EXAMENSARBETE INOM ELEKTROTEKNIK,

AVANCERAD NIVÅ, 30 HP
STOCKHOLM, SVERIGE 2017

Construction of an Active Rectifier

for a Transverse-Flux Wave Power
Generator

OLOF BRANDT LUNDQVIST

KTH
SKOLAN FÖR ELEKTRO- OCH SYSTEMTEKNIK
1 Sammanfattning
Vågkraft är en energikälla som skulle kunna göra en avgörande skillnad i om-
ställningen mot en hållbar energisektor. Tillväxten för vågkraft har dock inte
varit lika snabb som tillväxten för andra förnybara energislag, såsom vindkraft
och solkraft. Vissa tekniska hinder kvarstår innan ett stort genombrott för våg-
kraft kan bli möjligt. Ett hinder fram tills nu har varit de låga spänningarna och
de resulterande höga effektförlusterna i många vågkraftverk. En ny typ av våg-
kraftsgenerator, som har tagits fram av Anders Hagnestål vid KTH i Stockholm,
avser att lösa dessa problem. I det här examensarbetet behandlas det effekte-
lektroniska omvandlingssystemet för Anders Hagneståls generator. Det beskriver
planerings- och konstruktionsprocessen för en enfasig AC/DC-omvandlare, som
så småningom skall bli en del av det större omvandlingssystemet för generatorn.
Ett kontrollsystem för omvandlaren, baserat på hystereskontroll för strömmen,
planeras och sätts ihop. Den färdiga enfasomvandlaren visar goda resultat under
drift som växelriktare. Dock kvarstår visst konstruktionsarbete och viss kalibre-
ring av det digitala kontrollsystemet innan omvandlaren kan användas för sin
uppgift i effektomvandlingen hos vågkraftverket.

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2 Abstract
Wave power is an energy source which could make a decisive difference in the
transition towards a more sustainable energy sector. The growth of wave power
production has however not been as rapid as the growth in other renewable
energy fields, such as wind power and solar power. Some technical obstacles
remain before a major breakthrough for wave power can be expected. One
obstacle so far has been the low voltages and the resulting high power losses
in many wave power plants. A new type of wave power generator, which has
been invented by Anders Hagnestål at KTH in Stockholm, aims to solve these
problems. This master’s thesis deals with the power electronic converter system
for Anders Hagnestål’s generator. It describes the planning and construction
process for a single-phase AC/DC converter, which will eventually be a part
of the larger converter system for the generator. A control system based on
hysteresis current control is planned and assembled. The finished single-phase
converter shows agreeable results working as an inverter, generating a distinctly
sinusoidal AC voltage. However, some additional construction and calibration
in the digital control system remain, before the converter can be used in the
power conversion for a wave power plant.

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3 Acknowledgements
To my parents and to my brother I want to express my appreciation for their
love and support throughout my life.

To Anders Hagnestål for letting me be part of the development in his inno-

vative research project, which is contributing to the technical development and
future prospects of wave power.

To Aliro Cofre Osses for his good contribution to the project work and for
being a good friend.

To Nicholas, Matthijs, Rudi, Keijo, Panos, Dieter, Stefanie and the other
friendly people in the electrical laboratory for the good company and the help-
ful assistance during the practical work with the converter construction.

To captain Gregor, first mate Willy Wonka and the other sailors on the At-
lantic Cartier cargo ship who meet the power in the waves everyday.

To all the people working towards an expansion of renewable energy. It is

certainly an exciting time to enter the work life within electric power engineering,
considering the important difference that clean electrical energy can make in
building a sustainable future. It is my sincere wish to be a part in the work
towards this goal.

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4 Table of contents
1 Sammanfattning 2

2 Abstract 3

3 Acknowledgements 4

4 Table of contents 5

5 Nomenclature 10

I Introduction 11
6 Background 11

7 Summary of the technical work 12

8 Goals and scope limitations 12

9 Method 13

II Literature review 14
10 Technical theory review 14
10.1 Electrical machines . . . . . . . . . . . . . . . . . . . . . . . . . . 14
10.1.1 Electric generators . . . . . . . . . . . . . . . . . . . . . . 14
10.1.2 Rotating generators and linear generators . . . . . . . . . 14
10.1.2.1 Rotating generators . . . . . . . . . . . . . . . . 15
10.1.2.2 Linear generators . . . . . . . . . . . . . . . . . 15
10.1.3 Electrical machine types by magnetic flux direction . . . . 15
10.1.3.1 Radial-flux machines . . . . . . . . . . . . . . . 15
10.1.3.2 Axial-flux machines . . . . . . . . . . . . . . . . 15
10.1.3.3 Transverse-flux machines . . . . . . . . . . . . . 15
10.2 Power electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
10.3 Power semiconductors . . . . . . . . . . . . . . . . . . . . . . . . 16
10.3.1 Power diodes . . . . . . . . . . . . . . . . . . . . . . . . . 16
10.3.2 Power transistors . . . . . . . . . . . . . . . . . . . . . . . 16
10.3.2.1 Power MOSFETs . . . . . . . . . . . . . . . . . 16
10.3.2.2 Insulated-gate bipolar transistors . . . . . . . . . 17
10.3.2.3 Silicon carbide power MOSFETs . . . . . . . . . 17
10.3.2.4 Comparison between SiC MOSFETs and Si IGBTs 17
10.4 Switch-mode converters . . . . . . . . . . . . . . . . . . . . . . . 17
10.4.1 Pulse-width modulation . . . . . . . . . . . . . . . . . . . 17
10.4.2 DC-DC converters . . . . . . . . . . . . . . . . . . . . . . 18
10.4.3 DC/AC converters and AC/DC converters . . . . . . . . . 18
10.4.4 Single-phase voltage-source converters . . . . . . . . . . . 18
10.4.5 Active rectifiers . . . . . . . . . . . . . . . . . . . . . . . . 18
10.4.6 Three-phase voltage-source converters . . . . . . . . . . . 19

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 10.4.7 Total harmonic distortion . . . . . . . . . . . . . . . . . . 19
10.5 PWM control algorithms for voltage-source converters . . . . . . 20
10.5.1 Control of single-phase voltage-source converters . . . . . 20
10.5.1.1 Sinusoidal pulse-width modulation . . . . . . . . 20
10.5.1.2 Hysteresis current control . . . . . . . . . . . . . 21
10.5.2 Bipolar and unipolar PWM . . . . . . . . . . . . . . . . . 21
10.5.2.1 Bipolar voltage switching mode . . . . . . . . . 22
10.5.2.2 Unipolar voltage switching mode . . . . . . . . . 23
10.5.3 Frequency modulation index . . . . . . . . . . . . . . . . 23
10.5.4 Amplitude modulation index . . . . . . . . . . . . . . . . 24
10.6 Microcontroller applications for control of voltage-source converters 24
10.7 MOSFET gate driver circuits . . . . . . . . . . . . . . . . . . . . 24
10.8 Snubber circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
10.9 The DC-link and its function . . . . . . . . . . . . . . . . . . . . 25
10.9.1 Polarity of electrolytic capacitors . . . . . . . . . . . . . . 25
10.9.2 Bleeder resistors . . . . . . . . . . . . . . . . . . . . . . . 25
10.10Back-to-back coupling of voltage-source converters . . . . . . . . 25
10.11Level shifters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

11 Electric power generation from sea waves 26

11.1 The power in the waves . . . . . . . . . . . . . . . . . . . . . . . 26
11.2 Challenges in the design of wave power generators . . . . . . . . 27
11.3 Current status of wave power generation in the world . . . . . . . 27
11.4 Future potential for the field of wave power . . . . . . . . . . . . 28

12 Characteristics of the wave power generator of Anders Hagnestål 28

12.1 Generator characteristics . . . . . . . . . . . . . . . . . . . . . . . 28
12.2 Reducing the resistive losses . . . . . . . . . . . . . . . . . . . . . 29
12.3 Active power factor correction . . . . . . . . . . . . . . . . . . . . 30
12.4 Power level in the generator . . . . . . . . . . . . . . . . . . . . . 30
12.5 Cogging in the generator . . . . . . . . . . . . . . . . . . . . . . . 30

III Planning 31
13 Dimensioning the generator’s power electronic converter sys-
tem 31
13.1 Overview of the power electronic converter system . . . . . . . . 31
13.2 AC/DC-converter characteristics . . . . . . . . . . . . . . . . . . 31
13.2.1 Active power factor correction . . . . . . . . . . . . . . . 32
13.3 DC/AC-converter characteristics . . . . . . . . . . . . . . . . . . 32
13.4 BeagleBone Black microcontroller . . . . . . . . . . . . . . . . . . 32
13.5 Sizing of the converter’s electrical components . . . . . . . . . . . 33
13.5.1 Selection of power transistors . . . . . . . . . . . . . . . . 33
13.5.2 Selection of the converter’s voltage levels . . . . . . . . . 33
13.5.2.1 DC-link voltage level . . . . . . . . . . . . . . . 34
13.5.2.2 Generator side voltage level . . . . . . . . . . . . 34
13.5.3 Selection of the converter’s current levels . . . . . . . . . 34
13.5.4 Maximum power flow through the power converter . . . . 34
13.5.5 Selection of MOSFET drivers . . . . . . . . . . . . . . . . 34

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 13.5.6 PWM switching frequency . . . . . . . . . . . . . . . . . . 35
13.5.7 Sizing of a filter circuit on the generator side . . . . . . . 35
13.5.8 Sizing of the snubber circuits . . . . . . . . . . . . . . . . 35
13.5.9 Sizing of the DC-link filter capacitor . . . . . . . . . . . . 36
13.6 Electrical components for the initial laboratory test setup . . . . 36
13.6.1 DC-link capacitor for the initial lab testing . . . . . . . . 36
13.6.2 Bleeder resistor for the initial lab testing . . . . . . . . . . 37
13.6.3 Snubber circuits for the initial lab testing . . . . . . . . . 37
13.6.4 Level shifters . . . . . . . . . . . . . . . . . . . . . . . . . 38
13.7 Electrical isolation paper . . . . . . . . . . . . . . . . . . . . . . . 39
13.8 Heat sinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

14 Planning for the control system of the power electronic con-

verter 39
14.1 Beaglebone Black and the choice of the Python programming
language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
14.2 Development of a SPWM control Python code . . . . . . . . . . 40
14.3 Development of a hysteresis control Python code . . . . . . . . . 40
14.3.1 Flow chart for the bipolar hysteresis control code . . . . . 41
14.3.2 Flow chart for the unipolar hysteresis control code . . . . 41
14.4 Hysteresis control simulations for different sampling frequencies . 43
14.4.1 Switching frequencies for different sampling frequencies . 43
14.4.2 Current deviation from the reference current for different
sampling frequencies . . . . . . . . . . . . . . . . . . . . . 43
14.4.3 Conclusions about the necessary sampling frequency for
unipolar PWM hysteresis control . . . . . . . . . . . . . . 44

15 Planning for the construction of the active rectifier 44

15.1 Laboratory setup with machines and two converters . . . . . . . 45
15.2 Two modules instead of four during the initial testing phase . . . 45
15.3 Circuit diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
15.3.1 Simplified block diagram for the final laboratory setup
with two machines . . . . . . . . . . . . . . . . . . . . . . 46
15.3.2 Simplified circuit diagram for one single-phase converter
with four phase-legs . . . . . . . . . . . . . . . . . . . . . 46
15.3.3 Simplified circuit diagram for one single-phase converters
with two phase-legs . . . . . . . . . . . . . . . . . . . . . 47
15.3.4 Detailed circuit diagram for one single-phase converter
with two phase-legs . . . . . . . . . . . . . . . . . . . . . 48
15.3.5 Circuit diagram for the connection of the current sensor . 48
15.4 Practical design aspects to take into account . . . . . . . . . . . 50
15.4.1 Copper plate dimensions . . . . . . . . . . . . . . . . . . . 50
15.4.2 Elevation of the copper plates above the DC-link capacitor 50
15.4.3 Mechanical and electrical connection of the power modules 50
15.4.4 Placement of electrical cables . . . . . . . . . . . . . . . . 50
15.4.5 Attachment of the heat sinks . . . . . . . . . . . . . . . . 51
15.5 Safety aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
15.5.1 Position of the positive voltage DC-link copper plate . . . 51
15.5.2 Electrolytic DC-link capacitor polarity . . . . . . . . . . . 51
15.5.3 Limiting the charging current for the DC-link capacitor . 51

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 15.5.4 Protection against an eventual capacitor explosion . . . . 52
15.6 CAD model for the final design . . . . . . . . . . . . . . . . . . . 52
15.6.1 Plastic boxes for containing the snubber circuits . . . . . 52
15.7 CAD model for the laboratory setup of the converter . . . . . . . 54

IV Practical work 55
16 Construction of the active rectifier 55
16.1 Construction of the DC-link . . . . . . . . . . . . . . . . . . . . . 55
16.2 Construction of a wooden suspension for the copper plates . . . . 56
16.3 Preparation of the power modules . . . . . . . . . . . . . . . . . 56
16.4 DC-link capacitor connection . . . . . . . . . . . . . . . . . . . . 58
16.5 Connecting the power modules, snubber capacitors and high-
voltage cable connections . . . . . . . . . . . . . . . . . . . . . . 58
16.5.1 Choice of cable colors for marking out the different nodes 58
16.6 Connecting the PWM control system . . . . . . . . . . . . . . . . 59
16.6.1 Beaglebone Black pins . . . . . . . . . . . . . . . . . . . . 59
16.6.2 Conversion of the PWM signal voltage levels . . . . . . . 59
16.6.3 MOSFET driver input signals . . . . . . . . . . . . . . . . 59
16.6.4 MOSFET driver output signals . . . . . . . . . . . . . . . 60
16.7 Supply voltages for the control system . . . . . . . . . . . . . . . 61
16.8 Connecting the current sensor . . . . . . . . . . . . . . . . . . . . 61
16.8.1 Amplifying the sensor’s measurement signal . . . . . . . . 61

17 How to use the Beaglebone Black in Microsoft Windows 62

17.1 Logging in to Putty . . . . . . . . . . . . . . . . . . . . . . . . . 62
17.2 Calibration of the current sensor . . . . . . . . . . . . . . . . . . 63

18 Electrical experiments 64
18.1 Word of caution about the capacitor charging current . . . . . . 64
18.2 Inverter mode, unipolar sinusoidal PWM . . . . . . . . . . . . . . 64
18.2.1 Inverter, no load . . . . . . . . . . . . . . . . . . . . . . . 65
18.2.2 Inverter, resistive load of 24 Ohm . . . . . . . . . . . . . . 65
18.3 Rectifier mode, hysteresis control with unipolar PWM . . . . . . 66
18.3.1 Word of caution about the reference current . . . . . . . . 66
18.3.2 Initial evaluation of the microcontroller’s sampling fre-
quency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
18.3.3 Active rectifier with active power factor correction . . . . 67

V Analysis 69
19 Experimental results 69
19.1 Inverter mode, unipolar sinusoidal PWM . . . . . . . . . . . . . . 69
19.1.1 SPWM, gate pulses . . . . . . . . . . . . . . . . . . . . . 69
19.1.2 Inverter, no load . . . . . . . . . . . . . . . . . . . . . . . 69
19.1.2.1 Frequency analysis . . . . . . . . . . . . . . . . . 70
19.1.2.2 Switching frequency . . . . . . . . . . . . . . . . 70
19.1.3 Inverter, 24 Ohm load . . . . . . . . . . . . . . . . . . . . 71

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 19.2 Measurement of the Beaglebone Black’s sampling frequency . . . 71
19.3 Rectifier mode, hysteresis control with unipolar PWM . . . . . . 72

20 Discussion 72

21 Future work 74
21.1 Increase the microcontroller’s sampling frequency . . . . . . . . . 74
21.2 Implement hysteresis control . . . . . . . . . . . . . . . . . . . . 74
21.3 Connection of two more power modules for the single-phase VSC 75
21.4 Holes for the MOSFET drivers in the copper plates . . . . . . . . 75
21.5 Acquisition of film capacitors for the DC-link . . . . . . . . . . . 75
21.6 Holes in the plates for more DC-link capacitors . . . . . . . . . . 75
21.7 Connection of the snubber capacitors beneath the copper plates . 75
21.8 Acquire better understanding of the MOSFET driver signal pins 76
21.9 Connect all power modules and set up their control systems . . . 76
21.10Increase the voltage . . . . . . . . . . . . . . . . . . . . . . . . . 76

22 Conclusion 76

VI References 77

VII Appendix 80
22.1 Total electrical energy consumption in the Nordic countries . . . 80
22.2 Python simulation results . . . . . . . . . . . . . . . . . . . . . . 80
22.2.1 Unipolar SPWM simulation results . . . . . . . . . . . . . 80
22.2.1.1 Unipolar SPWM with a high switching frequency,
ma=0.6 and mf=25 . . . . . . . . . . . . . . . . 80
22.2.1.2 Unipolar SPWM low Hz switching frequency,
ma=0.6 and mf=25 . . . . . . . . . . . . . . . . 81
22.2.1.3 Unipolar SPWM 2800 Hz switching frequency,
ma=1 and mf=12.5 . . . . . . . . . . . . . . . . 81
22.2.2 Hysteresis control, bipolar switching, simulation results . 82
22.2.2.1 1 kHz sampling frequency . . . . . . . . . . . . . 82
22.2.2.2 4 kHz sampling frequency . . . . . . . . . . . . . 83
22.2.2.3 10 kHz sampling frequency . . . . . . . . . . . . 84
22.2.2.4 50 kHz sampling frequency . . . . . . . . . . . . 85
22.2.3 Hysteresis control, unipolar switching . . . . . . . . . . . 86
22.2.3.1 1 kHz sampling frequency . . . . . . . . . . . . . 86
22.2.3.2 4 kHz sampling frequency . . . . . . . . . . . . . 87
22.2.3.3 10 kHz sampling frequency . . . . . . . . . . . . 88
22.2.3.4 50 kHz sampling frequency . . . . . . . . . . . . 89
22.3 Python codes for the Beaglebone Black Microcontroller . . . . . 90
22.3.1 Unipolar SPWM . . . . . . . . . . . . . . . . . . . . . . . 90
22.3.2 Hysteresis control . . . . . . . . . . . . . . . . . . . . . . . 92

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5 Nomenclature
Symbol Unit Description
ε V EMF induced voltage
N - Number of windings
Ψ Wb Flux linkage
Φ Wb Magnetic flux
h m Peak-to-peak amplitude of a sea wave
rad
ωwave s Angular frequency of a sea wave
fwave Hz Frequency of a sea wave
I A Electric current
V V Voltage
P W Active electric power
Q VAr Reactive electric power
R Ω Resistance
ρ Ωm Resistivity
φ rad Current phase angle
Va V Phase voltage
LS H Stator winding inductance
γ - Switching state of a voltage-source converter
VO V Output voltage from a switch-mode converter
VDC V DC-link voltage
m
cg s Group velocity of sea waves
kg
ρwater m3 Density of water
m
g s2 Standard acceleration due to gravity
Hm0 m Significant wave height of sea wave
f0 Hz Fundamental frequency component of voltage signal
fk Hz Frequency component of order k for a voltage signal

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Part I
Introduction
6 Background
Wave power has good possibilities of becoming a significant energy source in the
future. The water masses in the ocean transport enormous amounts of energy.
Imagining a scenario where this energy could be harvested effectively, it may
seem strange that it has not yet been done to a larger extent. It is certainly
necessary to look for new sustainable energy sources, which do not rely on de-
pletable resources and do not contribute to climate change significantly. The sea
along the coasts of the Nordic countries, for example, have been estimated to
contain energy twice as high as the annual electricity consumption in Sweden,
Norway, Denmark and Finland together. Possibly we are just seeing the start of
the rise of wave power. The wind and solar energy sectors have certainly grown
tremendously during only the last ten years: 734 % for the globally installed
wind power capacity and an increase of 4451 % in the globally installed solar
PV power (2005-2015) [33].

Before wave power can become the fruitful energy source that it seemingly
could be, quite a few technical challenges have to be tackled. The challenge that
is the background for this master’s thesis is the low amplitudes in the voltages
generated in today’s wave power generators. These low voltages are caused by
the slow motion of the waves in the ocean. In order to extract high power at
a low voltage level, it is necessary to work with high electrical currents, which
typically causes high power losses. This is a problem which may have a solution,
which will be presented in this master’s thesis.

This master’s thesis describes the planning and the construction of a power
electronic converter system. The project was carried out as a group work to-
gether with Aliro Cofre Osses at the Royal Institute of Technology (KTH) in
Stockholm. The converter shall later be used in laboratory work, testing a new
wave power generator, which has been designed by Dr. Anders Hagnestål, a
researcher in electric power at KTH.

This thesis is divided into a technical theory part, describing the background
theory about the generator and the converter, and a practical part which de-
scribes the construction process of the converter. Finally, results are presented
from the electrical experiments performed on the constructed converter in the
laboratory, and conclusions are drawn about the results.

The proposed rectifier design relies on a previous master’s thesis, written by

Gustaf Falk Olson in 2016 and supervised by Anders Hagnestål. In the thesis
of Falk Olson, called Power Electronic Stages for a TFPMSM in Wave Power
Applications, the rectifier was dimensioned, hardware components were chosen
and a control system was planned.

Figure 1 shows an artistic depiction of the roaring energy in the ocean by

11
the 19th century Japanese painter Katsuhika Hokusai.

Figure 1: 19th century depiction of ocean waves by Katsuhika Hokusai.

7 Summary of the technical work

The wave power generator of Anders Hagnestål is a linear electric generator,
which can be attached to a buoy, oscillating together with the waves in the
ocean. The power electronic converter is intended to convert the AC power
from the generator into DC power and then back to AC power again. The
converter built during this master’s thesis deals with the first conversion stage -
from AC to DC. It is called an active rectifier. This type of rectifier can control
the wave shape and phase of the current in the generator. Thanks to the active
rectifier, the reactive power in the generator can be reduced by forcing the
current’s phase angle to be zero degrees and thereby forcing the power factor to
one.

8 Goals and scope limitations

The goal of this master’s thesis was to build an active rectifier. Eventually,
a laboratory setup will be used, with two converters distributing electrical en-
ergy to both a generator and a motor. Both these electrical machines have
three phases, making the total number of phases six for the converter system.
Therefore six identical single-phase voltage-source converter will eventually be
built for this system. Due to the limited amount of time available for a mas-
ter’s thesis, however, the task for this thesis is to build one of the single-phase
voltage-source converters. Even though the whole converter system will not be
finished during the work with this thesis, the final converter will be planned for

12
and partly prepared. The size of the DC-link copper plates will be dimensioned
based on the future topology with six phases and the CAD model is made so
that it illustrates the final converter. The remaining necessary work steps are
presented in the Future work section in the end.

9 Method
The following steps were followed in the process of planning and building the
single-phase voltage-source converter:
1. Acquirement of information about how the generator works and the special
characteristics of the power electronic converter system.

2. Review on the already dimensioned electrical parameters for the power

electronic system, done by Gustaf Falk Olson in 2016.
3. Review on relevant technical theory about the components and algorithms
to be used for implementing the power electronic system.
4. Development of codes and performing of software experiments with the
algorithms sinusoidal pulse-width modulation and hysteresis current con-
trol.
5. Design of a CAD model for the physical converter system to be built,
making sure that the chosen components are compatible with each other
and fit together geometrically.

6. Ordering of all necessary components for the construction.

7. Construction of the DC-link and connection of all electrical components.
8. Performing of electrical experiments and verification of the system’s proper
function.

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Part II
Literature review
10 Technical theory review
This section intends to give a review of the technical background theory neces-
sary for building the converter. The theory mainly deals with electrical machines
and power electronics.

10.1 Electrical machines

Electrical machines are machines which convert mechanical energy to electrical
energy, or vice versa. Examples of electrical machines are electric motors and
generators, but it is often convenient to use the term electrical machine instead
of electric motor or generator. This is because an electric motor can be used as
an electric generator and a generator can be used as a motor [14, p. 183].

10.1.1 Electric generators

Electric generators are electrical machines used for producing electric power.
Generators typically consist of a stationary part, called the stator, and a mov-
ing part termed rotor or actuator. If the moving part is rotating it is called
a rotor. If it is instead moving linearly it is called an actuator [14, p. 1] or a
translator.

The stator is made up of electrical conductors wound as coils, typically

around laminated pieces of a magnetic material, such as electrical steel [14,
p. 26]. The moving part of the generator either has permanent magnets creat-
ing a magnetic field, or windings supplied by electrical currents. Voltages are
induced in the stator coils as the rotor is moving, according to Faraday’s law
of electromagnetic induction in Eq 1. If a load is connected to the stator coils,
current will flow through the load. The magnitude of the electric power pro-
duced is determined by the magnitude of the mechanical torque or force applied
to the rotor or actuator.

Typically electric generators are three-phase generators, which means that

three-phase power is produced. Three-phase power has the benefit of being con-
stant, as opposed to single-phase power which is pulsating in time [36, p. 13].

dΨ dΦ
ε=− = −N (1)
dt dt

10.1.2 Rotating generators and linear generators

Two different types of electric generators are rotating generators and linear
generators. They are characterized by the type of motion which generates the
electric power. These generators will now be described briefly.

14
10.1.2.1 Rotating generators
Rotating electric generators use a stator and a rotor. The rotor is rotating
inside the stator. Examples of rotating generators are squirrel-cage induction
generators and permanent magnet synchronous generators [14].

10.1.2.2 Linear generators

A linear generator produces electric power from a linear motion. A translator is
moving linearly inside the stator. This induces voltages in the stator windings
[14, p. 234].

10.1.3 Electrical machine types by magnetic flux direction

If electrical machines are categorized based on the direction of their magnetic
flux, there are three types of electrical machines: radial-, axial- and transverse-
flux machines. A short review of these types will now be given.

10.1.3.1 Radial-flux machines

In a radial-flux machine, the magnetic flux has a direction which is radial out the
from the rotor axis. In cylindrical coordinates it can be expressed as the direc-
tion of the unit vector ~erc . Examples of such electrical machines are squirrel-cage
induction machines and radial-flux brushless DC machines.

10.1.3.2 Axial-flux machines

In an axial-flux machine, the magnetic flux has a direction which is axial, i.e.
parallel to the rotor axis [27]. In cylindrical coordinates this is along the unit
vector ~ez .

10.1.3.3 Transverse-flux machines

The magnetic flux in a transverse-flux machine has a direction which is clock-
wise around the machine’s axis, along the unit vector ~eφ if expressed in cylin-
drical coordinates [41]. The transverse-flux generator type is the one to be used
in the wave generator of Anders Hagnestål. This will be explained further in
Section 12.

10.2 Power electronics

Power electronic converters are used for conversion of electric power from one
form to another. For example an inverter converts power from DC to AC. A
rectifier converts power from AC to DC. There are also DC-DC converters,
converting a DC voltage to a DC voltage with different amplitude [24, p. 10].
An important part of power electronic converters are power semiconductors,
which will be described in the sections below.

15
10.3 Power semiconductors
Semiconductors are electronic components with an ability to be either current-
conducting or not conducting, depending on the situation [22]. Examples of
semiconductors for high electric power are power diodes and power transistors.
These components will be described briefly below.

10.3.1 Power diodes

A diode is a semiconductor which allows currents to flow in only one direction.
Current will flow through a diode if the voltage at its anode is higher than the
voltage at its cathode. This state is termed that the diode is forward-biased. If
the voltage at the anode is lower than the cathode voltage, the diode prevents
current from flowing. This current blocking state of the diode is called that the
diode is reverse-biased [9].

A power diode works like a standard diode in its function, but is character-
ized by its high power ratings. That means it can handle high voltages and high
currents [24, p. 529].

10.3.2 Power transistors

A transistor is a component which can also be either current conducting or non-
conducting, similar to a diode. While the diode has two terminals, however, a
transistor generally has three terminals; two of them giving path for currents to
flow and one acting as a control terminal which decides how much current should
be let through. Two common categories of transistors are bipolar junction tran-
sistors (BJTs) and field-effect transistors (FETs). The BJT has terminals called
base, collector and emitter, whereas a FET has terminals called gate, drain and
source [38].

Transistors are semiconductors with a high importance in contemporary elec-

tronics. Personal computers rely on billions of microscopic transistors, set up to
communicate in binary code. Transistors are also important in analogue elec-
tronics, e.g. in the field of amplifier design [44]. There are also power transistors
used in power electronics. These transistors have the ability to withstand sev-
eral hundreds of volts and amperes [32]. Power transistors will be of importance
during the practical part of this master’s thesis, i.e. the construction of an ac-
tive converter. Therefore topology and function of transistors will now be given
a brief presentation.

10.3.2.1 Power MOSFETs

A metal-oxide-semiconductor field-effect transistor, or MOSFET, is a type of
field-effect transistor. By manipulation of the electric field inside the transistor,
the behaviour of the MOSFET can be controlled [24, p. 578].

A power MOSFET is a MOSFET with high power ratings. A typical ap-

plication of power MOSFETs in power electronics is using them as switches in

16
switch-mode converters. It is possible to control whether a MOSFET is con-
ducting a current or not by applying a voltage to its gate terminal. If a gate
voltage of sufficient amplitude is applied, current flows from the drain terminal
to the source terminal. With no gate voltage applied, the transistor acts like an
open circuit and no current flows through the transistor [38].

10.3.2.2 Insulated-gate bipolar transistors

An insulated gate bipolar transistor (IGBT) is a type of transistor which com-
bines the features of a bipolar junction transistor and the features of a field-effect
transistor [24, p. 626]. Similar to power MOSFETs, IGBTs are often used as
switches in power electronic applications. The IGBT has traditionally been the
switch transistor of choice for power conversion [34].

10.3.2.3 Silicon carbide power MOSFETs

MOSFETs and IGBTs have traditionally both been made using substrates of
silicon (Si). Recently however, it has shown very promising to use silicon carbide
(SiC) substrates instead of silicon substrates. Silicon carbide is a compound
of silicon and carbon. SiC semiconductors have shown to have higher power
capabilities, much lower power losses, as well as better thermal properties [4].

10.3.2.4 Comparison between SiC MOSFETs and Si IGBTs

When SiC MOSFETs have been compared with Si IGBTs it has been discov-
ered that it is favourable to use SiC MOSFETs operating at high switching
frequencies [34]. MOSFETs in general have good performance at high switch-
ing frequencies. A high switching frequency can be beneficial, as smaller filter
circuits can be used for filtering out switching harmonics. SiC MOSFETs can
handle even higher power levels than Si MOSFETs, making SiC MOSFETs an
excellent choice as power transistors. The topologies of different power convert-
ers and switching algorithms will be explained in the theory sections 10.4 and
10.5 below.

10.4 Switch-mode converters

Switch-mode converters are power electronic converters relying on the use of
pulse-width modulation control [13]. There are different types of switch-mode
converters, such as DC-DC converters and DC-AC converters. These types of
converters will further be presented in this theory section.

10.4.1 Pulse-width modulation

Pulse-width modulation (PWM) is a common way of controlling power elec-
tronic converters. When PWM is used, a control voltage is fed to the gates
or bases of power transistors. This control voltage has a square waveform of
a certain frequency. A transistor’s drain-source voltage can be controlled by
sending voltage pulses to its gate terminal. The duty cycle for a PWM signal

17
is the percentage of the switching period when the control voltage is high. [24,
p. 162].

10.4.2 DC-DC converters

DC-DC converters are used for changing the amplitude of a DC voltage to an-
other DC amplitude. PWM is used for adjusting the average value of the output
voltage from the DC-DC converter. The type of DC-DC converter which lowers
the DC voltage amplitude is called a buck converter or step-down converter.
Other examples of DC-DC converters are boost converters, buck-boost convert-
ers, SEPIC converters and Cuk- converters [24].

10.4.3 DC/AC converters and AC/DC converters

DC/AC converters, also called inverters, are used for converting DC power to
AC. AC/DC converters, or rectifiers, convert from AC to DC. Some rectifiers,
such as diode rectifiers and thyristor rectifiers, can only be used as rectifiers. The
so-called voltage-source converter, however, can be used both as an inverter and
as a rectifier. Voltage-source converters exist both for single- and three-phase
systems [24, p. 243]. A voltage-source converter will be constructed in this
master’s thesis. The theory behind it will now be described further.

10.4.4 Single-phase voltage-source converters

A single-phase voltage-source converter (VSC) is a type of switch-mode con-
verter. When it runs as a rectifier it can convert single-phase AC power to
DC power. It can also be operated as an inverter for DC-AC conversion. This
inverter operation mode will first be described.

In the simplest application, single-phase VSCs are made up of two converter

phase-legs; each phase-leg consisting of two switching power transistors, for ex-
ample MOSFETs or IGBTs. A PWM control voltage is fed to each transistor’s
gate or base terminal, yielding the transistor to turn on or off.

The single-phase VSC is known by many names. It is also called an H-

bridge - referring to that the circuit diagram of the single-phase VSC resembles
the shape of the letter H [18]. The circuit diagram of a VSC can be seen in Fig 2.

10.4.5 Active rectifiers

Single-phase VSCs can be operated as rectifiers, transforming power from AC
to DC. When a VSC is used in the rectification mode it can be called an active
rectifier [21]. It is called active because it uses power transistors. The rectifier’s
output voltage level can therefore be controlled using PWM. This stands in
contrast to diode rectifiers, or line-commutated rectifiers, which lack this con-
trol possibility [8]. When the single-phase VSC operates as a rectifier, it can
be controlled in the same way as during inverter mode: using the bipolar or
unipolar voltage switching. However, the phase angle of the current’s active
(real) component is phase shifted 180 electrical degrees, compared with inverter

18
 Figure 2: Single-phase voltage-source converter [35].

mode. This reverses the flow of electrical energy through the converter, so that
power is converted from AC to DC [24, p. 243].

10.4.6 Three-phase voltage-source converters

A three-phase voltage-source converter (VSC) is another type of switch-mode
converter. It can be used as an inverter or rectifier for circuits with three phases
on the AC side. In the simplest type of implementation, three-phase VSCs are
made up of three phase-legs, with two power transistors per phase-leg. A circuit
diagram for this type of three-phase VSC can be seen in Fig 3.

Rectifier operation mode can be achieved by control of the currents’ phase

angles. If each of the three currents is shifted 180 degrees, it results in a re-
versed flow of electrical energy so that the three-phase VSC acts as a rectifier
[24, p. 244].

10.4.7 Total harmonic distortion

Total harmonic distortion (THD) is a concept in electrical engineering, used for
describing the purity of a signal. It is desired to have signals with low THD,
because a high THD indicates a distorted signal. One type of THD calculation
method is weighted total harmonic distortion T HDW . The benefit of weighted
THD is that it puts less importance on high frequency harmonics. This is
reasonable, since these harmonics are easier to filter out. The expression for
T HDW is given in Eq 2 below [35, p. 60], where V1 signifies the voltage signal’s
fundamental component and Vk the signal’s higher harmonics.

v
u P∞ V 2
k,RM S 2
t k=1 ( k ) − V1,RM S
u
T HDW = 2 (2)
V1,RM S

19
 Figure 3: Topology of a three-phase voltage-source converter [35].

10.5 PWM control algorithms for voltage-source

converters
In this section some different PWM control algorithms will be presented, which
can be used for controlling voltage-source converters - both single-phase and
three-phase converters.

10.5.1 Control of single-phase voltage-source converters

A PWM control system is necessary for making the single-phase VSC obtain the
right output voltage. There are several PWM algorithms for this, generating
different types of gate voltage signals for the MOSFETs in the converter. A
more detailed description on the SPWM and hysteresis control algorithms will
be presented in the next section.

10.5.1.1 Sinusoidal pulse-width modulation

A common technique for generating sinusoidal voltages from an inverter is sinu-
soidal pulse-width modulation (SPWM). The inverter uses SPWM for generat-
ing a sinusoidal voltage on its AC side. In order to decide the correct switching
state at a given moment, a sinusoidal reference voltage is compared with one or
two triangular carrier voltages. One carrier voltage is used for bipolar PWM and
two carrier waves for unipolar PWM (more about bipolar and unipolar switching
in Section 10.5.2). If the instantaneous amplitude of the carrier voltage is lower
than the sinusoidal reference voltage, a positive DC voltage is returned on the
AC side of the phase-leg. If it is lower, a zero voltage is returned. This results
in a series of voltage pulses on the AC side of the converter. In the frequency
spectrum, this pulsed voltage signal consists of a fundamental sine component,
superposed with higher frequency harmonics. If these harmonics are successfully
filtered out, the remaining signal is a fine sinusoidal AC voltage.

20
10.5.1.2 Hysteresis current control
Hysteresis current control is a technique which can be used for controlling the
current in a voltage-source converter. The phase current in the converter on
the AC side is measured with a current sensor. The instantaneous value of the
current is compared with a reference current. Based on the reference current it
is decided whether the phase current should be increased or decreased. If the
current should be increased, a positive DC voltage pulse is sent through the
converter from the DC-link. If it instead should be decreased, a negative pulse
is sent. The result is a phase current which has a triangular wave shape, oscil-
lating around the reference current’s wave shape. The derivative of the phase
current dI
dt on the AC side is dependent on the AC side’s inductance L and on
a

the amplitude of the DC pulse VDC from the converter, according to Eq 3. The
so-called tolerance bands set limits to how much the phase current is allowed
to deviate from the reference current. As the phase current goes outside of the
allowed interval set by the hysteresis bands, a new voltage pulse is sent from
the converter, causing a change in the phase current’s derivative. Similar to si-
nusoidal pulse-width modulation, both bipolar and unipolar switching schemes
can be used for hysteresis control.
dIa VDC
= (3)
dt L

Figure 4: An example of bipolar hysteresis current control, with the sinusoidal

reference current and the triangular phase current oscillating around the refer-
ence.

10.5.2 Bipolar and unipolar PWM

The concepts of bipolar and unipolar PWM concern the number of voltage levels
in the pulsed DC signal, sent from the converter to the AC side. This is relevant
since it affects the total harmonic distortion (THD) in the generated AC signal

21
on the converter’s output. The topic of bipolar and unipolar switching is hence
important to analyse, in order to achieve appropriate quality in the converted
electric power [26].

10.5.2.1 Bipolar voltage switching mode

Bipolar voltage switching or two-level driving mode is a type of PWM control
method for switch-mode converters. When bipolar switching is used for the
single-phase VSC operating as an inverter, the AC output voltage alternates
between two voltage values [35, p. 57]. The switching state γ is either 1 or -1.
The states of the power transistors, depending on the switching state, can be
seen in Eq 4 below. The converter’s output voltage VO as a function of the
switching state and the DC-link voltage can be seen in Eq 5.

Figure 5 shows the generated AC voltage on the VSC’s output, when bipolar
switching is used for sinusoidal PWM. The output AC voltage has a wave-shape
which is not a pure sinusoid. In the frequency spectrum, the AC voltage consists
of a sine wave fundamental mixed with multiple harmonics [24, p. 204]. This
sine wave fundamental, which is plotted with a dotted line in the lower graph,
has a peak amplitude of V̂O,1 = V̂control
V̂
VDC
2 [24, p. 206].
tri

( (
1 if S1 ON and S3 ON +VDC , γ=1
γ= VO (γ) =
-1 if S2 ON and S4 ON −VDC , γ = −1
(4) (5)

Figure 5: Graph showing an AC voltage signal generated by bipolar PWM.

22
10.5.2.2 Unipolar voltage switching mode
The unipolar voltage switching mode or three-level driving mode is another type
of PWM method. If a single-phase VSC is operated as an inverter with unipolar
switching, the AC output voltage has three voltage levels. The output voltage
also takes the value 0, in addition to taking the values VDC and −VDC . The
unipolar switching mode hence uses one more switching-state, compared with
the bipolar switching mode. These three switching-states can be seen in Eq 6
below. The converter’s output voltage, as a function of the switching-state and
the DC-link voltage, can be seen in Eq 7. The fundamental sine component has
a peak amplitude of V̂O,1 = V̂control
V̂tri
VDC [24, p. 216]. One benefit of choosing
unipolar switching over bipolar switching is that unipolar switching has a lower
weighted THD, compared with bipolar switching [35].

 
1 if S1 ON and S3 ON
 +VDC , γ = 1

γ = 0 if S1 and S4 ON or if S2 and S3 ON VO (γ) = 0, γ=0
 
-1 if S2 ON and S4 ON −VDC , γ = −1
 
(6) (7)

Figure 6: Graph showing an AC voltage signal generated by unipolar PWM.

10.5.3 Frequency modulation index

The frequency modulation index, used in SPWM, is the quota between the
frequency of the triangular carrier voltage and the frequency of the sinusoidal
reference voltage. The formula for mf can be seen in Eq 8. The higher the

23
frequency modulation index is, the lower the THD is in the AC output voltage
from the converter [24, p. 219].
ftri
mf = (8)
fref

10.5.4 Amplitude modulation index

The quota between the reference voltage’s amplitude and the triangular carrier
voltage’s amplitude is called the amplitude modulation index. The formula for
ma can be seen in Eq 9 [24, p. 219].
v̂ref
ma = (9)
v̂tri

10.6 Microcontroller applications for control of

voltage-source converters
A microcontroller is a small computer in a single integrated circuit. It is a
compact device which can be programmed in order to carry out different com-
putational tasks [5]. For power electronics, microcontrollers are useful for the
implementation of control, as they can be used for producing suitable control
signals. Microcontrollers typically have input and output ports. An input port
has an analog-digital-converter (ADC) which samples an analog voltage and
converts it to a digital signal [29]. The microcontroller can then process the
information carried by this digital signal. A microcontroller output pin can be
analog or digital. An analog output pin uses a digital-analog converter (DAC).
A digital output pin can only give two different discrete voltage levels. These
digital pins are suitable for generating the PWM voltages fed to power transis-
tors [23].

10.7 MOSFET gate driver circuits

The gate electrode of a MOSFET requires a certain gate current in order for
the MOSFET to be turned on. When the switching frequency is high, it is
important that a sufficiently high current is fed to the MOSFET’s gate terminal,
so that the turn-on and turn-off transitions do not take too long. The PWM
signal generated from a microcontroller’s output pin is however typically low
in power. Therefore, it is often necessary to connect a power amplifier which
amplifies the voltage and current from the microcontroller, in order to turn on
the MOSFET. This type of amplifier circuit is called a MOSFET gate driver
[31].

10.8 Snubber circuits

Undesired overvoltage spikes can occur during a power transistor’s switching,
typically due to stray inductances in electrical components and conductors. This
can result in both energy losses and electrical stress on the circuit components.
If the normal operation voltage of a converter is chosen to a level close to the
maximum voltage of the transistor, the transistor may break from the stress of

24
the transient overvoltage [24, p. 680].
Snubbers are circuits which are added in combination with the power electron-
ics in order to reduce or eliminate overvoltage and overcurrent spikes. There
are several types of snubber circuits for transistors; for instance turn-on snub-
bers, turn-off snubbers and overvoltage snubbers. During on- and off-switching,
electrical energy is discharged from the stray inductances, causing currents to
flow reversely towards the transistor. The turn-on and turn-off snubbers direct
these currents into a resistor instead of into the transistor. Overvoltage snub-
bers limit transient overvoltages by connecting a resistor in parallel with the
transistor [24].

10.9 The DC-link and its function

The DC-link is the electrical node placed on the DC side of an AC-DC or DC-
AC converter; for example a VSC. There is typically a filter capacitor in the
DC-link, which has the task of reducing the amplitude of the DC-voltage ripple,
i.e. the variation of the voltage around the desired constant DC value. A DC-
link with a capacitor can be seen in between the voltage-source converters in
Fig 7.

10.9.1 Polarity of electrolytic capacitors

During the experimental work in this master’s thesis, an electrolytic DC-link
capacitor will be used. With electrolytic capacitors it is very important to
connect them to the circuit with the right polarity. If the wrong polarity is
used, the capacitor may explode, which is very dangerous if a high amount of
electrical energy is stored in the capacitor.

10.9.2 Bleeder resistors

A so-called bleeder resistor is often connected between the terminals of a DC-link
capacitor. This is a safety measure, which helps with discharging the capacitor
in a controlled way when the converter system is turned off. This way, there will
not be a high voltage in the DC-link when the converter is not being used. The
bleeder resistor reduces the risk of injury for people in the converter’s proximity
[42].

10.10 Back-to-back coupling of voltage-source con-

verters
A so-called back-to-back connection of two voltage-source converters means that
two VSCs are interconnected with a DC-link in between. The back-to-back
coupling is useful as a way of interconnecting two asynchronous AC systems.
These two AC systems can be either operating at different AC frequencies or
at the same frequency but with different phase. The back-to-back coupling will
become relevant in this master’s thesis, as a way of setting up a wave power
generator for delivering power to the electric grid. The electric grid has a fixed
frequency and the generator’s frequency is variable, but this issue can be solved
by a back-to-back coupling of a rectifier and an inverter via a DC-link.

25
Figure 7: Back-to-back connection of two MOSFET-based three-phase voltage-
source converters.

10.11 Level shifters

A level shifter, or voltage level translator, is an electronic circuit which can be
used for changing one voltage level to another one [40]. A level shifter will be
used in the practical part of this thesis, changing the PWM signal voltage levels
in the control circuit. Level shifters often come in the form of integrated circuit
chips, which will be seen in Section 16.6.2.

11 Electric power generation from sea waves

Wave power is a field in renewable energy which has not yet been extensively de-
veloped. There have been ambitions to build wave power farms in many places
across the world, but the breakthrough of wave power still awaits [39]. In this
section a short theoretical introduction to the energy in sea waves will be given,
as well as on how this energy can be converted into electricity. Challenges ac-
quainted with the power conversion are discussed. Finally, a short presentation
is given to the current status of wave power across the world and its future
potential.

11.1 The power in the waves

The energy flux per area for sea waves is defined in Eq 10 and the surface power
flux J in Eq 11. The quantity Hm0 signifies the significant wave height [20].
1 2 kW h
ES = ρgHm0 [ 2 ] (10)
16 m

kW
J = cg ES [ ] (11)
m2
An example of the average power flux J in the waves is given in Eq 12, based
on the average wave parameters at the 44011 station [28]. These parameters
are listed in Table 1.
2
g ρgHm0 kW
J= ≈ 11.51[ 2 ] (12)
2 · 2πfwave 16 m

26
 Quantity Expression Unit Comment
g m
cg 2ωwave s Group velocity of the sea waves [37]
m
g 9.82 s2 Gravitational acceleration
1
fwave 6 Hz Frequency of sea waves [28]
kg
ρ 1000 m3 Density of water
Hm0 2 m Significant wave height [28]

Table 1: Average wave parameters at buoy 44011.

11.2 Challenges in the design of wave power gen-

erators
The frequencies of sea waves are low: typically around 16 Hz according to wave
period measurements along the North American Atlantic coast [28]. These low
frequencies of waves bring along problems for the design of wave power genera-
tors. This relates to Faraday’s law (Eq 1). Faraday’s law says that the voltage
induced in a conductor is equal to the negative of the derivative of the flux link-
age Ψ(t). Equation 13 shows the expression for the flux linkage in a linear wave
power generator [12, p. 4]. It can be seen in Eq 14 that the EMF (t) is depen-
dent on the angular velocity ωwave of the waves. If the sea waves oscillate slowly,
causing a low speed for the translator, it will result in a low EMF amplitude
in the stator windings. This in its turn means that high electric currents have
to flow through the phase conductors, based on the relation between current,
power and voltage, as seen in Eq 15. If the phase conductors are long, and have
high resistance, it results in significant power losses along the conductors. The
generator design of Anders Hagnestål offers a solution to the problems with the
low amplitude EMF. More about this will be explained in Section 12.
2π
Ψ(t) = Ψ̂sin( z(t)) (13)
λ

dΨ(t) πh
ε(t) = −N = Êcos(ωwave t)cos( sin(ωwave t)) =
dt λ
(14)
Ψ̂hπ πh
= ωwave cos(ωwave t)cos( sin(ωwave t))
λ λ

~ = P
|I| (15)
~
|U |cos(φ)

11.3 Current status of wave power generation in

the world
Different types of wave power plants have been built and tested around the
world. The variation is large in the designs. Some concepts use buoys, oscillating
together with the ocean’s surface, causing a translator to move up and down
inside a stator. Other designs use the energy from the waves for moving air
or water streams, in its turn causing a turbine to rotate. These are just two
examples, and many other power generation solutions exist [19]. The first wave
farm in the world was the Aguçadoura wave farm, situated outside the northern

27
coast of Portugal. This wave farm was however closed down permanently only
two months after its opening, due to technical and economic problems [6].

11.4 Future potential for the field of wave power

Even though wave power is still in an early stage of its technical development, it
is clear that the ocean transfers immense quantities of energy. The theoretical
wave energy resources along the Norwegian Atlantic coast have been estimated
to about 600 TWh per year [20, p. 5]. This is just an example of the potential
for wave power in the Nordic countries. The total electrical energy consumption
in Sweden, Norway, Denmark and Finland together is 384 TWh, as calculated
in Section 22.1. It shall however be noted that the value for the Norwegian
coast above refers to the kinetic energy flux along the coastline. That is not the
same as the amount of energy which can be extracted from a technical point of
view [20, p. 17].

12 Characteristics of the wave power gen-

erator of Anders Hagnestål
The wave power generator invented by Anders Hagnestål will be explained in
this section. Also, the converter topology proposed by Gustaf Falk Olson will
be presented. Later in this thesis the task will be to construct this converter
system.

12.1 Generator characteristics

The generator of Anders Hagnestål is a transverse-flux permanent-magnet syn-
chronous machine (TFPMSM). It consists of a stator and a translator. The
translator is moving linearly up and down inside the machine, surrounded by
the stator windings. The translator is driven by the forces applied by the sea
waves to a buoy, which is floating on the sea surface [17].

The translator can be divided into three segments, each containing stapled
blocks of iron (electrical steel), separated by blocks of an isolating material (G-10
fiberglass epoxy laminate). The stator has two segments, each containing blocks
of permanent magnets, separated by the stator windings. When the iron blocks
in the translator move, the magnetic circuit in the generator is changed, and
the stator windings are exposed to an alternating magnetic flux. This results
in voltages being induced in the stator windings. Figure 8 shows the segments
of the stator, surrounded by the segments of the translator. In the figure there
are four and three translator and stator segments, respectively. However, the
number of segments have later been changed to three for the translator and two
for the stator. A more detailed description of the generator’s mechanical and
electrical topology is available in the master’s thesis Mechanical design of trans-
verse flux linear generator for wave power, written by Erling Guldbrandzén and
Manthan Shah.

It has been estimated by Anders Hagnestål that the translator will typically
be moving at speeds lower than 2 m/s in the lab setup. As was explained in

28
Section 11.2, low speeds such as these can be a problem for generators, because
of the low voltages induced. The voltage amplitude will be somewhat raised
by the introduction of multiple poles in the stator, but the voltage will still be
relatively low, with high currents as a result. These high currents often bring
along high losses for wave power generators, but not in Anders Hagnestål’s
generator system. This is what the power electronic converter is intended to
solve. It enables high currents to be used, without bringing along high losses.

Figure 8: Illustration of the inside of the linear generator, depicting the segments
of translator and stator. The figure shows four translator segments, but recently
the number has been changed to three. The figure has been borrowed from the
master’s thesis of Erling Guldbrandzén [16].

12.2 Reducing the resistive losses

In order to reduce the resistive power losses in the stator windings, exception-
ally short windings are used in Anders Hagnestål’s generator. This is a way of
lowering the winding resistance, which is proportional to a conductor’s length
`cond according to Eq 16. The lowered resistance in its turn reduces the resis-
tive power losses, which are proportional to the resistance, according to Eq 17.

29
 ρ
R = `cond (16) P = RI 2 (17)
Acond

12.3 Active power factor correction

Stator windings have a resistive-inductive character, as illustrated in the gener-
ator’s single-phase equivalent in Fig 9. The reactance in the windings is usually
much higher than the resistance [14, p. 256]. As a result of this, reactive power
is typically high in electrical machines. Reactive power Q is defined in Eq 18.
It can be seen that it is proportional to sin(φ), where φ is the phase angle
between the voltage and current. If it is possible to adjust the phase angle to
zero, the reactive power can be eliminated. This can be achieved using Active
power factor correction (APFC), which is the main idea for reducing the reactive
power in Anders Hagnestål’s wave power generator. The principles for active
power factor correction will be presented in Section 13.2.1. The development of
a Python code for implementing APFC will be described in Section 14.3.

Q = U Isin(φ) (18)

Figure 9: Single-phase equivalent for the TFPMSM during steady-state.

12.4 Power level in the generator

Anders Hagnestål has estimated that the generator’s production of electric
kW
power will be around 200 m/s . The power production hence varies significantly,
depending on the vertical velocity of the sea waves.

12.5 Cogging in the generator

Cogging is a type of torque ripple in a generator, which means that the me-
chanical torque is oscillating around an average value [30]. In the generator of
Anders Hagnestål, this cogging effect will occur during the transitions, when the
iron pieces move from facing a permanent magnet to facing a stator winding [16].

The cogging in the generator both results in mechanical stress and vibrations
in the generator. The problems from the cogging can be greatly reduced by the
three-phase layout of the generator, but a ripple of 1-3 % in the rated force still
remains [17].

30
Part III
Planning
13 Dimensioning the generator’s power elec-
tronic converter system
The power electronic system for the wave power generator should force the AC
current to be in phase with the AC voltage, making the power factor equal to
one. The power electronic system should also convert the variable frequency
power from the generator into fixed frequency power, suitable for the grid. The
individual parts of the converter system will be described in this section of the
report.

13.1 Overview of the power electronic converter

system
The electrical frequency is variable on the generator side, because of the varia-
tion in the angular velocity of the sea waves. The AC power from the generator
first has to be converted to DC power, in order to remove the variable frequency.
The power is then converted once again back to AC; this time with a fixed and
controlled frequency and a fixed voltage amplitude. This AC power is suitable
for feeding into the electrical grid. A block diagram describing the conversion
system from generator to grid can be seen in Fig 10 below.

Figure 10: Topology of the whole converter system for the eventual generator,
with two three-phase converters connected back-to-back.

13.2 AC/DC-converter characteristics

The conversion from AC power to DC power is performed using three single-
phase active rectifiers, which are controlling the current and the power factor in
each phase. The power factor is controlled using hysteresis current control. The
reason for not using a standard dq-controller is that the voltages in the phases

31
do not make up a symmetrical three-phase system. This asymmetric character
of the generator phase voltages comes from the cogging effect in the generator,
described in Section 12.5.

13.2.1 Active power factor correction

The three single-phase voltage-source converters should be used as active recti-
fiers, performing active power factor correction. They have the task of shifting
the phase angle of the current, so that it is in phase with the phase voltage.
The goal is to make the power factor cos(φ) = 1, which increases the power
rating and efficiency of the generator. The current control is performed using a
unipolar hysteresis current control algorithm, which measures the current con-
tinuously and tells the converter to change it when necessary.

Since it is a unipolar hysteresis control, two tolerance bands are used for
the current. If the current exceeds the first tolerance band, the value of the
generator’s EMF voltage is first examined, before any switching is done. If
for example the phase current is too high, but the EMF is negative, the EMF
will be contributing to the reduction of the current. Therefore the converter
will wait with switching. If the EMF is however positive, the converter will
switch. Also, if the current is outside the second tolerance band, the converter
will always switch. Flow charts describing both unipolar and bipolar hysteresis
control will be presented in Section 14.3, as part of explaining the development
of the Python codes for hysteresis control.

13.3 DC/AC-converter characteristics

The DC/AC-converter between the DC-link and the AC grid is a standard
three-phase VSC, using dq-control. In contrast to the three-phase system on
the generator side, the three-phase system on the grid side is symmetrical. This
makes possible the use of this type of three-phase converter. Since it is a stan-
dard converter which can be bought from many manufacturers, it is not the
task of this thesis to build the converter.

13.4 BeagleBone Black microcontroller

A BeagleBone Black Rev C microcontroller is used for the purpose of producing
the PWM control voltages for the MOSFETs in the active rectifiers. Beagle-
Bone Black is a microcontroller with the specifications listed in Table 2 below.
An image of the Beaglebone Black can be seen in Fig 11.

32
 Parameter Value
CPU 1 GHz
RAM 512 MB DDR3
Flash memory 4 GB
I/O pins 65
I/O pins 8
Figure 11: The Bea- Analog input pins 7
glebone Black micro-
Table 2: Some important hardware characteris-
controller which is to
tics for the Beaglebone Black microcontroller [2].
be used during the
practical work in this
thesis.

13.5 Sizing of the converter’s electrical compo-

nents
The sizing of the converter system’s components has largely been performed in
2016 in the master’s thesis of Gustaf Falk Olson. The values of the components
chosen by Falk Olson will now be presented in this section.

13.5.1 Selection of power transistors

Power modules CAS300M12BM2 from Cree were chosen by Falk Olson as power
transistors. One module corresponds to one phase-leg in a two-level voltage-
source converter. Each module contains two silicon carbide (SiC) power MOS-
FETs with power ratings as listed in Table 3. As was discussed in Section
10.3.2.3, SiC MOSFETs have very good capabilities of dealing with high switch-
ing frequencies at high currents. This in its turn helps with reducing the power
losses.
Each of the power modules has a maximum current rating of 300 A. In order
to make maximum current for the converter higher, it was decided by Anders
Hagnestål to use two power modules in parallel for each of the converter’s phase-
leg. This makes the number of power modules per phase equal to four. For an
illustration of this, see Fig 21. A photograph of a Cree CAS300M12BM2 power
module can be seen in Fig 12 below.
Parameter Value
Drain-source blocking voltage 1200 V
Current rating 300 A
On-state resistance 4.2 mΩ
Size 106 x 62 x 30 mm
Material Silicon carbide
Figure 12: Cree
CAS300M12BM2 Table 3: Some important properties for the Cree
power module. CAS300M12BM2 power modules.

13.5.2 Selection of the converter’s voltage levels

The voltage levels in the converter should preferably be set high, since a higher
voltage gives a higher power for the same current, as was discussed in Section

33
11.2. There is however an upper limit for the voltage level, set by the voltage
ratings of the power modules.

13.5.2.1 DC-link voltage level

The voltage in the DC-link was chosen by Falk Olson to 900 V [12, p. 34]. Since
the maximum voltage for the power modules is 1200 V, there is a margin of 300 V
from the maximum voltage. The reason for this margin is that overvoltage spikes
may occur when the transistors are switching under load. If the voltage over the
modules exceeds 1200 V, the modules are destroyed. Snubber circuits, explained
in Section 10.8, will help with lowering the amplitude of the overvoltage spikes.
Still, it has to be experimented with whether 900 V is a suitable DC-link voltage
level, or if the margin to the maximum module voltage of 1200 V is too small.

13.5.2.2 Generator side voltage level

The voltage level on the generator side of the converter is not chosen to a fixed
value, since it depends on the linear velocity of the translator and on the number
of poles in the stator.

13.5.3 Selection of the converter’s current levels

In order to increase the possible extractable power from the generator, two
modules are used in parallel for every phase-leg, as was mentioned in Section
13.5.1. This doubles the maximum possible current through the converter, which
then becomes 600 A instead of 300 A. This is the maximum peak value of the
AC current. The phase current level during the operation of the power plant
will vary depending on the energy extracted from the sea waves. Also, it will
vary depending on the amplitude set for the reference current by the hysteresis
current controller.

13.5.4 Maximum power flow through the power converter

Based on the decided DC-link voltage level and the maximum RMS phase cur-
rent levels, the maximum power through the converter system can be calculated.
600
Pmax = 3Iphase,RM S,max VDC = 3 √ 900 ≈ 1.15M W (19)
2

13.5.5 Selection of MOSFET drivers

For the task of amplifying the gate pulses to the power modules, MOSFET
drivers CGD15HB62P1 from Cree were chosen. These MOSFET drivers are in-
tended for use with the CAS300M12BM2 power modules, described in Section
13.5.1. It was seen as a good idea to use these modules and drivers together,
since they are made to be compatible. Another important characteristic of this
driver is that it has a built-in blanking time (propagation delay time) of 300
nS [10]. This preconfigured blanking time can be a useful safety measure, since
it guarantees that short-circuits are avoided in the power modules. A photo
showing one of these MOSFET drivers can be seen in Fig 13. In Table 4 some

34
relevant electrical parameters for the drivers can be found.

Supply voltage level 15 V (DC)

Input signal amplitude [0,5] V
Output signal amplitude [-5,20] V
Maximum switching frequency 64 kHz

Table 4: Some electrical properties for the

Figure 13: A Cree CGD15HB62P1 MOSFET drivers [10].
CGD15HB62P1 MOS-
FET driver.

13.5.6 PWM switching frequency

The switching frequency for the hysteresis control algorithm is not set to a con-
stant value, in contrast to for sinusoidal PWM. The duration of each switching
period depends on how long it takes before a tolerance band is exceeded by the
phase current. How fast the current exceeds a tolerance band depends on the
derivative of the phase current, which can be seen in Eq 20. The higher the
derivative of the current is, the shorter the switching period. The parameter
with the highest influence on the current’s derivative is the inductance LS in the
stator winding. Also, the switching period is affected by the sampling frequency
of the microcontroller. This sampling frequency has to be fast enough, so that
it is detected quickly when the phase current exceeds a tolerance band.
dIa Va
= (20)
dt LS

13.5.7 Sizing of a filter circuit on the generator side

A low-pass filter circuit was designed for the generator in the master’s thesis of
Falk Olson. One LP filter should be connected in series with each of the three
stator windings on the generator side of the converter. Hence three filters should
be constructed. The inductance of each filter was dimensioned to 5 mH in Falk
Olson’s thesis. The construction of these filter circuits is however outside the
scope of this master’s thesis.

13.5.8 Sizing of the snubber circuits

Snubbers should be connected in parallel with the power MOSFETs, in order
to reduce overvoltage and overcurrent transients. The unwanted energy in the
transients is then directed into the snubbers, instead of into the semiconductors.
The destructive impact of the transients on the converter can then be alleviated.
In the master’s thesis of Falk Olson it was decided to use the snubber circuit
which can be seen in Fig 14. The values of the electrical components in the
snubber circuit are listed in Table 5.

It should be noted that it is necessary for the snubber capacitors to have a

low equivalent series resistance (ESR). The reason for this is that the current
through the capacitor is occasionally high, which leads to overvoltages if the
ESR is not low. A good type of snubber capacitor is a film capacitor, because

35
of its low ESR [12, p. 32].

Component Value Comment

L1 135 Turn-on snubber
nH inductor
R4 2.2 Ω Combined turn-on
snubber and over-
voltage snubber re-
sistor
C1 , C2 633 Turn-off capacitors
pF
R1 , R2 75 Ω Turn-off resistors
C4 100 Over-voltage ca-
nF pacitor
Figure 14: The snubber cir-
Table 5: The snubber circuit
cuit which was dimensioned
component values which were
for the power MOSFETs by
dimensioned by Falk Olson.
Falk Olson [12]

13.5.9 Sizing of the DC-link filter capacitor

The DC-link voltage level should be maintained at a stable voltage level, lim-
iting the DC-link’s voltage ripple. In Gustaf Falk Olson’s master’s thesis the
DC-link capacitor was dimensioned to a capacitance of CDC = 10mF .

13.6 Electrical components for the initial labora-

tory test setup
The components decided upon in Section 13.5 are the components which should
be used for the final high power laboratory testing. During this thesis, however,
power levels of the same magnitude will not be used. This is mainly because of
the time limitation for the project and because the initial tests should be kept
at fairly low power levels, in order to safely detect eventual problems or errors
in the prototype. Therefore, electrical components with lower power ratings can
be used for the initial laboratory testing. A different DC-link capacitor and a
different topology for the snubber circuits will be used. Also, as a result of the
changed energy storage level in the capacitor, a bleeder resistor will be chosen
based on that energy level.

13.6.1 DC-link capacitor for the initial lab testing

An electrolytic capacitor will be used in the DC-link during the initial testing.
This capacitor was present in the laboratory already. Some important values
for the electrolytic capacitor are listed in Table 6. The maximum current ripple
specifies the maximum allowed difference between the capacitor’s charge current
and discharge current.

36
 Capacitance 10 mF
Maximum voltage 160 V
Maximum current ripple 16 A

Table 6: Some important parameters

for the DC-link capacitor used during
the initial laboratory testing.

Figure 15: The capacitor with

maximum voltage 160 V, to be
used during the initial labora-
tory testing.

13.6.2 Bleeder resistor for the initial lab testing

The bleeder resistor is dimensioned in Eq 21 so that the capacitor will discharge
down to 10 % of its original voltage UC,0 within 14 minutes. Based on this
resistance value and on the power dissipation in 22, a 33.6 kΩ resistor with
power rating 2 W was chosen as a bleeder. This power rating was deemed as a
safe choice, based on the maximum power dissipation in the bleeder, calculated
in Eq 22.

t
duC (t) uc (t) − discharge
− = 0 =⇒ uC (tdischarge ) = UC,0 e CRbleeder = 0.1UC,0 =⇒
dt Rbleeder

tdischarge 13 · 60
Rbleeder = = ≈ 33874Ω
Cln(10) 10 · 10−3 ln(10)
(21)

2
VC,max 1602
P = = ≈ 0.76W (22)
Rbleeder 33600

13.6.3 Snubber circuits for the initial lab testing

It was decided to use a modified topology for the snubber circuits during the
initial testing, after a consultation with Matthijs Heuvelmans, a PhD student

37
at KTH in the field of power electronics. The solution decided upon was to use
one film capacitor of 330 nF in parallel with the DC terminals of each power
module. This could be regarded as a good enough solution during low voltage
testing, according to Heuvelmans. It may happen that a resonance oscillation
is later detected in the voltage drop over the lower MOSFET in a phase-leg. In
case this happens, a band-stop filter can be connected in parallel with the lower
MOSFET, attenuating the resonance frequency. The topology of this modified
snubber circuit with one capacitor across each phase-leg can be seen in Fig 22.

It was decided that the snubber capacitors should be connected to the power
modules by means of short cables, instead of fastening the capacitors directly
onto the terminals of the modules. A short cable brings along a certain extra
inductance before the snubbers, but the benefit of this connection is the modu-
larity; the snubbers can easily be removed or connected. This way experiments
can be performed with or without the snubbers, as a way of evaluating their
performance.

13.6.4 Level shifters

The Beaglebone Black microcontroller gives a PWM signal with a maximum
amplitude of 3.3 volts on its PWM pins. The MOSFET drivers require PWM
input signals with an amplitude of 5 volts. If signals of lower amplitude are
used, the voltages on the outputs of the drivers will not be high enough to open
the power transistors. For this reason, it is necessary to use level shifters to-
gether with the Beaglebone Black. Two reference voltages should be given to
each level shifter: 3.3 V on the input and 5 V on the output. This makes the
level shifter convert the 3.3 V signals to 5 V signals.

Low-pass filters were considered necessary in the signal path between the
level shifter and the MOSFET driver. The reason was to remove high-frequency
noise from the PWM signals. A circuit diagram for the level shifter and the filter
can be seen in Fig 16 below. The value of the filter resistor R in the diagram
is 1 kΩ and the capacitor C is 62 pF . This low-pass filter was dimensioned by
Aliro Cofre Osses [7].

Figure 16: Circuit diagram for the level shifter, with its low-pass filters visible
to the right.

38
13.7 Electrical isolation paper
Electrical isolation paper, surrounding the copper plates in the DC-link, is in-
tended to protect persons from the exposure to electrical hazard. It should also
make sure that different nodes do not come into contact - which would cause a
short-circuit. Most importantly, the isolation paper has to be placed so that it
surrounds and isolates the positive DC-link copper plate. This node will even-
tually, in later experiments, reach a voltage of 900 V.

Nomex 410 paper was ordered. This isolation paper can withstand voltages
kV
up to 33 mm . The ordered piece of paper had a thickness of 0.25 mm. This
means that it can withstand a voltage of 8.25 kV [11]. This paper should be
reliable enough if the DC-link voltage is kept around 900 V.

13.8 Heat sinks

A cooling system is required for the power modules, as they will be operating
at high currents, causing power losses during switching. The lost power is
dissipated as heat. Heat sinks LA6 from Fischer Electronics were chosen for the
cooling of this heat. The selection of these heat sinks was based on calculations
by Aliro Cofre Osses, available in his master’s thesis [7].

14 Planning for the control system of the

power electronic converter
The development of a PWM code was necessary to be able to control the active
rectifier. The PWM code controls the switching of the converter. It thereby de-
termines the type of output signal which is generated as a result. The first part
of the practical work during this master’s thesis was the development of such a
PWM code. In addition to this code development, some software experiments
were performed in order to investigate how the switching frequency affects the
control of the current using hysteresis current control.

The method which will be used for reducing reactive power in the TFPMSM
is active power factor correction. By using hysteresis current control, the cur-
rent can be forced to be in phase with the voltage in the stator winding. The
principles behind hysteresis control and active power factor correction were ex-
plained in section 10.5.1.2 and 13.2.1. In this section it will be explained how a
programming code was developed, intended for later use during the control of
the converter in the experiments in Section 18.

14.1 Beaglebone Black and the choice of the Python

programming language
The Beaglebone Black (BBB) microcontroller is versatile in the sense that many
programming languages can be used for programming it. It was originally
planned to program the BBB using C++. The reason for this was that C++ is
a typical and common language for programming microcontrollers [15]. Quite
some time was spent in learning the basics of C++ and a hysteresis control code

39
was eventually developed in C++. This code showed the correct results when
running in the IDE program Eclipse. There was however less success in getting
the BBB to return actual PWM voltages at its PWM pins. In order to get this
to work, the BlackLib C++ library for Beaglebone was downloaded. It was
tried extensively to achieve a PWM signal, but the attempts were unsuccessful.

Eventually a Python code was created and tried out with the BBB. This
turned out to work very effectively together with the preinstalled Adafruit
Python GPIO library. With this library it was possible to generate a PWM
signal from the BBB.

It is possible that the use of C++ could have been successful if there had
been more previous experience with C++. But since there was a lack of time
and Python seemed to work well already, it was decided to use Python instead
of C++ for the PWM code in this master’s thesis.

14.2 Development of a SPWM control Python

code
The first Python code to be created for the microcontroller was the code for
sinusoidal pulse-width modulation (SPWM). SPWM is used when an AC volt-
age with a sinusoidal waveform is desired on the AC side of a voltage-source
converter. The final SPWM code can be found in the appendix in Section
22.3.1.

14.3 Development of a hysteresis control Python

code
The next step was to develop a code for hysteresis control. When hysteresis
control is used, the converter should send a voltage pulse to the AC side when it
is desired to change the AC current’s derivative. This is achieved by switching
of the transistors in the converter. The theory for this was explained in Section
10.4.1.

A PWM code was written in Python, implementing hysteresis current con-

trol. This code can be found in the appendix in Section 22.3.2. The AC phase
voltage, phase current and reference current were plotted in the time domain.
These plots can be seen in Section 22.2 in the appendix. The inductance value
which is used for the stator winding is L=40 mH. The voltage on the DC side
is 40 V. The AC voltage has an amplitude of 20 V and a frequency of 50 Hz.

Two types of switching schemes for hysteresis control were tested in this sim-
ulation. First, bipolar switching was tested, with one tolerance band on each
side of the reference current. The converter should then send a voltage pulse
to the AC side, immediately when the phase current exceeds a tolerance band.
Secondly, unipolar switching was simulated, with two current tolerance bands
on each side of the reference current. Then, as the current’s value is between
the first and the second tolerance band, the sign of the AC side voltage is taken
into account before it is decided if a voltage pulse should be sent. This principle

40
was described in Section 12.3.

Two flow charts describing the functions of the bipolar and unipolar switch-
ing codes are presented in the sections 14.3.2 and 14.3.2 below.

14.3.1 Flow chart for the bipolar hysteresis control code

The flow chart in Fig 17 describes the different steps in the code which im-
plements the bipolar hysteresis control. The value of the actual phase current
is compared with the reference current’s value in each iteration. If the phase
current’s derivative is correct, the converter’s switching state is kept the same.
If the derivative is wrong, however, the switching state is changed.

The variables Ia and Iref in the flow chart are the phase current and the
reference current. C denotes the constant value of the tolerance band. Vdc is the
constant voltage value on the converter’s DC side, whereas Vconv is the voltage
value which appears at a given instant on the converter’s AC side.

Figure 17: Flow chart for the bipolar hysteresis control code.

14.3.2 Flow chart for the unipolar hysteresis control code

The flow chart in Fig 18 describes the code for implementing unipolar hystere-
sis control. As mentioned in Section 13.2.1, two hysteresis tolerance bands are
used. If the phase current exceeds the first tolerance band, the converter only

41
switches if the EMF voltage has a certain sign. If the phase current exceeds the
second tolerance band, the converter always switches.

The variables used in the flow chart in Fig 18 have the same names as in the
flow chart for bipolar hysteresis control, described in Section 14.3.1.

Figure 18: Flow chart for the unipolar hysteresis control code.

42
14.4 Hysteresis control simulations for different
sampling frequencies
After Python codes had been composed for implementing bipolar and unipolar
hysteresis control, simulations were performed in order to test the codes’ cor-
rect function. The results of these simulations are presented in the appendix in
Section 22.2. The purpose of these simulations was mainly to examine the effect
of the microcontroller’s sampling frequency on the deviation of the generated
phase current from the reference current. With sampling frequency is meant
how many times per second the microcontroller measures the value of the phase
current. This will become important during the experiment with hysteresis con-
trol, described in Section 18. The simulations for hysteresis control also measure
how the sampling frequency affects the switching frequency of the converter.

14.4.1 Switching frequencies for different sampling fre-

quencies
In Table 7 it can be seen how the switching frequency is changed for different
sampling frequencies.

Sampling frequency Switching frequency, Switching frequency,

bipolar switching [Hz] unipolar switching [Hz]
1 kHz 600 602
4 kHz 2500 2600
10 kHz 6300 7370
50 kHz 22698 14300

Table 7: Switching frequency, depending on sampling frequency and SPWM

algorithm.

14.4.2 Current deviation from the reference current for

different sampling frequencies
The phase current’s maximum deviation from the reference current can be seen
listed in Table 7, depending on sampling frequency and SPWM algorithm. The
current’s deviation plotted against the sampling frequency can be seen in Fig 19.

Sampling frequency Deviation, bipolar Deviation, unipolar

switching [%] switching [%]
1 kHz 107.66 107.66
4 kHz 32.58 26.56
10 kHz 8.25 7.83
50 kHz 2.88 0.90

Table 8: Current deviation, depending on sampling frequency and SPWM

algorithm.

43
14.4.3 Conclusions about the necessary sampling frequency
for unipolar PWM hysteresis control
The current’s deviation was plotted against the sampling frequency in Fig 19.
Based on this graph and on the data in Table 8 it is concluded that the sampling
frequency during hysteresis current control has to be at least 10 kHz. Then it
can be assumed that the current is safely controlled and monitored.

140 Phase current's deviation from the reference current

120

100

80
Percent

60

40

20

0
0 20 40 60 80 100
Sampling frequency [kHz]

Figure 19: The phase current’s deviation from the reference current, plotted
against the sampling frequency.

15 Planning for the construction of the ac-

tive rectifier
The construction of the converter system was divided into five stages:
1. Draw circuit diagrams for the converter
2. Take practical aspects for the construction into account
3. Setting up a CAD model of the system, based on the circuit diagrams and
the practical aspects
4. Ordering of electrical and mechanical components
5. Assembly of the converter

44
 These individual stages for the converter construction will be presented in
this section.

First the special characteristics for the laboratory prototype of the converter
system will be described in Section 15.1 below.

15.1 Laboratory setup with machines and two con-

verters
Two electrical machines, both with Anders Hagnestål’s design, will be used
together during the laboratory testing of the wave power plant. One of these
machines will be set up working as a motor, in order to simulate the motion of
the sea waves. This motor will be used for moving the generator, causing it to
generate electric power. Since two machines will be used, two power electronic
converter systems will also be needed. The motor will take electric power from
the DC-link and the generator will feed power into the same DC-link. The
circuit from the diagram in Section 15.3.2 will therefore be built two times,
connected to the same DC-link. Since each converter system uses 12 power
modules, there will in total be 24 modules placed out on the DC-link. CAD
models for the intended final converter system can be seen in Section 15.6.

15.2 Two modules instead of four during the ini-

tial testing phase
Four power modules per phase will be used in the final converter prototype. This
doubles the maximum current for each phase, as was described in Section 13.5.3.
In the single-phase converter which is built within the scope of this master’s
thesis, however, two power modules instead of four will be used per phase. The
reason for this is mainly to simplify the circuit, making a simpler circuit topology
work first, before more circuit elements are added. The operation principle with
two modules is the same as with four, but working with fewer components was
seen as beneficial, since it narrows down the number of possible errors, such as
loose connections and similar.

15.3 Circuit diagrams

The block diagrams and circuit diagrams for the AC/DC converter system will
now be presented. The circuit diagrams will both be presented in simplified
and detailed versions. The simplified diagrams intend to give an overview of
the double three-phase system described in Section 15.1, which will eventually
be constructed after the end of this master’s thesis. The detailed circuit diagram
for one phase in Fig 23 shows the circuit which will be built during this thesis.
In order to continue building the system with six phases, the circuit for one
phase can be built six times. After the finished construction of this six-phase
system, the rest is a matter of synchronizing the control of the whole system.

45
15.3.1 Simplified block diagram for the final laboratory
setup with two machines
The block diagram in Fig 20 shows a simplified representation of the final con-
verter system for the lab test setup with two three-phase converters. To the left
is the generator and to the right the motor.

Figure 20: Simplified block diagram of the final laboratory test setup with two
electrical machines.

15.3.2 Simplified circuit diagram for one single-phase con-

verter with four phase-legs
Figure 21 shows a simplified diagram for how one single-phase converter should
be connected. This should be done after the circuit in Fig 22 works well, as was
described in Section 15.2.

Figure 21: Simplified circuit diagram for one single-phase converter with four
phase-legs.

46
15.3.3 Simplified circuit diagram for one single-phase con-
verters with two phase-legs
The circuit diagram below in Fig 22 is a simplified representation of the circuit
which should be built during this master’s thesis. When this circuit works well,
it can be proceeded with building the circuit in Fig 21.

Figure 22: Simplified circuit diagram for one single-phase converters with two
phase-legs.

47
15.3.4 Detailed circuit diagram for one single-phase con-
verter with two phase-legs
Figure 23 shows a more detailed circuit diagram for the same circuit as in Section
15.3.3 above. In this schematic the level shifter and its filter is included. For
the values of this filter, see Section 13.6.4.

Figure 23: Detailed circuit diagram for one single-phase converter with two
phase-legs

15.3.5 Circuit diagram for the connection of the current

sensor
The current sensor has four terminals, which are listed in Table 9. A voltage
divider circuit is required for achieving the 2.5 V voltage level for the sensor’s
reference pin. Two voltage dividers are also necessary for the connection of the
current measurement signals to the Beaglebone Black. The reason for this is

48
 Current sensor pin Voltage level
VCC 5 V (in)
VDD 0 V (in)
VREF 2.5 V (out)
VOU T Variable ouput voltage: [0,5] V (out)

Table 9: The four pins and the voltage signals which should be connected to
the pins.

Current sensor pin Voltage level

P9 33 Sensor’s output signal: [0,1.8] V
P9 35 Reference voltage of 0.9 V

Table 10: The analog input pins on the Beaglebone Black to which the current
sensor signals should be sent.

that the AIN pins have a maximum voltage level of 1.8 V. If a higher voltage is
given to them, the BBB is destroyed. The selected input pins on the BBB and
their corresponding voltage ranges are listed in Table. Decoupling capacitors
are also connected for removing high-frequency noise from the measurement sig-
nals fed into the Beaglebone Black. These capacitors are connected as close as
possible to the pins on the BBB.

The circuit diagram for the connection of the current sensor can be seen in
Fig 24. The values for the electrical components in this circuit can be found in
Table 11.

Quantity Value
R1 1260 Ω
R2 560 Ω
R3 10 kΩ
C1 100 pF
C2 220 pF
C3 4700 pF

Table 11: Electri-

cal component val-
ues for the cur-
rent sensor circuit
in Fig 24.

Figure 24: Circuit diagram for the connection of the

current sensor.

49
15.4 Practical design aspects to take into account
The design of the power electronic converter depends not only on the electrical
system, but also on geometrical and mechanical aspects. This will be discussed
in this section.

15.4.1 Copper plate dimensions

The two copper plates, making up the nodes of the DC-link, should be large
enough to fit all the power modules. In total there are 24 power modules, as was
explained in Section 15.1. By setting up a CAD model, it could be visualised
how much space is needed for all the components in each phase-leg. This CAD
model will be presented in Section 15.6.

15.4.2 Elevation of the copper plates above the DC-link

capacitor
The DC-link capacitor has a certain height, and it should ideally be placed
underneath the copper plates. Placing it under the plates increases the safety,
for reasons which will be discussed in Section 15.5.4. The copper plates however
have to be elevated a bit into the air, so that the capacitor can fit below the
plates,

15.4.3 Mechanical and electrical connection of the power

modules
Each power module has three electrical terminals and these should be in contact
with three nodes: the positive and negative DC-link nodes and the AC node of
each phase in the three-phase system. The DC nodes are made up of the copper
plates. A good way of attaching a power module to a plate is to use bolts of ap-
propriate dimensions, in combination with washers and nuts. This is why there
is a threaded hole for each terminal in the power module. A bolt provides a sta-
ble mechanical connection, if it has the right length and is sufficiently tightened.
A metal bolt also leads current, so the bolts can be part of the electrical cir-
cuit. The bolts chosen for the converter in this master’s thesis are made of steel.

In order to pull the bolts through the copper plates, holes have to be made
in the plates. Some of these holes should be big, making it possible to avoid
contact. Other holes should be small, so that contact is made possible. The
chosen design for the copper plate holes will be presented in Section 15.6.

15.4.4 Placement of electrical cables

Only two cables are necessary for the DC-link: one positive and one negative.
These cables are connected to the terminals of the capacitor in the DC-link.
The colors of the DC side cables are chosen to red and black. For the AC-side
of each phase, two cables are also needed: one phase conductor and one neutral
conductor. These AC cables should be connected to the AC terminals of the
power modules.

50
15.4.5 Attachment of the heat sinks
Heat is developed as a result of losses in the power modules. This hot air moves
in an upward direction from the modules. For this reason, it was decided to
flip the power modules upside down, so that free way is given for the hot air to
move away. Holes should therefore be drilled in the modules’ undersides. These
holes can be used for screwing heat sinks onto the undersides of the modules.

15.5 Safety aspects

Since this is a high-voltage project, the safety is a very important aspect. This
applies both for the person executing lab work and for people not involved in the
project, who are also present in the lab. A few measures related to increasing
the safety of the lab setup will now be discussed.

15.5.1 Position of the positive voltage DC-link copper plate

The positive DC-link node could be placed either below or above the negative
node. Placing it underneath can be seen as safer, since it would then be placed
further away from the user of the converter. It was therefore decided to put the
positive plate below the negative plate.

15.5.2 Electrolytic DC-link capacitor polarity

An electrolytic DC-link capacitor will be used in the preliminary lab setup, used
for the experiments for this master’s thesis. It is very important for electrolytic
capacitors that the polarity is correct when currents flow into the capacitor. If
a positive voltage is connected to its negative terminal it may explode.

In later experiments, after the end of this thesis, film capacitors should be
used in the DC-link. Film capacitors are not polarized, so the aspect with the
capacitor polarity will not be important. But until the capacitors are changed,
this is a very important thing.

15.5.3 Limiting the charging current for the DC-link ca-

pacitor
Before each experiment is commenced, the DC-link should be charged up to the
right voltage. This can be achieved by first connecting a DC voltage source to
the DC-link, in order to charge up the capacitor. During the DC-link charging it
is very important to limit the charging current into the capacitor. The reason is
that a capacitor has a very low internal resistance. If the resistance approaches
zero, the current approaches infinity, according to Ohm’s law in Eq 23. This
happens regardless of the voltage level in the capacitor. The high current into
the capacitor can cause the capacitor to explode. In reality, the current is not
infinite, but it can become very high. The capacitor current has to be limited
by connecting a resistor in series with the DC voltage source [1].

In the experimental scenarios presented in Section 18, there is a built-in

current limit of 1.25 A for the DC voltage source. This maximum current is not

51
so high that it causes a risk of capacitor explosion. Therefore no resistor is used
in series with the capacitor in the experiments in Section 18.
Vc
Ic = limRc →0 =∞ (23)
Rc

15.5.4 Protection against an eventual capacitor explosion

A capacitor explosion can be very dangerous, since hard pieces of the capacitor’s
casing may be thrown away out in the room. Also, the release of heat from
the explosion and eventual short-circuits may cause a fire, depending on the
components and material surrounding the capacitor. A safety measure that can
be taken, in case of an explosion, is to block the flying capacitor pieces using a
wall. In this master’s thesis, an explosion protection will be built, covering the
space under the lower copper plate where the capacitor is located.

15.6 CAD model for the final design

In order to plan and to get a good overview before the construction of the con-
verter, a CAD-model was set up for the converter system. The CAD model
was also intended to help with choosing the right geometrical dimensions of the
copper plates and the isolation paper. The software used for making the CAD
model was SketchUp. First the individual power modules were drawn in 3D.
They were then flipped upside down in the model. The heat sinks were drawn
on top of the undersides of the power modules, facing upwards. The MOSFET
drivers were drawn connected to the pins of the power modules. Then these
entities - the modules, heat sinks and drivers - were copied and pasted 24 times
and placed out next to each other. A square area was drawn around the 24
modules, representing the two copper plates. It was found that an area of 1x1
metre for each copper plate would be sufficient. Isolation paper was drawn out
in between the plates.

The holes for attachment of the power modules were drawn out on the copper
plates. Two holes were made under each module. Small holes were drawn where
the bolts should have electrical contact with a plate and big holes where the
bolts should avoid contact. The CAD model of only the two copper plates can
be seen in Fig 25c. The plate to the left is the upper plate and the plate to the
right is the lower plate.

15.6.1 Plastic boxes for containing the snubber circuits

Red and blue plastic boxes were chosen as a way of containing the snubber circuit
for each power module. The plastic boxes can be seen in the CAD model in
Section 15.6. It was seen as practical to contain the snubbers this way, because
it isolates them from accidental contact with other devices. Another reason for
this solution was to make the circuit layout more clear. Using red and blue
colors was intended to show the user of the converter which power module was
connected to which AC node.

52
 (a) The two three-phase converters, as seen from above.

(b) The two three-phase converters, as seen from the side.

(c) The two copper plates, with the holes for the attachment of the power modules.

Figure 25: Preliminary CAD model for six phases (generator and motor). To
be used during the laboratory testing of the final wave power plant prototype.

53
15.7 CAD model for the laboratory setup of the
converter
There was not enough time during the execution of this master’s thesis for
building the whole converter system. Therefore it was decided, as previously
mentioned in Section 8, to build only one voltage-source converter during this
thesis’ work. The rest of the construction should be finished afterwards. Fig 26
shows the CAD model of the converter system which would be built during the
practical part of this thesis.

(a) CAD model for one phase. The converter seen from above.

(b) CAD model for one phase. The converter seen from the side.

Figure 26: Preliminary CAD model for one phase. To be used during the
laboratory work during this thesis.

54
Part IV
Practical work
16 Construction of the active rectifier
After the required components had been selected, they could be ordered and
the construction could begin. The process of building a laboratory prototype of
the converter system will now be described.

16.1 Construction of the DC-link

The first thing to arrive was a copper plate of size 2x1 metre. This big cop-
per plate, which can be seen in Fig 27, was sawn into two equally large plates
of 1x1 metre, using a metal saw. The holes for the connection of the power
modules were then drilled out. In order to assure a correct placement of the
holes, a marker pen was used for drawing straight lines with red ink across the
copper plates. At the correct places along the lines, drill hole placements were
marked out. The small holes were drilled out using a twist drill bit of diameter
8 mm, whereas the bigger holes were drilled with a circle cutter drill bit with a
diameter of 35 mm. In addition to the holes intended for connecting the power
modules, two holes were drilled in the middle of the DC-link plates, intended
for connecting the DC-link capacitor.

The isolation paper was placed on top of the two plates before the drilling of
the holes in the plates. The places for making holes in the paper were marked
out by looking at the copper plate markings below the paper. After that, round
holes with a diameter of 8 mm were made in the paper, using a twist drill bit.

The two copper plates, constituting the two nodes of the DC-link, were
placed on top of each other, separated by the sheets of isolation paper. The
upper sheet was folded, covering the upper copper plate on both sides. This
can be seen in Fig 28. The lower sheet was originally covered the lower plate
in the same way, on both sides. However, this lower part of the paper was
eventually cut off, making it easier to see the connections of the power modules
from below.

55
 Figure 27: 2x1 metre copper Figure 28: Isolation paper.
plate, before its division in two.

Figure 29: Photos showing the big copper plate, before it was divided in
two, and isolation paper which was folded around the copper plates.

16.2 Construction of a wooden suspension for the

copper plates
A wooden structure was built for suspending the copper plates above the table
beneath. This suspension structure, which can be seen in Fig 30a, was built
using wood planks from a pallet that had been sawn into two pieces. The two
pallet segments were then stacked on top of each other, rising approximately 16
cm above the table. The reasons for building this suspension were several:

• Making room for the DC-link capacitor under the copper plates
• Simplifying the connection and disconnection of the power modules from
the copper plates
• Providing an explosion safety barrier in case of an accident where the
electrolytic DC-link capacitor explodes

16.3 Preparation of the power modules

The heat sinks were first prepared with threaded bolt holes of diameter 6 mm,
using a threading machine. Thermal paste was applied to the undersides of the
two power modules and the heat sinks were steadily attached to the modules,
using bolts of 16 mm length and 6 mm diameter.

Electrical cables were connected to the six output pins of the MOSFET
drivers. One red cable was connected to the upper transistor’s drain terminal
and one yellow cable to the lower transistor’s drain. Four blue cables were

56
 (a) Wooden structure which suspends the DC-link above the table beneath - mak-
ing room for the capacitor and providing a safety barrier.

(b) Heat sinks attached to the undersides of the power modules.

Figure 30: Two photographs, showing the wooden suspension and a power mod-
ule with a heat sink attached.

57
connected to the driver outputs intended for sending the transistor gate-source
signals. These blue cables can be seen in Fig30b.

16.4 DC-link capacitor connection

The DC-link capacitor was placed under the copper plates, which had been
raised up by the wooden suspension. Two bolts of diameter 6 mm and lengths 19
mm, were put through the holes in the plates. Each bolt was thereby connected
to one DC-link node and to one capacitor terminal. Also, the bleeder resistor
was connected in between these bolts. The cables for connection of the DC
voltage source were also connected using these bolts.

16.5 Connecting the power modules, snubber ca-

pacitors and high-voltage cable connections
The power modules were connected to the DC-link copper plates using bolts
of diameter 6 mm (M6 bolts). To the bolt of the positive DC-link node, with
length 24 mm, one short red cable was connected. To the negative DC-link
node, a short blue cable was connected, using a bolt of length 19 mm. These
short cables were then connected to the terminals of the snubber capacitors.
The reason for connecting the snubbers in this way was to achieve a modular
setup, as was described in Section 13.6.3.

To the AC-terminals of the modules, cables with red or black female banana
connectors were connected; the red contact signifying phase-leg A and the black
contact signifying phase-leg B.

A photo showing one fully prepared power module from above can be seen in
Fig 32. It has a heat sink, a MOSFET driver and a snubber capacitor connected
to it. It also has three electrical cables connected to its transistor terminals,
but only the black AC side cable is visible in the photo.

16.5.1 Choice of cable colors for marking out the different

nodes
The choice of color for the cables was intended to mark clearly which node the
cable was part of; red signifying positive DC, blue negative DC and yellow the
AC side. Red and black contacts were chosen for the cables intended for con-
necting the AC load or AC source.

Cable color Converter node

Red Positive DC
Blue Negative DC
Yellow AC side

Table 12: The colors of the cables were chosen for marking out the associated
electrical nodes.

58
16.6 Connecting the PWM control system
The process of connecting the signal paths for the converter’s control system
will now be described. The signals travel from the microcontroller’s PWM pins
to the transistors’ gate terminals, amplified in several stages on the way.

16.6.1 Beaglebone Black pins

The gate pulses for the transistors are initially produced by the Beaglebone
Black PWM pins. The pin which shall generate a specific signal is decided by
the code in the microcontroller. The voltage level of all the PWM signals from
the BBB is 3.3 V.

The current sensor is also connected to the Beaglebone Black, to the analog
input pins. More about this in Section 16.8.

Pin Signal
P9 1 Common ground
P9 3 3.3 V reference for level shifter
P9 14 PWM signal for transistor A1
P9 16 PWM signal for transistor A2
P9 21 PWM signal for transistor B1
P9 22 PWM signal for transistor B2
P9 33 Current sensor output signal
P9 35 Current sensor reference voltage

Table 13: The signals con-

nected to the Beaglebone
Figure 31: The Beaglebone Black.
Black with current sensor and
level shifter connected.

16.6.2 Conversion of the PWM signal voltage levels

The PWM signals from the Beaglebone Black go to the level shifter, which shifts
the voltage level of the signals from 3.3 V to 5 V. On the outputs of the level
shifter are the low-pass filters, which were described in Section 13.6.4. One 3.3
V reference voltage is connected from pin P9 3 of the BBB to the input reference
of the level shifter. To the output reference of the level shifter is connected a
5 V reference voltage from the 5 V supply voltage. A photo showing how the
level shifter is connected to the Beaglebone Black can be seen in Fig 31.

16.6.3 MOSFET driver input signals

As there was a lack of information in the datasheets for the Cree MOSFET
drivers, the way of using them had to be found through trial and error. It was
found that the drivers would do what they should, amplifying gate pulses cor-
rectly, as long as a PWM signal was fed to its gate pins and a 5 V DC voltage
was fed to its reset pins. It is however not known what the purpose of the reset
signal is. Until its purpose is found out, a constant 5 V voltage can be fed to the
reset pins continuously. There are also two other unknown pins per transistor

59
in the MOSFET drivers. These pins are named ready and fault. It was found
out that the driver would work well with these pins disconnected. In Fig 33
a photo can be seen with the connections used for the MOSFET drivers. The
connections are also listed in Table 14. The supply voltage is connected at the
far right in the photo. The purple cable, which is connected to all the ground
pins of the driver, goes to a ground plane which is used as a common ground
for all the digital signals in the control system. This ground plane in its turn is
connected to the negative terminal of the 5 V DC supply voltage.

Figure 32: One power module with heat sink, MOSFET driver, snubber
capacitor and cables connected.

Pin number Signal

2 Gate upper
4 Reset upper (5 V)
10 Gate lower
12 Reset lower (5 V)
18 VCC 15 V
20 VCC 15 V
1,3,5,7,9,11,13,15,17,19 Common ground

Table 14: The input signals to a Cree MOS-

FET driver.
Figure 33: MOSFET
driver signal cabling.

16.6.4 MOSFET driver output signals

The output signals from the MOSFET drivers are the gate-source pulses for the
power MOSFETs. There are four cables for this: two for the gate terminals
and two for the source terminals. These cables had to be arranged so that they
cross each other. The reason for this was that the power module is turned upside
down, in order to make room for the heat sinks, as was explained in Section
13.8.

60
16.7 Supply voltages for the control system
Different components in the control system need different supply voltages in
order to operate. Also, the fans in the heat sinks need their own supply voltage
source. All these different supply voltages were provided through (switching)
DC power adapters. The cables from three different DC adapters were cut
off. The ends of these cut-off cables were then attached to lugs, using a cable
crimper. The cable ends were then screwed onto small copper plates on the
wooden structure next to the DC-link. In this way, supply voltage buses of dif-
ferent amplitude could be made available for the different devices in the control
system. The three supply voltage levels and the associated devices which are
fed by these can be seen in Table 15.

Supply voltage level Supplied devices

15 V MOSFET drivers
12 V Heat sink fans
5V Level shifter, current sensor and reset signals

Table 15: The supply voltage levels and the supplied electrical devices.

16.8 Connecting the current sensor

There were several things to consider during the connection of the current sensor.
The current sensor should have a supply voltage of 5 V and a reference voltage
of 2.5 V. Also, the analog in (AIN) inputs of the Beaglebone Black could only
take a maximum voltage of 1.8 volts. For this reason voltage dividers were
used for lowering the amplitude of the output signal from the current sensor.
A description on the details of these voltage dividers can be found in Section
15.3.5. An explanation about how the current sensor was calibrated, setting up
the BBB to interpret the sensor’s signals, will be given in Section 17.2.

(a) The current sensor’s whole circuit, with its two voltage dividers and the de-
coupling capacitors at the input of the Beaglebone Black.

16.8.1 Amplifying the sensor’s measurement signal

The current sensor HAIS 400-P was bought with the intention of measuring
high currents. The sensor can measure current amplitudes within the range
of [-600,600] A. In the initial laboratory testing for this thesis, however, the
current will be limited to around 1 A. The problem with using the HAIS 400-P
sensor for such a (relatively) low amplitude is that its voltage output signal is
only around 10 mV for a 1 A current. A voltage signal of this level is hardly
detectable by the microcontroller. But by winding the phase current conductor
52 times around the inside of the current sensor, this voltage signal could be

61
 (a) The current sensor, with the phase conductor wound 52 turns around the
sensor in order to amplify the voltage signal from the sensor.

amplified 52 times; returning a 520 mV voltage for a 1 A current. A photo of

the sensor with the wound phase conductor can be seen in Fig 35a.

17 How to use the Beaglebone Black in Mi-

crosoft Windows
In order to set up the microcontroller for controlling the converter in Microsoft
Windows, a program called Putty can be used for communicating with the
Beaglebone Black.

17.1 Logging in to Putty

In Putty, the Beaglebone Black can be accessed by connecting to the IP ad-
dress 192.168.7.2, with SSH chosen as the connection type. A Linux termi-
nal then opens in a Putty window. The username root should be given dur-
ing the login. No password is required. Then, by browsing to the directory
root/converter_codes in the Beaglebone Black, the Python programs used
in the experiments in Section 18 can be viewed and started. The procedure
for browsing to the directory and initiating the codes can be executed using
standard Linux terminal commands.

62
 (a) Putty log in screen. (b) Putty terminal window.

Figure 36: Two examples of the Putty interface, which can be used for interact-
ing with the Beaglebone Black.

Current [A] Voltage signal value in BBB

0.5 0.047579
1 0.086134
1.5 0.124689
2 0.163244
2.5 0.201799

Table 16: The values returned in the Putty terminal, used for linear regression
in order to calculate the phase current.

17.2 Calibration of the current sensor

As the voltage signal was initially fed into the Beaglebone Black’s analog inputs,
the values printed in the Linux terminal seemed like unreasonable voltage values.
Therefore, the current sensor’s measurements first had to be calibrated; meaning
that the linear relationship between the sensor’s voltage signal and the actual
measured current had to be found. This could be done by taking notes on the
voltage signal value for different currents through the sensor. The voltage values
retrieved during this process are listed in the table below.
From the values in Table 24, the linear function for the current on the form
f (v) = kv + m could be found through linear regression. The retrieved current
function can be seen in Eq 24 below.

As this function was written into the Python code, the Linux terminal started
returning the correct current values as the current was continuously measured.

1 0.009024
Iphase = k(Vsensor − Vref ) + m = (Vsensor − Vref ) − (24)
0.07711 0.07711

63
18 Electrical experiments
The plan was to carry out two laboratory experiments, in order to test the con-
structed voltage-source converter (VSC). The first experiment would be about
the inverter operation mode with sinusoidal-pulse width modulation (SPWM).
The task of the converter is then to generate an AC voltage with a given fre-
quency. The second experiment would be testing the rectifier operation mode,
with the converter controlled through hysteresis current control. Before the ex-
ecution of this second experiment it would however be necessary to check that
the microcontroller samples and iterates fast enough for a safe and reliable cur-
rent control.

All experiments were performed using two power modules in the VSC circuit
instead of four, as was described in Section 15.3.

18.1 Word of caution about the capacitor charg-

ing current
The DC voltage source, a Powerbox 3000, which is connected to the DC-link in
the first experiment, has a current limitation of 1.25 A. This is important and
must be considered. If another power source without a current limit would be
connected instead, then a resistor must be connected in series with the capacitor.

18.2 Inverter mode, unipolar sinusoidal PWM

In the first experiment the converter was operated as an inverter, converting
power from DC to AC. The DC source was connected at the terminals of the
DC-link capacitor, bringing the voltage in the DC-link up to 40 volts. The
Beaglebone Black microcontroller was turned on, running the code spwmunipo-
lar.py, which can be found in Section 22.3.1 of the appendix. This led to the
BBB feeding a sinusoidal PWM signal to the gate drivers, via the level shifter.
The reference sine wave in the SPWM code was given a frequency of 50 Hz.
The amplitude modulation index ma was set to 1 and the frequency modula-
tion index mf to 12.5. A photo can be seen in Fig 37, showing the laboratory
setup and how all the components were connected during the experiment. The
circuit diagram for the connection can be seen in Fig 38 and the component
values found in Table 17.

64
 Figure 37: The laboratory setup during the converter experiment with
sinusoidal PWM.

VDC 40 V
R 24Ω
L 0 mH

Table 17: Elec-

trical parameters
for the circuit
elements dur-
ing the SPWM
experiment.
Figure 38: Circuit diagram for the laboratory setup
during the experiment with sinusoidal PWM.

18.2.1 Inverter, no load

First the converter was run as an inverter with no load connected, i.e. RL =
LL = 0. The DC side voltage was set to 40 V using the DC voltage source. The
gate-source voltage signals of the MOSFETs were measured, as well as the DC
and AC side voltages.

18.2.2 Inverter, resistive load of 24 Ohm

Subsequently a resistive load of 24 Ω was connected on the AC-side. This was
done with the intention of bringing the DC current up to 1.25 A, which was the
maximum current value from the DC source at the "40 V"-setting. The reason
for testing the converter under load was to see if overvoltage spikes would appear

65
over the power transistors, or if these are eliminated by the snubber capacitors.

18.3 Rectifier mode, hysteresis control with unipo-

lar PWM
The second experiment was intended to test the converter together with the
PWM control algorithm which will later be used in the finished wave power
plant. This is the hysteresis current control algorithm, described in Section
14.3. The goal of this experiment was to make the converter force the AC current
from the grid in phase with the voltage. An inductor should be connected at
the input of the converter - between the AC source and the converter. This
inductance is necessary because it limits the derivative of the phase current,
according to Eq 3. Without this inductance, the current would in theory rise
infinitely fast and the current control would be impossible. Also, the inductor
makes the system look more similar electrically to the wave power generator,
where large inductances exist in the stator windings. The laboratory setup for
the hysteresis control experiment can be seen in Fig 41.

18.3.1 Word of caution about the reference current

The hysteresis control experiment can be dangerous if it is not performed in a
proper way. The current into the converter is set by the reference current given
in the microcontroller’s code. This current will flow into the DC-link, regardless
of the load on the DC side. This means that if no load is connected on the DC
side, and if the reference current is set too high for the bleeder resistance to
discharge the capacitor, the capacitor will keep charging until it explodes.

18.3.2 Initial evaluation of the microcontroller’s sampling

frequency
Another critical thing to evaluate before the hysteresis control experiment was
whether the sampling frequency of the Beaglebone Black is high enough. The
microcontroller will only give directives to switch the transistors if it knows
that the current has a too high or too low value. If it does not sample quick
enough, it will not notice in time when the current exceeds the tolerance bands.
Therefore, a too low sampling frequency will lead to an uncontrolled current,
which is dangerous, since it could lead to a capacitor explosion. For this reason
an experiment about the sampling frequency of the BBB had to be performed
before the hysteresis control experiment could be carried out.

An autotransformer was connected to the grid. On its input it had a 230 V

AC voltage and on its output an AC voltage of variable amplitude. This output
voltage was chosen to 24 V and then connected to a 24 Ω resistance, giving rise
to a current with peak amplitude 1 A. This current was led through the current
sensor and the measurements were saved to a text file. These sampling points
were then plotted together with the oscilloscope’s current measurement, in order
to make a comparison of the two measurements. The sampling frequency fs of
the BBB could be found by looking at the number of samples points for one

66
period in the 50 Hz current. The laboratory setup for this experiment can be
seen in Fig 39.

Figure 39: Laboratory setup in the experiment where the sampling fre-
quency of the microcontroller is measured.

V̂AC 24 V
RL 24 Ω

Table 18: Elec-

trical parameters
for the circuit
elements during
current measure-
Figure 40: Circuit di- ment.
agram for the labora-
tory setup during the
current measurement.

18.3.3 Active rectifier with active power factor correction

This section describes how the hysteresis control experiment can be performed.
As will later be explained in the results in Section 19, this experiment could not
be performed because of a too low sampling frequency in the Beaglebone Black.
But if a higher sampling frequency is eventually achieved, then these experiment
instructions can be followed for testing the hysteresis current control.

The autotransformer used in the sampling frequency experiment is connected

to the AC side of the voltage-source converter, via a variable inductor. A resis-
tive load is connected on the DC side of the converter. No DC power source is
connected to the DC-link. Based on the value of the resistive load, the refer-
ence current in the microcontroller is chosen. The current entering the DC-link
through the converter should be equal to the load current on the DC side. Oth-
erwise the capacitor will either keep charging or discharging, depending on if
the current is too big or too small, as was explained in Section 18.3.1.

67
 The current and the voltage on the AC side of the converter should be mea-
sured during this experiment. The hysteresis control is successful if the AC
current is in phase with the phase voltage and if the phase current has the same
waveform as the reference current.

A photo of the laboratory setup for hysteresis control can be seen in Fig 41
below. The circuit diagram and the used electrical parameters can be seen in
Fig 42 and Table 19.

Figure 41: Laboratory setup for the hysteresis control experiment.

V̂AC 24 V
CDC 10 mF
VDC
RL Iref

Table 19: Elec-

trical parameters
for the circuit ele-
ments during the
hysteresis control
experiment.

Figure 42: Circuit diagram of the laboratory setup

during the experiment with sinusoidal PWM.

68
Part V
Analysis
19 Experimental results
19.1 Inverter mode, unipolar sinusoidal PWM
Four graphs will now be presented for showing the results of the SPWM inverter
experiment. The first two graphs show the gate pulses sent from the MOSFET
drivers to the transistors. The third, fourth and fifth graphs show the DC
voltage, AC voltage and AC current during the no-load and load conditions.

19.1.1 SPWM, gate pulses

MOSFET A1, gate pulse MOSFET B1, gate pulse
30 30

20 20
10
[V]

[V]

10
0
0
-10
-10
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
[seconds] [seconds]
MOSFET A2, gate pulse MOSFET B2, gate pulse
30 30

20 20
[V]

[V]

10 10

0 0

-10 -10
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
[seconds] [seconds]

Figure 43: Gate pulses for phase- Figure 44: Gate pulses for phase-
leg A. leg B.

Figure 45: Plots showing the measured gate pulses for the power transistors.

19.1.2 Inverter, no load

The time domain measurements of the voltages in the converter during the
no-load condition can be seen in Fig 46.

69
 Sinusoidal PWM, no load, converter voltages
60
DC-link voltage
AC side voltage
40

20
[V]

-20

-40

-60
0 0.01 0.02 0.03 0.04 0.05
[seconds]

Figure 46: Graph showing the voltages on the DC and AC side of the
converter, as no load is connected on the AC side.

19.1.2.1 Frequency analysis

A Fourier transformation, performed on the AC voltage generated in the SPWM
experiment, can be seen in Fig 47.

Figure 47: Fourier transform of the AC voltage generated by the VSC. The
left graph shows frequencies between 0 and 500 Hz, whereas the right graph
shows 0 to 10 kHz.

19.1.2.2 Switching frequency

The switching frequency of the generated AC waveform in Fig 46 is 2185 Hz.
This frequency value was calculated in MATLAB, by measuring how often the
voltage level in the AC signal is changed.

70
19.1.3 Inverter, 24 Ohm load
The DC voltage, AC voltage and AC current for the converter, when a load of
24 Ω is connected, can be seen in Fig 48.
Sinusoidal PWM, 24 Ohm resistive load Sinusoidal PWM, 24 Ohm load, AC side current
50 2
DC-link voltage [V]
40 AC side voltage [V] 1.5
AC side current [A]
30
1
20
0.5
10

[A]
0 0

-10
-0.5
-20
-1
-30
-1.5
-40

-50 -2
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
[seconds] [seconds]

Figure 48: Time domain measure- Figure 49: Graph showing only
ments when a load resistor of 24 the AC current, when a 24 Ohm
Ohm is connected on the DC side. load is connected.

19.2 Measurement of the Beaglebone Black’s sam-

pling frequency
The graph in Fig 50 shows the current measurement from the Beaglebone Black
together with the oscilloscope’s current measurement.
Sampling frequency evaluation
1.5
Oscilloscope measurement
Beaglebone Black measurement
1

0.5
[A]

-0.5

-1

-1.5
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[seconds]

Figure 50: Graph showing the current measurement from the oscilloscope
and from the BBB. It should be noted that the BBB samples only 8 times
per period.

71
19.3 Rectifier mode, hysteresis control with unipo-
lar PWM
It was concluded before beginning of this experiment that it would not be safe
enough to perform the hysteresis control experiment because the sampling fre-
quency of the Beaglebone Black was too low. Therefore it was not performed.
The motivation for this decision will be given in the conclusions in Section 22.

20 Discussion
The experiment with sinusoidal pulse-width modulation was quite successful.
The constructed converter was able to convert a DC voltage into a 50 Hz AC
voltage. This result showed that the voltage-source converter system is func-
tional. If other conversion algorithms are desired, these can be implemented by
changing the programming code in the microcontroller.

The experiment on hysteresis current control was however not possible to

perform. The reason was that the sampling frequency of the microcontroller
was too low. In Fig 51 a simulation showing hysteresis control with a sampling
frequency of 300 Hz can be seen. The result with this frequency is an uncon-
trolled phase current where the current’s deviation from the reference current
is 200 %. This experiment would have been too dangerous to perform.

The sampling time for an AIN pin on the Beaglebone Black is 125 ns -
equivalent to a sampling frequency of 8 MHz [3]. Therefore it should not be the
hardware in the Beaglebone Black that is causing the problem with the slow
sampling frequency. The probable reason for the slow sampling is that Python
was used as a programming language. Python is a dynamically typed program-
ming language, which makes it relatively slow [43]. Since the sampling of the
current’s value is performed one time per iteration, the sampling frequency will
also be affected by the code’s slowness. It would probably be a good idea to
switch to a non-dynamic language, such as C++ or C, which are statically typed
languages. In this thesis, it was originally intended to use C++, but it showed
difficult to communicate with the GPIO pins in C++, since no library for that
was installed beforehand. With Python the GPIOs could be controlled right
from the start, so therefore Python was chosen.

Even though the control system’s slowness was probably caused by Python,
not by Beaglebone Black’s hardware, there are also some issues suggesting that
the microcontroller itself should be replaced. The first reason is that there are
too few PWM pins on the Beaglebone Black for controlling the whole converter
system, which will stand finished in the end. In this master’s thesis, experiments
were performed on one converter phase, but in the end there will be in total six
phases. This would require six microcontrollers if Beaglebone Black controllers
were to be used. It would not be easy to synchronize all these controllers, so
preferably one single microcontroller with more PWM pins should be used in-
stead. Alternatively it may be possible to use the GPIO pins instead of the
PWM pins for implementing PWM. There are 65 GPIO pins in a BBB [2]. In
that case, two Beaglebone Black microcontrollers could be used for controlling

72
the six-phase system. The reason for using two BBBs is that a total of 12 AIN
pins would be needed for measuring the six phase currents.

The other reason for an eventual replacement of the Beaglebone Black is

that the voltage level is 3.3 V out from the PWM and GPIO pins. The MOS-
FET drivers require PWM signals of amplitude 5 V. This resulted in that level
shifters were needed - an extra stage in the signal path, which would have been
unnecessary if the PWM voltage level had been 5 V from the start. The Ar-
duino microcontroller for example uses a 5 V voltage level in its PWM signals.
The Arduino is much too slow for controlling the converter built in this thesis,
but possibly there are other more advanced microcontrollers which also use 5 V
for their PWM signals. The level shifters can be seen as an unnecessary step.
Voltage supplies and filters need to be built for each level shifter. If six phases
are to be used in the final laboratory setup, it will require much work to build
these six level shifter circuits. Also, the risk increases for glitches and other
difficult-to-find errors to appear, as the number of components in the system
increase. If all these extra level shifters can be avoided, it would probably be
beneficial.

The frequency modulation index should not have been mf = 12.5. This was
a mistake. The intention was to set it to mf = 25. The expression for the
triangular carrier wave’s slope was however wrongly written, causing mf to be
halved. The slope of the triangle wave should have been set to dvdttri = 2·2·V̂tri
Ttri ,
but was accidentally set to dvdttri = 2·TV̂tri
tri
. This made the triangle wave’s fre-
quency, and thereby also mf , half as high as it should have been.

The amplitude modulation index was also set incorrectly. It should have
been set lower than 1, but now it was set to 1. Setting ma to 1 is acceptable,
distortion-wise, but it is better to set it lower, since that results in a lower THD
[24, p. 219].

73
 L=40mH, Vac=20V, Vdc=40 V, fsamp=300 Hz, fswitch=288.0 Hz
60
Phase voltage
40
20
0
[V]

−20
−40
−60
0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
[sec]
4
Phase curre t
3
2
1
0
[A]

−1
−2
−3
−4
0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
[sec]
1.0
Refere ce curre t
0.5
0.0
[A]

−0.5
−1.0
0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
[sec]

Figure 51: A simulation showing the phase current which would have resulted
for a hysteresis control experiment with a sampling frequency of 300 Hz.

21 Future work
Before the converter system can be used for its final task in the laboratory
prototype, several modifications and further work needs to be performed. In
this section it is attempted to summarize the necessary remaining steps, before
the laboratory prototype can stand finished.

21.1 Increase the microcontroller’s sampling fre-

quency
The first thing which has to be done is to guarantee that the microcontroller
samples quick enough. This could be done by changing the programming lan-
guage so that the code runs faster. Also, it might be worth considering to get
another microcontroller than the Beaglebone Black, for reasons mentioned in
the Conclusions section.

21.2 Implement hysteresis control

After the sampling frequency has been increased, the hysteresis control exper-
iment described in Section 18.3 should be performed with unipolar switching.
If the results are satisfying, more power modules can be added to the converter
circuit.

74
21.3 Connection of two more power modules for
the single-phase VSC
The electrical experiments in Section 18 were performed using two power mod-
ules in the VSC circuit. It should later be attempted to perform the experiments
on SPWM and hysteresis control with four power modules, according to the cir-
cuit diagram in Fig 21.

21.4 Holes for the MOSFET drivers in the copper

plates
The MOSFET drivers are currently connected to the power modules using four
short cables. The reason for this was that the power modules are screwed with
bolts onto the copper plates. It was not possible to connect the drivers directly
onto the power modules because of the lack of space beneath the modules’ input
pins. Also there is a plastic connector on the MOSFET drivers, taking up much
space. A possible alternative to the connection solution used now is to cut
holes in the copper plates beneath the module’s pins. Then the four cables can
be avoided. This would remove undesired cable inductances affecting the gate
pulses. The cutting could advisably be done using water jet cutting or similar,
so that high accuracy is obtained.

21.5 Acquisition of film capacitors for the DC-

link
An electrolytic capacitor was used for the experiments in Section 18. During
later experiments with higher power, film capacitors should be used instead.
These should be bought and connected.

21.6 Holes in the plates for more DC-link capac-

itors
It is probable that more than one film capacitor will be needed for the DC-link.
The reason is that both high voltage ratings and high capacitance is desired.
Therefore it may become necessary to drill or jet water cut more connection
holes for these capacitors.

21.7 Connection of the snubber capacitors beneath

the copper plates
A modular topology for the snubber circuits was used during the experiments
in this thesis, with the capacitors connected by means of cables. The reason for
this was explained in Section 13.6.3. In the final laboratory tests it is however
advisable to connect the snubber capacitors directly to the bolts under the DC-
link copper plates.

75
21.8 Acquire better understanding of the MOS-
FET driver signal pins
On the MOSFET drivers are three pins whose purposes were not properly un-
derstood during the work in this thesis. These pins are the reset, ready and
fault pins. They have not used in an organized manner, for the reason that the
information about them online was scarce. It later turned out that the drivers
could be used without these pins, but a proper understanding of their purpose
should preferably be gained before the final lab work.

21.9 Connect all power modules and set up their

control systems
The circuit which was tested in this master’s thesis was only one sixth of the
circuit for the final laboratory test setup. The final circuit can however be
assembled based on the planning which has been done in this thesis. The sim-
plified block diagram in Fig 20 shows the final test circuit. It can be achieved
by connecting the single-phase converter from the diagram in Fig 21 six times.
The intended setup is also illustrated in the CAD model in Fig 25.

21.10 Increase the voltage

The voltage levels can be increased when everything for the six phases is con-
nected and the whole control system is in place and fully working.

22 Conclusion
During the work of this master’s thesis, a single-phase voltage-source converter
has been constructed. The converter should be part of a back-to-back converter
topology with two three-phase converter systems interconnected via a DC-link,
converting electric power from AC to DC and then back to AC again. This
back-to-back converter will stand finished after further electrical construction,
which will continue based on the work of this thesis. The final goal for the back-
to-back converter will be to use it in the laboratory testing of the TFPMSM
wave power generator designed by Anders Hagnestål.

The electrical tests performed on the constructed single-phase VSC showed

good results for sinusoidal pulse-width modulation. This is promising, because
if SPWM works, other switching algorithms should also work well. There is
however an obstacle remaining before the hysteresis current control algorithm
can be tested. This obstacle is that the code in the Beaglebone Black micro-
controller is not iterating fast enough. The reason for the code’s slowness is
thought to be the use of Python. The programming language should therefore
be changed from Python to for example C or C++.

76
Part VI
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79
Part VII
Appendix
22.1 Total electrical energy consumption in the
Nordic countries
Mean annual consumed electrical energy, years 2010-2013
Country [GWh]
Sweden 139 576
Norway 127 843 [25]
Denmark 32 350
Finland 84 044
Total 383 813

22.2 Python simulation results

22.2.1 Unipolar SPWM simulation results
The plots in this section show the effect of the microcontroller’s switching fre-
quency on the frequency spectrum. Two examples are given with frequency
modulation index mf = 25: one with high switching frequency in Fig 52 and
one with lower switching frequency in Fig 53.

22.2.1.1 Unipolar SPWM with a high switching frequency, ma=0.6

and mf=25

m_a=0.6, m_f=25, f_iterate=18.1815454538 kHz, f_switch=13.4835337088 kHz

1.0 AC voltage frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 2 4 6 8 10
[kHz]

Figure 52: Frequency domain plot for a 50 Hz AC voltage, generated with

SPWM and a high switching frequency.

80
22.2.1.2 Unipolar SPWM low Hz switching frequency, ma=0.6 and
mf=25

m_a=0.6, m_f=25, f_iterate=4.08151020376 kHz, f_switch=1.61450403625 kHz

1.0 AC voltage frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 2 4 6 8 10
[kHz]

Figure 53: Frequency domain plot for a 50 Hz AC voltage, generated with

SPWM and a low switching frequency.

22.2.1.3 Unipolar SPWM 2800 Hz switching frequency, ma=1 and

mf=12.5
In Fig 54 can be seen a Python simulation of the AC voltage from the converter
with the same control parameters as were used in the physical experiment in
Section 18.2.
ma=1, mf=12.5, f_iterate=4.25501063751 kHz, fswitch=2.81300703251 kHz ma=1, mf=12.5, f_iterate=4.25501063751 kHz, fswitch=2.81300703251 kHz
1.0
Triangular carrier 1.0 AC voltage frequency spectrum
0.5
0.0
−0.5 0.8
−1.0
0.000 0.005 0.010 0.015 0.020
Normalized amplitude

1.0
Sine references
0.6
0.5
0.0
−0.5
−1.0
0.4
0.000 0.005 0.010 0.015 0.020

40
Phase voltage, AC-side
30
20 0.2
10
0
[V]

−10
−20
−30
−40 0.0
0.000 0.005 0.010 0.015 0.020 0 2 4 6 8 10
[sec] [kHz]

Figure 54: Python simulation with the same parameters as in the SPWM ex-
periment.

81
22.2.2 Hysteresis control, bipolar switching, simulation
results
22.2.2.1 1 kHz sampling frequency

L=40mH, Vac=20V, Vdc=40 V, fsamp=1.0 kHz, fswitch=600.0 Hz

60
Phase voltage
40
20
0
[V]

−20
−40
−60
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
3
Phase curre t
2
1
0
[A]

−1
−2
−3
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.0
Refere ce curre t
0.5
0.0
[A]

−0.5
−1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]

(a) Time-domain
L=40mH, Vac=20V, Vdc=40 V, fsamp=1.0 kHz, fswitch=600.0 Hz
1.0 Phase current frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 500 1000 1500 2000
[Hz]

(b) FFT

Figure 55: Simulation results for bipolar hysteresis control, when the sampling
frequency is 1 kHz.

82
22.2.2.2 4 kHz sampling frequency

L=40mH, Vac=20V, Vdc=40 V, fsamp=4.0 kHz, fswitch=2500.0 Hz

60
Phase voltage
40
20
0
[V]

−20
−40
−60
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.5
Phase curre t
1.0
0.5
0.0
[A]

−0.5
−1.0
−1.5
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.0
Refere ce curre t
0.5
0.0
[A]

−0.5
−1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]

(a) Time-domain
L=40mH, Vac=20V, Vdc=40 V, fsamp=4.0 kHz, fswitch=2500.0 Hz
1.0 Phase current frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 500 1000 1500 2000 2500 3000 3500 4000
[Hz]

(b) FFT

Figure 56: Simulation results for bipolar hysteresis control, when the sampling
frequency is 4 kHz.

83
22.2.2.3 10 kHz sampling frequency

L=40mH, Vac=20V, Vdc=40 V, fsamp=10.0 kHz, fswitch=6300.0 Hz

60
Phase voltage
40
20
0
[V]

−20
−40
−60
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.5
Phase curre t
1.0
0.5
0.0
[A]

−0.5
−1.0
−1.5
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.0
Refere ce curre t
0.5
0.0
[A]

−0.5
−1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]

(a) Time-domain
L=40mH, Vac=20V, Vdc=40 V, fsamp=10.0 kHz, fswitch=6300.0 Hz
1.0 Phase current frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 500 1000 1500 2000 2500 3000 3500 4000
[Hz]

(b) FFT

Figure 57: Simulation results for bipolar hysteresis control, when the sampling
frequency is 10 kHz.

84
22.2.2.4 50 kHz sampling frequency

L=40 H, Vac=20V, Vdc=40 V, fsa p=50.0 kHz, fswitch=22698.0 Hz

60
Phase voltage
40
20
0
[V]

−20
−40
−60
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.5
Phase current
1.0
0.5
0.0
[A]

−0.5
−1.0
−1.5
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.0
Reference current
0.5
0.0
[A]

−0.5
−1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]

(a) Time-domain
L=40mH, Vac=20V, Vdc=40 V, fsamp=50.0 kHz, fswitch=22698.0 Hz
1.0 Phase current frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 5000 10000 15000 20000 25000
[Hz]

(b) FFT

Figure 58: Simulation results for bipolar hysteresis control, when the sampling
frequency is 50 kHz.

85
22.2.3 Hysteresis control, unipolar switching
22.2.3.1 1 kHz sampling frequency

L=40mH, Vac=20V, Vdc=40 V, fsamp=1.0 kHz, fswitch=602.0 Hz

60
Phase voltage
40
20
0
[V]

−20
−40
−60
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
3
Phase curre t
2
1
0
[A]

−1
−2
−3
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.0
Refere ce curre t
0.5
0.0
[A]

−0.5
−1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]

(a) Time-domain
L=40mH, Vac=20V, Vdc=40 V, fsamp=1.0 kHz, fswitch=602.0 Hz
1.0 Phase current frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 500 1000 1500 2000
[Hz]

(b) FFT

Figure 59: Simulation results for unipolar hysteresis control, when the sampling
frequency is 1 kHz.

86
22.2.3.2 4 kHz sampling frequency

L=40mH, Vac=20V, Vdc=40 V, fsamp=4.0 kHz, fswitch=2750.0 Hz

60
Phase voltage
40
20
0
[V]

−20
−40
−60
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.5
Phase curre t
1.0
0.5
0.0
[A]

−0.5
−1.0
−1.5
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.0
Refere ce curre t
0.5
0.0
[A]

−0.5
−1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]

(a) Time-domain
L=40mH, Vac=20V, Vdc=40 V, fsamp=4.0 kHz, fswitch=2750.0 Hz
1.0 Phase current frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 500 1000 1500 2000 2500 3000 3500 4000
[Hz]

(b) FFT

Figure 60: Simulation results for unipolar hysteresis control, when the sampling
frequency is 4 kHz.

87
22.2.3.3 10 kHz sampling frequency

L=40mH, Vac=20V, Vdc=40 V, fsamp=10.0 kHz, fswitch=7370.0 Hz

60
Phase voltage
40
20
0
[V]

−20
−40
−60
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.5
Phase curre t
1.0
0.5
0.0
[A]

−0.5
−1.0
−1.5
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.0
Refere ce curre t
0.5
0.0
[A]

−0.5
−1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]

(a) Time-domain
L=40mH, Vac=20V, Vdc=40 V, fsamp=10.0 kHz, fswitch=7370.0 Hz
1.0 Phase current frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 500 1000 1500 2000 2500 3000 3500 4000
[Hz]

(b) FFT

Figure 61: Simulation results for unipolar hysteresis control, when the sampling
frequency is 10 kHz.

88
22.2.3.4 50 kHz sampling frequency

L=40mH, Vac=20V, Vdc=40 V, fsamp=50.0 kHz, fswitch=14300.0 Hz

60
Phase voltage
40
20
0
[V]

−20
−40
−60
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.5
Phase curre t
1.0
0.5
0.0
[A]

−0.5
−1.0
−1.5
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]
1.0
Refere ce curre t
0.5
0.0
[A]

−0.5
−1.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
[sec]

(a) Time-domain
L=40mH, Vac=20V, Vdc=40 V, fsamp=50.0 kHz, fswitch=14300.0 Hz
1.0 Phase current frequency spectrum

0.8
Normalized amplitude

0.6

0.4

0.2

0.0
0 500 1000 1500 2000 2500 3000 3500 4000
[Hz]

(b) FFT

Figure 62: Simulation results for unipolar hysteresis control, when the sampling
frequency is 50 kHz.

89
22.3 Python codes for the Beaglebone Black Mi-
crocontroller
22.3.1 Unipolar SPWM

import math a s MATH

import Adafruit_BBIO .PWM a s PWM
import Adafruit_BBIO . GPIO a s GPIO
import d e c i m a l
from time import s l e e p
import time
##
GPIO . c l e a n u p ( ) ;
PWM. c l e a n u p ( ) ;

#d e f i n e a m p l i t u d e s
Ampcontrol =1; #s i n e wave r e f e r e n c e a m p l i t u d e
amptri =1; #t r i a n g l e wave a m p l i t u d e
V t r i a n g u l a r =−1∗amptri ; #s t a r t v a r d e
trimax =1∗amptri ;
t r i m i n=−1∗amptri ;

#d e f i n e r e f e r e n c e f r e q u e n c y
mf=25; #f r e q u e n c y modulation i n d e x
f s i n =50; #s i n e wave r e f e r e n c e f r e q u e n c y
f t r i =mf∗ f s i n ; #t r i a n g l e wave c a r r i e r f r e q u e n c y
s l o p e t r i a n g=f l o a t ( 2 ∗ trimax ∗ f t r i ) ;

#d e f i n e GPIO
##
r e s e t 1 ="P9_23 "
r e s e t 2 ="P9_25 " ;
##
PWMswitchA1="P9_14 "
PWMswitchA2="P9_16 "
PWMswitchB1="P9_21 "
PWMswitchB2="P9_22 "

#i n i t i a l i z a t i o n

90
f r e q =200000; #a r j u bra , i f a l l l o o p e n j o b b a r s a snabbt

PWM. s t a r t ( PWMswitchA1 , 0 , f r e q );
PWM. s t a r t ( PWMswitchA2 , 0 , f r e q );
PWM. s t a r t ( PWMswitchB1 , 0 , f r e q );
PWM. s t a r t ( PWMswitchB2 , 0 , f r e q );
##
GPIO . s e t u p ( r e s e t 1 , GPIO .OUT) ;
GPIO . s e t u p ( r e s e t 2 , GPIO .OUT) ;

d e l a y=f l o a t ( 0 . 0 1 ∗ ( 1 / f r e q ) ) ;
d e l a y=f l o a t ( 5 0 0E−9); #200 ns . bra e n l i g t a r a s h . t a r hansyn d r i v e r och modul

switchA1 =0;
switchA2 =0;
switchB1 =0;
switchB2 =0;

GPIO . output ( r e s e t 1 , GPIO . HIGH)

GPIO . output ( r e s e t 2 , GPIO . HIGH ) ;

T r i a n g u l a r d e l t a=s l o p e t r i a n g ;
T r i a n g u l a r d e l t a p r e v=s l o p e t r i a n g ;

t i m e s t a r t=time . time ( ) ;
timenow =0;

while ( 1 ) :
#V c o n t r o l=Ampcontrol ∗MATH. s i n ( 2 ∗MATH. p i ∗ d e l t a d e g ∗Ndeg∗ f s i n )
t i m e l a s t=timenow ;
timenow=time . time ()− t i m e s t a r t ;
s t e p=timenow−t i m e l a s t ;
V c o n t r o l=Ampcontrol ∗MATH. s i n ( 2 ∗MATH. p i ∗ timenow ∗ f s i n )
V c o n t r o l n e g=−1∗V c o n t r o l ;

i f V t r i a n g u l a r+T r i a n g u l a r d e l t a ∗ s t e p >trimax :
T r i a n g u l a r d e l t a=−s l o p e t r i a n g ;
T r i a n g u l a r d e l t a p r e v=T r i a n g u l a r d e l t a ;

e l i f V t r i a n g u l a r+T r i a n g u l a r d e l t a ∗ s t e p <t r i m i n :
T r i a n g u l a r d e l t a=s l o p e t r i a n g ;
T r i a n g u l a r d e l t a p r e v=T r i a n g u l a r d e l t a ;

else :

91
 T r i a n g u l a r d e l t a=T r i a n g u l a r d e l t a p r e v ;

V t r i a n g u l a r =( V t r i a n g u l a r )+( T r i a n g u l a r d e l t a ) ∗ s t e p ;

#C o n t r o l t h e s w i t c h e s i n phase−l e g A
i f Vc ontrol >V t r i a n g u l a r :
PWM. s e t _ d u t y _ c y c l e ( PWMswitchA2 , 0 ) ;
sleep ( delay ) ;
PWM. s e t _ d u t y _ c y c l e ( PWMswitchA1 , 1 0 0 ) ;
switchA2 =0;
switchA1 =100;

e l i f Vcontr ol <V t r i a n g u l a r :
PWM. s e t _ d u t y _ c y c l e ( PWMswitchA1 , 0 ) ;
sleep ( delay )
PWM. s e t _ d u t y _ c y c l e ( PWMswitchA2 , 1 0 0 ) ;
switchA1 =0;
switchA2 =100;

else :
PWM. s e t _ d u t y _ c y c l e ( PWMswitchA1 , switchA1 ) ;
PWM. s e t _ d u t y _ c y c l e ( PWMswitchA2 , switchA2 ) ;

#C o n t r o l t h e s w i t c h e s i n phase−l e g B
i f V co ntr oln eg >V t r i a n g u l a r :
PWM. s e t _ d u t y _ c y c l e ( PWMswitchB2 , 0 ) ;
sleep ( delay )
PWM. s e t _ d u t y _ c y c l e ( PWMswitchB1 , 1 0 0 ) ;
switchB2 =0;
switchB1 =100;

e l i f Vc ont rol neg <V t r i a n g u l a r :

PWM. s e t _ d u t y _ c y c l e ( PWMswitchB1 , 0 ) ;
sleep ( delay ) ;
PWM. s e t _ d u t y _ c y c l e ( PWMswitchB2 , 1 0 0 ) ;
switchB1 =0;
switchB2 =100;

else :
PWM. s e t _ d u t y _ c y c l e ( PWMswitchB1 , switchB1 ) ;
PWM. s e t _ d u t y _ c y c l e ( PWMswitchB2 , switchB2 ) ;

22.3.2 Hysteresis control

import math a s MATH

import Adafruit_BBIO .PWM a s PWM
import Adafruit_BBIO . GPIO a s GPIO

92
import Adafruit_BBIO .ADC a s ADC
import time a s time
from time import s l e e p

GPIO . c l e a n u p ( ) ;
PWM. c l e a n u p ( ) ;
#ADC. c l e a n u p ( ) ;

#d e f i n e

f e m f =50
i r e f a m p =500E−3;

r e s e t 1 ="P9_23 "
r e s e t 2 ="P9_25 " ;
r e s e t 3 ="P9_24 " ;
r e s e t 4 ="P9_26 " ;

PWMswitchA1="P9_14 "
PWMswitchA2="P9_16 "
PWMswitchB1="P9_21 "
PWMswitchB2="P9_22 "

a n a l o g P i n ="P9_33 "
v r e f p i n ="P9_35 "

#i n i t i a l i z a t i o n

f r e q =200000;

PWM. s t a r t ( PWMswitchA1 , 0, freq );

PWM. s t a r t ( PWMswitchA2 , 0, freq );
PWM. s t a r t ( PWMswitchB1 , 0, freq );
PWM. s t a r t ( PWMswitchB2 , 0, freq );

GPIO . s e t u p ( r e s e t 1 , GPIO .OUT) ;

GPIO . s e t u p ( r e s e t 2 , GPIO .OUT) ;
GPIO . s e t u p ( r e s e t 3 , GPIO .OUT) ;
GPIO . s e t u p ( r e s e t 4 , GPIO .OUT) ;
ADC. s e t u p ( ) ;

#C o n s t a n t s and v a r i a b l e s
Tole=f l o a t ( 0 . 0 5 ) ;
#Tole2=f l o a t ( 0 . 2 ) ;

EMF=0;
d e l a y=round ( ( 0 . 0 1 ∗ ( 1 / f r e q ) ) , 9 ) ;

93
d e l a y 2 =0;
t =0;

switchA1 =0;
switchA2 =0;
switchB1 =0;
switchB2 =0;

R1=1200;
R2=560;

GPIO . output ( r e s e t 1 , GPIO . HIGH)

GPIO . output ( r e s e t 2 , GPIO . HIGH ) ;
GPIO . output ( r e s e t 3 , GPIO . HIGH)
GPIO . output ( r e s e t 4 , GPIO . HIGH ) ;

t i m e s t a r t=time . time ( )
t i m e l a s t=t i m e s t a r t ;
timenow =0;

i p h = [ ] ; #empty c u r r e n t v e c t o r
i r = [ ] ; #r e f e r e n c e c u r r e n t v e c t o r

w h i l e timenow <20E−3:

timenow=round ( ( time . time ()− t i m e s t a r t ) , 6 ) ;

I r e f=round ( i r e f a m p ∗MATH. s i n ( 2 ∗MATH. p i ∗ f e m f ∗ timenow ) , 4 ) ;

p e r c e n t V o l t=round (ADC. r e a d ( a n a l o g P i n ) , 6 ) ;
V18=p e r c e n t V o l t ∗ 1 . 8 ;
Vsensor=round ( ( ( V18 ∗ (R1+R2 ) ) / R2 ) , 6 ) ;
V r e f=round (ADC. r e a d ( v r e f p i n ) ∗ 1 . 8 ∗ 2 , 6 ) ;
V d i f f=Vsensor−V r e f ;

I p h a s e=round ( ( V d i f f −f l o a t ( 0 . 0 0 9 0 2 4 ) ) / f l o a t ( 0 . 0 7 7 1 1 ) , 4 )
#I p h a s e =( V d i f f − 0 . 0 0 9 0 2 4 ) / 0 . 0 7 7 1 1 ;
#I p h a s e =665.7876∗ Vsensor −1674.0 −4.16524; #c a l c u l a t e t h e phase c u r r e n t ’ s

i f Iphase <I r e f −Tole :

switchA2 =0;
switchB1 =0;
switchA1 =100;
switchB2 =100;

94
 PWM. s e t _ d u t y _ c y c l e ( PWMswitchA2 , 0 )
PWM. s e t _ d u t y _ c y c l e ( PWMswitchB1 , 0 )
sleep ( delay )
PWM. s e t _ d u t y _ c y c l e ( PWMswitchA1 , 1 0 0 )
PWM. s e t _ d u t y _ c y c l e ( PWMswitchB2 , 1 0 0 )

e l i f ( Iphase >I r e f+Tole ) :

switchA1 =0;
switchB2 =0;
switchA2 =100;
switchB1 =100;

else :
PWM. s e t _ d u t y _ c y c l e ( PWMswitchA1 , switchA1 ) ;
PWM. s e t _ d u t y _ c y c l e ( PWMswitchA2 , switchA2 ) ;
PWM. s e t _ d u t y _ c y c l e ( PWMswitchB1 , switchB1 ) ;
PWM. s e t _ d u t y _ c y c l e ( PWMswitchB2 , switchB2 ) ;

i p h . append ( I p h a s e ) ;
i r . append ( I r e f ) ;

#p r i n t ( i p h )
#p r i n t ( i r )
p r i n t ( " Antal s a m p l e s " )
p r i n t ( len ( iph ) )

p r i n t ( timenow )
print ( percentVolt )
p r i n t ( Vsensor )
p r i n t ( Vref )
p r i n t ( switchA1 )

95
TRITA EE 2017:114

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