FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO

Underwater Wireless Power Transfer

Hugo Miguel Guedes Pereira dos Santos

FINAL REPORT

DISSERTATION PREPARATION

Supervisor: Dr. Henrique Manuel de Castro Faria Salgado

Co-supervisor: Dr. Luís Manuel de Sousa Pessoa

February 11, 2016

c© Hugo Santos, 2015

Underwater Wireless Power Transfer

Hugo Miguel Guedes Pereira dos Santos

DISSERTATION PREPARATION

February 11, 2016

Abstract

This work is done within the scope of Dissertation Preparation course, which has the main goalof preparing, organizing and orienting the future work to be made on the second semester.

In this report work objectives, introduction to the theme and state-of-the-art analysis are pre-sented. A theoretical explanation about resonant structures, underwater medium and electronicsis also conducted in this report. Last but not least, the important strategies and work plan arepresented, so that a successful response to the previously identified challenges is accomplished.

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

i

ii

Contents

1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Work goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Report Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 State of the art 52.1 Wireless Power Transfer Hardware . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Basic magnetic coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Resonant magnetic coupling . . . . . . . . . . . . . . . . . . . . . . . . 62.1.3 Capacitive coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1.4 Inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.5 Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.6 Power driving electronics . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Water properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.1 Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2 Electric Permittivity and Magnetic Permeability . . . . . . . . . . . . . . 12

2.3 Loss mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Coupling losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Ohmic losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4 WPT methods review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.1 Magnetic coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.2 Capacitive coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Problem Characterization 153.1 Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Proposed solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3 System’s architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Work Schedule 194.1 Tasks and methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2 Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

iii

iv CONTENTS

List of Figures

2.1 Basic magnetic coupling wireless power transfer system . . . . . . . . . . . . . 62.2 Equivalent circuit for inductor with shunt capacitance . . . . . . . . . . . . . . . 72.3 Equivalent circuit for magnetically coupled shunt resonators . . . . . . . . . . . 82.4 Equivalent circuit for electrically coupled series resonators . . . . . . . . . . . . 92.5 Single-ended equivalent circuit for electrical coupling resonant frequency analysis 92.6 H bridge inverter simplified schematic . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 System operation illustration in shallow water . . . . . . . . . . . . . . . . . . . 163.2 System illustration in seabed research operations . . . . . . . . . . . . . . . . . 163.3 System’s architecture schematic . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.1 Gantt chart depicting work schedule . . . . . . . . . . . . . . . . . . . . . . . . 20

v

vi LIST OF FIGURES

Abreviaturas e Símbolos

AC Alternating CurrentAUV Autonomous Underwater VehicleCAD Computer-aided DesignDC Direct CurrentEMF Eletromotive ForcePCB Printed Circuit BoardROV Remotely Operated VehiclesSAR Search and RescueVNA Vectorial Network AnalyserWPT Wireless Power Transfer

δ Penetration depthε Electrical permittivityη Efficiencyµ Magnetic permeabilityω Angular frequencyρ Resistivityσ Electrical conductivityC CapacitanceD Diameterf Frequencykc Critical coupling factor between two inductorskM Coupling factor between two inductorsL InductanceLm Mutual inductanceN Number of turnsQ Quality factorRac AC resistanceS Water salinityT Water temperatureZL Load impedance

vii

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 inconvenient. 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.

1

2 Introduction

To bridge these gaps that are limiting for the successful and extended works in which AUVs

are needed, in this dissertation, battery charging via wireless power transmission is proposed. 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

Being some of the problems already identified, the clear objective of this work is to project,

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 WPT methods for

near field 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.

1.3 Report Structure 3

1.3 Report Structure

This report is divided in five chapters. In the first chapter an introduction is presented as well

as the motivation and objectives for the dissertation to be done.

The second chapter contains a state of the art survey, so that we can get acquainted with the

different ways to successful transfer power between two devices and the challenges behind it.

Different types of structures are analysed, as well as their equivalent circuits. Water properties,

loss mechanisms and power electronics are also under analysis.

In the third chapter follows a detailed description of the problem to be solved and the chosen

solution to meet the work objectives, based on the state of the art survey presented on the second

chapter.

The work plan, needed material resources and tools are presented. This will allow for an

efficient time management in the future.

Last but not least, on the last chapter we present the relevant conclusions that were reached

throughout this report that will have impact on the dissertation to be realized on the second

semester.

4 Introduction

Chapter 2

State of the art

The state of the art regarding the subject of this dissertation is under analysis in this chapter,

namely relevant knowledge about wireless power transfer. The hardware as a whole is exploited,

such as the near field structures that are suitable for this situation and the electronic circuitry

needed to drive the power frames. Electrical properties of water also play a main role for the

successful operation of the system under development, and as such are also under analysis in this

chapter. The loss mechanisms can pose some severe limitations to an efficient power transmission,

thus they are also reviewed. Finally, efficient and confirmed methods to successfully accomplish

the energy transfer between two unconnected ports are presented and analysed.

2.1 Wireless Power Transfer Hardware

The proper investigation results needed for a correct understanding of near field wireless power

transfer are presented in this section. Emphasis is given not only to the arrangements that are

suitable for WPT, but also to the theory subjacent to the advisable electronics.

2.1.1 Basic magnetic coupling

This type of wireless power transfer mechanism is actually the most common in our daily lives,

as it is the one that is widely used in most electrical and electronic devices. Magnetic coupling is

actually nothing more than the simple operation of a transformer in which a primary inductor has

a current that induces a magnetic field. This field in turn, passes through the secondary coil giving

rise to an induced emf imposed by Faraday’s law of induction [1, pp.786-787]. This interaction

between two inductors is known in literature by mutual inductance and can be clearly observed

when two coils are brought to proximity, so that they share their entire magnetic field or part of it.

So, we now know that by bringing to inductors into closeness, it is possible to make their mag-

netic fluxes to be shared, creating a transformer. In fact, for this kind of devices we try to maximize

the mutual inductance, in order to get maximum coupling coefficient. We also know that, by [2],

this factor is given by kM = Lm/√

L1 L2, where Lm corresponds to the mutual inductance and L1,

L2 are the primary and secondary inductances, respectively.

5

6 State of the art

In figure 2.1 a typical magnetic coupling power transfer system is depicted. For this type of

WPT, the frequency of operation is usually much lower than the self-resonance of the inductors,

which allows us to assume them as a simple RL series circuits. So, according to [3], the quality

factor of an inductor, assuming a sinusoidal excitation, is given by

Q = 2πmaximum energy stored

total energy lost per cycle= 2π

12 LI2

12 Rac I2 2π

ω

=ω LRac

. (2.1)

One can see from equation (2.1) that the quality factor should increase linearly with frequency.

However, as it will be explained in section 2.3, this is not the case as loss resistance, R, tends to

increase with frequency as well and so decrease the quality factor.

Figure 2.1: Basic magnetic coupling wireless power transfer system

Due to the low quality factors of such systems when using air cores, in our everyday lives we

usually see them enhanced with ferromagnetic material cores such as iron and ferrite. This im-

provement allows the confinement of magnetic field within the material, yielding better coupling

factors (close to 1) and reducing coupling losses. The downside of these basic magnetic induction

structures is the fact that they are only efficient at relatively short distances, as they either need a

bulky magnetic core shared by the two inductors or an air core that is small enough to allow for

high coupling factors and thus low divergence of the magnetic field lines. In fact, as reported in

[4], the figure of merit for a magnetic coupling system, either resonant or not, is given by

kM Q = kM√

Q1 Q2, (2.2)

where Q is the overall structure quality factor and Q1, Q2 are the unloaded quality factors for

each inductor. So by inspection of equation (2.2), one can explain the need for high coupling

coefficients in a system where the individual quality factors are not as high as desirable.

2.1.2 Resonant magnetic coupling

To make wireless power transfer a reality for distances that are comparable to the structures’

sizes, resonant circuits are typically implemented. This method has an advantage relative to basic

magnetic coupling, because resonance is the most efficient way to transfer energy to a system. A

2.1 Wireless Power Transfer Hardware 7

possible analogy to the mechanical world is that you can break a glass if you excite it with a sound

which has precisely its resonant frequency, but you can not do it at different frequencies.

From [4], we know that the quality factor for the equivalent inductor circuit in figure 2.2, is

given by

Q =ω0 LRac

, (2.3)

where Rac is the series resistance of the inductor, and so the component that is responsible for

ohmic losses in the circuit. From equation 2.3, one can figure out that the quality factor increases

by lowering resistor values and decreasing shunt capacitances. Equivalently one can conclude

that by increasing ω0, is possible to increase the resonator’s quality factor. However, rising the

frequency causes bigger losses and thus a cutback in the quality factor. For this reason, a compro-

mise must be met to operate the system at optimum Q and suitable frequency.

C

L Rac

Figure 2.2: Equivalent circuit for inductor with shunt capacitance

In this type of magnetic coupling, contrasting with simple transformers explained in subsection

2.1.1, the coupling coefficient, kM can have significant variations instead of being close to unity. So

for this reason, these systems may be classified as overcoupled when resonators are so close that

the receiver tends to collapse the magnetic field produced by the transmitter, tightly coupled like

in conventional transformers, critically coupled when the voltage gain is half the gain produced

by a single tuned circuit (check [5, pp.415]) and loosely coupled when most of magnetic field

lines produced by the primary inductor miss the secondary resonator, resulting in low coupling

coefficients.

As resonant systems by themselves, these structures have their own self-resonance. Nonethe-

less, when they are brought to proximity, mutual coupling starts to develop and other resonant

modes appear. To derive the frequencies at which such system will resonate, one employs the

equivalent circuit presented in figure 2.3. Applying Kirchhoff’s loop rule to it yields

jωLI1− j I1ω C + jωLmI2 = 0

jωLI2− j I2ω C + jωLmI1 = 0

(2.4)

8 State of the art

which in matrix form becomes[j(ωL− 1

ωC

)jωLm

jωLm j(ωL− 1

ωC

)][I1

I2

]=

[0

0

](2.5)

We know from basic linear algebra that equation (2.5) 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 (2.5), the only valid solution is the trivial

solution. To obtain the non-idle state resonant frequencies, we solve∣∣∣∣∣ j(ωL− 1

ωC

)jωLm

jωLm j(ωL− 1

ωC

)∣∣∣∣∣=(

ωL− 1ωC

)2

= 0. (2.6)

Getting through the maths of equation (2.6), we get

ω1 =1√

(L−Lm)C(2.7)

and

ω2 =1√

(L+Lm)C. (2.8)

C L CL

LmI1 I2

Figure 2.3: Equivalent circuit for magnetically coupled shunt resonators

As reported in [5, 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

≈

√k2

M−1

Q2 ≈√

k2M− k2

c , (2.9)

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

onators.

2.1.3 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

2.1 Wireless Power Transfer Hardware 9

wireless power transfer is the capacitance between two conductor plates.

In [6] the proposed solution consists of four plates, forming two capacitors and a coil to bring

the system to resonance. The circuit is depicted in figure 2.4, and is presented in single-ended

form suitable for resonance analysis in figure 2.5, assuming C1 =C2 and C3 =C4.

C3L

C2

L

C1

C4

+

- -

+

Vi Vo

Figure 2.4: Equivalent circuit for electrically coupled series resonators

C3L

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 figure 2.5, results in

V1jωL +2 jωC1V1 +(V1−V2) jωC3 = 0V2jωL +2 jωC1V2 +(V2−V1) jωC3 = 0,

(2.10)

which converting to matrix form, we can see that this is an homogeneous system of equations.

Recalling the arguments from subsection 2.1.2, results in two resonant frequencies

ω1 =1√

2LC1(2.11)

and

ω2 =1√

L(2C1 +2C3). (2.12)

10 State of the art

2.1.4 Inductors

For magnetic coupling wireless power transfer, elements capable of producing and responding

to magnetic fields are needed. Inductors present such behaviour and two types are presented,

namely solenoids and spiral inductors.

Solenoids are always a good option for this kind of WPT, as they are well studied elements

and provide good inductance values and high Q factors when correctly dimensioned. However, in

the particular case of wireless power for the charging of AUVs, their size becomes a disadvantage

as weight and space are critical. The inductance of a solenoid is given in [7, pp.39] as

L =µπD2N2

4h, (2.13)

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 the magnetic field’s

non-uniformity and its impact on inductance [8]. Frequency-dependent modifications also exist to

accommodate variations due to current-crowding effects [7, pp.40].

Spiral inductors are other type of structures that are widely used in underwater WPT [9, 10].

Their advantages consist of the small space and low weight needed to integrate them in an AUV,

as well as their easy implementation. However, as wires tend to be closer in this type of inductors,

usually, higher losses and more pronounced frequency-dependent effects can be expected. In [11],

the inductance formula for a spiral inductor is given as

L =µ ·c1 ·Davg ·N2

2·(

ln(

c2

ρ

)+ c3 ·ρ + c4 ·ρ2

), (2.14)

in which Davg is the inductors’s average diameter given by Davg = (Douter +Dinner)/2 and ρ the

fill ratio defined by ρ = (Douter−Dinner)/(Douter +Dinner).

2.1.5 Capacitors

These elements are the commonly used devices for electric field coupling wireless power trans-

fer. 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 [6, 12] as salt water presents a

high loss tangent, tanδ , which makes these elements extremely inefficient for underwater usage.

In [1, pp.630] the capacitance between two plates is given by

C = εAL, (2.15)

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

2.2 Water properties 11

2.1.6 Power driving electronics

The resonators presented so far, need to be driven with AC power so that transfer takes place.

From previous sections we know that for different coupling factors, there are distinct resonant

frequencies, which implies that our power transmitter must be easily tunable. Also, in every

power transmission system, high DC to AC conversion efficiencies are required.

Having the previously mentioned requirements in mind, the H bridge inverter is found to be the

best option for the resonator’s power driving. As it presents a switching behaviour, its theoretical

efficiency is 100%, assuming no switching losses. A schematic for such circuit is depicted in

figure 2.6. Transistors M1−M4 are used as switches, and their gates actuated by two control

signals that are dual. This makes transistors M1 and M4 to turn on while M2 and M3 are off,

resulting in a voltage VDC in the load impedance. When M2 and M3 conduct with M1 and M4

off, the voltage across the load switches to −VDC. By adequately adjusting the control signals of

the transistors, a square wave can be applied to the load impedance, which in turn will produce a

sinusoidal wave at the receiver, due to the resonant behaviour of ZL.

M4M3

ZL

M2M1

VDC

Figure 2.6: H bridge inverter simplified schematic

In [13], an H inverter is employed in series resonance wireless power transfer through air. The

transistor’s gates were actuated directly from a microcontroller, allowing for real time frequency

tuning and increased system flexibility, as software can be easily adjusted to fit new needs.

2.2 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.

12 State of the art

2.2.1 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

efficiencies.

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

to [14], for salinities ranging within 20ppt < S < 40ppt, 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

), (2.16)

in which σ0 is the conductivity for a salinity of S = 35ppt and is given as a function of temperature

by

σ0 = 2.9+8.6 ·10−2 ·T +4.7 ·10−4 ·T 2−3 ·10−6 ·T 3 +4.3 ·10−9 ·T 4. (2.17)

Despite the presented formulas, an average value of σ = 4S/m is typically used for salt water

[14] and for fresh water a reference of σ = 0.0546S/m is utilized [15].

2.2.2 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 [14], 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 [14] 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

), (2.18)

where εs and 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 the delay particles take to react

at field changes and εsalt a correction parameter that is a function of water’s salinity.

Magnetic permeability indicates how well a certain media can store magnetic energy. Being

water a non-magnetic material, implies that its permeability µ equals that of vacuum, so µr = 1.

2.3 Loss mechanisms 13

2.3 Loss mechanisms

This section exploits the loss mechanisms in a wireless power transfer system. These are

critical in determining the AC to AC power efficiency, as they contribute with losses in multiple

ways, resulting in a lower power at the receiver.

2.3.1 Coupling losses

According to [16], assuming perfect impedance matching of both transmitter and receiver,

efficiency can be given, in terms of the coupling factor, by

ηopt =(kMQ)2(

1+√

1+(kMQ)2)2 , (2.19)

where kMQ is the system’s figure of merit and Q the geometrical mean of the resonators’ quality

factors. By simple inspection of equation (2.19), is possible to conclude that as the system’s figure

of merit increases, efficiency approaches unity.

The system’s Q is independent of distance, as it is determined by parameters that only depend

on the resonators. Due to this fact, efficiency will only depend on the coupling coefficient for a pre-

determined quality factor. According to the notions presented in subsection 2.1.2, with increasing

distance, more magnetic flux lines will miss the receiver resonator’s core, which will result in

lower coupling factors.

2.3.2 Ohmic losses

When electrons flow through a conductor, their net movement produces heat which cause can

be interpreted as microscopic collisions. In an inductor, there are other effects that affect the

resistance such as frequency and proximity between wires.

Skin-effect losses, also known as current-crowding effect, results from opposing eddy cur-

rents that occur due to the changing magnetic field in a wire. These strengthen currents near the

wire’s edge and oppose the main flow in the centre of the wire, which results in a lower effective

conduction area in which electrons can flow. In [7, pp.41] penetration depth is given by

δ =

√ρ

f πµ0, (2.20)

and considering only skin-effect losses, the AC resistance’s expression is presented as

Rskin =L ·ρ

π(Dδ −δ 2), (2.21)

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 skin-effect, these are currents induced by adjacent conductors. As in an inductor

14 State of the art

wires are typically in close proximity, these effect starts to play its role and quality factor de-

creases as AC resistance increases. In [7, pp.43] a table depicting proximity factors for solenoids

is presented. The coefficients retrieved from that table shall be multiplied in by equation (2.21) to

obtain the AC resistance including both skin and proximity effects. For spiral inductors, another

approach is detailed in [17], which includes an empirical fitting parameter. Accordingly, the total

AC resistance for a spiral inductor is given by

RAC = Rskin(1+ k2eddy), (2.22)

where Rskin now represents the skin effect resistance for the total wire length of a spiral inductor

and keddy is an empirically fitted parameter proportional to f 3/2.

2.4 WPT methods review

2.4.1 Magnetic coupling

In [18] a successful topology for underwater WPT using magnetic coupling is presented. As

a matter of fact, the application is exactly the same as this work’s and the efficiencies obtained

are quite satisfactory, near 90%. However, in this implementation, ferrite cores were used which

are not suitable for smaller AUVs as they are bulky and can easily affect manoeuvrability. Similar

efficiencies were also obtained in [10], with smaller inductors. Both implementations made use

of Litz wire which significantly reduces skin effect losses discussed in subsection 2.3.2, yielding

higher efficiencies and quality factors for both transmitter and receiver coils.

According to [19], 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,

satisfactory results only appeared for distances up to 40mm with efficiencies of approximately

50%.

2.4.2 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 equiva-

lent series resistances that model the dielectric losses in the capacitor’s material, resulting in low

efficiencies.

In air, efficiencies around 80% are possible, even at higher frequencies [6, 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.

Chapter 3

Problem Characterization

In this chapter a detailed overview of the problem to be taken care of is depicted. The pro-

posed solution to surpass certain challenges and allow a successful solving of the problem is also

presented.

3.1 Problem definition

Autonumous underwater vehicles face serious range and endurance limitations that have to be

overcome, so that it becomes possible for them to be employed in long-term high seas missions.

For this work, the implementation of an underwater wireless power transfer system is proposed.

Such system enables the complete mitigation of expensive wet-mate connectors that are prone

to failure and require constant maintenance. This will enable AUVs to stay on the field for greater

durations and farther from shoreline. However, the employment of such power charging structures

has some limitations regarding seawater’s attenuation. Also, the usage of a remote docking station

poses serious challenges to avoid short period maintenances, in order to make the system viable.

AUVs, as moving vehicles, have size and weight limitations that have to be thought and ful-

filled when designing their autonomous charging system. This results in the need for size, weight

and efficiency optimization of both transmitter (docking station) and receivers.

The development of a complete autonomous charging system for AUVs allows their operation

with very little or absolutely no human intervention, enabling the possibility for lower operational

costs.

3.2 Proposed solution

The discussed solution consists of a remotely placed underwater docking station supported

by a buoy. At the water surface on top of the buoy, solar panels, eolic turbine and gas generator

will be installed along with DC batteries to power the system. These different energy producing

equipments are going to be installed for redundancy and improved system reliability.

15

16 Problem Characterization

On the docking station, the autonomous wireless power transfer system will be installed to

generate the AC power from the batteries and drive the transmitting equipment. The transmitter

resonator is the main focus of this work as it needs an elaborate and thorough study to maximize

power transfer efficiency.

AUVs will approach the docking station using visual guidelines and shut down when success-

fully docked, so that power transfer can take place. In figures 3.1 and 3.2 we can see a shallow

water operation schematic and a seabed research illustration, respectively.

Figure 3.1: System operation illustration in shallow water

Figure 3.2: System illustration in seabed research operations

3.3 System’s architecture 17

3.3 System’s architecture

In figure 3.3, a simplified schematic of the system’s architecture is depicted. This represents

the full topology of the AUV’s wireless charging system in underwater environment, as well as

the electronics and power generation structures that will be mounted on a buoy.

BatteryBank

Power generation

H-Inverter

Resonator Resonator

Docking Station

AUV

Water surface

Magnetic/Electric field

Controller

Rectifier

Figure 3.3: System’s architecture schematic

Power generation is determined to be a 1kW gas generator, a 80W wind turbine and a 100W

solar panel, which will be employed to charge the battery bank.

This, in turn, will consist of two 12V batteries, each with a capacity of 100Ah. 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 H-inverter’s

transistors gates, applying a square wave to the docking station resonator’s input.

The two resonators couple via magnetic or electric field, depending if they are made of in-

ductors or capacitors. By this coupling the energy transfers from the docking station to the AUV

where it will be rectified and delivered to the vehicle’s batteries.

18 Problem Characterization

Chapter 4

Work Schedule

In this chapter the work schedule for the dissertation is presented to the reader. Brief explana-

tions for each task to be accomplished are also shown, as well as their expected durations. Finally

the needed tools and materials for the system’s implementation are enumerated.

4.1 Tasks and methodology

To obtain the desired results, careful planning is usually needed. The tasks to be performed are:

1. Magnetic coupling simulation - 4 weeks

For inductive coupling, helical and spiral inductors will be under analysis. They will be

designed in 3D software and simulated in an electromagnetic simulator, after which an

optimization for both coils has to take place.

2. Capacitive coupling simulation - 4 weeks

To evaluate WPT through electrically coupled resonators, parallel plate capacitors will un-

dergo a process of design, simulation and optimization. This will occur at the same time as

task number 1.

3. Optimal transfer method identification - 2 weeks

After the simulation results of both magnetic and capacitive coupling, an optimal solution

must be chosen, in order to maximize WPT efficiency.

4. Method implementation - 3 weeks

The implementation will include the design of support and auxiliary structures for the opti-

mal method found in task 3. These either be hand assembled or 3D printed. After that, the

resonator itself will be built and the connections performed.

5. Measurements and simulation results comparison - 1 week

19

20 Work Schedule

This task comprises the implementation’s performance measurements in both air and fresh

water. Demonstrations in seawater will also be accomplished. A correlation between mea-

surements and simulations will be assessed to validate the theoretical and 3D electromag-

netic models.

6. Transmitter electronics development - 5 weeks

In this work phase, simulation of the H-inverter and transistors’ selection will take place.

The transistors will be chosen to minimize their on resistance, so that the inverter efficiency

approaches its theoretical performance. Next, a printed circuit board consisting of a con-

troller and the H-inverter itself will be designed, printed and tested.

7. Dissertation writing - 3 weeks

Three weeks are predicted for dissertation writing.

A chronological representation of the work schedule is presented in the form of Gantt chart in

figure 4.1.

ID Task Name Start Finish Durationmar 2016 abr 2016 mai 2016 jun 2016

1 4w11/03/201615/02/2016Magnetic coupling simulation

2 4w11/03/201615/02/2016Capacitive coupling simulation

3 2w17/03/201604/03/2016Identification of best transfer method

4 3w06/04/201617/03/2016Method implementation

5 1w12/04/201606/04/2016Measurements and simulation comparison

6 5w16/05/201612/04/2016Transmitter electronics development

7 3w03/06/201616/05/2016Dissertation writing

Figure 4.1: Gantt chart depicting work schedule

4.2 Tools

For successful completion of the project, multiple tools will be needed for the different phases.

These are enumerated as follows:

1. Electrical circuit simulation software - Task 6

This software will play a major role in H-inverter’s design, as well as in the simulation of

the controller’s gate driver.

2. RF circuit simulation software - Tasks 1,2,3 and 5

RF simulation software allows for the validation of resonator’s equivalent electrical cir-

cuits. It also provides the needed power for designing impedance matching networks that

are crucial for maximum power transfer to take place between transmitter-resonator and

resonator-rectifier pairs.

4.2 Tools 21

3. 3D electromagnetic simulation software - Tasks 1,2,3 and 5

3D electromagnetic simulation permits the evaluation of a structure’s behaviour when ex-

cited with some sort of electrical stimulus. This presents a great impact in the resonator’s

design as it will allow for parametric studies and their impact on the system’s efficiency.

4. PCB design software - Task 6

In order to have a fully working and ready to use solution, a PCB implementation of the

transmitter is needed. This PCB will be connected to the underwater resonator on the dock-

ing station.

5. PCB printing equipment - Task 6

6. Typical laboratory equipment - Tasks 4,5 and 6

For regular measurements and operating the developed circuits, typical lab equipment will

be needed. Namely, multimeter, oscilloscope, DC power supplies and vectorial network

analyser.

7. Water tank - Task 5

A water tank will be needed to measure the system’s behaviour in an underwater environ-

ment.

8. 3D printer - Tasks 4 and 5

3D printing will allow the development of support and auxiliary structures for the resonators.

22 Work Schedule

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