FUNDAMENTAL AND
ADVANCED TOPICS
IN WIND POWER
Edited by Rupp Carriveau
Fundamental and Advanced Topics in Wind Power
Edited by Rupp Carriveau Published by InTech
Janeza Trdine 9, 51000 Rijeka, Croatia
Copyright © 2011 InTech
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Contents
Preface IX
Part 1 Aerodynamics and Environmental Loading
of Wind Turbines 1
Chapter 1 Aerodynamics of Wind Turbines 3
Emrah Kulunk
Chapter 2 Wind Turbines Theory - The Betz Equation
and Optimal Rotor Tip Speed Ratio 19
Magdi Ragheb and Adam M. Ragheb
Chapter 3 Inboard Stall Delay Due to Rotation 39
Horia Dumitrescu and Vladimir Cardoş
Chapter 4 Verification of Lightning Protection Measures 65
Søren Find Madsen
Chapter 5 Extreme Winds in Kuwait
Including the Effect of Climate Change 89
S. Neelamani and Layla Al-Awadi
Part 2 Structural and Electromechanical Elements
of Wind Power Conversion 113
Chapter 6 Efficient Modelling of Wind Turbine Foundations 115
Lars Andersen and Johan Clausen
Chapter 7 Determination of Rotor Imbalances 175
Jenny Niebsch
Chapter 8 Wind Turbine Gearbox Technologies 189
Using Two Simulation Based Optimization Techniques 379
Orhan Ekren and Banu Yetkin Ekren
Chapter 18 Fuzzy Control of WT with DFIG
for Integration into Micro-grids 399
Christina N. Papadimitriou and Nicholas A. Vovos Preface
As the fastest growing source of energy in the world, wind has a very important role
to play in the global energy mix. This becomes increasingly apparent as many
countries begin to phase out traditional fossil fuels, while some re-evaluate their
comfort level with nuclear power generation. The conversion of wind’s kinetic energy
into another desired form dates back millennia. The years since have afforded some
time for maturation of the technology. However, while many advances have been
made in the last 40 years, challenges remain in the complex interdependent
mechanisms that comprise wind energy production.
The first of such challenges include the natural environment in which the industry
the demand for energy increases in both the developed and developing worlds, so will
also increase the variety of end applications for wind power. The complete picture of the
energy grid of the future is far from totally defined. What is clear however, is the signifi-
cant part that wind power will play.
This text covers a spectrum of leading edge topics critical to the rapidly evolving wind
power industry. The reader is introduced to the fundamentals of wind energy aerody-
namics; then essential structural, mechanical, and electrical subjects are discussed. The
book is composed of three sections that include the Aerodynamics and Environmental
Loading of Wind Turbines, Structural and Electromechanical Elements of Wind Power
Conversion, and Wind Turbine Control and System Integration. In addition to the
fundamental rudiments illustrated, the reader will be exposed to specialized applied
and advanced topics including magnetic suspension bearing systems, structural health
monitoring, and the optimized integration of wind power into micro and smart grids.
Rupp Carriveau Ph.D. P.Eng.
Associate Professor
Civil and Environmental Engineering
University of Windsor
Part 1
Aerodynamics and Environmental Loading
of Wind Turbines
1
Aerodynamics of Wind Turbines
Emrah Kulunk
New Mexico Institute of Mining and Technology
USA
and across which
there is a pressure drop from
u
p
to
d
p
as shown in Fig. 1. At the outset, it is important to
stress that the actuator disc theory is useful in discussing overall efficiencies of turbines but
Fundamental and Advanced Topics in Wind Power
4
it cannot be utilized to design the turbine blades to achieve a desired performance. Actuator
disc model is based on the assumptions like no frictional drag, homogenous,
incompressible, steady state fluid flow, constant pressure increment or thrust per unit area
over the disk, continuity of velocity through the disk and an infinite number of blades. Fig. 1. Actuator Disk Model
The analysis of the actuator disk theory assumes a control volume in which the boundaries
are the surface walls of a stream tube and two cross-sections. In order to analyze this control
volume, four stations (1: free-stream region, 2: just before the blades, 3: just after the blades,
4: far wake region) need to be considered (Fig. 1). The mass flow rate remains the same
throughout the flow. So the continuity equation along the stream tube can be written as
(4)
Since the flow is frictionless and there is no work or energy transfer is done, Bernoulli
equation can be applied on both sides of the rotor. If we apply energy conservation using
Bernoulli equation between station 1 and 2, then 3 and 4, Eqn 5 and Eqn 6 can be obtained
respectively.
1
2
1
2
(5)
Aerodynamics of Wind Turbines
5
1
side
(8)
where
(9)
Substituting equation 7 into equation 8 gives the thrust on the disk in more explicit form.
1
2
∞
(10)
Combining Eqn 3, 4 and 10 the velocity through the disk can be obtained as
12
(14)
To find the power output of the rotor Eqn 15 can be used.
(15)
By substituting equation 10 into 15 gives the power output based on the momentum balance
on both sides of the actuator disk rotor in more explicit form.
1
2
∞
(16)
2
∞
(19)
∞
(20)
Substituting Eqn 17 into Eqn 18, the power coefficient of the rotor can be rewritten as
41
(21)
Also using the equations 10, 13 and 17 the axial thrust on the disk can be rewritten as
21
(24)
Applying the conservation of the angular momentum on upstream and the wake region of
the flow domain gives
(25)
Also the torque caused by the angular momentum balance on the differential annular
element can be obtained using Eqn 26.
(26)
where 2. Also applying the Bernoulli equation between station 1 and 2 then
between 3 and 4 gives Bernoulli’s constants as
1
2
And taking the difference between these constants gives
1
2
1
2
∞
1
2
1
2
2
(29)Fundamental and Advanced Topics in Wind Power
8
In station 4, the pressure gradient can be written as
(31)
The equation of axial momentum for the given annular blade element in differential form
can be written as
/2
(34)
An exact solution of the stream-tube equations can be obtained when the flow in the
slipstream is not rotational except along the axis which implies that the rotational
momentum wr
has the same value for all radial elements. Defining the axial velocities as
uU
1a
andu
U
1b
(40)
The power generated at each radial element is given by dPΩdQ. Substituting Eqn 40 into
this equation gives
(41)
Also the power coefficient for each differential annular ring can be written as
(42)
Substituting Eqn 41 into the Eqn 42 and integrating from hub tip speed ratio to the tip speed
ratio gives power coefficient for the whole rotor.
(43)
By solving Eqn 39 for a
in terms ofa Eqn 44 can be obtained.
(44)
Solving the equations 43 and 44 together for the maximum possible power production gives
(45)
Also substituting Eqn 45 into Eqn 39 gives the angular induction factor for maximum power
in each annular ring.
twist distributions of the blade airfoil. For this reason blade element theory needs to be
added to the design method. In order to apply blade element analysis, it is assumed that the
blade is divided into N sections. This analysis is based on some assumptions including no
aerodynamic interactions between different blade elements and the forces on the blade
elements are solely determined by the lift and drag coefficients. Fig. 3. Rotating Annular Stream Tube
Since each of the blade elements has a different rotational speed and geometric
characteristics they will experience a slightly different flow. So 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 (Fig. 3, 4). Overall performance characteristics
of the blade are then determined by numerical integration along the blade span. Fig. 4. The Blade Element Model
Aerodynamics of Wind Turbines
11
Lift and drag coefficient data are available for a variety of airfoils from wind tunnel data. Since
most wind tunnel testing is done with the aerofoil stationary, the relative velocity over the
airfoil is used in order to relate the flow over the moving airfoil with the stationary test (Fig. 5). Fig. 5. Blade Geometry for the analysis of a HAWT Rotor
Examining Fig. 5, the following equations can be derived immediately.
(49)
(58)
The solidity ratio can be defined as
(59)
Finally, the general form of elemental torque and thrust equations becomes
(60)(61)
Eqn 60 and Eqn 61 define the normal force (thrust) and the tangential force (torque) on
annular rotor section respectively.
2.4 Blade Element Momentum (BEM) theory
As it is stated before BEM theory refers to the determination of a wind turbine blade
performance by combining the equations of general momentum theory and blade element
theory, so Eqn 36 and 61 can be equated to obtain the following expression.
(62)
Also equating Eqn 40 and 60 in the same manner gives
Aerodynamics of Wind Turbines
13
(63)
By rearranging Eqn 63 and combining it with Eqn 50
The total power of the rotor can be calculated by integrating the power of each differential
annular element from the radius of the hub to the radius of the rotor.
(72)
And rewriting the power coefficient given in Eqn 18 using Eqn 72 gives
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