Generally, a single phase Hbridge converter feeding a single primary track is employed in conventional inductive power transfer systems. However, these systems may not be suitable for some high power applications due to the constraints of the semiconductor switches and the cost. To resolve this problem, a novel dual coupled primary tracks IPT system consisting of two high frequency resonant inverters feeding the tracks is presented in this paper. The primary tracks are wound around an Eshape ferrite core in parallel which enhances the magnetic flux around the tracks. The mutual inductance of the coupled tracks is utilized to achieve adjustable power sharing between the inverters by configuring the additional resonant capacitors. The total transfer power can be continuously regulated by altering the pulse width of the inverters’ output voltage with the phase shift control approach. In addition, the system’s efficiency and the control strategy are provided to analyze the characteristic of the proposed IPT system. An experimental setup with total power of 1.4kW is employed to verify the proposed system under power ratios of 1:1 and 1:2 with a transfer efficiency up to 88.7%. The results verify the performance of the proposed system.
I. INTRODUCTION
Inductive Power Transfer (IPT) is a promising way to deliver power from a power source to a load or multiple loads via electromagnetic coupling in order to enhance system flexibility
[1]

[17]
. Nowadays, IPT systems have been employed in numerous applications which include low power wireless charging of biomedical implants
[10]
, electric vehicle charging systems
[16]
, and public transport systems
[17]
.
Only one primary track with an elongate loop or a pad is supplied by a single resonant inverter in conventional IPT systems, and an IPT pickup consists of a coil of litz wire in close proximity to the track wires positioned to capture magnetic flux around the track conductor as shown in
Fig. 1
. The magnitude and frequency of the track current, and the magnetic coupling and quality factor of the compensated circuit directly dictate the amount of power that can be transferred across the air gap. As a result, high voltage, high current, high frequency semiconductor devices are used to achieve a high power transfer. However, these semiconductor devices are relatively expensive and may not be easy to purchase.
Typical IPT system.
Multilevel technology
[18]

[20]
has advantages in terms of reducing the stress of semiconductor devices, and in implementing high power IPT systems by using lowcost and lowvoltage semiconductor devices. However, it is a challenge to implement such systems at high frequency and to get them to work under the soft switch condition. Multiinverter connected in parallel is another option to realize high power transfer by using low power capacity resonant inverters. A parallel topology for IPT systems by connecting identical LCLTbased IPT supplies in parallel across a shared ac track inductor was proposed in
[8]
. This topology can dramatically improve the system’s transfer power, availability and reliability. However, large circulating currents among the inverter modules may be generated by the component tolerance, and the control strategy used to minimize the circulating currents is complex.
Multicoil connected with multiinverter is employed in induction heating to enhance the magnetic fields, which can enhance the total output power by using multiple low power inverters
[21]

[26]
. On the one hand, the limitations of its single operation can be removed in aspects like heat dissipation, cost, short time overload, and component limitations. On the other hand, the multicoils connected with multiinverter also brings convenience in terms of maintenance and flexible operation for maximum efficiency and reliability. However, the mutual inductances among the coils makes it difficult to control the resonant currents flowing through the coils. An additional decoupling transformer is one of the solution to mitigate the influence of mutual inductances
[25]

[26]
. However, this comes with an increase in cost.
This paper presents a new IPT topology based on dual coupled tracks connected to double resonant inverters to meet the demand of highpower applications. The mutual inductance of the dual coupled tracks is utilized to achieve better power sharing between the inverters or to improve the power distribution by configuring the resonant capacitor. Resonant inverters with different power capacities can be chosen to achieve maximum power transfer by altering the additional capacitors with a careful design. An experimental setup with a total transfer power of 1.4kW is employed to verify the proposed system under power ratios of 1:1 and 1:2 between the two inverters with an approximate transfer efficiency of 88.5%. According to the results, an attractive option for integrating lowpower inverters of identical or different power capacities with dual coupled tracks is built to meet the demands of highpower applications.
The rest of this paper is organized as follows. A review of IPT systems based on a single track is shown in In Section II. In Section Ⅲ, a detailed description of the structure design and principle analysis of an IPT system based on dual coupled tracks connected with double resonant inverters is given; and the parameter design and power distribution method for the proposed IPT system is analyzed in detail. Then, Section Ⅳ shows steadystate results of an experimental system operating at 1.4kW. Some conclusions are then given in Section V.
II. REVIEW OF IPT SYSTEMS BASED ON A SINGLE TRACK
A conventional IPT system based on a single primary track is shown in
Fig. 2
. It comprises a high frequency Hbridge resonant inverter, a fullbridge rectifier, and resonant tanks.
L_{P}
and
L_{S}
are the inductances of the primary track and the pickup coil, respectively.
C_{P}
and
C_{S}
are the resonant capacitors used to compensate the primary track
L_{P}
and the pickup
L_{S}
. The equivalent series resistances of the track and the pickup coil are
R
_{1}
and R
_{S}
, which can be neglected since their values are relatively small compared to that of the load. The mutual inductances between the pickup coil and the primary tracks are denoted as
M
.
The structure of the IPT system based on single track.
The inverter is controlled by the phaseshift technique, which generates a fixedfrequency ac output voltage uP as shown in
Fig. 3
. The operating frequency of the inverter is equal to the resonant frequency
According to
[5]
, the RMS (Root Mean Square) of the track current can be obtained as:
According to
[5]
, the transfer power can be calculated by:
Principal operation waveforms of inverter.
Therefore, the transfer power of IPT systems can be upgraded by enhancing the equivalent track current.
III. ANALYSIS AND DESIGN OF IPT SYSTEMS BASED ON DUAL COUPLED TRACKS
 A. Description of the Proposed IPT System
An IPT system based on dual coupled tracks is shown in
Fig. 4
. The dual tracks are wound in parallel around an Eshaped ferrite core over severaltens of meters as a power transmitter, and each track is connected with an Hbridge resonant inverter as a power supply converter. In addition, all of the inverters share a common DC input voltage. A pickup coil is wound around an Eshaped ferrite core as a power receiver. The power receiver is intentionally shorter than the power transmitter, so that it can dynamically move over the primary tracks freely.
The structure of the proposed IPT system.
In order to analyze the magnetic field of the proposed structure, a commercial finiteelement analysis software, i.e., Flux is employed to provide the magnetic field image shown in
Fig. 5
. This is done with an energized current of 10A for a single track, 5A each for dual tracks, and 10A each for dual tracks. It is clear that the magnetic field intensity of 10A for a single track is very close to that of one 5A for each of the dual tracks due to the parallel structure. The magnetic field is dynamically strengthened by increasing the current to 10A each for the dual tracks as the equivalent current increases. In other words, the total magnetic field around the power transmitter is synthesized by the dual tracks’ currents. As a result, the transfer power is enhanced by the synthesized magnetic field, which is energized by the two currents. Under this condition, a relatively large mutual inductance
M
_{12}
exists between the coupled primary tracks. This large mutual inductance is utilized to obtain better power sharing performance of the IPT system instead of decoupling the inductor behavior to simplify the system as done in classical approaches
[25]
,
[26]
.
Magnetic field image of the single track and dual tracks structure with different energized currents.
The equivalent circuit of an IPT system with the seriesseries tuned topology is depicted in
Fig. 6
.
L
_{1}
,
L
_{2}
and
L_{S}
are the inductances of the primary track 1, track 2 and the pickup coil, respectively.
C
_{1}
,
C
_{2}
and
C_{S}
are the resonant capacitors used to compensate the primary tracks
L
_{1}
and
L
_{2}
, and the pickup coil
L_{S}
. The equivalent series resistances of the dual tracks and the pickup coil are
R
_{1}
,
R
_{2}
, and R
_{S}
. The mutual inductances between the pickup coil and the primary dual tracks are
M
_{1S}
and
M
_{2S}
, respectively. A full bridge rectifier is employed to convert high frequency AC power to DC power to feed the load
R_{L}
. The twoinverter units operate at an identical angular frequency of
ω
, which can be defined by:
The equivalent circuit of the proposed seriesseries tuned IPT system.
For simplicity of analysis and design, the structure of the dual primary tracks are designed identically. In addition, both of the mutual inductances between the pickup coil and the primary dual tracks are approximately identical,
M
_{1S}
=
M
_{2S}
.
The inverters are controlled by the phaseshift technique, which generates fixedfrequency ac output voltages
u
_{1}
and
u
_{2}
. Moreover, the voltages are identical to each other by employing synchronous control technology
[8]
, as shown in
Fig. 7
.
Principal operation waveforms of inverter 1 and inverter 2.
The fundamental voltage phasor of the inverters can be derived as:
 B. Modeling and Analysis of the Proposed IPT System
According to mutual coupling theories, the relationship between the current values and the voltages can be derived as:
where
Z
_{1}
,
Z
_{2}
and
Z_{S}
are the impedances of the dual primary tracks and the pickup, respectively. The impedances can be defined as follow:
For simplicity of the analysis, the equivalent series resistances of the dual tracks and the pickup coil are neglected since their values are relatively small compared to that of the load. That this is to say,
R_{S}
=
R
_{1}
=
R
_{2}
=0，
Z
=
Z
_{1}
=
Z
_{2}
=0, and
Z_{S}
=
R_{0}
.
According to
[27]
, the equivalent load
R
_{0}
of the rectified tank connected to a resistive load
R_{L}
can be expressed by:
By substituting (4), (6), and (7) into (5), the fundamental current phasor of the dual tracks can be derived by:
The impedances of the Hbridge inverter units can be yielded by:
Under this condition, the Hbridge inverter units’ impedances are not purely resistive due to the mutual inductance between the dual tracks. Therefore, the inverter units are not working under the resonant condition. That is to say, the capacitors are used to compensate the primary track since the traditional method do cannot meet the requirements of the resonance in dual coupled tracks IPT systems.
 C. Parameter Design and Power Distribution
According to the aforementioned analysis, in order to minimize the reactive power of the Hbridge inverters, additional capacitors
C
_{e1}
and
C
_{e2}
are added to ensure that the Hbridge inverters to work under the resonance condition. An equivalent circuit diagram with the additional capacitors is shown in
Fig. 8
.
The equivalent circuit diagram with additional compensation capacitors.
Assuming that
jX
_{1}
= (
jωC
_{e1}
)
^{1}
and
jX
_{2}
= (
jωC
_{e2}
)
^{1}
, according to (6), the impedance of the dual primary tracks can be derived by:
For the sake of convenience, the following variables in (11) are defined:
Under these conditions, substituting (4), (7), and (10) into (5), the fundamental current phasor of the dual tracks can be changed to:
The new impedances of the Hbridge inverter units can be yielded by:
In order to let the two Hbridge inverter work under the resonant condition, the Hbridge inverter units’ impedance has to be purely resistive. Meanwhile, to make the two inverter output power levels flexibly configured,
is set to be equal to
. Re(•) represents the real component operation for (•). That is to say, the output power of inverter 2 is
λ
times that of inverter 1. Consequently, it is possible to obtain:
The solution of (14) is given by
The value of the additional capacitors can be derived by:
Therefore, by adding the additional capacitors
C
_{e1}
and
C
_{e2}
, the impedances of the Hbridge inverter units are purely resistive as shown below:
The relationship between the dual tracks’ currents can be expressed by:
The output power of each inverter can be derived by:
where (•)* represents the conjugate operation for (•). The total output power (
P
) of the primary side can be given by:
All in all, the mutual inductance between the dual tracks is compensated by using the additional capacitors, which ensures that the inverters can work under the resonance condition. The inverters’ output power can be effectively allocated by choosing an appropriate value of
λ
. Moreover, no matter what the value
λ
is, the total output power of the inverters remains the same.
According to the aforementioned analysis, the voltage ratings of the semiconductor of a conventional IPT system and that of the proposed IPT system are decided by the DC input voltage E. The operating frequency of a conventional IPT system is identical to that of the proposed IPT system with the resonant frequency. Therefore, both the voltage rating and frequency of the semiconductor used for conventional IPT systems and the proposed IPT system are the same.
As can be seen from (1), (7), and (18), if
M
=
M
_{1S}
and
R
=
R
_{0}
, it is possible to obtain:
Therefore, the current ratings of the semiconductor for the proposed IPT system are 1/ (
λ
+ 1) or
λ
/ (
λ
+ 1) times the current ratings of the semiconductor for a conventional IPT system.
 D. Track Current Control
In order to simplify the pickup control, it is necessary to regulate the track current at a designed value since the received voltage by a pickup is directly proportional to the track current.
A simplified view of the control loop is illustrated in
Fig. 9
. The controller controls and regulates the amplitude of the total track current
i
_{sum}
(
i
_{1}
+
i
_{2}
) by varying the inverter conduction angle
θ
_{L}
shown in
Fig. 7
, which is the input to the current control loop. The primary objective of the controller is to improve the reference tracking performance of the power supply.
Current control diagram.
IV. SYSTEM EFFICIENCY
To analyze the system efficiency, the resistances R
_{S}
,
R
_{1}
, and
R
_{2}
in
Fig. 4
should be considered. Assume that the equivalent series resistances are equal (
R
_{1}
=
R
_{2}
) because the structure of the dual primary tracks are arbitrarily designed identically.
λ
= 1 is widely used to achieve better power sharing when the Hbridge inverters have identical power capacities. In order to simplify the analysis, the system efficiency is analyzed in detail considering only
λ
= 1. The impedance of the dual primary circuits can be derived by:
The output power of inverter 1 and inverter 2 can be expressed by:
The voltage phasor of the pickup coil can be derived by:
The current phasor of the secondary circuit is given by:
The output power of the IPT system is derived by:
Therefore, the efficiency of the IPT system can be derived by:
To achieve maximum efficiency, the equivalent series resistances of the dual tracks and the pickup coil R
_{S}
,
R
_{1}
, and
R
_{2}
should be designed as small as possible.
In order to calculated the maximum efficiency of the IPT system, the derivation of
η
should be set to zero.
The theoretical optimal load
R
_{0}
corresponding to the maximum efficiency can be obtained as:
Under this optimal load, the maximum efficiency can be obtained as:
By choosing an optimal load, maximum efficiency can be achieved.
V. EXPERIMENTAL VERIFICATION
 A. Prototype System
To validate the proposed topology and power distribution method, an experimental IPT prototype was constructed in a laboratory settings with dual primary tracks connected to dual Hbridge inverters as shown in
Fig. 4
. The prototype was designed to operate up to 20 kHz and 1.4kW in the experiment. It can implement the power distribution method by choosing proper additional capacitors.
The exterior appearance of the experimental setup is portrayed in
Fig. 10
. Two inverters are separately powered by a common DC supply, and the AC output of the two Hbridge inverters are connected to the tracks.
The exterior appearance of the proposed IPT prototype.
The gate pulse signals for the active switches are generated by a TMS320F28335 Digital Signal Processor (DSP, Texas Instrument). A CONCEPT2SC0108T2A017 is adopted as the power MOSFET drive to fulfill the requirements of a high switching frequency.
The dual tracks are wound with Litz wire around an E type ferrite core, and the pickup coil is also wound around an E type ferrite core with Litz wire. The ferrite core sizes are shown in
Fig. 11
. The air gap between the tracks and the secondary pickup coil is set to be 5cm.
The tracks and the pickup coil wound around ferrite core with Litz wire.
The mutual and track inductances were measured by an Agilent E4980A LCR meter. Moreover, an oscilloscope Agilent MSOX 4034A was used to measure and display the current and voltage waveforms of interest by means of N2780B current probes and N2891A differential probes, respectively.
The design specifications of the prototype and the experimental setup are listed in
TABLE I
.
THE CONFIGURATION OF THE IPT SYSTEM
THE CONFIGURATION OF THE IPT SYSTEM
 B. Experimental Results
Without a loss of generality, two settings (
λ
= 1 and
λ
= 2) are performed to validate the performance of the proposed algorithm. The additional compensation capacitors are calculated as
C
_{e1}
=
C
_{e2}
= 1.04
μF
and
C
_{e1}
= 4
C
_{e2}
= 0.52
μF
according to (16). Under these conditions, a number of experimental results have been tested by altering
θ_{L}
. However, only three sets of experimental waveforms are provided in
Fig. 12
and
Fig. 13
due to limitation on the paper’s length.
Output currents and voltages of the inverters: (a) λ = 1 and θ_{L} = π∕2, (b) λ = 1 and θ_{L} = π∕3, and (c) λ = 2 and θ_{L} = π∕2.
Pickup output current and voltage: (a) λ = 1 and θ_{L} = π∕2, (b) λ = 1 and θ_{L} = π∕3, and (c) λ = 2 and θ_{L} = π∕2.
The output currents
i
_{1}
,
i
_{2}
and voltages
u
_{1}
,
u
_{2}
of the two Hbridge inverters are illustrated in
Fig. 12
for the corresponding measured waveforms.
i
_{sum}
is the sum of the two inverter currents
i
_{1}
and
i
_{2}
. In
Fig. 12
(a) and (b), show that the currents of the two inverters are identical when
λ
= 1 with
θ_{L}
=
π
/2 and
θ_{L}
=
π
/3. In this case, the output current of one inverter is not only in phase with that of the other, but also in phase with the output voltage. This shows that both of the inverters are working under the resonance condition. When
λ
= 2, the current of the first inverter is in phase with the other but with twice the magnitude as shown in
Fig. 12
(c). The voltage and current waveforms of the load are illustrated in
Fig. 13
and the measured powers (
P
_{1}
and
P
_{2}
are the output power of inverter 1 and inverter 2, and
P_{o}
is the load consumption power) are listed in
TABLE II
PERFORMANCE OF PROPOSED IPT SYSTEM UNDER VARIOUCSONDITIONS
PERFORMANCE OF PROPOSED IPT SYSTEM UNDER VARIOUCSONDITIONS
The output power of Case A is approximately the same as that of Case C. The output power of both of the inverters in Case A are nearly identical, while the output power of one inverter in Case C is nearly twice as that of the other. This means the power sharing of the two inverters can be achieved by the proposed method. The output power and the system’s efficiency decrease as
θ_{L}
goes down for both cases, as shown in
Fig. 15
.
To provide a clear comparison of the different operating conditions, the experimental values of the output powers of each inverter and total output power against
θ_{L}
are given in
Fig. 14
. The experimental results clearly show that widerange output power regulation can be attained by altering
θ_{L}
, and that power sharing can be achieved by the proposed method.
Relation between the output power of the inverters and θ_{L}.
Relation between the efficiency and θ_{L}.
The dynamic current response with
λ
= 1 is shown in
Fig. 16
with two test cases. One is for changing the reference amplitude value of the current
i
_{sum}
from 18A to 24A and the other is for changing it from 24A to 18A. The blue line is the summation of the total track current
i
_{sum}
, and the red line is the first track current
i
_{1}
. It needs only 15ms to settle down to the reference current for both cases, which shows the good performance of the dynamic response. In addition,
i
_{1}
is half of
i
_{sum}
for both cases.
Closed loop system response to step change in reference track current: (a) From 18A to 24 A and (b) From 24A to 18A.
In conclusion, according to the aforementioned experimental results, the power distribution of the two inverters can be allocated by adopting different values of
λ
, which validates the proposed power distribution and control methods.
VI. CONCLUSION
A novel IPT system based on dual coupled primary tracks is proposed in this paper. The structure of an IPT system has been explained and described in detail. In addition, the magnetic, system’s efficiency and the control strategy are provided to analyze the characteristic of the proposed IPT system. The mutual inductance of the dual coupled tracks is utilized to achieve better power sharing between the inverters or to improve the power distribution by configuring additional capacitors. Furthermore, both of the inverters can work under resonance conditions. The output power can be continuously regulated by altering the output voltage pulse width of the inverters. A 1.4kW experimental prototype is set up and tested to verify power ratios of 1:1 and 1:2 with a transfer efficiency up to 88.7%. The experimental results verify the performance of the proposed IPT system and the power distribution approach, which is suitable for high power IPT applications with various power level requirements.
Acknowledgements
This work was supported by Scientific R&D Program of China Railway Corporation (2014J013B) and National Natural Science Foundation of China (Grant No. 51507147) and the Fundamental Research Funds for the Central Universities (2682015CX021).
BIO
Yong Li was born in Chongqing, China, in 1990. He received his B.S. degree in Electrical Engineering and Automation from Southwest Jiaotong University (SWJTU), Chengdu, China, in 2013, where he is presently working towards his Ph.D. degree in the School of Electrical Engineering. His current research interests include wireless power transfer, and modular multilevel converters supplying IPT systems for high power applications.
Ruikun Mai was born in Guangdong, China, in 1980. He received his B.S. and Ph.D. degrees from the School of Electrical Engineering, Southwest Jiaotong University (SWJTU), Chengdu, China, in 2004 and 2010, respectively. He was with AREVA T&D U.K. Ltd., London, England, UK, from 2007 to 2009. He was a Research Associate at The Hong Kong Polytechnic University, Hung Hom, Hong Kong, from 2010 to 2012. He is presently an Associate Professor in the School of Electrical Engineering, Southwest Jiaotong University. His current research interests include wireless power transfer and its application in railway systems, power system stability and control, and phasor estimator algorithms and their application to PMUs.
Liwen Lu was born in Jiangsu, China, in 1990. He received his B.S. degree in Electronics and Information Engineering from Southwest Jiaotong University (SWJTU), Chengdu, China, in 2014, where he is presently working towards the M.S. degree. His current research interests include inductive power transfer and power conversion in rail transit applications.
Zhengyou He was born in Sichuan, China, in 1970. He received his B.S. and M.S. degrees in Computational Mechanics from Chongqing University, Chongqing, China, in 1992 and 1995, respectively. He received his Ph.D. degree in Electrical Engineering from Southwest Jiaotong University (SWJTU), Chengdu, China, in 2001. He is presently a Professor at SWJTU. His current research interests include signal processing and information theory applied to power systems, and the application of wavelet transforms to power systems.
Dai X.
,
Zou Y.
,
Sun Y.
2013
“Uncertainty Modeling and Robust Control for LCL Resonant Inductive Power Transfer System,”
Journal of Power Electronics
13
(5)
814 
828
DOI : 10.6113/JPE.2013.13.5.814
Li Y. L.
,
Sun Y.
,
Dai X.
2013
“μSynthesis for Frequency Uncertainty of the ICPT System,”
IEEE Trans. Ind. Electron.
60
(1)
291 
300
DOI : 10.1109/TIE.2011.2170394
Pinuela M.
,
Yates D. C.
,
Lucyszyn S.
,
Mitcheson P. D.
2013
“Maximizing DCtoLoad Efficiency for Inductive Power Transfer,”
IEEE Trans. Power Electron.
28
(5)
2437 
2447
DOI : 10.1109/TPEL.2012.2215887
Wang Z.H.
,
Li Y.P.
,
Sun Y.
,
Tang C.S.
2013
“Load Detection Model of VoltageFed Inductive Power Transfer System,”
IEEE Trans. Power Electron.
28
(11)
5233 
5243
DOI : 10.1109/TPEL.2013.2243756
Hu A. P.
,
Ph.D. dissertation
2001
“Selected resonant converters for IPT power supplies,”
Univ. Auckland
Auckland, NZ
Ph.D. dissertation
Lee S.
,
Choi B.
,
Rim C. T.
2013
“Dynamics Characterization of the Inductive Power Transfer System for Online Electric Vehicles by Laplace Phasor Transform,”
IEEE Trans. Power Electron.
28
(12)
5902 
5909
DOI : 10.1109/TPEL.2013.2254500
Zhang W.
,
Wong S.C.
,
Tse C. K.
,
Chen Q. H.
2014
“Design for Efficiency Optimization and Voltage Controllability of SeriesSeries Compensated Inductive Power Transfer Systems,”
IEEE Trans. Power Electron.
29
(1)
191 
200
DOI : 10.1109/TPEL.2013.2249112
Hao H.
,
Covic G. A.
,
Boys J. T.
2014
“A Parallel Topology for Inductive Power Transfer Power Supplies,”
IEEE Trans. Power Electron.
29
(3)
1140 
1151
DOI : 10.1109/TPEL.2013.2262714
Neath M. J.
,
Swain A. K.
,
Madawala U. K.
,
Thrimawithana D. J.
2014
“An Optimal PID Controller for a Bidirectional Inductive Power Transfer System Using Multi objective Genetic Algorithm,”
IEEE Trans. Power Electron.
29
(3)
1523 
1531
DOI : 10.1109/TPEL.2013.2262953
Joun G. B.
,
Cho B. H.
1998
“An energy transmission system for an artificial heart using leakage inductance compensation of transcutaneous transformer,”
IEEE Trans. Power Electron.
13
(6)
1013 
1022
DOI : 10.1109/63.728328
Hasanzadeh S.
,
VaezZadeh S.
,
Isfahani A. H.
2012
“Optimization of a contactless power transfer system for electric vehicles,”
IEEE Trans. Veh. Technol.
61
(8)
3566 
3573
DOI : 10.1109/TVT.2012.2209464
Elliot G. A. J.
,
Raabe S.
,
Covic G. A.
,
Boys J. T.
2010
“Multiphase pickups for large lateral tolerance contactless powertransfer systems,”
IEEE Trans. Ind. Electron.
57
(5)
1590 
1598
DOI : 10.1109/TIE.2009.2031184
Huh J.
,
Lee S. W.
,
Lee W. Y.
,
Cho G. H.
,
Rim C. T.
2011
“Narrowwidth inductive power transfer system for online electrical vehicles,”
IEEE Trans. Power Electron.
26
(12)
3666 
3679
DOI : 10.1109/TPEL.2011.2160972
Song B.
,
Shin J.
,
Lee S.
,
Shin S.
“Design of a high power transfer pickup for online electric vehicle (OLEV),”
in IEEE International Electric Vehicle Conferrence(IEVC)
Mar. 2012
1 
4
Macpherson K. D.
,
Macpherson D. E.
2007
“An airborne radar power supply with contactless transfer of energypartI: Rotating transformer,”
IEEE Trans. Ind. Electron.
54
(5)
2874 
2884
DOI : 10.1109/TIE.2007.902044
Chopra S.
,
Bauer P.
2013
“Driving range extension of EV with onroad contactless power transfer—A case study,”
IEEE Trans. Ind. Electron.
60
(1)
329 
338
DOI : 10.1109/TIE.2011.2182015
Covic G. A.
,
Elliott G.
,
Stielau O. H.
,
Green R. M.
,
Boys J. T.
“The design of a contactless energy transfer system for a people mover system,”
in Proc. International Conference on Power System Technology
2000
Vol. 1
79 
84
Rahnamaee H. R.
,
Thrimawithana D. J.
,
Madawala U. K.
“MOSFET based Multilevel converter for IPT systems,”
In International Conference on Industrial Technology(ICIT)
Feb./Mar. 2014
295 
300
Rahnamaee H. R.
,
Madawala U. K.
,
Thrimawithana D. J.
“A multilevel converter for high powerhigh frequency IPT systems,”
in IEEE 5th International Symposium on Power Electronics for Distributed Generation Systems(PEDG)
Jun. 2014
1 
6
Nguyen B. X.
,
Vilathgamuwa D. M.
,
Foo G.
,
Ong A.
,
Sampath P. K.
,
Madawala U. K.
“Cascaded multilevel converter based bidirectional inductive power transfer (BIPT) system,”
in International Power Electronics Conference(IPEC)
May 2014
2722 
2728
Carretero C.
,
Lucía O.
,
Acero J.
,
Burdío J. M.
2011
“Phaseshift control of dual halfbridge inverter feeding coupled loads for induction heating purposes,”
Electronics Letters
47
(11)
670 
671
DOI : 10.1049/el.2011.1114
Carretero C.
,
Lucía O.
,
Acero J.
,
Burdío J. M.
2013
“Computational modeling of two partly coupled coils supplied by a double halfbridge resonant inverter for induction heating appliances,”
IEEE Trans. Ind. Electron.
60
(8)
3092 
3105
DOI : 10.1109/TIE.2012.2202360
Lucía O.
,
Carretero C.
,
Burdío J. M.
,
Almazan F.
2012
“Multipleoutput resonant matrix converter for multiple induction heaters,”
IEEE Trans. Ind. Appl.
48
(4)
1387 
1396
DOI : 10.1109/TIA.2012.2199456
Carretero C.
,
Lucía O.
,
Acero J.
,
Burdío J. M.
“FEA tool based model of partly coupled coils used in domestic induction cookers,”
37th Annual Conference on IEEE Industrial Electronics Society
Nov. 2011
2533 
2538
Aronson A. J.
1972
“Vacuum coating system with induction heating vaporizing crucibles,”
U.S. Patent 3 657 506
Ngoc H. P.
,
Fujita H.
,
Ozaki K.
,
Uchida N.
2011
“Phase angle control of highfrequency resonant currents in a multiple inverter system for zonecontrol induction heating,”
IEEE Trans. Power Electron.
26
(11)
3357 
3366
DOI : 10.1109/TPEL.2011.2146278
Erickson R. W.
,
Maksimovic D.
2001
“Fundamentals of power electronics,”
Springer