Finite Element Analysis of a Contactless Transformer · PDF fileFinite Element Analysis of a Contactless Transformer . ... Abstract —Inductively ... mathematic model and controller

Finite Element Analysis of a Contactless

Transformer

Jianyu Lan, Houjun Tang, and Xin Gen Key Laboratory of Control of Power Transmission and Transformation, Ministry of Education, Shanghai Jiao Tong

University, Shanghai, China

Email: [email protected]

Abstract—Inductively coupling power transfer is an

emerging technique, which enables power transfer to loads

through air. The contactless transformer is the key

component of it, and the design of a transformer is a time-

consuming work with a large number of tests. In this paper,

a design method of contactless transformer with finite

element analysis is presented. First the contactless

transformer model is deduced from Maxwell Equations, and

the self inductance and mutual inductance computational

equations are given as well. Then the magnetic field

distributions of contactless transformer with different air

gaps are presented by simulation of MAXWELL ANSOFT.

Furthermore, the skin and proximity effects are analyzed as

well. At last, the results are compared with the experimental

results with the same dimension and material. The analyses

show that there has a good agreement with each other. So by

this method, the design period of a contactless transformer

will be shorter than before.

Index Terms—Inductively Coupling Power Transfer,

Contactless Transformer, Finite Element Analysis

I. INTRODUCTION

Some applications require a power transfer without

direct contacts with source supplies. The wireless power

transfer (WPT) system allows transferring energy to

electronic appliances through an air gap [1]-[2]. As an emerging technique, the WPT has been a hot topic for

researchers. Currently, there are three types of WPT

techniques have been reported: electromagnetic radiation,

inductive coupling and magnetic resonance coupling [3].

Among these, the magnetic inductive coupling technique

can transfer higher power than others with higher

efficiency. The power transfer system using inductive

coupling technique is called Inductive coupled power transfer (ICPT) [4]. Because it has many advantages,

ICPT is often applied to transfer power in special

occasions. First, high voltage equipments applied ICPT

technique may increase their security level because there

is no need for user to handle the plugs and cables [1].

Second, in under-water, under-mine and corrosive

environments, the lifetime of this system will be longer

because of no exposition of coppers. Then, the ICPT systems allow removing brushes of mobile loads or

rotating systems, which often cause blasts in the case of

oil fields. In addition, in implanted medical applications,

it would be better to avoid any physical link between

inner body of the patient and the environment, as in [4].

So far efforts have been made to improve the efficiency

and enlarge transfer range of ICPT systems. Gyu

proposed an energy transmission system for an artificial

heart using leakage inductance compensation of transformer [5], and a contactless electrical energy

transmission system for portable telephone is discussed in

[1]. Besides, a design method of wireless power transfer

system based inductively coupled is presented by Shinya

[2]. Furthermore, other researchers focus on the

mathematic model and controller design about

bidirectional wireless power transfer system [6]. On the

other hand, Chen proposed a capacitive coupled contactless power transfer system [7], and an

optimization model of a wireless power transfer system

form medical implanted devices is presented in [8].

Nevertheless above mentions are mainly based on circuit

topologies, and not focused on the contactless power

transformer, which is a key element of an ICPT system.

In ICPT systems, the energy transfer through a

contactless transformer to loads by magnetic induction coupling. It is very important to have an accurate model

in order to design the transformer avoiding a large

number of tests on prototyping stages. Different methods

to model the transformer are proposed in the literature

[9]-[10]. But these models are based on analytical

equations, which do not have enough accuracy with

different separations between the primary and secondary

sides. Because those works did not take into account the frequency effects, such as skin and proximity effects. On

the other hand, models based on Finite Element Analysis

(FEA) are presented in [11]-[15], which have more

accurate results. A homogenization method and three

dimensional FEA have been used to estimate the losses of

a two-winding transformer with large air gap [16]-[17]. In

[18] Jesus presented an analysis of the mutual inductance

between two planar circular windings. Besides, a rectangular contactless transformer is proposed by use of

FEA [19]. In addition, Pascal employed FEA to analysis

the skin and proximity effects of a coreless transformer.

Based on which the losses of transformer are deduced

[20]-[22]. However, up to date, little work presents the

analysis of comparison of FEA simulation and

experimental results. In this paper, a transformer design

method by FEA is discussed, and the simulation results are compared with the experimental. The analyses show

2302 JOURNAL OF NETWORKS, VOL. 8, NO. 10, OCTOBER 2013

© 2013 ACADEMY PUBLISHERdoi:10.4304/jnw.8.10.2302-2309

that using FEA method can acquire an accurate

transformer model, and thus the design cost and time are

reduced.

This paper is organized as follows. In section II the

operation principle of ICPT system is reviewed. In

section III, the model of contactless transformer is

deduced by Maxwell Equations. In section IV, a design method of contactless transformer by FEA is presented.

First, the EE type core contactless transformer is

compared to the CC type core. Then, the skin and

proximity effects with different frequency are analyzed.

Furthermore, the experimental results with a contactless

transformer are compared to the results form FEA by

MAXWELL ANSOFT. At the end, the conclusions are

given in section V.

II. REVIEW OF ICPT SYSTEM

A typical ICPT system consists of the high frequency

plus-current generator, a resonant converter, a rectifier

and loads, shown in figure 1. The contactless power

transformer and the compensated net form a resonant

converter.

LoadResonant

Converter

Figure 1. Typical structure of ICPT System.

Because of a large air gap existed between the primary

coil and the secondary coil, the mutual coupling

inductance within ICPT systems is generally weak. So a resonant tank circuits should be added into both the

primary and secondary parts. Normally, the compensated

net includes the PP, PS, SP and SS or other high level

compensator [5]. Figure 2 shows the schematic of an

ICPT system studied in this paper, in which a half bridge

inverter is chose and the PP compensated net is applied.

sCM

R

pC1Q

2Q

dU

pL sL

Figure 2. Schematic of proposed half bridge ICPT system.

As seen from figure 2, a square wave voltage is

produced at the mid-node of the half bridge inverter by driving switches Q1 and Q2 alternately with 50% duty

cycle. The resonant tank consists of the contactless

transformer and capacitors connected in series both on

the primary coil and the secondary coil. In figure 3, Lp

and Ls denote the primary coil self-inductances and the

secondary coil self-inductances, respectively, M is the

mutual inductance between the primary coil and

secondary coil and R is the equivalent AC resistor of loads. By means of mutual inductance theory, the

equivalent circuit of this system is deduced and shown in

Figure 3.

MpCsC

sLpL

rZ cU

R

Figure 3. Mutual inductance equivalent circuit of the ICPT system.

In figure 3, Zr is the reflected impedance from the secondary side and Uc is the induced voltage of

secondary side, and Zr can be expressed by (1).

2 2 /r sZ M Z (1)

In which Zs is the lumped impedance of secondary side,

which is expressed in (2).

1/ ( )r s sZ j L j C R (2)

Substituting (2) into (1) the reflected resistance and

reactance from the secondary coil to the primary is,

respectively:

4 2

2 2 2 2 2Re

( 1)

s L

s s s L

C RZr

C L C R

(3)

And

3 2 2

2 2 2 2 2

( 1)Im

( 1)

s s s

s s s L

C M C LZr

C L C R

(4)

Then, the equivalent impedance looking from the input

side of half bridge inverter is:

1/ ( )eq p p p rZ j L j C r Z (5)

Therefore, the output power is deduced as equation (6)

[8]:

2

2 2

8Re r dc

out

eq

Z UP

Z (6)

And the output voltage is as following:

p L

out

s

j MI RU

Z

(7)

Define Mv as the gain of output voltage, which is

expressed as

out

v

in

UM

U (8)

Substituting (1) to (7) into(8) the voltage gain is：

(.)

(.)v

NM

M (9)

In which, N(.) and M(.) is expressed in (10) and (11).

2

2

2(.)

1 2 ( )(2 )

n

n

n

j f QknN

j f Q nf

(10)

JOURNAL OF NETWORKS, VOL. 8, NO. 10, OCTOBER 2013 2303

© 2013 ACADEMY PUBLISHER

2 2 2 2

22

2

(.)

(2 )12 1

(2 )1 2 ( )

(2 )

n

n

nn

n

M

f k Q nj f Q

fj f Q n

f

(11)

where fn=f/fr, and /s pn L L . The couple coefficient is

defined as k, and is the capacitor rate defined Cp/Cs.

The quality factor Q is defined as:

2 r pf L

QR

(12)

According to (9), the frequency response of the system

can be illustrated in figure 4.

vM

(Hz)nf

0.9 10.8 1.1 1.2

2

4

3

0

1

1.3 1.4

=1Q

=4Q

=2Q

=10Q

Figure 4. Voltage gain curves at different Q.

Figure 4 shows the curves of voltage gain vs. operation

frequency at different load, which mean that at resonant frequency the voltage gain is at maximum point, and with

the increasing of load the gain curve become sharper,

which mean that the voltage gain is sensitive with the

change of load.

III. MODEL OF CONTACTLESS POWER TRANSFORMER

Figure 5 shows the equivalent circuit of a contactless

power transformer, in which Lp and Ls are the self

inductances of primary and secondary winding, respectively, while M is the mutual inductance; Rp and Rs

are the equivalent series resistance of the primary and

secondary winding , respectively, and Rm is the mutual

resistance between windings.

The energy stored in the transformer is associated with

magnetic flux and magnetic field created by windings,

which is show in (1) [23].

Re2

p s p sB B H HE dv

(13)

On the other hand, the energy can be indicated by self

inductances and mutual inductances which are expressed

in (8).

2 21 1

2 2p p s s m p sE L I L I L I I (14)

where Ip is the rms current in the primary winding, Is is

the rms current in the secondary winding. Applying the

superposition theorem to solve the equations (13) and

(14), the inductance values can be calculated by

2

1p p p

p

L B H dvI

(15)

2

1s s s

s

L B H dvI

(16)

1

2m p s s p

p s

L B H B H dvI I

(17)

And, then the coefficient of mutual inductance is given

by

p s

Mk

L L (18)

To calculate the resistance, the equation to calculate

the power losses is about the function of the in current density associated with transformer, and it is expressed as

follows.

Rep s p sJ J J J

P dv

(19)

where σ is the electric conductivity, the power losses in

the model are calculated by

2 2 2p p s s m p sP R I R I R I I (20)

Comparing (19) and (20), and then apply the

superposition theorem; the resistances are calculated by

2

1 p p

p

p

J JR dv

I

(21)

2

1 s s

s

s

J JR dv

I

(22)

1

2

p s s p

m

p s

J J J JR dv

I I

(23)

IV. FEA ANALYSIS OF CONTACTLESS POWER

TRANSFORMER

A. Analysis of EE Core and CC Core

In this section, the EE core and CC core of contactless

power transformer will be analyzed to employ FEA. By

MAXWELL ANSOFT, the magnetic field distribution of

EE core with the air gap of 2mm is shown in figure 6,

while figure 7 shows the magnetic field distribution of a

CC core with the same dimension and air gap.

Comparing figure 5 and figure 6, it is easy to found

that the magnetic field distribution of EE type core is well distributes, while CC type core magnetic lines



distribution is asymmetrical. Also, it can be seen that the

magnetic flux density of EE core is more than that of CC

core.

pR sR

pLsL

mR

M

Figure 5. Model of contactless power transformer.

Figure 6. Flux distribution of EE type core.

Figure 7. Flux distribution of CC type core.


In the following part, the excitation position of coil

current in the EE core will be discussed. Figure 8 and figure 9 are the magnetic line distribution of EE type core

with the excitation on different position. Comparing

figure 6, figure 8 and figure 9, it is clearly seen that, the

magnetic flux density in figure 6 is more than others. On

the other hand, from the computational results of

MAXWELL ANSOFT, the mutual inductance of figure 6

is largest. So, when the excitation coil is in the position

like figure 6, the coefficient of contactless power

transformer will be largest, thus the efficiency of ICPT

system is highest than in other positions.


B. Analysis of Skin and Proximity Effects

High frequency currents (10 kHz – 5MHz) are injected

into the primary coil in order to generate a coupling

magnetic field, and a voltage is induced by varying

magnetic field on secondary coils. Both skin and

proximity effect are caused by the high frequency

currents. This section presents an analytical model of the

current distribution in a conductor of the cross-section as a function of the frequency. Based on this model, a

numerical integral resolution can be acquired by

computer. Thus, it is possible to determine the resistance

and internal inductance of the conductor.

This model of the current distribution for a single

conductor is generated from Maxwell equations. If one

assume that the conductor is infinite in length and that the

current flows through the z axis direction. Then, the cross-section is just situated in the x, y plane. The current

density J(x, y) is defined by the following integral

equation [24]-[27]:

0

2 2

0

( , ) ( , )2

ln ( ) ( ) ( , )

S

jJ x y J x y

x x y y dxdy J x y

(24)

Where ω is the frequency of the current, μ0 is the

permeability of free space, σ is the conductivity of the

conductive material, here σ = 58.82e6 S/m for copper, S is

the surface of the cross-section, Jω=0(x, y) =-σV is the

current density generated by the voltage supply and refers

to as the current density at low frequencies. Resolving this equation gives the current density distribution over

the cross section.

Knowing the distribution of the current over the cross

section, it is possible to calculate the per-unit-length

resistance and internal self inductance of the conductor

through energy relations as:

2

1

2

1

( , )

( , )

N

n n n

n

N

n n n

n

J x y S

r

J x y S

(25)



2

1

2

0

1

1

( , )

N

n n

n

iN

n n n

n

B S

l

J x y S

(26)

By FEA method, the arrayed copper coils with the

outside excitation current of 10 ampere in the frequency

2MHz are investigated. The current density distributions

are shown in figure 10.

Figure 10. Skin and proximity effects of copper coils.

Observed form figure 10, it can be known that the

strongest current density are displayed at the edge of

cooper coils, which demonstrates the skin and proximity effects well.

01

2

3

0.5 1 1.5 2 2.5

Frequency (MHz)

P-u

-l r

esis

tance

(/

)O

hm

m

4

5

6

Figure 11. Computed p-u-l resistance of copper coil.

To achieve the features of coil-resistance to the

frequency of excitation current, a group of data is computed by the software MAXWELL ANSOFT. The

results are plotted in figure 11, which shows that with the

increasing of excitation currents frequency, the per unit

length resistor will increases. This agrees with the above

theoretic analysis.

C. Experimental Result

In this section a contactless transformer with EE type

magnetic core is presented by FEA. The distributions of

magnetic field are shown by ANSOFT MAXWELL, and

different gaps between coils are analysis. Also, the

coefficients with the change of gaps are computed by

ANSOFT. At last the results are compared with the experimental results, which show good agreement with

each other. Figure 12 is the core studied in this paper, and

the material used is ferrite with relative permeability of

1000. The dimension values are shown in table 1.

a

b

c

d

d

Figure 12. EE type ferrite core.

(a) Flux distribution

(b) B vector distribution

(c) B amplitude distribution

Figure 13. Magnetic field distribution of contactless transformer with

gap at 2 mm.

Figure 14 and figure 13 show the magnetic field distribution with the excitation current of 10 ampere at

primary side. The figure 13 (a) is the flux distribution, (b)

is the B vector distribution and (c) is the magnetic density

distribution.



(a) Flux distribution

(b) B vector distribution

(c) B amplitude distribution

Figure 14. Magnetic field distribution of contactless transformer with

gap at 10 mm.

TABLE I. DIMENSION OF EE CORE

Parameters values

a 20 mm

b 8 mm

c 16 mm

d 11 mm

Primary winds 10 turns

Secondary winds 10 turns

The figure 13 shows the field distribution with the air

gap of 2mm, while figure14 shows the distribution with

the air gap of 10mm. Comparing with figure 13 and

figure 14, it is clearly shown that the field density at 2mm

is strong than 10mm. Furthermore, the mutual inductance and coefficient are

computed by ANSOFT with the gap from 2mm to 10 mm,

and the result is shown in table 2. At the same time, tests

on a prototype shown in figure 15 with the same core

dimension analyzed in simulation have been performed.

These tested results are compared with the simulation

results in table 2.

Figure 15. Prototype of contactless power transformer.

TABLE II. SIMULATION AND EXPERIMENTAL RESULTS

D (mm)

Simulation results Experimental results

M (μH) k M (μH) k

2 31.7 0.92 33.1 0.93

4 28.5 0.88 27.8 0.87

6 18.2 0.65 19.1 0.67

8 11.2 0.5 12.5 0.53

10 8.7 0.45 8.2 0.41

To indicate magnetic field features, figure 16 shows

the mutual inductance of the contactless transformer with

the increasing of the gap distance. It is clearly that with

the gap become bigger the mutual inductance of

contactless transformer will be small, and there is a good

agreement of the simulation results and experimental

results with each other.

0

10

20

30

2 4 6 8 10distance (mm)

Mutu

al i

nduct

ance

(H

)

Experiment

Simulation

Figure 16. Mutual inductance with different distances.

0

0.2

0.4

1

2 4 6 8 10distance (mm)

Coupli

ng c

oef

feci

ent

Experiment

Simulation

0.6

0.8

Figure 17. Coupling coefficient with different distances.

Similarly, the coupling coefficients of EE core

transformer are computed and tested by MAXWELL

ANSOFT and experimental setups in different distances.



The curves are shown in figure 17. From this plot, we can

see that the coupling coefficient drops with the increasing

of gap, which agrees with the theoretical analysis.

Figure 18 shows the skin and proximity effects of

primary coil. The tested results of resistors of primary

coil are compared with the computational results from

MAXWELL ANSOFT. The plot shows that with the increasing of excitation frequency, the resistor will

increases at the same time because of the skin and

proximity effects. And the experimental results are

according with the computational results well.

0

0.2

0.4

1

1 2 3 4 5frequency (MHz)

Res

ista

nce

Experiment

Simulation

0.6

0.8

1.2

Figure 18. Primary coil resistors with excitation frequency.

V. CONCLUSTIONS

Most problems related to contactless power transfer are

usually employing equivalent electric circuits as a tool for their analysis. Furthermore, its values usually acquired

from measurement results performed in prototypes, which

is an expensive and time consuming task. In this paper,

however, a FEA approach based on the Maxwell

Equations is presented, and the magnetic field

distributions are displayed by ANSOFT MAXWELL.

Moreover, experimental results from a prototype are

compared with the simulation results, which show good agreement with each other.

ACKNOWLEDGMENT

This work is supported by the National Natural

Science Fund of China (51277120).

REFERENCES

[1] Yungtaek Jang, and Milan M. Jovanovic, “A contactless electrical energy transmission system for portable-telephone battery chargers,” IEEE Transactions on Industrial Electronics, vol. 50(3), pp. 520-527, 2003.

[2] Shinya Matsutomo, So Noguchi, Hideo Yamashita, and Shigeya Tanimoto, “A new concept for optimal design method considering modeling accuracy of electromagnetic device,” IEEE Transactions on Magnetic, vol. 40(20), pp.

1232-1235, 2004. [3] S. Cheon, Y. H. Kim, S. Y. Kang, M. L. Lee, J. M. Lee,

and T. Zyung, “Circuit-Model-Based analysis of a wireless energy-transfer system via coupled magnetic resonances, IEEE Transactions on Industrial Electronics, 2906-2914, 2011.

[4] Y. X. Xu, J. T. Boys, and G. A. Covic, “Modeling and controller design of ICPT pick-ups,” IEEE International Conference on Power System Technology, 2002, vol. 3, pp. 1602-1606, 2002.

[5] Gyu Bum Joung and Bo H. Cho, 1998, “An energy transmission system for an artificial heart using leakage

inductance compensation of transcutaneous transformer,” IEEE Transaction on Power Electronics, vol. 13(6), pp. 1013-1022, 1998.

[6] Duleepa J. Thrimawithana, Udaya K. Madawala, and Michael Neath, “A synchronization technique for bidirectional IPT systems,” IEEE Transactions on Industrial Electronics, vol. 60(1), 301-309, 2013.

[7] Chenyang Xia, Yuejin Zhou, Juan Zhang, and Chaowei Li, “Comparison of power transfer characteristics between CPT and IPT system and mutual inductance optimization for IPT system, ” Journal of Computers, vol. 7(11), pp.

2734-2741, 2012. [8] Liangyu Bai, Houjun Tang, and Yang Xu, “Optimization

model of the transcutaneous energy transmission system for achieving maximum power transfer capability,” Journal of Computers, vol. 6(2), pp. 305-312, 2011.

[9] R. Prieto, R. Asensi, J. A. Cobos, O. Garcia, and J. Uceda, “New modeling strategy for high frequency magnetic components,” IEEE 21st International Conference on Industrial Electronic, Control and Instrumentation, vol. 1, 246-251, 1995.

[10] O. Garcia, J. A. Cobos, O. Garcia, and J. Uceda, “Model of the capacitive effects in magnetic components,” IEEE 26th

Annual Power Electronics Specialists Conference, vol. 2, pp. 678-683, 1995.

[11] Zhuo Yan, Chao Zhang, Haiyan chen, and Qingxin Yang, “Simulation analysis on detachable transformer in contactless electrical energy transmission system,” IEEE International Conference on Electrical Machines and Systems, pp. 1777-1780, 2010.

[12] Ying Zhang, Yumei Du, Ruihua Zhang, and Liming Shi, “Study on a novel flat winding transformer with sandwich construction magnet core in CPS system for high speed transportation,” IEEE International Conference on

Electrical Machines and Systems, pp. 1-4, 2012. [13] Shipeng Song, Guohai Liu, Wensheng Gong, and

Wenxiang Zhao, “Electromagnetic analysis of a new magnetic core of transformer for a contactless electric vehicle charging,” IEEE International Conference on Electrical Machines and Systems, pp. 1-4, 2011.

[14] J. A. Brandao Faria, “Poynting vector flow analysis for contactless energy transfer in magnetic systems,” IEEE Transactions on Power Electronics, vol. 27(10), pp. 4292-4300, 2012.

[15] C. Lopez, R. Asensi, R. Prieto, O. Garcia, and J. A. Cobos,

“Finite element analysis model of a contactless transformer for battery chargers in electric vehicles,” Applied Power Electronics Conference and Exposition Twenty-Seventh Annual IEEE, pp. 1902-1906, 2012.

[16] Jean-Romain sibue, Gerard Meunier, Jean-Paul Ferrieux, James Roudet, and Robert Periot, “Modeling and computation of losses in conductors and magnetic cores of a large air gap transformer dedicated to contactless energy transfer,” IEEE Transactions on Magnetics, vol. 49(1), pp. 586-590, 2013.

[17] Jean-Romain Sibue, Gatien Kwimang, Jean-Paul Ferrieus, Gerafd Meunier, James Roudet and Robert Periot, “A

global study of a contactless energy transfer system: analytical design, virtual prototyping, and experimental validation,” IEEE Transactions on Power Electronics, vol. 28(10), pp. 4690-4696, 2013.

[18] Jesus Acero, Ignacio Lope, Rafael Alonso, Oscar Lucia, and Jose M. Burdio, “Analysis of the mutual inductance of planar-lumped inductive power transfer systems,” IEEE



Transactions on Industrial Electronics, vol. 60(1), pp. 410-420, 2013.

[19] Yoon-Ho Kim, Kang-Hwan Jin, “Design and implementation of a rectangular-type contactless transformer,” IEEE Transactions on Industrial Electronics, vol. 58(12), pp. 5380-5384, 2011.

[20] Pasal Meyer, Paolp Germano, Miroslav Markovic, and Yves Perriard, “Design of a contactless energy-transfer system for desktop peripherals,” IEEE Transactions on Industry Applications, vol. 47(4), pp. 1643-1651, 2011.

[21] Pascal Meyer, Paolo, and Yves Perriard “FEM modeling of skin and proximity effects for coreless transformers,” IEEE International Conference on Electrical Machines and

Systems, pp. 1-6, 2012. [22] Pascal Meyer, Yves Perriard, “Skin and proximity effects

for coreless transformers,” IEEE International Conference on Electrical Machines and Systems, pp. 1-5, 2011.

[23] C. Lopez, R. Asensi, R. Prieto, O. Garicia, and J. A. Cobos, “Finite element analysis model of a contactless transformer for battery chargers in electric vehicles,” IEEE Applied Power Electronics Conference and Exposition, pp. 1902-1906, 2012.

[24] G. Antonini, A. Orlandi, and C. Paul, “Internal impedance of conductors of rectangular across section,” IEEE Transactions on Microwave theory and technique, vol. 47,

pp. 979-985, 1999. [25] D. DeZutter and L. Knockaert, “Skin effect modeling

based on a differential surface admittance operator,” IEEE Transactions on Microwave theory and technique, vol. 53, pp. 2526-2538, 2005.

[26] S. R. H. Hoole, Computer-aided Analysis and Design of Electromagnetic Devices. Elsevier, New York, 1989.

[27] P. Silvester, Modern Electromagnetic Fields. Prentice-Hall, Inc., Englewood Cliffs, N. I., 1968.

Jianyu Lan was born in Fujian province, China, in 1980. He received the B.S. degree in electrical engineering from Zhengzhou University, Zhengzhou, China, in 2002, and M.S. degree in electrical engineering from Shanghai Maritime University, Shanghai, in 2009. He is currently working toward his Ph. D.

degree in electrical engineering at Shanghai Jiao Tong University. His

research interests include power electronics emerging at power transfer. Houjun Tang was born in Shandong province, China, in 1957. He received B.S. and M.S. degrees in 1982 and 1988 respectively. He received Ph.D. degree in Yamagata University, Japan, 1997. He is professor of the Department of Electrical Engineering, Shanghai Jiao Tong University. His research interests include power electronics emerging at power transfer.

Xin Gen was born in Heilongjiang province, China, in 1980. He received the B.S. and M.S. degree in electrical engineering from Shanghai Jiao Tong University, Shanghai, China, in 2002, 2008. He is currently working toward his Ph. D. degree in electrical engineering at Shanghai Jiao Tong University. His research interests include power electronics emerging at power transfer.



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Finite Element Analysis of a Contactless Transformer · PDF fileFinite Element Analysis of a Contactless Transformer . ... Abstract —Inductively ... mathematic model and controller