Revista Universitaria en Telecomunicaciones Informática y Control. Volumen 1. N° 2. Noviembre 2012. ISSN 2227 - 3735
Fuzzy Proportional Integral Control for a 1.5 MW
Wind Turbine
Modeling and simulation for different wind speed scenarios
Luis Alberto Torres Salomao1, Hugo Gámez Cuatzin2
Universidad Michoacana de San Nicolás de Hidalgo1, Centro de Ingeniería y Desarrollo Industrial2
Santiago de Querétaro1, Morelia2
México
latsalomao@ieee.org, hgamez@cidesi.mx
(Recibido el 10 de Junio de 2012, Aceptado el 15 de Octubre de 2012)
Abstract —This paper presents a fuzzy logic proportional integral (Fuzzy PI) control design for a 1.5 MW horizontal axis wind
turbine. Design of the proposed Fuzzy PI control algorithm was achieved via tuning with the Ziegler-Nichols approach at low
and nominal wind speeds. The fuzzy section selects the desired PI gains according to wind speed with a smooth control
transition. Aerodynamic characteristics of the wind turbine were studied in order to gain a basic understanding of the system
dynamics. A 1.5 MW horizontal axis wind turbine model with a squirrel cage induction generator model was designed for
tuning as well as simulation performance studies. Simulation of the wind turbine was performed for two wind profiles, low
wind speed and near nominal with fast wind speeds to test the Fuzzy PI algorithm response. Results demonstrate the
effectiveness of the technique; appropriate responses were obtained for both simulation scenarios, achieving a controlled power
extraction near the nominal value and maximum power extraction in low wind speeds. Control response was achieved without
undesirable chattering effects.
Keywords-fuzzy logic control; proportional integral control; wind power; horizontal axis wind turbine
Resumen —Este artículo presenta un diseño de un controlador proporcional integral difuso (Fuzzy PI) para un generador
eólico de 1.5 MW de eje horizontal. El diseño del algoritmo Fuzzy PI propuesto se logró utilizando la metodología de
sintonización Ziegler – Nichols para velocidad de viento baja y velocidad de viento nominal. La sección difusa del algoritmo
selecciona las ganancias PI deseadas de acuerdo con la velocidad de viento incidente en la turbina mecánica. El control logra
esta transición de forma suave y sin efectos de chattering. Las características aeordinámicas del generador eólico se estudiaron
para obtener un entendimiento básico de la dinámica del sistema. Se diseñó un modelo de un generador eólico de 1.5 MW de
eje horizontal y con un generador de jaula de ardilla para realizar las pruebas y sintonización necesarias. La simulación del
generador eólico se realizó para dos perfiles de viento: viento a velocidad baja y viento a velocidades nominal y alta para
verificar el desempeño del algoritmo de control Fuzzy PI. Los resultados obtenidos demuestran la efectividad de la técnica
propuesta. Se obtuvieron resultados apropiados para ambos perfiles de viento, logrando una extacción de potencia controlada
y cercana al valor nominal. Además, se logró una extacción de potencia máxima para velocidades bajas de viento.
Palabras Clave-control con lógica difusa; control proporcional integral; generación eólica; aerogenerador de eje horizontal
I.
INTRODUCTION
Control algorithm design for renewable energy production
is a topic of great concern nowadays because of all the efforts
around the mitigation of greenhouse effects. Many countries
have modified their energy production plans for the near future
by advancing green energy technologies via government
funding and tax reductions [1]. Wind energy is the technology
with the most rapid growth, but since wind is an intermittent
resource, efficiency of this machine is of outmost importance.
In practice, the majority of the installed wind turbines have
pitch control systems with traditional Proportional – Integral
(PI) algorithms. These control systems are designed near the
nominal wind speeds and power extraction values because of
their good response for linear model systems as well 1as their
implementation simplicity. However, the dynamic properties of
large wind turbines make them highly non – linear systems,
and in order to obtain maximum power extraction, non – linear
control algorithms are required.
Fuzzy Logic Control (FLC) technique has been used for
over twenty years with many successful applications like in [2].
It is an ideal technique for complex systems that are difficult to
model or that present important parameter variation [3]. FLC is
sometimes considered a control algorithm that does not require
a mathematical model to operate. This is not entirely true
because an appropriate model is always required in order to
perform adequate simulations prior to real time tests. However,
1
Many thanks for the support of CONACyT.
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Revista Universitaria en Telecomunicaciones Informática y Control. Volumen 1. N° 2. Noviembre 2012. ISSN 2227 - 3735
a mathematical model is not required in the design procedure,
which focuses in gaining a basic understanding of the plant in
order to design an appropriate set of rules that can be directly
loaded into the fuzzy controller. This is completely opposite to
a traditional PI control or other “traditional” control approaches
(e.g., lead-lag or state feedback control), where focus is on
modeling and the use of this model. [4]
energy, wind speed is necessarily slowed on the vicinity and
sweep area of the wind generator rotor (See Fig. 2).
FLC provides a formal methodology for manipulating and
implementing human experience or heuristics knowledge of the
appropriate actions needed to control a plant. In this way, the
design procedure is simplified, and the non – linear model of
the plant can be directly used without linearization procedures.
[4]
However, FLC applied for wind turbine applications, where
fine control action is needed shows no robustness
characteristics when dealing with important parameter variation
and configuration changes that modify the turbine aerodynamic
characteristics. PI control schemes usually concentrate in
reducing the error generated from the desired nominal power
extraction value minus the actual power extraction and work
well near nominal wind speeds as well as for parameter
variations and configuration changes. Their downfall is when
analyzed for low wind speeds where non – linear action is
needed to achieve maximum power extraction.
In this a Fuzzy PI control algorithm is presented combining
the fuzzy logic control direct non – linear characteristics as
well as the PI control effectiveness for power extraction error
reduction. PI control algorithm gains were obtained using
Ziegler – Nichols tuning method and then, on a trial and error
basis, optimized to achieve better performance on simulation
for both wind profile scenarios. The fuzzy logic section was
designed to smoothly switch between both PI gains in
accordance to the incident wind speed. Performance curves
were analyzed to obtain a basic understanding of the wind
turbine as well as maximum power capabilities at low wind
speed. An understanding of the optimum way to control the
wind turbine was obtained from a direct analysis of these
performance curves, thus achieving maximum power extraction
for low wind speed as well as controlled power extraction near
nominal 1.5 MW value.
Fig. 1.
Wind turbine model diagram.
Fig. 2.
Wind turbine rotor sweep area.
When designing a wind turbine it is important to define the
amount of energy to be extracted. This idea is fully understood
by the most general equation that expresses the generable
energy. The kinetic energy of a wind parcel of mass 𝑚, flowing
at speed 𝑣, in direction 𝑥 is: [6]
1
𝐾 = 𝑚𝑣 2
(1)
2
Utilizing the wind parcel depicted in Fig. 3, it is possible to
define 𝑚 as:
𝑚 = 𝜌𝐴𝑥
(2)
3
Where 𝜌 is air density in 𝑘𝑔 𝑚 , A is the parcel’s sectional
area in 𝑚2 and x its width in 𝑚.
Section II describes the implemented 1.5 MW horizontal
axis wind turbine model, paying special attention to specific
dynamic properties needed for the Fuzzy PI algorithm design.
PI control gains design and optimization is discussed in section
III, which also present the final Fuzzy PI algorithm design.
Power extraction results and simulation considerations are
presented in section IV. Section V presents research
conclusions.
II. 1.5 MW WIND TURBINE MODEL
A wind turbine model is basically constructed with a
mechanical turbine (low speed rotor and blades), gearbox
(multiplicative) and the electric generator (high speed rotor) as
can be appreciated at Fig. 1.
A wind turbine is a device designed to extract kinetic
energy from wind [5]. When the wind generator absorbs this
48
Fig. 3.
Incident wind parcel.
If we visualize this wind parcel (Fig. 3) with its 𝑥 side
moving at speed 𝑣, and the opposite side fixed at the origin, we
can see that kinetic energy augments uniformly with 𝑥, as mass
augments uniformly. Wind power is then, the time derivative of
this kinetic energy:
Torres Salomao, L. A., et al.
Fuzzy PI Control for a 1.5MW Wind Turbine
𝑃𝑣 =
𝑑𝐾
𝑑𝑡
1
𝑑𝑥
2
𝑑𝑡
= 𝜌𝐴𝑣 2
1
= 𝜌𝐴𝑣 3
2
(3)
This equation represents the amount of energy theoretically
available for extraction. However, a limit exists in the
extractable energy. This limit is defined as the power
coefficient 𝐶𝑝 . The maximum 𝐶𝑝 available for extraction is
known as the Betz limit, and to date, no wind turbine has been
able to exceed it. This limit is not caused by any design
deficiency, but by pressure changes that cause the reduction of
the incident wind parcel in comparison with the rotor sweep
area [5]. Betz limit is:
𝐶𝑝 𝑙𝑖𝑚 =
16
= 0.593
27
(4)
A. Mechanical turbine
The mechanical turbine is the aerodynamically designed
element to extract power from the wind and to communicate
this power to the multiplicative gearbox. There are some
important aerodynamic aspects that have a specific relationship
with the mechanical turbine. One is the blade geometry and the
incident wind angle of attack. Wind velocity and blade rotating
speed have direct effects in the obtained 𝐶𝑝 . In order to study
these characteristics it is common to construct performance
graphics. With this objective in mind, the tip speed ratio
coefficient 𝜆 is defined [6].
𝜆=
Fig. 5 shows 𝐶𝑝 − 𝜆 curves for different 𝛽 of the studied
1.5 MW wind turbine.
𝑟𝜔 𝑡𝑢𝑟
Fig. 5.
In Table I aerodynamic design constants can be found, as
well as parameters needed for the drawing of Fig. 5 curves.
TABLE I.
Where r is the rotational turbine radio, 𝜔𝑡𝑢𝑟 is the angular
velocity of the mechanical turbine and 𝑣 is wind speed.
The performance curves commonly used to design a wind
turbine for a chosen average site wind speed are the 𝐶𝑝 − 𝜆
curves. These curves show information regarding wind speed
and angle of attack at which maximum power coefficient
𝐶𝑝𝑚𝑎𝑥 is obtained. The 𝐶𝑝 relates with 𝜆 with the following
expressions [7]:
𝐶𝑝 = 𝑐1
1
𝜆𝑖
=
𝑐2
𝜆𝑖
1
𝜆+𝑐6 𝛽
− 𝑐3 𝛽 − 𝑐4 𝑒
−
−𝑐 5
𝜆𝑖
𝑐7
𝛽 3 +1
(6)
(7)
Where 𝑐1 , 𝑐2 , … 𝑐7 are specific constants for each wind
turbine aerodynamic design. 𝛽 is the wind angle of attack at the
blade. 𝛽 = 0 corresponds to the blade’s cord aligned with the
incident wind angle. If rotating direction of the wind turbine is
against the rotating direction of a clock, a positive 𝛽 angle
indicates that the blade rotates in its axis getting farther from
earth at its frontal side as shown in Fig. 4.
WIND TURBINE AERODYNAMIC PARAMETERS
β
c1
c2
c3
c4
c5
c6
c7
λ
(5)
𝑣
𝐶𝑝 − 𝜆 curves for β=0,1,5,10,15 and 20.
=
=
=
=
=
=
=
=
=
0, 1, 5, 10, 15 y 20
0.4654
116
0.4
5
20.24
0.08
0.035
0 to 16
B. Gearbox
The gearbox is the mechanical element that multiplies
rotational speed of the mechanical turbine 𝜔𝑡𝑢𝑟 into the speed
needed for the electric generator 𝜔𝑚 . This generation rotational
speed is generally slightly faster than the synchronous speed
𝜔𝑠 . For the Mexican grid that works at a 60 Hz frequency,
𝜔𝑠 = 2π(60 Hz) = 376.99 rad ≈ 377 rad. Thus, electric
generator rotational speed is:
𝜔𝑚 = 𝑛𝜔𝑡𝑢𝑟
(8)
Where n is a multiplicative factor and 𝜔𝑡𝑢𝑟 is the
mechanical turbine (low speed rotor) angular velocity.
The mechanical power 𝑃𝑚 delivered at the output of an
ideal gearbox as the one considered in this paper is the same as
the one extracted from wind and multiplied by the power
coefficient 𝐶𝑝 , 𝑃𝑚 = 𝐶𝑝 (𝛽, 𝜆)𝑃𝑣 . For wind at standard
conditions (101.3 kPa y 273 K) density value is𝜌 = 0.647,
thus:
1
𝑃𝑚 = 0.647𝐶𝑝 (𝛽, 𝜆) 𝐴𝑣 3
2
(9)
This mechanical power is transmitted to the electrical
generator with the following expression of mechanical torque.
𝑇𝑚 =
Fig. 4.
𝑃𝑚
𝜔𝑚
(10)
Wind turbine blade profile to depict positive 𝛽 angle.
Torres Salomao, L. A., et al.
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Revista Universitaria en Telecomunicaciones Informática y Control. Volumen 1. N° 2. Noviembre 2012. ISSN 2227 - 3735
Where 𝑇𝑚 is mechanical torque and 𝜔𝑚 is angular speed,
both at the fast rotational side of the gearbox (rotational speed
of the electrical generator).
C. Electrical generator
For this paper a squirrel cage induction generator was
selected given that this type of generator is the most commonly
used. This generator’s angular velocity is of outmost
importance for proper functioning. The mechanical turbine is
designed to obtain maximum 𝐶𝑝 at nominal wind speed for
nominal power output. This specific rotational mechanical
angular speed (at nominal installation site wind speed) is then
transformed by the gearbox to an appropriate rotational speed
to obtain nominal power from the electrical generator (in this
case 1.5 MW).
The squirrel cage induction generator model (Asynchronous
machine) was obtained from the SimPowerSystems Toolbox
from Simulink MatLab®.
The mechanical turbine inertia constant was added with the
electrical generator own inertia, taking into account that this
constant is generally ten times bigger in comparison with the
generators’ [8].
D. Implementation of the complete wind turbine model
The complete wind turbine model was implemented in
Simulink of MatLab®. The mechanical turbine was constructed
with (6), (7) and (9). The gearbox was modeled as a simple
speed gain as in (8). Input to the implemented model is wind
speed incident to the mechanical turbine. Model’s output is
generated electrical power by the squirrel cage induction
generator model. Parameters for the 1.5 MW wind turbine can
be found in Table II.
TABLE II.
in order to modify the mechanical turbine aerodynamic
characteristics and thus modify its performance in accordance
to changing wind speed. The blade can be pitched with two
methodologies: pitching to stall or pitching to feather. The
selection of one or other method has important effects in the
wind turbine aerodynamic characteristics. With the pitching to
stall method, pitch control is achieved with small negative
angle adjustments (accordingly to Fig. 4). The problematic with
this methodology is due to undesirable damping and fatigue
effects that cannot be effectively modeled. Pitching to feather is
the preferred methodology due to the form the wind surrounds
the blade. This aerodynamic effect can be easily modeled and
as a consequence, mechanical stress can be foreseen with more
reliability. The problem with this type of pitch control is that
much bigger 𝛽 angles are needed to effectively control the
wind turbine, in this case positive [5]. For the present work,
pitching to feather methodology was chosen as can be observed
in the positive 𝛽 angles in Table I.
A. PI gains tuning
A Proportional – Integral (PI) control is a special case of
the classic controller family known as Proportional – Integral –
Derivative (PID). These types of controllers are up to date the
most common way of controlling industry processes in a
feedback configuration. More than 95% of all installed
controllers are PID. [9]
For wind turbine applications, PI control is the most
commonly chosen configuration. This controller is commonly
fed with an error signal of the desired response (reference)
minus the actual response. Control is cascaded in a closed loop
as shown in Fig. 6. [10]
WIND TURBINE MODEL PARAMETERS
Mechanical turbine
r
=
34 m
A
=
πr2
n
Pnom
Vnom
Fnom
Rs
Lls
Rr
Llr
Lm
𝐻
F
poles
Gearbox
=
152.49
Generator
=
1.5 M W
=
575 V
=
60 Hz
=
0.004843 pu
=
0.1248 pu
=
0.004377 pu
=
0.1791 pu
=
6.77 pu
=
Htur + Hg = 4.125 s
=
0.01 pu
=
3
Fig. 6.
A PI controller is basically a sum of proportional and
integral action. Proportional control action is simply a closed
loop gain that improves a plant’s response by augmenting the
error signal. The integral action integrates error and thus
increases response speed in accordance to the time the system
has in an error state, the response is proportional to the error
magnitude. Integral action is used when achieving the desired
response is important because it eliminates the stable state
error. The transfer function for the PI controller is [10]:
𝐾𝑝 1 +
III.
CONTROL DESIGN
The most common way of controlling a wind turbine
consists in varying attack angle 𝛽 at the blades (pitch control)
50
Feedback control closed loop for the PI controller.
1
𝑇𝑖 𝑠
(11)
Where 𝐾𝑝 is the proportional gain, 𝑇𝑖 is the integral gain,
and s is the Laplace frequency operator.
Torres Salomao, L. A., et al.
Fuzzy PI Control for a 1.5MW Wind Turbine
In wind turbine applications common PI controller error
signal is:
𝑒 𝑡 = 𝑃𝑒𝑑 (𝑡) − 𝑃𝑒 (𝑡)
(12)
Where 𝑃𝑒𝑑 is the desired output power or set point for the
wind turbine, in this case 1.5 MW, and 𝑃𝑒 is the actual delivered
power from the wind turbine. [5]
In order to understand the way electric power from the
wind turbine is obtained using the pitching to feather
methodology, performance curves can be constructed (like in
Fig. 5). The most useful performance curves for this purpose
are the 𝑃𝑒 − 𝑣, which show generated electric power versus
wind velocity at constant chosen 𝛽 angles. Fig. 7 shows some
of these curves.
The 𝑃𝑒 − 𝑣 curves were drawn for chosen β =0, 2, 12, 18
and 23. From the curves it is obvious how the β angle should be
increased in order to maintain a 1.5 MW power generation.
Additionally to nominal value power extraction it is also
important to obtain maximum generation at low wind speeds.
From Fig. 7 we can observe that for wind speeds below
8 𝑚 𝑠 , ideal angle for maximum power extraction is β = 2.
This is an interesting fact because most fixed speed wind
turbines maintain a β =0 for speeds below the nominal wind
speed.
B. Fuzzy logic section
A Fuzzy Logic Controller (FLC) is basically designed by
selecting its inputs and outputs, choosing the preprocessing
needed for the inputs and de post – processing needed for the
outputs, as well as designing each of its four basic components:
fuzification, rule – base, inference mechanism and
defuzification. Rule – base is a set of rules designed with the
knowledge of how to control the plant. This component
contains the experience and knowledge loaded to the FLC. The
inference mechanism weights the relevance of the loaded rules
in real time. Its output is the controlled signal to deliver to the
actual plant. The fuzification interface modifies the controller
inputs so they can be interpreted and compared with the rules
in the rule – base component. Defuzification component
converts the decisions reached by the inference mechanism into
inputs for the controlled plant. An FLC is an artificial decision
making system that operates in closed loop and real time. A
more detailed explanation of this methodology can be found in
[4 and 11].
For the proposed Fuzzy PI algorithm, the fuzzy logic
section was designed to smoothly switch between low speed PI
gains and nominal and faster wind speed PI gains. The
switching was performed following a heuristic approach based
in analyzing optimum β angles for different wind speeds from
Fig. 7. Following this reasoning the appropriate set of rules was
constructed. These rules can be found on Table III.
TABLE III.
Fig. 7.
Pe – v curves for β =0, 2, 12, 18 y 23.
In order to obtain the appropriate response for nominal
(11.75 m/s) and faster wind speeds an open loop analysis was
performed without altered aerodynamic blade pitch conditions
(v = 11.75 m/s, β = 0). The Ziegler – Nichols tuning method
was then applied to obtain initial gains, which were modified
on a trial and error basis to obtain a desirable response.
Obtained gains were: 𝐾𝑝 = −0.934 and 𝑇𝑖 = 0. 4 . This same
methodology was performed for lower than nominal wind
speeds (v = 6 m/s, β = 2) to obtain appropriate gains using the
Ziegler – Nichols method. β angle was modified from
inspection of Fig. 7 and analysis of aerodynamic characteristics
from, β = 0 to β = 2. Obtained gains for low wind speed
operation were: 𝐾𝑝 = 0.15 and 𝑇𝑖 = 20.
Output control signal of the Fuzzy PI controller is 𝛽(𝑡). It
is also important to mention that due to the big input signal to
the controller, the error was divided by a 105 factor and the
integral action saturated at a −45 lower level and a 0.5 upper
level.
Torres Salomao, L. A., et al.
FUZZY LOGIC SECTION SET OF RULES
𝒗
𝑲𝒑
𝑻𝒊
LWS
FWS
LSKp
FSKp
LSTi
FSTi
From Table III, left column is fuzzy input wind speed 𝑣,
with two levels, LWS, low wind speed and FWS, high wind
speed. Columns to the right are fuzzy outputs 𝐾𝑝 and 𝑇𝑖 , which
have two levels as well. LSKp, low speed 𝐾𝑝 , FSKp, fast speed
𝐾𝑝 , LSTi, low speed 𝑇𝑖 , FSTi, fast speed 𝑇𝑖 . To fully understand
how the fuzzy logic section is constructed, a diagram is
presented in Fig. 8.
Fig. 8.
Fuzzy logic section diagram.
Inference mechanism is basically defined with membership
functions, which are used to determine the relevance of the set
of rules of Table III. Implemented membership functions are
shown in Fig. 9, 10 and 11, 𝑣(𝑡) input, 𝐾𝑝 (𝑡) and 𝑇𝑖 (𝑡) outputs
respectively. Methods for implication and aggregation where
51
Revista Universitaria en Telecomunicaciones Informática y Control. Volumen 1. N° 2. Noviembre 2012. ISSN 2227 - 3735
defined as minimum and maximum respectively. Defuzification
process was selected as centroid. [4]
pertinence
1
0.5
0
0
5
9.510.25 11
15
20
25
wind speed (m/s)
Fig. 9.
Fig. 10.
Fig. 11.
Fuzzy logic section input wind speed 𝑣. LWS fuzzy set at left and FWS fuzzy set at right.
Fuzzy logic section output proportional gain 𝐾𝑝 . FSKp fuzzy set at left and LSKp fuzzy set at right.
Fuzzy logic section output ingegral gain 1/𝑇𝑖 . LSTi fuzzy set at left and FSTi fuzzy set at right.
The complete diagram of the Fuzzy PI control algorithm
can be observed in Fig. 12.
17.5
15
V (m/s)
From Fig. 12 input to the fuzzy logic section is wind speed
𝑣. Outputs to the fuzzy logic section are proportional gain 𝐾𝑝
and integral gain 𝑇𝑖 that are inputs along with the power error
𝑒 𝑡 (eq. 12) to the PI section. The PI section delivers the
control pitch angle β, input to the 1.5 MW wind turbine.
20
12.5
10
7.5
5
0
50
100
150
200
250
300
Time (s)
Fig. 13.
Wind speed 𝑣. Nominal and faster wind speed profile.
14
12
Fuzzy PI controller diagram.
IV.
SIMULATION RESULTS
For simulation purposes, wind signal was constructed with
two different profiles for a 300 s period. Fig. 13 and 14 show
these wind profiles, which correspond to near nominal and
faster wind speed operation and low speed operation
respectively.
V (m/s)
Fig. 12.
10
8
5
0
0
50
150
200
250
300
Time (s)
Fig. 14.
52
100
Wind speed 𝑣. Low wind speed profile.
Torres Salomao, L. A., et al.
Fuzzy PI Control for a 1.5MW Wind Turbine
Fig. 15 shows the generated power output of the 1.5 MW
wind turbine with the proposed Fuzzy PI control for the
nominal and faster wind speed profile. Fig. 16 and Fig. 17
show the β angle output and fuzzy logic section PI gains output
for the same nominal and faster wind speed profile
respectively.
2
x 10
Fig. 18 shows the generated power output of the 1.5 MW
wind turbine with the proposed Fuzzy PI control for the lower
than nominal wind speed profile. Fig. 16 and Fig. 17 show the
β angle output and fuzzy logic section PI gains output for the
same lower than nominal wind speed profile respectively.
6
Pe (W)
1.5
1
0.5
0
0
50
100
150
200
250
300
Time (s)
Fig. 15.
Extracted power 𝑃𝑒 . Nominal and faster wind speed profile.
25
2.5
2
Beta (deg)
Beta (deg)
20
15
10
5
0
0
Extracted power 𝑃𝑒 . Low wind speed profile.
Fig. 18.
1.5
1
0.5
50
100
150
200
250
300
Time (s)
Fig. 16.
Fuzzy PI output control β. Nominal and faster wind speed profile.
Fig. 17.
Fuzzy section outputs 1/𝑇𝑖 and 𝐾𝑝 . Nominal and faster wind speed
profile.
From Fig. 15 it can be observed how control action
maximizes power output at lower than nominal wind speeds
and how power output is cut at nominal 1.5 MW. Fig. 16
demonstrates the optimal control action. Small β angles can be
observed at low wind speeds, a β=0 angle can be observed at
nominal 11.75 m/s wind speed and bigger angles for faster
wind speeds to maintain power output at the desired 1.5 MW.
Fig. 17 shows the fuzzy PI gain outputs. Swift and smooth
control action is observed in the gain switching.
Torres Salomao, L. A., et al.
0
0
50
100
150
200
250
300
Time (s)
Fig. 19.
Fig. 20.
Fuzzy PI output control β. Low wind speed profile.
Fuzzy section outputs 1/𝑇𝑖 and 𝐾𝑝 . Low wind speed profile.
From Fig. 18 it can be observed how power output is
maximized for this wind profile. Fig. 19 shows how a small β
angle is needed for low wind speeds. Fig. 20 demonstrates the
fuzzy logic section PI gain outputs where a switching at the end
can be observed when wind speed reaches nominal and faster
wind speeds.
V.
CONCLUSIONS
Research presents a simulation of a Fuzzy PI control for a
1.5 MW horizontal axis wind turbine model.
53
Revista Universitaria en Telecomunicaciones Informática y Control. Volumen 1. N° 2. Noviembre 2012. ISSN 2227 - 3735
Fuzzy PI control algorithm achieves good performance for
power extraction near the nominal 1.5 MW for nominal wind
speeds (around 11.75 m/s) and higher speeds. This hybrid
control algorithm achieves maximum power extraction at low
wind speeds as well.
The presented 1.5 MW wind turbine model has important
non – linear characteristics, which make control an impossible
task for traditional PI controllers. Most installed wind turbines
are PI pitch control driven, which translates to poor power
extraction at lower than nominal wind speeds by maintaining a
0 degree pitch angle. Fuzzy PI control design is a good
solution to achieve a direct non – linear control response by
switching between different performance PI gains as needed.
The solution to the power extraction at low wind speeds is
straight forward with this methodology by allowing the
proportional and the integral gains to switch in accordance to
incident wind speed. Thanks to the fuzzy logic section, pitch
angle control behaves in a non – linear way by responding
with small positive angles for low wind speeds, cero angle for
nominal speed and bigger positive angles for faster than
nominal wind speeds.
Given that the wind resource presents intermittent as well as
highly non – linear characteristics, maximum power extraction
control is of sum importance, and Fuzzy PI control a simple
and effective means of achieving good control response.
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BIOGRAPHIES
LUIS ALBERTO TORRES SALOMAO: Elelctronic engineer from
the Electrical Engineering Department at the Universidad
Michoacana de San Nicolás de Hidalgo (2009). He is finishing
his master degree studies in Science and Technology with
Mechatronics speciality at the Centro de Investigación y
Desarrollo Industrial CIDESI (2012). He is accepted for PhD
studies at the Automatic Control and Systems Engineering
Department at the University of Sheffield. He is currently an
interin professor at the UMSNH as well as GOLD (Graduates
of the Last Decade) IEEE coordinator at the Centro Occidente
Section. His research interests are: classic and modern control,
fault diagnosis, mechatronics and biomedicine.
HUGO GÁMEZ CUATZIN: Received the bachelor's degree from
Instituto Tecnologico de Orizaba, the M. in Sc. from
CINVESTAV IPN, Mexico, and the Ph. D. from Institut
National des Sciences Appliquées - INSA de Lyon, France. He
is currently Senior Researcher and Project leader, PMP-PMI
Certified, for Centro de Ingeniería y Desarrollo Industrial CIDESI, located at Queretaro, Mexico. His research and
development interests are energy conversion, renewable
energies and nanotechnologies applied to green house gas
emissions reduction for climate change mitigation.
Torres Salomao, L. A., et al.