電気学会論文誌●（●●●●●●●部門誌）
IEEJ Transactions on ●●●●●●●●●●●●●●●
Vol.●● No.● pp.●-●●
DOI: ●.●●/ieejeiss.●●.●

Paper

General Analytical Model of Inductance Variation with
EMF-canceling Coil for Inductive Power Transfer System
Keita Furukawa＊, Student member, Keisuke Kusaka＊, Member,
Jun-ichi Itoh＊a), Senior member(Manuscript received Jan. 00, 20XX, revised May 00, 20XX)
This paper presents an analytical model and a design criteria for additional windings to reduce electromagnetic field (EMF)
generated from inductive power transfer (IPT) systems. In particular, the canceling windings are connected to the main windings
with common-mode connection, differential-mode connection, or short-circuited connection. Parameter variation, which may
degrade the system efficiency, occurs in the IPT system owing to the unwanted coupling between the main windings and thecanceling windings. Therefore, the theoretical analysis of the IPT system considering the canceling windings is conducted toevaluate the effects of the EMF shielding methods on system parameter variation. The calculation results of the systemparameters agree with the measurement results in the prototype of the four-winding IPT coils, the error is lower than 5%. The
simulation results with a 1-kW prototype IPT system indicate that the magnetic flux density at the distance of 50 cm from thebottom of the receiving coils decreases by at most 41% with the differential-mode connection.
Keywords : active shielding, electromagnetic field, inductive power transfer, multiple magnetic coupling1.

non-resonant reactive shielding method because the magnetic field
generated by the canceling windings are controllable [11].
The reduction effect of EMF by adding coils has been reported
in several papers [11–16]. Nevertheless, parameter variations of
the IPT coil due to the additional coils have not been analytically
discussed. In particular, the magnetic flux generated by thecanceling windings not only reduces the EMF but also crosses themain windings as an interlinkage flux. Thus, the self-inductanceand the mutual inductance of the entire IPT coil change due to theadditional coils [12]. This variation of the self-inductance changes
the resonant frequency. Therefore, the transmission power or theefficiency might be affected compared that of the non-cancelingwindings. This problem in the past work is that the influences ofadding the canceling windings to the entire IPT systems are notdiscussed in term of the inductance variation.
In this paper, the effect of the canceling windings is evaluated,focusing on the variations of the equivalent self-inductance andthe equivalent mutual inductance of the entire IPT coil. In
particular, a model of a four-winding IPT coils is theoreticallyanalyzed. The contribution of this paper is to provide a general
analytical model and design criteria to reduce the parametervariation due to the EMF canceling windings. In particular, thecanceling windings are connected in parallel to the main windings
to reduce EMF of IPT coils system as the non-resonant reactive
shielding method or the active shielding method. The equivalent
self-inductances and the equivalent coupling coefficientconsidering the influence of the canceling windings are calculated
from a view of the entire transmission system. Then, thecalculation results are confirmed with the measurement of theequivalent self-inductances and the equivalent coupling coefficientin prototypes of the four-winding IPT coils. Moreover, the effectof EMF reduction is simulated when the prototypes are installed to
the 1-kW IPT systems.

Introduction

In recent years, inductive power transfer (IPT) systems haveattracted much attention in terms of safety and convenient battery
chargers for electrical vehicles (EVs) [1–5]. The IPT systems
achieve power transmission using a magnetic coupling without
electrical contacts. Electromagnetic field (EMF) should beconsidered because EMF may cause health impairment or
malfunction of electrical equipment [5–7]. In particular,
high-power IPT systems such as quick battery chargers for EVs
generate high level of EMF. Therefore, it is necessary to reduceradiation noise to widespread use of the IPT system.
In order to reduce EMF, many studies have been conducted on
different circuit topologies, modulation methods andconfigurations of IPT coils [5–16]. In particular, non-resonant
reactive shield and active shield, which are focused on theconfigurations of the IPT coils, have been proposed [11–14].
Non-resonant reactive shielding methods require additional
short-circuited coils to reduce EMF [11–12]. The magnetic flux
induces a current which cancels the leakage magnetic field in the
short-circuited coils when a leakage magnetic flux crosses theshort-circuited coils. However, the EMF-reduction effectiveness is
low at the place far from the canceling windings because themagnetomotive force of the canceling winding is limited by theinterlinkage magnetic flux [11].
On the other hand, the active shielding method employs
canceling windings which are connected to the main windings oradditional power sources [11–14]. In this method, the current
flowing in the canceling windings is controllable with the main
windings or the power sources. Therefore, the cancellation of themagnetic field becomes more effective compared to thea) Correspondence to: Jun-ichi Itoh. E-mail: itoh@vos.nagaokaut.ac.jp＊
Nagaoka University of Technology.
1603-1, Kamitomioka-machi, Nagaoka, Niigata, Japan
940-2188© 200● The Institute of Electrical Engineers of Japan.

1Inductance Variation for EMF-canceling Methods on IPT System (Keita Furukawa et al.)Transmitting coils

Winding #1
Main winding

Path of discussed leakage magnetic flux
Winding #2
Winding #3
Main magnetic path

Canceling windings
Outside of coil

Magnetic core
Path of discussed leakage magnetic flux
Winding #4

Receiving coils(a)Fig. 1.

Outline of transmission coil.

(b)

Front view with magnetic paths.

(c)Configuration of coil at one side.

Investigated model of IPT coil as example. The solenoid-type IPT coil with the canceling windings (winding #2 andwinding #4). EMF upper and under cores is reduced by the canceling windings.
Winding #1

2.

Inside of coilFigure 1 shows the schematic of the analyzed IPT coils.
Although following analysis is possible to be applied to general
IPT coils, which fulfill some conditions as mentioned later, thesolenoid-type IPT coil is analyzed as an example.
In general, canceling windings or conductive plates are installedaround the circular pads in order to reduce EMF [11–15]. The
conductive plates or the canceling windings cancel magnetic flux
crossing themselves by the eddy current or the current of thecoils [11–16]. Moreover, the eddy current or the current of thecanceling windings generate antiphase magnetic field around thecanceling windings or the conductive plates, which is useful to
reduce leakage magnetic and EMF [11–16].
As shown in Fig. 1(b), the canceling windings are placed on theoutside of the cores at the transmitting and receiving coils to
reduce EMF which emits at the top and bottom the IPT coils. Boththe transmitting coils and the receiving coils have same size andsame configuration. The main windings, e.g. winding #1 andwinding #3, are wired on the cores as typical solenoid coils. The
canceling windings, e.g. winding #2 and winding #4, form a pairof the serial rectangular coil. The canceling windings are installedon the same core of the main windings. The four windings couples
to each other magnetically. Therefore, the IPT coils behaves as thefour-winding transformer.
Due to the placement of the canceling windings, the mutual
inductances between following windings, e.g. winding #2 andwinding #3, winding #2 and winding #4, and winding #4 andwinding #1, are negligibly weak. Thus, the relationship among thecurrent i1, i2, i3, i4 and the voltage v1, v2, v3, v4 of each windings in
Fig. 1 is expressed by the four-order inductance matrix as

 1
 v1  
 v2   L  kc  v3 
 kM
 

v
 4
 0

kc 

kM



0

0

1

0

kc 

Transmitting coils

ip

Configuration of IPT coils

Receiving coils

i1

vp

L

Leq_shorti2Winding #3

is

i3

kM

kc

L

vs

i4

Leq_short

kc

L

L
Winding #4

Winding #2

keq_short(a)

Short-circuited canceling windings.

Transmitting coils

Winding #1

ip

Receiving coils

Winding #3

i1

vp

L

Leq_com

L

i2

is

i3

kM

kc

kc

i4

L

CommonWinding #2

vsL

Leq_com

Winding #4

keq_com(b)

Canceling windings connected as common-mode coils.

Winding #1

Transmitting coils

ip

i1

vp

L

Leq_dif

L

i2

Winding #2(c)Receiving coils

Winding #3

is

i3

kM

kc

kc

i4

L
Differential

keq_difvsL

Leq_dif

Winding #4

Canceling windings connected as differential-mode coils.

Fig. 2.

Connection diagrams of main windings andcanceling windings.

Figure 2 shows the connection diagrams of the non-resonant
reactive shielding method and the active shielding method. In theactive shielding method, where the canceling windings areconnected as the common-mode coils or the differential-mode
coils, are considered. In particular, the common mode coils resultin the positive mutual inductance between the parallel-connectedcoils, whereas the negative mutual inductance between theparallel-connected coils occurs in the differential mode coils.

 i 
  1
0  d  i2 ........... (1),kc   dt  i3 
 
  
   i4 0where L is the self-inductance of the main windings, kM and kc are
the coupling coefficients between the main winding and the main
winding, and between the main winding and the cancelingwinding, respectively, and  is the self-inductance ratio between
the main windings and the canceling windings.

3. Parameter Derivation
In this section, the equivalent self-inductance and the equivalent
2

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Inductance Variation for EMF-canceling Methods on IPT System (Keita Furukawa et al.)coupling coefficient are formulated with a model of themulti-winding transformer when the canceling windings areconnected to the main windings in parallel or short-circuited. The
equivalent self-inductance is defined as self-inductances from theview of transmitting coils or receiving coils of the entire IPT coil.
The equivalent coupling coefficient is defined as a coupling
coefficient between the transmitting coils and the receiving coils.
Both of the equivalent values are essential to design a resonant
frequency and a transmission power for IPT systems.
3.1
Inverse Matrix of Inductance Matrix
In order toclarify the equivalent self-inductance and the equivalent coupling
coefficients, the inductance matrix is introduced in Eq. (1). It isconvenient to calculate the current of the coils from the input
voltage with the inverse matrix of the inductance matrix whenconditions of the input voltage is decided as shown in Fig. 2. The
relationship between the current and the voltage of each coil in Fig.
1 is also expressed by a four-order inverse matrix in (2), which islocated at bottom of this page, and (3)The equivalent self-inductance Leq-short (= Lpeq_short = Lseq_short) andthe equivalent coupling coefficient keq_short are expressed,

keq _ short  v p   Lpeq _ short   
 vs   M eq _ short 1  kc
 L 
 kM

2



0

0

1

0

kc 



0 

kc  

 



M

c M

p

s

c

2

c

M

In addition, the conditions of the input current ip = i1 + i2,
is = i3 + i4 are considered. The relationship between the voltage
and the current of the entire IPT coils is shown in (10) and (11)





1

c

c





   2  k 1 1 k 2  k 2ccM
 i p   i1  i2 
1 
   

2

i

i
 is   3 4  det L     kc kM  k  k  v dt   p .. (10),
2
2  v dt 
  2  kc  1 1  kc  k M    s  v p   Lpeq _ com   
 vs   M eq _ com

2

c

M





M eq _ com  d  i p   
Lseq _ com  dt  is 








   2  k 1 1 k 2  k 2
c
c
M


2
2

2
  2  kc  1  k M    kc k MkM  d  i p    ................................... (6),
1  kc 2  dt  is 

0



2

M eq _ short  d  i p   
Lseq _ short  dt  is 

kM



c



kM    v p dt .................. (5),
1  kc 2   vs dt 




kc 





2

L








  k  k d i  dt  i  .......... (11),
  


2

k

1
1

k

k






where Lpeq_short is the equivalent self-inductance of the transmitting
coils, Lseq_short is the equivalent self-inductance of the receiving
coils, and Meq_short is the equivalent mutual inductances between
the transmitting coils and the receiving coils.
Then, the self-inductance and the coupling coefficient of theentire IPT coil are varied from the original values L and kM,
respectively due to the employment of the canceling windings.

 1
 i1  i
 2   L1  kc 
 i3 
 kM
 

 i4 
 0

c

In addition, the conditions of the input current i1 = ip, i3 = is are
considered. The relationship between the voltage and the currentof the entire IPT coils is shown as

 i p   i1   1  kc 2
      is   i3  det L  kM   k k   k k k   v dt ............ (9).
    k  1  k     v dt 
1   k  1  k   k 







 





kM
............................................ (8).
1  kc 2





 kM
  1  kc 2

 i1 


 

k
k
2

   v p dt c M
 i2   1    kc 1  kc
 .. (4).
2
 i3  det L  1  kc
 v dt 

 kM
s
 


 
 i4   kc 1  kc 2 

k
k
c M







Leq _ short

where det L is the determinant of the four-order inductance matrixin (1).
3.2 Short-circuited Connection
When the cancelingwindings are shorted as shown in Fig. 2(a), the input voltage is v1= vp, v3 = vs and v2 = v4 = 0. Hence, the input current is expressedby

M eq _ short    k 1 k 2cc i1  
1   kc 1  kc 2  k M 2
 i2   1 
 i3  det L      kc k M  i4   k k k
c
c M




2



3.3 Common-mode Connection
The conditions of the
input voltage is v1 = v2 = vp and v3 = v4 = vs. Hence, when thecanceling windings are connected to the main windings as thecommon-mode coils as shown in Fig. 2 (b), the input current isexpressed by (9)det L   L 1  kc  1  kc   k M 2 ............................... (3),2Leq _ short  L 1  kc 2 .......................................................... (7)

2

c

M

p

2

c

2

c

s

M

where Lpeq_com is the equivalent self-inductance of the transmitting
coils, Lseq_com is the equivalent self-inductance of the receiving
coils, and Meq_com is the equivalent mutual inductances between  1  kc 2
 v1dt   k 1 k 2
 v dt cc2
 1 
 v dt  det L  kM 3 




v dt
 kc k M
 4 3 1  k   k
  kc 1  kc 2

 kM

2

 kc k M

2cM

 kc k M 1  kc 2  kc k M  kc 1  kc

2 v dt   1 
2
 v dt  kc k M  2  ..... (2)2   kc 1  kc   v3dt 
1  kc 2  kM 2    v4 dt  kc k M

2

 






IEEJ Trans. ●●, Vol.●●, No.●, ●●●Inductance Variation for EMF-canceling Methods on IPT System (Keita Furukawa et al.)the transmitting coils and the receiving coils. The equivalent
self-inductance Leq_com (= Lpeq_com = Lseq_com) and the equivalent
coupling coefficient keq_com are expressed in (12) and (13)

Leq _ com   2  k  1  k2ckeq _ com  L 1  kc 2  1    2kc   k M 2

M eq _ com
Leq _ com ............... (12)keq _ dif M1  k  1    2k    k
2

c

2



M



    k 1 k 2cc i1 2 
1   kc 1  kc  k M 2
 i2   1 
 i3  det L      kc k M
 

i
 4
  k k k
c
c M

















   k k




k
k
k


   v dt .......... (14).
    k  1  k     v dt 
1   k  1  k   k 
 

c

c

M

c M

p

2

c

s

c

2

c

2

c

M

In addition, the conditions on the input current ip = i1 - i2,
is = i3 - i4 are considered. The relationship between the voltage andthe current of the entire IPT coils is shown in (15) and (16)







   2  k 1 1 k 2  k 2ccM
 i p   i1  i2 
1   2 is   i3  i4  det L     kc kM  k  k  v dt   p . (15),  2  kc  1 1  kc 2  kM 2    vs dt  v p   Lpeq _ dif   
 vs   M eq _ dif


2

c

M





M eq _ dif  d  i p   
Lseq _ dif  dt  is 








   2  k 1 1 k 2  k 2
c
c
M

2
2

  2  kc  1  k M 2    k c k M




L






  k  k d i    ......... (16),  2  k  1 1  k   k  dt  i 
2

c

M

p

2

c

c

2

M



  2  k  1  k
2

M eq _ dif
Leq _ difkM

 ................ (17)2M  k 2c1  k  1    2k    k
2

c

c

2

........ (18).

M

3.5 Design Criteria of Canceling Windings
Figure 3
and 4 show the contour diagrams of the equivalent coupling
coefficients and the equivalent self-inductances derived from Eqs.
(7–8, 12–13, 17–18), respectively. Noted that the coupling
coefficient kM is fixed at 0.2, whereas the coupling coefficient kc
and the self-inductance ratio  are variables. In particular, kc isadjusted by changing installation location and configuration of thecanceling windings, whereas  is also adjusted by changing thenumber of the turns of the canceling windings.
Figure 3(a) shows that keq_short is improved by increasing kc,
whereas keq_short is not varied by . Meanwhile, Fig. 4(a) showsthat the Leq_short is decreased by increase kc, and Leq_short is also notvaried by . Hence, the parameter variation with theshort-circuited canceling windings is not influenced by the numberof the turns of the canceling windings.
Figure 3(b) shows that keq_com is improved by increasing kc or .
Figure 4(b) shows that Leq_com is decreasing due to the increase in
kc or the decrease in . Thus, in order to avoid the parametervariation which is caused by the common-mode-connectedcanceling windings, not only the number of the turns of thecanceling windings should be designed larger than the number of
the turns of the main windings, but also the canceling windings
have to be placed close to the main windings.
Figure 3(c) shows that keq_dif is improved in the range of high kc
and high . Meanwhile, Fig. 4(c) shows that Leq_dif is decreasing
due to the high kc and the decrease in . Therefore, not only thewinding turn should be much larger than the main windings, butalso the canceling windings have to be installed apart from themain winding in order to avoid the parameter variation which is
caused by the differential-mode-connected canceling windings.
However, setting the canceling windings apart from the main
windings degrades a canceling performance of EMF. There is thetrade-off between the parameter variation (decreasing of theequivalent self-inductance) and the canceling performance. Thus,
an operation frequency or the construction of an IPT coil should
be redesigned, when the canceling windings are installed in orderto reduce EMF.
In addition, the weight and the volume increases for thecanceling windings. The IPT coils with the common mode or thedifferential mode are heavier than the IPT coils with theshort-circuited connection to avoid the decrease of the equivalent
self-inductance. The turn number of the canceling windings withthe common mode and the differential mode needs to be muchlarger because Leq_com and Leq_dif are decreased by low aL.
Meanwhile, the turn number of the canceling windings with theshort-circuited can be low because Leq_short is not related to thenumber of the turn of the canceling windings.
As a conclusion, it is shown that the design criteria for the threeconnection methods of the canceling windings at the view point of
avoiding the parameter variations as follows:
1) the short-circuited connection (non-resonant reactive shield)the long distance between the main windings and the...... (13).

3.4
Differential-mode Connection
The conditions of
the input voltage is v1 = -v2 = vp and v3 = -v4 = vs when thecanceling windings are connected to the main windings as thedifferential-mode coils as shown in Fig. 2 (c). Hence, the input
current is expressed by (14)





2

c

c



 L 1  kc 2  1    2kc   kM 2
c2

  k 

kM

Leq _ dif swhere Lpeq_dif is the equivalent self-inductance of the transmitting
coils, Lseq_dif is the equivalent self-inductance of the receiving coils,
and Meq_dif is the equivalent mutual inductances between thetransmitting coils and the receiving coils. The equivalent
self-inductance Leq_dif (= Lpeq_dif = Lseq_dif) and the equivalent
coupling coefficient keq_dif are expressed in (17) and (18)4IEEJ Trans. ●●, Vol.●●, No.●, ●●●

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

0

2

4

6

8

Self-inductance ratio (a)10

keq_short (Short-circuited connection).

Coupling coefficient between main
winding and canceling winding kc

Coupling coefficient between main
winding and canceling winding kc

Coupling coefficient between main
winding and canceling winding kc

Inductance Variation for EMF-canceling Methods on IPT System (Keita Furukawa et al.)

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

Equivalent
coupling
coefficient

0.8

>0.9

0.7

0.8

0.6

0.7

0.5

0.6

0.4

0.5

0.3

0.4
0.3

0.2

0.2 (= kM)

0.1

0.1
0

(b)

2

4

6

8

10

Self-inductance ratio 0.0

keq_com (Common mode).

0

2

4

6

8

10

Self-inductance ratio (c)0

keq_dif (Differential mode).

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

0

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

2

4

6

8

10

Coupling coefficient between main
winding and canceling winding kc

Coupling coefficient between main
winding and canceling winding kc

Coupling coefficient between main
winding and canceling winding kc

Fig. 3. Relationship among equivalent coupling coefficients, coupling coefficient between main winding and cancelingwinding, and self-inductance ratio. The coupling coefficient kM is 0.2. Variation range of the coupling coefficient between themain winding and the canceling winding kc is from 0 to 0.89, whereas range of the self-inductance ratio  is from 0 to 10.

02

Leq_short / L (Short-circuited connection).

6

8

10

>0.9
0.7
0.8
0.6
0.7
0.5

0.6

0.4

0.5

0.3

0.4

0.2

0.3

0.1

0.2

0.0

0

Self-inductance ratio 

Self-inductance ratio (a)4

Ratio of equivalent
self-inductance to L

0.8

(b)

Leq_com / L (Common mode).

2

4

6

8

Self-inductance ratio 
(c)

10

0.1
0

Leq_dif / L (Differential mode).

Fig. 4. Relationship among ratio of equivalent self-inductances to self-inductance of main windings, coupling coefficient
between main windings and canceling windings, and self-inductance ratio. Conditions of kM, kc, and  are same as in Fig. 3.
canceling windings.
the low self-inductance of the canceling windings.
2) the common-mode connection
installation of the canceling windings by the main
windings.

twice or more the number of the turn of the cancelingwindings compared with the main windings.
3) the differential-mode connection
the long distance between the main windings and thecanceling windings.

twice or more the number of the turn of the cancelingwindings compared with the main windings.
The advantage of avoiding the parameter variations is reducing
the mismatch between the operation frequency and the resonant
frequency, which is necessary to operate IPT systems under theconditions of the high efficiency and the high power transmission.

(TDK Corp., N87). The number of turns of the main windings is
30 with 3.5-mm2 insulated wires, whereas the number of turn ofthe canceling windings is 130 with enameled wires. Note that the
number of turns of the transmitting coils and the receiving coils
are the same.
Table I shows the measurement results of the four-orderinductance matrix, the equivalent self-inductances and theequivalent coupling coefficients in the each connection. In order tocompare the equivalent self-inductance, the equivalent mutual
inductance, and the equivalent coupling coefficient, both themeasured values and the calculated values are shown. The
parameters of L,  and kc are average values of the transmitting
coils and the receiving coils. Note that the self-inductance, themutual inductance and the equivalent coupling coefficient without
the canceling windings are equal to L, kML and kM, respectively,
because the open coils do not influence the magnetic field.
In particular, the calculated values of the equivalent
self-inductances correspond to the measured values with amaximum error of 2.7%. The self-inductance is the importantfactor because the IPT system should be designed to resonate at
the transmission frequency. Thus, a precise calculation is crucial
for the design of the IPT system. Besides, the maximum error of
the equivalent coupling coefficients is 4.9%, which is larger thanthe error of the equivalent self-inductance because of the influenceof the ignored magnetic coupling between following windings, i.e.,

4. Experimental Verification with Prototype of IPT
coil
The self-inductances and the mutual inductances of the wired
coils are measured in order to confirm Eqs. (7–8, 12–13, 17–18)
with the prototype four-winding IPT coil.
Figure 5 shows the prototype of the IPT coil. In order to shield
EMF on the top and below, the canceling windings shaped
double-D are put on the outside cores. The core material is ferrite

5

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Inductance Variation for EMF-canceling Methods on IPT System (Keita Furukawa et al.)Winding #1 (main winding)145

Winding #2 (canceling winding)

200
16

65

65

190

190
Gap 120

16
Winding #3 (main winding)

195
280

Winding #4 (canceling winding)(a) Front view.

Unit: mm

Prop of transmitting-coils core(b) Top view.

(c) Side view.

Fig. 5. Outline of prototype of four-winding IPT coils. The main windings are wired on center of the cores (winding #1 andwinding #3). The canceling windings are put on top of the transmitting-coils core and bottom of the receiving-coils core (winding#2 and winding #4). The canceling windings construct the serial two coils. The four props support the transmitting-coils core.
Table I.

Experimental results: equivalent coupling coefficient and inductances of prototype of four-winding IPT coils.

Connection of canceling windings

W/o canceling windings

Inductance matrix as four-winding IPT coils

Average value
Average value
Average value
Measured value
Measured value
Equivalent transmitting self-inductanceCalculated value
Error of calculated equivalent transmitting self-inductance
Measured value
Equivalent receiving self-inductanceCalculated value
Error of calculated equivalent receiving self-inductance
Measured value
Equivalent mutual inductanceCalculated value
Measured value
Equivalent coupling coefficient
Calculated value
Error of calculated coupling coefficient

Short-circuited

Common mode

Differential mode

 399 432 70.4 12.2  432 3120 12.8 6.7  [H]
 70.4 12.8 393 422  12.2 6.7 422 3010 
396 H
7.94
0.382
0.178

Self-inductance of main winding L
Self-inductance ratio 
Coupling coefficient kc
Coupling coefficient kM

399 H334 H H
1.3%
332 H H
1.9%
67.5 H H
0.203
0.208
2.7%

393 H

70.4 H
0.178

396 H H
0.6%
391 H H0.7%
73.0 H H
0.185
0.183
1.2%

236 H H
2.3%
235 H H
2.7%
43.3 H H
0.184
0.193
4.9%

Winding #2 (canceling winding)

10

200

20

16
Winding #1 (main winding)

Case

Core

230

Gap: 120

Winding #3 (main winding)

350

Winding #4 (canceling winding)

195
280
(a)

Front view.

Unit: mm

105(b)

Top view.

(c)Side view.

Fig. 6. Outline of CAD model of prototype four-winding IPT coils. The size of the cores and the cases matches the prototypeof the four-winding IPT coils; the windings are constructed as the solid model, and the material of the cores is PC40. The cases
are treated as air, whereas the thickness of the cases and the main windings is 5 mm.
winding #2 to winding #3, winding #2 to winding #4, and winding#4 to winding #1.

following electromagnetic field analysis is considered with only
IPT coils at the fundamental harmonics component for
simplification because the magnetic flux distribution around the
IPT coils depends on the waveforms of the power source, forms
and materials of EVs. Thus, the following measuring methods do
not follow the guidelines such as ICNRP 2010. Note that theconventional method is considered as the two-winding IPT coils
without the canceling windings.
Figure 6 shows the computer-aided-design (CAD) model of the

5. EMF Reduction with Canceling Windings
5.1
Circuit and Model Configuration
In this chapter, the IPT coils are simulated with JMAG (JSOL
Corporation) to confirm the EMF reduction of the IPT coils withthe canceling windings. JMAG is a software for theelectromagnetic field analysis with a finite element method. The
6

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Inductance Variation for EMF-canceling Methods on IPT System (Keita Furukawa et al.)kM ,keq_short ,keq_com ,keq_dif
ffshort
fcom
fdif

Cs1
Vin
cos inL
Leq_short
Leq_com
Leq_difL
Leq_short
Leq_com
Leq_dif

Cs2

Vout

Req

Equivalent circuit of prototype four-winding IPT coils

Fig. 7. Circuit configuration of simulation model. The prototype of the four-winding IPT coils is equivalent to thetwo-winding IPT coils when the canceling windings are shorted or connected to the main windings in parallel. For individual
connection such as when the canceling windings are shorted, the equivalent self-inductance, the equivalent coupling coefficientand the operation frequency are chosen Leq_short, keq_short and fshort differently.
Table II.

IPT coil on JMAG. The structure and the size of the CAD model
are based on the prototype of the four-winding IPT coil as shownin Fig. 5. The wires are expressed as the colored solid models.
Noted that the eddy current and hysteresis loss are not considered.
Figure 7 shows the circuit configuration in the simulation model,
whereas Table II shows the specification of the circuit. The IPT
system is constructed with S/S topology, which has the resonantcapacitors connected to both of the transmitting coils and thereceiving coils of the IPT coil in series. The input voltage is thesinusoidal wave for focusing on fundamental frequency. The
capacitances of the resonant capacitors Cs1, Cs2 are decided inorder to resonate with the considered L at a resonance frequencyof 84.75 kHz. Noted that operating frequency is decided by theresonant conditions of the resonance capacitances and theequivalent self-inductance such as Leq_short, Leq_com, or Leq_dif. The
output power is 1 kW by adjusting the value of the equivalent load
resistance Req because the output current of the S/S resonant
circuit is inversely proportional to the equivalent mutual
inductance of the IPT coil at the LC resonance.
5.2 EMF Reduction Effect with Canceling Windings
Figure 8 shows the simulation results of the magnetic flux
distribution under the each condition. The result is obtained on the
cross-section of the center of the IPT coil as a representative case.
Note that the input power factor cos in is unity when theoperation frequencies of Fig. 8(a)–(d) are 84.75 kHz, 95.00 kHz,85.40 kHz, 115.5 kHz, respectively.
The flux distributions on the top and bottom of the IPT coils
decreaseswiththeshort-circuitedconnection
anddifferential-mode connection in comparison with the flux
distribution without the canceling windings. The magnetic flux
distribution of Fig. 8(a)–(d) are 13.8 T, 9.41 T, 12.6 T, and8.06 T at the 50-cm bottom of the receiving coils as therepresentative values, respectively. In addition, the magnetic
density at the outside of the canceling winding decreases by thecanceling windings. Moreover, the effect of EMF reduction ismore effective with the differential mode than that with theshort-circuited connection.
5.3
Current of Each Winding
Figure 9 shows theRMS values of the current in each winding. The current of thecanceling windings increases with the connection of the common
mode, the short-circuited and the differential mode. The relation of
the RMS values of the current in the canceling windings are
similar to the EMF reduction effect in Fig. 8. On the other hand,
the RMS values of the output voltage Vout are 165 V, 200 V, 183 V
and 160 V without the canceling coils, with the short-circuitedconnection,thecommon-mode
connection
andtheSimulation conditions.

Parameter
Input AC voltage
Rated power
Operation frequency
without canceling windings
Operation frequency withshort-circuited connection
Operation frequency with
common-mode connection
Operation frequency withdifferential-mode connection
Resonant capacitors

Symbol
Vin
P

252
1.0

Value
Vrms
kW

f

84.75

kHz

fshort

95.00

kHz

fcom

85.40

kHz

fdif

115.5

kHz

Cs1 ,Cs2

8.56

nF

differential-mode connection, respectively, which are not shownlarge differences. Thus, the RMS current value of the cancelingwindings, which effects the system efficiency, forms the trade-off
relationship with the EMF reduction effectiveness.
Figure 10 shows the estimate of the copper losses in the eachwinding from the RMS values of the current in the main windings
and the canceling winding in Fig. 9. The equivalent serial
resistances of each winding are measured with the prototype of the
four-winding IPT coils in Fig. 5. The values of equivalent serial
resistances from the winding #1 to the winding #4 are 1.39 ,
35.5 , 1.57  and 34.6 , respectively. The total estimatedcopper loss becomes higher in the ascendant order: thew/o-canceling windings, the common-mode connection, theshort-circuited connection and the differential-mode connection.
In particular, the values of the copper losses on the cancelingwindings with the short-circuited connection and thedifferential-mode connection are not negligible at a view of theefficiency of the whole IPT coils.

6. Conclusion
In this paper, the effect of the canceling windings on theparameter variation of the IPT system was considered regarding to
the equivalent self-inductance and the equivalent coupling
coefficient. Three connection methods of the canceling windings,
i.e. the short-circuited connection, the common-mode connection
and the differential-mode connection, were evaluated.
The calculated equivalent values agreed with the measured
values through the inductance measurement using the prototype of
the IPT coil attached the canceling windings. The relative error
between the calculated values and measured values was 4.9%.
In addition, EMF reduction near the canceling windings wereconfirmed with the short-circuit connection (by 32%) and thedifferential-mode connection (by 41%) in the simulation using
JMAG.
Above of the results, the design criteria focusing on avoiding
7

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Inductance Variation for EMF-canceling Methods on IPT System (Keita Furukawa et al.)

the parameter verifications are as follows:
the canceling windings far from the main windings at the
short-circuited connection.
the canceling windings closed to the main windings withthe large number of the turn at the common-mode
connection.

the canceling windings far from the main windings withthe large number of the turn at the differential-mode
connection.
Future plans are considerations of the parameter verifications
introduced cross couplings between canceling windings.

Magnetic
flex density
T
10-1
10-2
10-3
50 cm

10-4

50 cm

13.8 T

9.41 T

10-5
10-6

(a)

Without canceling windings.

(b)

Short-circuited coil.

Magnetic
flex density
T
10-1
10-2
10-3
10-4

50 cm

50 cm

8.06 T

12.6 T

10-5
10-6

(c)

Common-mode coil.

(d)Differential-mode coil.

Fig. 8. Magnetic flux distribution of prototype transmission coil. The transmission coils are placed at the center of the contour
plots (orange or yellow area). The upper-side core is the transmitting coils. The bottom-side core is the receiving coils. Note thatthe operation frequency is different for each the simulation conditions, which are shown in Table II. Transmission powers of
without-canceling windings, short-circuited connection, common-mode connection and differential-mode connection are 991 W,
1.16 kW, 1.03 kW and 1.27 kW, respectively.

6
6.0
5
5.0

250
250
W/o canceling windings
Short-circuited connection
Common mode
Differential mode

200
200

Copper loss W

RMS value of current A

7
7.0

4
4.0
3
3.0
2
2.0

150
150

Winding #4 (Canceling winding)Winding #3 (Main winding)Winding #2 (Canceling winding)Winding #1 (Main winding)

100
100

50
50

1.0
1
0.0
0

00

Winding
巻線1 #1Winding
巻線2 #2Winding
巻線3 #3

Winding
巻線4 #4(Main winding) (Canceling winding) (Main winding) (Canceling winding)W/o canceling
W/Owindings

Short-circuited
巻線短絡
同相駆動
逆相駆動mode
Commonmode Differential
connection

Fig. 10. Estimate of copper loss in each winding. The blue,
red, violet and green bars indicate the copper loss from thewinding #1 to the winding #4, respectively.

Fig. 9. RMS values of current. The blue, red, violet and green
bars indicate the RMS value of the current w/o the cancelingwindings, the short-circuited, the common mode and thedifferential mode, respectively.

8

IEEJ Trans. ●●, Vol.●●, No.●, ●●●Inductance Variation for EMF-canceling Methods on IPT System (Keita Furukawa et al.)Keita Furukawa(Student member) received
his B.S. and M.S. degrees in electrical, electronics andinformation engineering from Nagaoka University ofTechnology, Niigata, Japan in 2016 and 2018, respectively.
He is currently a Ph.D. candidate at Nagaoka University ofTechnology, Niigata, Japan. His research interests include
an inductive power transfer. He is a member of theInstitute of Electrical Engineers of Japan and the Instituteof Electrical and Electronics Engineers.

References
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(5)

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(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

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Keisuke Kusaka(Member) received the
B.S. and M.S. degrees in electrical, electronics andinformation from Nagaoka University ofTechnology, Niigata, Japan in 2011, 2013,
respectively. From 2015 to 2016, he was with
Swiss Federal Institute of Technology in Lausanne(EPFL), Switzerland as a trainee. In 2016, hereceived the Ph.D. degree in energy andenvironment science from Nagaoka University of Technology. He waswith Nagaoka University of Technology, Niigata, Japan as a researcher
from 2016 to 2018. Since 2018, he has been with Nagaoka University ofTechnology, Niigata, Japan as an assistant professor. His current researchinterests include the areas of IPT systems and high-frequency converters.
He is a member of Institute of Electrical Engineers of Japan, Society ofAutomotive Engineers of Japan and the IEEE.

Jun-ichi Itoh
(Senior member) received his
M.S. and Ph.D. degree in electrical and electronicsystems engineering from Nagaoka University ofTechnology, Niigata, Japan in 1996, 2000,
respectively. From 1996 to 2004, he was with Fuji
Electric Corporate Research and Development Ltd.,Tokyo, Japan. He was with Nagaoka University ofTechnology, Niigata, Japan as an associate professor.
Since 2017, he has been a professor. His research interests are matrix
converters, dc/dc converters, power factor correction techniques, energy
storage system and adjustable speed drive systems. He received IEEJ
Academic Promotion Award (IEEJ Technical Development Award) in 2007.
In addition, he also received Isao Takahashi Power Electronics Award in
IPEC-Sapporo 2010 from IEEJ, 58th OHM Technology Award from The
Foundation for Electrical Science and Engineering, November, 2011,
Intelligent Cosmos Award from Intelligent Cosmos Foundation for the
Promotion of Science, May, 2012, and Third prize award from Energy
Conversion Congress and Exposition-Asia, June, 2013. Prizes for Scienceand Technology (Development Category) from the Commendation for
Science and Technology by the Minister of Education, Culture, Sports,
Science and Technology, April 2017. He is a senior member of the Instituteof Electrical Engineers of Japan, the Society of Automotive Engineers ofJapan and the Institute of Electrical and Electronics Engineers.

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