电 工 技 术 学 报
2013 年
第 28 卷增刊 2
Vol.28
TRANSACTIONS OF CHINA ELECTROTECHNICAL SOCIETY
Sup.2
2013
无线电能传输系统线圈偏移研究综述：
分析，效率提升与定位
严茂水
1, 2
, 廖承林 1 , 陶成轩 1 , 王丽芳
（1. 中国科学院电力电子与电力驱动重点实验室, 电工研究所
2. 中国科学院大学
摘要
北京
1
北京
100190
100190）
线圈偏移在实际无线电能传输系统中经常出现，而偏移可能造成系统传输效率下降和
系统不稳定。本文从理论计算线圈互感和传输效率以及仿真的角度对存在线圈偏移的无线电能传
输系统进行分析。据此，本文介绍了现有的效率提升方法。线圈设计和阻抗网络设计已证明能有
效地提升系统对线圈偏移的忍受度。本文还介绍了线圈定位技术，线圈定位可以使电动汽车更加
方便地停靠进行无线充电。
关键词：无线电能传输
线圈偏移
分析
效率
定位
中图分类号：TM72
A Review on Wireless Power Transfer Coil
Misalignment: Analysis, Efficiency Improvement
and Positioning
Yan Maoshui 1,2 , Liao Chenglin 1* , Tao Chengxuan 1 , Wang Lifang 1
（1. Key Laboratory of Power Electronics and Electrical Drives
Chinese Academy of Sciences
Beijing
2. University of Chinese Academy of Sciences
Abstract
Institute of Electrical Engineering,
100190
Beijing
China
100190
China）
Coil misalignment often takes place in practical wireless power transfer (WPT)
systems, which may cause decrease of transfer efficiency and system instability. This paper analyzes
coil-misaligned WPT system with theoretical calculation of mutual inductance and transfer effic iency
and simulation. Existing ways to improve system efficiency are hereby discussed. To overcome problems
from misalignment, efforts on coil design and impedance network design have demonstrated their
feasibility on raising system tolerance with coil misalignment. Current solutions for positioning of WPT
coils which could facilitate the parking of Electric Vehicles (EVs) for wireless charging are also presented.
Keywords: Wireless power transfer, coil misalignment, analysis, efficiency, positioning
1
Introduction
Wireless power transfer (WPT) is a promising
technology to be applied in many areas, such as
electric vehicle (EV) charging, implantable device
charging, due to its superiority on convenience of
being cordless, safety during high-power charging,
Supported by the Beijing Municipal Science and Technology Program
(D121100004512001)
Received May 23, 2013
*
Liao Chenglin is the corresponding author.
ability to work in wet and harsh environment. At
present, inductive coupling and magnetic resonant
coupling are two major means of wireless power
transfer. In both cases, power is transferred from a
transmitter coil to a receiver coil. Generally, the two
coils need to be well aligned to make the system work
电 工 技 术 学 报
2
2013 年
in its best state. However, in practice, misalignment
between them often takes place. Coil misalignment
may cause significant impact on the transfer efficiency of inductive WPT system and may lead to system
instability of magnetic resonant WPT system [1] .
This paper reviews the existing works on wireless power transfer coil misalignment. It starts by
presenting theoretical analysis and simulation analysis
Fig.1
of inductive WPT system and magnetic resonant WPT
Lateral coil misalignment configuration of
TX and RX coils
system. Then, it discusses the ways to improve
X. L. Huang et al utilized the equivalent circuit
efficiency of WPT system when coil misalignment
happens. Positioning of WPT coils are discussed and
the paper is concluded with comments on present
model in Fig.2a and deduced the formula for transfer
efficiency at the angular frequency [1] .
works and prospects on future works.
2
2.1

Pout
( M )2 RL

100%
Pin ZS[Z P ZS  ( M )2 ]
（3）
Analysis of WPT system with coil misalignment
Inductive WPT system with coil misalignment
Coil misalignment configurations of inductive
WPT are shown in Fig.1. The mutual inductance M
can be derived by solving the double integral in
（a）Model of inductive WPT system
Neumann’s formula [1]
M
N Tx N Rx 0
4π
lTx lRx
dlTx  dlRx
R
（1）
where NTx, NRx, l Tx , lRx, dlTx and dl Rx define the coil
turns, the length of each turn and infinitesimal of l of
the resonant Tx and Rx coils, respectively. R is the
（b）Model of magnetic resonant WPT system
distance between dl Tx and dl Rx, and µ0 is the magnetic
Fig.2
permeability of free-space. Wu Ying et al did some
further study and obtained the mutual inductance
formulas for circular (expessed as Eq. (2)) and
rectangular coils [2] .
N N 
M  Tx Rx 0
4π

2π
0
d 
2π
0
r1r2 cos  d
| r1  r2 |
Studies in Ref. [3] show that mutual inductance
between inductive WPT coils drops sharply when coil
misalignment increases. Perfect alignment between
coils is required to keep the transferred power within
（2）
In which r1  r1 cos x  r1 sin  y , r 2 =r 2 cos(   )
x  [r2 sin(   )  d ] y  hz , r1 and r2 are radii of the
primary and secondary coils, respectively.
Model of the WPT system
the desired limits [4].
2.2
Magnetic resonant WPT system with coil
misalignment
At present, three ways to calculate the mutual
inductance of magnetic resonant WPT coils have been
proposed. Takehiro Imura et al calculated the mutual
inductance with Neumann formula and demonstrated
it the same with electromagnetic field analysis results [5].
Shawon Senjuti [6] and Ki Young Kim [7] both adopted
the filament method, using Eq. (4), while the former
deduced a computational integration equation and
第 28 卷增刊 2
严茂水等
无线电能传输系统线圈偏移研究综述：分析，效率提升与定位
produced a graph of coupling coefficient and axial
3
distance, similar to that in Fig.3a.
M
0
π
r1r2 cos 
π
0
 ( )
V3
d
（4）
3
Efficiency improvement of coil-misaligned WPT system
Eq. (3) and Eq. (6) imply that mutual inductance
and equivalent impedance could do obvious impact on
Based on coupled-mode theory, the wireless
WPT system transfer efficiency and strong mutual
power transfer efficiency can be solely expressed as a
inductance and suitable equivalent impedance suggest
function of the figure of merit, i.e. U   /   S T 
1/ 2
,
1/ 2
where    M  2  LS LD   is the coupling coeffi

[8, 9]
cient
. Based on the equivalent circuit in Fig.2b,
the power transfer efficiency of magnetic resonant
WPT can be calculated by Eq. (5), where 21 is
defined as the ratio of power transmission and S 21 is
the transmitted wave ratio [10] .
on shapes, turns, winding methods and the orientations
of the two coils. Thus, efforts have been made to
optimize topology and parameters of the impedance
network and coil design.
3.1
Coil design
Circle and rectangle are common coil shapes
used in WPT systems. Referring to Fig.4a, “The
21  S212 100%
2 jMZ 0


2
 2 2 
1 


M

Z

R

j

L







0

C  



high efficiency. From Eq. (2) and Eq. (4), M depends
2

（5）


100%



experimental and calculated results show that the
rectangular coil is more effective for stabilizing the
coupling in the contactless power supply system for
moving apparatus” [2] . Y. Nagatsuka et al [13] developed
In general cases, when the distance between the
a rectangular double-sided windings transformer for
transmitter and receiver coil, i.e. the air gap between
inductive EV charger. Experimental results showed
the coils, is less than the diameter, transmission
that the novel transformer could transfer 1.5kW at
coefficient S 21 curve, similar to that in Fig.3a, will
high lateral misalignment (misalignment: x 45mm, y
exist[11]. And Fig.3b shows that magnetic resonant
125mm, coil size: 240×250mm) with transformer
WPT systems are more tolerant with coil axial
efficiency maintaining over 90% (seen in Fig.4b). In
misalignment [12].
mobile inductive systems, quadrature winding systems [14]
and poly-phase systems [15,
16]
has been developed to
allow high misalignment.
（a）Model of inductive WPT system
lateral misalignment/mm
（a）Coupling curves between different coils
（b）Model of magnetic resonant WPT system
Fig.3
Efficiency parameters with axial misalignment
x/mm
y/mm
（b）WPT parameters with x and y misalignment
Fig.4
Efficiency improvement with coil design
电 工 技 术 学 报
4
Magnetic resonant WPT systems with coils made
of magneto plated wire have been proved more
efficient
[17]
, and Takehiro Imura
[12]
2013 年
the source could operate safely with even higher
misalignment.
believes that 10
turns are more suitable than 5 turns for the EV charger
coils they designed in tolerating misalignments.
3.2
Impedance network design
Younghwan Kim et al inserted additional series
capacitor to the both resonant coils for magnetic
resonant WPT system to remain high efficiency with
（a）Equivalent circuit model of SPS compensated inductive
misalignment [18] (seen in Fig.5a, where C 1 and C 2 are
WPT system
self-capacitances of the resonant coils). Experimental
resonator transmission efficiency maintains over 80%
with 0cm to 20cm misalignment at 4.22 MHz, 6.1%
higher than conventional resonator (seen in Fig.5b).
（b）Comparison of transfer efficiencies with misalignment
（a）Equivalent circuit model of magnetic resonant WPT
Fig.6
Inductive WPT system with SPS impedance network
S. G. Lee et al made some effort to adjust
system with additional capacitor
parameters of magnetic WPT system impedance
matching circuit and found that when mismatch
between source impedance and load impedance is
eliminated, efficiency of the WPT system with 50%
axial-misalignment would increase by 48.4% [9].
4
Positioning of WPT coils
Positioning of WPT coils can be useful for
applications like EV charging. Parking a vehicle into
（b）Comparison of measured transmission efficiencies at
misalignment case
Fig.5
Magnetic resonant WPT system with
additional capacitor
Juan L. Villa et al proposed a series-parallelseries(SPS) compensation capacitor topology (seen in
Fig.6a) for inductive WPT system [4]. Experimental
system with the compensation topology could transfer
rated power with high misalignment (up to 25% for
the studied system) of the receiving coil width without
requiring a specific control and with high efficiency
(seen in Fig.6b). Moreover, the system showed that
the right place with precision can be burdensome for
some drivers, yet wireless charging requires well
alignment of coils.
At present, few works have been done on the coil
positioning. Palakon Kotchapansompote et al proposed an electric vehicle automatic stop system by using
magnetic resonant WPT antennas(coils) [11] . Power
pattern at different displacement of the antennas is
studied and an experimental model presenting the
relationship between the received power (transmission
coefficient, S 21) and lateral coil distance is built. To
calculate and control the receiving antenna position,
第 28 卷增刊 2
严茂水等
无线电能传输系统线圈偏移研究综述：分析，效率提升与定位
5
received power gradient (RPG), the differential of
coupling characteristics of contactless power supply
received voltage waveform amplitude (A) with respect
system
to position (d), dA/dd, is used as the reference signal.
Technology of Electrical Engineering and Energy,
A PI controller based on the model and RPG is
2005, 24 (3):5-8.
designed to bring the vehicle to the maximum power
[3]
for
moving
apparatus[J],
Advanced
Michael L G Kissin, John T Boys, Grant A Covic.
transfer point, position 2 in Fig.3a, and to the
Interphase mutual inductance in polyphase inductive
maximum received power point, position 3 in Fig.3a.
power transfer systems[J]. IEEE Trans. Ind. Electron.,
Experiments have demonstrated the feasibility of the
2009, 56(7): 2393-2400.
system and more works are needed to diminish the
[4]
position fluctuation.
Juan L Villa, Jesús Sallán, et al. High misalignment
tolerant compensation topology for ICPT systems[J].
Another positioning system is designed in Ref.[19].
System input impedance (SII), the overall impedance
IEEE Trans. Ind. Electron., 2012, 59(2): 945-951.
[5]
Takehiro Imura, Yoichi Hori. Maximizing air gap and
measured on the two ends of TX coil, which is related
efficiency of magnetic resonant coupling for wireless
to system operating frequency, lateral distance and the
power transfer using equivalent circuit and neumann
load resistance, is used to calculate the position of the
formula[J]. IEEE Trans. Ind. Electron., 2011, 58(10):
receiving antenna. A mapping table of SII, system
4746-4752.
operating frequency and lateral distance is established
[6]
Shawon Senjuti, Kyle Fricke, et al. Misalignment
(load resistance is preset). When the coils are
analysis of resonance-based wireless power transfer to
approaching, the controller looks up the mapping
biomedical implants, 25th IEEE Canadian Confe-
table with the real-time operating frequency and SII,
rence on Electrical and Computer Engineering, 2012:
thus obtaining the position of the receiving coil.
1-5.
5
[7]
Conclusion
Ki Young Kim, Young Ho Ryu, et al. Analysis of
misalignments in efficiency of mid-range magnetic
The works on WPT coil misalignment are
resonance wireless power link[C]. IEEE Antennas and
comprehensively reviewed in this paper. Theoretical
Propagation Society International Symposium, 2012:
calculations of mutual inductance and transfer effi-
1-5.
ciency for inductive and magnetic resonant WPT are
[8]
Andr´e Kurs, et al. Wireless power transfer via
presented, while methods for the latter still need more
strongly coupled magnetic resonances[J], Science,
validation. Efforts on improving transfer efficiency of
2007, 317: 83-86.
coil-misaligned WPT system are discussed and future
[9]
Lee S G, Hoang H, Choi Y H, et al. Efficiency
works on optimizing the coil design and impedance
improvement for magnetic resonance based wireless
network are required. The few works on positioning of
power
the coils are briefly described and more refined work
Electronics Letters, 2012, 48(6): 339-340.
transfer
with
axial-misalignment[J].
are necessary to make the techniques more practical
[10] Teck Chuan Beh, Masaki Kato, Takehiro Imura, et al.
and thus accelerating deployments of WPT system on
Wireless power transfer system via magnetic resonant
EV charging and other applications.
coupling at fixed resonance frequency-power transfer
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Brief notes：Yan Maoshui
male, born in 1989, graduate student. His
main research interest is wireless power transfer. Liao Chenglin
male,
associate professor, research interest: wireless power transfer and vehicle
electronics..