Power Factor Correction Focusing on Magnetic
Coupling of Parallel-connected Wires for Inductive
Power Transfer System
Keita Furukawa, Keisuke Kusaka, Jun-ichi Itoh
Nagaoka University of Technology
Department of Electrical, Electronics and Information
Nagaoka, Niigata, Japanarcher_FK@stn.nagaokaut.ac.jp, kusaka@vos.nagaokaut.ac.jp, -itoh@vos.nagaokaut.ac.jp

Abstract— This paper proposes a power factor correction
method of a non-resonant IPT system using a four-windingtransformer. The proposed technique is applied to the IPT
system with a dual active bridge converter to reduce conduction
loss and winding loss. When two pairs of the primary-side andthe secondary-side wires are connected in parallel, the low
coupling coefficient between the wires driven by in-phase voltage
corrects the power factor from the viewpoint of the power supply
due to the improvement of an equivalent magnetic coupling. The
effect of the power factor correction is assessed by experimentswith two four-winding transformers, coupling coefficient of
which is different from each other. As experimental results, it isconfirmed that a maximum efficiency with the lower coupling
coefficient between the parallel connected wires is improved by
3.0% in comparison with the system, which has the high coupling
coefficient.
Keywords—wirelesspowertransfer;
multi-windingtransformer; non-resonant inductive power transfer; dual active
bridgeI. INTRODUCTION
In recent years, inductive power transfer (IPT) systems haveattracted many researchers as a safety and convenient battery
chargers for electrical vehicles (EVs) [1-6]. The IPT systems
are able to achieve power transmission without electricalcontacts. An increase in a transmission distance oftransmission coils causes a reduction of mutual inductance,
which results in a low power factor from the view of power
supply because the reactive current increases [7]. Large
reactive current is one of the factors reducing systemefficiency.
In order to correct the power factor, the IPT systems using
resonance phenomena have been proposed [1-6][8]. Resonantcapacitors are connected in series or parallel to thetransmission coils in order to compensate the reactance of thecoils by LC resonance [1-6]. Therefore, the resonant IPT
systems can achieve unity power factor at the resonancefrequency because reactive current is canceled. Consideringwith actual high-power applications, however, position

misalignment of coils or tolerance of resonant component
degrades the transmission efficiency because the resonant
frequency does not match an operation frequency [1], [6]. In
particular, capacitive load increases switching loss of a
primary-side inverter because ZVS (zero voltage switching)and ZCS (zero current switching) are not achieved [8].
In order to solve the above-mentioned problems of theresonant IPT system, the non-resonant IPT system utilizing adual active bridge (DAB) converter has been proposed [9]. In
the system, the transmission power is determined by a phasedifference between the inverter output voltages of the primaryside and the secondary side. This method achieves the power
factor correction without resonant capacitors [8]. Besides,
ZVS is achieved at all switching devices despite loadconditions [9]-[10]. However, high reactive current still leads
to the increase in a conduction loss of the switching devices
and the winding loss of the transmission coils due to low
magnetic coupling [10]. Thus the non-resonant IPT system has
to achieve the reduction of the conduction loss and thewinding loss when the system is employed to lower-magnetic
coupling applications.
This paper proposes a power-factor-correction method for
non-resonant IPT systems with a multi-winding transformer as
one of the solution to overcome issues of the high conduction
loss and winding loss. Two or more wires are connected to theprimary core and the secondary core in parallel. From theequivalent circuit of the systems, the weak coupling coefficient
kc between the parallel-connected wires decreases equivalentleakage inductance. Thus a low-kc transformer reduces thereactive current at the same load.
This paper is organized as follows; first, the theoreticalexpressions of output power and the power factor is derived.
Then, the comparative testing results are showed with a 1.1kW prototype using two multi-winding transformers whichhave different coupling kc: the conventional high-kc transformer
and the proposed low-kc transformer. As a result, power-factor
correction and reduction of input current are achieved in the
proposed transformer. Moreover, the maximum systemefficiency of the prototype circuit is improved from 87.3% to90.3% with the proposed transformer.
II. CONVENTIONAL METHODS OF IPT SYSTEMS
A. Conventional Resonant Inductive Power Transfer System
Fig. 1 shows the equivalent circuit of the resonant IPT
systems focusing on the AC voltage of fundamental frequency.
Resonant capacitors are connected to input and output of thetransmission coils in series (S/S type). The input current Iin andthe output current Iout of the system are expressed by (1) and(2) [8].
1 r  R  j L CIin 
Vp

1 
1 


2
r  R  j L   kL
r  j L 
C C .................................................................................... (1) jkLIout 
Vp

1 
1 


2
r  R  j L   kL
r  j L 
C C .................................................................................... (2)where Vp is the input voltage, L is the self-inductance of thetransmission coils, r is the equivalent series resistance, C is thecapacitance of the resonant capacitors, R is the load resistanceand k is the coupling coefficient between the transmission coils.

P

where Vin and Vout are the input and output DC voltage, L is theself-inductance of the transmission coils, and  is the lagging
phase difference between vs and vp.
The transmission power of the non-resonant IPT system iscontrolled by adjusting the lagging phase difference [9]. If  ispositive, the power flow is primary side to secondary side. On
the other hand, when  is negative, the power flow is secondaryside to primary side. Thus the non-resonant IPT systemachieves not only the control of the transmission power, butalso the bi-directional operation without additional
compensation circuits [9].

Iin

1
LC

r

C

(1-k)L(1-k)L

r

kL

V p

C

Iout

V s

R

2fsw

Fig. 1. Equivalent circuit of a S/S resonant IPT system. The selfinductance and the equivalent series resistances r in each the primary sideand secondary side are same value for simplify.
P

The value C is designed to cancel the reactance of the selfinductance of the transmission coils. The resonance angularfrequency  is decided by (3) [8].
0 


 
kVinVout    .................................... (4),2 
2f sw L1  k    (1-k)LVin

vp(1-k)L

ip

is
kL

vs

Vout

.............................................................. (3)The operation frequency fsw of the inverter is generally
designed same or a little larger than the resonance frequency
/ (2) to reduce switching loss with zero-voltage-switching(ZVS) or zero-current-switching (ZCS). However, the error of due to position misalignment of coils or tolerance of theresonant components causes the degradation of the systemefficiency and the output power. In particular, the inverters
operate neither ZCS nor ZVS with a capacitive load. In
addition, low power factor is caused by the increased reactance.
B. Non-resonant Inductive Power Transfer System Applied toDual Active Bridge
Fig. 2 shows the non-resonant IPT system utilizing the
DAB converter [9]. The single-phase full-bridge inverters are
employed at both the primary side and the secondary side of
the transmission coils.
Fig. 3 shows the operation principle of the non-resonant
IPT system. Not only the primary inverter but also thesecondary inverter supply AC voltage vp and vs to thetransmission coils. Note that the inverters output two-level
voltage and the frequency of the output voltage is same.
Transmission power P is presented by

=2fsw

Fig. 2. Non-resonant IPT system applied dual active bridge.

1/fsw
Vin



vp
-Vin
Vout
vs
-Vout
ip

is

Fig. 3. Voltage and current waveforms of non-resonant IPT systemutilized dual active bridge. The inverters are operated as two-level
inverter. Polarities of the voltage and directions of the current is definedin Fig. 2.

Pp
Lin

Vin

iout Ps

Four-winding transformer
S1

S3

Ip_rms,ip P’
vp cosqin

+
Cin
S2

Winding 1

Is_rms,is
S5

kM
v1

i1

S4

v2

Primary side

Winding 3

i2

LDAB

kDAB

LDAB

kc

kc

LDAB

LDAB

Winding 2

kM

i3

v3

+

vs

Cout
S6

i4

Lout

S7

Vout

S8

v4
Winding 4

Secandary side

Fig. 4. Circuit configuration of proposed IPT system using four-winding transformer. The cores of the four-winding transformer is shared in each the primaryside and the secondary side. The output power Pout is defined as lower value of |Pp| or |Ps|.

The total power factor from the view point of the inverter isalways lower than 1, because the excitation current flows forthe small mutual inductance regardless of  [9] [10]. In
particular, when the coupling coefficient k is significantly low(k = 0.01–0.2), the power factor is greatly decreased because of
the large excitation current. The increase in the excitation
current causes large conduction loss and copper loss. Therefore,
it is important to keep the coupling coefficient as high as
possible. In the next section, the proposed power-factorcorrection method with a four-winding transformer is described.
III. PROPOSED CIRCUIT CONFIGURATION
A. System Configuration
Fig. 4 shows the system configuration of the proposedsystem. The difference of the proposed system compared withthe conventional non-resonant IPT system (Fig. 2) is that the
four-winding transformer is introduced as the transmission
coils. Two primary side wires are wound onto one sharedprimary core. The same procedure is carried out at thesecondary side. Through this winding structure, the windings
on each side are magnetically coupled with the coupling
coefficient kc.
Considering the reduction of power loss in the converter,
the multiple single-phase full-bridge inverters should beconnected to the each winding. Besides, each of the primaryside inverters and the secondary-side inverters is driven inphase to avoid cross currents. However, only one DAB
converter drives the four-winding transformer in thisexperiment for the simplicity. A parallel connection of the fullbridge inverter is more effective to decrease the conduction
loss of MOSFETs because the current is divided into eachconverter. In next section, a method of increasing an equivalentmagnetic coupling between the primary side and the secondaryside is discussed.
B. Analysis of Four-winding Transformers
Fig. 5 shows the equivalent circuit of the four-windingtransformer [11]. Terminal voltages of windings m (m = 1, 2, 3,4) contain not only an induced electromotive force from thecurrent flowing through the winding m, but also the sum of theinduced voltages from the currents flowing in the otherwindings. Consequently, the magnetic coupling among four
windings has to be considered. The relationship between the

input voltage vm and the input current im of the winding m isexpressed by using a four-order inductance matrix LTrans asshown in
 v1 
 i1   L11 L12 L13 L14   i1 
  
v 
  
d i2   L21 L22 L23 L24  d i2  2  L

Trans
v3 
dt i3   L31 L32 L33 L34  dt i3 
  
 
  
v 4 
i4   L41 L42 L43 L44  i4 
L11
k12 L11 L22 k13 L11 L33 k14 L11 L44   i1 

  
L22
k23 L22 L33 k 24 L22 L44  d i2 k21 L11 L22
k L L
k32 L22 L33
L33
k34 L33 L44  dt i3 
 31 11 33  k41 L11 L44 k42 L22 L44 k43 L33 L44
 i4 
L44.................................................................................... (5),where Lmm is the self-inductance of the winding m, and Lmn (m≠ n, n = 1, 2, 3, 4) is the mutual inductance between thewinding m and the winding n. The matrix elements of Lmn and
Lnm at a specific combination of m and n have the same value.
Besides, the coupling coefficient kmn of two windings isdefined byLmn............................................................ (6).
k mn 
Lmm Lnn

The parameters in Fig. 5 are presented by (7) and (8) [11].
1
1
1 
 1



  Le

Le
Le
Le
11
12
13
14 

1
1
1 
 1



 Le21
Le22
Le23
Le24 
1
 LTrans ........... (7)
 1
1
1
1 





Le32
Le33
Le34 
 Le31
 1
1
1
1 





Le42
Le43
Le44 
 Le41
 1 
 1 
 Le 
 Le 
 10 
 1n 
 1 
 1 




4
 Le20     Le2 n  ................................................... (8)

 1 
 1 
n 1




 Le30  Le3n 
 1 
 1 




 Le40 
 Le4 n Next, restriction and relationship are given by the symmetryof the circuit. The first one is that the self-inductances of all
windings must have the same value LDAB. The second one isthat the coupling coefficients of kM, kDAB and kc are defined asshown in Fig. 4. Then the relationship of the voltage and thecurrent is expressed by (9).
kc
kM k DAB   i1 
 1
 v1 
 kv 
1k DAB k M  d i2  2  L  c.............. (9)DAB k M k DABv3 1
kc  dt i3 

  
 
kc
1  i4 v4 k DAB k M
The inductance values in Fig. 5 are presented by (10)-(13)Le12  Le34 

LDAB f kc , k DAB , k M ... (10),222
 2k M k DAB  kc 1  kc  k DAB  k M



v1

v3

Le30

Le12

Le34
Le23

i2

i4

Le24
v2

v4

Le40

Le20

Fig. 5. Equivalent circuit of four-winding transformer. This circuit
is extended from the -type equivalent circuit for two-port network.

ip

is
1 kc

LDAB
2

 kM  kDAB 
1
LDAB
2 


 kM  kDAB 
1
LDAB
2 


vp

kM  kDAB
2

vs

LDAB

Fig. 6. Equivalent circuit of proposed system. The four-windingtransformer is shown as the two-winding transformer. In addition, thetwo-level full-bridge inverters are shown as the square-wave voltage
sources.

Equivalent coupling
coefficient keq

0.6
0.5
k eq 

0.4

0

0.2

0.4

0.6

0.8





LDAB f kc , k DAB , k M ... (12),2
22
 2k M kc  k DAB k M  kc  k DAB  1



2

2

1  k   k  k
2

c

M

DAB

2 

................................................................................... (14)When the windings are connected in parallel in each theprimary side and the secondary side, the relationship of thevoltage and the current is shown in (15) and (16)k M  k DAB    v p dt 
1  kc   vs dt  ..................... (15),22LDAB 1  kc   k M  k DAB 

 1  kc2
k M  k DAB 1  kc
v p 2
   LDAB  k  k
M
DAB
vs 

2




k M  k DAB  d i p 2................ (16),
1  kc  dt is 
  
2


where vp is the input voltage of the primary side, vs is the input
voltage of the secondary side, ip is the equivalent input currentof the primary side and is is the equivalent input current of thesecondary side.
Moreover, the equivalent self-inductance Lp of the primaryside, the equivalent self-inductance Ls of the secondary sideand the equivalent mutual inductance M are expressed as in(17) and (18).

M 

1 kc
LDAB ................................................... (17)2k M  k DABLDAB .................................................... (18)2These equivalent values of Lp, Ls and M are useful to analyze
the four-winding transformer as a two-winding transformer.
Fig. 6 shows the equivalent circuit of the proposed system.
The negative inductance -LDAB(1-kc)/2 is connected in series tothe two-winding transformer, the coupling coefficient of whichis (kM+kDAB)/2. Therefore, the low kc is effective to reduce theleakage inductance. The equivalent coupling coefficient keq of
the equivalent circuit is presented by (19).
M
L p Lsk M  k DAB........................................... (19)1  kcFig. 7 shows the relationship of keq versus kc. Both of kM
and kDAB are fixed values. The equivalent coupling coefficient
keq is clearly improved with decreasing kc.

kM = 0.3
kDAB = 0.3

0.3

f kc , kDAB , kM   1  kc   kM  kDAB 

keq k M  k DAB
1  kc

Le10  Le20  Le30  Le40  LDAB 1  kM  kc  kDAB  .. (13),L p  Ls 

1 kc

LDAB
2

LDAB f kc , k DAB , k M ... (11),222
 2kc k DAB  k M 1  kc  k DAB  k M

where the function f(kc, kM, kDAB) is expressed by (14).

i p 
 
is 

i3

Le14

Le10

Le14  Le23 



Le13

i1

Le13  Le24 

1Coupling coefficient kc
Fig.7. Relationship of equivalent coupling coefficient versus coupling
coefficient kc. Only kc value is changed from 1 to 0. In order to verify theeffect of reducing kc, kM and kDAB are fixed value.

The reason why keq is increased with the decrease in kc suchas (19) and Fig. 7, is reduction of Lp and Ls from (17) and (18).
Generally, combined inductance of wounding in parallel islower than self-inductance of each winding because. Besides,
the combined inductance is much lower when the magnetic

coupling of the windings is smaller. Whereas, the value of M isdecided despite kc in the system. In consequence, keq, whichcorresponds to ratio of M versus the geometric mean of Lp and
Ls is improved.
C. Transmission Power and Power Factor of Proposed
System
In this section, the transmission power P’ and the power
factor of the inverter output are formulated from the equivalentcircuit shown in Fig. 6. Moreover, the relationship of the power
factor and the coupling coefficient kc is discussed in detail.
From (4), (17) and (19), P’ is given by (20) with substituting Lp
and keq for L and k.
P' 


 
2VinVout kM  kDAB     ...... (20)22LDAB 1  kc   kM  kDAB    

RMS values Ip_rms and Is_rms of ip and is are shown in (21)and (22).
I p _ rms 1f sw  f sw i p dt
20

 3 1  k c Vin  k M  k DAB Vout 2  41  k c k M  k DAB VinVout 2   3  2



LDAB 3 1  k c 2  k M  k DAB 2.............................................................................. (21)I s _ rms 1f sw  f sw is dt
20 3 1  k c Vout  k M  k DAB Vin 2  41  k c k M  k DAB VinVout 2   3  2



LDAB 3 1  k c 2  k M  k DAB 2



IV. EXPERIMENTAL RESULTS
A. Test Conditions
The proposed improvement method on the magnetic
coupling is experimentally verified. The test is carried out withthe system configuration shown in Fig. 4. Table I shows thetest conditions and parameters of the elements. Note that input
and output voltage is 280 V, and the rated power is 1.1 kW.
Fig. 9 shows the pictures of the two four-windingtransformers, which are used for the tests. The rectangularcores are made of 21 ferrite plates (TDK, B67345B4X87).
Two four-winding transformers have the same size of coresand the same distance between cores for a fair comparison.
The parallel-connected windings on the conventionaltransformer are wound close to each other in order to increasekc value. Whereas, the parallel-connected windings on the
proposed transformer are separately wound on the outside ofcoils and closely wound at the center of the coils in order toreduce kc value without decreasing kM and kDAB. The coupling
coefficients kc, kM and kDAB are determined by the dispositionsof the wires. The self-inductance LDAB is adjusted by turns ofcoils and given by (24) using maximum power Pmax.

VinVout kM  k DAB LDAB 
................ (24)2 Pmax 1  kc 2  k M  k DAB 2
Note that Pmax should be designed larger than the rated
power with a margin of 10%.



B. Parameters of Four-winding Transformers
Table II shows the measured and calculated parameters of
the four-winding transformers in Fig. 9. The equivalent values.............................................................................. (22)P'
Vin I p _ rms 12 kM  k DAB       1  kc   kM  k DAB   41  kc kM  k DAB 3  2  322................................................................................... (23)Fig. 8 shows theoretical curves of cos qin with the coupling
0 < kc < 1. Note that kM and kDAB are designed to be 0.3 for IPT
systems. Lower kc (higher keq) makes the systems higher power
factor cos qin over entire load range. Fig. 6 and Fig. 7 also showthat lower kc reduces the equivalent leakage inductance comingfrom the four-winding transformer. Thus kc value should besmall to improve cos qin.

Input power factor cos qin

0.7

When the input DC voltage Vin is as same as the output DC
voltage Vout, the power factor cos qin from the view point of
the output of the primary-side inverter is given by (23).

cosqin 

kM=0.3, kDAB=0.3

0.6

kc=0

0.5

kc=0.20.4

kc=0.4

0.3
0.2
0.1

kc=0.6kc=0.8kc=1(Discharge)

0
-90

-60

-30

0

30

Phase difference  degree(Charge)60

90Fig. 8. Theoretical curves of power factor given by (23). Only kc value ischanged from 1 to 0. The other coupling coefficients of kM and kDAB are
fixed value in order to verify effect of reducing kc.
Parameter
Input DC voltage
Output DC voltage
Rated power
Switching frequency
Dead time
Smoothing capacitors
Smoothing inductor
MOSFETs

Table I. Test conditions.
Symbol
Value
Vin
280 V
Vout
280 V
P
1.1 kWfsw
84.75 kHzTdead
300 nsCin ,Cout
2.7 mF
Lin ,Lout
2 mH
S1-S8
IXYS, IXFN80N60P3

280

Winding 1

Winding 2

16200
Gap 6916

Winding 3

195

Winding 4(a) Front view of conventional transformer.

Unit: mm(b) Top view of conventional transformer.

(c) Side view of conventional transformer.

280

Winding 2

Winding 1

16
200
Gap 6916

Winding 4

Winding 3

75
150

Unit: mm(d) Front view of proposed transformer.
(e) Top view of proposed transformer.
(f) Side view of proposed transformer.
Fig. 9. Two prototype four-winding transformers. The outline drawing from (a) to (c) are the conventional transformer whose windings of the primary or
secondary side are close to each other. The outline drawing from (d) to (f) are the proposed transformer whose windings of the primary or secondary side are
separated to introduce the proposed method.
Table II. Measurement results of inductance and coupling coefficients of conventional transformer and proposed transformer. The matrix elements of LTransare measured by a LCR meter. According to (9), the parameters LDAB, kc, kM and kDAB are averaged from the matrix elements of LTrans.
Parameters
Conventional Transformer
Proposed Transformer
Primary coils
8
9
Coils turns
Secondary coils
8
9Inductance matrix LTrans as 4-winding transformer
Self-inductance LDAB
Coupling coefficient kc
Coupling coefficient kM
Coupling coefficient kDAB

Measured value
Measured value
Measured value
Measured value
Measured value
Equivalent primary self-inductance Lp
Calculated value
Measured value
Equivalent secondary self-inductance Ls
Calculated value
Measured value
Equivalent mutual inductance M
Calculated value
Measured value
Equivalent coupling coefficient keq
Calculated value
Maximum error of calculated inductances
Error of calculated coupling coefficient

Lp, Ls, M and keq show both of calculate values and measured
values by connecting the windings in parallel. The coupling
coefficient kc of the proposed transformer is 0.497 weaker thankc of the conventional transformer of 0.958. Consequently, keq
of the proposed transformer improves to 0.377 from 0.329. In
addition, the validity of the formulations is also confirmed andall the errors of Lp, Ls, M and keq is below 2.4%.
Note that kM and kDAB of the proposed transformer are
weaker than the value of the conventional transformer because

 34.6 33.1 11.2
 11.2


33.1
34.6
11.1
11.1

11.2
11.1
35.2
33.7

11.2 

11.1 
 [H]
33.7 
35.2 

34.9 H
0.958
0.320
0.320
33.9 H
34.2 H
34.5 H
34.2 H
11.2 H
11.2 H
0.329
0.327
1.0 %
0.7 %

 57.6 30.2 17.3
 14.5


30.2
59.9
15.5
18.0

17.3
15.5
56.0
27.4

14.5 

18.0 
 [H]
27.4 
58.1 

57.9 H
0.497
0.304
0.260
44.4 H
43.3 H
42.4 H
43.3 H
16.4 H
16.3 H
0.377
0.376
2.4 %
0.2 %

the distances of the windings are longer. Equation (19) showsthat keq is proportional to the sum of kM and kDAB. Thus awinding method which only reduce kc without decreasing kMand kDAB is required to increase keq.
C. Operation Waveforms of Proposed System
Fig. 10 shows the operation waveforms at rated load and atlight load in the power charging and the discharging operation.
The phase difference  is 90 degree at rated load and 15

00
Primary inverter voltage vp 500 V/div

0

Primary inverter voltage vp 500 V/div
0

Primary inverter current ip 50 A/div
Secondary inverter voltage vs 500 V/div

Primary inverter current ip 50 A/div
Secondary inverter voltage vs 500 V/div

0

0

0

0
8 s/div

8 s/div

Output current iout 5 A/div(a) Rated load (1.1 kW) with charging operation.

0

Output current iout 5 A/div(b) Rated load (1.1 kW) with discharging operation.

0
Primary inverter voltage vp 500 V/div

0

Primary inverter voltage vp 500 V/div
0

Primary inverter current ip 50 A/div
Secondary inverter voltage vs 500 V/div

Primary inverter current ip 50 A/div
Secondary inverter voltage vs 500 V/div

0

0

0

0
8 s/div

Output current iout 5 A/div(c) Light load (300 W) with charging operation.

8 s/div

Output current iout 5 A/div(d) Light load (300W) with discharging operation.

degree at light load. At light load, the current is a triangle
wave because the reactive current is dominant.
The output DC current iout shows that power transmitting isachieved at the proposed transformer in both of the power
charging and the discharging operation.
D. Characteristics of Input Current, Power Factor andEfficiency
Fig. 11 shows characteristics of the primary current Ip_rms
versus output power Pout. Note that the measurement value isplotted in the graph, and the theoretical characteristics are
drawn by the solid line or the dotted lines. According to the
Ip_rms values at Pout = 0 W, the excitation current of the
proposed transformer reduces by 25% compared with theconventional values.
Fig. 12 shows characteristics of the input power factor cos
qin. The x-axis of Fig. 12 (a) is the phase shift angle . The xaxis of Fig. 12 (b) is Pout. The measurement value is plotted in
the graph, and the theoretical characteristics are drawn by thesolid line or the dotted lines. In order to measuring cos qin, ip
and vp are detected directly. Note that effect of the detection
parts are not taken into account in the calculation process oftheoretical cos qin value.

RMS value of primary current
Ip_rms A

Fig. 10. Operation waveforms of prototype circuit with proposed transformer. The transmission power and the operation mode are changed by the phasedifference between the primary-side inverter and the secondary-side inverter output voltage. (a)  = 90 degree. (b)  = -90 degree. (c)  = 15 degree. (b)  = -15
degree.

18
16
14

Conventional transformer (kc=0.958)
Proposed transformer (kc=0.497)

12
10
8

(Charge)(Discharge)-1500 -1000

-500

0

500

1000

1500

Output power Pout W

Fig. 11. Characteristics of RMS values of primary-side inverter AC output
current. The theoretical characteristics are shown by curves, whereas theplots are measurement values.

The maximum power factor of the proposed transformer is
17% larger than the conventional transformer. Moreover, cos
qin is improved the entire load range. Thus a low-kc
transformer improves the system efficiency owing to the
reduction of the reactive current.

Input power factor cos qin

Fig. 13 shows the system efficiency versus Pout. The systemefficiency is improved over the entire Pout with the proposedtransformer. The maximum efficiency of the proposedtransformer is 87.3% at 1.00 kW in the charging operation.
The efficiency of the proposed transformer is improved overentire load range compared to the conventional transformer. In
particular, the maximum efficiency of the proposedtransformer is 90.3 % at 891 W in the discharging operation,
which is 3.0% higher than that of the conventionaltransformer.
V. CONCLUSIONREFERENCES
[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

Siqi Li and Chunting Chris Mi: “Wireless Power Transfer for Electric
Vehicle Applications”, IEEE Trans. PE, Vol.3, No.1 pp. 4-17J. Clerk
Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2.
Oxford: Clarendon, 1892, pp.68-73.(2015)
Su Y. Choi, Beom W. Gu, Seog Y. Jeong and Chun T. Rim: “Advancesin Wireless Power Transfer Systems for Roadway-Powered Electric
Vehicles”, IEEE Trans. PE, Vol.3, No.1 pp.18 - 36 (2015)K. Elissa,“Title of paper if known,” unpublished.
Fei Lu, Hua Zhang, Heath Hofmann and Chunting Chris Mi: “AnInductive and Capacitive Combined Wireless Power Transfer System
With LC-Compensated Topology”, IEEE Trans. PE, Vol.24, No.4
pp.1115-1124 (2009)
Tsutomu Mizuno, Takuto Ueda, Shintaro Yachi, Ryuhei Ohtomo andYoshihito Goto: "Dependence of Efficiency on Wire Type and Numberof Strands of Litz Wire for Wireless Power Transfer of Magnetic
Resonant Coupling", IEEJ Journal of Industry Applications, Vol. 3, No.
1, pp. 35-40 (2014)
Hiroki Ishida, Hiroto Furukawa and Tomoaki Kyoden: "Development of
Design Methodology for 60 Hz Wireless Power Transmission System",
IEEJ Journal of Industry Applications, Vol. 5, No. 6, pp. 429-438 (2016)
Daisuke Shimode, Toshiaki Murai and Shunsuke Fujiwara: "A Study ofStructure of Inductive Power Transfer Coil for Railway Vehicles", IEEJ
Journal of Industry Applications, Vol. 4, No. 5, pp. 550-558 (2015)
H. Sakamoto, K. Harada, S. Washimiya, K. Takehara and Y. Matsuo:"Large Air-Gap Coupler for
Inductive Charger",IEEE
TRANSACTIONS ON MAGNETICS, Vol. 35, No. 5, pp. 3526-3528(1999)
Roman Bosshard, Johann Walter Kolar, Jonas Mühlethaler, Ivica
Stevanovi´c, Bernhard Wunsch, and Francisco Canales: " Modeling and
η-α-Pareto Optimization of Inductive Power Transfer Coils for Electric
Vehicles", IEEE Trans. PE, Vol.3, No.1 pp.50-64 (2015)

Phase shift angle  degree

Input power factor cos qin(a) Versus phase shift angle.

0.40
0.4
Proposed transformer (kc=0.497)
0.35
0.30
0.3
0.25
0.20
0.2
Conventional
0.15transformer(kc=0.958)
0.10
0.1
0.05 (Discharge)(Charge)
0.000-1500 -1000 -5000500 1000 1500
Output power Pout W(b) Versus output power of the system.
Fig. 12. Characteristics of power factor. The theoretical characteristics
are shown by curves, whereas the plots are measurement values. The
power factor cos qin is measured with the power analyzer(E.E.Corporation, PW6001) and Direct Current Measurement Option(E.E.Corporation, PW9100).

95
Proposed transformer (kc=0.497)

Efficiency (DC to DC) %In this paper, a power factor correction method was
proposed for the non-resonant IPT system utilizing the dual
active bridge converter in order to reduce conduction loss andwinding loss. The loose coupling coefficient kc between two
pairs of the primary-side and the secondary-side wires
connected in parallel contributed to the power factor
correction from the viewpoint of the power supply. Therefore,
the low-kc four-winding transformer improved efficiency
because of the strong equivalent coupling coefficient keq
between the primary side and the secondary side.
From the experiment, the maximum power factor of the
low-kc transformer, kc value of which is 0.497, was improvedby 17% compared with the high-kc transformer because ofstronger keq by 15%. Besides, the maximum efficiency of the
low-kc transformer was improved by 3.0%.
In the future, the proposed method will be introduced to aresonant IPT systems in order to improve efficiency.

0.40
0.4
Proposed transformer (kc=0.497)
0.35
0.30
0.3
0.25
0.20
0.2
0.15
Conventional
0.10
0.1transformer (kc=0.958)
0.05 (Discharge)(Charge)
0.000
-90
-60
-30
0
30
60
90

90
85
Conventionaltransformer(kc=0.958)

80(Discharge)

75-1500 -1000(Charge)

-500

0

500

1000

1500

Output power Pout W

Fig. 13. Efficiency of each four-winding transformer. The plots aremeasurement values under the conditions of Table I.
[9]

Keisuke Kusaka and Jun-ichi Itoh: “Non-resonant Inductive Power
Transfer System based on the Principle of Dual Active Bridge
Converter”, IEEJ Trans. I.A., Vol. 136, No.2, pp. 189-197(2015)[10] Mustansir H. Kheraluwala, Randal W. Gascoigne, Deepakraj M. Divan,
and Eric D. Baumann: “Performance Characterization of a High-Power
Dual Active Bridge dc-to-dc Converter”, IEEE Trans. IA, Vol.28, No.6
pp.1294-1301 (1992)[11] Keizo Inagaki, Masaru Higaki, Yoshiaki Matsui and Kentaro Kurita:“Digital protection method for power transformers based on an
equivalent circuit composed of inverse inductance”, IEEE Trans. PD,
Vol.3, No.4 pp. 1501-1510 (1988)