1. Indian Institute of Technology
Guwahati
Bachelors Thesis
Design of Emulator for Small Wind
Turbine Using Induction Motor
Report by :
Vishal K Gawade
Aayush Garg
ON : July 21, 2016
Supervisor:
Dr. Praveen Tripathy
A thesis submitted in fulfilment of the requirements
for the degree of Bachelor of Technology
in
Indian Institute of Technology
Department of EEE
2. i
CERTIFICATE
It is to certify that the work pertaining to the thesis "Design of Emulator for
Small Wind Turbine Using Induction Motor" by Vishal Gawade And
Aayush Garg has been carried out under my supervision And Guidance during
the Academic Session 2014-2015 And also This work involves No plagiarism and
has not been recorded anywhere in award of a degree.
Dr. Praveen Tripathy
Assistant Professor
Department of Electronics & Electrical
INDIAN INSTITUTE OF TECHNOLOGY
Guwahati-781039
Assam
India
Date: ———–
Signature: ———–
3. ii
ACKNOWLEDGEMENT
I am using this opportunity to express my gratitude to everyone who
supported us during the progress of Bachelor’s Thesis. I Specially
thank my Thesis Guide Dr. Praveen Tripathy for his aspiring
guidance and invaluably contructive critisism and friendly
advice during project work.I am sincerely grateful to them for sharing their
truthful and illuminating views on a number of issues related to the project.
VISHAL K GAWADE
Roll No: 11010839
Department of EEE
Indian Institute of Technology
Guwahati-781039
AAYUSH GARG
Roll No: 11010801
Department of EEE
Indian Institute of Technology
Guwahati-781039
4. iii
ABSTRACT
Widely used in many industrial applications, the induction motors represent the
starting point when an electrical drive system has to be designed. In modern control
theory, the induction motor is described by different mathematical models, according
to the employed control method. In the symmetrical three-phase version or in the
unsymmetrical two-phase version, this electrical motor type can be associated with
vector control strategy. Through this control method, the induction motor operation
can be analysed in a similar way to a DC motor. The goal of this research is to sum-
marize the existing models and to develop new models, in order to obtain a unified
approach on modelling of the induction machines for vector control purposes. Start-
ing from vector control principles, the work suggests the d-q axes unified approach
for all types of the induction motors. However, the space vector analysis is presented
as a strong tool in modelling of the symmetrical induction machines. When an elec-
trical motor is viewed as a mathematical system, with inputs and outputs, it can be
analysed and described in multiple ways, considering different reference frames and
state-space variables. All the mathematical possible models are illustrated in this
report. The suggestions for what model is suitable for what application, are defined
as well. As the practical implementation of the vector control strategies require dig-
ital signal processors (DSP), from the continuos time domain models are derived
the discrete time domain models. The discrete models permit the implementation of
the mathematical model of the induction motors, in order to obtain high efficiency
sensorless drives. The stability of these various models is analysed.
In the goal to implement an experimental wind energy board we have interest by a
survey and development of a wind emulator based on DC-machine. The development
of this subject has focused on modeling of a vertical axis wind turbine, a DC motor
with independent excitation and its control via a fourth quadrant chopper. To carry
out this work, we studied and designed the electrical and mechanical sensors dedi-
cated to the stand and a PWM control using 18F452 microcontroller. The presented
emulator permits to test some theoretical algorithm control used in the wind energy
control system, such as, system was the SCIG, DFIG or PMSM.
The conventional synchronous generators in wind energy conversion system are now
getting replaced by variable speed induction generator to extract maximum power
with wide range of wind speed limit. The design and performance of such systems
requires a simplified digital simulator, especially for the development of a optimal
control solution .The proposed work is to make a prototype of variable speed wind
conversion system simulator for a required operational condition under variable wind
speed. In this paper variable speed induction motor drive using scalar control is in-
terfaced in wind energy conversion system as an alternative to make the real time
wind simulator for wind energy researchers. The basic power curve from wind gen-
erator is carried out through d-SPACE and interface of induction motor through an
inverter control system. The induction motor is operated in wide speed range using
Volt /Hertz speed control scheme. The laboratory prototype consists of 3 kW, 415
Volt, 50Hz induction motor controlled by voltage source inverter for various wind
5. iv
speed. The paper demonstrates the steady state characteristics of wind turbine with-
out dependence on natural wind speed using Volt/Hertz. The basic control strategy
is implemented through hardware system. The result verifies that the wind turbine
simulator can reproduce the steady state characteristics of a given wind turbine at
various wind conditions
8. vii
LIST OF VARIABLES
CP Power coefficient of wind turbine rotor
CT Thurst Coefficient of wind turbine rotor
ν Wind speed
ν0 Free stram wind speed
νr Relative wind speed
νrated rated wind speed of turbine
¯ν Average wind speed
a Axial induction factor at rotor plane
a‘
Angular Induction Factor
b Number of blades of Rotor
N Number of blade elements
ρ Air density
P Produced power of wind turbine rotor
r Radial coordinate at rotor plane
rt Tip radius of blade
rr Rootradius of blade
ri Blade radius for ith
element
FD Drag Force on Blade element
FL Lift Force on blade element
Fa Axial force on blade element
Ft Edgewise force on blade element
CL Lift coefficient of an airfoil
CD Drag coefficient of an airfoil
F Tip loss factor
ω Rotational Rotor speed
c Blade chord length
α Angle of attack
β Pitch control angle
β0 Pitch fixed angle
φ Angle of relative wind speed with rotor plane
γ Twist angle
σ Solidity ratio.
9. 1
1. INTRODUCTION
1.1 OVERVIEW : Vector Control of Induction Motor
The electrical DC drive systems are still used in a wide range of industrial applica-
tions, although they are less reliable than the AC drives. Their advantage consists
in simple and precise command and control structures. The induction motors are
relatively cheap and rugged machines because their construction is realised without
slip rings or commutators. These advantages have determined an important devel-
opment of the electrical drives, with induction machine as the execution element,
for all related aspects: starting, braking, speed reversal, speed change, etc. The dy-
namic operation of the induction machine drive system has an important role on the
overall performance of the system of which it is a part. There are two fundamental
directions for the induction motor control:
1. Analogue: direct measurement of the machine parameters (mainly the rotor
speed), which are compared to the reference signals through closed control
loops;
2. Digital: estimation of the machine parameters in the sensorless control schemes
(without measuring the rotor speed), with the following implementation method-
ologies:
• Slip frequency calculation method;
• Speed estimation using state equation;
• Flux estimation and flux vector control;
• Direct control of torque and flux;
• Observer-based speed sensorless control;
• Kalman filtering techniques;
• Estimation based on slot space harmonic voltages;
Another classification of the control techniques for the induction machine is made
by Holtz (1998) from the point of view of the controlled signal:
1. Scalar control:
• Voltage/frequency (or v/f) control;
10. 1. Introduction 2
• Stator current control and slip frequency control. These techniques are
mainly implemented through direct measurement of the machine param-
eters.
2. Vector control:
• Field orientation control (FOC)
(a) Indirect method;
(b) Direct method;
• Direct torque and stator flux vector control. These techniques are re-
alised both in analogue version (direct measurements) and digital version
(estimation techniques).
1.2 Vector Control:Algorithm
Controlling the speed of an induction motor is far more difficult than controlling the
speed of a DC motor since there is no linear relationship between the motor current
and the resulting torque as there is for a DC motor.
The technique called vector control can be used to vary the speed of an induction
motor over a wide range.
In the vector control scheme, a complex current is synthesised from two quadrature
components, one of which is responsible for the flux level in the motor, and another
which controls the torque production in the motor.Vector control offers a number
of benefits including speed control over a wide range, precise speed regulation, fast
dynamic response, and operation above base speed.
The vector control algorithm is based on two fundamental ideas :
1. flux and torque producing currents: An induction motor can be modelled
most simply (and controlled most simply) using two quadrature currents rather
than the familiar three phase currents actually applied to the motor. These two
currents called direct (Id) and quadrature (Iq) are responsible for producing
flux and torque respectively in the motor. By definition, the Iq current is in
phase with the stator flux, and Id is at right angles. Of course, the actual
voltages applied to the motor and the resulting currents are in the familiar
three-phase system.
2. Reference Freme: The idea of a reference frame is to transform a quantity
that is sinusoidal in one reference frame(AC quantities), to a constant value
in a reference frame(DC quantities), which is rotating at the same frequency.
Once a sinusoidal quantity is transformed to a constant value by careful choice
of reference frame, it becomes possible to control that quantity with traditional
controllers.
11. 3
2. VECTOR TRANSFORMS
There are two types of vector transforms which are The Park and Clarke transforms.
The Park and Clarke vector transforms are one of the keys to vector control of
induction motors.
2.1 Clark Transform
The forward Clarke (1943) transform does a magnitude invariant translation from
a three phase system into two orthogonal components. If the neutral - ground con-
nection is neglected, the variables in a three-phase system (A, B, and C) sum is
equal to zero, and there is a redundant information. Therefore, the system can
be reduced to two variables, called X and Y. The Clarke transform is given by:
iXs (t)
iYs (t)
= 2
3
×
1 cos(γ) cos(2γ)
0 sin(γ) sin(2γ)
×
iAs (t)
iBs (t)
iCs (t)
Where:
γ = 2π
3
iAs (t) + iAs (t) + iAs (t) = 0
And the fact that:
cos(2π
3
) = cos(4π
3
) = -1
2
Thus, the Clarke transform can be simplified to:
iXs (t)
iBs (t)
=
iAs (t)
1√
3
· iAs (t) − iCs (t)
The Clarke transform can also be understood using a vector diagram as shown in
Fig. 1.1. In the figure, A, B, and C are the axes of a three phase system, each offset
120° from the other. X and Y are the axes of a two variable system where X is
chosen to be coincident with A. To perform the Clarke transform of a three variable
system (iA, iB, iC), iX is equal to iA and iY is the scaled projection of iB and iC
onto the Y axis. The scaling is necessary to preserve the signal magnitudes through
the transform.
12. 2. Vector Transforms 4
2.2 Park Transform
The Park (1929) transform is a vector rotation, which rotates a vector (defined by
its quadrature components) through a specified angle. The Park transform function
implements the following set of equations:
OutX(t)
OutY (t)
=
cos(θ) − sin(θ)
sin(θ) cos(θ)
×
InX(t)
InY (t)
where θ is the angle to rotate the vector through. A reverse vector rotation can
be accomplished simply by changing the sign on the sin(θ) input value.
Some references describe the Park transform as a combination of the Clark and
Park transforms presented here. Breaking into a three-variable-to-two transform
(i.e. the Clarke transform) and a vector rotation is done for efficiency of calculation:
with separate Park and Clarke transforms, only two trigonometric calculations are
required as opposed to 6 in the traditional Park transform.
Parks transformation, a revolution in machine analysis, has the unique property of
eliminating all time varying inductances from the voltage equations of three-phase
ac machines due to the rotor spinning.
Few Points :
1. The angular displacement θ must be continuous, but the angular velocity
associated with the change of variables is unspecified.
2. The frame of reference may rotate at any constant, varying angular velocity,
or it may remain stationary.
3. The angular velocity of the transformation can be chosen arbitrarily to best
fit the system equation solution or to satisfy the system constraints.
4. The change of variables may be applied to variables of any waveform and time
sequence;
5. Parks transformation is a well-known three-phase to two-phase transformation
in synchronous machine analysis.
13. 5
3. INDUCTION MOTOR
3.1 Introduction
The induction motor, which is the most widely used motor type in the industry, has
been favored because of its good self-starting capability, simple and rugged structure,
low cost and reliablilty, etc. Along with variable frequency AC inverters, induction
motors are used in many adjustable speed applications which do not require fast
dynamic response. The concept of vector control has opened up a new possibility
that induction motors can be controlled to achievedynamic performance as good
as that of DC or brushless DC motors. In order to understand and analyze vector
control, the dynamic model of the induction motor is necessary. It has been found
that the dynamic model equations developed on a rotating reference frame is easier
to describes the characteristics of induction motors. It is the objective of the article
to derive and explain induction motor model in relatively simple terms by using the
concept of space vectors and d-q variables. It will be shown that when we choose a
synchronous reference frame in which rotor flux lies on the d-axis, dynamic equations
of the induction motor is simplified and analogous to a DC motor.
3.2 Dynamic Model Of Induction Motor
Dynamic modeling and simulation of induction motor drives is of great importance
to both industry and academia due to the prevalence of these types of drives in var-
ious industrial settings. The induction motor has seen increased use in industry in
its evolution from being a constant speed motor to being a variable speed machine
with the advancement of power electronics.
Three-phase induction machines and voltage source inverters are now mass pro-
duced, have low costs, and are readily available; making them the top choice of
industry in many applications. Three-phase squirrel-cage induction motors of vari-
ous sizes are commonly used as the driving units for fans, pumps, and compressors.
All analysis and simulation are based on the d-q or dynamic equivalent circuit of
the induction motor represented in the rotating reference frame shown in Figure 1.
It should be noted that all quantities in Figure 1 have been referred to the stator.
3.2.1 IM Dynamic Model Equations
Vds = Rsids +
d
dt
λds − ωeλqs, (3.1)
14. 3. Induction Motor 6
Vqs = Rsiqs +
d
dt
λqs + ωeλds, (3.2)
Vdr = 0 = Rridr +
d
dt
λdr − (ωe − ωr)λdr (3.3)
And,
Vqr = 0 = Rriqr +
d
dt
λqr − (ωe − ωr)λqr (3.4)
where d is the direct axis, q is the quadrature axis,
Vds is the d-axis stator voltage, Vqs is the q-axis stator voltage, Vdr is d-axis rotor voltage,
Vqr is q-axis rotor voltage,
ids is the d-axis stator current, iqs is the q-axis stator current, idr is d-axis rotor current,
iqr is q-axis rotor current,
Rs is the stator resistance, Rr is the rotor resistance,
ωe is the angular velocity of the reference frame, ωr is the angular velocity of the rotor,
and λds, λdr, λqs, and λqr are flux linkages.
It is assumed that the induction motor analyzed is a squirrel cage machine, leading to the
rotor voltage in (3) and (4) being zero.
The flux linkages in (1-4) can be written as:
λds = Lsids + Lmidr, (3.5)
λqs = Lsiqs + Lmiqr, (3.6)
λdr = Lridr + Lmids, (3.7)
And,
λqr = Lriqr + Lmiqs, (3.8)
where Lr is the rotor self inductance, Ls is the stator self inductance, Lm is the magnetizing
inductance,
Llr is the rotor leakage inductance, and Lls is the stator leakage inductance. The self
inductances in (5-8) can be expressed as:
Ls = Lm + Lls, (3.9)
And,
Lr = Lm + Llr. (3.10)
The Currents Can be written as:
ids =
λds − Lmidr
Ls
, (3.11)
iqs =
λqs − Lmiqr
Ls
, (3.12)
idr =
λdr − Lmids
Lr
, (3.13)
And,
15. 3. Induction Motor 7
iqr =
λqr − Lmiqs
Lr
. (3.14)
After making substitutions, the currents can be expressed in terms of flux linkages as:
ids =
L − r
LrLs − L2
m
λds −
L − m
LrLs − L2
m
λdr, (3.15)
iqs =
L − r
LrLs − L2
m
λqs −
L − m
LrLs − L2
m
λqr, (3.16)
idr =
L − s
LrLs − L2
m
λdr −
L − m
LrLs − L2
m
λds, (3.17)
And,
iqr =
L − s
LrLs − L2
m
λqr −
L − m
LrLs − L2
m
λqs. (3.18)
The electromagnetic torque of the machine can be written as:
Te =
3
2
P
2
Lm[iqsidr − idsiqr] (3.19)
where P is the number of poles and Te is the electromagnetic torque. Neglecting mechanical
damping, the torque and rotor speed are related by:
d
dt
ωr =
P
2J
(Te − TL) (3.20)
where TL is the load torque and J is the inertia of the rotor and connected load.
The angle ,θe, is calculated directly by integrating the frequency of the input voltages as:
θe =
t
0
ωedt + θe(0) (3.21)
where θe(o) is the initial rotor position.
Three-phase voltages can be converted to the two-phase stationary frame using the follow-
ing relationship:
vs
qs
vs
ds
=
1 0 0
0 − 1√
3
1√
3
×
van
vbn
vcn
(3.22)
where the superscript s in (22) refers to the stationary frame. The voltages can be con-
verted from the two-phase stationary frame to the synchronously rotating frame using the
following:
vqs = vs
qs cos(θe) − vs
ds sin(θe), (3.23)
And,
vds = vs
qs sin(θe) + vs
ds cos(θe). (3.24)
The current variables can be found as:
is
qs = iqs cos(θe) + ids sin(θe), (3.25)
is
ds = −iqs sin(θe) + ids cos(θe), (3.26)
16. 3. Induction Motor 8
And,
ia
ib
ic
=
1 0
−1
2 −
√
3
2
−1
2
√
3
2
×
vs
qs
vs
ds
(3.27)
3.2.2 Equivalent Circuit Diagrams :
Figure 3.1: The Equivqlent Circuit Diagram about d-Axis
Figure 3.2: The Equivqlent Circuit Diagram about q-Axis
17. 3. Induction Motor 9
3.2.3 SIMULINK MODEL: induction motor
Figure 3.3: Induction Motor Model for dynamic control
Ls(H) = 0.04599
Lr(H) = 0.00766
Lm(H) = 0.012
Rs(ohm) = 4.163
Rr(ohm) = 5.470
JKg.m2 = 0.0161
3 phase;,400V,50 HZ
3.73 KW(5 HP)
1440 RPM
7.5 A
3.2.3.1 Explaination
as seen in the simulink model of induction machine for its dynamic control, we can point
out five different subsystems. all the subsystem blocks are shown below
18. 3. Induction Motor 10
3.2.4 Subsystems of IM Model
3.2.4.1 park and clarke outputs
Figure 3.4: Subsystem 1:
19. 3. Induction Motor 11
3.2.4.2 Current outputs for given lambda’s
Figure 3.5: Subsystem 2:
3.2.4.3 Current to torque output
Figure 3.6: Subsystem 3:
21. 13
4. SIMULATION RESULTS OF IM MODEL
Simulation Results of Dynamic model of Induction Motor obtained in MATLAB are For-
mulated based on following Equations:
4.1 Vqs Calculation
Vqs = Va cos(ωt) + Vb cos(ωt − 120) + Vc cos(ωt + 120) (4.1)
Vqs = Vm sin(ωt) cos(ωt) + Vm sin(ωt − 120) cos(ωt − 120) + Vm sin(ωt + 120) cos(ωt + 120)
(4.2)
Vqs =
Vm
2
(sin(2ωt) + sin(2ωt − 120) + sin(2ωt + 120)) (4.3)
Vqs = 0 (4.4)
Thus Vqs is 0.
4.2 Vds Calculation
Vds =
2
3
(−Va sin(ωt) − Vb sin(ωt − 120) − Vc sin(ωt + 120)) (4.5)
Vds =
−2Vm
3
(sin2
(ωt) + sin2
(ωt − 120) + sin2
(ωt + 120)) (4.6)
Vds =
−2Vm
6
(1 − cos(2ωt) + 1 − cos(2ωt − 120) + 1 − cos(2ωt + 120)) (4.7)
Vds =
−2Vm
6
(3) (4.8)
Vds = −Vm (4.9)
Thus we get Vds equal to Vm.
Hence the simulation Results Agree with the Calculated Values.
22. 4. Simulation Results of IM Model 14
4.3 Voltage output of subsystem 0:
4.3.1 Vqs :
Figure 4.1: Voltage output of subsystem 0, Vqs.
4.3.2 Vds:
Figure 4.2: Voltage output of subsystem 0, Vds.
23. 4. Simulation Results of IM Model 15
4.4 λ at Different Axes
(a) λqr (b) λqs
(c) λdr (d) λds
Figure 4.3: λ at different axes
4.5 Currents at different axes
(a) iqr (b) iqs
(c) idr (d) ids
Figure 4.4: currents at different axes
24. 4. Simulation Results of IM Model 16
4.6 Phase currents,Torque,ωr
(a) Ia (b) Ib
(c) Ic (d) Te
(e) ωr
Figure 4.5: Currents,Torque,ωr
25. 17
5. WIND TURBINE
5.1 Introduction
Energy is the primary and most universal measure of all kinds of work by human beings
and nature. Everything that happens in the world is an expression of energy in one of its
forms. Energy can neither be created nor be destroyed. It can only be converted from one
form into another.
Almost eighty percent of the world energy requirements are fulfilled by fossil fuels. The
main problems with fossil fuels are that they replenish with time and are harmful to
environment.
With the shortage of fossil fuels, alternative energy has been thrust into the national
spotlight as a major necessity in order to keep up with the increasing energy demands
of the world. Wind energy has been proven one of the most viable sources of renewable
energy. Wind turbine technology is one of the rapid growth sectors of renewable energy all
over the world. Wind energy is a comparatively clean and sustainable source of energy.
So can wind energy be converted from one form to another. Wind energy is readily con-
verted into mechanical energy through the turbine blades and is further converted into
electrical energy by connecting the turbine to an electrical generator.
A wind turbine is a rotary device that extracts energy from the wind. Rotor blade is a
key element in a wind turbine generator system to convert wind energy into mechanical
energy.As a core component of a wind turbine, it is a common view that the design and
manufacturing of rotor blades represent about 20% of the total investment of the wind
turbine.
Moreover, the performance of a wind turbine is highly dependent on the design of the rotor.
As well as rotor aerodynamic performance, the structure strength, stiffness and fatigue of
the blade are also critical to the wind turbine system service life.
Wind energy technology has cross its maturity limits after the designing of blades on the
basis of blade element moment theory. The main parameters of the wind turbine rotor
and the blade aerodynamic geometry shape are determined based on the principles of the
blade element momentum (BEM) theory. Based on the FE method, deflections and strain
distributions of the blade under extreme wind conditions are numerically predicted. The
results indicate that the tip clearance is sufficient to prevent collision with the tower, and
the blade material is linear and safe.
Another aspect of wind turbine is its various control mechanisms. The wind velocity in a
particular area is not constant but it varies with time. Fortunately the variation of wind
velocity in a particular area is predictable. The different control mechanisms are associated
with change in wind speed and change in wind direction. The turbine rpm changes with
26. 5. Wind turbine 18
changing the incoming wind so its output power also changes. One of the problems with
the wind energy is the unpredictable incoming wind speed. In order to have quality output
we incorporate various controls in wind turbine rotor. Among those controls one is pitch
angle control. As the wind flows over the wind turbine it exerts aerodynamic forces on
wind turbine blades. There are two types of aerodynamic forces, a lift and drag. By
rotating the wind turbine blades about its own axis, it changes these aerodynamic forces.
So in order to have a specific quality output we rotate the wind turbine blades in response
to the change in speed of the incoming wind.
The output torque is calculated for various wind speeds. A simulation setup is then created
by using MATLAB. The output torque of the simulations was compared with experimental
results.
5.2 Airfoil nomenclature
Figure 5.1: Airfoil Nomenclature
Figure 5.1 shows airfoil nomenclature and its terminology is as following:
• Mean Camber Line: Line halfway between the upper and lower surfaces.
• Leading Edge (LE): The front most point on mean camber line.
• Trailing Edge (TE): The rear most point on mean camber line.
• Chord line (C): Length from the LE to the TE of a wing cross section that is
parallel to the vertical axis of symmetry.
• Camber: Maximum distance between the mean camber line and the chord line,
measured perpendicular to the chord line
• Thicknes: Distance between upper surface and lower surface measured perpendic-
ular to the mean camber line
27. 5. Wind turbine 19
5.2.1 NACA four digit series (0018)
• First number is camber in percentage of chord (0)
• Second number is location of maximum camber in tenths of chord measured from
LE (0)
• Last two digits give maximum thickness in percentage of chord (18)
5.3 Blade design How it should be
5.3.1 Blade Airfoil Shape
For horizontal axis wind turbines, it is recommended to have a higher lift but lower drag
aerofoil. The thicker aerofoil shapes are often located at the inner part (close to rotor
centre) of the blade while the thinner ones are set in the outer part of the blade due to
ease of manufacturing and better strength and stiffness.
5.3.2 Blade Chord and Twist
Given the rotor design parameters (e.g. rotor diameter,tip speed, aerofoil, rated wind speed
and etc.), the main task of blade design is to determine the chord and twistdistributions
along the span of the blade. The optimal chords and twists are often calculated based on
blade element momentum (BEM) theory. In this theory, complex flows are simplified into
steady uniform conditions; and the total efficiency is integrated from several blade element
sections which experience different flow velocity and different attack angle for the same
hub wind speed.
5.3.3 Rotor Diameter and Material
The power extracted from the wind is proportional to the cube of wind speed as well as
the area of the rotor. It is often preferable to have an effective rotor but not a too big one
as the cost increases with the rotor size. And the material of the blade is resin-reinforced
fiber glass due to easy local availability.
28. 5. Wind turbine 20
5.4 Blade Element Momentum Theory
Blade Element Momentum Theory (BEMT) is a method of modelling the performance
of wind, current or tidal turbines. It is split into two parts, one dimensional momentum
theory with rotational momentum and blade element theory
Blade element theory relies on two key assumptions:
• The forces on the blade elements are solely determined by the lift and drag coefficients
• There are no aerodynamic interactions between different blade elements
Figure 5.2: BEM theory
29. 5. Wind turbine 21
Consider a blade divided up into N elements as shown in Figure 5.3. Each of the blade
elements will experience a slightly different flow as they have a different rotational speed
(Ωr), a different chord length (c) and a different twist angle (γ). Blade element theory
involves dividing up the blade into a sufficient number (usually between ten and twenty)
of elements and calculating the flow at each one. Overall performance characteristics are
determined by numerical integration along the blade span.
Figure 5.3: Blade Elements Divided in N parts
5.4.1 Momentum Theory
Based on some assumptions, a simple model,known as actuator disc model, can be used to
determine the power from an ideal turbine rotor and the thrust of the wind on the ideal
rotor. From axial momentum and angular momentum, the element of thrust δFa and the
element oftorque δTt can be obtained as:
δFa = 4πρν0
2
a(1 − a)rδr (5.1)
δTt = 4πρνωa‘
(1 − a)r3
δr (5.2)
30. 5. Wind turbine 22
Figure 5.4: Momentum Theory
5.4.2 Blade Element Theory
In order to apply blade element analysis, it is assumed that the blade is divided into N
sections(as shown in figure 5.3). The analysis is based on some assumptions, such as that
there is no aerodynamic interaction between different blade elements and the forces on the
blade elements are solely determined by the lift and drag coefficients.
Figure 5.5: Blade Element Theory
Figure 5.5 shows the velocities and forces on a blade element of a wind turbine blade. As
31. 5. Wind turbine 23
a result, the following equations are obtained:
φ = arctan
ν0(1 − a)
ωr(1 + a‘)
(5.3)
νr =
ν0(1 − a)
sin φ
(5.4)
α = φ − γ (5.5)
Lift and drag forces on an annular blade element are given by:
δFL =
ρc
2
νr
2
CLδr (5.6)
δFD =
ρc
2
νr
2
CDδr (5.7)
These lift coefficient CL and drag coefficient CD depend on the angle of attack α and the
blade profile. The element of thrust δFa and the element of torque δTt are expressed as,
δFa = b
ρc
2
νr
2
(CL cos φ + CD sin φ)δr (5.8)
δTt = b
ρc
2
νr
2
(CL sin φ − CD cos φ)rδr = rδFt (5.9)
5.4.3 Blade Element Momentum Theory
By combining equation 5.1 & 5.8 also equation 5.2 and 5.9 we get,
4πρν0
2
a(1 − a)rδr = b
ρc
2
νr
2
(CL cos φ + CD sin φ)δr (5.10)
4πρνωa‘
(1 − a)r3
δr = b
ρc
2
νr
2
(CL sin φ − CD cos φ)rδr (5.11)
After some algebraic manipulations and by adding the correction of the Prandtl tip loss
factor, the following relationships are obtained,
a =
1
4F sin2 φ
σ(CL cos φ+CD sin φ) + 1
(5.12)
a‘
=
1
4F sin φ cos φ
σ(CL sin φ−CD cos φ) + 1
(5.13)
where F is the Prandtl tip loss factor defined as:
F =
1
π
arccos{exp(
b(r − ri)
2r sin φ
)} (5.14)
and σ is the rotor solidity, defined as:
σ =
cb
2πr
(5.15)
32. 5. Wind turbine 24
It is to be noted that Eqn. (5.12) is valid for the axial induction factor value to be between
0 and 0.4. For axial induction factor greater than 0.4, there are several methods to obtain
it.
a =
18F − 20 − 3 2
CT (50 − 36F) + 12F(3F − 4)
36F − 50
(5.16)
where CT is the thrust coefficient of the wind turbine rotor. For each blade element, it can
be calculated as,
CT =
δFa
12ρν0
22πrδr
=
σ(1 − a)2(CL cos φ + CD sin φ)
sin2
φ
(5.17)
5.4.3.1 Tip Loss Correction
At the tip of the turbine blade losses are introduced in a similar manner to those found in
wind tip vertices on turbine blades. These can be accounted for in BEM theory by means
of a correction factor. This correction factor Q varies from 0 to 1 and characterises the
reduction in forces along the blade.
Q =
2
π
cos−1
(exp −
B2[1 − rR]
(rR) cos β
) (5.18)
After the Correction The Terms Become
δFx = QρV1
2
{4a(1 − 2)}πrδr (5.19)
δT = Q4a‘
(1 − a)ρV Ωπr3
δr (5.20)
33. 5. Wind turbine 25
5.5 Mathematical Model of Wind Turbine
We use Blade Element Momentum theory for formulating the Mathematical Model for
Wind Turbine. we proceed as below:
5.5.1 Algorithm
The algorithm that we follow for calculating performance parameters is given as follows :
• There should be few necessary input to the system which are:
θ Local pitch of blade,
B number of Blades,c chord length,
r radius,
δr Length of element,
ω Rotational Speed,
V1 wind speed,
ρ wind density and
table of lift and drag values.
• Guess a and a‘, {a = 0;a‘ =0 }
• Now we find the flow angle ϕ :
ϕ = tan−1
{
(1 − a)V1
(1 + a‘)ωr
} (5.21)
• Then we find angle of attack for wind turbine.
α = ϕ − θ (5.22)
And also we Extract Values of Lift (CL) and Drag (cD) coefficients.
• Find Force Coefficients
Cn = CL cos φ + CD sin φ (5.23)
CT = CL sin φ − CD cos φ (5.24)
• Find Solidity σ
σ =
bc(r)
2πr
(5.25)
• Find Tip Loss Factor
F =
1
π
arccos{exp(
b(r − ri)
2r sin φ
)} (5.26)
• If the guessed Value is above 0.2?
– Yes Calculate new Values for a and a‘
a =
1
2
(2 + k(1 − 2ac) −
2
K(1 − 2ac) + 22
+ 4(Kac
2
)) (5.27)
34. 5. Wind turbine 26
a‘
=
1
f4 sin φ cos φ
σCT
− 1
(5.28)
where, K = F4 sin2 φ
σCn
& ac = 0.2
– IF NO Calculate new Values for a & a‘
a =
1
F4 sin2 φ
σCn
+ 1
(5.29)
a‘
=
1
f4 sin φ cos φ
σCT
− 1
(5.30)
• Have a & a‘ changed from the guessed value ?
– YES Then We use the Latest Values of a & a‘ to Calculate Flow angle as given
in Eq. 5.18
– NO Then We calculate Forces:
T = FCn
1
2
ρV1
2
(1 − 2)2
cB
∆r
sin2
φ
(5.31)
M = FCT
1
2
ρV1(1 − a)ωr(1 + a‘
)cB
∆r
sin φ cos φ
(5.32)
• Then We calculate Power Production
P = Mωr (5.33)
35. 5. Wind turbine 27
5.6 Pitch Control
5.6.1 Introduction
The pitch control system is one of the most widely used control techniques to regulate the
output power of a wind turbine generator. The pitch control gives full control over the
mechanical power and if the most common method is used for the variable speed wind
turbines.
The method relies on the variation in the power captured by the turbine as the pitch angle
of the blades is changed. Hydraulic actuators are used to vary the pitch angle.
Figure 5.6: Volts/Hertz controlled induction generator
At wind speeds below the rated power of the generator, the pitch angle is at its maximum
though it can be lower to help the turbine accelerate faster. Above the rated wind speed,
the pitch angle is controlled to keep the generator power at rated power by reducing the
angle of blades.
The wind turbine generator describes the design of the pitch controller and discusses the
performance of the system in the presence of disturbances.
The pitch control system is found to have a large output power variation and a large
settling time.
The variable speed induction generator using Volts/Hertz control enables efficient wind
energy capture and is shown in Figure 5.6
For fixed speed turbines, the active stall can be used to limit the power, not by reducing
the pitch angle as in pitch controlled, but by increasing the pitch angle to a point where
the blade stalls and in that way reduces the force on the turbine. By regulating, the angle
to be on the limit of stalling, fast torque changes from the wind will be neutralized.
5.6.2 Pitch Control System Design
Pitch control means that the blades can pivot upon their own longitudinal axis. The pitch
control used for speed control, optimization of power production and to start and step the
turbine.
The control system structure used to generate the pitch angle reference is given in Fig-
ure 5.7, The pitch controller consists of two paths a nonlinear feed forward path, which
generates β0 and a linear feedback path, which generates ∆β.
36. 5. Wind turbine 28
Figure 5.7: Pitch Angle Reference Generator
The feed forward path uses the information about the desired power output, wind velocity
and the turbine speed to determine the pitch angle required. Equation (5.34) gives the
pitch angle as a function of the measured variables.
β0 =
2 1
0.22
(γ − 5.6 −
2Pref e0.17γ
Pw
) (5.34)
However, the feed forward term assumes that all the components are ideal and does not
account for the losses in the system. The feedback path compensates for the losses by de-
creasing the pitch angle, if the output power is less than the desired power, to increase the
power captured. The P-I controller (Proportional integration) for the system is designed
using the Zeigler-Nicholas rules for tuning PID (Proportional integration and differentia-
tion) controllers.
5.6.2.1 Zeigler Nicholas Rules
The method used here is the first method applicable for plants without integrators or
dominant complex conjugate poles, as the plant response for the wind system is found to
correspond to these requirements of the Zeigler-Nicholas rules.
5.6.2.2 PI Controller Design
In order to use the Zeigler-Nicholas rules for designing the P-I controller, the step response
of the plant is required. The block diagram showing the plant and controller used for gen-
erating the step response is shown in Figure 5.8. The actuator is modeled as an integrator
in a feedback loop, as shown in Figure 5.9. The rate limiter limits the rate of change of the
pitch angle, as most pitch actuators cannot change the pitch angle more than a particular
degrees/sec. The value used for the rate limiter in the simulations is 5 degree/sec.
37. 5. Wind turbine 29
Figure 5.8: Plant and Controller
Figure 5.9: Actuator
Thus above two diagram shows the Plant and controller definition and Hydraulic actuator
model used in the simulation.
38. 30
6. SIMULINK MODEL AND MATLAB CODES
6.1 Matlab Codes
In this Section the MATLAB codes for calculating various Blade parameters ,Blade angular
Speed and Blade torque using BEMT (Blade Element Momentum Theory). we have a look
at them one by one.
6.1.1 Code for Blade Parameters
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
% Blade Turbine Design Algorithm in Matlab Programming Code Main Function
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
c l e a r a l l
c l c
Sr = 2 . 5 ; % Station_radii (m)
Nb = 3; % Number of Blades
N_S= 20; % No of s e c t i o n s
TSR = 7 . 5 ; % Tip Speed Ratio
Cl = 0.9461; % C o e f f i c i e n t of l i f t
alpha = 0.0916; % Angle of attack ( rad )
V = 10; % Wind Velocity ( meter )
deltar= Sr/N_S; % Width of one d i f f r e n t i a l element
Li_1= ( deltar )/ Sr ;
Li = (2∗ deltar )/ Sr ; % Fractional Radiius ( dimensonless )
Incre=Li−Li_1 ;
r i = [ ] ; phi = [ ] ; theta = [ ] ; Ci = [ ] ;
lamda = [ ] ; Fi = [ ] ; sigmal = [ ] ; ai = [ ] ; bi = [ ] ; Vr = [ ] ; Lf = [ ] ; Q = [ ] ;
%Cld= [ ] ;
fo r i =1:(N_S−3)
i f i >= 2
Li ( i ) = Li ( i −1)+Incre ;
e l s e
Li ( i ) = Li ( i )+0;
end
r i ( i ) = Li ( i )∗ Sr ;
lamda ( i ) = TSR∗( r i ( i )/ Sr ) ;
phi ( i ) = (2/3)∗ atan (1/ lamda ( i ) ) ;
theta ( i ) = phi ( i )−alpha ;
Fi ( i )= (2/ pi )∗ acos ( exp((−(Nb/2)∗(1 −( r i ( i )/ Sr ) ) ) / ( ( r i ( i )/ Sr )∗ sin ( phi ( i ) ) ) ) )
Ci ( i ) = ((8∗ pi ∗ r i ( i ))/(Nb∗Cl))∗(1 − cos ( phi ( i ) ) ) ;
39. 6. Simulink Model and MATLAB codes 31
%Ci ( i ) = ((8∗ Fi ( i )∗ pi ∗ r i ( i )∗ sin ( phi ( i ) ) ) / (Nb∗Cl ))∗((1 − lamda ( i )∗ tan ( phi ( i ))
sigmal ( i )=(Nb∗Ci ( i ))/(2∗ pi ∗ r i ( i ) ) ;
%Cld ( i )=((4∗ Fi∗ sin ( phi ))∗( cos ( phi)−lamda∗ sin ( phi ) ) ) / ( sigmal ∗( sin ( phi)+lamd
ai ( i )=1/(1+(4∗( sin ( phi ( i )))^2)/( sigmal ( i )∗ Cl∗ cos ( phi ( i ) ) ) ) ;
bi ( i )=1/((4∗ cos ( phi ( i ) ) ) / ( sigmal ( i )∗ Cl ) −1);
% ai ( i )=1/(1+(4∗ Fi ( i )∗( sin ( phi ( i )))^2)/( sigmal ( i )∗ Cl∗ cos ( phi ( i ) ) ) ) ;
% bi ( i )=1/((4∗ Fi ( i )∗ cos ( phi ( i ) ) ) / ( sigmal ( i )∗ Cl ) −1);
Vr( i )=(V∗(1− ai ( i )))/ sin ( phi ( i ) ) ;
Lf ( i )=(1/2)∗1.225∗(Vr( i ))^2∗ Ci ( i )∗ Cl∗ deltar ;
Tf ( i )=Lf ( i )∗ sin ( phi ( i ) ) ;
Q( i ) = 4∗ pi ∗1.225∗ lamda ( i )∗(V)^2∗ bi ( i )∗(1− ai ( i ))∗( r i ( i ))^2∗ deltar ;
Qf( i ) = 4∗ Fi ( i )∗ pi ∗1.225∗ lamda ( i )∗(V)^2∗ bi ( i )∗(1− ai ( i ))∗( r i ( i ))^2∗ deltar ;
%Q( i ) = 4∗ Fi ( i )∗ pi ∗1.225∗TSR∗(V)^2∗ bi ( i )∗(1− ai ( i ))∗ r i ( i )∗ deltar ;
end
Display_ri = [ transpose ( r i ) ]
Display_lamda = [ transpose ( lamda ) ]
Display_phi = [ transpose ( phi ) ]
Display_theta = [ transpose ( theta ) ]
Display_Fi = [ transpose ( Fi ) ]
Display_Ci = [ transpose ( Ci ) ]
Display_sigmal = [ transpose ( sigmal ) ]
Display_ai = [ transpose ( ai ) ]
Display_bi = [ transpose ( bi ) ]
Display_Lf = [ transpose ( Lf ) ]
Display_Vr = [ transpose (Vr ) ]
Display_Tf = [ transpose ( Tf ) ]
Display_Q = [ transpose (Q) ]
Display_Qf = [ transpose (Qf ) ]
6.1.2 Code for Angular Speed
function rot = fcn2 (V)
R=2.5;
TSR=7.5;
rot=TSR.∗V/R;
end
6.1.3 Code for Blade Torque
function Tturb1 = fcn (V, rot , pitch )
%c l c
%c l e a r a l l
%global new_ax ax new_an an pitch ;
TSR=7.5;
%V=10;
% wind speed (m s )
B=3;
%no of blades
40. 6. Simulink Model and MATLAB codes 32
rho =1.225;
%density of the f l u i d
R=2;
%radiuss of the blade
deltar =0.1;
%pitch =0;
r =[0.3; 0 . 4 ; 0 . 5 ; 0 . 6 ; 0 . 7 ; 0 . 8 ; 0 . 9 ; 1; 1 . 1 ; 1 . 2 ; 1 . 3 ; 1 . 4 ; 1 . 5 ; 1 . 6 ; 1 . 7
%l o c a l radius of the blade
c =[0.3056; 0.2687; 0.2341; 0.2052; 0.1816; 0.1623; 0.1465; 0.1333; 0.1222;
%chord length
thetad =[22.51719745; 17.22038217; 13.47133758; 10.73121019; 8.661783439; 7
%TSR=(w∗R)/V;
n=length ( r ) ;
% number of blade elements
r_R=r ./R;
% radius r a t i o ( r /R)
l i f t =[ −0.8646; −0.9113; −0.9426; −0.9666; −0.9822; −0.9996; −1.0116; −1.01
% l i f t c o e f f i c i e n t at various angle of attack
drag =[0.12321; 0.10995; 0.10016; 0.09203; 0.08548; 0.07888; 0.07328; 0.068
% drag c o e f f i c i e n t at various angle of attack
AOA_data=[−19; −18.75; −18.5; −18.25; −18; −17.75; −17.5; −17.25; −17; −16
%rot=TSR∗V/R;
% rotor speed ( rad/ s )
RPM=rot ∗60/(2∗ pi ) ;
% rpm of the rotor
% Cl=zeros (n , 1 ) ; Cd=zeros (n , 1 ) ;
% i n i t i a l values of v a r i a b l e s
choice =1;
AOA=zeros (n , 1 ) ;
% i n i t i a l values of v a r i a b l e s
% i =1;
% blade pitch angle at hub( degree )
% while i<=m
% L_pitch=pitch+thetad ;
% pitch=pitch +0.625;
% i=i +1;
% end
% l o c a l pitch angle ( degree )
i =1;
41. 6. Simulink Model and MATLAB codes 33
Cl=zeros (n , 1 ) ; Cd=zeros (n , 1 ) ;
Cdmax=0.12321; Clmax=1.4713;
% maximum drag and l i f t c o e f f i c i e n t s
%SoM=zeros ( choice , 1 ) ;
Tturb1=zeros ( choice , 1 ) ;
new_ax=zeros (n , 1 ) ; ax=zeros (n , 1 ) ; new_an=zeros (n , 1 ) ; an=zeros (n , 1 ) ;
% i n i t i a l guess f or a x i a l and tangential induction f a c t o r
del_ax=ones (n , 1 ) ; del_an=ones (n , 1 ) ;
% change in a x i a l and tangential induction f a c t o r
CT=zeros (n , 1 ) ; F_tip=zeros (n , 1 ) ; %Qf=zeros (n , 1 ) ;
while ( i<=choice )
%del_ax=ones (n , 1 ) ; del_an=ones (n , 1 ) ;
% i n i t i a l values of change in a x i a l and tangential induction f a c t o r
L_pitch=pitch+thetad ;
% pitch
L_tsr=TSR.∗r_R;
% l o c a l tip speed r a t i o
Sol=B.∗ c ./(2∗ pi .∗ r ) ;
% l o c a l s o l i d i t y of rotor
phi=atand((1−ax ) . / ( L_tsr .∗(1+an ) ) ) ;
% Relative Inflow angle ( degree )
% AOA=round ( phi−L_pitch ) ;
AOA=(phi−L_pitch ) ;
% angle of attack ( degree )
V_rel=sqrt (((1 −ax ) . ∗V).^2+( rot .∗ r .∗(1+an ) ) . ^ 2 ) ;
% Relative Wind Velocity (m/ s )
Re=V_rel .∗ c ∗69000;
% Reynolds Number
fo r q=1:1:n
i f AOA(q)<=13
Cl (q)=interp1 (AOA_data, l i f t ,AOA(q ) ) ;
Cd(q)=interp1 (AOA_data, drag ,AOA(q ) ) ;
e l s e
Cl (q)=2∗Clmax∗ sind (AOA(q ))∗ cosd (AOA(q ) ) ;
Cd(q)=Cdmax∗ sind (AOA(q ) ) . ^ 2 ;
end
end
count =0;
42. 6. Simulink Model and MATLAB codes 34
while (max( del_ax ) >0.1 && count <=500)
F_tip=(2/ pi )∗ acos ( exp (B. ∗ (r_R−1)./(2∗r_R.∗ sind ( phi ) ) ) ) ;
% Correction due to tip l o s s e s
Cn=Cl .∗ cosd ( phi)+Cd.∗ sind ( phi ) ;
% Normal f o r c e
Ct=Cl .∗ sind ( phi)−Cd.∗ cosd ( phi ) ;
% Tangential f o r c e s
fo r q=1:1:n
i f ax (q) <0.4
new_ax(q)=1./(1+(4∗F_tip (q ) . ∗ ( sind ( phi (q ) ) . ^ 2 ) ) . / ( Sol (q ) . ∗Cn(q
e l s e
CT(q)=(8/9)+(4∗F_tip (q) −40/9).∗ ax (q)+(50/9−4∗F_tip (q ) ) . ∗ ax (q ) .
new_ax(q)=(18∗F_tip (q)−20−3∗ sqrt (CT(q).∗(50 −36∗ F_tip (q))+12∗F_
end
end
new_an=0.5∗( sqrt (1+4∗(new_ax − new_ax . ^ 2 ) . / ( L_tsr .^2)) −1);
% tangential induction f a c t o r
del_ax=abs (new_ax − ax ) ;
ax=new_ax ;
an=new_an ;
phi=atand((1−ax ) . / ( L_tsr .∗(1+an ) ) ) ;
% Relative Inflow angle ( degree )
% V_rel=sqrt ((V(q)∗(1−ax (q ))).^2+( rot ∗ r .∗(1+an (q ) ) ) . ^ 2 ) ;
% Relative v e l o c i t y (m/ s )
% Re1=V_rel .∗ c ∗69000;
% Reynolds number
fo r q=1:1:n
i f AOA(q)<=13
Cl (q)=interp1 (AOA_data, l i f t ,AOA(q ) ) ;
Cd(q)=interp1 (AOA_data, drag ,AOA(q ) ) ;
e l s e
Cl (q)=2∗Clmax∗ sind (AOA(q ))∗ cosd (AOA(q ) ) ;
Cd(q)=Cdmax∗ sind (AOA(q ) ) . ^ 2 ;
end
end
count=count +1;
end
Lf =(1/2)∗ rho ∗( V_rel ).^2.∗ c .∗ Cl∗ deltar ;
Df=(1/2)∗ rho ∗( V_rel ).^2.∗ c .∗Cd∗ deltar ;
Tf=Lf .∗ sind ( phi)−Df .∗ cosd ( phi ) ;
% Q=4∗pi ∗rho∗L_tsr ∗(V)^2∗an∗(1−ax )∗( r )^2∗ deltar ;
43. 6. Simulink Model and MATLAB codes 35
Qf=4.∗F_tip∗ pi ∗rho .∗ L_tsr ∗(V)^2.∗ an.∗(1 −ax ) . ∗ ( r ).^2∗ deltar ;
Tturb1 ( i )=sum(Qf ) ;
i=i +1;
%pitch=pitch + . 2 5 ;
end
%Qf
Tturb1
end
44. 6. Simulink Model and MATLAB codes 36
6.2 Simulink Models
in this section we present the Simulink models used in this project for Wind turbine and
it’s components such as pitch,etc.
6.2.1 Simulimk Model of Wind Turbine
Figure 6.1: Simulink Model of Wind Turbine
6.2.2 Pitch Model
Figure 6.2: Pitch Model
45. 37
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