Underwater Wireless Power Transfer

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F

ACULDADE DE

E

NGENHARIA DA

U

NIVERSIDADE DO

P

ORTO

Underwater Wireless Power Transfer

Hugo Miguel Guedes Pereira dos Santos

MASTER IN ELECTRICAL ANDCOMPUTERSENGINEERING Supervisor: Prof. Henrique Manuel de Castro Faria Salgado

Co-supervisor: Dr. Luís Manuel de Sousa Pessoa

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c

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Underwater Wireless Power Transfer

Hugo Miguel Guedes Pereira dos Santos

M

ASTER IN

E

LECTRICAL AND

C

OMPUTERS

E

NGINEERING

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Abstract

In this dissertation work different near-field wireless power transmission methods are evalu-ated, namely self-resonant magnetic coupling, capacitive transfer and compensated resonant mag-netic WPT.

The impact of numerous design variables is assessed and their effects explained based on theoretical expectations regarding basic electromagnetic principles.

Simulation results are promising yielding AC/AC power transfer efficiencies as high as 95 %, which can be considered high due to the lossy behaviour of surrounding water.

Two inductors are designed and produced to backup theoretical and simulation results. The full description and design procedure for the inductors’ structures and their measurements are also addressed. Experimentally, efficiencies of nearly 80 % were obtained and a good agreement with simulation and equivalent models was verified.

Keywords: Wireless Power Transfer, Underwater Wireless Power, Resonant Structures, Power transmission systems, Power Electronics, Mutual Inductance, Magnetic Coupling, Mutual Capac-itance.

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Acknowledgements

Hoping that no one is left behind, I would like to give special thanks to

Professor Henrique Salgado for supervising this dissertation and giving his excellent theo-retical and experimental support.

Dr. Luís Pessoa and Dr. Mário Pereira for unconditional guidance and assistance that al-lowed me to perform this work, as well as their friendship that contributed with the needed motivation to surpass certain difficulties.

all my work colleagues for offering an excellent work environment. INESC TEC for providing the needed financial and technical resources.

all my family, specially to my parents Henrique and Aurora that have been my base of support and comfort my whole life.

my girlfriend Marina for being with me in the most difficult moments and giving me moti-vation to carry on.

my Integrated Masters colleagues and friends Rui Gomes, Luís Perestrelo, Carlos Ferreira, Guilherme Carvalho, Carlos Sousa, Júnio Silva, Maria Miranda and José Valente, for their constant friendship and amusement moments provided.

the lab technicians from the Electrical Engineering Department Vitor Pinto, Carlos Graf and Rui Fernandes for supporting my work with their availability and technical expertise.

Hugo Santos

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“Power can be, and at no distant date will be, transmitted without wires, for all commercial uses, such as the lighting of homes and the driving of aeroplanes. I have discovered the essential principles, and it only remains to develop them commercially. When this is done, you will be able to go anywhere in the world — to the mountain top overlooking your farm, to the arctic, or to the desert — and set up a little equipment that will give you heat to cook with, and light to read by. This equipment will be carried in a satchel not as big as the ordinary suit case. In years to come wireless lights will be as common on the farms as ordinary electric lights are nowadays in our cities.”

Nikola Tesla

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2.5.1 Inductive Coupling . . . 10 2.5.2 Capacitive Coupling . . . 12 2.6 Two-port Networks . . . 13 2.6.1 Transmission Parameters . . . 13 2.6.2 S-Parameters . . . 14 2.7 Equivalent Circuits . . . 15 2.7.1 Coupled Inductors . . . 15 2.7.2 Coupled Capacitors . . . 16 2.8 Compensation Methods . . . 17 2.8.1 Series-series . . . 17 2.8.2 Series-parallel . . . 18 2.8.3 Parallel-parallel . . . 19 2.8.4 Overview . . . 20 2.9 Transmitter Electronics . . . 20 2.10 Previous Work . . . 21 2.10.1 Magnetic Coupling . . . 21 2.10.2 Capacitive Coupling . . . 21 vii

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viii CONTENTS

3 System Design and Assessment 23

3.1 System’s Architecture . . . 23

3.2 Self-resonant Magnetic Coupling . . . 24

3.2.1 Equivalent Model . . . 25

3.2.2 Validation . . . 25

3.3 Capacitive Coupling . . . 28

3.3.1 Equivalent Model . . . 28

3.3.2 Validation . . . 30

3.4 Resonant Inductive Coupling . . . 34

3.4.1 Equivalent Models . . . 34

3.4.2 Coil to Coil Efficiencies . . . 36

3.4.3 Quality Factor Optimization . . . 36

3.4.4 Coupling Coefficient Evaluation . . . 38

3.4.5 Fixed Load Design Trade-Offs . . . 44

3.4.6 System Integration Considerations . . . 45

3.4.7 System Impairments . . . 49

3.5 Current-mode Resonant Class D Inverter . . . 51

3.5.1 Circuit design . . . 51 3.5.2 Waveforms . . . 52 4 Experimental evaluation 55 4.1 Inductors Construction . . . 55 4.2 Resonating Circuitry . . . 55 4.3 Waterproofing . . . 56

4.4 Current-mode Class D Inverter . . . 59

4.5 System Demonstration . . . 61

4.6 Measurements . . . 62

4.6.1 Results and Discussion . . . 63

5 Conclusions 71 5.1 Goal Achievement . . . 71

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List of Figures

2.1 Series LC resonator . . . 9

2.2 Shunt LC resonator . . . 10

2.3 Equivalent circuit for magnetically coupled shunt resonators . . . 11

2.4 Equivalent circuit for electrically coupled series resonators . . . 12

2.5 Single-ended equivalent circuit for electrical coupling resonant frequency analysis 12 2.6 ABCD two port generic network . . . 13

2.7 S-parameters two port generic network . . . 14

2.8 Coupled inductors equivalent circuit . . . 16

2.9 Coupled inductors equivalent circuit with K impedance inverter . . . 16

2.10 Coupled capacitors equivalent circuit . . . 16

2.11 Coupled capacitors equivalent circuit with J admittance inverter . . . 17

2.12 Series-series compensation circuit . . . 17

2.13 Series-parallel compensation circuit . . . 18

2.14 Parallel-parallel compensation circuit . . . 19

3.1 System’s architecture schematic. . . 23

3.2 Inductive WPT FEKO simulation model. . . 24

3.3 Electric field distribution on coils’ surroundings for air and fresh water. . . 25

3.4 Self-resonant coil equivalent circuit. . . 26

3.5 Self-resonant magnetic WPT system equivalent circuit. . . 26

3.6 S11parameter magnitude comparison between proposed model and simulation re-sults for self-resonant magnetic coupling in air. . . 27

3.7 S21parameter magnitude comparison between proposed model and simulation re-sults for self-resonant magnetic coupling in air. . . 28

3.8 S11parameter magnitude comparison between proposed model and simulation re-sults for self-resonant magnetic coupling in fresh water. . . 29

3.9 S21parameter magnitude comparison between proposed model and simulation re-sults for self-resonant magnetic coupling in fresh water. . . 29

3.10 Capacitive WPT FEKO simulation model. . . 30

3.11 Capacitive WPT system equivalent circuit. . . 30

3.12 S11parameter magnitude comparison between proposed model and simulation re-sults for capacitive coupling in air. . . 31

3.13 S21parameter magnitude comparison between proposed model and simulation re-sults for capacitive coupling in air. . . 32

3.14 S11parameter magnitude comparison between proposed model and simulation re-sults for capacitive coupling in fresh water. . . 33

3.15 S21parameter magnitude comparison between proposed model and simulation re-sults for capacitive coupling in fresh water. . . 33

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x LIST OF FIGURES

3.16 Resonant inductive WPT FEKO simulation model . . . 35

3.17 Series-series compensated magnetic WPT system equivalent circuit. . . 35

3.18 Series-parallel compensated magnetic WPT system equivalent circuit. . . 35

3.19 Parallel-parallel compensated magnetic WPT system equivalent circuit. . . 36

3.20 Series-series compensation theoretical maximum efficiencies as a function of cou-pling coefficient for different quality factors. . . 37

3.21 Series-parallel or parallel-parallel compensation theoretical maximum efficiencies as a function of coupling coefficient for different quality factors. . . 37

3.22 Inductor quality factor and fitted curves as a function of frequency for different numbers of turns. . . 39

3.23 AC series resistance and fitted quadratic curves as a function of frequency for different numbers of turns. . . 39

3.24 Quality factor as a function of inner radius for 100 kHz and different numbers of turns. . . 40

3.25 Coupling factor as a function of distance for 5 turns spiral and multiple inner diameters. . . 41

3.26 Coupling factor as a function of distance for 15 turns spiral and multiple inner diameters. . . 41

3.27 Coupling factor as a function of distance for 5 turns spirals with outer diameters of 10 cm and 16 cm. . . 42

3.28 Coupling factor as a function of distance and fitted curves for 5 turns spirals with outer diameters of 10 cm and 16 cm. . . 43

3.29 Coupling factor as a function of misalignment for 15 turn inductors with 16 cm outer diameter at a distance of 4 cm. . . 43

3.30 Series-parallel or parallel-parallel compensated system efficiency as a function of coupling factor for Q = 100, RL= 50 Ω and different inductor reactance values. . 44

3.31 Series-series compensated system efficiency as a function of coupling factor for Q= 100, RL= 5 Ω and different inductor reactance values. . . 45

3.32 Efficiency as a function of distance for parallel-parallel compensated inductors of 15 and 5 turns. . . 46

3.33 Input resistance as a function of distance for series-series compensated WPT sys-tem terminated with RL= 50 Ω. . . 47

3.34 Input resistance as a function of distance for series-parallel compensated WPT system terminated with RL= 50 Ω. . . 47

3.35 Input resistance as a function of distance for parallel-parallel compensated WPT system terminated with RL= 50 Ω. . . 48

3.36 Efficiency as a function of water conductivity for 4 cm spacing and ESR = 0 Ω. . 50

3.37 Efficiency as a function of capacitor equivalent series resistance for 4 cm spacing and water conductivity σ = 4 S/m. . . 50

3.38 Resonant magnetic coupling WPT system driven by a current-mode class D inverter 51 3.39 Efficiency as a function of load resistance for WPT system driven by current mode class D inverter . . . 52

3.40 Control voltages applied to the transistors’ gates. . . 53

3.41 Voltage on transmitting resonator (top) and load voltage (bottom). . . 54

4.1 5 Turn inductor model. . . 56

4.2 15 Turn inductor model. . . 56

4.3 5 turn inductor supporting structure in 3D software. . . 57

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LIST OF FIGURES xi

4.5 Rings to attach spirals support structure of the coils. . . 57

4.6 5 turn inductors inside salt water attached to PVC pipe support. . . 58

4.7 15 turn spiral inductors (on the right) attached to wooden supporting structure. . . 58

4.8 Adjustable resonance board schematic. . . 58

4.9 Adjustable resonance board with series connected capacitor. . . 59

4.10 Adjustable resonance board with one parallel connected capacitor. . . 59

4.11 Adjustable resonance boards with two parallel connected capacitors each. . . 59

4.12 Cylinder cup for epoxy pouring in 3D design software . . . 60

4.13 Cylinder cups for epoxy pouring after 3D printing . . . 60

4.14 Cylinder cup with epoxy insulating cable and inductor junction . . . 60

4.15 Current-mode class D inverter PCB . . . 61

4.16 Current-mode class D inverter fabricated PCB inside 3D printed box. . . 61

4.17 From left to right: Class D inverter, spiral inductors transfering power and LED lamp as load. . . 62

4.18 AUV shell mounted WPT prototype. . . 62

4.19 Measurement setup with portable VNA and salt water tank . . . 63

4.20 S11 magnitude measurement as a function of distance for 5 turn inductors with parallel-parallel compensation . . . 63

4.21 S11 magnitude measurement as a function of distance for 5 turn inductors with series-parallel compensation . . . 64

4.24 Efficiency measurement as a function of distance for 5 turn inductors with parallel-parallel compensation . . . 65

4.25 Efficiency measurement as a function of distance for 5 turn inductors with series-parallel compensation . . . 66

4.30 Efficiency measurement as a function of distance for 15 turn inductors with parallel-parallel compensation . . . 68

4.31 Efficiency measurement as a function of distance for 15 turn inductors with series-parallel compensation . . . 69

4.32 Efficiency measurement as a function of distance for 5 and 15 turn inductors with parallel-parallel compensation . . . 70

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List of Tables

2.1 Summary table for compensation schemes . . . 20

3.1 ADS fitted values for self-resonant magnetic coupling in air. . . 27

3.2 ADS fitted values for self-resonant magnetic coupling in fresh water. . . 27

3.3 ADS fitted values for capacitive coupling in air. . . 31

3.4 ADS fitted values for capacitive coupling in fresh water. . . 32

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Abbreviations and symbols

AC Alternating Current

AUV Autonomous Underwater Vehicle CAD Computer-aided Design

DC Direct Current EMF Eletromotive Force

ESR Equivalent series resistance PCB Printed Circuit Board PDL Power Delivered to Load PTE Power Transfer Efficiency ROV Remotely Operated Vehicles SAR Search and Rescue

VNA Vectorial Network Analyser WPT Wireless Power Transfer

δ Penetration depth ε Electrical permittivity η Efficiency µ Magnetic permeability ω Angular frequency ρ Resistivity σ Electrical conductivity a Wire radius C Capacitance D Diameter f Frequency G Gain I Current

k Coupling factor between two inductors L Inductance N Number of turns P Power Q Quality factor R Resistance S Water salinity T Water temperature V Voltage X Reactance Z Impedance xv

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Chapter 1

Introduction

Numerous working solutions have been proposed in the scope of wireless power transmission (WPT), for applications in which a physical connection is an inconvenient or simply impossible to establish. This area has been propelled by the proliferation of mobile electronic devices such as tablets, smartphones and others.

In their vast majority, wireless power transfer solutions fall in the context of nearly lossless media such as air. However, there are more strict uses for this technology like applying it in underwater environment, which is the basis of this dissertation.

This work is made within the scope of ENDURE project and thus its main focus is to provide a charging system for the batteries of AUVs. These vehicles are responsible for a vast number of missions embedded in the TEC4SEA infrastructure (http://www.tec4sea.com/), which will certainly become more efficient in energy use, operational resources allocation and costs.

1.1 Motivation

The increasing number of underwater sensors deployment is progressively becoming essential for innumerous applications such as collecting data on water or seabed and maintenance of perma-nent infrastructures placed on an underwater environment. These devices can be installed in fixed structures or mounted in mobile frames, being the latter more relevant due to their operational versatility. These mobile sensors are usually deployed in ROVs or AUVs. However, autonomous underwater vehicles are the preferred option as they do not need a support vessel for their con-tinuous operation. This advantage in relation to ROVs makes them more cost effective, as the lack of specialized support and operation is not an inconvenience. The AUVs main disadvantage is the fact that their range and mission time are severely limited due to low battery endurances and the impossibility of recharging without a support boat. Another serious limitation is imposed by the battery charging that requires wet-mate connectors which are prone to failure, need con-stant and expensive maintenance and make docking stations very complex in order to be able to accommodate them.

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2 Introduction

To bridge these gaps that are limiting factors for the successful and extended works in which AUVs are needed, in this dissertation, battery charging via wireless power transmission is pro-posed. In spite of all the advantages subjacent to wireless charging, there are some challenges to surpass due to the high losses of the underwater media and high electrical permittivity. These factors pose some austere difficulties to the project of a system capable of transferring energy with satisfactory efficiencies (ideally above 50 %). Despite of the existence of underwater wireless power transfer systems, they are still applied in bulky structures and thus inadequate for smaller autonomous vehicles.

Nonetheless, getting over these severe challenges can unlock new possibilities, allowing for AUVs to extend their operational range and improve useful mission time from few hours to months or even years. This will also allow to establish remote charging stations offshore which can push autonomous vehicles bounds even further. The reason behind these improvements is that the system to be installed in the docking station is also autonomous and thus can be deployed and forgot. In fact, the maintenance periodicity of such a system is quite large, allowing for time consuming missions to be accomplished in high seas or in coastal areas.

This implementation allows for some specific missions to be succeeded like oceanographic studies, SAR operations, monitoring of water parameters and even weather reporting in open ocean.

1.2 Work goals

Having identified some of the problems already, the clear objective of this work is to design, implement and test a docking station capable of containing an autonomous wireless charging sys-tem. This is done so that multiple AUVs can recharge their batteries at once, download mission data and if possible, having the energetic capability to do so, to be reassigned for a new mission.

To fulfil the proposed requirements, the demand of investigating different near-field WPT methods arises. A thorough study is done to evaluate the viability of magnetic and capacitive coupling as well as the most suitable types of inductors and capacitors, respectively. After this, an effort is made to integrate the best resonant structure both in the confined space available in an AUV and in the docking station itself. Despite the obvious limitations, a certain degree of freedom is given for the docking station as it is a system to be developed from scratch and can be made to suit our needs.

The need for a solution capable of generating a power signal suitable to drive the resonant structures, using the available DC power at the docking station, must be met. The rectifying and signal conditioning electronics should also be implemented in order to charge the AUV’s battery with a filtered DC voltage. A careful and complete investigation on this type of devices is accomplished to allow for the correct embedding in the frame of the docking station, as well as in the body of the AUV using modular structures.

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1.3 Document Structure 3

1.3 Document Structure

This report is divided in five chapters. In the first chapter an introduction is presented as well as the motivation and objectives of the dissertation to be carried out.

The second chapter contains the fundamentals of WPT and literature review, so that we can get acquainted with the different ways to wirelessly transfer power between two devices and the chal-lenges behind it. Water properties, fundamental parameters for inductors and capacitors, coupled mode theory, two port networks, resonance schemes and power electronics are also analysed.

The third chapter provides a detailed description of the simulation procedure adopted, namely the assessment of different wireless power transfer schemes and design parameters. The relevant simulation results are also presented in this chapter.

Experimental procedure and results are detailed in the fourth chapter. A comparison between simulation and theoretical results is also presented and discussed.

Last but not least, on the last chapter we present the relevant conclusions that were reached throughout this work. Recommendations for future developments on underwater WPT are also given.

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Chapter 2

Fundamentals of Near-Field WPT

The fundamentals required for the understanding of this work are under analysis in this chap-ter. Water properties are studied as they have a crucial impact on how the power transfer takes place. The reactive linear elements capable of forming tuned circuits (resonators) are also anal-ysed, due to their major role on the magnetic and electric fields responsible for the near-field power transmission. Quality factors of both shunt and series resonators are briefly presented. Coupled mode theory is extensively explained as it is the basis concept of inductive and capacitive coupling. Different resonance arrangements are studied and their expressions derived. A review of suitable power electronics to integrate in the transmitter is presented. Finally, the relevant publications are discussed and an overview of what has been achieved in underwater WPT is conducted.

2.1 Water Properties

In this section an overview of the water properties is presented, namely its conductivity, electric permittivity and magnetic permeability. Such properties are crucial for determining the fields between the transmitter and the receiver, as well as understanding how losses can take place and resonant frequencies can be affected.

2.1.1 Conductivity

From general knowledge we know that water is naturally a conductive media. This, in turn, presents a setback on electric and magnetic fields, because it will dissipate their energy and reduce efficiency on WPT methods.

For accurate design and implementation of WPT systems for underwater usage, the need for precise determination of conductivity arises. This crucial design property, depends on water salin-ity measured in parts per thousand (ppt), S, and temperature in degrees centigrade T . According

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6 Fundamentals of Near-Field WPT

to [1], for salinities ranging within 20 ppt < S < 40 ppt, conductivity in S/m is given by

σ (S, T ) = σ0· S · 37.5 + 5.4 · S + 0.015 · S2 1004.8 + 182.3 · S + S2 1 + 6.9+3.3·S−0.1·S2 84.6+69·S+S2 · (T − 15) 49.8 − 0.23 · S + 0.2 · S2_{+ T} ! , (2.1)

in which σ0is the conductivity for a salinity of S = 35 ppt and is given as a function of temperature by

σ0= 2.9 + 8.6 · 10−2· T + 4.7 · 10−4· T2− 3 · 10−6· T3+ 4.3 · 10−9· T4. (2.2) Despite these formulas, an average value of σ = 4 S/m is typically used for salt water [1] and for fresh water a reference of σ = 0.0546 S/m is utilized [2].

2.1.2 Electric Permittivity and Magnetic Permeability

Electric permittivity measures the capability of a material to react when an external electrical field is applied to it. In a microscopic point of view, it expresses how easily a material can have its molecules oriented in a way that opposes the external electrical field.

Due to the fact that water molecules are of polar nature, we expect this material to present a high permittivity. In fact, according to [1], water’s relative permittivity is usually set at εr= 81. However, due to its variation with salinity and temperature, a more accurate permittivity is also presented in [1] as being εr(ω) = ε∞+ εs− ε∞− εsalt 1 + (ω · τ)2 − j · σ ω · ε0 +ω · τ · (εs− ε∞− εsalt) 1 + (ω · τ)2 , (2.3) where εsand ε∞are the real relative permittivities at low and high frequencies, respectively given by εs= 81 and ε∞= 4.5. τ represents the relaxation time which is interpreted as the delay particles take to react at field changes and εsalta correction parameter that is a function of water’s salinity.

Magnetic permeability indicates how well a certain media can store energy in the form of magnetic field. Being water a non-magnetic material, implies that its permeability µ equals that of vacuum, so µr= 1.

2.2 Inductors

Inductors are reactive linear components capable of storing energy in the form of magnetic fields. When excited with a current they generate the fields which can be coupled to another inductor which will then convert this to an induced emf, according to Faraday’s law of induction [3, pp.786-787]. These devices can assume numerous shapes, although the most common are the helical shaped and spiral coils. The first type is suitable to fit in cylindrical shapes, whereas the second is better suited for planar arrangements.

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2.2 Inductors 7

2.2.1 Helical

Helical coils are always a good option for magnetic coupling WPT, as they are well studied el-ements and provide acceptable inductance values and high Q factors when correctly dimensioned. However, in the particular case of wireless power for recharging AUVs, their size becomes a dis-advantage as weight and space are critical. The inductance of an helical shaped inductor is given in [4, pp.39] as

L=µ π D 2_N2

4h , (2.4)

where D represents the coil diameter, N its number of turns and h the coil’s height. However, this simple formula has been given some attention by H. Nagaoka to consider non-uniformity of the magnetic field and its impact on inductance [5]. Frequency-dependent modifications also exist to accommodate variations due to current-crowding effects [4, pp.40].

Also according to [4, pp.42], the stray capacitance of an helical inductor can be given by

C= 4hε π 1 +3 2β 1 + h π ND 2! , (2.5)

assuming that the core material is equal to the surroundings and β = 0.717D_h + 0.933 D_h3/2+ 0.106 D_h2.

Two main types of parasitic resistance arise in an inductor: skin-effect and proximity-effect. Skin-effect losses, also known as current-crowding effect, results from opposing eddy currents that occur due to the changing magnetic field in a wire. These strengthen currents near the edge of the wire and oppose the main flow in its centre, which results in a lower effective conduction area in which electrons can flow. In [4, pp.41] penetration depth is given by

δ = r

ρ f π µ0

, (2.6)

and considering only skin-effect losses, the AC resistance is given as

Rskin=

L· ρ

π (Dδ − δ2), (2.7)

where L is the total wire length and D its diameter.

Proximity effect losses, are a complex physical phenomena also due to eddy currents. How-ever, unlike the skin-effect, these are currents induced by adjacent conductors. As in an inductor wires are typically in close proximity, this effect starts to play its role and AC resistance increases. In [4, pp.43] a table depicting proximity factors for solenoids is presented. The coefficients re-trieved from that table should be multiplied by equation (2.7) to obtain the AC resistance including both skin and proximity effects.

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2.2.2 Spiral

Spiral inductors are another type of structures that are widely used in underwater WPT [6,7]. Their advantages consist on the small space and low weight needed to integrate them in an AUV, as well as their ease of implementation. However, as wires tend to be closer in this type of inductors, higher losses and more pronounced frequency-dependent effects can be expected. In [8], the inductance formula for a spiral inductor is given as

L= µ · c1· Davg· N 2 2 · ln c2 φ + c3· φ + c4· φ2 , (2.8)

in which Davgis the average diameter of the inductor given by Davg= (Douter+ Dinner)/2 and φ the fill ratio defined by φ = (Douter− Dinner)/(Douter+ Dinner). The constants c1, c2, c3and c4are dependent on the inductor’s shape.

As reported in [9], parasitic capacitance for spiral inductors depends on the permittivity of the conductors, diameter of each turn, number of turns and pitch. It gets increasingly difficult to calculate the capacitance with higher number of turns, due to the non-linear adjacent capacitance between wires. Typically, the values for this stray capacitance are in the order of pF.

An approach to calculate the parasitic series resistance for spiral inductors is detailed in [10], which includes an empirical fitting parameter. Accordingly, the total AC resistance for a spiral inductor is given by

RAC= Rskin(1 + k2eddy), (2.9) where Rskin now represents the skin effect resistance for the total wire length of a spiral inductor and keddyis an empirically fitted parameter proportional to f3/2.

2.3 Capacitors

These passive elements are the commonly used devices for electric field coupling wireless power transfer. They rely on the electric field within two conductive plates to transfer energy between the transmitter and the receiver. Only parallel plate capacitors are discussed due to their easy and inexpensive fabrication process.

Parallel plate capacitors are mostly used in WPT through air [11, 12]. In [3, pp.630] the capacitance between two plates is given by

C= εA

L, (2.10)

where A is the plates area and L their gap length.

Capacitors, such as any other reactive elements, present a non-ideal behaviour. The losses on a capacitor are mainly due to the dielectric dipole relaxation phenomena. In [13], the impedance

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2.4 Quality Factor 9 of a capacitor is given by ZC= tan δ ωC − j ωC, (2.11)

where tan δ represents the dielectric loss tangent. It can be seen that these losses take the form of a real part in the capacitor’s impedance (resistor) and that the imaginary part of such impedance is the one that is associated with an ideal capacitor. This series resistance is called the ESR (Equivalent Series Resistor) and is calculated according to

ESR =tan δ

ωC . (2.12)

By [14, pp.74], is possible to rewrite this equivalent series resistance in terms of conductivity of the dielectric as

ESR = σ

ω2ε C (2.13)

2.4 Quality Factor

The quality factor of a passive device represents its ability to store energy in the form of either electric and/or magnetic field. In accordance with [15], it can be calculated by its definition, using

Q= 2 π maximum energy stored

total energy lost per cycle. (2.14)

2.4.1 Series Resonator

For the series resonator of figure2.2we can calculate its quality factor, as reported in [15], by applying Q= ω0L Rs+ ESR = 1 ω0(Rs+ ESR)C , (2.15)

where Rsis the parasitic series resistance of the inductor and ESR the equivalent series resistance of the capacitor, which can be calculated using equation (2.12).

C L

ESR

Rs

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2.4.2 Shunt Resonator

Conforming to [15] again, one can calculate the quality factor for the resonator in figure2.2, by resorting to

Q=RPL//RPC ω0L

= ω0(RPL//RPC)C , (2.16) in which RPL and RPC represent the equivalent parallel resistances for both the inductor and the capacitor, respectively. These can be obtained by applying series-parallel transformation of each element at resonant frequency, ω0.

C L

RPC

RPL

Figure 2.2: Shunt LC resonator

2.5 Coupled Mode Theory

2.5.1 Inductive Coupling

These structures are resonant systems by themselves and have their own self-resonance. Nonethe-less, when they are brought to proximity, mutual coupling starts to develop and other resonant modes appear. So for this reason, these systems may be classified as overcoupled, tightly coupled like in conventional transformers, critically coupled when the voltage gain is half the gain pro-duced by a single tuned circuit ([16, pp.415]) and loosely coupled when most of magnetic field lines produced by the primary inductor miss the secondary, resulting in extremely low coupling coefficients.

To derive the frequencies at which such systems will resonate, one employs the equivalent circuit presented in figure2.3. Applying Kirchhoff’s loop rule to it yields

jωLI1− j_{ω C}I1 + jωLmI2 = 0 jωLI2− j_{ω C}I2 + jωLmI1 = 0

(2.17)

which in matrix form becomes " j ωL −_ωC1 jωLm jωLm j ωL −_ωC1 # " I1 I2 # = " 0 0 # (2.18)

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2.5 Coupled Mode Theory 11

We know from basic linear algebra that equation (2.18) is the representation of an homogeneous system of equations. However, the trivial solution I1= I2= 0 is not of interest as it represents the system in idle state, thus without any energy. From the familiar Cramer’s rule we know that if det(A) 6= 0, where A is the coefficient matrix of equation (2.18), the only valid solution is the trivial solution. To obtain the non-idle state resonant frequencies, we solve

j ωL −_ωC1 jωLm jωLm j ωL −_ωC1 = 0. (2.19)

Solving equation (2.19), yields

ω1= 1 p(L − Lm)C (2.20) and ω2= 1 p(L + Lm)C . (2.21) C L L C Lm I1 I2

Figure 2.3: Equivalent circuit for magnetically coupled shunt resonators

As reported in [16, pp.415], the gap between resonant frequencies can be given as a function of the coupling coefficient and the quality factor of the resonators by

|ω2− ω1| ω0 ≈ s k2_M− 1 Q2 ≈ q k2_M− k2 c, (2.22)

where kc is the critical coupling coefficient and ω0 the resonant angular frequency of the res-onators.

Also, the coupling coefficient of an unloaded system can be calculated exactly by combining equations (2.20) and (2.21) to obtain

k=|ω 2 1− ω22|

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2.5.2 Capacitive Coupling

Despite of magnetic coupling being a mature technology, in our everyday lives, due to its presence in transformers, electric resonant coupling is also a possibility. The basis for this type of wireless power transfer is the capacitance between two conductor plates.

In [11] the proposed solution consists of four plates, forming two capacitors and a coil to bring the system to resonate. The circuit is depicted in figure2.4, and is presented in single-ended form suitable for resonance analysis in figure2.5, assuming C1= C2and C3= C4.

C3 L C2 L C1 C4 + - -+ Vi Vo

Figure 2.4: Equivalent circuit for electrically coupled series resonators

C3 L 2C1 L 2C1 V1 V2

Figure 2.5: Single-ended equivalent circuit for electrical coupling resonant frequency analysis

Applying Kirchhoff’s node rule in the circuit of figure2.5, results in

V1

jωL+ 2 jωC1V1+ (V1−V2) jωC3= 0 V2

jωL+ 2 jωC1V2+ (V2−V1) jωC3= 0,

(2.24)

which converting to matrix form, we can see that this is an homogeneous system of equations. Recalling the arguments from subsection2.5.1, results in two resonant frequencies

ω1= 1 √

2LC1

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2.6 Two-port Networks 13 and ω2= 1 p L(2C1+ 2C3) . (2.26)

2.6 Two-port Networks

Two-port networks are described by a 2x2 matrix that relates parameters at the input and out-put of a device. Their mathematical description is useful to characterize both passive and active devices. In this section, transmission and scattering parameters are under analysis.

2.6.1 Transmission Parameters

Transmission parameters, often called ABCD matrix, are very useful because they express voltages and currents at port 2 in terms of inputs given at port 1 or vice-versa, according to figure

2.6. This allows a simpler analysis of cascaded networks, as matrices can be multiplied to obtain the overall response.

[a]

V1 V2

I1 I2

Figure 2.6: ABCD two port generic network

To describe the network of figure2.6, as given in [17, pp.189], we employ the expression

" V1 I1 # = " A B C D # " V2 I2 # , (2.27) in which A=V1 V2 I2=0 , B=V1 I2 V2=0 , C= I1 V2 I2=0 , D=I1 I2 V2=0 .

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From these we can derive other important quantities such as input impedance, voltage gain, net-work efficiency, optimal load resistances for both maximum PTE and PDL. For a load resistance of RLplaced at port 2, it is possible to write V1as a function of I1and obtain

Zin= V₁ I1 = A+ B/RL C+ D/RL . (2.28)

Voltage gain can be also obtained by writing V2in terms of V1, yielding

G= 1

A+ B/RL

. (2.29)

Making use of equations (2.28) and (2.29), allows us to derive the network efficiency as being

η = PLoad PDelivered = 1/2 × |G| 2_|V 1|2/RL Re(1/2 × |V1|2/Zin) = |G| 2_/R L Re(1/Zin) , (2.30)

where Zin denotes the complex conjugate of the input impedance and Re(1/Zin) the real part of the complex conjugate of input admittance. Expanding the above equation, differentiating and equating to zero, results in the value for RLthat maximizes network efficiency (PTE). Such value is given as RPT E= p Re(B · D) q Re(A ·C) . (2.31)

Using the same method, one can obtain the load that maximizes the power delivered to the load (PDL). This load resistance is expressed by

RPDL= |B|

|A| (2.32)

2.6.2 S-Parameters

Scattering parameters (or S-parameters) relate incident, reflected and transmitted waves. They are the typical measuring parameter when dealing with high frequency measurements, due to the difficulties in creating the short and open circuits required in the measurement of other parameters. S-parameters are usually available in measuring equipments such as VNAs. In figure 2.7 the generic representation of a scattering parameter network is depicted [17, pp.178].

[s]

V1+

V1- V2

-V2+

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2.7 Equivalent Circuits 15

The mathematical representation of the network in figure2.7can be accomplished by using " V₁− V₂− # = " S₁₁ S₁₂ S21 S22 # " V₁+ V₂+ # , (2.33) where S11= V₁− V₁+ V₂+=0 , S₁₂=V − 1 V₂+ V₁+=0 , S21= V₂− V₁+ V₂+=0 , S22= V₂− V₂+ V₁+=0 .

From the above, one understands that S11 and S22 correspond to the reflection coefficients of the network at ports 1 and 2, respectively. The parameters S12 and S21 represent the reverse and forward transmission coefficients. According to [17], it is possible to perceive that |S21|2is a ratio of the power delivered to the load Z0to the power available at the generator. Also, 1 − |S11|2is the ratio between the power delivered to the network and power available at the generator. Moreover, it is possible to obtain the input impedance of a network terminated with Z0, by the expression

Zin= Z0 1 + S11 1 − S11

. (2.34)

Hence, the network efficiency can be calculated by

η = Pload/Pavailable Pdelivered/Pavailable = Pload Pdelivered = |S21| 2 1 − |S11|2 (2.35)

2.7 Equivalent Circuits

2.7.1 Coupled Inductors

When two inductors are brought to proximity, they can share their magnetic fields. This can be represented as a mutual inductance. However, since field lines exist that do not couple from one inductor to the other, also a self inductance will exist.

The equivalent model for two magnetically coupled inductors is presented in figure2.8, where Lmrepresents the mutual inductance and Rsis the parasitic series resistance for each inductor.

This equivalent circuit can be also expressed as in figure2.9, where the mutual inductance and its effect on the self inductances of an uncoupled system are embedded on a K impedance inverter, [17, pp.422].

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L-Lm R_s

Lm

L-Lm

Rs

Figure 2.8: Coupled inductors equivalent circuit

L _R_s _R_s L

K=ωLm

Figure 2.9: Coupled inductors equivalent circuit with K impedance inverter

2.7.2 Coupled Capacitors

In the case that two capacitors are coupled through an electric field, the dual case of coupled inductors can be obtained. Figure2.10depicts the equivalent circuit for coupled capacitors. The ESRassociated with self capacitance is neglected in this model.

Cm C-Cm C-Cm Cm ESR/2 ESR/2 ESR/2 ESR/2

Figure 2.10: Coupled capacitors equivalent circuit

For lossless media analysis (ESR ≈ 0), the equivalent model of figure2.10reduces to the one in figure2.11.

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2.8 Compensation Methods 17

C

C J=ωCm

Figure 2.11: Coupled capacitors equivalent circuit with J admittance inverter

2.8 Compensation Methods

Due to the fact that both capacitive and inductive WPT are usually loosely coupled, it is nec-essary to resonate the leakage capacitance or inductance. Failing to do so would result in high voltage or current drops that would decrease the efficiency, as almost no real power would be delivered.

In this section, compensation schemes are presented for inductive coupling WPT. The same arguments apply to capacitive WPT, although their dual behaviour must be taken into account.

Employing the ABCD parameters for each element of the compensation schemes, allows us to obtain a mathematical circuit description based on the two port network theory of section2.6. Moreover, all the approximations in this section are made assuming that Q is large and that k is fairly low (|k| < 0.5), which is usually true for resonant WPT.

2.8.1 Series-series

Series-series compensation consists in resonating the leakage inductance with a series capac-itor, by placing it as shown in figure2.12. The resulting resonant frequency can be given simply by making ω0= √1_LC. This result, comes from the fact that, at resonance, Xc= XL. By means of equations (2.30,2.31,2.32), we obtain expressions for the power transfer efficiency and optimal loads. C L C L Lm

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For a series-series compensated system, the power transfer efficiency is given by

η = Q 3_k2_X L2RL Q2_X L2k2+ QXLRL+ XL2 (QRL+ XL) , (2.36)

where XL is the reactance of the coil and RL the load resistance. To maximize power transfer efficiency, the optimal load RPT E can be found by differentiating the efficiency and solving for zero. This yields

RPT E= XL Q p 1 + k2_Q2_{= R} s p 1 + k2_Q2_{≈ k X} L, (2.37)

where Rsrepresents the coil parasitic series resistance. In order to maximize power delivered to the load, we should calculate RPDLas

RPDL= Rs(1 + k2Q2). (2.38) Voltage gain, is also an important parameter for the electronics that will rectify the AC signal. When RL= RPT E, it can be expressed by

|G| = k 2_Q2

k2_Q2_{+ kQ + 1}≈ 1. (2.39)

2.8.2 Series-parallel

In series-parallel compensation, a series capacitor is placed on the side of the transmitter and a shunt capacitor is connected at the receiver side, as in figure2.13.

C

L L C

Lm

Figure 2.13: Series-parallel compensation circuit

Applying the same arguments as in series-series compensation, we can write the network efficiency as η = Q 3_X L3k2RL (Q2_{+ 1) X} L4+ 2 QXL3RL+ Q2XL2k2+ RL2 XL2+ Q3XL3k2RL+ Q2k2XL2RL2 . (2.40)

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2.8 Compensation Methods 19

Once again, by differentiating and equating to zero, the optimal load resistance that maximizes PTE is given by RPT E= XL p Q2_k2_{+ Q}2_{+ 1} p 1 + Q2_k2 ≈ Q XL p 1 + Q2_k2 ≈ XL k . (2.41) Maximizing PDL, yields RPDL= XL p Q4_k4_{+ 2 Q}2_k2_{+ Q}2_{+ 1} 1 + Q2_k2 ≈ XL Q2k2 1 + Q2_k2 ≈ XL. (2.42) The voltage gain for RL= RPT E can be expressed as

|G| = Q 2_k p Q4_k6_{+ Q}4_k4_{+ 2 Q}3_k3_{+ 2 Q}2_k4_{+ 3 Q}2_k2_{+ 2 Qk + k}2_{+ 1}≈ k Q2 Q2_k2 ≈ 1 k (2.43) 2.8.3 Parallel-parallel

Parallel-parallel compensation consists in placing a capacitor in shunt with the inductors at both the transmitter and receiver, establishing a parallel LC resonant circuit. In figure2.14 the placement of the capacitor is depicted.

C L L C

Lm

Figure 2.14: Parallel-parallel compensation circuit

Noticeably both efficiency and optimal load to maximize PTE are the same as in the series-parallel compensation. However, the load that maximizes PDL is given by

RPDL= p Q4_k4_{− 2 Q}4_k2_{+ Q}4_{+ 2 k}2_Q2_{+ 2 Q}2_{+ 1X} L p Q4_k4_{+ 2 k}2_Q2_{+ Q}2_{+ 1} ≈ XL k2, (2.44) and the voltage gain can be approximated by

|G| ≈k RL XL

, (2.45)

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2.8.4 Overview

The derived parameters are important in order to assess the circuitry that is to be placed in both ends of the WPT system. They are also crucial to understand the implications that design variables have on system parameters, such as input impedance, power driving capability and voltage gain.

In table2.1, a summary of compensation schemes is depicted. We can see that in series-series resonance, both the input impedances and optimal load for PTE are the lowest. On the other hand, parallel-parallel has the higher input impedance of all. This means that with series-series com-pensation we will have power flowing in low-voltage/current and in parallel-parallel high-voltage/low-current. Series-parallel compensation presents capabilities that lie between the last discussed schemes. Additionally, it presents a voltage gain greater than unity which can improve diode conduction angle at the rectifier side, and thus DC/AC conversion efficiency.

Compensation Input impedance Voltage gain Load PTE Load PDL Series-series Lowest < 1 Lowest Fair Series-parallel Fairly low > 1 Fair Lowest Parallel-Parallel Fair < 1 Fair Highest

Table 2.1: Summary table for compensation schemes

2.9 Transmitter Electronics

In order to maximize DC-AC efficiency on the transmitter side, an adequate power amplifier class is needed.

According to [18], to achieve high efficiencies, non-linear (switching) power amplifier classes should be used, as linear PA topologies dissipate huge amounts of energy. Class AB power am-plifiers require biasing, which means that power will be dissipated even if it is not amplifying any signal. For this reason they are inadequate to achieve very high efficiencies. Classes D, E and F are capable of 100 % theoretical efficiency, though. On the other hand, class F amplifiers need infinite harmonic tuning to achieve 100 %. For these reasons, classes D and E are the most suitable option, as high drain efficiencies are realizable.

In class E PAs, only one transistor is used for switching, whereas in both CMCD (Current-mode Class D) and VMCD (Voltage-(Current-mode Class D), two switching transistors are used. Class D raises another problem due to this fact, which implies that no overlap between the conduction angles of the two transistors exist. This demands an extra effort on controlling their gates.

In [19] a class E topology implemented in GaN was proposed with 95 % drain efficiency for an output power of 300 W. The system efficiency was reported to be nearly 85 %.

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2.10 Previous Work 21

2.10 Previous Work

2.10.1 Magnetic Coupling

In [20], the authors showed that magnetic coupling WPT was possible through a gap of 15 cm with an efficiency of 81 %. They also realized that optimized resonators would be able to achieve higher efficiencies. A successful topology for underwater WPT using magnetic coupling is pre-sented in [21]. As a matter of fact, the application is exactly the same as in this work and the efficiencies obtained are quite satisfactory, nearly 90 %. Similar efficiencies were also obtained in [7], with smaller inductors. However, in all previously mentioned works, a thorough analysis of design parameters, restrictions and optimizations is lacking. Efficiency maximizations depending on the application have not been reported yet, as well as the influence of design variables in link ef-ficiency. Additionally, dedicated electronics design and compensation methods are not addressed in any of these works. In this dissertation, these evaluations are made in order to obtain maximum possible efficiency and electronics compatibility.

According to [22], it is possible to transfer both power and data between two underwater systems using magnetic coupling. Nonetheless, due to the high frequency of the Zigbee RF transceiver, authors only obtained good results for distances up to 40 mm with efficiencies of ap-proximately 50 %. These are not satisfactory at all for the application addressed in this dissertation, as this system uses high frequencies that degrade efficiency.

2.10.2 Capacitive Coupling

Due to high loss tangents in seawater media, no WPT solutions were found. As previously mentioned, electric field coupling relies on capacitances. However, these present high equivalent series resistances that model the dielectric losses in the material of the capacitor, resulting in low efficiencies.

In air, efficiencies around 80 % are possible, even at higher frequencies [11, 12]. For this reason, an evaluation of a capacitive wireless power system in fresh water is viable, as its losses will be much lower than those of seawater. In this dissertation, such analysis is made for the first time, where capacitive power transfer is assessed in a electrically lossy medium.

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Chapter 3

System Design and Assessment

In this chapter a detailed overview of the addressed topology for recharging AUVs is depicted. Additionally, the equivalent circuits and simulation results are presented and compared, in order to assess the validity of theoretical expectations. The design and optimization of the resonators is also described in this chapter, as well as the simulation of a power amplifier.

3.1 System’s Architecture

In figure 3.1, a simplified schematic of the system architecture is depicted. This represents the full topology of the AUV wireless charging system in underwater environment, as well as the electronics and power generation structures that will be mounted on the buoy.

Battery Bank Power generation Inverter Resonator Resonator Docking Station AUV Water surface Magnetic/Electric field Controller Rectifier

Figure 3.1: System’s architecture schematic.

Power generation is determined to be a 1 kW gas generator, a 80 W wind turbine and a 100 W solar panel, which will be employed to charge the battery bank.

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24 System Design and Assessment

This, in turn, will consist of two 12 V batteries, each with a capacity of 100 Ah. Along with the battery bank, remote switches and a charge stabilizer will be set up, in order to allow remote operation of the system and autonomous charge control.

A controller, composed by a microcontroller and pre-driver, will actuate on the transistors gates of the inverter, applying a square wave to the input of the docking station resonator.

The two resonators couple via magnetic or electric field, depending if they are made of induc-tors or capaciinduc-tors. From this coupling energy transfer takes place from the docking station to the AUV where it will be rectified and delivered to the batteries of the vehicle.

3.2 Self-resonant Magnetic Coupling

Recent work has been done in self-resonant magnetic coupling WPT for air, fresh water and seawater. In [23], measured efficiencies of 73 % have been reported in air, 3 % in fresh water and 0.02 % in seawater. These, however, are quite unsatisfactory as efficiencies are extremely low for WPT to be viable.

The results presented in this section are for coils that are placed 1 cm apart, with air boxes around their wires. In figure3.2the employed FEKO simulation model is presented. For air, the electrical parameters of vacuum are used, whereas for fresh water the typical values discussed in section2.1are employed.

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3.2 Self-resonant Magnetic Coupling 25

3.2.1 Equivalent Model

From section2.2, we know that a stray capacitance develops between turns due to a current dis-tribution that appears at high frequencies. In figure3.3, the electric fields magnitude is displayed for air and fresh water. It is clear that due to the high dielectric loss tangent of water, electric fields only exist inside the insulating box. However, in air fields exist all around the coils. This effect can be translated by adding an ESR to the stray capacitance to represent its losses.

(a) Air (b) Fresh water

Figure 3.3: Electric field distribution on coils’ surroundings for air and fresh water.

The equivalent model for a self-resonating coil, according to the arguments of the previous paragraph, is then depicted in the circuit of figure3.4. In this schematic, Rs represents the AC resistance for the inductor that takes into account proximity-effect, skin-effect, radiation and eddy-current losses in the surroundings of the coil. Additionally, ESR represents the equivalent series resistance that models the dielectric losses on the stray capacitance between turns. L and C repre-sent the self inductance and stray capacitance, respectively.

Furthermore, due to the usage of driving loops, two more coupled inductances appear. The full equivalent circuit is depicted in figure3.5, in which Lloop represents the inductance of each driving loop, kloop stands for the coupling factor between loop and resonator and finally k is the coupling coefficient between two resonators.

3.2.2 Validation

According to [23], the only known parameter in the model is the inductance of the coil with the same dimensions used in this case, from which we know that L ≈ 31 µH. To fit simulated and

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C L

ESR

Rs

Figure 3.4: Self-resonant coil equivalent circuit.

C L ESR Rs C L ESR Rs k kloop Lloop kloop Lloop

Figure 3.5: Self-resonant magnetic WPT system equivalent circuit.

model responses, the unknown parameters C, kloop, k and Rswere adjusted for air, being ESR = 0. Additionally, ESR was tuned for the case in which free space is composed of fresh water, for a good match between the theoretical and simulated results.

3.2.2.1 Air

The final fitted values for air are shown in table3.1. The corresponding results for S11and S21 are plotted in figures3.6and3.7, respectively. As it can be seen, a good agreement exists between simulation and the modelling. It is clear from S21magnitude behaviour that high efficiencies can be obtained in air. Moreover, we should note that these are only valid for air, as in fresh water we expect higher capacitances, due to the high relative permittivity. Also higher losses are expected, as conductivity is not negligible as it is the case for air.

3.2.2.2 Fresh Water

The values obtained from parameter fitting in ADS are presented in table3.2. It is clear that permittivity and conductivity dependent values such as C, ESR and k suffered major changes.

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3.2 Self-resonant Magnetic Coupling 27 Parameter Value C 2.39 pF kloop 0.2945 k 0.1755 Rs 5.045 Ω ESR 0 Ω

Table 3.1: ADS fitted values for self-resonant magnetic coupling in air.

15 16 17 18 19 20 21 22 23 24 25 Frequency (MHz) -30 -25 -20 -15 -10 -5 0 S 11 Magnitude (dB) Model FEKO

Figure 3.6: S11parameter magnitude comparison between proposed model and simulation results for self-resonant magnetic coupling in air.

Due to the fact that electric field is spread in both the case of the coil that is filled with air and the surrounding medium ()fresh water), an effective permittivity exists, ε0< εe f f < εwater. As expected the capacitance value increased due to the fact that εe f f > ε0. ESR increased as well, due to a greater loss tangent (higher conductivity of fresh water as compared to air). The coupling factor k decreased because of eddy current losses in the water. This is translated in less field lines being coupled to the receiver, hence a smaller k.

Parameter Value C 16.39 pF kloop 0.2945 k 0.0201 Rs 5.045 Ω ESR 72.99 Ω

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28 System Design and Assessment 15 16 17 18 19 20 21 22 23 24 25 Frequency (MHz) -30 -25 -20 -15 -10 -5 0 S 21 Magnitude (dB) Model FEKO

Figure 3.7: S21parameter magnitude comparison between proposed model and simulation results for self-resonant magnetic coupling in air.

From figures3.8and3.9it is possible to confirm that the theoretical fitted model results for the magnitude of S21 agree well with the simulated response. However, due to the added frequency dependence by fresh water on certain parameters such as k and C, a slight divergence is visible as frequency deviates from the 7 MHz anti-resonance. Additionally, it is clear that in seawater results will be much worse than the ones presented for fresh water in terms of both insertion and return loss. As such the magnetic coupling technique is not viable in seawater and its performance will not be assessed.

3.3 Capacitive Coupling

In this section, electrically coupled resonators are assessed for WPT in both air and fresh water. The system under evaluation consists of four plates that will form two mutual capacitances (two plates per capacitor) and 1 µH coils to introduce a resonance with the leakage capacitance. Figure

3.10depicts the simulation model where the 16 cm diameter plates are placed 2 cm apart, with a 3 cm gap between each pair of plates. Both the receiver and transmitter are enclosed in an air box to minimize losses.

3.3.1 Equivalent Model

Figure3.11represents the model of the capacitive wireless power transfer system. Cmstands for the mutual capacitance between opposite plates, C is the self capacitance between adjacent

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3.3 Capacitive Coupling 29 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 Frequency (MHz) -6 -5 -4 -3 -2 -1 0 S 11 Magnitude (dB) Model FEKO

Figure 3.8: S11parameter magnitude comparison between proposed model and simulation results for self-resonant magnetic coupling in fresh water.

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 Frequency (MHz) -70 -60 -50 -40 -30 -20 -10 S 21 Magnitude (dB) Model FEKO

Figure 3.9: S21parameter magnitude comparison between proposed model and simulation results for self-resonant magnetic coupling in fresh water.

plates, Ccrossthe capacitance across diagonal plates, Rsrepresents the series resistance of the wires connecting to the plates, ESR and ESRcrossaccount for the equivalent series resistance that models

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Figure 3.10: Capacitive WPT FEKO simulation model.

dielectric losses, just as in subsection3.2.1.

Cm C-Cm C-Cm Cm ESR/2 ESR/2 ESR/2 ESR/2 L L L L Rs Rs Rs Rs Ccross ESRcross Ccross ESRcross

Figure 3.11: Capacitive WPT system equivalent circuit.

3.3.2 Validation

The mutual capacitances are composed of parallel plates,and upon employing equation (2.10) we obtain Cm≈ 3.38 pF. By tuning we can figure out L, which includes both tuning and wire inductance. C, Ccross, Rs, ESR and ESRcross are also unknowns to be tuned. In the case where free space is composed of air, ESR = 0, whereas when fresh water is between the plates an ESR develops.

3.3.2.1 Air

After fitting the equivalent model in ADS to the simulation, the final values obtained are pre-sented in table3.3. As it is clear, the pre-calculated value for Cmsuffered a slight change. This is

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3.3 Capacitive Coupling 31

due to the fact that equation (2.10) neglects fringing fields, despite of their existence. Also, as ex-pected, L increased to a value slightly above 1 µH, due to the extra inductance added by the wires that connect to the plates. Noticeably, due to the low permittivity of air, the cross capacitance between plates can be neglected and so can be their ESR.

Parameter Value Cm 4.54 pF C 8.47 pF Ccross 0 pF L 1.3 µH Rs 2.49 Ω ESR 0 Ω ESRcross 0 Ω

Table 3.3: ADS fitted values for capacitive coupling in air.

From the plots of figures3.12and3.13is possible to state that an acceptable agreement be-tween theoretical predictions and simulation results exists for both S11and S21, respectively.

25 30 35 40 45 50 55 −25 −20 −15 −10 −5 0 Frequency (MHz) S 11 Magnitude (dB) Model FEKO

Figure 3.12: S11parameter magnitude comparison between proposed model and simulation results for capacitive coupling in air.

3.3.2.2 Fresh Water

The values obtained from the ADS fitting to the simulation are presented in table3.4. As it is visible the mutual capacitance Cmincreased to a value about 70 times greater than in air, which is to be expected as the fresh water relative permittivity is εr= 81. Moreover, the cross capacitance is

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32 System Design and Assessment 25 30 35 40 45 50 55 −20 −18 −16 −14 −12 −10 −8 −6 −4 −2 0 Frequency (MHz) S 21 Magnitude (dB) Model FEKO

Figure 3.13: S21parameter magnitude comparison between proposed model and simulation results for capacitive coupling in air.

no longer null and larger values for equivalent series resistances come out from the fitting, which is due to different electrical field distribution and larger dielectric loss tangent, respectively. The medium independent values such as L and Rsremained unaltered.

Parameter Value Cm 274.6 pF C 293.6 pF Ccross 18.9 pF L 1.3 µH Rs 2.49 Ω ESR 1.42 kΩ ESRcross 20 Ω

Table 3.4: ADS fitted values for capacitive coupling in fresh water.

From the comparison between the theoretical model and simulation results in figures3.14

and3.15, one can state that an adequate compliance exists. It is also possible to state that this architecture is unsuitable for underwater WPT due to extremely high insertion losses even at close proximity between the plates.

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3.3 Capacitive Coupling 33 14 16 18 20 22 24 26 28 Frequency (MHz) -30 -25 -20 -15 -10 -5 0 S 11 Magnitude (dB) Model FEKO

Figure 3.14: S11parameter magnitude comparison between proposed model and simulation results for capacitive coupling in fresh water.

14 16 18 20 22 24 26 28 Frequency (MHz) -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 S 21 Magnitude (dB) Model FEKO

Figure 3.15: S21parameter magnitude comparison between proposed model and simulation results for capacitive coupling in fresh water.

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3.4 Resonant Inductive Coupling

Due to the high losses of both systems presented so far, a novel approach was needed. For acceptable efficiencies to be attained, the minimization of losses is essential. Both self-resonant and capacitive coupling systems have inherent losses that can not be mitigated.

One possibility is to introduce passive elements, such as capacitors, to create resonances at lower frequencies minimizing radiation and eddy current losses on the inductors. Eddy currents also exist in a conductive medium such as water. From [24, pp.31] it is known that the power lost per unit mass is proportional to frequency and given as

Peddy=

π2σ t2J2pf

6δ , (3.1)

where t is the thickness of the material, Jpthe peak magnetic field and δ the density of the material. If the tuning capacitors used to lower the resonant frequency and minimize eddy losses are much greater than the stray capacitance, we can neglect the intrinsic capacitor of the inductor, since at lower frequencies it will behave approximately as an open circuit. Doing so, means that their high ESR, due to dielectric losses on fresh and seawater, will also be neglected and the power loss minimized.

In this section the design and assessment of the resonant magnetic coupling system is pre-sented. This work is accomplished having in mind the size limitations imposed by the MARES AUV, [25]. Thus, the outer diameter of the inductors is fixed at 16 cm, which is the AUV inner diameter and all the remaining parameters are tunable, such as number of turns, shape and inner diameter. The wire diameter is also fixed at 1.7 mm due to future implementation limitations. In [26] a comparison between helical shaped coils and spiral based inductors is made, from which it is concluded that spiral resonators outperform helical shape inductors. Moreover, it is understood that spiral shaped inductors are easier to integrate in confined space of the AUV. For these reasons, only spiral inductors are under analysis. In figure3.16the simulation model of two such inductors is depicted. The wires are coated to avoid electrical contact between wires and the surrounding water.

3.4.1 Equivalent Models

As lower frequencies are typically used in this kind of WPT, we can drive the resonators directly instead of using driving loops that will act as baluns to balance the currents in the coil. However, to do so, a compensation network has to be added in order to achieve a resonance at lower frequencies. These compensation methods are explained and their equations derived in section2.8.

In figures3.17,3.18and3.19, the equivalent models for resonant inductive coupling are de-picted. Just like in the previous cases, ESR represents the equivalent series resistance of the capacitor. However, this capacitor is an additional lumped element that can be chosen with an al-most negligible ESR in contrast with self-resonant magnetic coupling where the stray capacitance

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3.4 Resonant Inductive Coupling 35

Figure 3.16: Resonant inductive WPT FEKO simulation model

ESRis determined by the surrounding medium. In all of these models, the parasitic capacitances are neglected since Ctune is assumed to be much larger than any of them. Similarly to section2.7, Lmstands for mutual inductance, Rsthe series resistance of the inductor and L − Lm the leakage inductance inherent to the loosely coupled transformer.

L-Lm R_s

Lm

Ctune

ESR _R _L-L_m

s Ctune ESR

Figure 3.17: Series-series compensated magnetic WPT system equivalent circuit.

L-Lm _R_s Lm L-Lm Rs Ctune ESR Ctune ESR

(56)

36 System Design and Assessment L-Lm R_s Lm L-Lm Rs Ctune ESR Ctune ESR

Figure 3.19: Parallel-parallel compensated magnetic WPT system equivalent circuit.

3.4.2 Coil to Coil Efficiencies

For a matched system that maximizes efficiency, i.e. RL= RPT E, we can rewrite the efficiencies for all the compensation methods. In the series-series compensation the efficiency is given as

ηmax,ss=

Q2k2pQ2_k2_{+ 1}

Q2_k2₊p_Q2_k2_{+ 1 + 1} p_Q2_k2_{+ 1 + 1} ,

(3.2)

and for the series-parallel or parallel-parallel compensation it becomes

ηmax,pp=

Q3k3

Q3_k3_{+ Q}2_k4_{+ 2 Q}2_k2_{+ 2 Qk + k}2_{+ 1}. (3.3) From the above equations, it is clear that the efficiencies only depend on the coupling coeffi-cient and the quality factor. Curves of the dependence of the efficiency with coupling and quality factor are plotted in figures3.20and3.21. High coupling coefficients can be achieved by increas-ing the size of the inductors. However, due to the imposed size limitations the diameter can not be extended any further than 16 cm. For this reason, the only option is to increase Q to the highest possible value in order to achieve maximum coil to coil efficiency.

From the theoretical curves in figures3.20and3.21is possible to conclude that for low cou-pling factors, increasing Q is highly desirable. Since the main components of the compensated magnetic coupling WPT are loosely coupled transformers, optimization of the quality factor for each of the resonators is essential for any of the compensation methods. Additionally, is clear that it is not worthwhile putting effort in increasing the quality factor to a value much higher than Q = 150, unless operating with extremely low coupling coefficients such as in the case of self-resonant magnetic coupling in fresh water.

3.4.3 Quality Factor Optimization

According to [27], it is possible to achieve the highest quality factor for a given inductor geometry by sweeping the tuning capacitance and the number of turns. Doing so, will result in sweeping resonant frequencies, inductance values and coil pitch. The maximum Q value should be chosen in order to achieve higher coil to coil efficiencies.

Underwater Wireless Power Transfer

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Underwater Wireless Power Transfer

Hugo Miguel Guedes Pereira dos Santos

Underwater Wireless Power Transfer

Hugo Miguel Guedes Pereira dos Santos

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Abstract

Acknowledgements

Contents

List of Figures

List of Tables

Abbreviations and symbols

Chapter 1

Introduction

1.1

Motivation

1.2

Work goals

1.3

Document Structure

Chapter 2

Fundamentals of Near-Field WPT

2.1

Water Properties

2.2

Inductors

2.3

Capacitors

2.4

Quality Factor

2.5

Coupled Mode Theory

2.6

Two-port Networks

2.7

Equivalent Circuits

2.8

Compensation Methods

2.9

Transmitter Electronics

2.10

Previous Work

Chapter 3

System Design and Assessment

3.1

System’s Architecture

3.2

Self-resonant Magnetic Coupling

3.3

Capacitive Coupling

3.4

Resonant Inductive Coupling