Upload
others
View
0
Download
0
Embed Size (px)
Citation preview
Politecnico di Milano
SCUOLA DI INGEGNERIA INDUSTRIALE E DELL'INFORMAZIONE
DIPARTIMENTO DI ENERGIA
Corso di Laurea Magistrale in Ingegneria Energetica
Tesi di laurea magistrale
Potentiality of Large and Small Scale Wind Turbines for
Electricity Generation
Laureando:
Raaele SANZI
Matricola: 872264
Relatore:
Prof. Federica FOIADELLI
Anno Accademico 2017/2018
Ai miei genitori e alla mia
famiglia, per tutto il supporto.
A Roncio, Ga, Ja e a Re Claudio,
compagni di viaggio al PoliMi.
Ai miei compagni di Piacenza.
Ricorderò sempre le nostre feste.
A Federica, Violeta, Asmaa e
Federica, amiche preziose.
A Bollaverde Live, che mi fa
vivere il Sogno.
A Claudio, Bianca, Davide,
Francesca, Matteo e Mauro, per le
avventure che immaginiamo
attorno a un tavolo. E a Verdiana
per i suoi dolci.
Contents
Abstract vii
Sommario vii
Introduction x
1 The wind resource 1
1.1 Denition of wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Interaction between wind and the ground . . . . . . . . . . . . . . . . . 1
1.3 Interaction between wind and buildings . . . . . . . . . . . . . . . . . . 2
1.4 Wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Measuring wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.6 Concepts of statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.6.1 Events and their probability . . . . . . . . . . . . . . . . . . . . 6
1.6.2 Random variables and probability distribution functions . . . . 6
1.7 Wind speed distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.7.1 The Weibull model . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.7.2 The Rayleigh model . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Wind turbines 13
2.1 Horizontal axis wind turbines . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Betz's elementary momentum theory . . . . . . . . . . . . . . . . . . . 14
2.3 Rotor aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 Drag devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.2 Lift devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.3 Blade element theory . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Vertical axis wind turbines . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.1 Savonius type . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.2 Darrieus type . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.3 Other VAWT shapes . . . . . . . . . . . . . . . . . . . . . . . . 24
i
ii CONTENTS
3 Electric power conversion 27
3.1 Fundamentals of electromagnetism . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Magnetic ux and ux density . . . . . . . . . . . . . . . . . . . 27
3.1.2 Induced voltage and force . . . . . . . . . . . . . . . . . . . . . 28
3.2 Power transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Electrical machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.1 Rotating magnetic elds . . . . . . . . . . . . . . . . . . . . . . 31
3.3.2 Synchronous machines . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.3 Induction machines . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3.4 Other types of generators . . . . . . . . . . . . . . . . . . . . . 35
3.4 Connection with the electrical grid . . . . . . . . . . . . . . . . . . . . 35
3.4.1 Fixed-speed generator systems . . . . . . . . . . . . . . . . . . . 36
3.4.2 Variable speed generator systems with inverter . . . . . . . . . . 38
3.4.3 Directly rotor-driven variable-speed generators . . . . . . . . . . 41
4 Wind turbine control 43
4.1 Maximum power point tracking (MPPT) . . . . . . . . . . . . . . . . . 43
4.1.1 MPPT with turbine power prole . . . . . . . . . . . . . . . . . 44
4.1.2 MPPT with optimal TSR . . . . . . . . . . . . . . . . . . . . . 45
4.1.3 MPPT with torque control . . . . . . . . . . . . . . . . . . . . . 45
4.2 Over-speed protection . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.1 Pitch control (active stall) . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 Passive stall control . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.3 Furling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Power electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.1 p-type and n-type silicon . . . . . . . . . . . . . . . . . . . . . . 48
4.3.2 pn junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3.3 Forward and reverse bias . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Semiconductor devices . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4.1 Power diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4.2 Bipolar junction transistors . . . . . . . . . . . . . . . . . . . . 55
4.4.3 Power MOSFETs . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.4 Thyristors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4.5 Insulated gate bipolar transistors . . . . . . . . . . . . . . . . . 61
4.5 Power conversion circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5.1 AC to uncontrolled DC . . . . . . . . . . . . . . . . . . . . . . . 62
4.5.2 AC to controlled DC . . . . . . . . . . . . . . . . . . . . . . . . 69
4.5.3 DC to DC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
CONTENTS iii
4.5.4 DC to AC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5 Small-scale wind power generation 83
5.1 Design of small wind turbines . . . . . . . . . . . . . . . . . . . . . . . 84
5.1.1 Blade design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.1.2 Blade manufacturing . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Blade testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3 The no-blade technologies . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3.1 Vortex Bladeless . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3.2 The Saphonian . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.4 Building-integrated wind turbines . . . . . . . . . . . . . . . . . . . . . 92
6 Economic evaluations of wind turbines 97
6.1 Energy yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Estimation of losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.1 Losses due to power control and operational sequence . . . . . . 99
6.2.2 Losses due to the mechanical-electrical energy conversion . . . . 99
6.3 Economic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3.1 General framework . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3.2 Main cost components . . . . . . . . . . . . . . . . . . . . . . . 101
6.4 Economics of small wind turbines . . . . . . . . . . . . . . . . . . . . . 104
Conclusions 108
List of Figures 112
List of Tables 113
List of Symbols 115
List of Acronyms 122
Bibliography 124
Abstract
Renewable energy sources are on the rise due to the ever increasing electric energy
demand. The pollution caused by the conventional energy conversion systems, which
mainly use fossil fuels, also contributes to the popularity of these cleaner systems.
Among the dierent solutions for renewable energy, one of the most promising one is
wind power. This work aims at exploring the potentiality of wind turbines for electricity
generations. The wind resource will be studied, as well as the physical principles
behind the functioning of these systems. Some time will be dedicated to smaller-scale
wind turbines, in particular to the newer and innovative solutions which include the
integration with buildings. A solid economic framework will allow to determine whether
they represent an economically competitive alternative to other small-scale renewable
energy systems.
Keywords: building-integrated wind turbines, renewable energy, small-scale
wind turbines, wind energy, wind turbines
v
Sommario
Le fonti rinnovabili di energia stanno prendendo piede a causa dell'incessante aumento
della domanda di energia elettrica. Anche l'inquinamento causato dai sistemi conven-
zionali di conversione dell'energia, che utilizzano principalmente combustibili fossili, è
un fattore che contribuisce alla popolarità di questi sistemi più "verdi". Tra le varie
soluzioni per l'energia rinnovabile, una delle più promettenti è l'energia eolica. Questo
lavoro ha lo scopo di esplorare le potenzialità delle turbine eoliche per la produzione di
energia elettrica. La risorsa vento sarà studiata, così come i principi sici che stanno
dietro al funzionamento di questi sistemi. Del tempo sarà dedicato alle turbine di pic-
cola taglia e in particolare alle soluzioni più nuove e innovative, inclusa l'integrazione
con gli edici. La teoria economica permetterà di determinare se rappresentano una
valida alternativa dal punto di vista economico, rispetto ad altre soluzioni per l'energia
rinnovabile.
Parole chiave: energia eolica, energia rinnovabile, turbine eoliche, turbine
eoliche di piccola taglia, turbine eoliche integrate con gli edici
vii
Introduction
The demand for electrical energy is increasing year after year. The International Energy
Agency (IEA) predicted that, from 2007 until 2030, the demand for primary energy
would increase by 40% [8]. However it is commonly known that fossil fuels, which are
employed in the traditional energy conversion plants, have nite reserves, and they
are bound to run out in the long run. Also, they cause serious pollution: combus-
tion processes produce signicant amounts of particulate matter (although nowadays
power plants are equipped with state-of-the-art air pollution control systems to reduce
their emission) and of compounds which are dangerous to the atmosphere, such as the
infamous carbon dioxide.
In this context, renewable energy sources are allowed to ourish. In fact, they are
able to supply a good part of the increasing demand, and in much cleaner ways, with al-
most no CO2 emissions. Their energy conversion processes are very much similar to the
traditional power plants: rotating machines and thermodynamic cycles are involved,
as well as electrical machines and power converters. Nevertheless, the primary energy
which constitutes the rst step of the energy conversion chain does not come from a
fossil fuel, but from sources that are self-renovating, from which they are termed as
renewables. The reserves of these renewable energy sources are almost innite: the Sun
is not supposed to stop giving us its energy until around 5 billion years in the future,
while the wind, even if it intermittent, is generated by atmospheric phenomena which
never stop; urban waste is instead continuously produced by the everyday activities of
people.
Between all these dierent solutions for green energy, wind power is particularly
interesting. The energy of the wind has been harnessed since the beginning of human
civilization. The ancestors of the modern wind turbines are windmills, about which the
rst reliable information dates back to 644 A.D. [6]. Wind power technology has since
had centuries of perfecting and improving, until the modern wind turbines arrived.
The aim of this work is to provide a wide understanding of the potentiality of large
and small scale wind turbines for electricity generation. At present the technology
of large-scale wind power production is very sound, with high levels of reliability. It
ix
x INTRODUCTION
also represents a competitive alternative to the other traditional power plants, both
from an economic point of view and in terms of power generation. So much so that in
2015, according to the Global Wind Energy Council, the installed wind capacity had
increased by an average of 23% over the world during the past 18 years [4]. Also, in the
same year wind energy accounted for 44.2% of power capacity installations in Europe
[17]. Smaller-scale wind power generation needs particular attention. Mini and micro
wind turbines are not just a scaled-down version of their larger counterparts, but they
can be considered a new technology altogether. Innovative design solutions set them
apart from other wind turbines, but their potential for power generation is undisputed:
in fact, they are able to exploit the wind which is not interesting for large-scale power
production, such as air currents between buildings or low height wind. Small wind
turbines are especially useful for localised generation.
Chapter 1 of this work studies the wind resource: its interaction with the ground
and the buildings will be seen, as well as the means to measure wind speed . The
next chapter will introduce the topic of wind turbines: the physical principles that
regulate their functioning will be explained. The two dierent types of wind turbines,
horizontal-axis and vertical-axis will also be seen. Chapter 3 enters into the details
of the conversion of the power generated by a turbine's rotor, studying the theory
behind the functioning of the electrical machines. Then, the dierent types of electrical
generator will be seen, as well as the dierent solutions for coupling the generator itself
to the electrical grid. The fourth chapter explains the dierent methods by which
the mechanical power output of a wind turbine can be controlled Also the electrical
control of a turbine will be studied: semiconductor devices will be introduced, then
the dierent power conversion circuits will be seen. Chapter 5 is dedicated to small-
scale wind turbines. After explaining some particular design solutions and seeing the
processes of manufacturing and testing of their blades, some innovative technologies for
small wind turbines will be seen. To close the chapter, the topic of building-integrated
wind turbines will be introduced. The nal chapter gives some economic perspective.
A general economic framework, which works for a generic power plant, will be given
rst. Then, the dierent cost components regarding specically wind turbines will
be explored. Since it does not make sense to compare large wind turbines and small
ones from an economical standpoint, a case study will compare a small wind turbine
with a small-scale solar PV system, to see if mini and micro wind turbines represent a
valid alternative to other small-scale green technologies. The hope is that a small wind
energy conversion system will be competitive.
Chapter 1
The wind resource
Before studying the conversion of wind energy, it is important to understand the wind
as a resource. A denition of wind will be given, then, since the practical interest
is in low altitudes, its interaction with the ground and the buildings will be studied.
Finally, the focus will switch to the measuring and modelling (with some insight on
the statistics principles behind it) of wind speed for practical uses related to power
production.
1.1 Denition of wind
Wind can be dened as the movement of air masses with respect to the still surface,
due to atmospheric pressure dierences and to convective currents, caused by the non-
uniform heating from the Sun; also Earth's rotation has an eect, causing the so-called
Coriolis eect.
1.2 Interaction between wind and the ground
In the context of wind engineering the interest is in "supercial" winds, i.e. up to a
height of 600 to 1000 m; this is because it should be taken into account the eect
that the ground has on wind speed and direction: the air mass closer to the ground is
slowed down by friction, slowing in turn the air above it. This eect is less and less
pronounced as height increases, up to a value where it does not aect anymore the
movement of the air. This behaviour creates a well determined turbulence zone, called
Planetary Boundary Layer (PBL).
The roughness of the ground acts as an obstacle to wind movement. It can be
considered then that a stratication occurs, where wind speed is assumed to be zero,
1
2 CHAPTER 1. THE WIND RESOURCE
up to a certain height, called roughness length Z0 ; it is dened as the average height of
the vortexes that are generated by the contact of the air mass with the ground prole
(see Fig. 1.1), and corresponds to the height of the PBL. When the height is higher
than Z0 wind speed starts to increase. Of course the value of Z0 is strongly dependent
on the considered geographic area.
Figure 1.1: Graphical representation of the roughness length Z0 (Source: [16])
The shear stress caused by the wind in its interaction with the ground can be
evaluated through the friction speed, which can be calculated at a specic height z by
using the following formula:
ln
(z
Z0
)= K
uzuz0
(1.1)
Where:
• z = considered height;
• K = 0.33÷ 0.43 = Von Karman constant;
• uZ0 = friction speed at height Z0;
1.3 Interaction between wind and buildings
In the applications of wind power, especially at small scale, it is key to understand
how wind interacts with buildings. This is to estimate the power production of a
roof-mounted small turbine, or to assess the loads due to turbulence.
Like most of the man-made structures, buildings are blu bodies [7]. One of the
characteristics of blu bodies is the formation of large vortices in their wakes. These
vortices are due to a phenomenon called vortex shedding : air wraps around the building
on the top and on the sides, generating a turbulence which causes sudden and large
variations in pressure, as shown in Fig. 1.2. This pressure variation causes in turn an
unpredictable wind ow, both in terms of speed and direction. Another inuence on
1.4. WIND SPEED 3
Figure 1.2: Pressure coecients variation in a CFD simulation (Source: [2])
wind that buildings might have is a sort of "tunnel eect", where the ow cross section
decreases due to a relatively narrow passage between two buildings and wind speed
increases.
The subject is still being studied, since it is important also in other elds, like civil
engineering, where it is crucial to determine the loads that the wind imposes on high
rise buildings [7] [2].
1.4 Wind speed
The moving air masses in the lower Troposphere are inuenced by other eects coming
from the ground, such as heat transfer and moisture transfer. Another zone, called
Atmospheric Boundary Layer (ABL) creates. Wind speed increases with height up to
a constant value at a set height, called gradient height.
In the ABL wind speed Uzcan be evaluated at each height value z only as an
average value due to the many factors that inuence it. Typically this average speed
is simply measured (see Section 1.5); however, when such data is not available, it can
be calculated. Taking a reference height zrefwhere the wind speed Uref is known, the
following formula can be used:
UzUref
=
(z
zref
)α(1.2)
4 CHAPTER 1. THE WIND RESOURCE
Where α is the roughness coecient, which depends on the characteristics of the
ground. An example of the calculation of wind speed can be found in [16].
Of course wind speed is expressed in m/s in the SI system of units. However, for
a very rst assessment of the wind regime the Beaufort scale is used: it associates
visible eects to diferent ranges of wind speeds (see Table 1.1). Another scale that
is commonly used is the Griggs-Putnam scale, which is based only on the reaction of
trees to the action of the wind (see [16]).
1.5 Measuring wind speed
Being able to measure the wind speed in the chosen location is one of the rst crucial
steps in determining the feasibility of a wind turbine.
The main parameters that must be measured are essentially two:
• Direction: it can be measured with a simple vane, free to rotate on a vertical
axis. Its angular position with respect to a reference will indicate the wind
direction;
• Speed: many instruments are designed to measure this parameter. The simplest
is a hemispherical cup rotor, whose rotation velocity is proportional to wind
speed; the advantage of this type of sensor is that it has a very low inertia, so it
is able to respond very rapidly to the slightest variations in wind speed.
Both direction and speed sensors can be combined into anemometers.
In any case, no instantaneous values of wind speed are registered, but only average
values. For very rst estimates, small sampling intervals, such as ve to ten minutes
long, can suce. In that case, the data are elaborated into hourly, daily, monthly or
even yearly values. More commonly, measuring campaigns are put in place, which can
last from one year to several years. This is useful, however, only for a rst analysis;
more precision is needed. For this reason, since typically a huge amount of data is
registered over a long period of time, a statistical evaluation of the wind speed is more
suitable in order to have a more general insight on the wind patterns of the chosen
site. Before continuing with the elaboration of the registered data, it is important to
understand the fundamental concepts driving their analysis.
1.5. MEASURING WIND SPEED 5
Table
1.1:TheBeaufort
windspeedscale
Windspeed(m
/s)
Beaufort
scalevalue
Windforcenotation
Visibleeects
inland
0÷
0.2
0Calm
Smokerisesvertically
0.3÷
1.5
1Lightair
Smokeindicates
wind,windvanes
don't
1.6÷
3.3
2Lightbreeze
Windperceptibleon
face,windvanes
move
3.4÷
5.4
3Gentlebreeze
Leavesandthin
branches
move,windextendspennants
5.5÷
7.9
4Moderatebreeze
Thin
branches
move,dust
andpaper
areraised
8.0÷
10.7
5Fresh
breeze
Smalltreesbegin
tosw
ay,whitecapsform
onlakes
10.8÷
13.8
6Strongbreeze
Thickbranches
move,telegraphlines
whistle
13.9÷
17.1
7Moderategale
Wholetreesmove,di
cultto
walk
17.2÷
20.7
8Fresh
gale
Branches
break
otrees
20.8÷
24.4
9Stronggale
Minor
dam
ageto
houses(roof
tiles)
24.5÷
28.4
10Wholegale
Trees
areuprooted
28.5÷
32.6
11Storm
Signicantdam
ageto
houses
32.7÷
5612÷
17Hurricane
Storm
dam
age,widespread
devastation
6 CHAPTER 1. THE WIND RESOURCE
1.6 Concepts of statistics
1.6.1 Events and their probability
According to the theory of probability (see [14]) an experiment is any phenomenon
or process that produces an outcome. The sample space is the set of all the possible
outcomes of an experiment. Any of its subsets, containing a set of outcomes, is called
an event ; an event is indicated by capital letters (A, B, . . . ).
Consider a repeated experiment with sample space S. For each event A exists a
number P (A), called probability of A, that indicates the proportion of times that
the outcome is contained in A. It is equivalent to its long-run relative frequency. The
probability of an event has the following properties:
1. 0 ≤ P (A) ≤ 1;
2. P (S) = 1;
3. Consider another event B. If A and B are disjoint, i.e. they are mutually exclu-
sive, then P (A ∪B) = P (A) + P (B).
To better see the probability of an event as a relative frequency, take as an example
the simulation of a number n of coin tosses [14]. The results of the experiment are
reported in Table 1.2:
Table 1.2: Results of simulated coin tosses (Source: [14])
nNumber of Number of Relative probability
heads tails of "heads"
10 3 7 0.350 21 29 0.42100 46 54 0.46500 248 252 0.4962000 1004 996 0.5026000 3011 2989 0.50188000 3974 4026 0.496810000 5011 4989 0.5011
1.6.2 Random variables and probability distribution functions
When performing an experiment, very often the interest is not on the single results,
but rather on some other numerical quantity determined by them. For instance in dice
tossing, usually what is of interest is the sum, and not the values on the individual
dice. These quantities are called random variables. Since the value of a random
1.6. CONCEPTS OF STATISTICS 7
variable depends directly on the outcome of the experiment, it is possible to apply the
concept of probability to them, too.
Consider for example a family with three children of unknown sex. The sample
space of this observation is as follows:
(b, b, b) , (b, b, g) , (b, g, b) , (b, g, g) , (g, b, b) , (g, b, g) , (g, g, b) , (g, g, g)
Assume that all outcomes are equally likely, i.e. each of them has probability 1/8. A
random variable, denoted by X, could be the number of female children. It is clearly
dependent on the result of the observation, so it can assume the values of X = 1, 2, 3.
The probability of observing only one girl is then:
P (X = 1) = P (b, b, g) , (b, g, b) , (g, b, b) =3
8
The complete example can be seen in [14].
A random variable is discrete if its possible values are separated points on R , like in
the example above. Calling its n possible values x1, x2, x3, . . . , the probability that X
is equal to one of them is denoted as P (X = xi). The collection of these probabilities
is called the probability distribution of X. Moreover, it is evident that:
n∑i=1
P (X = xi) = 1 (1.3)
An example of a graphical representation for a probability distribution is presented in
Fig. 1.3.
Figure 1.3: Probability distribution of a discrete random variable (Source: probability-course.com)
8 CHAPTER 1. THE WIND RESOURCE
The expected value, or mean, of a random variable is dened as:
E [X] = µ =n∑i=1
xiP (X = Xi) (1.4)
It is the weighted average of the possible values of X. Interpreting the probability
of an outcome as its relative frequency, E[X] is the average value of X over a large
number of repetitions of an experiment. It is important to notice that the expected
value of a random variable can be a value that is not included in all the possible ones,
for example it can be in between two discrete values.
The expected value is a very useful parameter, however it cannot give a measure of
the variation, or spread, of the possible values. While X takes on values around µ, the
natural way of measuring the spread of the values is to consider their distance from the
mean value on average (E[|X − µ|]). However, it results more convenient to consider
the square of the dierence; thus, the variance of the random variable is dened as:
V ar(X) = σ = E[(X − µ)2
](1.5)
A continuous random variable can assume all the values contained in an interval,
rather than having discrete values. Every variable of this type has a curve associated to
it, called a probability density function. Consider the probability density function
represented in Fig. 1.4: taking two points a and b, with a < b, the probability that
Figure 1.4: Probability density function of a continuous random variable (Source: weibull.com)
X assumes a value in between those two is equal to the area under the curve between
them. Also, in parallel with formula (1.3), it is evident that the total area under the
curve is equal to 1.
1.7. WIND SPEED DISTRIBUTION 9
1.7 Wind speed distribution
The registered wind speed data is reported in a graph, giving a frequency distribution;
for every time step t1, t2 . . . , tn there will be corresponding values for the wind speed
u1, u2, . . . , un. It can then be considered:
• maximum speed umax = max(u1, u2, . . . , un);
• minimum speed umin = min(u1, u2, . . . , un);
• average speed um =u1 + u2 + · · ·+ un
n.
This last parameter is of course the most important to assess the experimental data; in
order to determine the dispersion of this data around the average value, the standard
deviation can be used:
δ =√σ2 =
√(u1 − um)2 + . . . (u1 − un)2
n
Single values of wind speed can occur many times along the whole measuring inter-
val, which can be as long as three years. It is then convenient to report the frequency
at which they are present; calling ny the number of times the speed y was measured in
a pool of N samples on a number X of time intervals, its frequency is:
fy =nyN
It goes without saying that f1 +f2 + · · ·+fX = 1. The result is a frequency distribution
that can be easily plotted. This is extremely useful when making estimates of the total
energy produced by a turbine for an economic evaluation.
1.7.1 The Weibull model
One mathematical model to simulate the real frequency distribution of wind speeds
(which is often not enough, since the wind is a very variable resource) is the Weibull
model. For every value of speed u we can derive a probability density :
f(u) =k
A
( uA
)k−1exp
[(−ua
)k](1.6)
Where:
• k = form factor, depending on the site;
10 CHAPTER 1. THE WIND RESOURCE
• A = scale factor, given by A = (0.586 + 0.433/k)1/k.
In a(u, f(u)
)graph, the area under this function represents the total distribution,
equal to 1. An example of a Weibull function with varying k and constant um can be
seen in Fig. 1.5.
Figure 1.5: Weibull function depending on the k parameter, with constant um = 6 m/s(Source: homerenergy.com)
Of course this model cannot simulate particular distributions, such as one with two
peaks, but it is still very useful. An example of how well this function can approximate
measured data is shown in Fig. 1.6.
Figure 1.6: Weibull function vs experimental data (Source: [12])
1.7.2 The Rayleigh model
The frequency distribution of this model is as follows:
f(u) =π
2
u
umexp
[−π
4
(u
um
)2]
(1.7)
1.7. WIND SPEED DISTRIBUTION 11
Making the comparison with Eq. (1.6), it is evident that the Rayleigh model is a
particular case of the Weibull model, corresponding to k = 2. The parameter k in the
Weibull model takes a set value in similar climatic areas, for example 1.5 in mountain
areas, 2 in mild climate and coastal areas, and 3 in very windy areas.
Chapter 2
Wind turbines
The conversion of the kinetic energy of the wind into mechanical energy requires the
use of rotating machines. Like the more common gas or steam turbines, wind turbines
are able to receive the ow of a uid and, due to their particular shape, convert its
kinetic energy into mechanical energy. Then, the revolving rotor is connected to a
generator, which will convert the mechanical energy into electrical energy that can be
distributed into the network.
This Chapter will explore rst the more common conguration of wind turbines,
with a horizontal rotation axis: after a small introduction, the physical principles
behind their functioning will be studied, considering the dierent aerodynamic forces
that inuence power conversion. Then, vertical axis wind turbines (VAWTs) will be
seen.
2.1 Horizontal axis wind turbines
Horizontal axis wind turbines (HAWTs) constitute the most part of the wind turbines
used at present. Their realisation is typically based on the "propeller-like" concepts,
whose advantages are the main reasons why the horizontal conguration is the most
used:
• Rotor speed and power output can be easily controlled by regulating the blade
pitch and by other methods (see Chapter 4);
• The blade shape can be aerodynamically optimized in order to maximize the
exploitation of the lift force (see Section 2.3);
• The technology in the design of propellers is very sound and is a decisive factor.
Two main congurations exist, depending on the positioning of the rotor with re-
spect to the tower:
13
14 CHAPTER 2. WIND TURBINES
• Upwind: A turbine built with this conguration can be seen on the left of
Fig. 2.1: the rotor faces the wind directly without interference from the tower.
This means a higher eciency since all the swept area of the rotor interacts with
the ow. This type of turbine is also quiet. The main drawback of this congu-
ration is that it is not self-aligning and it needs a tail vane or yaw servomotors.
Its blades also need to be stier in order not to hit the tower while rotating;
• Downwind: in this conguration (on the right of Fig. 2.1) the wind encounters
the tower rst, then acts on the blades; it is evident then that its eciency is
lower with respect to an upwind HAWT. This drawback is compensated by the
fact that such a turbine is self-aligning. It can also withstand stronger winds
since it has a exible rotor, but is noisier.
Figure 2.1: Upwind HAWT VS Downwind HAWT
2.2 Betz's elementary momentum theory
Between 1922 and 1925, Albert Betz published writings showing that, by applying
elementary physical laws, the mechanical energy extractable from an air stream is
only a proportion of the energy or power contained in it. This momentum theory
assumes that the energy converter, i.e. the turbine rotor, works without losses and
in a frictionless airow; it is also a very simplied model, and its results are useful
only for rough estimates in practice. However, it provides a very solid basis for the
understanding of wind energy conversion.
Some more assumptions have to be made:
• Homogeneous, incompressible, steady state ow;
• No frictional drag;
2.2. BETZ'S ELEMENTARY MOMENTUM THEORY 15
• Innite number of blades (from which this theory is sometimes called actuator
disc theory);
• Uniform thrust over the rotor area;
• Non-rotating wake;
• Static pressure far upstream and far downstream are equal to the undisturbed
ambient static pressure.
The maximum theoretical value of power that can be extracted from the wind
depends on its kinetic energy:
Pmax = m · EK = m1
2V 2∞ =
1
2ρSV 3
∞ (2.1)
Where V∞ is the wind speed and S is the rotor swept area. Considering a control
volume bounded by the surface of a stream tube and two of its cross-sections (see
Fig. 2.2), continuity imposes:
m1 = m2
ρ1V1S1 = ρ2V2S2
With constant mass ow, velocity after the energy converter must decrease; this means
that, at the same time, ow cross-section has to increase.
The mechanical power extracted from the wind is equal to the power dierence
across the rotor:
PW =1
2mV 2
1 −1
2mV 2
2 (2.2)
This equation clearly shows that the maximum value of power, already dened in
Eq. (2.1), is obtained for V2 = 0, i.e. the air stream should be completely stopped
Figure 2.2: Flow conditions of a free-stream air ow through an energy converter (Source:commons.wikimedia.org)
16 CHAPTER 2. WIND TURBINES
by the converter. This result, however, does not make sense physically: if the outow
velocity is zero, then also the inow velocity must be zero, resulting in no ow at all. It
can then be assumed that there will exist an optimal value for V2/V1 where the power
extracted has its maximum value.
The force, or thrust, acting on the rotor during the process comes from momentum
conservation:
T = m (V1 − V2)
By the second principle of dynamics, the converter exerts an equal force on the air
ow, which pushes the air mass at velocity v′. The power required for this is:
PT = T · v′ = m(V1 − V2)v′ (2.3)
It is evident that it must be PT = PW :
m(V1 − V2)v′ =1
2m(V 2
1 − V 22 ) (2.4)
Solving for v′, it turns out that ow velocity through the converter is exactly equal to
the arithmetic mean of the velocities before and after the converter:
v′ =V1 + V2
2(2.5)
The mass ow becomes:
m = ρSv′ =1
2ρS(V1 + V2)
and the mechanical power output of the converter can be expressed as:
P =1
4ρS(V 21 − V 2
2 ))
(V1 + V2) (2.6)
Taking as reference the maximum power that in theory can be extracted from the
wind (see Eq. (2.1)), the power coecient Cp is dened:
Cp =P
Pmax=
14ρS (V 2
1 − V 22 )) (V1 + V2)
12ρSV 3
1
(2.7)
This expression can be re-arranged in order to express Cp as a function of the velocity
ratio V2/V1:
Cp =1
2
[1−
(V2V1
)2][
1 +V2V1
](2.8)
2.2. BETZ'S ELEMENTARY MOMENTUM THEORY 17
It represents the fraction of maximum power that can be extracted from an air stream.
Fig. 2.3 shows a graphical representation of Cp as a function of V2/V1. It can be
Figure 2.3: Power coecient as a function of the velocity ratio (Source: [6])
analytically found in a simple way that it exists a maximum for V2/V1 = 1/3. This
value of the ideal power coecient is called the Betz limit (or Betz factor):
Cp,max =16
27' 0.593 (2.9)
Another approach, which yields the same nal results, denes the axial induction
factor:
a =V1 − v′
V1(2.10)
It represents the fractional decrease in wind velocity between the free stream and the
rotor plane. By combining Equations (2.5) and (2.10), all the velocities in the analysis
can be written as functions of a and V1:
v′ = V1(1− a) V2 = V1(1− 2a)
Also equation (2.3) can be rewritten:
PT = mv′(V1 − V2) =
= ρS2v′2(V1 − V2) =
= ρS2V21 (1− a)2 [V1(1− 2a)] =
= 2ρS2a(1− a)V 31
(2.11)
Equations (2.1) and (2.11) can be combined to dene the power coecient Cp as a
18 CHAPTER 2. WIND TURBINES
function of a:
Cp =PTPmax
=2ρSa(1− a)2V 3
112ρSV 3
1
= 4a(1− a)2 (2.12)
Again, a maximum value for Cp as a function of a exists (see Fig. 2.4), and simple
calculus allows to calculate it. The value of a for which this maximum exists is again
Figure 2.4: Power coecient as a function of the axial induction factor
a = 1/3, and the nal result for the Betz facotr is the same as Eq. (2.9).
As it was pointed out before, Betz's momentum theory is based only on physical
principles, and its result is an ideal limit for the extraction of power from an air
stream. It does not consider the design of the energy converter, which is a key factor
in determining the power that can be converted in real conditions. A more thorough
analysis is needed.
2.3 Rotor aerodynamics
The rotor is clearly the primary element of a wind turbine. Its capability to convert
wind energy are a direct result of its aerodynamic properties, which determine the
energy and power output. Other factors that are aected by the aerodynamics of the
rotor are the torque (which must be kept uniform), the loads imposed on the mechanical
and electrical elements (which must be kept as low as possible), and the functioning of
the control system. The design of a turbine rotor is thus a key step in the construction
of a wind turbine.
In this section are presented the physical principles describing the aerodynamic
force that develops on bodies exposed to a uid ow. Such force can be resolved
2.3. ROTOR AERODYNAMICS 19
into its components: drag D in the direction of ow, and lift L, perpendicular to it.
The mechanisms for the production of mechanical power can exploit either of the two,
however one the real power coecients strictly depend on which of the two is dominant.
2.3.1 Drag devices
Drag devices are the simplest type of energy converters. Fig. 2.5 shows a surface of
this type facing the wind. The aerodynamic drag is expressed as:
D = CD1
2ρ(vw − vr)2A (2.13)
Where:
• CD = drag coecient;
• vw = wind velocity;
• vr = relative velocity;
• A = surface area.
The corresponding power is:
PD = Dvr = CD1
2ρ(vw − vr)2Avr (2.14)
Using a similar approach as the momentum theory, and by comparing this power with
the maximum value extracted from the free ow stream, it can be found that the power
coecient has its maximum value at the velocity ratio of vr/vw = 1/3, and is equal to
Cp,drag,max = 427CD. The drag coecient of a concave surface curved against the wind
Figure 2.5: Aerodynamic forces on a drag device (Source: [6])
20 CHAPTER 2. WIND TURBINES
direction hardly exceeds a value of 1.3; thus, the maximum power coecient of a pure
drag rotor is:
Cp,drag,max ≈ 0.2
A drag-type device, then, only achieves about one third of the Betz factor. It is
important to notice that this derivation only applies to a translational motion of the
surface, even though Fig. 2.5 shows a rotating motion just to show the application to
a wind rotor.
2.3.2 Lift devices
In this type of devices wind velocity vw is vectorially combined with the peripheral
velocity of the blade u. As for every other body hit by an air stream, the drag and lift
forces develop. In particular the lift force can be resolved into its components: the one
in the plane of rotation is responsible for the rotor torque and is termed Ltorque, while
the one perpendicular to it, Lthrust, causes rotor thrust.
Modern airfoils used for wind energy derive from aircraft wings design. Its key
characteristic is the lift-to-drag ratio (E), which can have values up to 200. This shows
qualitatively how much more eective the exploitation of the lift force is with respect to
drag. However, for the explicit calculation of the power coecient, elementary physical
relationship are not sucient anymore, and a more sophisticated analysis is needed.
2.3.3 Blade element theory
As an extension of Betz's momentum theory, this model assumes a tri-dimensional
approach: the rotating converter does not only slow down the ow, but it also imparts
a rotating motion, or spin, to the rotor wake. The energy contained in the spin is of
course a proportion of the stream's energy, thus it reduces the extractable mechanical
energy with respect to the ideal value given by Betz. The power coecient then must
be smaller than the one found with the momentum theory.
Moreover, it must be considered that now the air stream has both rotating and
translational motions. The power coecient then will depend on the ratio between the
tangential velocity of the rotor blades and the undisturbed air velocity; this ratio is
called tip speed ratio (TSR) λ, since it is usually referred to the tangential velocity
of the blade tip:
λ =u
vw(2.15)
By introducing rotor blade geometry into the model, the relationship between the
2.4. VERTICAL AXIS WIND TURBINES 21
actual rotor shape and its aerodynamic properties can be found. The blade element
(hence the name of the theory) is determined by a set distance r from the rotor centre
and a radial "thickness" dr, which determine a "strip", as shown by Fig. 2.6; this is
why this theory is sometimes called strip theory.
Figure 2.6: Blade element denition (Source:[9])
Without entering into details (see [9] for the complete analysis), it repeats locally
on the strip the linear momentum analysis, considering a control volume that moves
with the angular velocity of the blades. It denes a local thrust dT depending on both
the angular velocity of the element Ω and on the angular speed imparted to the ow
stream ω; these two parameters are also used to dene the angular induction factor:
a′ =ω
2Ω(2.16)
This, combined with a, allows to dene an incremental torque dQ exerted on the rotor,
from which the power generated at each element dP = ΩdQ. This power is a function
of the axial and angular induction factors, and of the tip speed ratio.
Each element gives its incremental contribution to the power coecient:
dCp =dP
12ρSv3w
(2.17)
At the conditions of maximum power production, Cp,max can be derived exclusively as a
function of the tip speed ratio. Fig. 2.7 shows that the Betz limit acts as an asymptote
for Cp as λ increases.
2.4 Vertical axis wind turbines
Vertical axis wind turbines (abbreviated as VAWTs) present several advantages with
respect to HAWTs. Firstly, they are not bound to wind direction, so they always have
22 CHAPTER 2. WIND TURBINES
Figure 2.7: Power coecient as a function of the tip speed ratio (Source: [9])
a positive power output (provided of course that the wind speed is sucient). Then,
their design is overall simpler:
• They don't need a yaw mechanism;
• Blade design is possibly simpler;
• There is a single moving part.
These advantages combine into a lighter rotor, which is faster to accelerate and decel-
erates slower, thus increasing the eciency with variable wind speed. This makes them
more suited for urban installation, where the wind is very unsteady. As far as operation
is concerned, they can be located closer to the ground, allowing easier installation and
maintenance; they are also quieter.
Their main downside is that the bearings at the base have to sustain the whole
weight of the tower and of the blades. This exposes them to great pressure, which
translates into quicker wear, causing more frequent maintenance interventions. Also,
maintenance on a VAWT requires the turbine to be disassembled, with an obviously
long interruption of its operation.
The main forces acting on the blades of a VAWT are the same as any airfoil, i.e.
lift and drag. Just as HAWTs (see Section 2.3), they can exploit them in dierent
proportions; the most common two designs will be explained, then some less common
congurations will be seen.
2.4.1 Savonius type
This type of VAWT was given its name by its inventor, the Finnish engineer S. J.
Savonius, in 1929. It is a drag force driven wind turbine.
It has a "S-shaped" cross section, constructed by two semicircular buckets slightly
2.4. VERTICAL AXIS WIND TURBINES 23
overlapped, and a shaft (see Fig. 2.8). Its operating principle is based on the drag
Figure 2.8: A Savonius rotor (Source: wikipedia.org)
dierence between the concave and the convex parts of the buckets, similarly to what
was described in Section 2.3.1.
Its advantages are many:
• Simple design and very low cost;
• Large torque at startup;
• Low noise emission;
• Insensitive to wind direction.
The main drawback, however, is that it has a very low eciency: its Cp does not
exceed 0.25 when optimized, and it occurs at low tip speed ratios. As a consequence
of this, the Savonius VAWT is mainly used for small power applications, such as water
pumping, or as a starter for other kinds of VAWT.
2.4.2 Darrieus type
This type of VAWT was developed by the French Engineer Georges Jean-Marie Dar-
rieus. It is a lift driven turbine, and it is constituted of two or more airfoil-shaped
blades attached to the rotating vertical shaft.
The most common structure has curved blades and is called troposkien shape from
the greek "turning rope"; it is sometimes called also the egg beater for its resemblance
to the kitchen utensil. Other names are D-Darrieus or φ-Darrieus. Fig. 2.9 shows a
VAWT of this type, the Dornier Darrieus 50. This shape allows for lower stress on the
blades, at the price of a more complex blade design. It is optimal for medium scales
applications.
24 CHAPTER 2. WIND TURBINES
Figure 2.9: The Dornier Darrieus 50 VAWT (Source: en.wind-turbine-models.com)
The principle of operation of a Darrieus turbine resides in the fact that the relative
wind velocity (called Wr in Fig. 2.10) has a certain angle of attack on the blade, which
depends on wind direction and rotation speed. Then, the lift generated on the airfoil
creates torque at the shaft; it is important to notice that the rotation direction is
counter-intuitive with respect to the usual theory and practice of airfoils (see [9] for a
thorough analysis). This model assumes that the turbine is already rotating. It is then
Figure 2.10: Forces on an airfoil for VAWTs (Source: researchgate.com)
evident that the startup of the turbine is dicult, since when the rotational speed ω
is equal to zero very low torque is generated. Variable pitch blades can be used.
2.4.3 Other VAWT shapes
Other notable dierent shapes for VAWTs consist mainly in variations of the "original"
designs. For example, a Savonius with four buckets or with eccentric palettes. Its blades
can also be much longer and arranged into a spiral, as shown in Fig. 2.11.
Turbines can even be combined: as it was anticipated in Section 2.4.1, a Dar-
rieus turbine can have two or more starter Savonius, changing its name into Dar-
2.4. VERTICAL AXIS WIND TURBINES 25
Figure 2.11: A VAWT with spiral blades (Source: wxnaiermic.en.made-in-china.com)
rieus/Savonius turbine. Fig. 2.12 shows the Dornier Darrieus/Savonius 5.5 kW.
Figure 2.12: The Dornier Darrieus/Savonius 5.5 kW (Source: wind-turbine-models.com)
A Darrieus could have straight blades and would be called a Gyromill, a H-Darrieus
or a Cyclo-turbine. Its simpler blade design allows for lowers mechanical stress, and it
is optimal for small scale applications.
The blades of a Darrieus VAWT can be arranged in many other dierent ways,
synthesized by Fig. 2.13.
Figure 2.13: Dierent shapes of a Darrieus-type VAWT (Source: vawtturbine.wordpress.com)
26 CHAPTER 2. WIND TURBINES
Finally, the blades could also be curved into a helical shape, as shown in Fig. 2.14.
Figure 2.14: A VAWT with helical blades (Source: quietrevolution.com)
Chapter 3
Electric power conversion
Electric machines are fundamental components in power production. In all typical
applications where a revolving part is present, from steam and gas cycles to wind
turbines, an electric machine is always needed in order to convert the mechanical power
extracted from the uid into electric power. If the usual application is as generators,
sometimes smaller electric machines are used also as starting motors.
The physical principles behind their functioning will be explained, then the main
electric machines used in wind power production will be analysed. Finally, the dierent
types of connection of a wind turbine to the electric grid will be seen.
3.1 Fundamentals of electromagnetism
3.1.1 Magnetic ux and ux density
A magnetic eld H (Te) is induced in the vicinity of a conductor where current ows,
according to Ampère's law: ∮H dl = I (3.1)
Where:
• I = current owing in the conductor;
• dl = innitesimal length of the generic path along which the magnetic eld in-
tensity is calculated.
The magnetic ux density B (Wb/m2) is linearly dependent on the the magnetic eld
intensity:
B = µH (3.2)
µ (Wb/Am) is the permeability and it can be expressed as the product of two terms:
the permeability of free space µ0 = 4π × 10−7 Wb/Am, and the dimensionless relative
27
28 CHAPTER 3. ELECTRIC POWER CONVERSION
permeability of the material µr. The typical materials used in practical applications
are ferromagnetic materials, due to the fact that their relative permeability is very
high, in the order of 103 ÷ 105.
Strong magnetic elds, however, can also be generated by the use of wire coils,
where the intensity of the magnetic eld is proportional to the current and the number
of turns. Considering the simplest case of a solenoid of length L and with N turns, the
magnetic eld direction will be parallel to its axis. Ampère's law allows to calculate
the magnitude of the ux density:
B = µIN
L(3.3)
while the magnetic ux φ is the integral of B across the wire's cross-section:
φ =
∫B • dA
Note that by the dot product it is intended to take into account the directions of
the areas crossed by the ux density, and of the ux density itself. Assuming all
innitesimal areas are normal to the ux density, the magnetic ux is simply:
φ = BA (3.4)
3.1.2 Induced voltage and force
A changing magnetic eld induces an electromotive force (EMF) E, corresponding to
a voltage, in a conductor within the eld. This behaviour is described by Faraday's
law of induction:
E = −dφdt
(3.5)
The minus sign is due to the fact that the direction of the induced current opposes the
change that produced it, according to Lenz's law. It is also important to notice that
the symbol E is used instead of V to indicate induced voltages. In a coil, the induced
EMF is proportional to the number of turns:
E = −d(Nφ)
dt= −dλ
dt(3.6)
The term λ is typically referred to as the ux linkages.
Magnetic elds and currents interact by means of forces, according to the following
3.2. POWER TRANSFORMERS 29
equation:
dF = Idl × dB (3.7)
where:
• dF = incremental force acting on the conductor;
• dl = incremental length of conductor;
• I = current owing in the conductor.
Consequently, in the case of a motor, the current owing in the presence of the
magnetic eld results in an induced force acting on the conductor. Instead, in the
case of a generator, a conductor moving through a magnetic eld will have an induced
current owing in it.
3.2 Power transformers
Power transformers are very important components in AC systems and in wind tur-
bines. Their main use for those applications is to convert the generated power to the
voltage of the local electrical network.
A transformer is a device constituted by two (or more) coils, typically made of
copper, which are wound on a laminated metal core. The core is made by layers of
metal sheets separated by insulation, in order to minimize eddy currents (i.e. losses) in
the core. In the most common situation one winding is known as the primary, while
the other is called the secondary.
Its functioning is based on Faraday's law of induction (see Eq. (3.5)). Fig. 3.1 shows
the electrical circuit for an ideal transformer. Subscripts 1 and 2 refer respectively to
Figure 3.1: Equivalent circuit for an ideal transformer (Source: [9])
the primary and secondary windings. The symbol E represents the induced voltage,
while N indicates the number of turns of a winding. In the ideal transformer, some
assumptions need to be taken into account:
30 CHAPTER 3. ELECTRIC POWER CONVERSION
• No losses in the windings;
• No losses in the core;
• No ux leakage.
The ratio between the voltages across the windings is equal to the ratio of the
number of turns, commonly called turns ratio a. The currents are instead inversely
proportional to it. These concepts can be condensed into the following equation:
E1
E2
=I2I1
=N1
N2
= a (3.8)
Real transformers present obviously losses in both the core and the windings, and
ux leakages. With respect to the ideal transformer, the equivalent circuit of a real
transformer (see Fig. 3.2) takes this into account by adding some elements: the resis-
tances of the windings (R1 and R2) and their leakages (X1 and X2), while the core is
represented by its resistance Rc and the magnetizing inductance XM .
Figure 3.2: Equivalent circuit for a real transformer (Source: [9])
3.3 Electrical machines
The term electrical machines refers to both generators and motors, since every machine
can be used as one or the other. For wind power applications the only use is of course
as generators.
The simplest electrical machine is made of two magnetic poles generating the eld,
and a loop of wire, called armature, which can rotate. Brushes and slip rings allow
current to ow from a static frame of reference to a rotating one. The functioning as
a motor is as follows: when current is owing in the armature, a force develops due to
3.3. ELECTRICAL MACHINES 31
the interaction with the magnetic eld; then, since the current ows on both sides of
the armature in opposite directions, these forces generate a torque. Conversely, when
no current is initially owing in the armature wires, if the armature is rotated through
the eld, a voltage will be induced at its terminals according to Faraday's law (see
Eq. (3.5)); a current will ow in the armature if it is part of a closed circuit. This is
the functioning as a generator.
3.3.1 Rotating magnetic elds
The operating characteristics of the machine are determined by the interaction be-
tween the stator's rotating magnetic eld and the rotor's magnetic elds. A suitable
arrangement of windings can allow to generate the rotating magnetic eld.
To obtain such a result, the tri-phase stator coils are placed 120 degrees (2π/3
radians) apart, with balanced AC currents. The resultant magnetic eld H in phasor
form can be expressed as the sum of the individual magnetic elds:
H = Hejωt +Hej(ωt+2π3 ) +Hej(ωt+
4π3 ) (3.9)
The eld has constant magnitude and an angular position of 2πft radians: this means
that it rotates at a constant speed of f revolutions per second, which the same as the
electrical system frequency.
Only one pair of magnetic poles per phase was implicitly involved in the previous
explanation. Of course the discussion can be generalized for any number p of pairs
of magnetic poles, noting however that the resulting magnetic eld will rotate more
slowly with increasing number of poles. When no load is present, the rotor of an
electrical machine rotates as the same speed as the rotating magnetic eld, called the
synchronous speed n:
n =60f
p(3.10)
n is measured in rpm, while f is the system frequency. With a frequency of 60 Hz,
the synchronous speed of a four-pole machine is equal to 3600 rpm.
3.3.2 Synchronous machines
In this type of machine, the rotor eld is generated by a DC current provided either
by a smaller DC generator (called exciter), or via slip rings and brushes. An example
of a synchronous generator can be seen in Fig. 3.3.
If the rotor is revolving at synchronous speed, the rotor and stator elds do not
32 CHAPTER 3. ELECTRIC POWER CONVERSION
Figure 3.3: Salient-pole, wound-rotor synchronous generator (Source: [20])
have any relative motion (slip) between them. However, if the rotor is displaced with
respect to its idling position, a resistant torque is generated in order to align the elds;
this torque can be balanced by a mechanical torque, which has to be continuously
applied. Then, the rotor eld and the stator eld will have a constant angle between
them, called the power angle (or load angle) ϑ. When ϑ > 0 the machine behaves as
a generator, otherwise it will be a motor. It is evident that the torque characteristic
of a synchronous machine is a function of the load angle, as shown in Fig. 3.4. Stable
Figure 3.4: Torque characteristic of a synchronous machine (Source: [6])
operation is only possible in the range of −180 < ϑ < +180, while the highest torque
is reached at ϑ = 90.
Synchronous machines are not self-starting: they need to be brought up to speed
by either an external prime mover, or by embedding the rotor with tamper bars (which
allow it to start like an induction machine), and then synchronized to the grid. Syn-
3.3. ELECTRICAL MACHINES 33
chronizing the generator to the electrical network means to match the angular position
of the rotor and the electrical angle of the AC power at the moment of connection. For
wind turbines, this problem is less important (or absent at all) in isolated electrical
grids, where the AC power is supplied directly by the generator to either a diesel en-
gine or the turbine. In larger energized AC networks, however, synchronization must
be taken into account and the process is helped via active speed control of the turbine.
Moreover, in the usual grid-connected applications with constant terminal voltage, syn-
chronous machines may serve as a source of reactive power that needs to be provided
to the loads.
3.3.3 Induction machines
Induction machines, also called asynchronous machines, are commonly used as motors
in industrial and commercial applications, however they are also used as generators for
distributed generation (for example hydroelectric), and are currently the most common
type of generators for wind turbines. This is due to several advantages over synchronous
generators:
• They have a simple construction;
• They are relatively inexpensive;
• Their connection with the grid is simpler.
The stator of an induction machine is very much similar to the one of a synchronous
machine, constituted of multiple windings. Instead, the rotor can have windings or
not: in the rst case it is referred as wound rotor, which is mainly used in variable-
speed turbines. In the second case (which is the most common), it has conducting bars
embedded in a solid, laminated core. The bars resemble a cage, from which this type
of rotor is called squirrel cage. This type of rotor is less expensive and more rugged
than a wound rotor. An example of a squirrel cage generator is shown in Fig. 3.5.
An important parameter for characterizing induction machines is the slip s, dened
as:
s =ns − nns
(3.11)
Where ns is the synchronous speed and n is the mechanical rotational speed. When
slip is positive, the machine is acting as a motor, otherwise it is a generator. The
torque characteristic is a function of the slip, as shown in Fig. 3.6.
When operating as a generator, the rotor needs to be supplied with a magnetizing
current via slip rings; it requires then an external source of reactive power and an
34 CHAPTER 3. ELECTRIC POWER CONVERSION
Figure 3.5: Squirrel-cage induction generator (Source: [20])
Figure 3.6: Torque characteristics of a squirrel cage induction machine (Source: [20])
external constant frequency source to control the rotational speed. For this reason,
induction generators are typically connected to large electrical networks, where other
synchronous generators connected to prime movers set the grid frequency and provide
the reactive power.
Start-up and connection to the grid of a generator can be attained in two ways:
1. The machine is accelerated by the prime mover, then it is connected.
2. The machine is rst connected, then it brings the prime mover up to operating
speed by acting as a motor.
The rst method requires of course a self-starting turbine, such as a pitch-controlled
one; it is also required to monitor the generator speed in order to ensure that it is as
close as possible to the synchronous speed when the connection is made. The second
method is instead commonly used in stall-controlled turbines; it is necessary to monitor
3.4. CONNECTION WITH THE ELECTRICAL GRID 35
the wind speed so that is is in the appropriate range for the operation of the turbine.
The power factor of induction machines is generally poor. It can be improved by
connecting capacitors at or near the point of connection to the network.
As far as applications are concerned, induction machines can be used as generators
in small networks or even in isolated ones. Special measures must be taken for proper
operation, such as reactive power supply and maintaining frequency stability.
3.3.4 Other types of generators
An important type of electrical machine for wind turbine applications is the shunt
wound DC generator, which was used in the past in small wind turbines for the charging
of batteries. In this type of generator the eld is on the stator, while the armature
is on the rotor. The eld winding is in parallel with the armature windings, and the
electric eld is created by currents passing through the former. Then, the generated
power is rectied to DC, and the generated current is passed out through brushes. The
operation of this generator strongly depends on its speed, since the main parameters
(eld current, magnetic eld, armature voltage and electrical torque) increase with
it; also, the actual turbine speed results from a balance between rotor torque and
electrical torque. This type of generator is now seldom used because of its high cost
and maintenance requirements.
A type of generator which is rising in popularity is the permanent magnet generator.
It is commonly used in small wind turbines up to 10 kW , but it can be used for
larger applications. It is evident that this type of generator does not require windings
or current supply, since it is a permanent magnet that generates the magnetic eld.
There is also no need for slip rings or brushes, since he power is taken from a stationary
armature. Its operation is very much similar to the one of synchronous machines, from
which it is commonly referred to as permanent magnet synchronous generator (PMSG).
Some generators are directly driven by the rotor, hence the name direct drive gen-
erators. This type of generator is essentially a synchronous machine with a special
design: its number of poles is very high, so to eliminate the need for a gearbox and to
allow the generator to turn at the same speed as the rotor.
3.4 Connection with the electrical grid
Once the electric power has been generated, it must be fed into the grid. It is necessary
to couple the generator to the grid, which means to match the frequency of the generator
36 CHAPTER 3. ELECTRIC POWER CONVERSION
to the constant frequency of the grid. In the following subsections, the main solutions
and congurations put in place to accomplish that will be explained.
3.4.1 Fixed-speed generator systems
Synchronous generator directly coupled to the grid
This conguration, shown in Fig. 3.7, represents a technically extreme case: synchroni-
Figure 3.7: Synchronous generator directly coupled to the grid (Source: [6])
sation to the xed-frequency grid is dicult and some complex automatic synchronisa-
tion equipment is necessary. Also, the grid coupling is sti, resulting in uneven power
output of the wind turbine, since the wind uctuations that are captured by the rotor
are passed on to the grid without any smoothing.
Its advantages are its simplicity and its compatibility with the standard generator
technology for feeding the three-phase grid. Also, the control of the reactive power
is made easier by direct current excitation of the rotor. No additional equipment for
reactive power compensation is required for isolated operation.
However, the drawbacks of this solution surpass the advantages. Firstly, only very
small load angles are possible in order to compensate for the dynamic loads imposed
on the generator by the turbine rotor. Then, a loss of synchronisation could be caused
by large load variations, for example in case of strong gusts. Finally, the synchronous
generator is not able to properly dampen the oscillation that might occur in response
to load peaks (even small) such as frequency uctuations on the grid.
Induction generator directly coupled to the grid
This network connection type has historically been used for decades. Fig. 3.8 shows
its scheme. Synchronisation can occur without eld excitation in the case of small
induction generators, which have relatively high nominal slip values that make them
more compliant to the grid. In the case of larger generators, the inrush current must
be avoided in most cases; it is limited by the so-called soft grid coupling : after it has
3.4. CONNECTION WITH THE ELECTRICAL GRID 37
Figure 3.8: Induction generator directly coupled to the grid (Source: [6])
reached the synchronous speed, the generator is connected to the grid via a controller,
which is bypassed after a few seconds.
Large wind turbines in the megawatt range present dierent drawbacks to the use of
this solution. In fact, their large generators sacrice nominal slip in favour of increased
eciency. When connected to the grid, their behaviour is very much similar to the
one of a synchronous generator: wind uctuations are passed directly on to the grid
without smoothing and high dynamic loads on the turbine rotor are present.
The situation can be improved by increasing the nominal slip of the generator,
however it is detrimental to its eciency. Moreover, the mass of the generator depends
on nominal slip, causing a cost increase. Finally, the most important issue of gener-
ators with increased slip is heat dissipation: the cooling system should be oversized,
determining another cost increase.
A nominal slip of 2÷3% is an acceptable compromise between speed compliance and
eciency loss (plus additional cost). It is worth noting that generators with larger slip
are an option mainly for small wind turbines: They do not usually have a frequency
converter, which is considered too sophisticated and expensive for them, and which
could compensate the cost increase deriving from increasing the slip.
Other solutions
The slip of the induction generator can be varied for improved speed compliance. It is
accomplished simply by the use of external resistors, as shown in Fig. 3.9. They are
connected only when needed, in order to produce the desired slip when the load on the
turbine increases. Moreover, cooling of the generator is simpler.
Another solution to better adapt the rotor speed to the wind speed, mainly used in
smaller turbines, is multi-speed operation: two constant speeds are chosen, the lower
of which is used for partial load conditions. Then, a so-called speed stepping is put in
place. No signicant advantages are present regarding the wind variability issues and
38 CHAPTER 3. ELECTRIC POWER CONVERSION
Figure 3.9: Induction generator directly coupled to the grid with external resistors for slipcontrol (Source: [6])
the dynamic loads on the turbine, however the rotor's energy yield is increased. The
turbine results to be also quieter.
The use of two generators is the oldest way of implementing speed stepping. The
smaller one, with a lower speed, is used at partial-load conditions. It allows to improve
the electrical eciency at partial load and to utilise a more favourable power factor.
The larger generator is instead sized for rated power and it is supposed to provide
enough torque to keep the generator coupled to the grid. It goes without saying that
this conguration is costly due to the doubling of the components of the mechanical-
electrical drivetrain, and because of the more dicult control and operation.
A pole-changing induction generator could also be used. It has two electrically
isolated stator windings, which have two dierent number of poles (typically 4 and 6,
or 6 and 8). It is however a questionable solution: the cost increase is evident, and the
eciency is actually poorer at lower speeds. It could be justied in areas where the
wind is a scarce resource.
3.4.2 Variable speed generator systems with inverter
An inverter is necessary in order to control the variable-speed operation of a turbine's
rotor. In fact, it can adjust the output frequency of the generator to the constant fre-
quency of the grid. Although expensive and known to cause eciency losses, inverters
also help reduce the dynamic loads, and they allow the rotor's operation to be more
compliant with its aerodynamic properties with respect to constant-speed operation.
The basis of variable-speed generator systems can be either a synchronous generator,
or an induction generator.
3.4. CONNECTION WITH THE ELECTRICAL GRID 39
Synchronous generator with inverter
The variable-speed operation of the synchronous generator is accomplished via an in-
verter with DC link: the generator outputs variable-frequency AC, which is then rec-
tied to DC and eventually re-inverted to AC for grid connection (see Fig. 3.10). The
Figure 3.10: Synchronous generator with DC link (Source: [6])
DC link allows to decouple the generator speeds, and thus the rotor speed, from the
grid frequency. Then, a wide speed range is usable, which permits to optimize the rotor
aerodynamic operation. Of course this solution completely eliminates the unwanted
dynamic characteristics which directly-coupled generators have.
Controlling the DC link circuits allows to control in turn the generator's torque.
This however can lead to low-frequency oscillations in the DC link itself, making the
control more dicult. This problem can be avoided by not having damper windings,
which make for a more rapid control.
This solution presents several operational advantages:
• The rotational speed of the turbine can be accelerated by using the machine as
a motor, and it can be reduced by using the machine as an electrical brake;
• Electric braking in case of grid failure can be implemented very easily by means
of an ohmic resistor;
• Grid synchronisation and inrush current problems are not present.
In the early stages of this conguration, its main drawbacks were high requirements
for reactive power, low overall electrical eciency, and high cost. Technological progress
allowed to solve the rst two issues.
Induction generator with oversynchronous cascade
This conguration, represented in Fig. 3.11, requires a simple link circuit constituted
by an uncontrolled rectier and an AC inverter. The power ow, however, is only
40 CHAPTER 3. ELECTRIC POWER CONVERSION
Figure 3.11: Oversynchronous cascade for variable-speed operation of the induction generator(Source: [6])
from the rotor to the grid; the uncontrolled rectier does not allow otherwise. Thus,
the generator can only be operated in the oversynchronous mode. The torque of the
generator can be controlled by adjusting the current in the DC link. The reactive
power requirement of this solution is reduced by restricting the speed range: in pure
economic terms, the convenient speed range is 100÷ 130% of the nominal speed. It is
a solution that is however not much used.
Doubly-fed induction generator
As a solution to the previous conguration, the doubly-fed induction generator, or
DFIG (see Fig. 3.12), allows the power ow to be in both ways: the slip power of
the generator is fed into the grid, but at the same time the grid provides power to
the rotor. The inverter superimposes its generated frequency on the frequency of the
Figure 3.12: Doubly-fed induction generator (Source: [6])
rotating eld of the rotor; the resulting frequency is essentially constant.
Due to the power ow being able to go both ways, both oversynchronous (i.e. as a
motor) and subsynchronous (i.e. as a generator) operation of the generator is possible.
3.4. CONNECTION WITH THE ELECTRICAL GRID 41
The reactive or active current can be set by adjusting the magnitude and phase of the
AC in the rotor circuit; thus, the generator can operate with any power factor that is
required.
Of course the dierent modes of operation require a complex control system for the
proper switching and control arrangements of the inverter. To compensate for that,
the doubly-fed induction generator combines the advantages of both the synchronous
and asynchronous machines. Apart from the obvious variable-speed operation, it is
able to provide separate active and reactive power control.
Also, about a third of the nominal generator power ows through the rotor circuit,
thus through the inverter. The consequence of this is that the inverter can be much
smaller than, for instance, in the case of the variable-speed synchronous generator,
where all the power is converter. Thus, costs are reduced, as well as the eciency loss
caused by the inverter.
3.4.3 Directly rotor-driven variable-speed generators
The idea of having the rotor drive the generator directly, without any other component
in between, dates back to the very rst applications of wind turbines. However, in
practice the generator would require a very high number of poles in order to reach the
grid frequency, due the low rotor speed. The diameter and the weight of the generator
would be excessive. Inverters come into play to eciently and conveniently compensate
for that, allowing the generator to not produce the frequency required for the grid.
The rst and standard solution is using a synchronous generator with electric ex-
citation. The input to the grid is made via a DC link circuit with an inverter (see
Fig. 3.13). The main control variable is the reactive power output cosφ, as in all
Figure 3.13: Direct-drive variable-speed synchronous generator (Source: [6])
synchronous generators. Moreover, the minimum and maximum frequency for opera-
tion on the grid can be set. In this way, the grid frequency can be kept stable. This
congurations however has some grave drawbacks:
42 CHAPTER 3. ELECTRIC POWER CONVERSION
• Assembly problems with increasing size of the wind turbine;
• Cooling of the generator is dicult;
• A high number of poles is required, which translates into more material (basically
copper) and increased costs, as well as weight;
• High torque loading due to a slowly rotating larger generator.
The use of a permanent magnet generator would allow to have a more compact
construction for direct-drive. This reects into a lower weight, with competitive costs
with respect to the previous solution.
Chapter 4
Wind turbine control
Controlling a wind turbine has three goals:
• Keep rotational speed within the optimal range for power production;
• Extract the maximum power from the intermittent source;
• Start and stop the turbine.
The rst two points involve maximum power point tracking (MPPT), whose strategies
will be explained in the rst section of this chapter. Then, the last point of the list
will be discussed in the next section. Finally, purely electrical control strategies will
be discussed.
4.1 Maximum power point tracking (MPPT)
For a given wind speed, the power curve of a turbine presents a maximum power point
(MPP), corresponding to the optimal tip speed ratio λopt. This control strategy aims
at adjusting the rotor speed in order to maintain the optimal TSR over the operating
speed range of the turbine.
The locus of the MPPs of a power curve can be seen in Fig. 4.1. It can be thought
as a power curve itself, described by a curve which is proportional to the third power
of the mechanical rotational speed:
PM ∝ ω3M =⇒ TM =
PMωM∝ ω2
M (4.1)
The generator can be controlled by determining the optimal speed or torque, using the
previous relation.
In a power curve, three distinct modes can be determined:
43
44 CHAPTER 4. WIND TURBINE CONTROL
Figure 4.1: Wind turbine power curve and MPP operation (Source: [20])
1. Parking mode: at v∞ < vcut−in the turbine cannot produce any positive power
output. The blades are pitched out of the wind and the mechanical brake is
activated. The same occurs when wind speed exceeds the cut-out value;
2. Generator control mode: at vcut−in < v∞ < vrated, blades are pitched with
their optimal angle of attack and the turbine operates at variable speed. This,
coupled with proper generator control, allows to track the MPP;
3. Pitch control mode: when vrated < v∞ > vcut−out, the power output needs to
be kept constant to protect the turbine from damage, while still being able to
deliver the rated power to the network. The blades are gradually pitched out of
the wind and the generator speed is adjusted.
4.1.1 MPPT with turbine power prole
This method is entirely determined by the power curve which is provided by the man-
ufacturer of the turbine. This curve gives a prole of reference power values P ∗m as
a function of wind speed, which is measured in real time by a sensor. Then, these
values are compared to the measured power from the generator Pm by a controller.
The controller scheme can be seen in Fig. 4.2. The controller then sends signals to the
converters, which eventually force the mechanical power of the generator to be equal
to the reference in steady-state, where the maximum power operation occurs.
4.1. MAXIMUM POWER POINT TRACKING (MPPT) 45
Figure 4.2: Control scheme of MPPT with power prole (Source: [20])
4.1.2 MPPT with optimal TSR
The functioning is very similar to the one explained in the previous subsection, however
in this case the inputs of the controller are the generator rotational speed ωm and the
reference value ω∗m, which is determined by the optimal TSR λT,opt (see Fig. 4.3 for the
control scheme). The converters control the generator speed to keep it at the reference
Figure 4.3: Control scheme of MPPT with tip speed ratio (Source: [20])
in steady-state, where the system operates at MPP.
4.1.3 MPPT with torque control
As it was explained above by Eq. (4.1), mechanical torque TM is a function of the
mechanical rotational speed of the turbine ωM . Both can be easily converted into the
generator torque and rotational speed, respectively Tm and ωm. The latter is used to
46 CHAPTER 4. WIND TURBINE CONTROL
calculate the torque reference T ∗m through a coecient Kopt, which in turn is calculated
from the rated parameters of the generator. Finally, the generator torque is compared
to the reference by the controller, which sends signals to the converters. The control
scheme is represented in Fig. 4.4. In the end it will be Tm = T ∗m in steady state,
Figure 4.4: Control scheme of MPPT with tip torque control (Source: [20])
realizing the MPPT. It is important to notice that this control strategy does not need
to measure the wind speed.
4.2 Over-speed protection
The cut-o speed, which is the highest velocity with positive power output, represents
a safety margin with respect to structural damage in case of extreme wind speeds
or power outages. It is evident that sometimes it is necessary to limit the mechanical
power produced by a wind turbine in order to avoid issues. Three main control methods
exist.
4.2.1 Pitch control (active stall)
Fig. 4.5 represents a generic airfoil, which can be assumed to be a turbine blade. Blade
pitch θ is the angle formed between a reference plane, typically the horizontal one, and
the blade chord. The angle of attack α is instead determined by the blade chord and
the direction of the wind.
In this type of control, blade pitch is continuously adjusted in order to have the
desired angle of attack. The reduction of the output power is obtained in the simplest
way by decreasing the pitch (feathering). On the other hand, increasing it produces
rst a temporary increase in power output, however at some point the critical angle of
4.2. OVER-SPEED PROTECTION 47
Figure 4.5: Pitch angle and angle of attack on a generic airfoil (Source: avia-tion.stackexchange.com)
attack will be reached, where the blade stalls (the ow separates from it, lift drops and
drag rises). This method is known as active stall.
Pitch control allows precision and steady operation: the electrical output power
can be kept constant along the whole range of rated wind speed. However the change
in pitch is not immediate for obvious reasons: in practice, gusts may occur faster than
the blade can be pitched, causing large load uctuations.
4.2.2 Passive stall control
Now the blade pitch is assumed to be xed. As wind speed increases, so does the
angle of attack, making the power output increase. At some point however, the attack
angle becomes so high that the blade stalls, with consequent decrease of the power
output. This control method is then completely passive and self-regulating, which is
very practical for small size turbines.
Of course the rotor blade geometry must be carefully designed for this control
method to work properly, namely to ensure that the ow separates at the selected
wind speed, which is typically around 15 m/s.
Sometimes the so-called turnable tips (see Fig. 4.6) are used. They are activated
Figure 4.6: Turntable tips for stall control
automatically by centrifugal force and act as an aerodynamic brake.
48 CHAPTER 4. WIND TURBINE CONTROL
4.2.3 Furling
This control method, which has been the rst one to be ever used, consists in simply
turning the rotor out of the wind. Yawing the rotor causes the reduction of the wind
velocity component acting perpendicularly to the rotor plane, reducing in turn the
eective rotor swept area. The decrease in rotor power coecient is even stronger due
to an earlier separation of the ow at greater yaw angles (see Fig. 4.7).
Figure 4.7: Rotor power coecient dependance on the rotor yaw (Source: [6])
4.3 Power electronics
In the turbine, mechanical power is converted by the generator into electrical power.
Then, this power needs to be manipulated again in order to obtain suitable character-
istics for grid compliance and for the nal users. Regulation and control of the power
output is done by means of specic devices able to handle high power. Such devices are
combined in particular circuits where the necessary steps occur. The physics behind
their functioning will be explained, then the focus will switch to the devices themselves.
Finally, the circuits used for the main conversions (such as AC to DC or DC to AC)
will be studied.
4.3.1 p-type and n-type silicon
The usual material for the devices is silicon. A single crystal of silicon is composed of
a regular array of atoms. Since the element has four valance electrons, each atom in
the array is bonded to its four nearest neighbours by covalent bonds. Some of these
bonds can be broken by energy carried by the silicon atom due to its random thermal
4.3. POWER ELECTRONICS 49
motion about its equilibrium position. This process is known as thermal ionization. An
electron is released as a consequence, and a xed positive charge is left on the nucleus
of the silicon atom where the bound was broken. The process of thermal ionization is
represented in Fig. 4.8.
Figure 4.8: Silicon lattice showing thermal ionization (Source: [11])
Another free electron, coming from another ionized atom, may be attracted to that
positive charge, restoring the bound. However, the atom from which the free electron
originated now has a positive charge. The end result of this whole process is then the
"movement" of the positive charge, which now gets the name of hole since it originates
from an empty bound. Of course the thermal ionization process generates an equal
number of electrons and holes, having their thermal equilibrium density.
The thermal equilibrium density of holes and electrons can be changed by doping
the semiconductor, i.e. adding appropriate impurity elements. Specically for silicon,
these are elements from the third column of the periodic table, such as boron, or from
the fth column, such as phosphorus.
Consider doping by a column III element, for example boron. Since this element
has only three valance electrons, it needs to acquire or accept another electron in order
to be able to bond in the crystal's mesh. The missing electron comes conveniently from
the ones released by thermal ionization; in turn, a hole is left free to move through
the crystal. The silicon now has more free holes, now called majority carriers, than
electrons (or minority carriers). The silicon now is said to be doped p-type with an
acceptor impurity.
Doping by a column V element, such as phosphorus, leaves silicon with an excess
of electrons, since this doping element has ve valance atoms and has to release one
(hence the name of donor impurity) in order to bond. The resulting positive charge
is a trapped or bound hole. Now it is the electrons that take the name of majority
carriers, and the silicon is said to be doped n-type.
50 CHAPTER 4. WIND TURBINE CONTROL
In any case the impurity levels are orders of magnitude lower than the density of
semiconductor atoms. In this way the presence of doping elements will not aect the
thermal ionization process in terms of rate at which the covalent bonds are broken or
restored.
4.3.2 pn junctions
A pn junction is formed when an n-type region in a silicon crystal is put in contact with
a p-type region in the same crystal. This in practice is performed by either diusing
acceptor impurities in a n-type crystal, or by diusing donor impurities in a p-type
crystal.
The junction is characterized by two factors:
• How the doping changes from n-type to p-type: we can distinguish step junctions,
in which the change is abrupt, or linearly graded junctions;
• The relative doping densities on each side of the junction: for example, if the
acceptor density on the p-type side is much higher than the donor density on
the n-type side, the junction is called a p+n junction. Other combinations are
explained in [11].
Some of the majority carriers on either side of the junctions diuse to the opposite
side, where they are the minority. A space charge layer, or depletion layer, shown
in Fig. 4.9, is created on either side of the junction; this is due to the fact that the
Figure 4.9: A pn junction with the depletion layer shown (Source: [11])
diusing carriers leave behind ionized impurities that are not screened by enough free
carriers for electrical neutrality. The result is a space charge density ρ , which in turn
4.3. POWER ELECTRONICS 51
generates an electric eld E . The electric elds gets stronger as more ionized im-
purities are exposed because of the diusing carriers, however it retards the diusion
process because it acts to push back the electron and holes to their respective sides of
the junction. Eventually an equilibrium will be reached when the carrier ux due to
diusion is balanced by the carrier ux due to the electric eld.
4.3.3 Forward and reverse bias
The electric eld gives rise to a potential barrier, whose magnitude is called the contact
potential. When an external voltage V is applied between the p and n regions, if it
is positive on the p side (as seen in Fig. 4.10) it opposes the contact potential and
decreases the magnitude of the potential barrier; the junction is said to be forward
biased. This alters the equilibrium between diusion and drift in favour of the former;
Figure 4.10: A forward-biased pn junction (Source: [11])
the result of this is a steep increase, called injection, of the density of minority carriers
in the electrically neutral regions on both sides of the junction. Eventually the carriers
recombine, causing a decrease of the excess-minority-carrier density with distance,
which depends exponentially on the forward-bias voltage: as a result of this voltage
dependence, the carrier densities vary greatly for small variations of the applied voltage.
This results in large gradients in the carrier densities in the regions adjacent to the
depletion layer, which in turn cause high diusion currents. This current has a high
temperature sensitivity.
When instead V makes the n side more positive, the potential barrier height is
increased and the junction is reverse biased. If the potential barrier is increased, the
probability of carriers diusing across the junction becomes very small; consequently,
the carrier densities at either side of the junction become almost zero at the edge of the
52 CHAPTER 4. WIND TURBINE CONTROL
depletion region. The small gradients cause a ux of diusing minority carriers towards
the depletion region. Then, the large electric elds in the space charge layer will displace
them into the electrically neutral region on the other side of the junction. The carriers
will swap sides, creating a small leakage current called the reverse saturation current
Is, which is independent of the reverse voltage. The i−v characteristic of a pn junction
can be seen in Fig. 4.11.
Figure 4.11: (a) i-v characteristic of a pn junction. The reverse saturation current is toosmall to be appreciable in (a), so the reverse bias portion is represented in (b)(Source: [11])
There exists a limit for the reverse bias voltage, called reverse breakdown, or
avalanche breakdown BVBD. A free electron with sucient kinetic energy gained from
an applied electric eld (like indeed a reverse voltage) can strike a silicon atom and
break a covalent bond, releasing another electron. This process is called impact ioniza-
tion. The newly liberated atom can in turn gain enough kinetic energy from the electric
eld to break another bond. The overall process can cascade very quickly, producing
a large number of electrons and thus a large current. The high power dissipation can
quickly destroy the device, and this is why breakdown operation should be avoided.
4.4 Semiconductor devices
4.4.1 Power diode
The basic structure of a power diode, including its circuit symbol, is shown in Fig. 4.12.
It is constituted by three layers, from bottom to top:
• Heavily doped n-type substrate, forming the cathode of the device;
• Lightly doped n− epitelial layer of specied thickness;
4.4. SEMICONDUCTOR DEVICES 53
Figure 4.12: Scheme of a power diode (Source: [11])
• Heavily doped p-type region, completing the pn junction and forming the anode
of the device.
The n− layer, often called the drift region, has the function to absorb the depletion
layer of the reverse biased p+n− junction, thus setting the reverse breakdown voltage.
The i − v characteristic of a power diode is quite similar to a standard pn junction
(see Fig. 4.13): for forward bias the current grows, although linearly rather than expo-
nentially, with voltage, while in reverse bias the current steeply increases with voltage
near the breakdown value.
Figure 4.13: i-v characteristic of a power diode (Source: [11])
54 CHAPTER 4. WIND TURBINE CONTROL
In the real device the pn junction has some kind of curvature with respect to the
parallel plane description of the ideal case, due to how the impurities are diused in
practice (masked diusion, as presented in Fig. 4.14): impurities diuse faster laterally
than vertically. Also, the electric eld in the depletion layer becomes non uniform
Figure 4.14: Masked diusion of a pn junction (Source: [11])
in space and its magnitude is inversely proportional to the curvature radius. The
nal result of this is a reduction of the breakdown voltage. The natural solution that
comes to mind is to keep the curvature radius as large as possible, however studies
assess that at breakdown the radius should be 6 times larger than the depletion layer
thickness of an ideal junction to keep the breakdown voltage within 90% of the ideal
case. This would require deep diusions into the substrate, which in turn would require
impractically long realisation times. Other solutions have been found to this problem:
• Electrically oating eld plates: these act as an equipotential surface and can
redirect the electric eld lines in order to avoid excessive curvature of the depletion
layer, at the price of requiring a large amount of silicon. This solution is shown
in Fig. 4.15;
• Guard rings: p-type guard rings are allowed to oat electrically. Their depletion
layers merge with the growing depletion layer of the reverse biased junction,
preventing the increase of the curvature radius. The advantage of having the rings
oat is to make them almost unaected by breakdown, even if their curvature
radius can be relatively small;
• Extending the metallurgical junction to the surface of the silicon: the high eld
4.4. SEMICONDUCTOR DEVICES 55
Figure 4.15: Field plates for depletion layer boundary control in a power diode (Source: [11])
Figure 4.16: Guard rings for depletion layer boundary control in a power diode (Source: [11])
depletion layer intersects the boundary between the semiconductor and air, im-
posing a curvature of the depletion layer even if the device is arranged in a
parallel-plate conguration. The electric elds at or near the surface can cause
premature breakdown and a performance degradation. To counteract this neg-
ative impact it is possible to shape the device dierently, such as beveling, in
order to minimize the surface electric elds; another solution is to coat the sur-
faces with materials like silicon dioxide or other insulators, which help control
the electric eld at the surface.
4.4.2 Bipolar junction transistors
A bipolar junction transistor (BJT or just transistor) is formed by four layers of alter-
nating p and n-type material, in dierent congurations (the most common are pnp or
56 CHAPTER 4. WIND TURBINE CONTROL
npn). It has three terminals:
1. Base or input terminal;
2. Collector or output terminal;
3. Emitter, common between input and output.
The scheme for a BJT, as well as its circuit symbol, are shown in Fig. 4.17. The vertical
Figure 4.17: Cross-section of a BJT (Source: [11])
structure is intended to maximize the cross-sectional area for current to ow, thus
minimizing the on-state resistance and the power dissipation (involving also thermal
resistance).
The i − v characteristic of a BJT depends on the base current (see Fig. 4.18).
It is important to notice that there exists a maximum collector-emitter voltage that
can be sustained when considerable collector current ows, called BVSUS. When the
base is open circuited (i.e. zero base current), the maximum voltage between collector
and emitter is increased to BVCEO, which is used as the transistor's voltage capability.
When instead it is the emitter to be open circuited, the maximum collector-base voltage
is BVCBO.
4.4. SEMICONDUCTOR DEVICES 57
Figure 4.18: i-v characteristic of a npn BJT (Source: [11])
The so-called primary breakdown occurs due to avalanche breakdown of the C-B
junction, and the consequent large current which causes destructive power dissipation.
Secondary breakdown is caused by the intrinsic properties of the device: minority-
carrier devices have a negative temperature coecient of resistivity, i.e. resistivity is
inversely proportional to temperature. This means that the power dissipation will in-
crease as the resistance drops as long as voltage remains constant. The rate of heat
removal is linear with temperature, however if power dissipation varies more than lin-
early, temperature will increase, causing further power dissipation. This situation is
often called thermal runaway. Secondary breakdown appears on the output character-
istic as a steep drop in the C-E voltage at large values of collector current. As this
voltage drops, collector current can further increase, causing a non-uniformity of the
current density and high power dissipation. The breakdown is even more dangerous
because the dissipation is not uniformly spread over the volume of the device, but it is
concentrated in regions where the local temperature may grow very quickly, eventually
causing a melting and recrystallization of the silicon.
Another issue regarding BJTs is quasi-saturation. Consider the one-dimensional
model of the BJT. Assume that the transistor is initially in the active region, so the B-
E junction is forward biased and the base current is allowed to increase. As a response,
58 CHAPTER 4. WIND TURBINE CONTROL
the collector current rises as well, dropping the C-E voltage because of the increased
voltage drop across the collector load. However there is a simultaneous increase in
the voltage drop in the drift region: the reverse bias across the C-B junction will get
smaller and smaller, until it becomes forward biased. At this point holes are injected
from the base into the collector drift region, while electrons are injected at the same
time for charge neutrality. Carriers build up in the drift region and the quasi-saturation
region of the i− v characteristic is entered. The stored charge accumulates in the drift
region only on the C-B junction side. The drift region gradually becomes shorted, with
consequent decrease of the voltage across it even if the current becomes larger.
4.4.3 Power MOSFETs
Metal-oxide-semiconductor eld eect transistors (or MOSFETs) are constituted by
multiple cells. Each cell has a vertically oriented four-layer structure of alternating p
and n-type material, as shown in Fig. 4.19; the p-type layer in the middle is dened the
Figure 4.19: Cross-section of a MOSFET cell (Source: [11])
core of the device, while the n− layer is the drain drift region setting the breakdown
voltage. Such a device has two terminals, the source and the drain. Apparently no
current could ow, since one of the pn junctions is reverse biased regardless of the
polarity of the voltage. However a third terminal, the gate, is isolated by a small
silicon dioxide layer; when it is applied a voltage that biases the gate positive with
respect to the source, it converts the silicon surface beneath the gate oxide into a n-
type channel, allowing the ow of current. The gate is then the input terminal of the
device.
Many of these gate/source regions are connected in parallel when constructing the
complete device. This is purposely done in order to maximize the width (i.e. the
dimension perpendicular to the current ow) of the gate region compared to its length.
4.4. SEMICONDUCTOR DEVICES 59
Also, a parasitic BJT is formed between the drain and source contacts, with the body
region serving as its base. To avoid the possibility of it turning on, the body region is
shorted to the source region by overlapping the source metallization onto the p-type
body region. As a result, a parasitic diode called integral diode is connected between
the drain and the source. The gate metallization is overlapped as well across the drift
region, with two purposes:
• Enhance the conductivity of the drift region at the n−−SiO2 interface by forming
an accumulation layer. This helps minimize the on-state resistance;
• Act as a eld plate when the MOSFET is o, thus preventing the curvature radius
of the drain-body junction's depletion region from getting too small, which would
reduce the breakdown voltage.
As previously introduced, the MOSFET has three terminals: gate (input), drain
(output) and source (common between input and output). The output characteristic
describes drain current as a function of the drain-to-source voltage, with gate-to-source
voltage as a parameter (see Fig. 4.20). The usual application for a MOSFET is as a
Figure 4.20: i-v characteristic of a power MOSFET (Source: [11])
switch to control the power ow to a load, similarly to a BJT. The device is said to
be in the cuto region when the gate-source voltage is less than a threshold value:
the device is an open circuit and must be able to withstand the power supply voltage
which is applied to the circuit. To avoid breakdown and the subsequent high power
dissipation, then, the drain-source breakdown voltage must then be larger than the
applied drain-source voltage. If breakdown should occur, it would be due to avalanche
breakdown of the drain-body junction.
60 CHAPTER 4. WIND TURBINE CONTROL
4.4.4 Thyristors
Semiconductor-controlled rectiers (SCRs), more commonly called thyristors, have a
unique four-layer construction, as represented by Fig. 4.21 along with its circuit symbol.
They have three terminals: the anode, the cathode and the gate.
Figure 4.21: Circuit symbol and cross-section of a thyristor (Source: [11])
The i − v characteristic of a thyristor shows the anode current as function of the
anode-to-cathode voltage (see Fig. 4.22). The reverse characteristic is very much similar
to the one of a diode, while in the forward direction a thyristor has two stable states
(or modes), with an unstable mode, shown as a negative resistance, in-between:
• Forward blocking state, or o state, characterized by low current and high voltage.
The maximum values of current and voltage in this state are called respectively
breakover current and forward-blocking voltage, and they are dened at zero gate
current (i.e. the device is open-circuited);
• Forward on-state, characterized by low voltage and high current. The minimum
values of current and voltage that can ow in the device while in this state, are
called respectively holding current and voltage.
The device is turned on by a large gate current: it does not have to be a DC current,
but it can also be a pulse. Turn-on of a thyristor follows a transient where the anode
current increases at a certain rate, which is set by the external circuit (switching time
of other devices or stray inductance in the circuit). However, the thyristor cannot be
turned o simply by zeroing the gate current, but the external circuit must force a
4.4. SEMICONDUCTOR DEVICES 61
Figure 4.22: i-v characteristic of a thyristor (Source: [11])
current which is lower than the holding current for a specied amount of time. The
turn-o transient is much faster than the turn-on transient.
4.4.5 Insulated gate bipolar transistors
Insulated gate bipolar transistors (or IGBTs) are somewhat a combination of a BJT
and a MOSFET, in order to compensate for the defects of both, while exploiting the
advantages of both.
Its structure is similar to the one of a generic MOSFET, with the dierence of
a p+ layer forming the drain of the BJT (see Fig. 4.23); this forms a pn junction
Figure 4.23: Scheme of a IGBT (Source: [11])
62 CHAPTER 4. WIND TURBINE CONTROL
injecting minority carriers into the drain region of the vertical MOSFET. The gate and
source of the IGBT are arranged in a geometry similar to a MOSFET. A problem that
this combination brings is that the IGBT has a parasitic thyristor: its turn-on is not
desirable, and for this reason some structural details (such as the shorting of the body
and the source) are dierent to minimize the possibility of its activation.
The i− v characteristic of a IGBT in the forward direction is similar to the one of
a BJT, with the gate-source voltage as a parameter rather than a current like in the
BJT. It is represented in Fig. 4.24. Operation of the device is controlled by the same
Figure 4.24: i-v characteristic of a IGBT (Source: [11])
parameter: when it is lower than a threshold value, the device is in its o state; when
it is higher, turn-on occurs.
4.5 Power conversion circuits
4.5.1 AC to uncontrolled DC
The act of converting an AC input into a DC output is called rectication. Most of these
application use simple diodes, however the the conversion occurs in an uncontrolled way.
In a diode rectier, power can ow only from the AC side to the DC side. Also, as will
be better explained later, in order to have a DC voltage as ripple-free as possible, a
large capacitor is inserted o the DC side, acting as a lter.
4.5. POWER CONVERSION CIRCUITS 63
Single-phase bridge rectier
In a single-phase bridge rectier, whose circuit scheme is shown in Fig. 4.25, the utility
supply is modelled as a sinusoidal voltage vs, in series with its internal (mainly induc-
tive) impedance Ls. As a rst approximation, it can be assumed Ls = 0. Also, the
Figure 4.25: Circuit schemes of the single-phase bridge rectier (Source: [11])
DC side is replaced by either a resistance R or a constant DC current source Id. In
both cases the circuit can be redrawn with a circuit including two groups of diodes (see
Fig. 4.26). Current id can ow continuously through one diode of the top group and
Figure 4.26: Redrawn circuit of the single-phase bridge rectier (Source: [11])
one diode of the bottom group.
Consider the top diode group. The cathodes ofD1 andD3 are at the same potential.
The diode with the highest anode potential will conduct id: this means that when vs
is positive it is the turn of D1, with vd = vs and is = id. D3 is seen as reverse biased.
It is very easy to understand what happens when vs becomes negative, when vd = −vsand is = −id.
64 CHAPTER 4. WIND TURBINE CONTROL
In the bottom group, it is the anodes of the diodes that are at the same potential.
Therefore, the conducting diode is the one to have the highest cathode potential. With
positive vs, D2 conducts while D4 is reverse biased, and the situation is inverted when
the voltage becomes negative.
According to what was said above, at any time the DC-side output voltage can be
expressed as:
vd(t) = |vs|
While the AC-side current is:
is =
id if vs > 0
−id if vs < 0
The output waveforms of the rectiers in Fig. 4.25 are shown in Fig. 4.27.
Figure 4.27: Output waveforms of the single-phase bridge rectiers of Fig. 4.25 (Source: [11])
Having Ls = 0 means that the switch between the two values of current is instanta-
neous. The average value of the DC output voltage Vdo (where the subscript o means it
is in the idealized case of zero inductance) is obtained by integrating vs =√
2Vs sin (ωt)
over half a period. The nal result is:
Vdo = 0.9Vs (4.2)
Introduce now Ls into the discussion. The eect of this inductance is that on the
DC side the passage from is to ±Id is not instantaneous, but it will require some
period of time called the current commutation time or commutation interval u; also,
the process where the current conduction switches from one diode to the other is called
current commutation process.
4.5. POWER CONVERSION CIRCUITS 65
Figure 4.28: Basic circuit to illustrate current commutation (Source: [11])
Consider the simple circuit in Fig. 4.28 with vs =√
2Vs sin (ωt). Prior to ωt = 0,
vs is negative and Id ows through D2 with vd = 0, is = 0. When vs becomes positive,
D1 starts conducting. The build-up of is can be better seen on the redrawn circuit in
Fig. 4.29, which is valid only for 0 < is < Id: D2 becomes a short circuit with vd = 0,
allowing the build-up of is. Also, is cannot exceed the value of Id as it will result in
Figure 4.29: Basic circuit during current commutation (Source: [11])
a negative value of iD2 , which is not possible. Diode D2 stops conducting at ωt = u,
resulting in another circuit, shown in Fig. 4.30.
Figure 4.30: Basic circuit after current commutation (Source: [11])
Extending this analysis to the previous circuit (on the right-side of Fig. 4.25), which
is redrawn in Fig. 4.31 prior to ωt = 0 diodes 3 and 4 conduct Id and is = −Id.After, vs becomes positive and diodes 1 and 2 start conducting while the other
two serve as a short-circuit. All four diodes conduct during the commutation interval.
A similar calculation can be carried out as well for the average value of the DC-side
66 CHAPTER 4. WIND TURBINE CONTROL
Figure 4.31: Single-phase bridge rectier with inductance (Source: [11])
voltage, which yields:
Vd = 0.9Vs −2ωLsIdπ
(4.3)
Since the output side of the rectier is DC, it is natural to assume that the DC side
voltage is constant, in other words vd(t) = Vd. This assumption considers a large value
of C and that the circuit conditions are such that id is zero during the zero crossing of
vs. The equivalent circuit (see Fig. 4.32) can be drawn.
Figure 4.32: Single-phase bridge rectier with constant DC voltage (Source: [11])
It can be shown that Id depends on Vd and vice versa (see [11]).
4.5. POWER CONVERSION CIRCUITS 67
Three-phase full bridge rectier
This type of rectier is common in industrial applications, where three-phase AC volt-
ages are available. The circuit of the rectier is shown in Fig. 4.33. The lter capacitor
Figure 4.33: Idealized circuit for the three-phase full-bridge rectier (Source: [11])
is present also in this case.
Similarly to the single-phase rectier, it can be assumed at rst that Ls = 0.
Considering the redrawn circuit in Fig. 4.34, the functioning of the rectier is very
similar to a single-phase one: for the top group, the diode with the highest anode
Figure 4.34: Three-phase full-bridge rectier with Ls = 0 (Source: [11])
potential conducts, while in the bottom group it is the diode with the highest cathode
potential. The instantaneous waveform of vd (see Fig. 4.35) consists of six segments per
68 CHAPTER 4. WIND TURBINE CONTROL
cycle of line frequency, from which a common name for this device is six-pulse rectier.
Each diode conducts for 120, so for phase a the current waveform is as follows:
Figure 4.35: Output voltage waveform of the three-phase full-bridge rectier with Ls = 0(Source: [11])
ia =
Id when D1 conducts
−Id when D4 conducts
0 when neither D1 nor D4 conducts
Since Ls = 0, the commutation is instantaneous.
The average value of the output DC voltage is computed by averaging one of the six
segments over a π/3 radians interval. Calling VLL the rms value of of the line-to-line
voltages, the nal result is:
Vdo = 1.35VLL (4.4)
Then, using the denition of rms value, the rms value of the line current is is:
Is = 0.816Id (4.5)
The voltage waveforms are exactly the same if a resistance Rload is used instead of a
current source Id.
As said in the previous section, having Ls 6= 0 means that the current commutations
are not instantaneous. The same concepts of commutation interval and current build-
up are valid. The consequence is again a reduction of the average DC-side voltage with
respect to the idealized case, which is calculated as:
Vd = 1.35VLL −3
πωLsId (4.6)
Assuming constant DC-side voltage vd(t) = Vd, i.e. a large value of the lter
capacitance, the analysis can be simplied by considering that the current id on the
4.5. POWER CONVERSION CIRCUITS 69
DC side ows discontinuously. Then, only two diodes (one per group) conduct at any
given time.
4.5.2 AC to controlled DC
In some specic applications, such as battery chargers, it is necessary to be able to
control the DC voltage. This is done not by means of diodes, but by means of thyristors.
Their functioning principle can in fact allow to better control the output voltage.
Basic thyristor circuits
The study of very basic thyristor circuits starts by considering a purely resistive circuit
(see Fig. 4.36). In the positive half cycle of vs, the supply of the gate current pulse to
Figure 4.36: Simple purely resistive circuit for the study of thyristor switches (Source: [11])
the thyristor is delayed by an angle α; when the thyristor is conducting vd = vs. Then,
the current follows the voltage waveform until ωt = π, where it becomes zero until
another cycle begins and the gate pulse is supplied again. Introducing an inductance
causes a non-instantaneous switch, and some current still lingers when vs becomes
negative. The average value of the DC voltage vd can be controlled by adjusting the
ring angle α. The same is valid for the power supply.
Single-phase converters
The functioning of a single-phase thyristor converter is very similar to a single-phase
uncontrolled rectier, where current Id ows into a thyristor (instead of into a diode)
in the top group and one thyristor in the bottom group. Fig. 4.37 shows the circuit
scheme of the rectier. The ring angle α delays the thyristor's conduction with respect
to its instant of natural conduction, which is the instant at which a thyristor would
conduct if the gate current was continuously applied, i.e. if the device behaved as a
diode. This causes voltage vd to be negative when 0 < ωt < α. Since the DC voltage
70 CHAPTER 4. WIND TURBINE CONTROL
Figure 4.37: Circuit scheme of the single-phase thyristor rectier (Source: [11])
can be controlled by controlling α, as it was said before, the average value of voltage
vd can be calculated as:
Vdα = 0.9Vs cosα (4.7)
The output voltage waveform is presented in Fig. 4.38
Figure 4.38: Output voltage waveform in the idealized single-phase thyristor rectier (Source:[11])
With a non-negligible inductance, once the ring angle is given, the commutation
takes a nite time u to occur. The overall functioning is similar to a diode converter
(see Section 4.5.1), with:
Vd = 0.9Vs cosα− 2ωLsIdπ
(4.8)
The output waveform is as presented in Fig. 4.39.
When the ring angle is greater than 90 but lower than 90, Vd has negative values.
The converter can then operate in inverter mode, i.e. power ows form the DC side
to the AC side. To better understand this particular operation, the DC side of the
converter can be replaced by a current source outputting Id. The average value of vd
will be negative (see Fig. 4.40), as well as the AC-side average power.
4.5. POWER CONVERSION CIRCUITS 71
Figure 4.39: Output voltage waveform in the single-phase thyristor rectier with non-negligible inductance (Source: [11])
Figure 4.40: Output voltage waveform in the inverter-mode operation of the single-phasethyristor rectier (Source: [11])
Three-phase converters
The circuit for a converter of this type is shown in Fig. 4.41. Assuming at rst Ls = 0,
the overall functioning is similar to a diode converter, with the same Vdo = 1.35VLL
(see Fig. 4.42 for the output voltage waveform). The eect of having a ring angle on
all three phases causes a reduction of the average DC voltage by a factor cosα:
Vdα = Vdo cosα (4.9)
A non-negligible inductance further delays the current commutation by the con-
duction interval u. The nal result is a reduction of the average value of the DC
voltage:
Vd =3√
2
πVLL cosα− 3ωLs
πId (4.10)
The three-phase converter can work in inverter mode, too.
4.5.3 DC to DC
The transformation of DC from one level to the other is accomplished by using switches.
In particular, their on and o durations, ton and toff , are controlled. The main control
method that is commonly used is called Pulse-width modulation (PWM) switch-
72 CHAPTER 4. WIND TURBINE CONTROL
Figure 4.41: Circuit of the three-phase thyristor rectier (Source: [11])
Figure 4.42: Waveforms of the three-phase thyristor rectier (Source: [11])
ing: switching is done at constant frequency, i.e. a constant switching time period
Ts = ton+ toff is employed. Control is achieved by varying the duty ratio D = ton/Ts,
thus only the on duration is adjusted.
The switch control signal is generated by comparing a repetitive sawtooth waveform
with a control voltage signal vcontrol, as shown in Fig. 4.43. The latter is determined by
amplifying the error, which is the dierence between the actual output voltage value
and the desired one. The frequency of the sawtooth wave sets the switching frequency.
The switch duty ratio can be expressed in terms of voltage values:
D =vcontrol
Vst(4.11)
Where Vst is the peak of the sawtooth wave.
4.5. POWER CONVERSION CIRCUITS 73
Figure 4.43: Pulse-width modulation (Source: [11])
Step-down converter
Step-down converters, also called buck converters, produce an average output voltage
that is lower than the input. Their typical application is in regulated DC power supplies
and DC motor speed control.
The basic circuit of a buck converter for a purely resistive load is shown in Fig. 4.44.
With an ideal switch and a constant instantaneous input voltage Vd, the instantaneous
Figure 4.44: Basic circuit of a buck converter for a purely resistive load (Source: [11])
output voltage is of course a function of the switch position; thus, the average output
voltage can be calculated in terms of the duty ratio:
Vo =1
Ts
∫ Ts
0
vo(t) dt =1
Ts
(∫ Ton
0
vo(t) dt+
∫ Ts
ton
0 dt
)=tonTsVd = DVd (4.12)
74 CHAPTER 4. WIND TURBINE CONTROL
Substituting Eq. (4.11) allows to derive:
Vo =Vd
Vstvcontrol = kvcontrol
Where k is a constant. The output voltage can thus be regulated by varying the duty
ratio of the switch. It is also important to notice that Vo varies linearly with the control
voltage.
The circuit that was just presented, however, is not t for real applications. Firstly,
the load is never purely resistive: if an inductance isn't explicitly present, some stray
inductance is associated to the resistance; thus, the switch would have to absorb or
dissipate energy, risking destruction. Secondly, the output voltage is not actually
constant, but it uctuates between zero and the input average value, which is not
acceptable in the majority of applications.
The rst problem is solved by adding a diode to the circuit, while voltage uctua-
tions are mitigated by introducing a low-pass lter, which is constituted by an inductor
and a capacitor. The resulting circuit, along with the output waveforms, can be seen
in Fig. 4.45.
Figure 4.45: Circuit and waveforms of a real buck converter (Source: [11])
As it was anticipated before, a buck converter has two modes of operation. In the
continuous conduction mode the inductor current ows continuously, i.e. i:(t) > 0.
4.5. POWER CONVERSION CIRCUITS 75
During ton, the switch conducts the inductor current and the diode is reverse-biased.
The result is a positive voltage across the inductor, which causes a linear increase in
its current. When the switch is turned, o some current continues to ow due to the
inductance; this current ows through the diode. It can be derived (see [11]) that the
voltage output depends exclusively on D, from which it depends linearly for a given
input voltage. Therefore, a buck converter operating in this mode is equivalent to a
DC transformer with variable turns ratio, which is controlled by adjusting the duty
ratio of the switch.
If the average inductor current (and also the average output current) falls lower than
a boundary value, the converter will operate in discontinuous conduction mode.
Depending on the application of the converter, two cases can be distinguished with
dierent threshold values for the output current, but their discussion goes beyond the
scope of this work.
Step-up converter
Opposite to buck converters, step-up converters, also called boost converters, have an
output voltage which is greater than the input. The discussion about a purely resistive
loads is very much the same as the one for a buck converter, so Fig. 4.46 already
shows the circuit of a "complete" boost converter. Similar concepts regarding the
Figure 4.46: Circuit for a boost converter (Source: [11])
boundary between the two modes of operation apply, so the discussion will consider
only continuous conduction mode.
In continuous conduction mode, the diode is reverse biased when the switch is on;
thus, the output stage is isolated and the input supplies energy to the inductor. When
the switch is turned o, both the input and the inductor supply energy to the output
(see Fig. 4.47). Again, it can be derived (see [11]) that a boost converter operating in
this mode behaves the same as a transformer.
76 CHAPTER 4. WIND TURBINE CONTROL
Figure 4.47: Continuous conduction mode of operation of a boost converter (Source: [11])
Full-bridge DC-DC converter
In this type of converter, the output voltage Vo can be controlled both in magnitude
and in polarity. Also, the magnitude and direction of the output current io can be
adjusted. Therefore, the power ow through the converter can be in both directions.
The topology of the full-bridge converter is shown in Fig. 4.48. It is constituted by
two legs, A and B. Each leg is formed two switches and their antiparallel diodes. In
theory, the two switches of a leg are never in the same state at the same time, i.e. if
one is on the other is o. Nevertheless, in practice there exist a small time interval,
called blanking time, where they are both o. This is to avoid short circuiting of the
DC input. The following discussion will assume ideal switches.
That said, if the switches in each leg are not o simultaneously, the output current
io will ow continuously. This means that the output voltage depends exclusively on
the status of the switches and on their duty ratio.
Single-switch converters are pulse-width modulated by comparing a sawtooth wafevorm,
but the polarity of the output voltage is uni-directional . The full-bridge DC-DC con-
verter instead has a voltage whose polarity can be controlled, so PWM needs to be done
in other ways. A switching-frequency triangular waveform is used, and two dierent
4.5. POWER CONVERSION CIRCUITS 77
Figure 4.48: Circuit of a full-bridge DC-DC converter (Source: [11])
strategies exist:
1. Bipolar voltage switching: (TA+, TB−) and (TA−, TB+) are considered as two
switch pairs; switches in each pair are turned on or o simultaneously. It can
be derived that a converter controlled in this way behaves similarly as a linear
amplier [11];
2. Unipolar voltage switching (or double-PMW switching): the switches in each
leg are controlled independently of the other leg; the behavior of this type of
converter is similar to the previous one, but with the same switching frequency
it results in a lower rms ripple component in the output voltage [11].
4.5.4 DC to AC
This type of conversion is done by means of switches, whose combination results in
devices called inverters. It is used in applications (such as AC motor drives and AC
power supplies) where it is necessary to produce a sinusoidal AC output with control-
lable magnitude and frequency.
In this subsection, the studied inverters will have an input DC voltage, hence their
name of voltage source inverters (VSIs). Moreover, they can be divided into three
general categories:
1. Pulse-width-modulated inverters: the input DC voltage has constant mag-
nitude, so the inverter needs to control both magnitude and frequency of the AC
output; then, the switches of the device are controlled by PWM;
78 CHAPTER 4. WIND TURBINE CONTROL
2. Square-wave inverters: the magnitude of the AC voltage is controlled by
adjusting the input DC voltage, so the inverter needs to control only the frequency
of the AC output, which has a waveform similar to a square wave;
3. Single-phase inverters with voltage cancellation: working only for single-
phase conversion, they combine the characteristics of the previous inverters,
therefore they are able to control the magnitude and the frequency of the AC
output even if the DC input has constant magnitude, and without the use of
PWM.
These three control schemes will be explained better later. Before that, the simple
single-phase converter will be studied in order to have a general understanding of the
working principles of inverters.
Single-phase inverter
The generic scheme of this converter is shown in Fig. 4.49. The typical application is
Figure 4.49: Generic scheme of a single-phase inverter (Source: [11])
in the supply of inductive loads, such a AC motors, therefore the output current and
the output voltage are not in phase. Considering their waveforms, represented in Fig.
4.50, it can be seen that the instantaneous power ows from the DC side to the AC side
when vo and io; conversely, the opposite occurs when the output voltage and current
have dierent signs, corresponding to a rectier mode of operation.
Figure 4.50: Waveforms of the output current and voltage of an inverter (Source: [11])
4.5. POWER CONVERSION CIRCUITS 79
This means that the inverter can actually operate in all four quadrants of the io−v0plane during each cycle of the AC output. The full-bridge converter of Section 4.5.3
could do that as well, meaning it can work as an inverter. One of its legs, which can
be called one-leg switch-mode inverter (see Fig. 4.51), will be used as a basis to derive
the topologies described later.
Figure 4.51: One-leg switch-mode inverter (Source: [11])
PWM switching scheme
Dierently from what was described for DC to DC converters (see Section 4.5.3), PWM
for DC to AC inverters is more complex: in order to control the frequency of the output
voltage, the control signal will be generated at the desired frequency. The waveform
of the control signal is then compared with a triangular waveform, as normal. Its
frequency and its amplitude Vtri are kept constant. One important parameter is the
amplitude modulation ratio, dened as:
ma =Vcontrol
Vtri(4.13)
Where Vcontrol is the peak of the control signal.
Considering the one-leg inverter, the switches are controlled based on the compari-
son between vcontrol and vtri. The output voltage will be, independently of the direction
of io:
vcontrol > vtri =⇒ TA+ ON =⇒ vAo =1
2Vd
vcontrol < vtri =⇒ TA− ON =⇒ vAo = −1
2Vd
The output voltage will then oscillate between those two values, as shown by Fig. 4.52.
80 CHAPTER 4. WIND TURBINE CONTROL
Figure 4.52: Sinusoidal PWM (Source: [11])
Square-wave switching scheme
In this switching scheme, each switch of the inverter leg is ON for half a cycle of
the desired output frequency. The resulting output voltage will then have a square
waveform. It is important to notice that this switching scheme is a particular case of
the previous one, when ma is so large that the control waveform intersects with the
triangular waveform only when the former crosses zero.
One advantage of this strategy is that each inverter switch doesn't change its state
too frequently, which is good in the typical high power applications where switches
generally have slow turn-on and turn-o speeds. However, the main drawback is that
an inverter operating with this switching scheme is not able to control the output
voltage magnitude; it is the input DC voltage which needs to be adjusted in order to
accomplish that.
Single-phase inverters
The rst single-phase inverter is the half-bridge single-phase inverter, whose circuit is
shown in Fig. 4.53. Two equal capacitors C+ and C− are connected in series across
the DC input. Their capacitance needs to be high enough so to maintain constant
potential at their midpoint o with respect to the negative DC bus N . Therefore, the
circuit conguration is totally equivalent to a basic one-leg converter, with vo = vAo.
Current io splits equally between the two capacitors, however it cannot have a DC
component in steady state. Thus, the capacitors act as DC blocking capacitors. The
4.5. POWER CONVERSION CIRCUITS 81
Figure 4.53: Circuit of the single-phase half-bridge inverter (Source: [11])
Figure 4.54: Circuit of the single-phase full-bridge inverter (Source: [11])
peak voltage and currents of the switches are as follows:
VT = Vd IT = io,peak
The full-bridge inverter is made up of two one-leg inverters (see Fig. 4.54). With
the same input voltage, this inverter is able to output twice the voltage as a half-bridge
inverter, meaning that the output current and the switch currents are half of those for
a half-bridge inverter, for the same power. This is a distinct advantage at high power
levels, since it requires less paralleling of devices.
Three-phase inverters
The supply of power to a three-phase load is made possible simply by combining three
single-phase inverters: each inverter would produce an output displaced by 120 with
respect to the others, however it would require either a tri-phase output transformer or
separate access to each phase of the load, and 12 switches. The most frequently used
82 CHAPTER 4. WIND TURBINE CONTROL
three-phase inverter circuit, shown in Fig. 4.55, is constituted by three legs. Each leg
Figure 4.55: Circuit of the tri-phase inverter (Source: [11])
works exactly as the basic one-leg inverter, so its output depends only on Vd and the
switch status.
In this type of converter, PWM does not only control the magnitude and frequency
of each phase, but it also needs to keep the three-phase voltages balanced. This goal is
accomplished by comparing a single triangular voltage waveform with three dierent
sinusoidal control signals that are 120 out of phase.
In square-wave operation, each switch is on for 180, thus three switches are on
simultaneously at any time. As it was said before, it is impossible to control the
magnitude of the output AC voltage with this control strategy, if the input DC voltage
is not controllable.
Chapter 5
Small-scale wind power generation
A HAWT is dened as small, according to the International Electrotechnical Com-
mission (IEC) Standard for small wind turbine safety (IEC 61400-2), if it has a rotor
swept area of less than 200 m2; it corresponds to a rated power of around 50 kW [19].
However it is a denition that is not strictly followed by all countries: for example,
in Spain the limit for a turbine to be considered small is 100 kW , and in the United
States it ranges from 50 to 200 kW depending on the single State [8]. Sub-categories
exist, as synthesized by Table 5.1, but they are not regulated by the standard; they
are more used in an informal manner.
Table 5.1: Categories of small-size wind turbines (Source: [8])
Size Nominal power Rotor diameter Tower height Typical applications
XS 100÷ 800 W 1÷ 2 m 2÷ 6 mBoats, RVs, smallisolated users
Micro 1÷ 6 kW 2÷ 5 m 6÷ 8 m
Houses, shops, smallindustries, ground
or roof-mounted, isolatedor grid-connected users
Mini 6÷ 60 kW 5÷ 18 m 8÷ 30 m
Campings, vilages,farms, small industries,
ground-mounted,grid-connected users
Small 60÷ 200 kW 18÷ 30 m 30÷ 60 m
Farms, small industries,ground-mounted,
grid-connected users
The increasing economic feasibility of such small systems, due to the technological
progress aimed at optimizing the performance, pushes their popularity and the interest
in localized generation, especially for "user-level" applications, such as in houses. It is
83
84 CHAPTER 5. SMALL-SCALE WIND POWER GENERATION
essential then to explore the small turbines in detail, which is the aim of this chapter.
The main dierences in the design with respect to larger-scale turbines will be given,
then some time will be spent describing the manufacturing of the blades. After that,
two particular and innovative designs will be seen. Finally, the focus will switch to
building-integrated wind turbines, with its advantages and issues.
5.1 Design of small wind turbines
In this section will be presented some design elements of small scale wind turbines.
Even though VAWTs are preferred over HAWTs for urban applications, the design of
small-scale HAWTs presents quite a challenge, since their smaller rotors require more
attention during the design phase with respect to the "usual" larger turbines.
5.1.1 Blade design
The optimization of the performances of a small-scale wind turbine involves primarily
the optimization of its aerodynamics. Due to the fact that little literature exists about
small wind turbines to date, newer and newer technologies help researchers in their
empirical work, allowing them to cheaply test multiple designs in order to nd the
most suitable one.
A useful example is the study done by a group of PhD students at the James Madi-
son University (JMU) [4]. The two-year project started in the context of a competition
put on by the Department of Energy of JMU. Its purpose was to design and build a
mini HAWT that could work in the speed range of 5 ÷ 14 m/s to produce 10 W of
power.
The team started by determining the key requirements for their project, which are
presented in Table 5.2. Of course technical requirements were given priority. The
design concepts were conceived by taking the blade shape as a starting point.
The National Advisory Committee for Aeronautics (NACA) database of airfoil
shapes was used for this goal, sorting the dierent designs by their lift to drag ra-
tio. Considering HAWTs, the optimal shapes maximize lift; the rst one chosen for
further development was the result of a weighted decision matrix considering factors
such as cut-in speed and manufacturing cost.
Once the shape was selected, other factors needed to be analysed:
• Blade size;
• Number of blades;
5.1. DESIGN OF SMALL WIND TURBINES 85
Table 5.2: Requirements of the JMU project (Source: [4])
Cut-in speed below 3 m/s
Technical Wind speed range of 3÷ 4 m/s
requirements 10 MW power output
Maximum volume 45 cm3 in anydirection (wind tunnel size constraint)
Economic Maximum cost 500 $requirements (project budget constraint)
Use of standard parts wherever possible
Environmental Maximize reuse and minimizerequirements disposal of parts
Recyclability of the components
Minimization of safetySocial hazards to users
requirements User-friendly system in installation,use and maintenance
• Material selection.
Blade size was constrained by physical limitations: since the testing tunnel size was of
45 cm3, after accounting for hub size and some clearance, the maximum blade length
was calculated. Then, blade width was selected by studying existing design data:
obviously the blade tapers from the hub to the tip Finally, pitch was set from the
NACA data, and then adjusted along the blade to account for apparent wind.
The blades were then manufactured and tested. By improving cut-in speed and
power output the team obtained the so-called Alpha prototype (see Fig. 5.1). The
Figure 5.1: The Alpha prototype of the JMU project (Source: [4])
Alpha design was further optimized to operate in lower wind speeds; this could be
done cheaply and fast by using specic computer software such as Qblade. The team
then selected new airfoils based only on lift rather than on the L/D ratio, as explained
86 CHAPTER 5. SMALL-SCALE WIND POWER GENERATION
by the National Renewable Energy Laboratory (NREL). Another airfoil shape was
chosen for best performance.
Once the blade shape was assessed, the inuence of the number of blades on turbine
performance was studied. Previous tests showed that increasing the number of blades
is benecial to power output. Iterations with 5, 6 and 7 blades conrmed these results
in theory and by Qblade siulations. For further conrmation in practice, the blades
were manufactured and tested to compare cut-in speeds and power outputs in dierent
conditions. The results are presented in Fig. 5.2 and in Table 5.3.
Figure 5.2: Power curves of the tested turbine models for the JMU project (Source: [4])
Table 5.3: Results of the JMU project (Source: [4])
Blade ModelCut-in Maximum testing Power
Eciency (%)speed (m/s) speed (m/s) output (W)
Alpha 4.66 6.84 2.73 6.15 Blade 3.35 5.97 2.61 20.26 Blade 3.79 n/a n/a n/a7 Blade 3.79 6.84 2.73 14
The 5-blade model has the lowest cut-in speed, while the one generating the most
power is the 7-blade model. The Alpha model still fares good against the other models,
being signicantly more robust than the 6-blade model. The project results in a mod-
ular turbine with interchangeable sets of blades that are to be used according to the
environment. The Alpha design eventually is recommended for use because of safety
reasons.
5.1. DESIGN OF SMALL WIND TURBINES 87
5.1.2 Blade manufacturing
The blades for small wind turbines need special attention in their manufacturing. Once
the blade shape is selected, blade connection should be considered, bearing in mind
that thick sections near the blade hub are undesirable for structural strength. The
majority of small blades are held in rectangular section "holders", where the blade
is held in place by bolts. Very often the the attachment section lies in the plane of
rotation.
Another feature worth noting is that the leading edge of the blade is straight, mainly
for manufacturing purposes when moulds are used.
As far as materials are concerned, a wide range of choices exists. The material
selection depends mainly on blade length.
The typical material which is used for wind turbine blades in general is resin. This
material is best suited for longer blades, since they benet from composite manufac-
turing. This manufacturing technique requires the use of moulds, which are created
by machining templates. The making of a mould by machining is shown in Fig. 5.3.
Separate moulds are made for the upper and lower part of the blade, then the moulds
Figure 5.3: Machining of a blade mould (Source: [19])
are coated with a thin laminate (which gives structural strength) made with resin and
reinforced by glass or carbon bers. Each blade half is made by vacuum infusion, then
the two parts are heated for faster curing, and joined. The region of maximum thick-
ness is sometimes further reinforced by a small box, called shear web, which is inserted
in the chord direction and keeps the two blade halves separated, avoiding buckling due
to the continuous operation in compression of the upper (downwind) half of the blade.
The main advantage of this manufacturing technique is its low cost, once the moulds
have been made.
Timber is one of the new "innovative" material, and it is fairly good: wood is a
88 CHAPTER 5. SMALL-SCALE WIND POWER GENERATION
relatively cheap and readily available material (it can be grown in plantations), and it
has good mechanical properties [19]. Also, this material is used already in practice for
plane propellers and turbine blades. It presents however some downsides, the main of
which is that lamination is costly, so the only feasible manufacturing technique today
is to derive the blade, either by carving or machining, from solid blanks. Also, it is not
suitable for long blades, since it is almost impossible to obtain long blanks that are
knot-free and without defects.
A manufacturing method which is rising in popularity, not only for industrial appli-
cations, is additive manufacturing, also commonly known as 3D printing. Design
of the blade is simplied by the aid of a computer, which makes it faster and cheaper
[13].
First, blade element theory can be implemented into a code, which is after elabo-
rated for the calculation of the blade parameters (prole, pitch, chord length). Then,
the blade shell is modelled by using CAD (computer-aided design) software. Finally,
the model is processed by a CAM (computer-aided manufacturing) software and printed
via a fused deposition modelling (FDM) process. The material which is commonly used
is PLA plastic. Also, due to the length of the turbine blade with respect to the size of
a standard 3D printer, a custom device is needed. The blade shell is nally reinforced
with the usual materials, such as glass bre and epoxy resin. See [13] for the dierent
reinforcing methods and their comparison.
5.2 Blade testing
The testing of wind turbine blades is a very important step in determining their safety.
Of course one single test is not enough, so many need to be performed.
The rst tests are coupon tests, performed on the single blade and aimed at de-
termining the dependence on temperature of its material properties, such as Young's
modulus and yield stress.
Other tests are static tests, which require the mounting of the blade on the actual
turbine. They measure mainly deection against load, with the purpose of verifying
the structural modelling of the blade, for example to ensure that blades don't touch
the tower when under the action of the wind. These tests also include torsional tests
and derivation of the natural frequency of the blade.
One nal test is a fatigue simulation over the whole life of the turbine. This is
performed on a rig (see Fig. 5.4) where mechanical arms, driven by an electric motor,
shake the blade.
5.3. THE NO-BLADE TECHNOLOGIES 89
Figure 5.4: Rig for the blade fatigue test (Source: [19])
5.3 The no-blade technologies
In order to make small scale wind turbines economically protable, one of the rst
things that comes to mind is to save material. Some manufacturers went along this road
by trying and removing the blades, while utilizing alternative methods to convert wind
power into electricity. Two examples of these no-blade technologies will be presented
here.
5.3.1 Vortex Bladeless
The tragic collapse of the Tacoma Narrows Bridge in 1940 (see Fig. 5.5) inspired the
Spanish David Yáñez to try and exploit the phenomena of resonance and vorticity
for the production of electric power, instead of avoiding it as the usual practice sug-
gests. Together with David Suriol and Raul Martin, Yáñez founded the startup Vortex
Figure 5.5: An image of the collapsing Tacoma Narrows Bridge
90 CHAPTER 5. SMALL-SCALE WIND POWER GENERATION
Bladeless.
The idea behind Vortex Bladeless turbines is to exploit the vortex shedding eects,
as explained by Suriol in an interview with Renewable Energy Magazine [18]. As
the wind passes a vertical mast, a cyclical pattern of vortices is generated. Once the
structure enters into resonance with the vortices, it starts oscillating. The energy of this
oscillation is then converted into electricity by a linear alternator. A Vortex Bladeless
turbine is shown in Fig. 5.6.
Figure 5.6: A Vortex Bladeless turbine
All this sounds too good to be true, and it might be: according to Sheila Widnall, an
aeronautics and astronautics professor at MIT, thin cylinders and slow wind velocities
result in "an absolutely pure frequency or tone"; but as cylinders get bigger and wind
speed gets very high, what comes out is a range of frequencies. A turbine like the Vortex
ones will not be able to capture as much wind energy as it is claimed to, because "the
oscillation is fundamentally turbulent" [10].
Despite some doubts that may arise, this idea received some recognizement and
funding, starting in 2012 on the rst edition of Repsol's Fondo de Emprendedores. In
2014 some private investors joined in, providing funds together with non equity public
funds. This funding led to extensive research and testing, however the results of the
tests on 4 and 6 meters prototypes are not encouraging: in fact, they are able to exploit
30% less wind energy with respect to conventional wind turbines. According to Suriol
in an article from Le Monde [5], this defect can be compensated by the fact that a
higher number of the Vortex turbines can be placed in the same space as a single
conventional turbine.
Vortex claims that by removing the blades it is possible to save about 53% in man-
ufacturing costs and 51% in operating costs compared to conventional wind turbines.
5.3. THE NO-BLADE TECHNOLOGIES 91
The absence of blades also removes the problems of shadow icker, bird strike and -most
importantly- noise, which are almost completely solved. Then, avoiding the contact
between moving parts means that there is no friction between mechanical parts, thus
requiring no lubricant, and also the intervals between maintenance or the substitution
of parts are longer. This reduces overall maintenance costs by 80%. They claim also
to be "greener" than conventional wind turbines, reducing their carbon footprint by
40%.
Their rst model is the Vortex Atlantis, outputting a power of 100 W for 3 metres
of height. It is used for household needs and the power curve can be balanced with the
help of solar panels. A bigger scale turbine, the Vortex Mini, which is in development,
is supposed to be 12.5 metres high and to output 4 kW of power. They are also
developing a 150 metres high, 1 MW turbine, the Vortex Gran.
5.3.2 The Saphonian
This type of unconventional turbine takes its name from the Carthagian god Baal
Saphon, the divinity of wind. Its inventor is the Tunisian Anis Aouini, who co-founded
Saphon Energy with Hassine Labaíed.
Saphon Energy's No-Blade Technology is inspired by boat sails, which convention-
ally use the wind energy for transportation. So, instead of being removed, the blades
are transformed into a non-rotational sail-shaped body (see Fig. 5.7). As claimed by
Figure 5.7: A Saphonian turbine (Source: [1])
Saphon Energy, this body would have a high aerodynamic drag coecient CD, which
makes it capture twice as much kinetic energy as conventional bladed wind turbines
for the same swept area.
92 CHAPTER 5. SMALL-SCALE WIND POWER GENERATION
To produce electric energy a Saphonian turbine follows a back and forth 3D knot
motion, instead of rotating [1]. An hydraulic system acts as an intermediary link
between the mechanical and electrical stages: the hydraulic pressure could either be
stored in an hydraulic accumulator (partially solving the intermittency issue), or di-
rectly converted into electricity via a hydraulic generator.
The particular movement of the machine, coupled with the removal of the blades,
allows it to "set itself free from the Betz's limit". Also, Saphon energy claims that for a
Saphonian the concepts of "rated wind speed" and "tip speed ratio" cannot be applied,
meaning it can work in any condition. Turbulent wind, instead of being detrimental
to the machine, has a minor impact on its performance. This makes the Saphonian a
good deal for the use in urban areas.
With respect to a conventional wind turbine, the replacement of the blades with the
sail-shaped body signicantly reduces the overall size of the machine and its weight,
reducing in turn manufacturing costs. A further cost reduction can be obtained by cen-
tralizing the hydraulic and electrical system on the ground, exploiting higher economies
of scale and lower operating and maintenance costs.
Regarding the typical problems that aect conventional wind turbines, a Sapho-
nian's compact sail-shaped body is more easily identied by birds, reducing the prob-
lem of bird strike. The problem of shadow icker is practically non-existent, since the
machine's sail-shaped body remains virtually stable upwind. Also, it is less noisy due
to the removal of the blades and of the gearbox. The removal of the blades reduces the
risk of accidents, too: having no blades means no blade breakdown.
Many prototypes have been designed, tested and developed. Saphon Energy claims
that the results of their tests show that the Saphonian is a robust, resistant and as
scalable as conventional bladed wind turbines.
5.4 Building-integrated wind turbines
Small wind turbines really have a chance to shine in urban environments, where they
allow to recover the energy of an otherwise "wasted" wind source which is actually
decent (with high speeds), in order to produce power for small users or appliances,
such as houses or stores. Integration of wind turbines into buildings is an increasing
trend, driven mainly by the fact that it results in a better ratio between produced
energy and land usage, with respect to other small-scale energy conversion systems [3].
Building Integrated Wind Energy Conversion Systems (BIWECS) present multiple
advantages [15]. The principal ones are:
5.4. BUILDING-INTEGRATED WIND TURBINES 93
• Absence of overhead or underground lines;
• Reduced losses because no energy transportation is needed;
• Less storage required;
• Increased reliability;
• Higher eciency, since they are located right near the loads.
As it was said before, VAWTs are preferred for this specic applications.
The rst applications of BIWECS are on low-rise buildings, for example on rooftops
of gas stations or stores. The production of an array of turbines is able to power
the lighting system, for instance. Even public buildings, like museums, are t for
integration with a power conversion system. Fig. 5.8 shows a 12 kW VAWT on the
roof of the Museum of Science in Boston, Massachussetts.
Figure 5.8: BIWECS on the roof of the Boston Museum of Science (Source: [15])
Only very few models exist today for high-rise buildings, while research is still being
done. One example of a BIWECS installed in a tall building is the 50 storey Bahrain
World Trade Center Building, which can be seen in Fig. 5.9. The three turbines, made
by Danish producer Norwin, are able to output a rated power of 225 kW . It is worth
noting that the angle of the building walls are designed in such a way that they can
keep the wind strong and consistent for all the three turbines.
A new innovative solution for BIWECS mimics the functioning of a hydraulic tur-
bine. it is called aeolian roof, studied by researchers at the University of Cagliari, and
is shown in Fig. 5.10. The external static structure acts as a stator and conveys the
ow to the center of the roof, where the vertical-axis centripetal turbine is placed.
94 CHAPTER 5. SMALL-SCALE WIND POWER GENERATION
Figure 5.9: BIWECS on the World Trade Center Building (Source: [15])
Figure 5.10: The Aeolian roof (Source: [3])
CFD models and experiments on a prototype showed its potentialities; of course there
is always room for performance increase.
Due to their dimensions, building-integrated wind turbines are compatible with
elements of urban furniture, as presented by [8]. Applications where these systems
seem promising is in the coastal areas of cities.
For example, the breakwaters of ports can act as a base element for the towers of
small VAWTs (see Fig. 5.11). No underground structures would be needed, the turbine
can simply be placed on the docks.
Another solution, more blended into the urban furniture of a sea side walkway, is
a sort of aeolic bench, as presented in Fig. 5.12. The tower of the turbine acts as a
normal lamppost where specically designed LED lamps are installed, and the base of
the turbine is transformed into a bench.
5.4. BUILDING-INTEGRATED WIND TURBINES 95
Figure 5.11: Model of a small VAWT for placing on port breakwaters (Source: [8])
The issues regarding BIWECS are the same as larger systems, with little dierences.
Noise is generated by both the rotating parts and the wind interacting with the blades,
just like larger turbines. Small building-integrated turbines, however, present another
source of noise due to the machine resonating with the already existing structure. It is
an issue that is not easily quantiable since it strongly depends on the rotor type and
on how the supporting structure is xed to the building.
BIWECS are generally safer for birds. The probability of a collision can be assumed
to be proportional to the swept area, which of course is decreased in the case of small-
scale turbines. Moreover, dierent studies show that the higher rotating speed of the
smaller turbines is better perceived by birds with respect to the slow-turning large
blades of the large-size turbines [8].
Electromagnetic interference is mainly due to the rotating blades and the gener-
ator's magnetic eld. While the rst source of interference has already been dealt
with (less and less metallic materials are used for the construction of the blades), the
Figure 5.12: An aeolic bench (Source: [8])
96 CHAPTER 5. SMALL-SCALE WIND POWER GENERATION
disturbance coming from the generator, which for large turbines has been reduced by
insulating the nacelle, is further decreased in the case of small turbines. In fact, due to
their compact size and low power, also the induced magnetic eld of the generator will
have a lower intensity, which is less likely to interfere with the electromagnetic waves
that are sent from or received by a building. In any case, if there should ever be a
problem of this kind, the antennas of the disturbed devices (e.g. TVs, decoders, . . . )
can simply be redirected.
Shadow icker is a problem that is more important in small building-integrated
turbines. The constant moving of the blades casts intermittent shadows, which can be
annoying to the human eye, in the surrounding buildings. The problem is even more
relevant if houses or oces are involved. It is essential then that particular care is
put in the design phase of the BIWECS: it must be estimated where shadows are cast
on the building during the year, in order to place a turbine in such a position that it
cannot project shadows on the nearby structures.
Chapter 6
Economic evaluations of wind turbines
In the previous chapters the focus was on the technical and performance aspects of wind
turbines. This chapter will instead discuss the economical aspects, since it is crucial
to consider them in order to determine if a wind turbine can be a viable contender
for energy production. Firstly, the energy yield of a wind turbine will be assessed,
including a discussion on the sources of losses that are present in the mechanical-
electrical energy conversion chain. Then, the general framework for the economic
analysis of a generic power plant will be explained; the very same concepts can be
applied to wind turbines. The main cost components to consider in the economic
analysis of a wind turbine system will be briey studied afterwards. Finally, small
wind turbines will be considered in order to understand the dierences with respect
to larger scale systems. A comparison between small-scale wind power and small-scale
solar power will close the discussion.
6.1 Energy yield
The calculation of the annual energy yield is essential in order to assess the economic
feasibility of a wind turbine. It is based on the wind speed data, the rotor power
coecients at dierent rotational speeds, and is strongly aected by the eciencies of
the overall conversion system (including mechanical and electrical components) in a
turbine. The power coecient of the turbine is calculated by taking into account this
factor:
Cp = Cpr · ηmech−el (6.1)
The electrical output is then calculated as a function of the wind speed from the
denition of the power coecient (Equation 2.7 on page 16). Fig. 6.1 shows an example
of dierent power curves for varying rotor speeds. The energy yield over a certain time
interval is simply the product between the power output at a set wind speed and the
97
98 CHAPTER 6. ECONOMIC EVALUATIONS OF WIND TURBINES
Figure 6.1: Power curves for dierent rotor speeds (Source: [6])
time interval during which that wind speed is expected within the given period of time.
It is evident that having the power curve of the turbine, as well as the cumulative wind
speed frequency distribution, is crucial, because it greatly simplies the calculations.
The cumulative frequency distribution is split into intervals (also called bins) with a
set width ∆vw and the mean generated power Pel is easily read from the curve in each
corresponding interval. Then, the annual energy yield E (ex. GWh/y) is calculated
as follows:
E = 8760
vcut−out∑vcut−in
Pel∆ϕ (6.2)
Where ∆ϕ is the wind speed frequency dierence and 8760 is the number of hours in
a year.
6.2 Estimation of losses
The power coecient expressed by Eq. (6.1) takes into account the fact that some
losses exist inevitably, by allowing the calculation of a sort of "net" power. It is worth
to explore the sources of these losses, which is the aim of this section. Some of the
losses are due to how the power control and the operational sequence work, while other
losses are caused simply by the friction between mechanical components in the energy
conversion chain.
6.2. ESTIMATION OF LOSSES 99
6.2.1 Losses due to power control and operational sequence
The control systems and the operational sequence cause losses in performance by limit-
ing its "free" operation, but fortunately their eects are only appreciable in the partial
load range [6].
Power control aects the turbine performance as follows:
• With a generator that is directly coupled to the grid, the wind turbine must
operate at constant rotor speed. The rotor can then be operated only at one
point corresponding to the theoretically best CPR, since the TSR cannot be
adapted to the variable wind speed;
• In the partial load range, the rotor is generally operated with constant blade
pitch, since generator power cannot be used as a reference parameter.
• In the full load range, the rotor power output is limited by the pitch angle, which
is controlled in order to make sure that the maximum generator power is not
exceeded.
Yawing, with its unavoidable inertia, is also a source of power loss. The operational
sequence logic introduces losses by setting the cut-in and cut-out speeds, thus limiting
the usable wind speed range. Also, the process of cutting the turbine in and out
presents a hysteresis (according to [6]), which leads to important power losses in sites
where the mean wind speed is subject to frequent variation.
6.2.2 Losses due to the mechanical-electrical energy conversion
The various mechanical components in a wind turbine introduce losses in the power
chain. Some sources of losses are:
• Friction in bearings;
• Mechanical friction in the gearbox;
• Eciency of the generator and of the inverter;
• losses in the transformers along the connection with the grid;
• "self consumption" of the turbine.
Fig. 6.2 shows an example of energy ow through the mechanical-electrical energy
conversion chain in a turbine. Of course this type of losses depends on the design
of the individual elements, which determines their mechanical eciency, but it also
depends on size. The components of smaller wind turbines, having a much simpler
design, will have lower eciencies.
100 CHAPTER 6. ECONOMIC EVALUATIONS OF WIND TURBINES
Figure 6.2: Example of energy ow through the mechanical-electrical energy conversion chainin a turbine (Source: [6])
6.3 Economic analysis
6.3.1 General framework
Once the "net" power output has been assessed, and the consequent gain from its selling
is determined, for a thorough economic analysis it is necessary to consider all the other
components involved, i.e. costs. The basic framework of the economic analysis for a
generic power plant expresses the cost of the production of a single product or service
(such as electricity) as:
C
[e
unit
]=fixed costs
production+ variable costs (6.3)
Fixed costs are the ones which do not depend on the volume of production: cost of
personnel, xed maintenance costs, insurance, permits, annual fraction of investments
costs, etc. Variable costs instead are proportional to the volume of production: ma-
terials, fuels, reactants, etc. Eq. (6.3) can be rewritten according to what was just
expressed, and extended to the electricity sector, in order to calculate the cost of elec-
6.3. ECONOMIC ANALYSIS 101
tricity (COE):
COE
[e
MWhe
]=Cinv + CO&M + Cpersonnel + Cfuel
PnomNeq
(6.4)
Where the cost components C are annual costs, Pnom [MW ] is the nominal power of
the plant, and Neq [h/year] is the number of equivalent hours. It is of course lower than
the 8760 hours in a year because it is natural to assume that a power plant does not
always operate, but it is sometimes closed due to maintenance, faults, or other reasons.
The main indicator of the overall value generated during the life of the enterprise
is the net present value (NPV). It is dened as:
NPV =∑i
CFi(1 + r)i
(6.5)
Where CF is the net cash ow at year i and r is the discount rate, which is the interest
rate of a risk-free investment. NPV is often evaluated at the start of the enterprise,
so every cash ow is actualized to year zero. The typical "life" of the enterprise is
typically 20 years for most applications, including wind turbines.
The discount rate that makes the NPV equal to zero, corresponding to the interest
rate for which the enterprise just pays back its initial investment (without generating
added value), is called internal rate of return (IRR). It can be found by deriving r
from Eq. (6.5), putting NPV = 0. For a xed r, instead, the time required to reach
NPV > 0 is called payback time (PBT). It corresponds to the time required to pay
back the initial investment.
6.3.2 Main cost components
Operating costs
Operating costs, often referred to as Operating expenditures (OPEX), are peri-
odic expenses. They include annual xed costs, such as insurance, taxes, land rental,
maintenance etc. For wind turbines, maintenance costs contribute for the most part
to OPEX.
The rst aspect to include in the discussion is maintenance and repairs. They are
constituted by routine checks, normal periodic maintenance, blade cleaning, mainte-
nance of the electrical equipment, unscheduled maintenance. In the rst years of the
modern wind power practice, routine checks were much more frequent, due to the higher
incidence of faults in a relatively new technology. Also unscheduled maintenance was
102 CHAPTER 6. ECONOMIC EVALUATIONS OF WIND TURBINES
performed more often [6]. Today the technology is solid enough that these costs are
greatly reduced due to the higher reliability of the systems.
Another component adding to OPEX is insurances. They exist to cover the nancial
risk associated with stretching the life of the system as long as possible. An insurance
that is almost indispensable is the so-called liability insurance, which covers the risk
against damage claims by third parties. Another important insurance for the operator
of the wind turbine is a loss-of-prot insurance, which compensates the loss of revenue
when the turbine (or the wind farm) is not operating due to repairs, maintenance,
faults, etc.
Lastly, other parts of the operating costs are constituted by land leasing (if the land
is not owned by the operator himself) and taxes on the gained prot.
Capital costs
These cost components are often called Capital expenditures (CAPEX). They are
cash ows related to the enterprise's capital, such as bank loan payment, depreciation,
taxes, etc. Distributing CAPEX along the whole duration of the enterprise presents a
challenge. EPRI (Electric Power Research Institute) has proposed a helpful approach:
the desired return on capital, which can be thought of as a sort of IRR, is xed a priori,
and the cash ows (including the selling of the good or service at a certain cost, to be
determined) are calculated in order to attain it. Also, in this approach the CAPEX are
spread along the life of the plant by dividing them into actualized annual quotas. Each
of them is called levelized carrying charge (LCC) and corresponds to he fraction of
total investment to be accounted for each year. LCC is a complex function of nancial
variables:
• Capital division between equity and debt;
• Nominal return on equity and on debt;
• Ination rate;
• Duration of the construction of the plant;
• Life of the enterprise;
• Taxes;
• Owner's costs (e.g. start-up, royalties, land, . . . );
• etc.
6.3. ECONOMIC ANALYSIS 103
The annual plant cost can be eventually calculated as:
Cinv
[e
year
]= TPC · LCC (6.6)
Where TPC is the total plant cost, determined assuming that construction occurs
overnight before the very rst day of the enterprise. In the specic case of wind power,
it is challenging to determine the capital costs of a wind energy system. This is mainly
due to the fact that wind turbine manufacturers do not really want to share their own
cost gures with anybody, let alone their competitors. It is also the reason why cost
comparisons between wind turbine projects are hard [9].
Another aspect which needs to be taken into account is the scale eect : the specic
investment cost of the plant Cinv
[e
MWe
]= Cinv
Pnomdecreases with the nominal power.
To generalize this concept to each dierent piece of equipment of a plant, the following
equation (graphically represented in Fig. 6.3) holds:
Cinv
[e
unit size
]= ˆCinv0
(S
S0
)f−1(6.7)
Where f is the scale factor and S is the size of the piece of equipment. Subscript
0 indicates reference values for both the specic investment cost and the size. It is
Figure 6.3: Graphical representation of the scale eect
important to remark that the concept of "size" does not apply only to the power
generation equipments, where it is represented by rated power, but also to any other
plant component that contributes to the investment cost: for example, the "size" of a
104 CHAPTER 6. ECONOMIC EVALUATIONS OF WIND TURBINES
heat exchanger is represented by heat transfer area. For wind turbines, size is usually
represented by the rotor swept area or the rated power; Fig. 6.4 (from the Danish
Wind Industry Association) shows the specic cost range for production of Danish
wind turbines in 2006.
Figure 6.4: Cost of Danish wind turbines as a function of their rated power (Source: [9])
6.4 Economics of small wind turbines
For small-scale wind turbines, one of the important parameters that determine their
economic feasibility is the initial cost, which roughly corresponds to the capital cost.
Due to their small size, it is evident that small turbines do not benet from scale
eects: their capital cost then can be assumed to be generally higher than standard-
sized systems, leading, at least at rst sight, to a longer payback time [17].
Another important factor contributing to the feasibility of a small turbine is the
cost associated with the generation of energy. With a smaller size, also the wind
energy captured from the wind is lower. This, paired with the lower eciency of
the smaller-sized mechanical and electrical components in the energy conversion chain
greatly increases the cost of generating the electrical power.
If small and micro wind turbines are obviously no match for their larger counterparts
from an economic standpoint, it is fairer to make a comparison with other small-scale
energy conversion systems. A study was performed on the dierence in the levelised
cost of energy (LCOE) between a small wind turbine and a small solar PV [17].
The study was aided by the optimization software HOMER, which simplies the
calculation of the LCOE based on the associated energy source data, system compo-
nents and load demand. The levelised cost of energy is calculated similarly to the COE
6.4. ECONOMICS OF SMALL WIND TURBINES 105
that was explained in the previous sections, according to the following equation:
LCOE
[e
kWh
]=
Cann,totEprim + Edef + Egrid,sales
(6.8)
The denominator of the fraction is the sum of the primary load served, the deferrable
load served and the total grid sales, respectively. The numerator of the fraction is
the total annualised cost of the system, equal to the sum of the annualised capital
cost(equal to the initial capital cost multiplied by a capital recovery factor or CRF,
which is a function of the annual real interest rate and of the lifetime of the system),
annualised replacement cost and annual O&M cost.
The chosen wind turbine was the Southwest Sky Stream 3.7, with a rated power of
2.4 kW . Its power curve is shown in Fig. 6.5. The PV system was instead modelled in
Figure 6.5: Power curve of the Skystream 3.7 wind turbine (Source: [17])
order to have the same peak power capability.
Power generation is determined by HOMER considering hourly based wind and
irradiance data, while grid sales are calculated based on generation and demand data
over the course of a year. Also, the comparison was for installations in urban envi-
ronment. A rural (airport site) environment was additionally considered for the wind
turbine only, in order to compare the power generation potentiality in dierent envi-
ronments; a higher power production can be expected in this environment, since the
wind is generally faster and unimpeded, while in an urban environment the buildings
can act as an obstacle.
Cost-wise, the capital cost of the wind turbine is higher, as well as the O&M costs,
which were assumed to be 3% of the capital cost. Maintenance for the PV system is less
106 CHAPTER 6. ECONOMIC EVALUATIONS OF WIND TURBINES
of an issue if the inclination of the panels is higher than 5, but still a nominal annual
maintenance cost, corresponding to about 0.8% of the capital cost, was considered.
The comparison of the main economic parameters is summarized in Table 6.1.
Table 6.1: Economic parameters comparison between a small wind turbine and a small solarPV system (Source: [17])
Wind system PV system
Capacity (kW) 2.4
Capital cost (e) 14520 6240
Cost/kW (e) 6050 2600
Real interest rate (%) 5
Annual maintenance cost (e) 436 50
Unit cost (purchase) (e) 0.18
Unit cost (sale) (e) 0.09
Considering only the wind energy system, which was studied in two dierent envi-
ronments, the results show that in the rural environment the wind turbine generates
yearly 4477 kWh, which is about 3.3 times the amount of energy it produces in the
urban environment (1339 kWh/y), as expected. In both environments, the turbine
alone is not able to cover the annual household electricity demand of 5074 kWh/y.
The comparison between the two power generation systems clearly shows that the
micro wind turbine is not economically competitive with the solar PV system (see [17]).
In fact, the solar PV system is able to generate 2250 kWh/y in the urban environment,
of which it sells 823 kWh; the wind turbine is able to sell only 215 kWh. It is also
useful to remark that the main contributing factor to the LCOE of the wind energy
system is the local wind speed, and not the capital cost, as it would be natural to
think. The nal results on the LCOE of the two systems are presented in Table 6.2.
Table 6.2: Results of the LCOE analysis of wind and solar PV systems (Source: [17])
Rural wind Urban wind Urban solar PV
Cost of wind (solar)
0.36 1.2 0.24energy generation(e/kWh/mean wind (mean irradiance)
Conclusions
This work provided the basis for understanding the potentiality of wind turbines, both
of large and small scale, for the generation of electricity. The wind resource was
studied in detail: its speed increases with height, and the interaction with buildings
is very interesting. Solid statistic theory allows to estimate wind speed at the chosen
location. After that, wind turbines were introduced. The physical principles regulating
their functioning were seen. This allowed to show how the wind turbine technology
has an enormous potential for the generation of mechanical power. The mechanical
power needs then to be converted into electrical power; electrical machines (especially
generators) and their functioning were explained. The dierent congurations for the
connection of a wind turbine with the electrical grid were seen: each solution has its
own pros and cons, and the end choice will be a result of an economical evaluation.
Since the power output needs to be adjusted according to the needs of both the users
and the electrical grid, methods of aerodynamic and electric control of wind turbines
were studied. Converters, which are a combination of semiconductor devices, are the
standard choice for these operations. Some time was then dedicated to the study of
small-scale wind turbines. Finally, the economic framework was explained: it allows
to assess the economic feasibility of a wind turbine of every scale.
Wind turbines for large-scale power generation are nowadays a solid technology
which has been perfected and innovated year after year. They have already been
proven to be extremely competitive not only with other renewables, but also with the
other traditional power plants. The added advantage is the near-zero emission of CO2.
As far as smaller-scale wind turbines are concerned, they present obvious dierences
in the design with respect to their larger counterparts. Blade shape and its aerodynamic
parameters need in fact to be carefully selected, as demonstrated by the JMU study.
Also, blade manufacture is made cheaper by newer technologies such as 3D printing.
Besides, they have great potential for electricity generation as well: their small size
allows them to be placed in locations where the unstable wind at low heights or between
buildings can be exploited easily. In this context, they result very useful for isolated
generations of single users. Since small wind turbines represent a technology that is
107
108 CONCLUSIONS
relatively new, research and development have been pushed to the extreme, also thanks
to the creativity and will to innovate of young entrepreneurs. Vortex Bladeless and the
Saphonian concept are good examples of this.
However, if their potential for electricty generation is now evident, economic evalu-
ations are not in their favour. Their aerodynamic characteristics are inevitably poorer
due to their size, which reduces their overall energy output, thus reducing the income
from the sale of electricity. Also its electrical component present several losses due to
their small volume. FInally size, although convenient in terms of their capability to
produce power, represents an issue from an economical standpoint, since smaller sys-
tems do not benet at all from scale eects. Unfortunately all these factors make small
wind turbines not economically competitive with other green power systems, such as
PV solar. And this turns into a giant obstacle for their diusion.
The hope for the future is however that technological progress will help reduce the
overall costs and make the smaller wind turbines more convenient, since their ability
to catch the wind in every direction, and in places where it represents a decent source
of energy, is evident. One particular use that might push its potential even further is
for providing electricity to villages in developing countries.
List of Figures
1.1 Graphical representation of the roughness length Z0 . . . . . . . . . . . 2
1.2 Pressure coecients variation in a CFD simulation . . . . . . . . . . . 3
1.3 Probability distribution of a discrete random variable . . . . . . . . . . 7
1.4 Probability density function of a continuous random variable . . . . . . 8
1.5 Weibull function depending on the k parameter . . . . . . . . . . . . . 10
1.6 Weibull function vs experimental data . . . . . . . . . . . . . . . . . . 10
2.1 Upwind HAWT VS Downwind HAWT . . . . . . . . . . . . . . . . . . 14
2.2 Flow conditions of a free-stream air ow through an energy converter . 15
2.3 Power coecient as a function of the velocity ratio . . . . . . . . . . . 17
2.4 Power coecient as a function of the axial induction factor . . . . . . . 18
2.5 Aerodynamic forces on a drag device . . . . . . . . . . . . . . . . . . . 19
2.6 Blade element denition . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 Power coecient as a function of the tip speed ratio . . . . . . . . . . . 22
2.8 A Savonius rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.9 The Dornier Darrieus 50 . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.10 Forces on an airfoil for VAWTs . . . . . . . . . . . . . . . . . . . . . . 24
2.11 A VAWT with spiral blades . . . . . . . . . . . . . . . . . . . . . . . . 25
2.12 The Dornier Darrieus/Savonius 5.5 kW . . . . . . . . . . . . . . . . . . 25
2.13 Dierent shapes of a Darrieus-type VAWT . . . . . . . . . . . . . . . . 25
2.14 A VAWT with helical blades . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1 Equivalent circuit for an ideal transformer . . . . . . . . . . . . . . . . 29
3.2 Equivalent circuit for a real transformer . . . . . . . . . . . . . . . . . 30
3.3 Salient-pole, wound-rotor synchronous generator . . . . . . . . . . . . . 32
3.4 Torque characteristic of a synchronous machine . . . . . . . . . . . . . 32
3.5 Squirrel-cage induction generator . . . . . . . . . . . . . . . . . . . . . 34
3.6 Torque characteristics of a squirrel cage induction machine . . . . . . . 34
3.7 Synchronous generator directly coupled to the grid . . . . . . . . . . . 36
3.8 Induction generator directly coupled to the grid . . . . . . . . . . . . . 37
109
110 LIST OF FIGURES
3.9 Slip control of a directly-coupled induction generator . . . . . . . . . . 38
3.10 Synchronous generator with DC link . . . . . . . . . . . . . . . . . . . 39
3.11 Induction generator with oversynchronous cascade . . . . . . . . . . . . 40
3.12 Doubly-fed induction generator . . . . . . . . . . . . . . . . . . . . . . 40
3.13 Direct-drive variable-speed synchronous generator . . . . . . . . . . . . 41
4.1 Wind turbine power curve and MPP operation . . . . . . . . . . . . . . 44
4.2 Control scheme of MPPT with power prole . . . . . . . . . . . . . . . 45
4.3 Control scheme of MPPT with tip speed ratio . . . . . . . . . . . . . . 45
4.4 Control scheme of MPPT with torque control . . . . . . . . . . . . . . 46
4.5 Pitch angle and angle of attack on a generic airfoil . . . . . . . . . . . . 47
4.6 Turntable tips for stall control . . . . . . . . . . . . . . . . . . . . . . . 47
4.7 Rotor power coecient dependance on the rotor yaw . . . . . . . . . . 48
4.8 Silicon lattice showing thermal ionization . . . . . . . . . . . . . . . . . 49
4.9 A pn junction with the depletion layer shown . . . . . . . . . . . . . . 50
4.10 A forward-biased pn junction . . . . . . . . . . . . . . . . . . . . . . . 51
4.11 i-v characteristic of a pn junction . . . . . . . . . . . . . . . . . . . . . 52
4.12 Scheme of a power diode . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.13 i-v characteristic of a power diode . . . . . . . . . . . . . . . . . . . . . 53
4.14 Masked diusion of a pn junction . . . . . . . . . . . . . . . . . . . . . 54
4.15 Field plates for depletion layer boundary control in a power diode . . . 55
4.16 Guard rings for depletion layer boundary control in a power diode . . . 55
4.17 Cross-section of a BJT . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.18 i-v characteristic of a npn BJT . . . . . . . . . . . . . . . . . . . . . . . 57
4.19 Cross-section of a MOSFET cell . . . . . . . . . . . . . . . . . . . . . . 58
4.20 i-v characteristic of a power MOSFET . . . . . . . . . . . . . . . . . . 59
4.21 Circuit symbol and cross-section of a thyristor . . . . . . . . . . . . . . 60
4.22 i-v characteristic of a thyristor . . . . . . . . . . . . . . . . . . . . . . . 61
4.23 Scheme of a IGBT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.24 i-v characteristic of a IGBT . . . . . . . . . . . . . . . . . . . . . . . . 62
4.25 Circuit schemes of the single-phase bridge rectier . . . . . . . . . . . . 63
4.26 Redrawn circuit of the single-phase bridge rectier . . . . . . . . . . . . 63
4.27 Output waveforms of the single-phase bridge rectiers . . . . . . . . . . 64
4.28 Basic circuit to illustrate current commutation . . . . . . . . . . . . . . 65
4.29 Basic circuit during current commutation . . . . . . . . . . . . . . . . . 65
4.30 Basic circuit after current commutation . . . . . . . . . . . . . . . . . . 65
4.31 Single-phase bridge rectier with inductance . . . . . . . . . . . . . . . 66
4.32 Single-phase bridge rectier with constant DC voltage . . . . . . . . . . 66
LIST OF FIGURES 111
4.33 Idealized circuit for the three-phase full-bridge rectier . . . . . . . . . 67
4.34 Three-phase full-bridge rectier with Ls = 0 . . . . . . . . . . . . . . . 67
4.35 Output voltage waveform of the three-phase full-bridge rectier with
Ls = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.36 Simple purely resistive circuit for the study of thyristor switches . . . . 69
4.37 Circuit scheme of the single-phase thyristor rectier . . . . . . . . . . . 70
4.38 Output voltage waveform the idealized single-phase thyristor rectier . 70
4.39 Output voltage waveform the single-phase thyristor rectier with non-
negligible inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.40 Output voltage waveform in the inverter-mode operation of the single-
phase thyristor rectier . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.41 Circuit of the three-phase thyristor rectier . . . . . . . . . . . . . . . . 72
4.42 Waveforms of the three-phase thyristor rectier . . . . . . . . . . . . . 72
4.43 Pulse-width modulation . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.44 Basic circuit of a buck converter for a purely resistive load . . . . . . . 73
4.45 Circuit and waveforms of a real buck converter . . . . . . . . . . . . . . 74
4.46 Circuit for a boost converter . . . . . . . . . . . . . . . . . . . . . . . . 75
4.47 Continuous conduction mode of operation of a boost converter . . . . . 76
4.48 Circuit of a full-bridge DC-DC converter . . . . . . . . . . . . . . . . . 77
4.49 Generic scheme of a single-phase inverter . . . . . . . . . . . . . . . . . 78
4.50 Waveforms of the output current and voltage of an inverter . . . . . . . 78
4.51 One-leg switch-mode inverter . . . . . . . . . . . . . . . . . . . . . . . 79
4.52 Sinusoidal PWM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.53 Circuit of the single-phase half-bridge inverter . . . . . . . . . . . . . . 81
4.54 Circuit of the single-phase full-bridge inverter . . . . . . . . . . . . . . 81
4.55 Circuit of the tri-phase inverter . . . . . . . . . . . . . . . . . . . . . . 82
5.1 The Alpha prototype of the JMU project . . . . . . . . . . . . . . . . . 85
5.2 Power curves of the tested turbine models for the JMU project . . . . . 86
5.3 Machining of a blade mould . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4 Rig for the blade fatigue test . . . . . . . . . . . . . . . . . . . . . . . . 89
5.5 An image of the collapsing Tacoma Narrows Bridge . . . . . . . . . . . 89
5.6 A Vortex Bladeless turbine . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.7 A Saphonian turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.8 BIWECS on the roof of the Boston Museum of Science . . . . . . . . . 93
5.9 BIWECS on the World Trade Center Building in Bahrain . . . . . . . . 94
5.10 The Aeolian roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.11 Model of a small VAWT for placing on port breakwaters . . . . . . . . 95
112 LIST OF FIGURES
5.12 An aeolic bench . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.1 Power curves for dierent rotor speeds . . . . . . . . . . . . . . . . . . 98
6.2 Energy ow in a wind turbine . . . . . . . . . . . . . . . . . . . . . . . 100
6.3 Graphical representation of the scale eect . . . . . . . . . . . . . . . . 103
6.4 Cost of Danish wind turbines in 2006 . . . . . . . . . . . . . . . . . . . 104
6.5 Power curve of the Skystream 3.7 wind turbine . . . . . . . . . . . . . . 105
List of Tables
1.1 The Beaufort wind speed scale . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Results of simulated coin tosses . . . . . . . . . . . . . . . . . . . . . . 6
5.1 Categories of small-size wind turbines . . . . . . . . . . . . . . . . . . . 83
5.2 Requirements of the JMU project . . . . . . . . . . . . . . . . . . . . . 85
5.3 Results of the JMU project . . . . . . . . . . . . . . . . . . . . . . . . 86
6.1 Cost comparison between small-scale wind and solar PV systems . . . . 106
6.2 Results of the LCOE analysis of wind and solar PV systems . . . . . . 106
113
List of Symbols
α Blade angle of attack, page 46
α Firing angle, page 69
α Roughness coecient, page 4
δ Standard deviation, page 9
m Air mass ow rate, page 15
ηmech−el Mechanical-electrical eciency, page 97
C Cost per unit size, page 103
V Peak of a voltage waveform, page 72
λ Flux linkages, page 28
λ Tip-speed ratio, page 20
R Set of real numbers, page 7
B Magnetic ux vector, page 27
I Electric current vector, page 28
µ Expected value of random variable X, page 8
µ Magnetic permeability, page 27
µ0 Magnetic permeability of free space, page 27
µr Relative magnetic permeability, page 28
Ω Angular velocity of the blade element, page 21
ω Angular speed of the ow stream, page 21
115
116 LIST OF SYMBOLS
ω Rotational speed, page 43
φ Magnetic ux, page 28
ρ Air density, page 15
ρ Charge density, page 50
σ Variance of random variable X, page 8
H Magnetic eld vector, page 27
θ Blade pitch angle, page 46
C Annual cost, page 101
ϕ Wind speed relative frequency, page 98
ϑ Load angle, page 32
A Scale factor of the Weibull model, page 9
A Surface area, page 19
a Axial induction factor, page 17
a Turns ratio of a transformer, page 30
a′ Angular induction factor, page 21
BV Breakdown voltage, page 52
C Specic cost to production, page 100
CD Drag coecient, page 19
Cpr Rotor power coecient, page 97
Cp Power coecient, page 16
CFi Cash ow at year i, page 101
dA Incremental wire cross-section, page 28
D Drag force, page 19
D Duty ratio, page 72
dQ Incremental torque, page 21
LIST OF SYMBOLS 117
dT local incremental thrust, page 21
E [X] Expected value of random variable X, page 8
E Electric eld, page 51
E Energy, page 105
E Induced voltage, page 28
E Lift-to-drag ratio of a blade, page 20
E Wind turbine annual energy yield, page 98
Ek Kinetic energy, page 15
F Electrical force acting on a conductor, page 28
f Frequency, page 31
f Scale factor, page 103
fy Frequency of wind speed y, page 9
H Magnetic eld intensity, page 27
I Electric current, page 27
Id DC-side current in a converter, page 63
Is Reverse saturation current, page 52
K Von Karman constant, page 2
k Form factor of the Weibull model, page 9
L Length of a solenoid, page 28
L Lift force, page 20
l length, page 27
Ls Inductance, page 63
ma Amplitude modulation ratio, page 79
N Number of turns of a solenoid, page 28
n Mechanical rotational speed, page 33
118 LIST OF SYMBOLS
n Synchronous speed of an electrical machine, page 31
ns Synchronous speed, page 33
Neq Number of equivalent hours, page 101
P Mechanical rotor power, page 16
p Number of poles of an electrical machine, page 31
P (A) Probability of event A, page 6
PD Drag power, page 19
PM Mechanical power, page 43
Pel Electrical power, page 98
Pmax Maximum theoretical power extractable from the wind, page 15
Pnom Nominal power, page 101
PT Thrust power, page 16
PW Mechanical power extracted from the wind, page 15
R Resistance, page 63
r Discount rate, page 101
S Rotor swept area, page 15
S Sample space of events, page 6
S Size, page 103
s Slip of an induction machine, page 33
T Thrust, page 16
t Time, page 28
u Blade velocity, page 20
u Commutation interval, page 64
Uz Wind speed at height z, page 3
uz Friction speed, page 2
LIST OF SYMBOLS 119
uz0 Friction speed at reference height Z0, page 2
V Voltage, page 51
V Wind speed, page 15
vr Relative wind velocity, page 19
vs Sinusoidal voltage, page 63
vw Wind velocity, page 19
V∞ Undisturbed wind speed, page 15
V ar(X) Variance of random variable X, page 8
Wr Relative velocity on the blade, page 24
X Random variable, page 7
z Height from the ground, page 2
Z0 Roughness length, page 2
zref Reference height, page 3
List of Acronyms
ABL Atmospheric Boundary Layer
AC Alternated Current
BIWECS Building-Integrated Wind Energy Conversion System
BJT Bipolar Junction Transistor
CAD Computer Assisted Design
CAM Computer Assisted Manufacturing
CAPEX CAPital EXpenditures
CFD Computational Fluid Dynamics
COE Cost Of Energy
CRF Capital Recovery Factor
DC Direct Current
DFIG Doubly-Fed Induction Generator
EMF ElectroMotive Force
EPRI Electric Power Research Institute
FDM Fused Deposition Modelling
HAWT Horizontal-Axis Wind Turbine
IEA International Energy Agency
IEC International Electrotechnical Commission
IGBT Insulated Gate Bipolar Transistor
IRR Internal Rate of Return
121
122 LIST OF ACRONYMS
JMU James Madison University
LCOE Levelised Cost Of Energy
MOSFET Metal-Oxide Semiconductor Field Eect Transistor
MPP Maximum Power Point
MPPT Maximum Power Point Tracking
NACA National Advisory Committee for Aeronautics
NPV Net Present Value
NREL National Renewable Energy Laboratory
OPEX OPerating EXpenditures
PBL Planetary Boundary Layer
PBT Pay-Back Time
PMSG Permanent Magnet Synchronous Generator
PWM Pulse-Width Modulation
SCR Semiconductor-Controlled Rectier
TPC Total Plant Cost
TSR Tip Speed Ratio
VAWT Vertical-Axis Wind Turbine
VSI Voltage-Source Inverter
Bibliography
[1] Saphon Energy website. url: http://www.saphonenergy.com/.
[2] Aly Mousaad Aly. Inuence of Turbulence, Orientation, and Site Conguration
on the Response of Buildings to Extreme Wind. In: The Scientic World Journal
(2014). Ed. by Hindawi Publishing Corporation. url: http://dx.doi.org/10.
1155/2014/178465.
[3] S Carcangiu and A. Montisci. A Building-integrated Eolic System for the Ex-
ploitation of Wind Energy in Urban Areas. In: 2nd IEEE ENERGYCON Con-
ference and Exhibition (2012).
[4] Dixon P. Drumheller et al. Design of a Micro-Wind Turbine for Implementation
in Low Wind Speed Environments. In: IEEE Systems and Information Engi-
neering Design Symposium (2015).
[5] Audrey Garric. Bientôt des éoliennes sans pales? Le Monde. url: http : / /
ecologie.blog.lemonde.fr/2015/05/19/bientot-des-eoliennes-sans-
pales/.
[6] Erich Hau.Wind Turbines - Fundamentals, Technologies, Application, Economics.
2nd edition. Springer, 2009.
[7] Peter A. Irwin. Blu body aerodynamics in wind engineering. In: Journal of
Wind Engineering and Industrial Aerodynamics (2008). Ed. by Elsevier.
[8] Enrico Lambertini. I mini aerogeneratori eolici e le loro potenzialità energetiche:
caratterizzazione dei siti di produzione e studi sperimentali di integrazione ar-
chitettonica. PhD Thesis. Università degli Studi di Udine, 2012. url: http:
//hdl.handle.net/10990/66.
[9] J.F. Manwell, J.G. McGowan, and A.L. Rogers.Wind Energy Explained - Theory,
Design and Application. 2nd edition. Wiley, 2009.
[10] Phil McKenna. Bladeless Wind Turbines May Oer More Form Than Func-
tion. MIT Technology Review. url: https://www.technologyreview.com/s/
537721/bladeless-wind-turbines-may-offer-more-form-than-function/.
123
124 BIBLIOGRAPHY
[11] N. Mohan, T. M. Undeland, and W. P. Robbins. Power Electronics - Converters,
Applications, Design. 2nd edition. John Wiley and Sons, 1995.
[12] Rodolfo Pallabazzer. Sistemi di conversione eolica - La tecnologia delle moderne
macchine del vento. Hoepli, 2011.
[13] Sean Poole and Russel Phillips. Rapid Prototyping of Small Wind Turbine
Blades Using Additive Manufacturing. In: Pattern Recognition Association of
South Africa and Robotics and Mechatronics International Conference (PRASA-
Robmech) (2015).
[14] Sheldon M. Ross. Introductory Statistics. 3rd edition. Elsevier, 2010.
[15] Ziyad Salameh and Chintan Vinod Nandu. Overview of Building Integrated
Wind Energy Conversion Systems. In: Power and Energy Society General Meet-
ing (2010).
[16] Angelo Selis. Energia eolica - Progettazione del sito onshore e oshore. Tecniche
Nuove, 2011.
[17] Keith Sunderland et al. Levelised cost of energy analysis: A comparison of urban
(micro) wind turbines and solar PV systems. In: (2016).
[18] Robin Whitlock. The Power of the Vortex: An Interview with David Suriol of Vor-
tex Bladeless. Renewable Energy Magazine. url: https://www.renewableenergymagazine.
com/interviews/the-power-of-the-vortex-20150407.
[19] David Wood. Small Wind Turbines - Analysis, Design and Application. Springer,
2011.
[20] B. Wu et al. Power Conversion and Control of Wind Energy Systems. Wiley,
2011.