Inductive Charging of Electrical Vehicles

Inductive Charging of Electrical VehiclesSystem Study

Mikael Cederlöf

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Abstract

A prerequisite of a fast increasing market of the electrical vehicles is the access to charging and reliability/accessibility of the charging systems. Wireless charging i.e. charging without a cord, is an interesting alternative that has been put forward during recent years.

In this work a system study of topologies for inductively coupled power transfer over an air gap of tens of centimetres has been investigated. In order to obtain an effective power transfer compensation capacitors are used to achieve resonance circuits.

In the thesis four different compensation topologies for inductively coupled power transfer are examined. Expressions for the compensation capacitances and the output voltage or current are derived.

An example design for each of the four topologies capable of handling a transfer of 3 kW of power over an air gap of 20 cm with an efficiency of at least 96% is examined. These designs use an outer radius for both coils of 30 cm, and an operating frequency of 20 kHz. The efficiency only encompasses the windings, and does not take into account the efficiency of any power electronics before or after the coils.

Prototype housing for the primary coil has been designed and built using basalt fibre reinforced high performance concrete, and magnetic measurements on the materials used are included in the report.

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Acknowledgements

First of all I would like to thank Sten Bergman at Elforsk for initiating this thesis work, for his enthusiasm and for contributing time and resources to this project. Then I would like to thank professor Göran Engdahl, my supervisor at KTH, for his support, feedback and proof reading. I also would like to thank Hector Zelaya de la Parra, Ener Salinas, Tomas Tegnér and Zichi Zhang at ABB for taking the time to help, guide, encourage and support me.

Further more I would like to thank Göte Lindfors and Günter Villman at Aquafence AB for building the concrete housing of the prototype, Stefano Bonetti and Johan Persson at NanOsc AB for performing the magnetic measurements. Also I would like to thank Johan Silfwerbrand at CBI for taking an interest in this thesis work, Niklas Thulin at Volvo, Thomas Bergfjord and Bjorn Karlstrom at ElectroEngine.

Finally I would like to thank my wife Malin for her constant care, support and encouragement.

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Table of ContentsAbstract...............................................................................................................................................iiiAcknowledgements..............................................................................................................................v1: Background of wireless power transfer............................................................................................1

1.1 History.......................................................................................................................................11.2 Overview of wireless power transfer.........................................................................................1

2: Theory behind inductive power transfer...........................................................................................32.1 Maxwell's Equations..................................................................................................................32.2 Magnetic field, magnetic flux and inductance...........................................................................32.3 The Coils....................................................................................................................................42.4 Mutual inductance model...........................................................................................................62.5 Leakage Flux..............................................................................................................................82.6 Power.........................................................................................................................................92.7 Resonance..................................................................................................................................92.8 Compensation alternatives.......................................................................................................102.9 The need for High Frequency..................................................................................................102.10 Skin Depth and Proximity Effect...........................................................................................112.11 Litz Wire................................................................................................................................122.12 Field shaping materials..........................................................................................................12

3: Modeling .......................................................................................................................................153.1 Field simulation program.........................................................................................................153.2 Field simulation geometry.......................................................................................................153.3 Interpreting obtained values.....................................................................................................163.4 Circuit analysis program..........................................................................................................163.5 Compensation Topologies........................................................................................................17

3.5.1 Secondary side impedance...............................................................................................173.5.2 Primary side impedance...................................................................................................193.5.3 Primary coil with constant amplitude current..................................................................21

3.6 Series-Series topology.............................................................................................................233.7 Series-Parallel topology...........................................................................................................243.8 Parallel-Series topology...........................................................................................................253.9 Parallel-Parallel topology........................................................................................................26

4: Models............................................................................................................................................274.1 Model names............................................................................................................................274.2 Model 230SS16A40.................................................................................................................284.3 Model 230SP420V40...............................................................................................................294.4 Model 230SP420V20...............................................................................................................304.5 Model 230SS36A20.................................................................................................................314.6 Model 230SP230V20...............................................................................................................324.7 Model 230PS230V20...............................................................................................................334.8 Model 230PP33A20.................................................................................................................344.9 Summary of the introduced models.........................................................................................35

5: Prototype Design............................................................................................................................375.1 Components and alternatives...................................................................................................375.2 Housing....................................................................................................................................375.3 Shielding material....................................................................................................................375.4 Core..........................................................................................................................................385.5 Coil...........................................................................................................................................385.6 Power electronics.....................................................................................................................38

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5.7 Output Constant Voltage or Constant Current.........................................................................396: Concrete Housing...........................................................................................................................41

6.1 Basalt fibers.............................................................................................................................416.2 Measurements..........................................................................................................................416.3 Comments................................................................................................................................42

7: Parameter study..............................................................................................................................437.1 Magnetic field calculations......................................................................................................43

7.1.1 Coil Radius.......................................................................................................................437.1.2 Coil Turns.........................................................................................................................447.1.3 Distance between primary and secondary coils...............................................................457.1.4 Frequency.........................................................................................................................45

7.2 Non-symmetrical sides............................................................................................................467.2.1 Coil Radius.......................................................................................................................467.2.2 Coil Turns.........................................................................................................................47

7.3 Simulink Studies......................................................................................................................487.4 Coil Resistances.......................................................................................................................487.5 Compensation Capacitors........................................................................................................49

7.5.1 Series-Series.....................................................................................................................507.5.2 Series-Parallel..................................................................................................................527.5.3 Parallel-Series..................................................................................................................547.5.4 Parallel-Parallel................................................................................................................56

7.6 Distance between Coils............................................................................................................577.6.1 Series-Series.....................................................................................................................587.6.2 Series-Parallel..................................................................................................................597.6.3 Parallel-Series..................................................................................................................607.6.4 Parallel-Parallel................................................................................................................61

7.7 Features and comments regarding the studied topologies.......................................................628: Recommendations..........................................................................................................................63

8.1 Suggested compensation topologies for demonstration purposes...........................................638.2 Suggested control alternatives.................................................................................................63

8.2.1 Adjusting the input voltage..............................................................................................638.2.2 Adjusting the distance between the two coils..................................................................648.2.3 Adjusting the frequency...................................................................................................64

8.3 Relative size of the two coils...................................................................................................648.4 Further work............................................................................................................................64

9: Results and Conclusions.................................................................................................................6710: References....................................................................................................................................69Appendices.........................................................................................................................................71

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1: Background of wireless power transfer

A pre-study on the feasibility of wireless power transfer was performed at KTH in the form of a Masters Thesis in 2009 [1]. That study gave good insight into the theory of inductive and resonant transfer of electric energy and how to design an inductive charging system.

1.1 History

Electromagnetic induction was discovered independently by Michael Faraday and Joseph Henry in 1831. Faraday published his results first and became the officially recognized discoverer of the phenomenon.

In Faraday's experimental demonstration of electromagnetic induction, he wrapped two wires around opposite sides of an iron torus. He plugged one wire into a galvanometer, watched it as he connected the other wire to a battery, and observed a transient current (which he called a "wave of electricity") both when he connected the wire to the battery and when he disconnected it [2]. The SI unit for capacitance is named after him.

Henry's experiment consisted of an electromagnet perched on a pole, rocking back and forth. The rocking motion was caused by one of the two leads on both ends of the magnet rocker touching one of two battery cells, causing a polarity change, and rocking the opposite direction until the other two leads hit the other battery. This apparatus allowed Henry to recognize the property of self inductance [3]. The SI unit for inductance is named after him.

James Clerk Maxwell later formulated the classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory [4]. This theory was later distilled down to the four famous equations known as Maxwell's equations by Oliver Heaviside [5].

Wireless transmission of energy was demonstrated in 1891 by Nikola Tesla. His many revolutionary developments in the field of electromagnetism were based on the theories of electromagnetic technology discovered by Michael Faraday [6]. The SI unit for the magnetic field was named after him.

1.2 Overview of wireless power transfer

Wireless power supply of an electric vehicle is considered by many as a ground breaking innovation, given that it is safe enough and can show an appropriate efficiency. No hassle with cords would be welcomed by many drivers.

Since a number of years back innovative concepts on electric vehicle charging has been going on, and wireless inductive charging has efficiently been used used in environments where conductive power transfer has been a problem.

In New Zealand, at the University of Auckland, the wireless technology for electric vehicle (EV) charging has been a key subject, and their technology has been patented and commercialized through the University by UniServices. Licenses have been sold and patents are now spread around the globe.

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In Asia, Europe and US many attempts have been made to develop wireless power technology for both consumer applications and large power industrial use. Bombardier is e.g. using wireless inductive power transfer to feed continuous power to their trams. One successful demonstrator already runs in Berlin and development projects to feed heavy trucks at highways are going on.

Inductive power transmission is now getting into focus not only for personal vehicles but also for a number of mobile applications. The power transfer demonstrated so far include power levels up to about 7-10 kW but with ambitions to reach hundreds of kW within this decade. Efficiencies are reported to be between 80 – 95%.

Despite the fact that a potential customer only have to park the car at a given spot there are many things that must work and be synchronized. This includes performance, safety, interoperability, communication, frequency, and battery management issues.

International standardization efforts have been started within this field. Both in Japan, Europe and US standardization bodies are now forming task forces and defining areas of interest. The Society of Automotive Engineers (SAE) task force on wireless charging and positioning of electric vehicles (SAE J2954) has grown to form six sub teams.

Put together, there is a rapidly increasing interest of wireless charging of electric vehicles which is reflected trough the many ongoing university and industrial cooperation projects worldwide.

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2: Theory behind inductive power transfer

Wireless transmission of energy using induction is based on the theory described by Maxwell's equations. A current through a conductor produces a magnetic field. Variations in the magnetic field creates an electric field. The electric field causes the electrical charges to move, producing a current.

2.1 Maxwell's Equations

Maxwell's equations is a collective name for four famous equations. These equations were discovered and refined by Gauss, Ampère, Faraday and Maxwell.

∮SE⋅ds=

Qϵ0

(2.1)

∮SB⋅ds=0 (2.2)

∮CE⋅dl=

−d ΦB

dt(2.3)

∮CB⋅dl=μ0(I+ϵ0

d ΦE

dt ) (2.4)

The first equation relates the electrical field with electrical charges. The second equation states that there are no sources or sinks for magnetic fields, all field lines are closed loops. The third equation states that the electrical field is related to the change in the magnetic flux. The fourth equation relates the magnetic field with a current and the change in the electric flux.

2.2 Magnetic field, magnetic flux and inductance

Figure 2.1: A closed loop and magnetic flux lines.

According to equation (2.4), running a current through a closed loop will create a magnetic field, also known as magnetic flux density, B. This closed loop encloses a surface S. Through this surface there flows a magnetic flux ΦB, henceforth called Φ.

ΦB=∫SB⋅dS (2.5)

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The magnetic flux density is proportional to the applied current, meaning the magnetic flux is also proportional to the current. This proportionality coefficient is the inductance L.

Φ=LI (2.6)

Figure 2.2: Two closed loops with mutual flux Φ12.

Placing a second closed loop in the vicinity of the first will cause some of the magnetic flux from the first loop, due to B1, to pass through the surface of the second loop, S2. This is designated as the mutual flux Φ12.

Φ12=∫S 2

B1⋅dS2 (2.7)

Running a current through the second loop instead, will produce another mutual flux.

Φ21=∫S1

B2⋅dS1 (2.8)

The proportionality coefficient between the current and the mutual flux is the mutual inductance.

Φ12=L12 I 1 (2.9)

Φ21=L21 I 2 (2.10)

It turns out that the mutual inductances are the same [7].

M=L12=L21 (2.11)

2.3 The Coils

To run a current through a closed loop a coil is used. If a coil has N coil turns, the current in each turn will add to the magnetic flux density. In other words, B is proportional to the number of turns carrying the current I.

B∝NI (2.12)

The number of turns the magnetic flux links with determines the flux linkage, Ψ.

Ψ=N Φ (2.13)

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For a coil with more than one turn the flux linkage is used to calculate the inductance.

L=ΨI

(2.14)

Now, L is proportional to NΦ, and Φ is proportional to B, and B is proportional to NI. This means that the self inductance is proportional to the square of the number of turns of the coil.

L∝N 2 (2.15)

The same reasoning is done with the mutual inductance. A current I1 runs through a coil with N1

turns, causing a magnetic flux density B1.

B1∝N1 I1 (2.16)

The flux density B1 will cause a mutual flux Φ12 which will link to the second coil.

Φ12=∫S 2

B1⋅dS2 (2.17)

If the mutual flux links with N2 turns of the second coil, the flux linkage becomes N2Φ12.

Ψ12=N2 Φ12 (2.18)

From the flux linkage the mutual inductance is calculated.

M=Ψ12

I 1

(2.19)

Now, M is proportional to N2Φ12, and Φ12 is proportional to B1, and B1 is proportional to N1I1. This means that the mutual inductance is proportional to the product of the number of turns in the coils.

M ∝N1 N2 (2.20)

The inductance of a coil is determined by the geometrical shape and the physical arrangement of the conductor as well as the permeability of the medium [7]. The mutual inductance between two coils is further dependent on the distance and relative position of the two coils.

The ratio between the mutual inductance and the square root of the product of the self inductances is the coupling coefficient, k.

k=M

√( L1 L2)(2.21)

0⩽k⩽1 (2.22)

This coefficient measures the magnetic coupling between the coils and is independent of the number of turns in the coils. It only depends on the relative positions of the two coils and the physical properties of the media in the vicinity of these coils.

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2.4 Mutual inductance model

According to Faraday's law, equation (2.3), an alternating flux linkage will cause an induced electromotive force, or voltage.

u2(t)=d ψ12( t)

dt(2.23)

Here the negative sign has been compensated for by changing the direction of the winding of the second coil. From the current I1 through the first coil a voltage U2 will be induced in the second coil.

Figure 2.3: Two magnetically coupled coils with good coupling.

If the second coil is closed, a current I2 will flow in the second coil. This current will cause a magnetic flux density B2, which in turn will cause a magnetic flux. This flux will oppose the mutual flux from the first coil. Using superposition the total flux linkage of the second coil will be described as a combination of the self-flux linkage Ψ22 and the mutual flux linkage Ψ12.

ψ2(t)=ψ12(t)−ψ22(t) (2.24)

Some flux from the current in the second coil will link with the first coil, and the total flux linkage of the first coil is defined in the same way.

ψ1( t)=ψ11( t)−ψ21( t) (2.25)

These equations are now described in terms of inductances.

ψ1( t)=L1i1(t)−M i2(t) (2.26)

ψ2( t)=M i1(t )−L2i2(t) (2.27)

Using Faraday's law on the total flux linkages of each coil, assuming the inductances are time invariant leads to the relationship between input voltage and current and output voltage and current [8].

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u1(t)=L1

di1(t)dt

−Mdi2(t)

dt(2.28)

u2(t)=Mdi1(t)

dt−L2

di2(t)dt

(2.29)

Assuming all currents are sinusoidal and steady-state these equations can be written on phasor form.

U1= jω L1 I 1− j ωM I 2 (2.30)

U2= jω M I1− j ω L2 I 2 (2.31)

A non-ideal coil consist of a resistance in series with an inductance. The equations are modified to include these resistances.

U1=R1 I 1+ j ω L1 I 1− j ω M I 2 (2.32)

U 2= jω M I1−R2 I 2− jω L2 I 2 (2.33)

Figure 2.4 illustrates equations (2.32) and (2.33) in a circuit diagram.

Figure 2.4: Circuit diagram of mutual inductance model.

Equation (2.33) can be seen as an induced voltage Uind due to the current in the primary coil, and a voltage drop Udrop due to the current in the secondary coil.

U2=U ind−U drop (2.34)

Where

U ind= jω M I1 , (2.35)

U drop=( R2+ j ω L2) I 2 . (2.36)

Connecting the load resistance Rload to the secondary coil will create a closed circuit.

j ω M I 1=R2 I2+ j ω L2 I 2+Rload I 2 (2.37)

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The current through the second coil is given by the induced voltage divided by the total impedance.

I2=j ωM I 1

R2+ j ω L2+Rload

(2.38)

And can be rewritten as

I 2=j ω M I 1

Z2

(2.39)

Where Z2 is the total impedance of the second coil and load. This is inserted into the expression for the first coil, equation (2.32).

U1=R1 I 1+ j ω L1 I 1+ω

2 M 2

Z2

I 1 (2.40)

It is now clear that from the point of view of the first coil, the second coil is seen as a transformed impedance from the secondary side, ZS.

Z s=ω

2 M 2

Z2

(2.41)

2.5 Leakage Flux

The self-flux linkages are composed of two parts. The main flux linkage that connects with other coils and the leakage flux linkage that does not connect with any other coil. The name main flux linkage comes from the fact that in transformers the main flux linkage is the dominant part of the flux linkage. This is not the case with inductive power transfer.

Ψ11=Ψ11m +Ψ11

l (2.42)

The main flux linkage is the mutual flux linkage linked with the coil that produced it.

Ψ11m =N1 Φ12 (2.43)

The main flux linkage is scaled by a factor N2/N2,

N1 Φ12=N 1

N 2

N 2Φ12 , (2.44)

and is expressed as a scaling of the mutual inductance.

Ψ11m=

N 1

N 2

M I 1 (2.45)

Dividing by the current gives the main inductance.

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L1m=

N1

N2

M (2.46)

This gives the leakage inductance expressed in inductances.

L1l =L1−L1

m (2.47)

It is easy to see that in the case of no secondary coil, the mutual inductance is zero, and the self inductance consists only of the leakage inductance. If the coupling coefficient k goes to one, then the leakage inductance goes to zero. This can be seen in equation (2.43), if Φ12 is the total flux produced by the coil, then this is the definition of the self inductance.

2.6 Power

Due to the large leakage flux most of the magnetic energy will only link with the coil itself, and return the energy. This energy is what causes the current in the coil to lag the voltage. The product of the voltage and current is called the power.

p (t)=u(t )i( t) (2.48)

When dealing with complex voltages and currents on phasor form, the power will be complex and denoted S. Complex power, S, consists of Active power, P, and Reactive power, Q.

S=P+ jQ (2.49)

A current and voltage in phase will always have a positive product. This is active power, and it is the power that conducts work. When the voltage and current are out of phase with each other, part of the time the power will be positive and part of the time the power will be negative. This is reactive power, and it will flow back and forth in the system without performing any net work. It will however give cause to resistive losses in the system.

2.7 Resonance

Inductances and capacitances cause phase shifts. The phase shift is expressed by the equation of the impedance.

Z L= j ω L (2.50)

Z C=1

j ωC

=− jωC

(2.51)

Since one of the components cause a phase shift of +90 degrees, and the other a phase shift of -90 degrees, they can be used to cancel each other out.

ω L=1

ωCor L=

1

ω2C

or C=1

ω2 L

or ω=1

√ LC(2.52)

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This is called resonance. When resonance occurs the current caused by the collapsing magnetic field in the inductor charges the capacitor. The discharging capacitor then drives a current through the inductor that produces a magnetic field. The energy in the system shifts between magnetic energy and electric energy. In the ideal case there are no losses and the system will continue to resonate. In reality however there are resistances in the inductor and capacitor that will lead to losses and the ringing will die out.

2.8 Compensation alternatives

Resonance can be achieved with series compensation or with parallel compensation. The following equations expresses the impedance of the series case and the parallel case.

Z Series=Z L+Z C (2.53)

ZParallel=Z L ZC

Z L+ZC(2.54)

These can be rewritten as

Z Series=j(ω2 L C−1)

ωC, (2.55)

and

ZParallel=ω L

j (ω2 LC−1). (2.56)

During resonance the impedance of the series compensated case goes to zero, and the impedance of the parallel compensated case goes to infinity.

limω →

1

√ LC

Z Series=0(2.57)

limω →

1

√ LC

Z Parallel=∞(2.58)

In both these cases the resonance is used to preserve the energy from the leakage flux of the coil, and use it to maintain the magnetic coupling of the system. Without this preservation only a very small amount of the energy entered into the system would arrive at the other end.

2.9 The need for High Frequency

The equation for the induced voltage in the secondary coil is

U ind= jω M I1 . (2.59)

If the distance between the two coils is increased, only the value of the mutual inductance M will

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change in this equation. As the distance increases, the mutual inductance decreases. To keep the induced voltage constant without running a larger current through the first coil the frequency needs to be increased.

As the frequency increases there are some things that needs to be taken into consideration.

2.10 Skin Depth and Proximity Effect

Conductivity, σ, is the ability of a material to conduct electric currents. Metals are very good conductors, for example copper has a conductivity of 5.8x107 S/m, iron has a conductivity of 107

S/m, and rubber which is an isolator has a conductivity of about 10-15 S/m.

In the case of a direct current, the current density distribution is constant over the cross section area. An alternating current however will change the current density distribution. Reducing it at the center of the conductor and concentrating it at the surface.

Figure 2.5: Current density distribution for low, medium and high frequency.

The skin depth, δ, is defined as the depth at which the current density falls to 1/e, (about 0.37), of the current density at the surface. This can be approximated with

δ=√ 2ρ

ωμ, (2.60)

where ρ is the resistivity of the material and is related to the conductivity as 1/σ, and μ is the permeability of the material.

When conductors are placed in parallel near each other, as with the the windings of a coil, they will be affected by the proximity effect. Figure 2.6 shows how this further affects the current density distribution.

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Figure 2.6: The influence of the proximity effect on the current density distribution for a medium frequency

These effects increases the AC resistance of a conductor or wire dramatically, especially at higher frequencies.

2.11 Litz Wire

Since the skin depth determines the effective current carrying area of a conductor, a conductor thicker than the skin depth will not be an effective use of material. A Litz wire consists of many thin strands, each individually insulated, wound into a wire. Each strand is no thicker than the skin depth, this ensures an effective use of the conductive area. The strands are then woven together so that the location of each strand alternates between the center of the wire and the edge of the wire. This ensures that the proximity effect will affect each strand the same, and thus carry the same current.

This will not remove the influence of the proximity effect and skin depth, but it will significantly decrease the AC resistance compared to normal wires.

2.12 Field shaping materials

A magnetic field created by a coil will extend equally above and below the coil. For inductive power transfer this is undesirable. There are however ways to shape the field.

Figure 2.7: A conductor without field shaping materials.

The Relative Permeability, μr, defines the ability of a material to conduct magnetic fields. In vacuum the relative permeability is equal to one, whereas iron has a relative permeability in the range of 4x103. Magnetic materials can be roughly classified into three groups.

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Diamagnetic: μr is slightly smaller than one.Paramagnetic: μr is slightly larger than one.Ferromagnetic: μr is much larger than one.

When a magnetic field encounters a paramagnetic material such as copper, the relative permeability is almost equal to one, and the field will only slightly prefer the copper over free space. However, copper is conductive and there will be eddy currents induced in the copper. These eddy currents will create their own magnetic field, a field in the opposite direction of the external field. This will cause the external field to bend off instead of entering the material. This effect is called repulsion.

When a magnetic field encounters a ferromagnetic material, the high permeability causes the field to prefer the material over open space. The magnetic field will be captured by the material.

Iron is a ferromagnetic material that is also conductive, in this case the relative permeability of the iron is high enough to overcome the repulsive effects of the eddy currents, but there will be a lot of eddy current losses due to the captured magnetic field. These losses will heat the iron.

In transformers an iron core is often used to conduct the magnetic flux between the coils. In order to limit the eddy current losses the transformer core consists of thin insulated sheets of iron. This laminated core will prevent much of the eddy currents, and substantially reduces the losses.

The magnetic field can be shaped by placing a ferromagnetic material with low conductivity on a paramagnetic material with high conductivity. The ferromagnetic material will conduct the magnetic field while the conductive material will repel the magnetic field.

Figure 2.8: A conductor with field shaping materials.

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3: Modeling

Calculating the inductance can be done by solving differential equations. Adding field shaping materials will significantly increase the complexity of these equations. A finite element program can handle complex geometries with different materials and produces a numerical solution to the problem.

In this work the program FEMM was used for finite element calculations. FEMM stands for Finite Element Method Magnetics. The results were then used in Matlab to perform circuit analysis.

3.1 Field simulation program

FEMM [9] is a free program that can be controlled from within Matlab or Octave. A 2-dimensional geometry is defined either in a in a matlab script or in the program itself, and after the simulation information such as the inductances, resistances and losses can be extracted.

In order for FEMM to be able to use a material in its simulations, the material must be defined. When defining a material the two most important parameters are its conductivity σ and its relative permeability μr. Values for these parameters can be found in text books [7] or Wikipedia [10][11]. FEMM accepts the conductivity in mega Siemens per meter. That is 106 S/m.

Table 3.1: FEMM material definitions.Material Conductivity σ [S/m] FEMM σ [MS/m] Relative Permeability μr

Air 5 x 10-15 0 1

Aluminium 3.54 x 107 35.4 1

Copper 5.80 x 107 58 1

Ferrite 1 10-6 1000

When it comes to the relative permeability of the ferromagnetic material it comes down to what the manufacturer can supply. For example Mumetal is a special alloy that has a relative permeability of about 100000. In comparison pure Iron has a relative permeability of 4000. In this work the relative permeability of ferrite will be set to 1000.

3.2 Field simulation geometry

FEMM can solve both planar problems or axisymmetric problems. A planar problem takes a 2-dimensional problem definition and then applies a depth. The axisymmetric problem takes a 2-dimensional problem definition and then rotates it around a central axis. This work uses the axisymmetric definition and will therefore correspond to a circular geometry.

The primary side of the Inductively Coupled Power Transfer (ICPT) will consist of a copper coil on top of a ferrite core and an aluminium shield. The secondary side will be a mirror image of the primary side. This design will shield the area above and below the ICPT and focus the field in the area between the two coils. Surrounding the geometry a large volume of air is defined. Figure 3.1 illustrates the geometry used in the field calculations.

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Figure 3.1: FEMM image of two coils with shields and cores.

3.3 Interpreting obtained values

Circuit definitions are used to define the parts of the geometry that conduct defined currents, and are used to run a current through a coil. Coil turns can be individually modeled and included in the same circuit.

FEMM will calculate the voltage drop and the flux linkage for each circuit definition. From this the resistance of the coil, R, is calculated by taking the real part of the ratio between the voltage and the current. The inductance of the coil, L, is calculated by dividing the flux linkage, Ψ, with the current, I.

R=Real UI (3.1)

L=ΨI (3.2)

The mutual inductance is calculated by first running the current I1 through the first coil and saving the flux linkage Ψ11, then running the current I2 through the second coil and saving the flux linkage Ψ22, then finally running the current I1 through the first coil while simultaneously running the current I2 through the second coil and obtaining the total flux linkage for each coil, Ψ1 and Ψ2.

M=(Ψ1−Ψ11)

I 2

=(Ψ2−Ψ22)

I 1

(3.3)

Which is the same as the definition of the mutual inductance.

M=Ψ21

I 2

=Ψ12

I1(3.4)

It does not matter which mutual flux linkage is used to define the mutual inductance, since FEMM produces the same result for both cases. This is in accordance to the theory in chapter 2.

3.4 Circuit analysis program

Figure 3.2 shows the basic circuit model used to simulate the inductively coupled power transfer. It is simulated in the Matlab toolbox Simulink using the library SimPowerSystems [12], and consists of a voltage source connected to a mutual inductance model of a transformer. On the other side of the mutual inductance block, the load will be simulated using a resistance.

A small line resistance is included to prevent errors when a capacitor is connected in parallel to the mutual inductance block.

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Figure 3.2: Circuit model without compensation.

The mutual inductance block uses six variables to model a transformer. Primary Winding Impedance [R1, L1], Secondary Winding Impedance [R2, L2] and Mutual Impedance [Rm, Lm].

Figure 3.3: SimPowerSystems mutual inductance block circuit diagram.

Figure 3.3 shows the circuit diagram of the mutual inductance block. If the mutual resistance, Rm, is set to zero, this circuit diagram is equivalent to the mutual inductance model in figure 2.4. The mutual resistance is used to model eddy current losses and hysteresis losses in a transformer core. These losses will be disregarded in this work.

3.5 Compensation Topologies

Both sides of the inductively coupled power transfer needs a resonant capacitance. Since the capacitor can be connected either in series or in parallel with the coil, this gives a total of four different compensation topologies.

3.5.1 Secondary side impedance

Figure 3.4: Secondary impedance with series compensation and with parallel compensation.

17

Figure 3.4 illustrates the total impedance of the secondary side, Z2, as seen by the induced voltage in the secondary coil. The total impedance of the secondary side when using series compensation is given by equation (3.5)

Z2=Z L2+ZC2+RLOAD , (3.5)

and the total impedance of the secondary side when using parallel compensation is given by equation (3.6)

Z2=Z L2+1

1ZC2

+1

RLOAD

. (3.6)

Figure 3.5 illustrates how the voltage over the load resistance varies with the compensation capacitance when the secondary side is series compensated and is connected to a voltage source with a constant amplitude.

4 5 6 7 8 9

x 10-7

60

80

100

120

Compensation capacitance [F]

Load

vol

tage

[V]

Load resistance = 300 OhmLoad resistance = 25 OhmLoad resistance = 10 OhmLoad resistance = 5 Ohm

Resonance occursfor C2 = 6.3e-7 [F]

Figure 3.5: Series connected compensation capacitance.

Figure 3.6 illustrates how the current through the load resistance varies with the compensation capacitance when the secondary side is parallel compensated and is connected to a voltage source with a constant amplitude.

4 5 6 7 8 9

x 10-7

6

7

8

9

10

Compensation capacitance [F]

Load

cur

rent

[A]

Load resistance = 0 OhmLoad resistance = 10 OhmLoad resistance = 20 OhmLoad resistance = 30 Ohm

Resonance occursfor C2 = 6.3e-7 [F]

Figure 3.6: Parallel connected compensation capacitance.

18

The value of the resonant capacitance, C2, is the same in the parallel compensated case as in the series compensated case.

C2=1

ω02 L2

(3.7)

Applying equation (3.7) to equation (3.5) and equation (3.6) gives the total impedance of the secondary side, Z2, when the secondary side is in resonance. The impedance of the secondary side series compensated by C2 is given by equation (3.8)

Z2=RLOAD , (3.8)

and the impedance of the secondary side parallel compensated by C2 is given by equation (3.9)

Z2=ω0

2 L22

RLOAD− j ω0 L2

. (3.9)

Combining equation (3.8) and equation (3.9) with equation (2.41) results in ZS, which is the total impedance of the secondary side as seen by the primary coil. When the secondary side is series compensated, ZS is given by equation (3.10)

Z S=ω0

2 M 2

RLOAD

, (3.10)

and when the secondary side is parallel compensated, ZS is given by equation (3.11)

Z S=ω0

2 M 2 ( RLOAD− j ω0 L2 )ω0

2 L22 =

M 2 RLOAD

L22 − j

ω0 M 2

L2

. (3.11)

This means that when the secondary side is parallel compensated, a phase shift is introduced into the system. That phase shift can only be compensated on the primary side.

3.5.2 Primary side impedance

Figure 3.7: Primary impedance with series compensation and with parallel compensation.

Figure 3.7 shows the total impedance of the primary side, Z1, as seen by the voltage source. When using series compensation the total impedance of the primary side is given by equation (3.12)

19

Z1=ZC1+ZL1+ZS , (3.12)

and when using parallel compensation the total impedance of the primary side is given by equation (3.13)

Z1=ZC1 ( ZL1+ZS )ZC1+ZL1+ZS

. (3.13)

Resonance is achieved on the primary side if the total impedance on the primary side, Z1, is purely resistive. If the secondary side is series compensated, ZS is purely resistive as per equation (3.10), and the resonant capacitance on the primary side, C1 is given by equation (3.14)

C1=1

ω02 L1

. (3.14)

If the secondary side is parallel compensated, ZS has a reactive part as per equation (3.11), and the resonant capacitance on the primary side, C1 is given by equation (3.15)

C1=1

ω02(L1−

M 2

L2) . (3.15)

The resonant capacitance on the primary side, C1, has the same value for the parallel compensated case as for the series compensated case. Applying equation (3.14) to equation (3.13) gives the total impedance of the primary side, Z1, when the primary side is parallel compensated and the secondary side is series compensated

Z1=ω0

2 L12

ZS

− j ω0 L1 . (3.16)

Combining equation (3.16) with equation (2.41) gives the total impedance on the primary side, Z1, as a function of the total impedance on the secondary side, Z2,

Z1=Z2 L1

2

M2 − j ω0 L1 . (3.17)

Equation (3.17) puts some constraints on Z2 in order for the system to be in resonance. Z2 is divided into its resistive part RZ2 and its reactive part XZ2,

Z2=RZ2+ j X Z2 . (3.18)

The criteria for resonance is now that the reactance of the secondary side compensates for the inductance of the primary coil, L1. The expression for this is given by equation (3.19),

X Z2=ω0 M 2

L1

. (3.19)

20

The reactance XZ2 is introduced into Z2 by adjusting the secondary compensation capacitance C2.

C2=1

ω02(L2−

M 2

L1) (3.20)

When the primary side is parallel compensated a phase shift is introduced to the the secondary coil, that brings the secondary side out of resonance. Using the compensation capacitance defined by equation (3.20) brings the secondary side back into resonance again.

Parallel compensation introduces phase shifts into the system that must be compensated for on the opposite side.

3.5.3 Primary coil with constant amplitude current

Figure 3.5 shows that the series compensated secondary side behaves as a voltage source, and figure 3.6 shows that the parallel compensated secondary side behaves as a current source. This is only true if the secondary side is fed by an induced voltage with a constant amplitude.

The voltage induced in the secondary coil, Uind, is proportional to the current through the primary coil, IL1,

U ind= jω M I L1 . (3.21)

The current through the primary coil, IL1, is determined by the input voltage, U1, and by the the total impedance of the secondary side as seen by the primary coil, ZS. When the primary side is series compensated the current through the primary coil is

I L1=U 1

Z S, (3.22)

and when the primary side is parallel compensated the current through the primary coil is

I L1=U 1

Z L1+Z S. (3.23)

The current through the primary coil can be kept constant in amplitude if the input voltage is varied as a function of ZS. That would result in an induced voltage in the secondary coil, Uind, with a constant amplitude. Which in turn would result in the series compensated secondary side behaving as a voltage source, and the parallel compensated secondary side behaving as a current source.

The amplitude of the load voltage, ULOAD, when the secondary side is series compensated is given by equation (3.24)

U LOAD=ω0 M I L1 , (3.24)

and the amplitude of the load current, ILOAD, when the secondary side is parallel compensated is given by equation (3.25)

21

I LOAD=ML2

I L1 . (3.25)

However, this is only the case when the input voltage is regulated to keep the amplitude of the current through the primary coil constant. The following pages will show the behavior of the different compensation topologies when the inductively coupled power transfer is supplied by a constant amplitude voltage source.

22

3.6 Series-Series topology

Figure 3.8: Series-Series compensation model.

The resonant compensation capacitances are

C1=1

ω02 L1

, (3.26)

and

C2=1

ω02 L2

. (3.27)

The series-series topology behaves like a current source. It will produce a constant output current.

1 2 3 4 50

100

200

300Primary side input

Vol

tage

[V] a

nd C

urre

nt [A

]

Load Resistance [Ω]

VoltageCurrent

1 2 3 4 50

100

200Secondary side output

Vol

tage

[V] a

nd C

urre

nt [A

]


VoltageCurrent

Figure 3.9: Series-Series topology voltage and current plot.

The amplitude of the output current can be approximated by

I LOAD=1

ω0 MU1 , (3.28)

as long as the frequency is high enough and the load resistance is low enough.

23

3.7 Series-Parallel topology

Figure 3.10: Series-Parallel compensation model.


C1=1

ω02( L1−

M 2

L2) , (3.29)

and

C2=1

ω02 L2

. (3.30)

The series-parallel topology behaves like a voltage source. It will produce a constant output voltage.

5 10 15 200

100

200


Vol

tage

[V] a

nd C

urre

nt [A

]


VoltageCurrent

5 10 15 200

100

200


Vol

tage

[V] a

nd C

urre

nt [A

]


VoltageCurrent

Figure 3.11: Series-Parallel topology voltage and current plot.

The amplitude of the output voltage can be approximated by

U LOAD=L2

MU 1 , (3.31)

as long as the frequency and load resistance is high enough.

24

3.8 Parallel-Series topology

Figure 3.12: Parallel-Series compensation model.


C1=1

ω02 L1

, (3.32)

and

C2=1

ω02( L2−

M 2

L1) . (3.33)

The parallel-series topology behaves like a voltage source. It will produce a constant output voltage.

5 10 15 200

100

200


Vol

tage

[V] a

nd C

urre

nt [A

]


VoltageCurrent

5 10 15 200

100

200


Vol

tage

[V] a

nd C

urre

nt [A

]


VoltageCurrent

Figure 3.13: Parallel-Series topology voltage and current plot.

The amplitude of the output voltage can be approximated by

U LOAD=ML1

U 1 , (3.34)

as long as the frequency and load resistance is high enough.

25

3.9 Parallel-Parallel topology

Figure 3.14: Parallel-Parallel compensation model.

The primary resonant capacitance is

C1=1

ω02( L1−

M 2

L2) , (3.35)

and

C2=1

ω02( L2−

M 2

L1) . (3.36)

The parallel-parallel topology behaves like a current source. It will produce a constant output current.

1 2 3 4 50

100

200


Vol

tage

[V] a

nd C

urre

nt [A

]


VoltageCurrent

1 2 3 4 50

100


Vol

tage

[V] a

nd C

urre

nt [A

]


VoltageCurrent

Figure 3.15: Parallel-Parallel topology voltage and current plot.

The amplitude of the output current can be approximated by

I LOAD=M

ω0 ( L1 L2−M 2)U 1 , (3.37)

as long as the frequency is high enough and the load resistance is low enough.

26

4: Models

Several models were produced during the run of this project. The early models were used as a guideline for the output levels and the size of the coils. Each model is designed to be used with a specific compensation topology. The compensation topology determines if the system produces a constant output voltage or a constant output current, and the model determines the ability of the system to deliver a constant output.

4.1 Model names

The models have been named by the input voltage, the compensation topology, the output quantity and the frequency in kilohertz. For example, model 230SS16A40 when fed with a voltage of 230 V and used with the series-series compensation topology will produce an output current of 16 A when the frequency is 40 kHz.

27

4.2 Model 230SS16A40

Table 4.1: Geometry specifications and resulting simulated values.Litz wire specifications Simulation parameters

Number of strands 200 Frequency 40 [kHz]

Strand diameter 0.20 [mm]

Conductor diameter 3.94 [mm]

Geometry specifications Simulated values

Primary coil turns 25 Primary coil inductance 2.80e-4 [H]

Secondary coil turns 25 Secondary coil inductance 2.80e-4 [H]

Coil radius 0.20 [m] Mutual inductance 5.50e-5 [H]

Core radius 0.40 [m] Primary coil resistance 1.05e-1 [Ω]

Shield radius 0.50 [m] Secondary coil resistance 1.04e-1 [Ω]

Coil to coil distance 0.20 [m]

Figure 4.1 is an illustration of model 230SS16A40, which is intended to be used with the series-series compensation topology. It will produce an output current with an amplitude of about 16 A if fed by a voltage of 230 V and a frequency of 40 kHz.

Figure 4.1: Geometry visualization of model 230SS16A40.

Table 4.2 lists the simulated output voltage, output current and input current when the model is used to transfer 3 kW to the secondary side.

Table 4.2: Circuit analysis of model 230SS16A40.Circuit model parameters 3 kW Transferred power

Topology SS Load 11.3 [Ω]

Output current 16 [A] Efficiency 98.5%

Frequency 40 [kHz] Power factor 1.0

3 kW Source input 3 kW Load output

Voltage 230 [V] Voltage 185 [V]

Current 13.5 [A] Current 16.5 [A]

28

4.3 Model 230SP420V40








Coil radius 25 [cm] Mutual inductance 1.72e-5 [H]

Core radius 40 [cm] Primary coil resistance 1.46e-1 [Ω]

Shield radius 50 [cm] Secondary coil resistance 2.29e-2 [Ω]

Coil to coil distance 25 [cm]

Figure 4.2 is an illustration of model 230SP420V40, which is intended to be used with the series-parallel compensation topology. It will produce an output voltage with an amplitude of about 420 V if fed by a voltage of 230 V and a frequency of 40 kHz.

Figure 4.2: Geometry visualization of model 230SP420V40.


Table 4.4: Circuit analysis of model 230SP420V40.Circuit model parameters 3 kW Transferred power

Topology SP Load 60 [Ω]

Output voltage 420 [V] Efficiency 97.0%





29

4.4 Model 230SP420V20
















Topology SP Load 60 [Ω]






30

4.5 Model 230SS36A20












Figure 4.4 is an illustration of model 230SS36A20, which is intended to be used with the series-series compensation topology. It will produce an output current with an amplitude of about 36 A if fed by a voltage of 230 V and a frequency of 20 kHz.

Figure 4.4: Geometry visualization of model 230SS36A20.


Table 4.8: Circuit analysis of model 230SS36A20.Circuit model parameters 3 kW Transferred power

Topology SS Load 2.4 [Ω]






31

4.6 Model 230SP230V20
















Topology SP Load 16.9 [Ω]






32

4.7 Model 230PS230V20












Figure 4.6 is an illustration of model 230PS230V20, which is intended to be used with the parallel-series compensation topology. It will produce an output voltage with an amplitude of about 230 V if fed by a voltage of 230 V and a frequency of 20 kHz.

Figure 4.6: Geometry visualization of model 230PS230V20.


Table 4.12: Circuit analysis of model 230PS230V20.Circuit model parameters 3 kW Transferred power

Topology PS Load 18.0 [Ω]






33

4.8 Model 230PP33A20












Figure 4.7 is an illustration of model 230PP33A20, which is intended to be used with the parallel-parallel compensation topology. It will produce an output current with an amplitude of about 33 A if fed by a voltage of 230 V and a frequency of 20 kHz.

Figure 4.7: Geometry visualization of model 230PP33A20.


Table 4.14: Circuit analysis of model 230PP33A20.Circuit model parameters 3 kW Transferred power

Topology PP Load 2.8 [Ω]






34

4.9 Summary of the introduced models

Table 4.15 contains a summary of the models introduced in this chapter. In the coil turns column Na corresponds to the number of turns in the primary coil and Nb corresponds to the number of turns in the secondary coil. The efficiency was measured when 3 kW power was transferred to the secondary side, and the load corresponds to the resistance used for the 3 kW power transfer.

Table 4.15: Summary of models.Model Name Input Output Frequency Coil Turns

Na-NbLoad3 kW

Efficiency3 kW

230SS16A40 230 [V] 16 [A] 40 [kHz] 25-25 11.3 [Ω] 98.5 %

230SP420V40 230 [V] 420 [V] 40 [kHz] 20-4 60 [Ω] 97.0 %

230SP420V20 230 [V] 420 [V] 20 [kHz] 20-4 60 [Ω] 92.8 %

230SS36A20 230 [V] 36 [A] 20 [kHz] 20-20 2.4 [Ω] 99.0 %

230SP230V20 230 [V] 230 [V] 20 [kHz] 20-2 16.9 [Ω] 96.4 %

230PS230V20 230 [V] 230 [V] 20 [kHz] 2-20 18.0 [Ω] 96.1 %

230PP33A20 230 [V] 33 [A] 20 [kHz] 3-2 2.8 [Ω] 97.7 %

In general the series-series and parallel-parallel compensation topologies have a higher efficiency than the series-parallel and parallel-series compensation topologies. Chapter 4.3 and 4.4 shows that increasing the frequency increases the efficiency of a model, and the series-parallel and parallel-series compensation topologies are capable of transferring power with high efficiency. There is a limit to how much the frequency can be increased though. Increasing the frequency increases the resistances of the coils and it increases the switching losses in the power electronics used to power the coils.

One interesting feature of a parallel compensated coil is that power can be transferred using relatively few coil turns. Few coil turns results in a low inductance however, and a large reactive current when using parallel compensation. This means that the compensation capacitor needs to be dimensioned to handle large currents. These large currents is the cause of the reduced efficiency of the parallel compensated topologies. Increasing the frequency increases the impedance, reduces the currents and increases the efficiency.

35

36

5: Prototype Design

In order to demonstrate the feasibility of inductively coupled power transfer over a large air gap, and to verify simulated results, a 3 kW prototype was designed.

5.1 Components and alternatives

Inductive charging of electrical vehicles is a potentially huge market. Inductive charging has a number of advantages over conductive charging. No charging posts, no cables, isolation of circuits and the possibility to hide the charger from view.

If the primary coil is situated in the concrete of a parking lot, and the secondary coil is incorporated into the undercarriage of a car, the battery of the car can be charged when the vehicle is parked.

This prototype will be used to verify that the primary coil can be encased in concrete and transfer the designed power with high efficiency.

5.2 Housing

The housing of the primary coil needs to withstand the pressure of a vehicle driving over it. It also needs to withstand temperature variations and elemental effects such as sun, rain and snow. For this reason a concrete housing was chosen.

The size of the coils is determined by the distance between the two coils, the desired transfer capability and the target efficiency. To meet the required ground clearance of modern cars a distance between the coils of 20 cm was decided on.

Some initial simulations using series-series compensation revealed that it was possible to achieve a high efficiency and reasonable currents at a distance of 20 cm using a frequency of about 40 kHz and a coil radius of about 20 cm. Additional space is needed by the core and shield in order to control the spread of the magnetic field.

A concrete housing design was finalized with an area of 1m x 1m available for the shield, core and coil. In addition there is space allocated for the power electronics driving the coil. This concrete housing was manufactured by the company AquaFence AB1, who specializes in high performance concrete.

5.3 Shielding material

In order to shield magnetic fields a material needs a high conductivity and a low relative permeability. Copper is an excellent shielding material, but high copper prices and the increasing risk of copper theft is a big concern. Since aluminium fulfills all the criteria for a good shield it was chosen instead of copper.

To shield the surrounding area from the magnetic field, the shield needs to extend outside the edge of the coil and core. The further the shield extends the more it will prevent the magnetic field from

1 AquaFence AB, Olof Palmes Gata 20 B, SE-111 37 Stockholm, Sweden

37

spreading. In order to keep dimensions small a design was suggested where the plate containing the coil, core and power electronics was surrounded by plates containing only shielding material.

5.4 Core

A core is used to conduct the magnetic field away from the shield. This significantly reduces the eddy current losses in the shield. Due to the high frequency of the inductively coupled power transfer the core needs to have a low conductivity as well as a high relative permeability.

Ferrite has these characteristics. It is usually made by mixing a compound of iron oxide with other oxides. The iron oxide will retain the ferromagnetic properties of iron while the impurities of other oxides will decrease the conductivity dramatically.

Due to its brittleness ferrite needs to be ordered in small pieces that are then assembled to a full core.

5.5 Coil

At high frequencies the skin effect will concentrate the current to the surface of the conductor, no current will be conducted in the center of the conductor. This is why copper tubes is eligible as a coil conductor material. Tubes do however still show the same high resistance at high frequencies as solid conductors.

Litz wire with its low resistance even at high frequencies was the principal choice for coil conductor material. Litz wire samples from Germany with a total diameter of about 12 mm and consisting of 4500 strands of about 0.1 mm diameter each were examined.

Talks were also initiated with a Chinese company capable of manufacturing Litz wire with a total of 7000 strands of 0.1 mm strand diameter and a total diameter of 15 mm.

5.6 Power electronics

For effective wireless power transfer a high frequency alternating current is necessary. This frequency is in the order of 10 kHz to 100 kHz, which is much higher than the 50 Hz of the electrical grid. The desired frequency is achieved by combining a rectifier with an inverter.

In order to keep losses at a minimum soft switching is preferred, where the transistors of the inverter only switches on or off when the current is zero. The inverter produces a square voltage waveform, but since it is connected to a resonant circuit the current will be sinusoidal.

0 1/f 2/f-Vdc

0

VdcVoltage and current

Time [s]

Am

plitu

de

VoltageCurrent

Figure 5.1: Square voltage and sinusoidal current.

38

Two options were discussed. Implementing a power electronics design would give full control over resulting waveforms and voltage levels. Using existing solutions would result in faster manufacturing of a prototype.

The decision was made to examine an existing induction cooker. According to its data sheet the induction cooker is capable of delivering 1.8 kW in one coil, and uses an operating frequency of 20 kHz. There is however no way to control the waveform or voltage level.

5.7 Output Constant Voltage or Constant Current

ElectroEngine AB2 is a company specializing in battery management systems and batteries. They were contacted to gain information regarding the preferred output of the inductively coupled power transfer. Depending on the compensation topology the system can supply a constant current or a constant voltage. With an output of 420 V DC the inductively coupled power transfer could be connected directly to the DC line of their battery management system, providing an easy integration.

2 Electroengine in Sweden AB, Stålgatan 8, SE-754 50 Uppsala, Sweden

39

40

6: Concrete Housing

A simple concrete housing design was created at ABB. The design specifies an area of 1m x 1m for the aluminium shield, space for a ferrite core with a diameter of 800 mm and a coil with a diameter of 600 mm.

Figure 6.1: The concrete housing design.

The concrete needs to be reinforced in order to support the weight of vehicles. However normal steel reinforcement bars have a very high μr and would affect the magnetic field. Steel also have a high σ and would cause eddy current losses. This is why basalt fibers were used as reinforcement instead of steel.

6.1 Basalt fibers

Basalt is a common volcanic rock. It is heated to its melting point at 1400 C and formed to continuous filaments of basalt fibers. The individual fibers are commonly between 9 and 13 μm thick. These fibers are then glued together to the desired total diameter. The fiber bundles used to reinforce the concrete housing had a diameter of about 5 mm. The tensile strength of basalt fiber is 4.8 GPa which is greater than the tensile strength of steel.

6.2 Measurements

The company NanOsc AB3 was contracted to perform magnetic measurements on the concrete and basalt fibers. The measurements were conducted using an alternating gradient magnetometer from Princeton Measurements.

3 NanOsc AB, Electrum 205, SE-164 40 Kista, Sweden

41

The measurements showed that both the concrete and the basalt fibers are paramagnetic, with a relative permeability slightly larger than one.

μrBasalt Fiber

=1.00012

μrConcrete

=1.00024

The report from NanOsc AB is included in the appendix.

6.3 Comments

Simulations using these relative permeability values showed a negligible increase of the inductance compared to when a relative permeability of one was used, and it can be concluded that for all practical purposes the concrete and basalt fibers are magnetically inert and behave the same as air.

42

7: Parameter study

This chapter presents obtained results regarding the influence of certain variables in the system. First the influence of variations in the geometry on the resulting inductances and resistances is illustrated. Then the influence of variations in coil resistances, coil inductances and compensation capacitances on the resulting output voltage and current levels, efficiency and power factor is presented.

7.1 Magnetic field calculations

A parametric study has been performed where the outer coil radius, the number of coil turns, the distance between the two coils and the frequency have been varied. In these magnetic field calculations the primary and secondary sides have been symmetrical. The base configuration in the simulations consists of five coil turns for both primary and secondary side with an outer coil radius of 30 cm. The radius of the ferrite cores is 40 cm, thus extending 10 cm outside the outer radius of the coils. Finally the aluminium shields have a radius of 50 cm, meaning they extend 10 cm outside the outer radius of the ferrite cores. The distance between the two coils is 20 cm, and the frequency is 20 kHz. The conductors consists of Lits wire with 4500 strands, with a strand diameter of 0.1 mm, and a total conductor radius of 12 mm.

7.1.1 Coil Radius

When performing the coil radius variations the above mentioned base configuration was used. The outer radius of the coils were varied between 10 cm and 90 cm. The ferrite core extended 10 cm outside the outer radius of the coils and and the aluminium shield extended 20 cm outside the outer radius of the coils.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.4

0.8

1.2

1.6

2x 10

-4

Indu

ctan

ce [H

]

Radius [m]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

Cou

plin

g co

effic

ient

L1,L2

M

k

0.2 0.4 0.6 0.80

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Res

ista

nce

[ Ω]

Radius [m]

R1,R2

Figure 7.1: Influence of coil radius.

The inductances increases as the outer radius of the coils increase. The increase in conductor length also increases the resistance. In absence of shields and cores the resistance is linearly dependent on the outer radius of the coils. Increasing the coil radius increases the mutual inductance and thereby the coupling coefficient.

43

7.1.2 Coil Turns

As in the variation of the outer radius of the coils, the base configuration was used when the number of coil turns in both the primary and secondary side were varied. The number of coil turns was varied from 2 to 14 turns, and the outer radius of the coils was kept fixed. This means that each new coil turn was added inside the last.

2 4 6 8 10 12 140

0.5

1

1.5x 10

-4

Indu

ctan

ce [H

]

Turns

2 4 6 8 10 12 140.1

0.2

0.3

0.4

Cou

plin

g co

effic

ient

L1,L2

M

k

2 4 6 8 10 12 14

0.005

0.01

0.015

0.02

Res

ista

nce

[ Ω]

Turns

R1,R2

Figure 7.2: Influence of the number of coil turns.

The self inductances and mutual inductance increase with the number of coil turns, as also the coil resistances because of the increased conductor length. Due to the fixed outer radius of the coils, the coupling coefficient is affected.

In chapter 2 it is stated that the coupling coefficient is independent of the number of coil turns. However for the coupling coefficient to be independent of the number of turns in the two coils the distribution of the coil turns needs to be considered. By defining an outer and an inner radius of the coil, and winding the coil such that the conductor is evenly distributed over that interval, the coupling coefficient becomes independent of the number of coil turns.

44

7.1.3 Distance between primary and secondary coils

The base configuration was used to define the geometry used in the distance variations. The distance between the two coils was varied from 5 cm to 50 cm.

0.1 0.2 0.3 0.4 0.50

0.5

1x 10

-4

Indu

ctan

ce [H

]

Distance [m]

0.1 0.2 0.3 0.4 0.50

0.5

1

Cou

plin

g co

effic

ient

L1,L2

M

k

0.1 0.2 0.3 0.4 0.52

4

6

8

10

12x 10

-3

Res

ista

nce

[ Ω]

Distance [m]

R1,R2

Figure 7.3: Influence of coil-to-coil distance.

The distance mainly influences the mutual inductance. But due to the vicinity of the opposite core the self inductances change too. Once the distance is great enough, the value of the self inductances stabilizes, but the mutual inductance continues to decrease. The vicinity of the opposing core is also influencing the proximity effect, causing a change in coil resistance. Without shields and cores the self inductance and coil resistance is unaffected by the distance between the coils.

7.1.4 Frequency

Using the base configuration as a basis, the frequency used in the simulations was varied between 10 kHz and 90 kHz.

2 4 6 8

x 104

0

2

4x 10

-5

Indu

ctan

ce [H

]

Frequency [Hz]

2 4 6 8

x 104

0

0.25

0.5

Cou

plin

g co

effic

ient

L1,L2

M

k

2 4 6 8

x 104

0.005

0.01

0.015

0.02

Res

ista

nce

[ Ω]

Frequency [Hz]

R1,R2

Figure 7.4: Influence of frequency.

45

The inductances and coupling factor are independent of the frequency, but the skin and proximity effects of the coil are highly influenced by the frequency. Increasing the frequency increases the resistance significantly. Litz wire, which was used in these simulations, is designed to minimize the influence of the skin and proximity effects, but is is still affected by them. Conductors of solid copper are affected even more by the skin and proximity effect.

7.2 Non-symmetrical sides

In these simulations the two sides are not symmetrical. The general geometry comes from the base configuration, and the frequency is 20 kHz. The primary side is kept fixed, while the outer coil radius and the the number of coil turns in the secondary side are varied.

7.2.1 Coil Radius

When performing the coil radius variations in the case with non-symmetrical sides the base configuration described in chapter 7.1 was used. The outer radius of the secondary coil was varied between 10 cm and 50 cm, while the outer radius of the primary coil was 30 cm. The secondary ferrite core extended 10 cm outside the outer radius of the secondary coil and the secondary aluminium shield extended 20 cm outside the outer radius of the secondary coil.

0.1 0.2 0.3 0.4 0.50

2

4

6

8x 10

-5

Indu

ctan

ce [H

]

Radius [m]

0.1 0.2 0.3 0.4 0.50

0.1

0.2

0.3

0.4

Cou

plin

g co

effic

ient

L1

L2

M

k

0.1 0.2 0.3 0.4 0.50

0.005

0.01

0.015

0.02

Res

ista

nce

[ Ω]

Radius [m]

R1

R2

Figure 7.5: Influence of non-symmetrical radii.

When the radius of the secondary coil differs too much from the radius of the primary coil the coupling coefficient is low. This is due to the increased distance from the primary coil conductors to the secondary coil conductors. The primary self inductance is slightly affected by the vicinity of the secondary core.

The secondary core is also what is influencing the primary coil resistance. Running the simulations without a secondary core and shield results in a slight increase in primary coil resistance when the secondary and primary coils have the same radius. This is the expected influence of the proximity effect.

46

7.2.2 Coil Turns

The base configuration was used to define the geometry. Keeping the number of coil turns of the primary side constant at 5 turns, the number of coil turns on the secondary side was varied between 1 turn and 10 turns. The outer radius of the two coils was kept fixed, meaning the extra coil turns on the secondary side was added inside earlier coil turns.

2 4 6 8 100

1

2x 10

-4

Indu

ctan

ce [H

]

Turns

2 4 6 8 100.2

0.25

0.3

Cou

plin

g co

effic

ient

L1

L2

M

k

2 4 6 8 100

0.005

0.01

0.015

Res

ista

nce

[ Ω]

Turns

R1

R2

Figure 7.6: Influence of non-symmetrical number of coil turns.

The self inductance of the secondary coil increases with the number of coil turns, as also the resistance of the secondary coil. The mutual inductance increases almost linearly with the number of secondary coil turns. This is as expected from the theory. Again, the coupling coefficient increases slightly due to the fact that no consideration has been taken to the placement of the secondary coil turns.

By using an unsymmetrical number of coil turns in the two coils the mutual inductance can be made larger than one of the self inductances. In figure 7.7 the distance between the two coils was 15 cm, and the number of coil turns of the primary coil was set to 20 turns. The number of coil turns of the secondary coil was varied between 1 turn and 5 turns.

1 2 3 4 50

1

2

3

4

5x 10

-5

Indu

ctan

ce [H

]

Turns

1 2 3 4 50

0.2

0.4

0.6

0.8

1

Cou

plin

g co

effic

ient

L1

L2

M

k

Figure 7.7: Non-symmetrical number of coil turns.

47

The mutual inductance is larger than the inductance of the secondary coil. The inductance of the primary coil is much larger than the mutual inductance and the inductance of the secondary coil. This can be utilized in the series-parallel or parallel-series compensation topologies to achieve a desired output voltage.

7.3 Simulink Studies

The two most important quantities in the Simulink simulations are the efficiency and the power factor. The efficiency is the ratio of the active power delivered to the load over the active power supplied by the voltage source.

η=Pload

P source(7.1)

The power factor is the ratio of the active power over the apparent power. The apparent power, S, consists of the active power, P, and the reactive power ,Q.

S=P+ jQ (7.2)

PF =P

∣S∣(7.3)

Since reactive power does not perform any active work it should be kept low and the power factor close to one.

7.4 Coil Resistances

The series-series topology is used in combination with self inductance values of 1.67x10 -4 H and a mutual inductance of 5.06x10-5 H. The value of the coil resistances are 2.15x10-2 Ohms. This produces an output current of about 36 A when an input voltage of 230 V and a frequency of 20 kHz is used. Three different values for the coil resistances are used in these simulations.

10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1


Effi

cien

cy

R1,R2 = 0.02 OhmR1,R2 = 0.25 OhmR1,R2 = 1.00 Ohm

Figure 7.8: Influence of coil resistance on efficiency.

48

The power received by the secondary coil from the primary coil is divided between the coil resistance of the secondary coil, R2, and the load resistance, RLOAD. Reducing the resistance of the secondary coil will increase the amount of the received power that reaches the load, thus increasing the efficiency, η. Equation (7.4) illustrates the relationship between the efficiency and the resistances of the secondary side.

ηreceived=RLOAD

R2+RLOAD(7.4)

The power fed from the voltage source is divided between the coil resistance of the primary coil, R1, and ZS, the total impedance of the secondary coil as seen by the primary coil. The power over ZS is the power that is transmitted to the secondary coil. Reducing the resistance of the primary coil will increase the amount of the power fed by the voltage source that reaches the secondary coil, thus increasing the efficiency. Equation (7.5) illustrates the relationship between the efficiency and the impedances of the primary side.

ηtransmitted=Z S

R1+Z S(7.5)

The total efficiency of the series-series compensation topology is given by equation (7.6).

ηseries−series=ηtransmitted⋅ηreceived (7.6)

By minimizing the coil resistances, the efficiency is maximized. When building an inductively coupled power transfer, there are additional resistances introduced by the compensation capacitors. In this work ideal capacitors have been used containing only a capacitance, but in reality the impedance of a capacitor, ZC, consists of a small internal resistance, RC, in series with the capacitance, C. Equation (7.7) gives the impedance of a capacitor.

ZC=RC−j

ωC(7.7)

These resistances will decrease the efficiency of the inductively coupled power transfer. Due to this it is important to use coils with a small coil resistance, and capacitors with a small internal resistance, in order to achieve a high efficiency.

7.5 Compensation Capacitors

Compensation capacitors are used to preserve the magnetic energy of the coils. Without resonance this energy will be drawn from the voltage source, in the form of a phase shifted current, and will affect the power factor of the voltage source. The efficiency is expressed in active power and will not be reliable when the system is out of resonance.

In these simulations the models defined in chapter 4 were used to conduct simulations depicting the influence of the compensation capacitances. For each of the four compensation topologies two capacitance variations were performed. In the first case the primary compensation capacitance, C1, was varied between 50% and 150% of its resonant value, while the secondary compensation capacitance, C2, was kept fixed at its resonant value. In the second case the primary compensation capacitance, C1, was kept at its resonant value, while the secondary compensation capacitance, C2, was varied between 50% and 150% of its resonant value.

49

7.5.1 Series-Series

While examining the series-series compensation topology, model 230SS36A20 was used. The system was connected to a 10 Ω load resistance, fed by a 230 V input voltage and a frequency of 20 kHz. This corresponds to about 13 kW of transferred power.

In figure 7.9, the primary capacitance, C1, was varied from 50% to 150% of its resonant value, while the secondary capacitance, C2, was kept at its resonant value.

0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]

Primary side input

UI

0

100

200

300

Capacitance [F]V

olta

ge [V

] and

Cur

rent

[A]

Secondary side output

UI

2 2.5 3 3.5 4 4.5 5 5.5

x 10-7

0

0.2

0.4

0.6

0.8

1

Capacitance [F]

Power Factor and Efficiency

← Resonant CapacitanceEfficiencyPower Factor

Figure 7.9: Influence of primary compensation capacitance, C1, in the series-series case.

When the primary capacitance is varied, the reactive parts of the impedance on the primary side no longer cancels each other out. The impedance on the primary side increases, causing the current through the primary coil to decrease. In accordance with equation (2.35) the induced voltage in the secondary coil decreases with the current through the primary coil. Since the current through the primary coil no longer is in phase with the source voltage, the power factor decreases.

50

In figure 7.10, the primary capacitance, C1, was kept fixed at its resonant value, while the secondary capacitance, C2, was varied between 50% and 150% of its resonant value.

0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]

Primary side input

UI

0

100

200

300

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]


UI

2 2.5 3 3.5 4 4.5 5 5.5

x 10-7

0

0.2

0.4

0.6

0.8

1

Capacitance [F]



Figure 7.10: Influence of secondary compensation capacitance, C2, in the series-series case.

The current through the secondary side is kept constant independently of the secondary capacitance, C2. This is due to the fact that as long as the primary compensation capacitance, C1, compensates for the primary inductance, L1, the current through the secondary side is independent of the impedance of the secondary side. Equation (7.8) expresses the total impedance of the primary side, Z1, when the primary side is in resonance. Z2 is the total impedance of the secondary side.

Z1=ω

2 M 2

Z2(7.8)

As the system is fed by a voltage source, the current through the primary coil, I1, is determined by the total impedance of the primary side, Z1, and the input voltage, U1. Since Z1 consists only of the total impedance of the secondary side as seen by the primary coil, equation (7.9) depicts how the current through the primary coil is dependent on the total impedance of the secondary side, Z2.

I 1=U 1

Z 1

=Z 2

ω2 M 2 U 1 (7.9)

The current through the secondary side, I2, is determined by the induced voltage in the secondary coil, and the total impedance of the secondary side, Z2. Combining equation (2.35) and equation (7.9) results in the induced voltage in the secondary coil. Dividing the induced voltage in the secondary coil with the total impedance of the secondary side, Z2, results in the current through the secondary coil, I2. This is expressed in equation (7.10).

I 2=j ωM I 1

Z2

=j ωM Z 2

ω2 M 2 Z 2

U 1=j

ω MU 1 (7.10)

51

Since the current through the secondary coil is independent of the total impedance of the secondary side, the change in compensation capacitance C2 does not alter the current I2. The change in impedance does however slightly change the load voltage, since it is determined by the current I2

and the impedance Z2. The secondary side is unaffected by the secondary compensation capacitance C2, but not the primary side. When the secondary side falls out of resonance the resulting phase shift affects the impedance of the primary side, resulting in a phase shift in the current through the primary side I1. This in turn results in the drop in power factor seen in figure 7.10.

7.5.2 Series-Parallel

While examining the series-parallel compensation topology, model 230SP230V20 was used. The system was connected to a 5 Ω load resistance, fed by a 230 V input voltage and a frequency of 20 kHz. This corresponds to about 10 kW of transferred power.


0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]

Primary side input

UI

0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]


UI

2 2.5 3 3.5 4 4.5 5 5.5

x 10-7

0

0.2

0.4

0.6

0.8

1

Capacitance [F]



Figure 7.11: Influence of primary compensation capacitance, C1, in the series-parallel case.

As in the series-series case, varying the primary compensation capacitance, C1, increases the primary impedance, Z1, and decreases the primary current, I1. This in turn causes the induced voltage in the secondary coil to decrease, which causes the secondary side output to decrease. It also causes the power factor to decrease.

52


0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]

Primary side input

UI

0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]


UI

4 5 6 7 8 9 10 11

x 10-6

0

0.2

0.4

0.6

0.8

1

Capacitance [F]



Figure 7.12: Influence of secondary compensation capacitance, C2, in the series-parallel case.

As with the series-series compensation topology, in the series-parallel compensation topology it is the primary compensation capacitance, C1, that keeps the secondary side output independent of the secondary impedance. The current through the primary coil is affected by the change in the impedance of the secondary side, causing the power factor to drop.

53

7.5.3 Parallel-Series

While examining the parallel-series compensation topology, model 230PS230V20 was used. The system was connected to a 5 Ω load resistance, fed by a 230 V input voltage and a frequency of 20 kHz. This corresponds to about 10 kW of transferred power.


0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]

Primary side input

UI

0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]


UI

4 5 6 7 8 9 10 11

x 10-6

0

0.2

0.4

0.6

0.8

1

Capacitance [F]



Figure 7.13: Influence of primary compensation capacitance, C1, in the parallel-series case.

When the primary side is parallel compensated, the primary compensation capacitance does not influence the current through the primary coil. The current through the primary coil, IL1, is determined by the input voltage, U1, the impedance of the primary coil and the total impedance of the secondary side as seen by the primary coil. The expression for the current through the primary coil is given by equation (7.11).

I L1=U 1

j ω L1+ω

2 M 2

Z 2

(7.11)

As can be seen by equation (7.11) the current through the primary coil is independent of the primary compensation capacitance, C1. Since the current through the primary coil determines the induced voltage in the secondary coil, the secondary side is unaffected by the primary compensation capacitance, C1. The change in primary compensation capacitance does however move the primary side out of resonance. The primary current increases and since it is no longer in phase with the voltage, the power factor decreases.

54


0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]

Primary side input

UI

0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]


UI

2 2.5 3 3.5 4 4.5 5 5.5

x 10-7

0

0.2

0.4

0.6

0.8

1

Capacitance [F]



Figure 7.14: Influence of secondary compensation capacitance, C2, in the parallel-series case.

When the primary side was series compensated, the resonance of the primary side kept the secondary side output independent of the impedance of the secondary side. But due to the nature of the parallel compensation, the primary compensation capacitance does not affect the current through the primary coil.

As can be seen in figure 3.5, it is the secondary capacitance, C2, that keeps the voltage independent of the load when the secondary side is series compensated. As C2 is varied, the secondary side is no longer in resonance, and the output voltage no longer remains constant.

The phase shift introduced to the system when the secondary side falls out of resonance causes the power factor to drop.

55

7.5.4 Parallel-Parallel

While examining the parallel-series compensation topology, model 230PP33A20 was used. The system was connected to a 10 Ω load resistance, fed by a 230 V input voltage and a frequency of 20 kHz. This corresponds to about 10 kW of transferred power.


0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]

Primary side input

UI

0

50

100

150

200

250

300

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]


UI

2 2.5 3 3.5 4 4.5 5 5.5

x 10-6

0

0.2

0.4

0.6

0.8

1

Capacitance [F]



Figure 7.15: Influence of primary compensation capacitance, C1, in the parallel-parallel case.

As with the parallel-series compensation topology, the current through the primary coil is independent of the primary compensation capacitance, C1. Thus it does not affect the output of the secondary side. It does however cause a phase shift, resulting in a reduced power factor.

56


0

50

100

150

200

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]

Primary side input

UI

0

50

100

150

200

250

300

Capacitance [F]

Vol

tage

[V] a

nd C

urre

nt [A

]


UI

4 5 6 7 8 9 10 11

x 10-6

0

0.2

0.4

0.6

0.8

1

Capacitance [F]



Figure 7.16: Influence of secondary compensation capacitance, C2, in the parallel-parallel case.

Since the current through the primary coil is independent of the primary compensation capacitance, the primary compensation capacitance cannot keep the secondary output independent of the secondary impedance. As can be seen in figure 3.6, when the secondary side is parallel compensated it is the secondary compensation capacitance, C2, that keeps the output current independent of the load resistance. When the secondary side no longer is in resonance the output current no longer remains constant.

The phase shift introduced to the system when the secondary side falls out of resonance causes the power factor to drop.

7.6 Distance between Coils

Varying the distance between the two coils changes the mutual inductance. However, due to the proximity of the opposite core the self inductances change too. This means that if a system is perturbed from its designed coil to coil distance, it will potentially fall out of resonance due to the change in self inductances.

The models defined in chapter 4 were used to conduct simulations depicting the influence of varying the distance between the two coils. The compensation capacitances, C1 and C2, were dimensioned for the designed self inductances, L1 and L2, and the mutual inductance, M. During the simulations the compensation capacitances were kept fixed.

57

7.6.1 Series-Series

While examining the series-series compensation topology, model 230SS36A20 was used. The system was connected to a 2.3 Ω load resistance, fed by a 230 V input voltage and a frequency of 20 kHz. This corresponds to about 3 kW of transferred power.

The designed distance between the two coils is 20 cm. In figure 7.17, the distance between the two coils was varied between 10 cm and 30 cm. During these simulations the values of the compensation capacitances were kept fixed.

0.1 0.2 0.30

100

200

300

Primary side input

Distance [m]

Vol

tage

[V] a

nd C

urre

nt [A

]

UI

0.1 0.2 0.30

50

100

150


Distance [m]

Vol

tage

[V] a

nd C

urre

nt [A

]

UI

0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1Power Factor and Efficiency

Distance [m]

EfficiencyPower Factor

Figure 7.17: Influence of distance variation in series-series case.

Since the current through the secondary coil is inversely proportional to the mutual inductance, see equation (3.28), the transferred power increases when the mutual inductance decreases. The compensation capacitances are independent of the mutual inductance and the system remains in resonance as long as the self inductances remains constant. When the distance decreases the self inductances increase due to the vicinity of the opposite core and the system falls out of resonance, decreasing the power factor.

58

7.6.2 Series-Parallel

While examining the series-parallel compensation topology, model 230SP230V20 was used. The system was connected to a 16.8 Ω load resistance, fed by a 230 V input voltage and a frequency of 20 kHz. This corresponds to about 3 kW of transferred power.


0.1 0.2 0.30

100

200

300

Primary side input

Distance [m]

Vol

tage

[V] a

nd C

urre

nt [A

]

UI

0.1 0.2 0.30

100

200

300

400


Distance [m]

Vol

tage

[V] a

nd C

urre

nt [A

]

UI

0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8


Distance [m]


Figure 7.18: Influence of distance variation in series-parallel case.

The secondary output voltage is inversely proportional to the mutual inductance, see equation (3.31), and increases when the distance increases. Like the series-series compensation topology the power factor is reduced when the distance decreases due to the increased self inductances. When the distance increases the mutual inductance decreases and as a result the primary compensation capacitance no longer perfectly compensates the phase shift introduced from the parallel compensated secondary side. This causes the power factor to decrease as the distance increases.

59

7.6.3 Parallel-Series

While examining the parallel-series compensation topology, model 230PS230V20 was used. The system was connected to a 18 Ω load resistance, fed by a 230 V input voltage and a frequency of 20 kHz. This corresponds to about 3 kW of transferred power.


0.1 0.2 0.30

100

200

300

Primary side input

Distance [m]

Vol

tage

[V] a

nd C

urre

nt [A

]

UI

0.1 0.2 0.30

100

200

300

400


Distance [m]

Vol

tage

[V] a

nd C

urre

nt [A

]

UI

0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8


Distance [m]


Figure 7.19: Influence of distance variation in parallel-series case.

When the primary side is parallel compensated, the secondary side output is directly proportional to the mutual inductance, unlike the series compensated primary side where the secondary side output is inversely proportional to the mutual inductance. As a result, when the distance increases and the mutual inductance decreases, the output voltage of the secondary side decreases. This is in accordance with equation (3.34).

Despite the increase in self inductances when the distance between the two coils is reduced, the power factor remains close to one.

60

7.6.4 Parallel-Parallel

While examining the parallel-series compensation topology, model 230PP33A20 was used. The system was connected to a 2.8 Ω load resistance, fed by a 230 V input voltage and a frequency of 20 kHz. This corresponds to about 3 kW of transferred power.


0.1 0.2 0.30

100

200

300

Primary side input

Distance [m]

Vol

tage

[V] a

nd C

urre

nt [A

]

UI

0.1 0.2 0.30

50

100

150

200


Distance [m]

Vol

tage

[V] a

nd C

urre

nt [A

]

UI

0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8


Distance [m]


Figure 7.20: Influence of distance variation in parallel-parallel case.

The secondary output current is directly proportional to the mutual inductance, see equation (3.37), and decreases when the distance increases. The power factor in the parallel-parallel compensation topology is kept close to one even for very close coil to coil distances.

Compared to the series compensated primary side, the power factor of the parallel compensated primary side is very resilient to the influence of changes in the self inductances. It is only when the distance is increased and the mutual inductance becomes small the system falls out of resonance.

61

7.7 Features and comments regarding the studied topologies

The topologies with a series compensated primary side are very sensitive to a decreased distance between the two coils. The change in self inductances due to the opposite core increases the reactive currents of the system and decreases the power factor. Reactive currents lead to additional losses in the system. On the other hand, increasing the distance between the two coils does not affect the power factor, and the efficiency remains high. Increasing the distance between the two coils 10 cm only slightly decreases the efficiency. The power factor of the series-series compensation topology is unaffected by the increased distance. With an increased distance the output levels increase. This means that the topologies with a series compensated primary side are well suited for transferring large amounts of power over large distances.

The topologies with a parallel compensated primary side are less sensitive to a decreased distance between the two coils than the topologies with a series compensated primary side. The efficiency is increased when the two coils are moved closer to each other. The power factor is reduced when the distance between the two coils is increased however, and so is the efficiency. With a decreased distance the output levels increase. This means that the topologies with a parallel compensated primary side are well suited for transferring large amount of power over small distances.

The features of the different topologies examined in this chapter is summarized in table 7.1.

Table 7.1: Features of the different topologies.Topology Output Insensitive to

changes in4Power Factor5 Efficiency6

@ decreased distance

@ increased distance

Series-Series Current source C2 Low Very high Very high

Series-Parallel Voltage source C2 Low High Medium

Parallel-Series Voltage source C1 High Medium Medium

Parallel-Parallel Current source C1 Very High Medium High

4 See chapter 7.55 See chapter 7.66 See chapter 4.9

62

8: Recommendations

It is recommended that the models provided by this thesis work are validated. Especially the model cases where one or both of the two coils has a low number of coil turns. When using coils with few coil turns the impedance of the coil becomes small. This small impedance results in a large current through the coil when the coil is parallel compensated. A large current will produce a large magnetic field, and care must be taken that the ferrite cores are not saturated.

Designing an inductively coupled power transfer is a complicated task. In this chapter a few suggestions about the preferred compensation topologies, control alternatives and the relative size of the two coils are presented. The consequences of these choices are also described.

8.1 Suggested compensation topologies for demonstration purposes

For demonstration purposes it would be convenient with an inductively coupled power transfer that outputs a constant voltage with an amplitude of 230 V and a frequency of 50 Hz. Existing equipment such as a motor heater (in the case of a hybrid vehicle), a compartment heater and a battery charger could be connected to such a system, demonstrating the convenience and capabilities of wireless power transfer.

This demonstrator can be realized by using model 230SP230V or model 230PS230V. The high losses of these topologies can be reduced by increasing the frequency. A frequency of 50 kHz would increase the efficiency to 98.9% for these models when a 3 kW load is connected. These losses do not include the losses in the power electronics needed on the primary and the secondary side of such a system.

8.2 Suggested control alternatives

With the primary coil in the ground and the secondary coil under a vehicle there is no way to guarantee a specific distance between the two coils. Tire pressure, load weight of the car and any variations in the ground around the primary coil all affect the distance between the two coils. Since variations in the distance between the two coils affects the mutual inductance, see figure 7.3, and the mutual inductance determines the output levels of the system, see equations (3.28), (3.31), (3.34) and (3.37), there is no way to guarantee a specific output level.

Depending on the topology used, there are two or three variables that control the output level. For the series-parallel and parallel-series compensation topologies the output voltage is determined by the self inductances of the coils, the mutual inductance and the input voltage. For the series-series and parallel-parallel compensation topologies the output current is determined by the self inductances of the coils, the mutual inductance, the frequency and the input voltage.

8.2.1 Adjusting the input voltage

Since the input voltage determines the output level, a voltage controller could be implemented that manages the output level by varying the input voltage. The advantage of a input voltage controller is a precise control of the output level. The disadvantage is the need for a feedback loop involving communication between the two sides of the system, and if the input voltage is managed by varying the pulses controlling the switching in the inverter it will lead to increased switching losses.

63

8.2.2 Adjusting the distance between the two coils

By incorporating the secondary coil in a platform located under the car that can be lowered and raised, the mutual inductance can be varied until the desired output level is received. The advantage of varying the distance between the two coils is that the output level can be managed by a controller in the vehicle without any communication between the two sides of the system. The disadvantages are that the mechanical platform will need extra space under the car, the platform will be in an exposed position and will collect dirt or snow, it can get stuck and it will be affected by wear.

8.2.3 Adjusting the frequency

The frequency can be used to vary the output current in the series-series and parallel-parallel compensation topologies. For both topologies increasing the frequency lowers the amplitude of the output current, and lowering the frequency increases the amplitude of the output current. The disadvantage is that the two resonant capacitances needs to be adjusted if the frequency changes in order to maintain the resonance of the system.

8.3 Relative size of the two coils

To make the system less sensitive to misalignment, a secondary coil with a small radius has been suggested. Since the magnetic field produced by a coil is largely homogeneous over the area in the center of the coil, a small secondary coil could be placed arbitrarily within the edges of the primary coil and still receive the same amount of magnetic flux. This would decrease the influence of misalignment, but severely increase the amount of leakage flux.

The magnetic field is produced by the current through the coil. The leakage flux can be considered as losses in the sense that it takes a current to produce the leakage flux. If the leakage flux is minimized, the current used to produce the magnetic field can be reduced while still providing the same amount of mutual flux.

8.4 Further work

This thesis work focuses on the underlying theory and basic behavior of the four different compensation topologies. However for a commercial system much work remains to be done.

• Validate models• Operating frequency• Power electronics• Controller• Battery management system• Communication• Scaling the models to different power levels• Vehicle to grid power transfer• Standardization• Weight reduction• Coil shape

64

The models developed in this thesis work needs to be validated experimentally.

The optimal operating frequency depends on the model used, and the components used. A high frequency yields a high efficiency. But a high frequency results in high coil resistances and high switching losses. High frequency capacitors are also very expensive. A study on the optimal frequency should examine the trade off between efficiency and cost.

In order to keep the efficiency of the wireless power transfer as high as possible high quality power electronics are needed. One interesting material is silicon carbide. Transistors made from silicon carbide can handle higher voltages, higher temperatures, and have lower losses than transistors made from silicon.

A controller needs to be implemented managing the output levels of the system. Chapter 8.2 gives some suggestions for different approaches. A controller should also be able to start the system when charging is commencing, and stop the system when charging is completed.

A battery management system should be implemented, handling the charging of the batteries.

There is a need for communication between the two sides of the system. Parking assistance is needed to help the driver position the vehicle correctly over the charging coil. A controller requires communication between the two sides in order to start and stop the power transfer and for managing the output level. For commercial systems the payment options needs to be negotiated. Private systems should probably be able to restrict the charger to authorized vehicles only.

The models should be scaled to different power levels. For home use a power level of about 3.6 kW is enough. A 230 V wall socket with a 16 A fuse will be able to supply 3.68 kW power. However for an industrial system charging heavy vehicles a much higher power level is preferred.

During mornings and evenings the power consumption peaks in a home. During these hours the vehicle could be used as a battery pack, and power could be transferred to the house. This would reduce the strain on the power grid during peak hours, and the power consumption would be reduced during hours when the spot price for electricity is the highest.

There is a great need for standardization when it comes to wireless power transfer. Power levels, operating frequency, communication, control, safety and coil shape. All these things need to be standardized in order to achieve interoperability. Public charging stations must work with any kind of receiver coil, regardless of brand or manufacturer.

The weight of the secondary side should be reduced as much as possible. This involves the coil conductor, the shield and the core. A coil conductor with a smaller cross sectional area has a smaller weight but a higher resistance. The thickness of the shield could probably be reduced near the edge of the shield where the magnetic field is weaker.

The shape of the coils and its influence on different kinds of misalignment should be examined.

65

66

9: Results and Conclusions

Inductive charging of electrical vehicles is a very convenient way of transferring power. No need for charging posts, no handling of cords, and no risk of electrical shock. A wireless charging system with its ease of use would be beneficial to the market for electrical vehicles. With the primary coil hidden in the ground of a parking lot, and the secondary coil incorporated into the undercarriage of a vehicle, the driver would only need to position the vehicle over the primary coil and the system would automatically charge the battery while the vehicle is parked.

In this thesis work expressions for the output levels of the four compensation topologies and expressions for the compensation capacitances have been derived. A study of the basic behavior of the different compensation topologies has been performed, and magnetic field calculations that clarifies the influence of geometrical parameters have been performed.

A model capable of transferring 3 kW was developed for each compensation topology. These models are intended to be used as a prototype demonstrating the feasibility of inductively coupled power transfer. The concrete housing of this prototype has been manufactured. Magnetic measurements have been performed on the concrete with basalt fibers used as reinforcement. The results show that the material is slightly paramagnetic.

The models presented in this thesis work indicate that each compensation topology is capable of transmitting 3 kW of power over an air gap of 20 cm with an efficiency of at least 96% when a frequency of 20 kHz is used.

The output voltage of the series-parallel and parallel-series topologies is determined by the ratio between the mutual inductance of the two coils and the self inductance of the parallel compensated coil. Since the self inductance of the series compensated coil does not affect the amplitude of the output voltage, the required mutual inductance can be achieved by adapting the parameters of the series compensated coil.

Chapter 7.6 shows the importance of a function for managing the output levels of the system. A slight variation in the distance between the two coils give a large variation in the output levels of the system. Chapter 8.2 presents recommended approaches for such a controller.

Inductive power transfer has some design challenges, but the ease of use is indisputable. Trials in Germany on inductively charged electrical vehicles are quite promising [13], and it is proven that the user with the help of parking assistance can position the vehicle correctly to achieve maximum efficiency. When it comes to adapting new technological solutions ease of use is of the utmost importance.

67

68

10: References

[1] Tomas Tegnér, Automatic inductive charging of electric vehicles – modelling and simulation (2009)[2] Wikipedia (english) http://en.wikipedia.org/wiki/Faraday%27s_law_of_induction (2012-01-26)[3] Wikipedia (english) http://en.wikipedia.org/wiki/Joseph_Henry (2012-01-26)[4] Wikipedia (english) http://en.wikipedia.org/wiki/James_Clerk_Maxwell (2012-01-26)[5] Wikipedia (english) http://en.wikipedia.org/wiki/Oliver_Heaviside (2012-01-26)[6] Wikipedia (english) http://en.wikipedia.org/wiki/Nicola_Tesla (2012-01-26)[7] David K. Cheng, Field and Wave Electromagnetics, Second Edition[8] I.D.Mayergoyz and W.Lawson, Basic Electric Circuit Theory[9] D. C. Meeker, Finite Element Method Magnetics, Version 4.2 (09Nov2010 Build), http://www.femm.info[10] Wikipedia (english) http://en.wikipedia.org/wiki/Electrical_conductivity (2012-01-26)[11] Wikipedia (english) http://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29 (2012-01-26)[12] Mathworks, www.mathworks.com/products/simpower/ (2012-01-26)[13] Conductix-Wampfler, http://www.wampfler.com/index.asp?id=14&news_id=346&lang=E (2012-01-26)

69

http://en.wikipedia.org/wiki/Faraday's_law_of_induction

http://www.wampfler.com/index.asp?id=14&news_id=346&lang=E

http://www.mathworks.com/products/simpower/

http://en.wikipedia.org/wiki/Permeability_(electromagnetism)

http://en.wikipedia.org/wiki/Electrical_conductivity

http://www.femm.info/

http://en.wikipedia.org/wiki/Nicola_Tesla

http://en.wikipedia.org/wiki/Oliver_Heaviside

http://en.wikipedia.org/wiki/James_Clerk_Maxwell

http://en.wikipedia.org/wiki/Joseph_Henry

70

Appendices

Appendix A:

Output level of the different compensation topologies

Appendix B:

Design of an inductive charging emitter encased in reinforced concrete

Appendix C:

Magnetic characterization of basaltic fibers and concrete

71

72

Output level of the different compensation topologies

While calculating the output level of the different compensation topologies two simplifications are done. The coils and the capacitors are considered ideal and contain no internal resistance. This corresponds to replacing resistances R1 and R2 with a short circuit in figure A1.

Figure A1: Mutual inductance circuit diagram.

On the secondary side the induced voltage is given by equation (A.1).

U induced= jω M I1 (A.1)

The impedance seen by the induced voltage consists of the inductance L2, the compensation capacitance C2 and any load connected over the output terminals, RLOAD. This impedance is called the secondary impedance Z2. Depending on whether the secondary side is series or parallel compensated the expression for this impedance changes. Figure A2 illustrates the two different compensation alternatives.

Figure A2: Series and parallel compensated secondary side.

Equation (A.2) and (A.3) gives the expressions for the secondary impedance when using series compensation, and the secondary impedance when using parallel compensation.

Z2S= jω L2−

jωC2

+RLOAD (A.2)

Z2P= jω L2+

1

jωC2+1

RLOAD

(A.3)

A1

The current through the secondary side, I2, also called the secondary current, is given by the induced voltage and the secondary impedance. Equation (A.4) gives the generic expression for the secondary current.

I 2=jωM I1

Z2(A.4)

Combining equation (A.4) with the expression for the induced voltage in the primary coil, -jωMI2, results in a virtual impedance, ZS. This impedance is the secondary impedance transformed to the primary side. It is expressed in equation (A.5).

Z S=ω

2 M 2

Z2(A.5)

Figure A3 illustrates the impedance of the primary side as seen by the voltage source for the two different compensation alternatives. The impedance of the primary side, Z1, also called the primary impedance, consists of the inductance of the primary coil, L1, the capacitance of the primary compensation capacitance, C1, and the transformed impedance of the secondary side, ZS.

Figure A3: Series and parallel compensated primary side.

Equations (A.6) and (A.7) gives the expressions for the primary impedance when using series compensation, and the primary impedance when using parallel compensation.

Z1S= jω L1−

jωC1

+ZS (A.6)

Z1P=

1

jωC1+1

jω L1+ZS

(A.7)

A2

Output level of series-series topology

The expressions for the resonance capacitances in the series-series topology is given by equations (A.8) and (A.9).

C1=1

ω2 L1

(A.8)

C2=1

ω2 L2

(A.9)

By combining equation (A.8) with (A.6) the series compensated primary impedance becomes independent of the inductance and capacitance on the primary side. This is expressed in equation (A.10).

Z1S=ZS (A.10)

The impedance of the secondary side compensated with C2 defined in equation (A.9) is given by equation (A.11).

Z2S=RLOAD (A.11)

The current through the primary coil is given by the source voltage, U1, divided by the primary impedance, Z1.

I 1=U 1

Z1(A.12)

Combining equations (A.12) and (A.10) with equation (A.5) results in equation (A.13).

I 1=Z2

ω2 M 2 U 1 (A.13)

Combining equation (A.13) with equation (A.4) results in equation (A.14), expressing the current through the secondary side as a function of the source voltage, U1. The current through the secondary side, I2, is the same as the current through the load resistance, ILOAD. The current through the load resistance is the output current of the system.

I LOAD=jω M Z2

ω2 M 2 Z2

U 1=j

ω MU 1 (A.14)

A3

Output level of series-parallel topology

The expressions for the resonance capacitances in the series-parallel topology is given by equations (A.15) and (A.16).

C1=1

ω2(L1−

M 2

L2) (A.15)

C2=1

ω2 L2

(A.16)

Inserting equation (A.16) in equation (A.3) gives the secondary impedance using parallel compensation. The resulting expression is given by equation (A.17).

Z2P=

ω2 L2

2

RLOAD− jωL2

(A.17)

Inserting equation (A.15) in equation (A.6) gives the primary impedance series compensated by C1.

Z1S= jω

M 2

L2

+ZS (A.18)

Combining equation (A.18) with equation (A.5) and (A.17) gives the primary impedance as a function of the secondary impedance. Equation (A.19) gives the resulting expression.

Z1S= jω

M 2

L2

+ω

2 M 2(RLOAD− jω L2)

ω2 L2

2 =RLOAD M 2

L22 (A.19)

The load resistance, RLOAD, is connected in parallel with the compensation capacitance C2, and the combined impedance, ZP, is given by equation (A.20).

Z P=

RjωC2

1jωC 2

+RLOAD

(A.20)

Inserting the expression for C2 given by equation (A.16) into equation (A.20) results in equation (A.21).

Z P=− jω L2 RLOAD

RLOAD− jωL2(A.21)

The output voltage, ULOAD, is given by the impedance ZP and the secondary current I2.

U LOAD=ZP I 2 (A.22)

A4

Combining equation (A.17) with equation (A.4) gives the expression for the secondary current I2.

I 2=jωM (RLOAD− jωL2 )

ω2 L2

2 I 1 (A.23)

Inserting equation (A.23) into equation (A.22) and combining with equation (A.21) results in equation (A.24).

U LOAD=ω

2 M L2 RLOAD (RLOAD− jω L2 )

ω2 L2

2(RLOAD− jω L2 )

I 1=RLOAD M

L2

I 1 (A.24)

The primary current, I1, is given by equation (A.25)

I 1=U 1

Z1S (A.25)

Combining equation (A.25) with equation (A.19) gives the primary current as a function of the load resistance, RLOAD.

I 1=L2

2

RLOAD M 2 U1 (A.26)

Finally, inserting equation (A.26) into equation (A.24) results in equation (A.27), expressing the output voltage, ULOAD, as a function of the source voltage U1.

U LOAD=L2

MU 1 (A.27)

Output level of parallel-series topology

The expressions for the resonance capacitances in the parallel-series topology is given by equations (A.28) and (A.29).

C1=1

ω2 L1

(A.28)

C2=1

ω2(L2−

M2

L1) (A.29)

When the primary side is parallel compensated, the current through the primary coil, IL1, is given by the inductance of the primary coil, L1, the impedance of the secondary side, Z2, and the source voltage, U1. The expression for the current through the primary coil is given by equation (A.30).

A5

I L1=U1

jω L1+ω

2 M 2

Z2

(A.30)

Combining equation (A.29) with equation (A.2) gives the expression for the secondary impedance Z2 when the capacitance C2 is connected in series with the secondary coil and the load. The expression is given by equation (A.31).

Z2S= jω

M 2

L1

+RLOAD (A.31)

The current through the secondary side, I2, is given by equation (A.32).

I 2=jωM

Z2S

I L1 (A.32)

Combining equation (A.32) with equation (A.31) and equation (A.30) gives the secondary current as a function of the source voltage. This is expressed in equation (A.33).

I 2=jωM

jωL1( jωM 2

L1

+RLOAD)+ω2 M 2

U 1=M

RLOAD L1

U 1(A.33)

The output voltage, ULOAD, is given by the current through the load resistance. This is expressed in equation (A.34).

U LOAD=RLOAD I 2 (A.34)

Finally, combining equation (A.34) and equation (A.33) gives the expression for the output voltage as a function of the source voltage. This is expressed in equation (A.35).

U LOAD=ML1

U 1 (A.35)

A6

Output level of parallel-parallel topology

The expressions for the resonance capacitances in the parallel-series topology is given by equations (A.36) and (A.37).

C1=1

ω2(L1−

M 2

L2) (A.36)

C2=1

ω2(L2−

M2

L1) (A.37)

Combining equation (A.37) with equation (A.3) gives the expression for the secondary impedance when using parallel compensation. This is expressed in equation (A.38).

Z2P= jω L2+

11

− jω (L2−M 2

L1)+

1RLOAD

=

ω2 L2(L2−

M 2

L1)+ jω

M 2

L1

RLOAD

RLOAD− jω(L2−M 2

L1)

(A.38)

The output current, ILOAD, is the current through the load resistance, RLOAD, and depends on the secondary current I2. The expression for the output current is given by equation (A.39).

I LOAD=

− jω(L2−M 2

L1)

RLOAD− jω(L2−M 2

L1)I 2 (A.39)

The expression for the current through the primary coil, IL1, is given by equation (A.40).

I L1=U1

jω L1+ω

2 M 2

Z2P

(A.40)

The expression for the secondary current, I2, is given by equation (A.41).

I 2=jωM

Z2P

I L1 (A.41)

Combining equations (A.41) and (A.40) results in the expression for the secondary current as a function of the source voltage. This is expressed in equation (A.42).

A7

I 2=jω M

jωL1 Z2P+ω

2 M 2U1 (A.42)

Combining equation (A.42) with equation (A.39) results in the expression for the output current, ILOAD, as a function of the source voltage, U1. This is expressed in equation (A.43).

I LOAD=

ω2 M (L2−

M 2

L1)

(RLOAD− jω(L2−M 2

L1)) ( jωL1 Z2

P+ω

2 M 2 )

U 1 (A.43)

Combining equation (A.43) with equation (A.38) results in equation (A.44).

I LOAD=

ω2 M (L2−

M 2

L1)

jωL1(ω2 L2(L2−M 2

L1)+ jω

M 2

L1

RLOAD)+ω2 M 2(RLOAD− jω (L2−

M2

L1))

U 1 (A.44)

Expanding the expression in the denominator in equation (A.44) results in equation (A.45).

I LOAD=

ω2 M (L2−

M 2

L1)

jω3 L1 L2(L2−M 2

L1)−ω

2 M 2 RLOAD+ω2 M 2 RLOAD− jω3 M 2(L2−

M2

L1)U1 (A.45)

Equation (A.45) reduces to equation (A.46).

ILOAD=M

jω ( L1 L2−M 2 )U 1 (A.46)

A8

Appendix B

Design of an inductive charging emitter encased in reinforced concrete

1000 mm

30 mm

100 mm

Electronic

circuit here Ferrite

40 mm 40 mm 50 mm

15 mm

5 mm

500 mm

Filler Litz wire

conductors

Ducts for

conductors

800 mm

600 mm

25 turns coil

5mm thick aluminium plate

20 mm

1000 mm

Reinforced

concrete

Depending on the design, the filler (in yellow, above the aluminium blue sector), can be:

reinforced concrete

glass fibre

bakelite

Should some additional field guiding material be added, the filler can be moulded accordingly.

Appendix C

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Magnetic characterization of basaltic fibers

Contents

INTRODUCTION .......................................................................................................................................................... 2

Measurement setup....................................................................................................................................................... 2

Sample preparation ....................................................................................................................................................... 2

MEASUREMENTS ........................................................................................................................................................ 3

Basaltic fiber .................................................................................................................................................................. 3

Results ....................................................................................................................................................................... 3

Interpretation of the results ...................................................................................................................................... 3

Concrete ......................................................................................................................................................................... 5

Results ....................................................................................................................................................................... 5

Interpretation of the results ...................................................................................................................................... 5

CONCLUSIONS ............................................................................................................................................................ 6

Authors: Stefano Bonetti (NanOsc AB)

Johan Persson (NanOsc AB)

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Introduction

Measurement setup

In order to measure the magnetic moment of the sample, we used an alternating gradient magnetometer

(AGM) from Princeton Measurements. In this instrument, the sample is placed in the constant magnetic

field in the opening gap of a two-pole electromagnet. On top of the constant field, an alternating magnetic

field is created by two small coils mounted on the poles of the electromagnet. Such field is not

homogeneous, giving rise to a field gradient (which is also alternating) which in turn exerts an alternating

force on the sample. This sets the sample in a forced oscillations regime, which can be amplified by hitting

the mechanical resonance of the system. Such amplified oscillation is then detected by a piezo-electric

sensor connected to the sample.

Further details on this system can be found here on the vendor’s homepage:

http://www.princetonmeasurements.com/

Sample preparation

The samples were cut in dimensions suitable to the measurement setup.

In the basaltic fibers case, the cut was done with normal steel scissors. The sample was then mechanically

cleaned with Aceton before measurement, in order to remove traces of steel dust (that would show a

ferromagnetic signal).

For the concrete, we hit the corners of the block with different steel based objects so as to crack the

concrete. Some of the broken material had the correct measurement size. Also in this case, we carefully

cleaned the sample before performing the measurements.

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Measurements

Basaltic fiber

Figure 1. Magnetic moment as a function of applied magnetic field for the

basaltic fibers.

Results

Figure 1 shows the magnetization of the basaltic fibers as a function of applied magnetic field up to 0.5 T (5

kOe). Three types of magnetic behavior can be observed in the plot:

1. A general paramagnetic behavior (increasing field gives almost linearly increasing magnetization) of

the raw data. The red line shows the linear slope of the magnetization at fields above 0.2 T.

2. If the linear slope is subtracted, one can observe a residual ferromagnetic response, indicated by

the blue-line in the plot.

3. Finally, the plot also shows (black line) the diamagnetic background of the measurement,

originating from the sample holder, made of glass.

Interpretation of the results

1. The sample is dominantly paramagnetic. Which material is causing the paramagnetism cannot be

guessed without knowing the composition of the fiber. A quick search on basalt revealed that alkali

metals could be present in the rock. Alkali metals are strongly paramagnetic.

2. The ferromagnetism could be due to two reasons. The first one is intrinsic, and due to the presence

of iron oxide particles in the fibers. The other reason is extrinsic and could be due to magnetic

impurities. The fibers were cut with steel scissors, and one could see a factor 2 reduction of the

ferromagnetic contribution when measuring the sample as cut, and after cleaning with aceton

under mechanical friction. The two effects may be present at the same time.

3. The diamagnetic signal comes from the sample holder, made of plastic and glass.

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Since the ferromagnetic (2) and the diamagnetic (3) contribution approximately cancel each other at 0.5 T,

one consider the paramagnetic slope to be an approximate estimation of the volume susceptibility. (The

volume susceptibility is calculated as Χ = M/H. When both M and H have dimensions of Tesla, the volume

susceptibility is a non-dimensional constant.)

From Fig. 1, the paramagnetic slope can be estimated to be 2.5E-4emu/0.5T ≈ 5E-4 emu/T. In order to get a

non-dimensional constant, the magnetic moment has to be converted to the magnetization value M, which

is found by dividing the magnetic moment by the volume of the sample.

The volume is estimated in the following way. The basaltic fibers sample can be thought as a cylinder. The

diameter of the cylinder was 0.12 cm and its length 0.48 cm. This gives a volume π*0.06*0.06*0.48 cc =

0.0054 cc.

Now, the volume susceptibility is Χ = 5E-4/0.0054 ≈ 9.5E-2 (emu/cc)/T. The conversion factor between

emu/cc and Tesla is 4π/1E4, which gives the final estimation of volume susceptibility Χfibers = +1.2E-4.

The largest source of error in this calculation is the volume estimation. If we assume a pessimistic case

where we are off by 50% (both under and over estimation), we can say that the estimated number may

vary between 6E-5 and 2.4E-4. (The uncertainty is asymmetric because the volume is in the denominator.)

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Concrete

Figure 2 Magnetic moment as a function of applied magnetic field for the

concrete block.

Results

Figure 2 shows the magnetization of the concrete block as a function of applied magnetic field up to 1.4 T

(14 kOe). Once again, three types of magnetic behavior can be observed in the plot:

1. A paramagnetic behavior of the raw data at fields higher than 0.5 T. The red line shows the linear

slope of the magnetization at fields larger 0.5 T.

2. When the linear slope is subtracted, one can observe an evident residual ferromagnetic response,

indicated by the blue-line in the plot.

3. Again, the plot also shows (black line) the diamagnetic background of the measurement,

originating from the sample holder, made of glass.

Interpretation of the results

1. The sample shows a paramagnetic behavior. As before, in order to indicate which elements are

responsible for the paramagnetism, one would need to know the composition of the concrete.

2. The relatively strong ferromagnetic response was unexpected, and could be due to the presence of

small ferromagnetic particles in the concrete. As a tentative guess, such particles may have entered

in the concrete during the fabrication process.

3. The diamagnetic signal comes again from the sample holder, which is made of plastic and glass.

The sample was approximated to be a cylinder with 0.35 cm diameter and 0.2 cm length. Using similar

calculations as in the previous section, the paramagnetic slope gives a volume susceptibility Χconcrete, paramag ≈

+9E-6. However, the susceptibility of interest here is the one which is observed when a field of magnitude

0.1 T is applied to the sample. In this field region, the slope is larger, hence the susceptibility, which is

estimated to be Χconcrete, ferromag ≈ +2E-4.

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Conclusions

Figure 3, show comparison of M vs H (i.e. the magnetic moment is normalized for the sample volume) for

the basaltic fibers and the concrete, with a piece of relatively “non-magnetic” stainless steel (will not get

stuck on a normal fridge magnet). In such a plot, the signal from the fibers and the concrete is almost

negligible.

Figure 3 Magnetization vs applied magnetic field for three different samples: basaltic fibers, concrete

and stainless steel.

Summarizing, the maximum relative permeability for the basaltic fibers can be estimated to be µbasaltic fibers =

1.00012, and for the concrete µconcrete = 1.00024. In both cases, the relative permeability is several orders of

magnitude smaller than for “non-magnetic” stainless steel.

Most probably, the small amount of magnetism will not affect appreciably a magnetic field which will go

through these materials. However, given the large volumes involved, one should include such numbers in

order to perform accurate calculations.

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