, such as those analyzed in the
previous section, which alter the control variables.
The control strategy shows high reliability in
response to the effect of wind behavior and the influence
of disturbances. As can be seen in Fig. 10, the power is
generated within the average values with the presence of
noise when compared with the response in an ideal
behavior of the system. Similarly, the electromagnetic
torque, Fig. 11, and the speed of rotation of the machine,
Fig. 12, bases of the Fuzzy control, operate with a rapid
reaction to sudden changes in the conditions to which the
turbine was subjected.
Figure 8: Noise input as mechanical disturbance
Figure 9: Power generated with incremental wind input
Figure 11: Electromagnetic torque produced in response to
incremental wind input
6
Muñoz et al. / Fuzzy PI Control Strategy Applied to a DFIG Wind Turbine for MPPT in Presence of Disturbances
Figure 10: Generator speed in response to incremental wind input
The reference current
, Fig. 13, by the effect of the
estimated
, also responds quickly, allowing efficient
operation of the involved variables.
Regarding the power coefficient, it remains in its
maximum power extraction value, Fig. 14, with small
deviations due to sudden changes in external conditions,
but achieving good stabilization, reflecting the
robustness of the controller in the first test of functioning.
Figure 11: Control current in response to incremental wind input
Figure 12: Power coefficient in response to incremental wind
input
6.2. System Response to a Realistic Wind Speed
In this second test carried out, the wind speed signal,
which directly influences the generation of disturbances,
is recreated. The behavior of the wind in this simulation,
Fig. 15, presents permanent oscillations similar to the
reality due to changes in pressures of the environment.
Figure 15: Realistic wind speed with oscillations
The turbulent airflow impacts the turbine and affects
the conversion of energy from the mechanical elements
that capture the wind. The signal of mechanical
disturbances added to the system, Fig. 16, as in the
previous test, defining other mechanical disturbances that
occur in addition to the entry of wind, recreates a non-
ideal work situation that is normal during the
commissioning of a wind turbine.
Figure 13: Mechanical disturbance input to the system
As a response of the wind generation system for this
second case of study, with the presence of a greater
number of alterations, it is evident that the extracted
power, Fig. 17, is around the optimal values, presenting
variations due to constant changes of the system
conditions and the effect of inertia that delays
stabilization. The electromagnetic torque also shows a
similar behavior, Fig. 18, maintaining a trend in the
correct follow-up of the reference given by the controller
within the appropriate values.
Figure 14: Power generated with realistic wind input
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Edición No. 18, Issue I, Julio 2021
Figure 15: Electromagnetic torque produced in response to
realistic wind input
The speed of the generator, Fig. 19, is directly
affected to maintain the respective relation to the
and
achieve maximum power extraction, making this work
more difficult due to the inertia of the system, but with
good precision with respect to the ideal response. The
current reference
, Fig. 20, fulfills its objective,
reacting to each variation of the electromagnetic torque
estimated in the controller, allowing the system to adapt
to the changes caused by disturbances. Finally, the
measurement of the power coefficient, Fig. 21, in
harmony with the trend reflected in the analyzed
variables, shows the following of the ideal value, with
expected oscillations in its dynamics, due to both the
dynamics of the system and the alterations in its normal
operating conditions.
Figure 16: Generator speed in response to realistic wind input
Figure 20: Reference current in response to realistic wind input
Figure 17: Power coefficient in response to realistic wind input
In this way, the robustness of the direct speed control
technique is validated with the incorporation of a Fuzzy
controller complemented with a PI, which allows
obtaining an effective response of the system, reacting
adequately to the influence of external disturbances.
7. CONCLUSIONS AND RECOMMENDATIONS
The existence of unwanted external factors in a wind
turbine is inevitable and affects its performance directly,
before which, the control systems to be incorporated
must be able to operate efficiently and solve as much as
possible the alterations caused by these disturbances. In
this sense, the control technique presented in this study,
based on the use of a Fuzzy PI controller applied in a
DFIG 9MW wind turbine model, demonstrated good
performance in the extraction of maximum power,
integrating the mechanical and electrical elements to
operate in response to dynamics that change sharply over
time.
The effectiveness of the incorporation of the
controller was reflected with its robustness in the
measurement of the
, reaching a value that oscillates
around its maximum possible despite the influence of
noise in the system, achieving an effective response of
the estimation of electromagnetic torque to regulate the
speed of the turbine to the necessary magnitude of
optimal operation depending on the conditions to which
it was subjected.
The analyzed variables that intervene in the
controller, as well as those influenced and necessary in
the modeling of the wind turbine, as evidenced
throughout the investigation, react quickly and with
sufficient precision to the effects of the disturbances of
wind and noise introduced, giving validity to the control
method used.
The evaluation of the controller under the influence
of electrical alterations and different network conditions
is recommended for subsequent studies within the line of
research dealt with, to verify the robustness of the
method, as well as the use of other examples of
generators used in the production of wind energy.
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Muñoz et al. / Fuzzy PI Control Strategy Applied to a DFIG Wind Turbine for MPPT in Presence of Disturbances
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Eduardo Muñoz Palomeque.- He
was born in Cuenca, Ecuador in
1997. Currently, he is finishing his
undergraduate studies in
Mechatronics Engineering at the
Salesian Polytechnic University
Cuenca del Ecuador Headquarters.
His research interests include
signal processing techniques, autonomous systems, and
power electronics.
Edy Ayala Cruz.- He was born in
Cuenca in 1987. She received her
degree in Electronic Technologist
in 2009 and Electronic Engineer in
2011, both from the Salesian
Polytechnic University of Ecuador;
and his Master of Engineering
Science (Electrical and Electronic)
degree from Swinburne University of Technology in
Australia, 2015. Currently, he is pursuing his Doctorate
studies in Engineering at the University of Ferrara. His
field of research is related to control systems in
engineering and renewable energies.
Nicolás Pozo Ayala.- He was born
in Cuenca, Ecuador in 1998. He is
a Mechatronics student with a
major in Industrial Automation
since 2016 at the Salesian
Polytechnic University. His areas
of study are focused on the
automation of food processes and
the development of devices for people with disabilities.
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