INOM
EXAMENSARBETE ELEKTROTEKNIK, AVANCERAD NIVÅ, 30 HP
STOCKHOLM SVERIGE 2017,
Construction of an Active Rectifier for a Transverse-Flux Wave Power Generator
OLOF BRANDT LUNDQVIST
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.
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.
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.
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
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 . . . 3113.2 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
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
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 . . . 5516.2 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 . . . 6919.1.1 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
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 . . . 8022.2 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
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 ωwave rad
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
cg m
s Group velocity of sea waves ρwater mkg3 Density of water
g sm2 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
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
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
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.
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].
ε = −dΨ
dt = −NdΦ
dt (1)
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.
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.
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
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
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
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 V1signifies the voltage signal’s fundamental component and Vk the signal’s higher harmonics.
T HDW = v u u t
P∞ k=1(V
2 k,RM S
k ) − V1,RM S2
V1,RM S2 (2)
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.
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 dIdta on the AC side is dependent on the AC side’s inductance L and on the amplitude of the DC pulse VDCfrom 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
dt =VDC
L (3)
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
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 ˆVO,1= Vˆcontrolˆ
Vtri
VDC
2 [24, p. 206].
γ =
(1 if S1 ON and S3 ON -1 if S2 ON and S4 ON
(4)
VO(γ) =
(+VDC, γ = 1
−VDC, γ = −1 (5)
Figure 5: Graph showing an AC voltage signal generated by bipolar PWM.
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 ˆVO,1 = Vˆcontrolˆ
Vtri 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].
γ =
1 if S1ON and S3 ON
0 if S1and S4ON or if S2 and S3 ON -1 if S2ON and S4 ON
(6)
VO(γ) =
+VDC, γ = 1
0, γ = 0
−VDC, γ = −1 (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
frequency modulation index is, the lower the THD is in the AC output voltage from the converter [24, p. 219].
mf = ftri
fref (8)
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].
ma= ˆvref
ˆ
vtri (9)
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
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.
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].
ES = 1
16ρgHm02 [kW h
m2 ] (10)
J = cgES[kW
m2] (11)
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.
J = g
2 · 2πfwave
ρgHm02
16 ≈ 11.51[kW
m2] (12)
Quantity Expression Unit Comment
cg 2ωg
wave
m
s Group velocity of the sea waves [37]
g 9.82 ms2 Gravitational acceleration fwave 1
6 Hz Frequency of sea waves [28]
ρ 1000 mkg3 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 ωwaveof 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.
Ψ(t) = ˆΨsin(2π
λz(t)) (13)
ε(t) = −NdΨ(t)
dt = ˆEcos(ωwavet)cos(πh
λ sin(ωwavet)) =
= Ψhπˆ
λ ωwavecos(ωwavet)cos(πh
λ sin(ωwavet))
(14)
|~I| = P
| ~U |cos(φ) (15)
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
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
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.
R = `cond ρ
Acond (16) P = RI2 (17)
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 power will be around 200 m/skW. 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].
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
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.
Figure 11: The Bea- glebone Black micro- controller which is to be used during the practical work in this thesis.
Parameter Value
CPU 1 GHz
RAM 512 MB DDR3
Flash memory 4 GB
I/O pins 65
I/O pins 8
Analog input pins 7
Table 2: Some important hardware characteris- tics for the Beaglebone Black microcontroller [2].
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.
Figure 12: Cree CAS300M12BM2 power module.
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
Table 3: Some important properties for the Cree 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
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.
Pmax= 3Iphase,RM S,maxVDC= 3600
√2900 ≈ 1.15M W (19)
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
