IN
DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS
,
STOCKHOLM SWEDEN 2019
Modelling a Novel Linear
Transverse Flux Machine and
Designing a Hysteresis Current
Controller for Power Factor
Correction
AHMED ALHAIDARI
KTH ROYAL INSTITUTE OF TECHNOLOGY
Modelling a Novel Linear
Transverse Flux Machine and
Designing a Hysteresis
Current Controller for Power
Factor Correction
AHMED ALHAIDARI
Degree Project in Electrical Energy Conversion, Second Cycle 30.0 credits
Date: October 22, 2019
Supervisor: Anders Hagnestål Examiner: Oskar Wallmark
School of Electrical Engineering and Computer Science Swedish title: Modellera en linjär maskin och designa en hysteresströmstyrenhet för effektfaktorkorrigering
iii
Abstract
In this thesis, the basics of electromagnetic theory for wave-energy conversion are reviewed, some of the characteristics of the ocean wave are investigated, some of the power take-off (PTO) systems are introduced, and details about linear permanent magnetic machines, in particular, are discussed. The thesis aims to model the novel linear transverse flux machine designed by Anders Hagnestål and to build hysteresis current controller for power factor correc-tion. Although this machine is expected to have high performance in terms of efficiency, it also exhibits a strong mutual interaction between the three phases of the machine. Thus, simplification of the actual model of the machine is im-posed to mitigate the complexity of the machine and facilitate the Simulink model. Four cases of the double band hysteresis control are studied. The cur-rents seem to be responding properly to the control scheme; however, software and hardware programming of a microprocessor would be preferable to ensure the applicability of the control strategy in a real environment.
Keywords: double band hysteresis current controller, linear machine,
mag-netic circuit model, power take-off, transverse flux permanent magnet syn-chronous machine, wave energy conversion.
Sammanfattning
I detta examensarbete undersöks elektromagnetisk teori och havsvågors egen-skaper. Några energiomvandlingssystem introduceras och permanentmagneti-serade maskiner diskuteras i detalj. Syftet med avhandlingen är att modelle-ra en ny linjär tmodelle-ransversalflödesmaskin som är designad av Anders Hagnestål och att bygga en hysteresbaserad strömkontroll för denna. Även om maskinen förväntas prestera bra, uppvisar den också en stark ömsesidig magnetisk inter-aktion mellan de tre faserna. För att kunna hantera detta problem och därmed kunna genomföra simuleringar införs en förenklad elektromagnetisk modell av maskinen. En strömkontroller har implementerats i Simulink, där fyra fall av dubbelbandshystereskontroll studerats. Resultaten från simuleringarna vi-sar att strömkontrollern fungerar. Nästa steg i projektet är att utföra mjukvaru-och hårdvaruprogrammering av en mikrokontroller för att testa systemet i en verklig miljö.
Acknowledgement
First of all, I dedicate a special thanks to my beloved father, who died during the master course, for his unconditional support throughout my study period. His spiritual words and continuous involvement were very essential for keep-ing me on track whenever I feel overwhelmed. I am also grateful to my mother and siblings for their kindness, patience and tenderness.
No words can describe my gratitude to my wife who sacrificed her time for being with me throughout my master course. I owe her my endless appre-ciation and love.
I express my gratitude to my supervisor Anders Hagnestål who has pro-foundly shaped my thought about the field of wave energy conversion. His sincere advices and valuable comments have enriched my personal and work experience. I am also thankful to my examiner Oskar Wallmark for his help-ful remarks, comments, and questions about the thesis. Also, I would like to extend my thanks to the course coordinator Cristina La Verde who provided me with unlimited assistance whenever needed.
Lastly, many thanks to my uncle Mohammed Altairi for his appreciable guidance, and all of my friends for being caring.
Ahmed Abdullah Alhaidari
October 2019
1 Introduction 1
1.1 Background . . . 1
1.2 Aim of The Thesis . . . 2
1.3 Outline of The Thesis . . . 2
2 Review of Electromagnetic Theory 4 2.1 Magnetic Materials . . . 4
2.2 Ampere’s Law . . . 7
2.3 Faraday’s Law of Induction . . . 9
2.4 Core losses . . . 10
2.4.1 Hysteresis Losses . . . 10
2.4.2 Eddy current losses . . . 11
3 Power Electronic System 13 3.1 Semiconductor Devices . . . 14 3.1.1 Diodes . . . 14 3.1.2 Thyristors . . . 16 3.1.3 Transistors . . . 17 3.2 Power converters . . . 18 3.3 Switching Losses . . . 19
4 Wave Energy Conversion 23 4.1 Characteristic of ocean waves . . . 23
4.2 Power Take-Off Devices for Wave Energy Extraction . . . 25
4.2.1 Oscillating Water Column (OWC) . . . 26
4.2.2 Archimedes Wave Swing (AWS) . . . 27
4.2.3 Heaving Buoy (Point Absorbers) . . . 28
4.3 Linear Electrical Machines . . . 29
4.3.1 Transverse Flux Permanent Magnet Synchronous Ma-chines (TFPMSM) . . . 30
CONTENTS vii
4.3.2 Operating Principle of the Linear Variable Reluctance Permanent Magnets Synchronous Machines
(LVRP-MMs) . . . 37
4.4 Challenges in WEC . . . 39
5 Modelling a Linear Transverse Flux Permanent Magnet Machine (TFPMSM) 42 5.1 General Dynamic Model for linear PMSM . . . 43
5.2 Magnetic Circuit Model of the TFPMSM . . . 44
5.2.1 The stator current . . . 46
5.2.2 The Magnetic Flux . . . 47
5.2.3 The Phase and Leakage Reluctance . . . 48
5.2.4 The Magnetomotive Forces of the Permanent Magnets 50 5.2.5 The Induced Voltage . . . 50
5.3 Simplified model of Linear TFPMSM . . . 55
6 Hysteresis Current Controller for Power factor Correction 58 6.1 Single Band Hysteresis Current Controller (SBHCC) . . . 58
6.2 Double Band Hysteresis Current Control (DBHCC) . . . 60
6.2.1 Verification of the Developed DBHCC on the Simpli-fied Model of Linear TFPMSM . . . 65
7 Future work and conclusion 88 7.1 Furture Work . . . 88
7.2 Conclusion . . . 89
2.1 The regions of domain on the B-H characteristic curve: (1) the non-linear region, (2) the linear region ,and (3) the saturation
region). . . 6
2.2 A generic B-H characteristic curve shows the hysteresis loop. . 7
2.3 A ferromagnetic core with N-turns conductors to illustrate the production of the magnetic flux using Ampere’s law. . . 8
3.1 A block diagram of a power electronic system. . . 13
3.2 A diode: (a) The symbol of the diode. (b) The i − v Charac-teristic curve of the diode. . . 14
3.3 A diode: (a) Operating in forward biased mode. (b) Operating in reverse biased mode. . . 15
3.4 A generic symbol for the thyristor. . . 16
3.5 A symbol for an ideal switch. . . 17
3.6 The symbol of N-Channel MOSFET. . . 18
3.7 A comparison between some of the controllable switches ca-pabilities in terms of voltage ratings, current ratings and fre-quencies. The information in the figure are taken from [9]. . . 19
3.8 Half-bridge Module of the power converter for the TFPMSM. . 20
3.9 A generic switching characterestics of a semiconductor device. 21 4.1 A conceptual picture for wave energy conversion process. . . . 25
4.2 The operation principle of the oscillating water column (OWC). 26 4.3 The basic parts of the Archimedes Wave Swing (AWS) for un-derstanding the operating principle. . . 27
4.4 (A) The machine is immersed in the water. (B) The machine is hold above the water surface level. The concept has been inspired by [16]. . . 28
4.5 The no load induced emf for a linear PMSM when the trans-lator is directly coupled to a monochromatic ocean wave. . . . 30
LIST OF FIGURES ix
4.6 The three different airgap flux direction for different PMSM topologies: (a) radial flux (b) axial flux (c) transverse flux. . . 31 4.7 The basic transverse flux machine. . . 32 4.8 One phase of the flux switching transverse flux machine (FSTFM). 34 4.9 A single phase double rotor transverse flux machine (DRTFM). 35 4.10 A cross section of the KTH transformer TFM, refer to [6] for
more details. . . 36 4.11 The basic double-sided TFM. . . 37 4.12 A cross section of a single phase VHM. . . 38 4.13 Part of the linear Vernier hybrid machine (VHM) showing the
useful forces on the translator. . . 40 5.1 The steady-state equivalent circuit for a single phase
perma-nent magnet synchronous motor. . . 43 5.2 The magnetic circuit model of linear transverse flux machine. . 45 5.3 The stator current, Ia, in terms of flux, Φaand postion, z. . . . 47 5.4 The variation of the reluctance of the linear TFPMSM with
respect to the stator current. . . 49 5.5 Simulink model of novel linear transverse flux permanent
mag-net synchronous machine (TFPMSM). . . 57 6.1 The behavior of the controlled current for a SBHCC. . . 59 6.2 The four possible switching cases with three switching states
+Ud, 0, −Ud. . . 60 6.3 The DBHCC tolerance band zones. . . 62 6.4 The actual current (i∗) waveform for the developed DBHCC
for the linear TFPMSM. . . 65 6.5 A generic picture shows the 90o out-of-phase actual current
with respect to the emf and the proposed reference current for emf tracking. . . 67 6.6 The three phases stator terminal voltages with 1 to 2 inner to
outer tolerance bands ratio. . . 69 6.7 The three phase armature currents with 1 to 2 inner to outer
tolerance bands ratio. . . 69 6.8 The stator of phase a within the tolerance bands with 1 to 2
inner to outer band ratio. . . 70 6.9 The stator of phase b within the tolerance bands with 1 to 2
inner to outer band ratio. . . 70 6.10 The stator of phase c within the tolerance bands with 1 to 2
6.11 The airgap flux of the three phases for the case of 1 to 2 inner to outer band ratio. . . 71 6.12 The leakage flux of the three phases for the case of 1 to 2 inner
to outer band ratio. . . 72 6.13 The three phases stator terminal voltages with load disturbance
on phase a. . . 74 6.14 The three phase armature currents with load disturbance on
phase a. . . 74 6.15 The stator of phase a within the tolerance bands with load
dis-turbance on phase a. . . 75 6.16 The stator of phase b within the tolerance bands with load
dis-turbance on phase a. . . 75 6.17 The stator of phase c within the tolerance bands with load
dis-turbance on phase a. . . 76 6.18 The airgap flux of the three phases with load disturbance on
phase a. . . 76 6.19 The leakage flux of the three phases with load disturbance on
phase a. . . 77 6.20 The three phases stator terminal voltages with larger inner band. 79 6.21 The three phase armature currents with larger inner band. . . . 79 6.22 The stator of phase a within the tolerance bands with larger
inner band. . . 80 6.23 The stator of phase b within the tolerance bands with larger
inner band. . . 80 6.24 The stator of phase c within the tolerance bands with larger
inner band. . . 81 6.25 The airgap flux of the three phases with larger inner band. . . . 81 6.26 The leakage flux of the three phases with larger inner band. . . 82 6.27 The three phases stator terminal voltages with smaller inner
band. . . 84 6.28 The three phase armature currents with smaller inner band. . . 84 6.29 The stator of phase a within the tolerance bands with smaller
inner band. . . 85 6.30 The stator of phase b within the tolerance bandswith smaller
inner band. . . 85 6.31 The stator of phase c within the tolerance bandswith smaller
inner band. . . 86 6.32 The airgap flux of the three phases with smaller inner band. . . 86 6.33 The leakage flux of the three phases with smaller inner band. . 87
List of Tables
2.1 The magnetic characteristics of the materials . . . 5 4.1 Classification of the wind generated ocean surface wave [12]. . 24 6.1 The Double Band Hysteresis Current Control (DBHCC) Zones 63 6.2 The parameters for the simulation of the DBHCC . . . 66
Chapter 1
Introduction
A general background knowledge related to the master thesis topic with details about the content of each chapter will be provided in the part of the thesis.
1.1
Background
The global demand for electricity increased by 4% in 2018 to reach 23000 TWh/year [1]. The heat and cold waves hitting some nations thought to be one of the reasons behind this rise where air-conditioning is needed. About one quarter of the electrical power production came from renewable resources [1]. The main renewable energy contributors are the hydropower, the solar and the wind while the wave power is still at its development stage [2]. The wave power potential was estimated to be about 32000 TWh per year [3].
To take-over more than half of electricity production generated from un-sustainable energy sources and to diversify the un-sustainable sources, many re-searches started to investigate the wave energy capturing techniques. The first patented wave energy converters were recorded in 1799 in France [3]. Since the early beginnings of wave energy conversion to electricity, conventional ro-tating electric machines have been the means for converting the wave power to electrical power. The low reciprocating motion of the wave requires a gearbox, hydraulic system, pneumatic system or other mechanical device to drive the high-speed rotating machines [4][5]. Considerable energy losses occur during the conversion from mechanical to electrical energy through these devices.
Recently, Anders Hagnetål has invented a linear transverse flux machine which is a direct drive machine to replace the need for a mechanical interface. This novel linear transverse flux permanent magnet machine (TFPMSM) has a predicted efficiency of about 98% [6]. Although the invented machine shows
high potential in wave power applications, the reactive power in the machine about 50% to 60% of the total power. This means that the machines need a power factor correction, and hence the stress is placed on the power converters and how they are modulated.
1.2
Aim of The Thesis
This thesis aims to study the model of the novel linear transverse flux perma-nent magnet synchronous machine (TFPMSM) and investigate the feasibility of the double band hysteresis current controller (DBSCC) scheme for power factor correction using Simulink software.
1.3
Outline of The Thesis
This master thesis constitutes of 7 chapters including this chapter. The content of each chapter is exhibited in order as follows:
Chapter 2 The essential electromagnetic theory which forms the basis of the
electrical machines is reviewed in this chapter. It starts by exploring the prop-erty of the materials focusing on their susceptibility to a magnetic field. Then the chapter proceeds to explaining the laws which relate the magnetic field to the electric field and vice versa, Ampere’s law and Faraday’s law of induction. Also, it investigates the core losses initiate when the materials are exposed to a magnetic field and propose methods to reduce the negative impacts of the energy dissipated in the machine’s components.
Chapter 3 The focus here is on basic elements of the power electronic
sys-tem and in particular the components of the power converter proposed for the control scheme in the chapter 6. The characteristics of each component of the half-bridge converter, the diodes and the switches, are outlined. The chapter ends by studying the power losses during the turn-on and turn-off process of the switching devices.
Chapter 4 This chapter illustrates the wave energy conversion process by
describing some of the devices intended for capturing the power of the wave. It begins with laying out the characteristic of the ocean surface wave and then proceeds with explaining the concept of some of the most recognized power take-off devices. Also, the chapter introduces the linear electrical machines
CHAPTER 1. INTRODUCTION 3
with more details about the structure of the novel transverse flux machines topologies. The operating principle of the linear variable reluctance machine that shows how the forces exerted on the translator develop is explained in this part. Last section points out the challenges facing the progress of the extraction of the wave energy.
Chapter 5 The general dynamic model for linear permanent magnet
syn-chronous machine is discussed in this part. In particular, this chapter identify the three-phase magnetic circuit model for the linear transverse flux machine developed by Anders. It explains how the stator current of the machine is re-lated to the developed magnetic flux and the position of the translator. Also, this chapter illustrates how the reluctance of changes with both the current and the translator’s position. The mathematical relations between all of the ma-chines elements are stated. The voltage model of the TFPMSM is derived and then some simplifications on the model has been introduced. The simplifed model is used as the reference for the Simulink analysis for this report.
Chapter 6 The hysteresis current controller concept is explained in this
chap-ter. The chapter start by explaing the hysteresis control. First, the basic single band hysteresis current controlled has been introduced. Then, more details about the double band hysteresis current controller (DBHCC) and why it has been chosen for this machine are being discussed. The steps required for im-plementing this method is detailed in this part. The feasibility of this control scheme on the linear TFPMSM has been examined in this part by simulating four different cases using Simulink software.
Chapter 7 This chapter discusses the future work and highlights some
con-cerns that might need to be investigated. It also summaries the main points of the report.
Review of Electromagnetic
The-ory
Electrical power conversion in the electrical machines are based on the inter-action between the electrical and the magnetic field. For machines operated in motoring mode, the conductor that carries a current is placed in the mag-netic field which induces a force that govern the motion of the rotor and the translator for the rotating and linear prototype respectively. In the generator action, a voltage within a moving conductor is developed due to its presence within a magnetic field [7]. This chapter provides the reader with some back-ground knowledge about the behavior of the magnetic materials undergoing magnetization and also introduces the basic electromagnetic theory needed for understanding the power development process in electrical machines.
2.1
Magnetic Materials
Different materials have different magnetic properties. The magnetic charac-teristics of materials is identified by the relation between the magnetic flux density B(W b/m2, T esla) and magnetic flux intensity H(A.t/m)
~
B = µ ~H (2.1) where the notation µ represents the permeability of the materials. This mag-netic permeability is composed of the free space permeability (µ0) which has a constant value of 4π · 10−7(H/m), and the relative permeability (µr) which is a dimensionless constant that varies with the type of the magnetized material. The relation between both of them is given by equation 2.2.
CHAPTER 2. REVIEW OF ELECTROMAGNETIC THEORY 5
Table 2.1: The magnetic characteristics of the materials Classification Relative permeability Degree of Magnetizeability Example
superconducting µr = 0 perfect magnetic insulator some elements and com-pounds at at the critical temperature.
paramagnetic µr = 1 + ; > 0 very weak and induces a mag-netic field in the same direc-tion of the applied one causes attraction force [8]
Air which has a relative per-meability (µr = 1.0000004) diamagnetic µr = 1 − ; > 0 very weak and induces a
mag-netic field in the opposite di-rection of the applied one causes repulsion force [8]
copper, lead, and silver nonmagnetic µr = 1 exhibit no magnetic property Vaccum
ferromagnetic µr 1 very high where most of the magnetized core of electri-cal machines and transform-ers are made of
iron is the most common ex-ample of this class
µ = µ0µr (2.2) A linear relation between the magnetic flux density (B) and the magnetic flux intensity (H) implies that the permeability is constant and can be calcu-lated from the slope of the B-H curve. This is the case for vacuum which has a relative permeability µr of 1. In fact, most materials exhibit a non-linear behavior on the B-H curve. The only exception from this rule is the super-conductors which are recognized as magnetic insulator with a zero relative permeability. Thus, machines designers are required to have a critical under-standing of what happens to materials when exposed to an external magnetic field. Table 2.1 summaries some of the magnetic characteristics of the mate-rials.
The ferromagnetic materials are of special interest in the construction of the electrical machines since the iron or steel, which are among this category, are most likely used materials for the stator cores and the translators/rotors in the linear and rotating machines prototypes. Although these materials ex-hibit high magnetization capability, their magnetic properties face significant
changes at the Curie temperature. For the electrical iron and silicon core iron, the Curie point is within 760oC − 800oC. In electromagnetic systems such as the electrical machines, many important magnetic properties should be care-fully investigated before building the machines so that the system behave as expected [8]. The most crucial ones are identified as follows:
• The materials temperature: the turning point of the magnetic properties of the permanent magnets.
• The magnetic saturation point: over which the increase in the magnetic force, the magnetic field intensity, causes a small variations to the mag-netic flux density. At the saturation level, the magnetizable materials behave like a non-magnetic materials. The magnetic flux density then become linearly related to the magnetic flux intensity.
• The hysteresis characteristics: the normal behavior of the magnetic ma-terials when the mama-terials encounter a magnetic field. Typically, there exists three region on the B-H curve that characterize the magnetic ma-terials as illustrated in figure 2.1.
Figure 2.1: The regions of domain on the B-H characteristic curve: (1) the non-linear region, (2) the linear region ,and (3) the saturation region).
A general B-H characteristic curve shown in figure 2.2. The enclosed area within the B-H curve changes according to the materials crystal structure.
CHAPTER 2. REVIEW OF ELECTROMAGNETIC THEORY 7
When magnetizing a material for the first time by applying a positive magnetic force (+H), the materials follow the virgin curve that start at the origin of the B-H curve (B = 0, H = 0) until the maximum magnetic flux density (Bmax) is reached. However, exposing the material to a circulating magnetic flux in-tensity form a hysteresis loop bounded by the positive and negative residual flux density (Br) along the vertical axis and the coercive flux intensity (±Hc) along the horizontal axis. The excited material acquires this residual flux den-sity, Br, at a zero magnetic flux intensity. To retain the original starting point on the B-H curve and demagnetize the material, a coercive force equal in mag-nitude to that of Hcneed to be applied with the proper direction to cancel the residual flux effect.
Figure 2.2: A generic B-H characteristic curve shows the hysteresis loop.
2.2
Ampere’s Law
Ampere’s law state the closed loop integral of the magnetic field along a de-fined path equals to the current enclosed by that path. The law is represented mathematically using either B or H as given in equation 2.3 and 2.4 respec-tively.
I ~ B · ~dl = µIen (2.3) I ~ H · ~dl = Ien (2.4) Where Ienis the electrical current enclosed by the path of integration, and thedl is the length of the amperian loop in the direction of integration which is~ aligned with the direction of the produced flux intensityH. To understand the~ flux production within the stator core for a machine, simple conductors with N turns surrounded by a ferromagnetic core is used for this purpose as illustrated in figure 2.3.
Figure 2.3: A ferromagnetic core with N-turns conductors to illustrate the production of the magnetic flux using Ampere’s law.
The current flows into the page produces a flux in the clockwise direction. Assuming that no leakage flux exists outside the ferromagnetic core, which means that the region of operation on the B-H characteristic curve is within the linear region, region 2, in figure 2.1, implementing ampere’s law give a measure to the intensity of the flux through the core. The path of integration depends on the geometry of the core which can be manipulated to direct the
CHAPTER 2. REVIEW OF ELECTROMAGNETIC THEORY 9
flux as desired, which is one of the way for concentrating the flux in the sta-tor cores. For the proposed shape in figure 2.3, performing the closed loop integration give the results in equation 2.5.
H = N I
lc (2.5) where lcrepresent the mean circumference of the core which can be a rectan-gular (H l = xy) as for the BTFM as well. However, the path length varies with the core shape which could be circular(H l = 2πr) like in the some pf rotating machines or it might have other shapes.
The total flux for a uniform flux distribution is equal to the magnetic flux density multiplied by the cross section area of the core as in equation 2.6.
Φ = B · A (2.6) where Φ is the total flux within the magnetized core, A is core’s cross sectional area. In case of unequal distribution of the flux, the integration of the magnetic flux density over the perpendicular surface area should be considered for total flux calculation as given by equation 2.7.
Φ = Z
~
B · ~dA (2.7) The equations presented in this section gives the essential knowledge for finding the magnetic circuit model of the electrical machines.
2.3
Faraday’s Law of Induction
A magnetic field that is varying with time induces voltages in the coil presence in it even if the conductor ending is not shorted or connected to an electrical circuit component. The rate of change of the magnetic flux determines the magnitude of that induced voltages. This is known as the Faraday’s law of induction, and the general form of the law is given by equation 2.8. The direc-tion of the induced electromagnetic force (emf) is such that the flux generated by a purely inductive current driven by this emf is opposing the change of the flux that induces it. Hence, a negative sign in mathematical representation of Faraday’s law indicates this principle which is called Lenz’s law. In some electrical machines books, the sign is not included in Faraday’s equation and hence in this report
emf = dΨ dt = N
dφ
where emf is the voltage induced in the wire and dΨdt is the rate of change of the flux linkage attached to that wire. For the armature winding, the coils may not experience the exact same induced emf if the variation of the magnetic field is not equally distributed through the stator core. This may exist in a high leakage flux machines like the TFM, and if that is the case then Faraday’s law can be re-written as in the following equation:
emf = dΨ dt =
d(PNi=1φi)
dt (2.9) where the termPNi=1φi) is the sum of the flux on each turn of the armature winding.
2.4
Core losses
Losses in the stator core which most likely made of iron develops due to its exposure to a time varying magnetic field. There are two type of core losses: The eddy current losses and the hysteresis losses. These losses reduces the efficiency of the machine. In fact, they cause a rise in the temperature of the core material, and hence understanding how to counteract their effect on the machine is of high importance [7]. In this section, these two losses will be discussed.
2.4.1
Hysteresis Losses
The area enclosed by the B-H curve in figure 2.2 is proportional to the hystere-sis losses for one magnetic period. The magnetized material, iron for example, reorient its domains to become aligned with the direction of the magnetic field it is exposed to. This process requires an external source of energy to make it happens. When a time varying current is applied in a wire around a core, it produces a magnetomotive force (mmf/MMF) which generates a torque that aligns the magnetic domains with the magnetic field. Increasing the current in the conductor results in higher magnetomotive force, and thus larger energy stored in the core until the saturation point is reached. This concept is adapted from Ampere’s law explained earlier in this chapter, and hence the hysteresis loop develop which are characterized by the B-H curve of a given material [7]. For a sinusoidal current, this hysteresis loss is expressed by the following equation [8]:
CHAPTER 2. REVIEW OF ELECTROMAGNETIC THEORY 11
where Ph,l(W ) represents the hysteresis power loss, βh(J/m3) is the Steinmetz hysteresis coefficient that are specified by the magnetized material, f is the fre-quency of the time varying flux through the material volume, Bmaxa (W b/m2) is the maximum flux density with Steinmetz exponent a ranges from (1.5-2.0), and Vmm(m3) is the volume of magnetic material of the core.
2.4.2
Eddy current losses
Beside the fact that the time varying magnetic flux induces a useful voltage in the armature coils, it also induces a harmful voltage within the material of the core. This induced voltage similar in concept to that explained by Faraday’s law causes a current to circulate within the core which causes energy losses known as eddy current losses [7]. Two factors govern the amount of power dissipation:
1. The current loop’s size and shape within the core. 2. The resistivity of the material of the core.
If the magnetized core of a machine is large then the induced voltage due to the variation of the flux is higher and hence the current swirls within the magnetized material will be larger. Since the power dissipation is directly propertional to the to the square of the current, this machine will experience high losses especially if the core’s metal has a low resistivity [7].
There are two ways to reduces the eddy current losses, one related to the construction of the core and the other one related to the property of the core material. These methods are shown respectively in the following list:
1. Laminating the material of the core: the core is usually built up of small laminated sheets of iron. The thinner these laminations are the better the eddy current reduction. The laminations reduce the current paths in the material core, and hence lower the power dissipation. It has proven its effectiveness in both electrical machines and transformers where al-most no alterations in the magnetic property of the magnetic material are casued by this method [7]. However, in some linear machines where the mechanical construction is weak, this method may even cause an increase in the overall frailty of the machines’ structure .
2. Choosing a material with high resistivity: to increase the electrical resis-tivity of the core material, silicon is added in that material. The induced voltage will be higher than the current flowing in the core, and hence
dissipated power will be lower in the core. Although the resistivity of the material can be increased by a factor of 4 by adding silicon, this method is not sufficient by itself.
The energy dissipation in the ferromagnetic core causes the material a rise in the temperature of of the core. Assuming that a sinusoidal magnetic flux is used to excite the machine and neglecting the demagnetization effect due to the opposing field from the eddy currents and the saturation effect, the following equation can be used to express the eddy current losses [8]:
Pe,l = βef Bmax2 d 2
tVmm (2.11) where Pe,l(W ) represents the eddy current losses, βe(J/m3) is a constant of proportionality decided the based in the material core, f (Hz) is the frequency of the changing flux, Bmaxa (W b/m2) is the maximum flux density, dt is the thinkness of the lamination, and Vmm(m3) is the volume of the core.
Chapter 3
Power Electronic System
In this project, the power electronic system is mainly to control the stator cur-rents of the linear TFPMSM and align their phases with the induced emf so that the output power factor become as close as possible to unity.
The power electronic system is used to shape and control the input or the output voltages and currents to the system so that they meet the mechanical load requirements. In other words, it conveys the electrical energy in a way that the wave energy converter is optimally operated. A block diagram illustra-tion of the power electronic system is shown in figure 3.1. The power factor of the input power and the output power of the power electronic system are able to mutate depending on the processing method used to control the power flow. Hence, power electronic systems are widely used to change the voltage and current amplitude and frequency to match the mover speed and the force re-quirement of the electrical machine. Normally, the output voltages or currents are measured and compared to reference values with desired characteristics. The deviation of the actual values are processed using digital signal processors and/or linear integrated circuits to be controlled by the semiconductor devices.
Figure 3.1: A block diagram of a power electronic system.
3.1
Semiconductor Devices
The power electronic systems can be constructed from one or several semi-conductor devices.They can be fit into three categories based on their ability to switch on and off : diodes, thyristors and transistors. In the following sec-tions, the characteristics of these semiconductor devices will be investigated.
3.1.1
Diodes
The symbol and the i − v characteristic curve of a basic diode is show in figure 3.2. Diodes has two operational regions based on the applied voltage in relation of the cathode and anode points:
Figure 3.2: A diode: (a) The symbol of the diode. (b) The i − v Characteristic curve of the diode.
• Forward biased: when a sufficiently high voltage is applied in the for-ward direction, the diodes conduct. They can be considered as switches being turned on. The normal forward voltage that can turn the diode
CHAPTER 3. POWER ELECTRONIC SYSTEM 15
on ranges from 0.3V-1V depending on the type of diodes used for the application.
• Reverse biased: in this state, the diodes are ideally considered as open circuit until the applied voltage reaches its break down value which varies based on the manufacturer design of the diode. The break down voltages ranges from 50V to few hundred kV. Proper diodes should be selected based the on the application that are needed for. The charac-teristics of the diodes in both modes, forward and reverse mode, is pre-sented in figure 3.3.
Figure 3.3: A diode: (a) Operating in forward biased mode. (b) Operating in reverse biased mode.
There is a transient state that some diodes require during their turning off process to discharge the energy stored in them during the turn on process. It is called a reverse-recovery time (trr). However, the power converter used for Anders’s transverse flux machine project, overcome the negative consequences of having reverse recovery current, such as over heating. According to the data sheet, the build in diodes in the half-bridge converter have zero reverse recovery current . Also, the turn on voltage (Von) for this specific diodes range between 1.6V to 2V where the highest switch on values are measured at a junction temperature of 150oC.
3.1.2
Thyristors
A thyristor is a semiconductor device where the flow of the current from the anode to cathode of the device is allowed by a positive current signal applied to its gate. The gate pules can trigger the on-state of the device; however, to turn-off the device a reverse biased voltage should be applied. Hence, it has almost the same characteristics as the diode except the advantage of controlling the current through the device. The turned-on voltage drop ranges from 1V to 3V . Thyristors have two breakdown voltages that are specified by the manufacturer: the forward voltage breakdown and the reverse voltage breakdown. The former measures the ability of the thyristor to withstand the forward biased voltage applied on the device to prevent any severe damages to the device, and the latter is similar to that of the diode [9]. A generic symbol of an ideal thyristor is shown in figure 3.4.
Figure 3.4: A generic symbol for the thyristor.
There are many types of the thyristors classified based on the following characteristics: the voltage and current rating, the time it takes for the thyristor to block the current, and the rate at which the voltage and the current build up during the off-state and on-state respectively. Some of the thyristors classes are given in the following list:
• Converter thyristor. • Inverter-grade thyristor. • Light activated thyristor.
CHAPTER 3. POWER ELECTRONIC SYSTEM 17
• Gate assisted turn-off thyristor (GATT).
• Asymmetrical silicon-controlled rectifier (ASCR). • Reverse conducting thyristor (RCT).
• Gate turn-off thyristor (GTO). • MOS-controlled thyristor (MCT).
Other types also exist and the selection of the proper thyristors depend on the application [9].
3.1.3
Transistors
Transistors are semiconductor devices that can be switched on and off by con-trol signals. The transistors and some types of thyristors, which can be turned-off by their gates, are called controllable switches. The first term controllable comes from the ability to control the terminal of the semiconductor devices by control signals which enable them to behave like the circuit breakers used for turning on and off the light in a room, for example. A generic symbol for a controllable switch is shown in figure 3.5
Figure 3.5: A symbol for an ideal switch.
The three most recognized transistors are the bipolar Junction Transis-tors(BJTs), the insulated gate bipolar transistors (IGBTs), and the metal-oxide-semiconductor field effect transistors (MOSFETs). The power converter used for Anders’s novel TFM machine adapt the latter. Thus, brief details about the MOSFETs in the following paragraph.
A Metal-Oxide-Semiconductor Field Effect Transistor (MOSFET) is a volt-age controlled transistor. This means that the device can be turned on/off by
applying a voltage pulse on its gate. When the gate to source voltage (VGS) is higher than or equal to the threshold voltage (VGS(th)), the device turns on ;oth-erwise, if that condition has not been met or a voltage lower than the threshold is applied then the device turns off. Through this process, the switching on and off of the MOSFET’s gate, the desired output can be achieved [9]. The symbol of this device is shown in figure 3.6.
Figure 3.6: The symbol of N-Channel MOSFET.
MOSFETs are known for their high switching frequencies in comparison with the other semiconductor switches as shown in figure 3.7. Another advan-tage of the MOSFETs is that they can be easily paralleled because the on-state resistance increases as the temperature of the MOSFET increases. This means that when one of the paralled MOSFETs heat up, the current follows the other low resistive path which then heat up again and reach a balanced state where all on-state resistances for the devices become equal. However, the voltage ratings of the MOSFETs are limited due to the fact that the on-state resistance of the devices increases significantly with their blocking voltage. Some MOS-FETs has a voltage rating above 1000V at the expense of smaller current rating at the range of 100A [9].
3.2
Power converters
The power converter is a combination of semiconductor devices aimed to con-vert the electrical power from AC to DC, DC to AC, or keep the same form but with variable magnitude, phase and/or frequency of the targeted output. A switch mode voltage source converter is adapted for TFPMSM to convert the varying frequency to grid frequency and to correct the phase angle of the
CHAPTER 3. POWER ELECTRONIC SYSTEM 19
Figure 3.7: A comparison between some of the controllable switches capabil-ities in terms of voltage ratings, current ratings and frequencies. The informa-tion in the figure are taken from [9].
current to approach a unity power factor. Several topologies of the power con-verters can be found in [9] and more details about the power converter for the TFM can be attained in [10][11].
Wave energy conversion requires the presence of the power converters in two steps: the first one to control the output of the electrical machine and the second one to connect the system to the power grid.
Two power modules, half-bridges, paralleled to form a full-bridge con-verter used for the power factor correction of ATFM as explained in chapter 6. The controllable switches of the actual power module built at KTH laboratory are of MOSFETs type and the diodes are of zero reverse recovery current. This module is shown in figure 3.8.
3.3
Switching Losses
The power from the control signals are dissipated in the semiconductor devices which may cause irreversible damages to the switches and lead to changes in their expected physical behavior. This may also damage the transverse flux machine components. However, the dissipated power in the controllable
semi-Figure 3.8: Half-bridge Module of the power converter for the TFPMSM. conductor switches is of generic nature [9].
To understand how energy develops in the controllable power switches dur-ing the transient from the on-state to the off-state or vice versa, what happen during the switching instances will be examined.
When a positive signal is sent to the controllable switch’s gate, the current start to flow through the switch while the voltage across the switch is still high and start to decrease afterward. The time for the voltage to reach its lowest value during the on-state is called the voltage fall time (tvf), and the time for the current to reach its highest value during this interval is called the current rise time (tir). During this transient time, the power start to dissipate in the switches and this power can be estimated from figure 3.9. The approximate measurement of the energy losses during the on-state period for the switch can be calculated from the waveform curves in figure 3.9 as follows:
WL,on = 1 2VdcIL(tvf + tir) = 1 2VdcILt(on)cond (3.1) Where,
• WL,on: is the energy dissipation during the on-state.
CHAPTER 3. POWER ELECTRONIC SYSTEM 21
• t(on)cond = tvf + tir: is the total on-state transition period where both
voltage and current over the switches are conducting simultaneously. • IL: is the current flowing through the load.
Figure 3.9: A generic switching characterestics of a semiconductor device. The power loss during the on-state switching interval can be calculated by integrating the dissipated energy as follows:
PL,on =
Z Ts−t(on)cond
t(on)cond
WL,ondt (3.2)
Where,
• PL,on: is the power dissipation during the on-state
• Ts: is the switching period for the signal sent to the switch’s gate. Likewise, when the gate of a controllable switch receives a negative signal, the voltage start to rise to its maximum value during a period that is called the voltage rise time (tvr). At the same time, the current is still conducting and then start to decline during a period of time called the current fall time (tif). The energy dissipated in the switching during the turn-off transition period can be calculated in a similar way to the WL,on as follows:
WL,of f =
1
2VdcIL(tvi+ tif) = 1
During the off-state transition period, the power dissipated in the switches can be calculated by integrating the energy loss through the same time as fol-lows:
PL,of f =
Z Ts
Ts−t(of f )cond
WL,of fdt (3.4)
What worth investigating is the average switching power losses PL,avg
dur-ing the switchdur-ing transition period (Ts).
From the total average energy dissipation (WL = WL,on + WL,of f = VdcIL(t(i,v)cond
2 ) and the total conducting time t(i,v)cond = t(on)cond + t(of f )cond,
the average dissipated power can be calculated using the following equation: PL,avg = (
VdcIL
2 )(t(i,v)cond)fs (3.5)
• PL,avg: is the average power dissipation during the switching period
• fs = T1
s: is the switching frequency.
Equation 3.5 provides important information that are needed to manage the energy losses in the switches. Here is facts that can be used to reduce the stress on the switches during the on-state and off-state transition period:
• the first important parameter that has a direct influence on the power losses of the switches is the switching frequency (fs). The switching power losses are linearly related to the swiching frequency (PL,avg∝ fs) which means that to reduce the losses the switching frequency should be pushed to minimum.
• The second point is the total switching transition time (t(i,v)cond), and this
time is decided by the manufacturer. Thus, the power converter designer should choose a power switches with the least possible on-state and off-state transition period to limit the power dissipation due to switching.
Chapter 4
Wave Energy Conversion
Wave energy converter (WEC) includes the whole conversion chain to elec-tricity and often also the converter. The power take-off PTO is a subsystem of the WEC that perform the energy conversion from mechanical input energy to electrical energy. The generator is in most cases a subset of the PTO system. In conventional electrical machines like the induction and synchronous gener-ators, mechanical systems such as hydraulic systems, air-turbines or gear boxes are used to convert the linear up-and-down motion of the wave into rotational motion. Today, these systems are very large and expensive.
However, a direct drive systems have been proposed for direct conversion of the wave power which means that the PTO in such devices are integrated with the electrical machines. A generic picture of the wave energy conversion process with a direct drive system is depicted in figure 4.1. In this chapter, some of the characteristic of the ocean wave, the WEC subsystems, and the challenges in WEC will be studied.
4.1
Characteristic of ocean waves
The water of the ocean and sea has a persistence reciprocating motion that are caused by friction between the surface of the water and the wind that blows on top of it. The speed of the wind shapes the amplitude and the frequency of the actual waves. Since the wind speed alter with respect to the weather condition, the waves’ properties changes accordingly. Some of the characteristics of the ocean surface waves are listed in table 4.1, and more details about the waves properties can be found in [12].
Modelling the actual behavior of the ocean surface wave seems to be a quite challenging task since the study of an accurate turbulent airflow model
Table 4.1: Classification of the wind generated ocean surface wave [12]. Type of surface wave Frequency of oscilliation Comments
Capillary waves fwave > 10Hz These surface waves are ob-served at the start of the wind blowing at a speed of 3ms. The wavelength of such waves normally within a range of few millimeters (λwave < 0.015m).
Ultragravity waves 10Hz > fwave> 1Hz As the wind speed increases on the water surface, the capillary waves enter an-other classification where the wavelengths become longer typically within this range (0.015m < λwave < 0.017m).
Gravity waves 1Hz > fwave > 201Hz When the wind velocity exceeds the one that gener-ates the ultragravity waves, a new category of surface waves emerges where the wavelength may reach up to 900m. At certain points, the energy stored in these waves become useless if they oscillate ,for example, at a frequency less than a 1Hz with a small amplitude. This is not aberrant especially when the wave evolved from faraway distances from their capturing points.
CHAPTER 4. WAVE ENERGY CONVERSION 25
Figure 4.1: A conceptual picture for wave energy conversion process. on the surface of the water is essential. Many theories in this matter have been proposed in [13]. However, the surface elevation of a monochromatic wave can be modelled mathematically as a sinusoidal function given by equation 4.1. This equation assumes an ideal behavior of the wave with an amplitude of a2 and an angular frequency of ωwave[10].
f (t) = a
2cos(ωwavet) (4.1) The function f(t) can also represent the vertical linear motion of a translator that are attached to the sea waves which oscillate with an angular frequency of ωwave = 2πfwave. The wave complete one full cycle in a few seconds or sometimes even less than a second for small waves. The frequency of the wave will be referred to as (fwave). The speed of the translator of a linear generator attached to the wave depends on the rate at which the wave oscillates and typically ranges from 0 to 3 m/s [6].
4.2
Power Take-Off Devices for Wave Energy
Extraction
Deep water and shoreline wave energy is extracted with WEC devices. De-pending on the type of the WEC, the wave energy preserved in on the surface of the ocean or the deep water waves can be extracted and then converted to electricity. In this section, a description of some of the WEC devices will be elaborated.
4.2.1
Oscillating Water Column (OWC)
This type of Wave Energy Converter (WEC) has an empty chamber that con-fines air within. One side of the chamber is immersed in water and has a win-dow that allows the oscillation of the wave to press the air in the chamber. The other side is above the water surface level and has hole open to the atmosphere which allows the air within the chamber to move in and out. This bidirectional motion of the air normally used to drive the PTO device like air-turbines [14]. The basic structure of the OWC and the operation principle is explained in fig-ure 4.2. The concept of the OWC can be adapted to drive the translator for the Permanent Magnet Transverse Flux Machine (TFM) developed at KTH, but it is not the most favorable case since an air turbine solution can be low cost. The KTH transformer TFM is partly explained in this chapter, see chapter 5 for more information about the machine.
CHAPTER 4. WAVE ENERGY CONVERSION 27
4.2.2
Archimedes Wave Swing (AWS)
The concept of the AWS has originated from Archimedes’ principle which states that the weight of the displaced fluid when an object is partially or com-pletely submerged in the fluid, gas or liquid, is equal to the buoyant force act on the object. The AWS is meant for the extraction of the ocean/sea wave energy, and hence the concerned fluid, in this case, is the water.
Figure 4.3: The basic parts of the Archimedes Wave Swing (AWS) for under-standing the operating principle.
The Archimedes Wave Swing (AWS) is constituted of two parts: Upper part and lower part. The upper part is movable and has a piston chamber where water can enter and leave. The lower part is fixed. Both parts are connected by a piston that has a gas spring in the center. This gas spring helps in controlling the vertical upward and downward movement of the piston. When this WEC is immersed underneath the water surface, the oscillation of the wave above
the AWS decide on the position of the piston. At the crest of the wave, the water sneak out of the piston chamber since the force acting on the surface of the upper part’s is higher than the buoyant force that push the piston up. At the trough of the wave, the opposite is happening which means that the piston is moving upward to its outermost position. Thus, the piston changes position repeatedly with respect to the wave cycle as illustrated in figure 4.3. In order to enhance the mechanical performance of the AWS, a gas spring is used. By regulating the amount of water moving in and out of the AWS chamber, it is possible to alter/set/adjust the gas spring’s stiffness [15].
4.2.3
Heaving Buoy (Point Absorbers)
The size, the general structure and the material of the buoy varies with the design and the intended wave climate on the installation site. In this concept, two positions of the linear machines are possible which are shown in figure 4.4. The wave of the ocean hits the buoy that carry or hold the movable part of the PTO system, e.g. the translator, and makes it move in a reciprocating motion. Thus, the power conversion to electricity occurs instantly with the oscillation of the wave. More details about the linear machine is provided in the following section.
Figure 4.4: (A) The machine is immersed in the water. (B) The machine is hold above the water surface level. The concept has been inspired by [16].
CHAPTER 4. WAVE ENERGY CONVERSION 29
4.3
Linear Electrical Machines
Linear machines are similar in concept to the ordinary machines except that the rotational motion of the rotor is replaced by a linear motion of the mover core. Hence, forces in the airgap of the linear electrical machines develops while torques are recognized in the rotational prototypes. Many useful application of the linear machines exist. They can be used in electrical traction systems where the part of the machine can be attached to the vehicle and the other part can be placed in the track [8]. Also, they might be adapted for wave energy extraction where many proposed linear machines topologies show high potential in this field.
Linear electrical machines exist as AC current induction machines and per-manent magnet synchronous machines or as a DC current linear DC machines. There are pros and cons with linear machines. For example, all of the linear electrical machines have an end effect problem, which increases cogging ef-fects. On the other hand, they show high potential for many applications where direct drive is needed like the case for the wave energy conversion [17]. The synchronous speed and the slip for the LIM are given by the following equa-tions respectively [8]:
vs = 2τ f (4.2) s = vs− v
vs (4.3)
where vs(m/s) is the synchronous velocity, τ (m) is the pole pitch, and v(m/s) is the speed of the translator relative to the stator of the LIM.
The discovery of the rare-earth pemanent magnet has motivated the use of the linear permanent magnet synchronous machines [16]. If the translator of the machine is directly coupled to the point absorber, the translator reciprocate with the frequency of the ocean wave oscillation, fwave. The induced emf in the armature winding will oscillate with a higher frequency than the translator frequency as given by the following equation:
fe(t) = a 2λm
cos(ωwavet) (4.4) where fe(Hz) is the electrical frequency of the induced emf and hence the armature current, a2 represents the amplitude of the wave, and λm(m) is the magnetic wavelength which has a value of twice the pole pitch (2τ ).
Φ = AΨ· cos aπ
λmcos(ωwavet)
(4.5) where Φ is the induced flux and AΦis the amplitude of the induced flux. The rate of change of flux linkage, the induced flux multiplied by the number of winding turns, gives the induced voltage. This emf can be represented by the following equation: d dtΨ = Aemf · sin aπ λm cos(ωwavet) sin(ωwavet) (4.6) where dtdΨ = N d
dtΦ is the induced emf, Aemf =
N AΦaπωwave
λm
is the ampli-tude of the induced emf, and ωwaveis the angular frequency of the wave. The induced emf will have waveform like the one shown in figure 4.5.
Figure 4.5: The no load induced emf for a linear PMSM when the translator is directly coupled to a monochromatic ocean wave.
4.3.1
Transverse Flux Permanent Magnet Synchronous
Machines (TFPMSM)
Machines in general can be excited electrically or or by permanent magnets depending on the application the machines are designed for. Some
applica-CHAPTER 4. WAVE ENERGY CONVERSION 31
tions prefer the electrically excited machines since magnetic field can be easily controlled by adjusting the field current that generates the flux in the machine or by other mean of machines control technique. Other applications prefer the magnetically excited machines since the losses in the field winding can be avoided. In the case of the wave energy harvesting, it is preferable to use per-manent magnet (PM) to excite the machines which are designed to be placed offshore. The KTH transformer TFM is of a permanent magnet synchronous machine (PMSM) prototypes. Thus, this section of the report focuses on the permanent magnet transverse flux machine (PMTFM) topologies and briefly discusses some of the general structures and configurations of these kind of machines.
There are three possible directions for the flux loop orientation for the Per-manent Magnet Synchronous Machine (PMSM) which play a major role in defining the machines’ topology: axial flux direction, radial flux direction, and transverse flux direction. The transverse flux Machines (TFM) fit into the PMSM category, and the name of the TFM is originated from the fact that the flux in these machines forms a loop in the transverse direction. The realiza-tion of these topologies of the Permanent Magnet Transverse Flux Machine (PMTFM) with their flux path are shown in figure 4.6 [18].
Figure 4.6: The three different airgap flux direction for different PMSM topologies: (a) radial flux (b) axial flux (c) transverse flux.
The research in the transverse flux machines area is still active, and many topologies and configurations are being investigated. The concept of the newly emerged and the existing TFM topologies has been inspired by the basic trans-verse flux configuration shown in figure 4.7. In order to grasp a good under-standing of the KTH transformer TFM, basic knowledge about the available configurations and the basic TFM configuration is recommended.
The basic structure of the transverse flux machine is constituted of two parts: the stator which is the fixed part of the TFM and the translator or the
Figure 4.7: The basic transverse flux machine.
mover which represents the moving part of the TFM like the rotor in the con-ventional machines. The stator core has slots that carry the armature winding. In the ideal configuration, the stator core has a rectangular C-shape that is de-signed from laminated sheets of steel or iron to reduce the eddy current losses and to enhance the transverse flux path since the isolation parts of the stator core prevent or at least reduce the stray flux in the axial direction that coin-cides with the direction of the mover [18]. The translator are made of iron and the permanent magnets, preferably neodymium magnets (Nd-Fe-B), which are stacked on the surface of the mover that faces the stator of the TFM. This type of TFM is called a single-sided transverse flux machine and the details for this single-phase topology is shown in figure 4.7.
A linear combination of three single-phase TFM result in a three-phase TFM machine by introducing some modifications on the physical orientation of the permanent magnets or the jointed stator cores. Due to the manufactur-ing complexity of the TFM, machine developers tend to mechanically displace the magnets between the combined single-phases TFM in order to achieve the electrical phase shift of 120o between the phases of the voltages and the currents. Unless a multiphase approach is made, the force will be heavily fluctuating which will have severe consequences for the mechanical
construc-CHAPTER 4. WAVE ENERGY CONVERSION 33
tion. Note that the force for each phase approximately is a squared sinusoidal function, and that for example three phases that are phase shifted 120 degrees between each phase ideally gives a constant force.
The permanent magnets are not necessarily placed on the surface of the mover iron core. In the PMSM, the rotor’s magnets can have three different configurations: surface-mounted magnets, buried magnets, and inset magnets. The same also applies for the TFM’s translator. However, in some designs like the KTH transformer TFM the permanent magnets are placed in the stator instead of in the mover. The main reason for this is that for long stroke length machines only a fraction of the magnets would be used at the same time if they were placed in the translator. Note that the magnets are very expensive.
The developers of the transverse flux permanent magnet synchronous ma-chine (TFPMSM) have proposed several shapes for stator and the mover cores. Examining some of the proposed designs of the TFPMSM can lead to a conclu-sion that the more complicated the machine’s design the better the machine’s performance which might be considered a rule of thumb for the existed TF-PMSM topologies. In the following section, a review of the general structure of two rotating prototypes and two linear prototypes of the TFPMSM is dis-cussed respectively .
4.3.1.1 Flux Switching Transverse Flux Machine (FSTFM)
The FSTFM has a U-shaped stator core and round rotor core. The stator core which is constructed from laminated sheets or soft magnetic composites (SMC) have the armature winding slots and the permanent magnets. This ma-chine is of the salient pole PMSM type due to its structural design and hence the saliency effect are present for this topology. Part of the machine, a single phase, are shown in figure 4.8, and to build a three phase FSTFM a three sin-gle phases stacked radially together to complete the radial structure with an electrical phase shift of 120o between the phases [19].
4.3.1.2 Double Rotor Transverse Flux Machine (DRTFM)
The DRTFM type of transverse flux machine has one stator core and two rotor cores. The shape of the stator core is similar to the one for the FSTFM. The ar-mature winding is placed in stator core slot. However, the permanent magnets are not in the stator side but in the rotor side instead. The inner rotor carries the permanent magnets which are buried in the rotor along its circumference, and this rotor is called the permanent magnet rotor (PMR). The outer toothed rotor, which is called the transverse flux rotor (TFR), rotates between the stator
Figure 4.8: One phase of the flux switching transverse flux machine (FSTFM). and the PMR within the inner and outer airgaps that surrounds it. The basic details of the single phase DRTFM are illustrated in figure 4.9. Like most of the transverse flux machines, the three phase DRTFM is built by combing three single phases of the DRTFM by stacking them in the axial direction. However, a small distance between the stacked phases should be kept so that the leakage fluxes in the axial direction from one phase will not interfere with the other phases. The TFR parts of each phase are shifted mechanically by120n degree, n number of pole, to achieve a balanced three phase system. More details about this topology can be found in [20].
CHAPTER 4. WAVE ENERGY CONVERSION 35
Figure 4.9: A single phase double rotor transverse flux machine (DRTFM).
4.3.1.3 Tubular Flux-Reversal Transverse Flux Machine (TFRTFM)
This topology presents a novel linear TFM structure. The machine has tubular toothed stator core. The the armature winding are placed around the stator’s teeth, the stator poles, and the permanent magnets are surface mounted on these teeth as well. The mover core, the translator, is of cylindrical toothed core prototype. Two three-phase configurations proposed for the TFRTFM: the axial three phase and circumferential three phase. Both hold the same pri-mary side, stator core, structure. However, the key difference that distinguish between the two arrangement are on the mover core structure as illustrated in [21].
4.3.1.4 The KTH transformer TFM machine
This novel machine, designed by Anders, is among the linear transverse flux machine prototypes with flux concentration setup. This means that both sides of the mover core along the axial plane, the direction of movement, are cov-ered by the overall structure of the stator cores in order to reduce the leakage flux as much as possible. Hence, the conceptual realization of this prototype motivated by the double-sided TFMs in figure 4.11. Looking through a cross section in the direction of motion, some of the structural details about the machine can be outlined, refer to figure 4.10. The TFPMSM has two double-sided -shaped stators and one three-sectioned toothed translator. The outer double-sided stator core is symmetrical about the translator, and it has three teeth where the three phase armature winding are arranged along. The inner
double-sided stator core has a rectangular shape where the permanent magnets are axially buried in a flux-concentrating structure. The translator reciprocate within the six airgaps where the two outermost airgaps are different than the in-ternal four airgaps and have surface mounted magnets. This is not preferable, but emerged as a consequence of the mechanical design [6].
Figure 4.10: A cross section of the KTH transformer TFM, refer to [6] for more details.
In the basic topology of the three phase TFM, the electrical, and of course the magnetic, circuit model of the machine can be represented by a single phase model of the machine. This gives a rather simple uncoupled set of equa-tions for the three phases, where the equaequa-tions for each phase are separate. This type of configuration is called a separate flux path arrangement. Studying and analyzing such topology is similar to some extent to investigating the Y and ∆ configurations of the three single phase transformers, but of course with keeping the variable reluctance nature of the TFM in mind. Unfortunately, the TFPMSM studied in this thesis has a more complex electromagnetic in-teraction between the stator and the translator parts since it is designed like
CHAPTER 4. WAVE ENERGY CONVERSION 37
Figure 4.11: The basic double-sided TFM.
a three-phase transformer and has a magnetic interaction between the phases. This leads to complications for the analysis of the machine model and increases the difficulty of designing a converter, since the current in one phase affects the voltage in the other phases.
4.3.2
Operating Principle of the Linear Variable
Re-luctance Permanent Magnets Synchronous
Ma-chines (LVRPMMs)
The principle of operation for the linear variable reluctance permanent magnet machines (LVRPMSM) is similar to that of the conventional linear electrical machines. Since the overall structure of the vernier hybrid machine (VHM), vernier hybrid generator in particular, is much simpler than most of the linear transverse flux machine, it will therefore be used in this part to explain the development of the useful forces in linear machines. A cross section of the basic topology of the VHM in figure 4.12 used for this purpose. In the first paragraph some information about the VHM topology will be provided, and the rest of the text will be about how the reaction force build up in the linear machines.
Figure 4.12: A cross section of a single phase VHM.
the flux lines are parallel to the direction of motion. It has double-sided C-shaped stator cores made of iron laminations and a toothed translator made of a ferromagnetic material such as electric steel laminations or SMC. The double-sided stator cores carry the armature winding and the permanent magnets. The latter are surface mounted on the edge of the stator cores at the airgap. The translator teeth and the permanent magnets pitch are of equal surface area, and the adjacent magnets have different polarities. A cross section of the basic single phase VHM is shown in figure 4.12.
In generating mode, the back and forth motion of the translator creates a time-varying magnetic flux due to the interaction between the permanent mag-nets in the stator and the translator iron teeth on the translator. The reason for this is that when the translator is in direct position, the teeth helps to conduct the flux from the magnets of one polarity, and the slots reduces the flux from the magnets with the opposite polarity. Thereby, the total flux becomes non-zero at this position and a time-varying flux can be achieved. The magnetic field originating form the permanent magnets induces an electromotive force (emf) in the armature winding. This armature reaction causes a current to flow in coils attached to the stator poles. The current in the conductors then
