potentiality of large and small scale wind turbines …...2015, according to the global wind energy...

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)


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


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)

https://www.probabilitycourse.com/chapter3/3_1_3_pmf.php

https://www.probabilitycourse.com/chapter3/3_1_3_pmf.php


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.

weibull.com

weibull.com

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;


• 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)

homerenergy.com

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)

commons.wikimedia.org


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


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])


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


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


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.

wikipedia.org


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-

en.wind-turbine-models.com

researchgate.com


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)

wxnaiermic.en.made-in-china.com

wind-turbine-models.com

vawtturbine.wordpress.com

vawtturbine.wordpress.com


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)

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:


• 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


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


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


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


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


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.


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


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.


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:


• 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


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.

https://aviation.stackexchange.com/questions/21035/does-stall-angle-of-attack-in-inverted-flight-change-due-to-the-camber-of-an-asy

https://aviation.stackexchange.com/questions/21035/does-stall-angle-of-attack-in-inverted-flight-change-due-to-the-camber-of-an-asy


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.


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


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])


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


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


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.


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,


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.


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.


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


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])


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.


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.


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


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]).


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


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


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


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.


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-


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.


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)


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.


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.


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


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;


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])


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.


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


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


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


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


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


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.


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.


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])


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.


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


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


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


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

http://www.saphonenergy.com/

http://dx.doi.org/10.1155/2014/178465

http://dx.doi.org/10.1155/2014/178465

http://ecologie.blog.lemonde.fr/2015/05/19/bientot-des-eoliennes-sans-pales/



http://hdl.handle.net/10990/66

http://hdl.handle.net/10990/66

https://www.technologyreview.com/s/537721/bladeless-wind-turbines-may-offer-more-form-than-function/

https://www.technologyreview.com/s/537721/bladeless-wind-turbines-may-offer-more-form-than-function/

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.

https://www.renewableenergymagazine.com/interviews/the-power-of-the-vortex-20150407

https://www.renewableenergymagazine.com/interviews/the-power-of-the-vortex-20150407

potentiality of large and small scale wind turbines …...2015, according to the global wind energy...

Documents