20189177

Analysis of Circuit for Dynamic Wireless Power Transfer
by Stepping Stone System
Hiroshi Uno 1) Jun Yamada1) Yasuyoshi Kaneko 1) Toshiyuki Fujita 2) Hiroyuki Kishi 2)
1) Saitama University, Graduate school of Science and Engineering,
255 Shimo-Okubo, Sakura-ku, Saitama-shi, Saitama, 338-8570, Japan (E-mail: h.uno.418@ms.saitama-u.ac.jp)
2) Technova Inc.,
13th Fl. The Imperial Hotel Tower, 1-1 Uchisaiwai-cho, 1-chome, Chiyoda-ku, Tokyo, 100-0011, Japan
Presented at EVS 31 & EVTeC 2018, Kobe, Japan, October 1 - 3, 2018
ABSTRACT: Electric Vehicles (EVs) has risen to prominence as a research topic due to contemporary environmental

concerns and the resultant need for energy conservation. One of the challenges in designing EVs is extending their cruising
distance. An approach to address this problem is dynamic wireless power transfer. This paper aims to provide a reallysimple model dynamic wireless power transfer system. Specific attention is given to verifying the coupling coefficientwhen the secondary coil is misaligned. The model is used to analyze voltage and current characteristics in two different in
two topologies, series-series (SS) and parallel–series (PS). Findings are tested validated via a simulation and an
experiment.
KEY WORDS: Wireless Power Transfer, Dynamic Wireless Power Transfer, Circuit Topology
stationary system(4). With respect to the PS topology, one of the
1. INTRODUCTION

characteristics is that the input impedance approaches infinity

Contemporary environmental concerns and the resultant needwhen the secondary side of the topology is absent. DWPT is

for energy conservation has highlighted electric vehicles (EVs) as

proposed to take advantage of this characteristic(5). Very few

one of cars worthy of siginificant research focus. One of theprevious works have analyzed both topologies including variablebiggest problems presented by EVs is that the cruising distance isvoltage and current by misalignment of running direction; if all

shorter and fueling time is longer than that of a car powered bypossible phenomena are included, the analysis becomes

fuels. Dynamic wireless power transfer (DWPT)(1)

is proposed asa method for solving these problems. Two main approaches exist,

complicated and it is very difficult to make any predictions.
In this paper, the aim is to construct as simple a model of a(2)

namely the loop coll approach , and the location with spacing

DWPT system as possible. This paper focuses on the verification

approach(1)(3)(4)(5), within which there are specific differentof the coupling coefficient when the secondary coil is misaligned,

methods. This paperdraws on “the stepping stone system”

providing insight into the common tendency of voltage andmethod proposed in references (1) and (3). Compared with thecurrent fluctuation in such circuits. Two topologies are analyzed:

loop coil method, “the stepping stone system” is expected to beseries SS topology, specifically a series connection of primarycheaper and easier to implement, in terms of the laying of thecoils connected in series to resonant capacitors, and parallel PS(1)ground coils . Proposed DWPT circuit topologies in “thetopology, specifically the parallel connection of primary coils

stepping stone system” are series-series (SS) and parallel-seriesconnected in parallel to resonant capacitors, with two primary(PS). The SS topology is one of the most common circuit

coils and a secondary coil. These topological approaches are

topologies used to implement wireless power transfer (WPT).

validated via an electrical circuit simulator and via an experiment.

Previous studies used this topology for constant current(1), power

The structure of this paper is as follows. Section 2 gives an(3)

supply, in the repeater coil method , for comparison with aoverview of the SS and PS topologies as this applies to a primary

Copyright © 2018 Society of Automotive Engineers of Japan, Inc. All rights reserved

16mm

20189177

coil and a secondary coil. Section 3 provides results and analysis

due to misalignment of the secondary coil, input impedanceof input and output data for voltage, current and output power

approaches zero.

using the series SS and parallel PS topologies and considering
misalignment in the running direction, and describes relevant
features. Section 4 details the circuit simulator, and Section 5

2.2. PS topology
This section describes the PS topology, shown in Fig. 2.

describes the result of the experiment. Finally, Section 6summarizes the research and presents conclusions.

M

Iin

IL

2. Circuit topology of a primary coil and a secondary coilThis section examines basic characteristic of the SS and PS

L1

Vin

topologies using a primary and secondary coil. In this paper,

L2

CP

CS

RL

VL

wind resistance is much smaller than reactance at the resonantFig.2 PS topology

frequency. Moreover, the input of square wave voltage for actual
applications has little influence on the higher harmonics ofIn the figure shown in this figure, for resonant capacitors, CP, Cs,current because WPT is a resonant circuit. Therefore, only the

1
L1
1
,
, Cs = 2=w 2 L1w L1L2 - M 2 w 2 L2 1 - k 2

(

)

(

)

root mean square (RMS) of the fundamental wave component isCp =considered.

where the input and output characteristics are given by

2.1. SS topology
This section describes the SS topology, which, as previously
mentioned, is one of the most widely used in WPT. A circuit
diagram with an SS topology is shown in Fig. 1.

Iin
Vin

L1

ö
÷
÷æVL ö ,÷ç ÷
L2 ÷çè I L ÷ø
k
L1 ÷ø
0

(5)

and input impedance is given byM

CS1æ 1 L1öç
0 ÷ç÷æçVL ö÷ = ç k L2
M ÷ç I ÷è Lø ç 0
L1 ÷ø
ç
è

æ L1
æVin ö çç Mçç ÷÷ =
è I in ø çç 0
è

(4)

CS2

RL

L2

2

IL

1 L
æL ö
Zin = ç 1 ÷ RL = 2 1 RL .
M
k L2
è ø

(6)

From Eq. (5), the PS topology has the ideal transformer which

VL

outputs a constant voltage when input remains at a constantvoltage. If the primary coil and secondary coil have the sameFig.1 SS topology

shape,In this circuit, for resonant capacitors Cs1, Cs2 ,

Cs1 =

1

w 2 L1, Cs 2 =1

w 2 L2

secondary side. It is necessary to increase the number of turns on(1),

the secondary side when taking voltage and current at the sameratio as the primary side, because the coefficient coupling kwhere the input and output characteristics are given byæ 0æVin ö ççç ÷÷ = ç 1
è Iin ø ç jwM
è

L1 L 2 is the turn ratio between the primary side and theæ0- jwM ö÷æVL ö ç÷ç
1=0 ÷÷ç I L ÷ ççè ø ç jwk L Lø
1 2ècauses secondary self-inductance. From Eq. (6), when the- jwk L1L2 ö÷æVL ö ,
÷çç ÷÷
0÷÷è I L øø

(2)coupling coefficient k decreases due to misalignment of thesecondary coil, input impedance approaches infinity. The PS
topology enables the performance of passive switching.

and the input impedance is given by

Zin =(wM )2 = (wk )2 L1L2 .
RL

(3)

RL

(6)

From Eq. (2), the SS topology has immittance converter which
outputs a constant current when input remains at a constant

3. Analysis of circuit topology for two primary coils and asecondary coilFig. 3 shows the series SS topology circuit, and Fig. 4 shows
the parallel PS topology circuit.

voltage. From Eq. (3), when the coupling coefficient k decreases

Copyright © 2018 Society of Automotive Engineers of Japan, Inc. All rights reserved

20189177

Table 1. The voltage and current characteristics for constant
input voltage

Vin

Series SS topology
Constant

Parallel PS topology
Constant

RL(k13 + k 23 )
L3
Vin
2
2
L RL + j k - k13- k 23wL3

I in(k13 + k23 )2 w 2 LL3

VL

j

IL

Vin

RL

Vin

L3
k13 + k 23
Vin
2
2
L RL + j (k - k13- k 23)wL3(k13 + k23 )w LL3(k13 + k 23 )2 w 2 LL3
Iin(k13 + k23 )2 RL
L3Vin2
L R 2 + k - k 2 - k 2 2 w 2 L2

Vin2

(

L

13

23

)

Parallel PS topologyVinw (k13 + k23 ) LL3
I in
RL

2
2
wL3
- k 23
L RL + j k - k13
I in
2
L3
(k13 + k 23 )I inConstant

Constant

VL

jw (k13 + k 23 ) LL3 I in

RL
L
I in
L3 k13 + k 23

M13(=k13)

I3

CS3

Iin2

Vin

L3

I2

V3

)

I in

I in
L
L3 k13 + k 23

w (k13 + k23 )2 LL3 2
I in
RL

2
L
RL I inL3 (k13 + k23 )2

RL
2

PL

x=600mm

x=0mm

IL

V1
CS2

jw (k13 + k 23 ) LL3

IL

(

2

2

Car side(secondary coil)

L1

Vin1

Series SS topology

3

I1

CS1

Iin1

)

(k13 + k23 )RL
L3
Vin
2
2
L RL + j (k - k13
- k23
)wL3

V

RL

PL

(

(k13 + k 23 )w LL3 inj

2

Table 2. The voltage and current characteristics for constant
input current

VL

moving direction x

135mm

RL

L2
Vin2

Road side(primary coils)

M23(=k23)

V2

Fig.3 Series SS topology
Iin1
ICP1
Vin
Vin1 CP1

I3

L3

I2
ICP2

Vin2

CP2

IL

CS

V1

Iin2

V3

VL

RL

L2
M23(=k23)

V2

Fig.4 Parallel PS topology

0.25
0.2
0.15
0.1
0.05

In the circuit analysis of Figs. 3 and 4, the following conditions

0

are taken into consideration for simplicity.
lWhen the separation between the primary coils is suitable,l

All primary coils are the same shape and perform the same.
(L=L1=L2)
Resonant capacitors apply the resonance condition of
inductances at the 0 mm point, and do not change on theway. (Fig. 5)

w L

w L3

600

150

135

,

(7)

and the capacitance in the parallel PS topology are determined

L1
L2
L3

155

140

2

500

160

topology are determined as follows:
2

400

165

145

1

300

170

When applying the conditions, the capacitance in the series SS, CS 3 =200

Fig.6 Variable coupling coeffient

self inductance [µH]

Winding resistances are suitably smaller than reactances.

1

100

175

l

CS1 = CS 2 =0distance [mm]mutual coupling is ignored.

l

k12
k13
k23
k13+k23

0.3

M13(=k13)
L1

coupling coefficient [-]Iin

Fig.5 Pattern diagram

I1

0

100

200

300

400

distance [mm]Fig.7 Variable self inductanceas follows:

Copyright © 2018 Society of Automotive Engineers of Japan, Inc. All rights reserved

500

600

20189177

Table 3. Specifications of solenoid coils

Winding[mm]135H-shaped core
320×446×31.5
270×270×21.5
300×420×20
250×250×10
172×424×20
172×166×16.5
20T×2p22T×1pGround side
Vehicle side

2000

w 2L

, CS =1w 2 (1 - k ) L3,

where k represents the coupling coefficient k132+k232 at the 0 mm
point setting on the secondary side. Tables 1 and 2 list thevoltage and current characteristics for constant input voltage, andconstant input current, respectively. From Tables 1 and 2, the1500

sum of coupling coefficients k13, k23 shows a large fluctuation on2

theoretical(Const Vin)simulation(Const Vin)theoretical(Const Iin)
simulation(Const Iin)
Power factor(simulation)(8)
output power[W]C P1 = C P 2 =

1

1.5

1000

1

500

0.5

power factor[-]Gap[mm]Coil type
Size[mm]
Ground side
Vehicle side
Core Size[mm] Ground side
Vehicle side
Winding Size[mm] Ground side
Vehicle side

Table 4. Simulation parametersGap[mm]135
Frequency[kHz]85
17
Load Resistance[W]0.0214
Cs1,Cs2[µF](SS)0.0249Cs3[µF](SS)0.0214
Cp1,Cp2[µF](PS)
0.0261Cs[µF](PS)Vinmax[V]141.2
IinSSmax[A]5.0
IinPSmax[A]0.5

voltage and current. For example, when k13+k23 decreases, thevalue increases if this parameter is the numerator, and when

0
0

100

200

k13+k23 decreases, the value increases if this parameter is the

300

400

500

0
600

distance[mm]Fig.8 Output power of series SS topology(Simulation)

misalignment influence than the series SS topology because an
140

when the secondary coil moves from the 0 mm point.

120

output power[W]imaginary component appears in the equations in this topology

theoretical(Const Vin)simulation(Const Vin)theoretical(Const Iin)
simulation(Const Iin)
Power factor(experiment)

1.4
1.2

100

1

80

0.8

60

0.6

40

0.4

The coil shape parameters are listed in Table 3. In this paper, the

20

0.2

value obtained by actually measuring the constant of the coil at

0

4. Simulation
The simulation is run using by PSIM, a circuit simulator, tovalidate the equations presented in Section 3.The coils uses an Hshaped solenoid, which has high misalignment performance(7).

0

100

200

300

400

500

power factor[-]denominator. Furthermore, the parallel PS topology has a bigger

0600

intervals of 100 mm between 0 and 600 mm was used. The coildistance[mm]parameters obtained by measurement are given in Figs. 6 and 7.

Fig.9 Output power of parallel PS topology(Simulation)
Table 5. Experiment parameters

Moreover, Table 4 lists the various constants used in thesimulation. The value of capacitors use parameters at 0 mm pointfrom Fig. 5. A simulation is carried out using the above values.
The output wave form of the inverter source uses a sine wave,
and the load uses only pure resistance without a rectifier. Figs. 8
and 9 shows the output power using the series SS and parallel PS
topologies, respectively, as well as input power factors, and show
how the calculated value is reproduced approximately in thesimulation. There are places where the values deviate in Fig. 8 at
the time of constant input voltage and Fig. 9 at the time of
constant input current. This may be due to loss caused bywinding resistance, not considered by analysis, and/or due an

Gap[mm]Frequency[kHz]DC Load Resistance Rd[W]Cs1,Cs2[µF](SS)Cs3[µF](SS)Vin[V]
IinSS[A]

135
85
18.7
0.02170.0249100
5.0

error that increases as the total value of the coupling coefficientdecreases.
5. Experiment
An experiment is carried out to validate the equations calculated
in Sections 3 and 4, with experimental verification limited to the

Copyright © 2018 Society of Automotive Engineers of Japan, Inc. All rights reserved

20189177

Fig. 10 Experiment circuit of series SS topology
series SS topology. Fig. 10 shows experiment circuit of SS

1000

1

800

0.8

600

0.6

400

0.4

Additionally, Table 5 lists various constants used in the
output power[W]experiment. The input wave uses the RMS (square wave),
converted between square wave voltage Vinv and fundamental
wave voltage Vin , as

Vin =

2 2

p

Vinv .

(9)
200

0

0

100

200

300

400

500

0
600

distance[mm]

8

p

0.2

theoretical(Const Vin)experiment(Const Vin)
Power factor(experiment)

Moreover, a load RL uses a combination of DC electronic
resistance and a full bridge rectifier. The conversion formula(8) is

RL =power factor[-]

topology. The experimental circuit is shown in Fig. 10.

R .
2 d

(10)

(a) constant Vin

The result for output power of the series SS topology is shown in
Fig. 11. There is a large difference between the calculated

600

1.2

500

1

400

0.8

300

0.6

200

0.4

invisible factor during the analysis. The larger the change invalues, the greater the influence of the power factor change
becomes; the smaller the change in values, the smaller the
influence of the power factor change. Nevertheless, thequalitative changes are in approximate agreement.

100
0

0.2

theoretical(Const Iin)
experiment(Const Iin)
Power factor(experiment)
0

100

200

300

400

power factor[-]

They may be due to a variation of the power factor by an

output power[W]theoretical values and the experimental values in Fig. 11 (a).

500

0
600

distance[mm]6. CONCLUSION
This paper analyzes the input voltage and current, and the(b) constant Iin
Fig. 11 Output power of series SS topology(experiment)

output voltage, current, and power of the series SS and theparallel connection of primary coils inseries to resonant

parallel PS topologies using two primary coils and a secondary

capacitors, and perform a comparative analysis of the results on

coil, with a focus on the series SS topology for experimental

the series SS and parallel PS topologies. Moreover, it willverification. The trends of the theoretical equation and the circuit

analyze the impact of increasing the number of primary coils.

simulation value are in approximately agreement. There areplaces where the values deviate significantly when constant

REFERENCES

voltage is input, probably because of a variation of the power(1) T.Yasuda, T. Fujita, and M, Sato , “Proposed dynamic

factor caused by an invisible factor in the analysis. In the future,contactless power transfer system,” in Proc. EVS28, 2015,

this work will be extended to include experimental verification of

vol. B5-02, pp. 1—6.

the parallel PS topology, including parallel SS topology, i.e.,

Copyright © 2018 Society of Automotive Engineers of Japan, Inc. All rights reserved

20189177(2) Y. Chen, S. Park, J. Kim, H. Kim, K. Hwang, J. Kim, and S.
Ahn, “System and electromagnetic compatibility ofresonance coupling wireless power transfer in on-line
electric vehicle,” -in Proc. ISAP, 2012, no. 1E3-1, pp.
158—161.
(3) K. K. Kim, T. Imura, and Y. Hori, “New wireless powertransfer via magnetic resonant coupling for charging moving
electric vehicle, ” in Proc. EVTeC and APE 2014, 2014, no.
20144026, pp. 1—5.
(4) T. Fujita, T. Yasuda, and H. Akagi, “A dynamic wirelesspower transfer system applicable to a stationary system,”IEEE Trans. Industry Applications, vol. 53, no 4, pp.
3748—3757, Jun. 2017(5) J. Yamada, K Tsuda, R. Kobayashi, Y. Kaneko, “Circuit
analysis and characterization of contactless power transfer
system with variable impedance,” IEEJ Trans. Industry
Applications, vol. 137 no.11, pp. 815—826, Nom. 2017 (injapanese)(6) H.Irie and Y. Yamada, “Immittance converter suitable forpower electronics,” Elect. Eng. Japan, vol. 124, no. 2, pp.
53—62, Jul. 1998
(7) C. Kato, K. Tsuda, T. Matsumura, Y. Kaneko, T. Fujita, andT. Yasuda, “Investigation of wireless power transfer systemwith spaced arranged primary H-shaped core coils formoving EVs,” in Proc. IEEE IECON 2015, 2015, pp.5197—
5201.
(8) R. L. Steigerwald, “A comparison of half-bridge resonant
converter topologies,” IEEE Trans. Power Electronics, vol.
3, no. 2, pp. 174—182, Apl. 1988

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