energies
Article
Analysis and Performance Improvement of WPT
Systems in the Environment of Single
Non-Ferromagnetic Metal Plates
Linlin Tan 1,2, *, Jiacheng Li 1,2 , Chen Chen 1,3 , Changxin Yan 1,2 , Jinpeng Guo 1,2 and
Xueliang Huang 1,2
1
2
3
*
Department of Electrical Engineering, Southeast University, No. 2 Sipailou, Nanjing 210096, China;
[email protected] (J.L.); [email protected] (C.C.); [email protected] (C.Y.);
[email protected] (J.G.); [email protected] (X.H.)
Jiangsu Key Laboratory of Smart Grid Technology and Equipment, Zhenjiang 212009, China
State Grid Jiangsu Economic Research Institute, Nanjing 210096, China
Correspondence: [email protected]; Tel.: +86-25-8379-4691 (ext. 815); Fax: +86-25-8379-1696
Academic Editor: Sheldon S. Williamson
Received: 29 March 2016; Accepted: 28 June 2016; Published: 25 July 2016
Abstract: Wireless power transfer (WPT) is greatly affected when the transmission channel is
surrounded by non-ferromagnetic metallic objects and the alternating magnetic field interacts with
the metal conductor, which is more of an issue in wirelessly charged electric vehicle (EV) applications.
This paper analyses the performances of a WPT system in an environment with a non-ferromagnetic
metal plate. The impedance model of the WPT system in the metal environment is established.
Moreover the variation law of a coil’s equivalent inductance and resistance is deduced when the coil
is surrounded by the non-ferromagnetic metal plate. Meanwhile, simulations, theory and experiments
all confirm that the model is correct. Finally, since the system performance of a wireless charging
system is influenced by non-ferromagnetic metals, this paper puts forward a method to improve the
performance, that is, to place ferrite cores between the receiving coil and a metal plate. Experiments
are carried out to verify the method, and the desired results are achieved.
Keywords: wireless power transfer; resonator; metal; impedance model; ferrite cores
1. Introduction
By using resonance and the coupling of magnetic fields and electric fields to transmit power,
WPT technology has many advantages over cable transmission. Currently it is widely used in
consumer electronics such as mobile phones, tablets, laptops, electric toothbrushes, hutch cables, TVs,
electric cars, electric buses and so on for charging devices and supplying power [1–8].
In terms of different application environments and fields, researchers at home and abroad have
conducted in-depth research and analysis [9–11]. Research shows that, in a certain transmission space,
a magnetic coupling resonant WPT system can achieve high power transfer efficiency (PTE) in the air
when the transmission channel is not surrounded by metal objects. The transmission channel actually
is not an ideal air transmission medium; there is more or less interference from different types of metal
objects. Some of these metal objects are interferences from external obstacles, while some are required
for improving system robustness. For example, in a wireless charging system for EVs (as shown in
Figure 1), a transmitting coil is generally placed in a parking space on the ground and a receiving coil
is installed in electric vehicle chassis that is composed of a metal plate of high strength. The existence
of the metal material changes the distribution of the magnetic field in the power transfer space,
and affects the wireless charging system. This effect includes two aspects: (1) the performance of the
Energies 2016, 9, 576; doi:10.3390/en9080576
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WPT
is reduced
or weakened,
leading
to lowered
transferred
powertoorlowered
PTE; (2)transferred
the model
(1)
thesystem
performance
of the
WPT system
is reduced
or weakened,
leading
using
air
as
a
medium
is
no
longer
accurate.
power or PTE; (2) the model using air as a medium is no longer accurate.
air-gap
connected rectifier
voltage stabilizing
charging circuit
Metal chassis
receiving coil
connect to power
ground
transmitting coil
Figure
Figure1.
1.The
Theinteraction
interactionbetween
betweenEVs
EVswireless
wireless charging
charging system
system and
and metal
metal plate.
plate.
At present, few researches have been conducted on the characteristics of magnetic coupling
At present, few researches have been conducted on the characteristics of magnetic coupling
resonance WPT systems under the influence of metal objects. To address the problem caused by the
resonance WPT systems under the influence of metal objects. To address the problem caused by the
existence of metal objects, an experimental analysis method is the one most frequently used to study
existence of metal objects, an experimental analysis method is the one most frequently used to study
the influences of external metal objects [12,13]. However, this method has great limitations, that is, it
the influences of external metal objects [12,13]. However, this method has great limitations, that is,
doesn’t effectively play a guiding role in system design and is only used as an auxiliary means to
it doesn’t effectively play a guiding role in system design and is only used as an auxiliary means to
analyze the performance.
analyze the performance.
Toshiba has proposed that measuring the reflection coefficient can decide whether a metal
Toshiba has proposed that measuring the reflection coefficient can decide whether a metal barrier
barrier exists between a transmitter and a receiver or not [14]. Reference [15] studies the influence of
exists between a transmitter and a receiver or not [14]. Reference [15] studies the influence of the
the application of an aluminum sheet in a WPT system, and analyses the influence on system
application of an aluminum sheet in a WPT system, and analyses the influence on system performance
performance when external metal objects exist in the system. In that paper, the reduction in PTE is
when external metal objects exist in the system. In that paper, the reduction in PTE is observed when a
observed when a small-size aluminum sheet is near the transmitting coil.
small-size aluminum sheet is near the transmitting coil.
In addition, KAIST scientists have reported that the amount of electromagnetic radiation of EVs’
In addition, KAIST scientists have reported that the amount of electromagnetic radiation of EVs’
wireless charging systems can be reduced by a reverse magnetic field produced through using a LC
wireless charging systems can be reduced by a reverse magnetic field produced through using a
resonant coil, and the reduction can reach 64%, while additional power input is not needed [16]. It is
LC resonant coil, and the reduction can reach 64%, while additional power input is not needed [16].
further studied and pointed out [17] that the use of double LC resonant coil shielding can improve
It is further studied and pointed out [17] that the use of double LC resonant coil shielding can improve
the shielding effectiveness (SE), and the resonance frequency is changed due to environmental
the shielding effectiveness (SE), and the resonance frequency is changed due to environmental changes
changes and subsequently the PTE is lowered. By comparing the PTE of two-coil structures with
and subsequently the PTE is lowered. By comparing the PTE of two-coil structures with aluminum
aluminum plates and that of two-coil structures without aluminum plates, it is concluded that
plates and that of two-coil structures without aluminum plates, it is concluded that aluminum’s
aluminum’s effect on reflection coefficient is the main reason for the lowered PTE; by comparing the
effect on reflection coefficient is the main reason for the lowered PTE; by comparing the PTE of
PTE of a four-coil structure with aluminum plate and that of a four-coil structure without aluminum
a four-coil structure with aluminum plate and that of a four-coil structure without aluminum plate,
plate, it is evident that aluminum’s effect on conductor loss is the main factor causing the decrease in
it is evident that aluminum’s effect on conductor loss is the main factor causing the decrease in PTE,
PTE, while, aluminum exerts relatively little effects on the PTE of a four-coil system [18]. A study
while, aluminum exerts relatively little effects on the PTE of a four-coil system [18]. A study done
done by Osaka Industrial University [19] used ferrite cores and a metal plate conductor
by Osaka Industrial University [19] used ferrite cores and a metal plate conductor simultaneously to
simultaneously to improve the electromagnetic field of a WPT system which is calculated by the
improve the electromagnetic field of a WPT system which is calculated by the Ampere’s Law, but this
Ampere’s Law, but this paper does not analyze the modeling of WPT systems with metal plates. By
paper does not analyze the modeling of WPT systems with metal plates. By defining a SE formula,
defining a SE formula, a University of L’Aquila in Italy work analyses absorption loss, reflection loss
a University of L’Aquila in Italy work analyses absorption loss, reflection loss and additional effects of
and additional effects of multiple reflections and transmissions, and finally draws the conclusion
multiple reflections and transmissions, and finally draws the conclusion that the magnetic material
that the magnetic material helps to improve the coupling. The conclusion is verified by experiments
helps to improve the coupling. The conclusion is verified by experiments and simulation in a 20 kHz
and simulation in a 20 kHz system [12,20]. Based on the TEM wave theory, Lawson and others [21]
system [12,20]. Based on the TEM wave theory, Lawson and others [21] analyzed how the PTE of a
analyzed how the PTE of a WPT system varies with the frequency when a ferrite material exists in
WPT system varies with the frequency when a ferrite material exists in the system.
the system.
When metal objects exist, there is always a deviation between the theoretical analysis based on
When metal objects exist, there is always a deviation between the theoretical analysis based on
current models and experimental results. The alternating magnetic field from the transmitting coil
current models and experimental results. The alternating magnetic field from the transmitting coil
and the receiving coil, and the metal conductor produce electromagnetic induction coupling and
and the receiving coil, and the metal conductor produce electromagnetic induction coupling and
eddy current occurs in metal objects. The eddy current in metal objects creates an induced magnetic
eddy current occurs in metal objects. The eddy current in metal objects creates an induced magnetic
field which affects the original magnetic field, thus changing coil impedance and the resonant
circuit. Therefore, the existence of metal objects breaks down system’s original “electric resonance”
Energies 2016, 9, 576
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state,
so thataffects
WPT the
system
maymagnetic
not work
properly
or its system
performance
be deteriorated
field which
original
field,
thus changing
coil impedance
andmay
the resonant
circuit.
substantially.
In
addition,
since
the
existence
of
eddy
current
increases
eddy
current
losses
when
Therefore, the existence of metal objects breaks down system’s original “electric resonance”
state,
so
power
is
transmitted,
it
further
aggravates
the
deterioration
of
system
performance.
The
impacts
of
that WPT system may not work properly or its system performance may be deteriorated substantially.
metal
objects
on
systems
are
more
complex,
since
these
are
influenced
collectively
by
permeability,
In addition, since the existence of eddy current increases eddy current losses when power is transmitted,
conductivity,
geometry
of the metalofobjects,
geometric parameters
of ofresonator
coils,onworking
it further aggravates
the deterioration
system performance.
The impacts
metal objects
systems
frequency
and
other
parameters.
are more complex, since these are influenced collectively by permeability, conductivity, geometry of
In sum,
previous
research
has failed
to build coils,
a resonance
transfer
modelparameters.
under the
the metal
objects,
geometric
parameters
of resonator
workingpower
frequency
and other
influences
of previous
metal objects.
It has
has failed
also failed
to adiscuss
the power
influences
of metal
on
In sum,
research
to build
resonance
transfer
model objects
under the
transmission
parameters
such
as
system
power,
efficiency
and
resonant
frequency.
Both
the
influences of metal objects. It has also failed to discuss the influences of metal objects on transmission
theoretical
experimental
aspectsefficiency
of this problem
need further
study. Both
This paper
mainly deals
parametersand
such
as system power,
and resonant
frequency.
the theoretical
and
with
two
problems:
how
to
cope
with
the
influences
of
metal
plates
on
the
system
and
how
to
build
an
experimental aspects of this problem need further study. This paper mainly deals with two problems:
accurate
model
of
it.
how to cope with the influences of metal plates on the system and how to build an accurate model of it.
2.
2. The
TheInfluence
Influenceof
ofaaSingle-Side
Single-SideMetal
MetalPlate
Plateon
on Coil
Coil Parameters
Parameters
Single-Turn Coil
2.1. Influence of a Single-Side Metal Plate on a Single-Turn
Coil
a metal
plate
on coils,
we firstly
analyze
the influence
of theof
metal
In order
order to
toanalyze
analyzethe
theeffect
effectofof
a metal
plate
on coils,
we firstly
analyze
the influence
the
plate on
a single
turn coil,
this
and we
work
out the
of theofmetal
plateplate
on a
metal
plate
on a single
turnand
coil,on
and
onbasis,
this basis,
and
we work
outinfluence
the influence
the metal
multi-turn
coil with
help
the superposition
method.method.
The coil The
radius
is radius
a. The angular
on
a multi-turn
coilthe
with
theofhelp
of the superposition
coil
is a. Thefrequency
angular
frequency
of the current
of the
is ω.
current
The line
is ω.crossing
The linethe
crossing
centralthe
point
central
of the
point
coilof
and
thevertical
coil and
tovertical
the coilto
surface
the coil
is
surface
as the
z axis.
The
metal
plate isat
placed
z =the
0 and
the relative
position
theiscoil
definedisasdefined
the z axis.
The
metal
plate
is placed
z = 0 at
and
relative
position
of the of
coil
z = is
d,
zwhich
= d, which
is displayed
in Figure
The thickness
the metal
τ is
the volume
resistivity
is displayed
in Figure
2. The2.thickness
of the of
metal
plate isplate
h. Ifisτ h.
is If
the
volume
resistivity
of the
of
the sheet,
then
theresistivity
area resistivity
ζ can
be described
sheet,
then the
area
ζ can be
described
by τ/h.by τ/h.
Z
single-turn coil
single-turn coil
a
d
h/2
O
metal plate
-h/2
Figure 2. Position
Position distributions
distributions of single turn coil and metal plate.
According
tothe
thevector
vector
symmetry,
a cylindrical
coordinate
the magnetic
vector
According to
symmetry,
in a in
cylindrical
coordinate
system,system,
the magnetic
vector potential

A
potential
A
generated
by
the
coil
current
and
generated
by
eddy
current
are
only
in
the
direction
1
A generated by the coil current and A generated by eddy current are only in the direction of φ, so this
of
so this
is in z axis
symmetrical.
Since the
electromagnetic
of  , in
is in z, axis
symmetrical.
Since
the electromagnetic
field
is independentfield
of φ, is
in independent
cylindrical coordinates,
cylindrical
if B
indicateinduction
the direction
of magnetic
induction
intensity
ρ
if Bρ is usedcoordinates,
to indicate the
direction
of to
magnetic
intensity
ρ generated
by the coil
carrying
ρ is used
current, so:by the coil carrying current, so:
generated
n
8
ÿ
2jζ B n Aφ
2ζ
1
n
Aφ ` Aφ “  p´
q nA n « j
B
(1)
2µω
jζ  Bz
2ζµω ρ

“1( 
A +A n
)

j
B
(1)
μω zn
μω ρ
n 1
Because the magnetic vector potential of eddy current is symmetrical around a metal plate, then:
Because the magnetic vector potential of eddy current is symmetrical around a metal plate, then:
2ζ
A1φ pρ, zq “ ´Aφ pρ, ´zq ` j
Bρ pρ, ´zq
(2)
2ζ
µω
A (ρ, z)   A (ρ, z)  j
Bρ (ρ, z)
(2)
μω
Equation (2) shows that the eddy currents induced by the metal plate are approximately
equivalent to a mirror electromagnetic field generated by the coil at the far side. This field has two
Energies 2016, 9, 576
4 of 16
Equation (2) shows that the eddy currents induced by the metal plate are approximately equivalent
to a mirror electromagnetic field generated by the coil at the far side. This field has two components.
One component is the magnetic flux density of the image coil with equal and opposite current. The
other component is B field produced by the image coil with a quadrature current of amplitude
proportional to 2ζ{ωµ.
The coil voltage ∆V induced by the electromagnetic field generated by the eddy current of the
metal plate can be expressed as:
.
∆V “ ´jωp2πaqA1φ pa, dq
(3)
According to the Equation (2), Aφ and Bρ represent the magnetic vector potential and magnetic
induction intensity generated by current per unit running through coil respectively. Through further
simplification, it can be obtained that:
∆Z “
.
∆.V
I
“ jω∆L ` ∆R
“ jωr2πaAφ pa, ´dqs `
(4)
4πaζ
µ Bρ pa, ´dq
∆L represents the self-inductance variation and ∆R represents the effective series resistance variation
changed by the presence of the metal plate. Also, the magnetic vector potential Aφ (ρ,´z) is:
µ
Aφ pρ, ´zq “
2π
in which:
c
a
Gpkq
ρ
(5)
$
Gpkq “ p 2k ´ kqKpkq ´ 2k Epkq
’
’
’
’
’
c
’
’
’
4aρ
’
& k“
2
2
pa`ρq `pz´dq
(6)
şπ{2
’
’
’
K “ 0 ? dψ
’
’
1´k2 sin2 ψ
’
’
’
a
’
ş
%
π{2
E“ 0
1 ´ k2 sin2 ψdψ
from Equations (4)–(6), we can conclude that:
$
∆L “ aµGp ? 2a 2 q
’
’
a `d
’
’
&
a2 `2d2
∆R “ ? 2ζd
r´Kpkq ` ?
Epkqs
a2 `d2
a2 `d2
’
’
’
’
% k“ ? a
2
2
(7)
a `d
2.2. Influence of a Single-Side Metal Plate on Multi-Turn Coil
In practical applications, a coil with several turns wound with Litz wire is commonly used to
increase the inductance. On the basis of the analysis in Section 2.1, superposition method can be
applied to calculate the variations of both ∆L and ∆R of a coil with N turns:
$
N
N
ř
ř
’
’
∆Li ` 2 ∆Mij
’
& ∆L “
i “1
N
’
ř
’
’
∆Ri
% ∆R «
i “1
i‰ j
(8)
Energies 2016, 9, 576
5 of 16
N
N

5 of 16
L   Li  2 Mij

i 1
i j
(8)

N
R  R

i

The proximity effect and the skin effect
are
ignored
for the calculation of ∆R as long as the
i 1
Energies 2016, 9, 576
constraints shown in Equation (9) [22,23] and Equation (10) [24] are satisfied:
The proximity effect and the skin effect are ignored for the calculation of ΔR as long as the
$ and Equation (10) [24] are satisfied:
constraints shown in Equation (9) [22,23]
h
’
& Dď 3
 bh
D
’
2
% h “ 3
2π f µ µ γ
(9)
0 r

2

h

$
2πfμ 0dμ`
γ
r D ´ xq
& e “ sinhkpkDq coshp
2
%

k
sinh( kD)
(9)
(10)
d
2
k2e“ j2π f µ0 µrcosh(
γ
 D  x)

(10)
 k 2 inner
where D represents the diameter of every
stranded wire, h denotes the skin depth of
j 2πfμ 0flexible
μr γ

the wire. F stands for the current frequency. µ0 is the magnetic permeability of free space and equals
where
represents
every inner
flexible stranded
wire, to
h denotes
the the
skinconductivity.
depth of
to 4π ˆ
10´7DH/m.
µr isthe
thediameter
relative of
magnetic
permeability.
γ is used
represent
the wire. F stands for the current frequency. μ0 is the magnetic permeability of free space and equals
E is used to denote
current density factor. d is the space between any two inner flexible stranded wires.
to 4π × 10−7 H/m. μr is the relative magnetic permeability. γ is used to represent the conductivity. E is
x shows
the
exact
position
of the wire.
used to denote current density factor. d is the space between any two inner flexible stranded wires.
Inx shows
this paper,
theposition
relative
magnetic
the exact
of the
wire. permeability of the Litz wire is µr = 1 and the electric
7 S/m. The diameter of each inner flexible stranded wire is D = 0.05
conductivity
is γpaper,
= 5.8 ˆ
In this
the10
relative
magnetic permeability of the Litz wire is μr = 1 and the electric
mm. The
calculated
ranges
0 toof200
kHz
according
to Equation
conductivity
is γ frequency
= 5.8 × 107 S/m.
The from
diameter
each
inner
flexible stranded
wire is(9).
D =Furthermore,
0.05 mm.
The calculated
frequency
ranges
from 0frequency
to 200 kHz
according
Equation
(9). the
Furthermore,
according
to Equation
(10) when
current
ranges
from to
0 to
200 kHz,
variation of
according
Equation
(10) when
current
ranges from
200inner
kHz, flexible
the variation
of current
current
density to
can
be neglected
when
the frequency
spacing between
each0 to
two
stranded
wires is
can be
neglected
when
the can
spacing
between each two inner flexible stranded wires is 0–0.05
0–0.05density
mm. Thus
the
proximity
effect
be ignored.
mm. Thus the proximity effect can be ignored.
3. Modeling and Experimental Research of WPT Systems with a Single-Side Metal Plate
3. Modeling and Experimental Research of WPT Systems with a Single-Side Metal Plate
3.1. Modeling and Parameter Idetification of Systems with a Single-Side Metal Plate
3.1. Modeling and Parameter Idetification of Systems with a Single-Side Metal Plate
A magnetic resonant WPT system includes a transmitting coil and a receiving coil, which are
A magnetic resonant WPT system includes a transmitting coil and a receiving coil, which are
placed coaxially, as shown in Figure 3. The transmitting coil has N1 turns wound in a circle of radius a.
placed coaxially, as shown in Figure 3. The transmitting coil has N1 turns wound in a circle of radius
The receiving
coil has
Nhas
wound
in aincircle
ofof
radius
metalplate
plateisis
parallel
to the
2 turns
a. The receiving
coil
N2 turns
wound
a circle
radiusb.b. The
The metal
parallel
to the
coilscoils
and the
distance
from
the
metal
plate
to
the
transmitter
and
that
from
the
plate
to
the
receiver
and the distance from the metal plate to the transmitter and that from the plate to the receiver are c are
c and d,
respectively.
and
d, respectively.
Z
transmitting coil
b
c
a
d
receiving coil
h/2
O
-h/2
Figure
3. Position
relation
betweentwo
two coils
coils and
Figure
3. Position
relation
between
andthe
themetal
metalplate.
plate.
The impact of the metal plate on inductance L, mutual inductance M and resistance R can be
calculated according to Equation (8). If there is no metal plate, the mutual inductance between the
transmitting coil and the receiving coil can be described by:
?
M0 “ µN1 N2 abGp
d
4ab
2
pa ` bq ` pc ´ dq2
q
(11)
transmitting coil and the receiving coil can be described by:
M0  μN1 N2 abG(
4ab
)
( a  b)  (c  d)2
(11)
2
Energies 2016, 9, 576
6 of 16
If there is a metal plate, the mutual inductance can be described as:
N1 N
2
If there is a metal plate, the
mutual
inductance can be described
as:
4ab
M   Mij M0  μ abG(
M“
N
N
i 11 ÿ
j 21
ÿ
?
( a  b)2  (c  d)2
d
)
(12)
4ab
∆Mij “M0 ´ µ abGp
(12)
q
2
pa
`
bq
`
pc
´
dq
systems with metal
1
i“1 j“circuit
equivalent
2
In conclusion, the
model of
plates can be obtained, as
displayed inInFigure
4. Apart from the equivalent model of systems without metal plates, Figure 4
conclusion, the equivalent circuit model of systems with metal plates can be obtained,
also shows
the equivalent
ofequivalent
systems model
usingofair
as a medium.
To simplify
the4analysis,
as displayed
in Figurecircuit
4. Apartmodel
from the
systems
without metal
plates, Figure
also shows
the equivalent
circuit
systems
using
as a medium.coil
To simplify
the analysis,
the mutual
inductance
between
the model
metalofplate
and
theair
transmitting
is neglected.
The mutual
the
mutual
inductance
between
the
metal
plate
and
the
transmitting
coil
is
neglected.
The
mutual
inductance between the metal plate and the closer coil and the mutual inductance between the
the metal plate and the closer coil and the mutual inductance between the two
two coilsinductance
are takenbetween
into consideration.
coils are taken into consideration.
R3
L3
R1
VS
M13
R2
M23
L1
L2
RL
M12
C1
C2
Figure 4. System equivalent circuit with metal plate.
Figure 4. System equivalent circuit with metal plate.
In Figure 4, R3 represents the loss of metal plates caused by magnetic field. L3 denotes the
equivalent
of the metal
plate.ofCircuit
matrix
equation
is then
by:field. L3 denotes
Figure 4, inductance
R3 represents
the loss
metal
plates
caused
by expressed
magnetic
In
equivalent inductance of the metal plate. Circuit. Tmatrix
. T equation is then expressed by:
the
Z¨ I “ V
(13)
T
T
(13)
Z  I fi
V
»
R1 ` jX1
jωM12
jωM13
”
ı
”
ı
T . T
T
.
.
.
.
—
ffi . T
where
R2 ` R L ` jX
– jωM12jωM
 RZ
=jX
jω2M13jωM
 23 fl, I “ I 1 I 2 I 3 , V “ V s 0 0 ,
1
1
12
T
T

 jX
jωM
jωM
R `
where Z =  jωM12 R2 13 RL  jX2 23 jωM233  , I3T   I1 I 2 I 3  , V T  Vs 0 0  ,
X1 = ωL1 ´ 1/(ωC1 ), X2 = ωL2 ´ 1/(ωC2 ), X3 = ωL3 .
Since
jωMthe
jωM23
R
 jX3 the metal plate and the transmitting coil is neglected,
between
13 mutual inductance
3
M « 0. The currents in each circuit loop can be calculated by solving Equation (13) and thus, can be
X1 = ωL1 −131/(ωC1), X2 = ωL2 − 1/(ωC2), X3 = ωL3.
described by:
$ .
`the metal2 plate
˘ ´1 . and the transmitting coil is neglected,
Since the mutual inductance between
I 1 “ Z22 Z33 ´ Z23
ξ Vs
’
’
’
’
M13 ≈ 0. The currents in each circuit loop
by solving Equation (13) and thus, can be
& . can be calculated
.
´
1
(14)
I 2 “ ´Z12 Z33 ξ V s
described by:
’
’
’
’
.
% .
´1 V 2
Z
Z
ξ
12
13
II3 “
 Z Z  Zs ξ 1V


22 33
23
s
 12
1
where
“ Z11 Z22 Z33 ´
´Z
Z
;
impedance
of
the
transmitting coil Z11 “ R1 ` jX1 ;
13
 I 212 Z12 Z33ξ Vs
impedance of the receiving coil Z22 “
R
`
R
`
jX
;
impedance
of the metal plate Z33 “ R3 ` jX3 ;
 I 2 Z LZ ξ 21V
mutual impedance between the transmitting
and
12 coil
13
s the receiving coil Z12 “ Z21 “ jωM12 ;

 3
ξ´1
where
2
Z11 Z23
(14)
mutual impedance between the transmitting coil and the metal plate Z13 “ Z31 “ jωM13 ; mutual
1
and the metalofplate
23 “ Z32 “ jωM
23 . Z  R  jX ; impedance
; impedance
theZtransmitting
coil
ξimpedance
 Z Z between
Z  Zthe
Z2receiving
 Z2 Z coil
11
22
33
11
23
12
13
11
1
1
of the receiving coil Z22  R2  RL  jX2 ; impedance of the metal plate Z33  R3  jX3 ; mutual
impedance between the transmitting coil and the receiving coil Z12  Z21  jωM12 ; mutual
Energies 2016, 9, 576
7 of 16
impedance between the transmitting coil and the metal plate Z13  Z31  jωM13 ; mutual impedance
between the receiving coil and the metal plate Z23  Z32  jωM23 .
Energies 2016, 9, 576
7 of 16
According to Equations (8) and (13), the influence of the metal plate on the receiving coil can
be
represented by:
According to Equations (8) and (13), the influence of2 the metal plate on the receiving coil can be
 ωM23  L0
represented by:
$L 
2
pωM q2 L 2
’
’
∆L « ωM 2323 2 0R2 0
&
(15)

pωM23 q `
2 R0
(15)
ωM 23 2 R0


’
R « pωM23 q2 R0
’
%∆R
22
M 2323q2 `RR

 ωpωM
00

Power loss caused by eddy currents is described by:
Power loss caused by eddy currents is described by:
ˇ . ˇ2
ˇ ˇ2
(16)
P0P“ ˇ I 3I ˇ RR0
(16)
0
3
0
System
Systemtransferred
transferredpower
powerand
andPTE
PTEcan
canbe
becalculated
calculatedby:
by:
ˇ . ˇ22
$

ˇI ˇ R
’
ˇ I2 ˇ R LL
’

’
η

ˇ
ˇ
ˇ
ˇ
ˇ . ˇ2 2
η
“
’
2
.
.
2
2
&

ˇ ˇ
ˇ ˇ2
ˇ ˇ
R2 `RR
I 3 ˇI R0 R
ˇ
L q`
I1 ˇ I 1Rˇ 1R1 `Iˇ2I 2 ˇ pR


2
L
3
0

’
2
’
ˇ
ˇ
’
2 
 P  0.5 I 2 ˇ .  R
’
%
 P “ 0.5 ˇ I ˇˇ LpR
q
2
(17)
(17)
L
3.2.
3.2.Simulation
Simulationand
andExperimental
ExperimentalResearch
ResearchofofaaCoil
Coilwith
withaaSingle-Side
Single-SideMetal
MetalPlate
Plate
On
Onthe
thebasis
basisofoftheoretical
theoreticalanalysis,
analysis,simulation
simulationaided
aidedby
byCOMSOL
COMSOLisiscarried
carriedout
outto
toanalyze
analyzethe
the
parameter
variations
of
the
receiving
coil
working
in
an
environment
with
metal
plates,
as
shown
parameter variations of the receiving coil working in an environment with metal plates, as showninin
Figure
coils
areare
employed
in this
research.
Coils
are are
tightly
wound
so that
the
Figure5a.
5a.Circular
Circularplate
platespiral
spiral
coils
employed
in this
research.
Coils
tightly
wound
so that
turn-to-turn
distance
is negligible.
Coil Coil
parameters
are specifically
tabulated
in Table
1. 1.
the turn-to-turn
distance
is negligible.
parameters
are specifically
tabulated
in Table
Vector network analyzer
Transmitting coil
coil
Receiving coil
Aluminum plate
Aluminum plate
(a)
(b)
Figure5.5.(a)
(a)Simulation
Simulationmodel;
model;(b)
(b)Experiment
Experimentmodel.
model.
Figure
Table 1. Coil parameters.
Table 1. Coil parameters.
Parameter
Parameter
External radius
Inner radius
External radius
Inner radius
Coil turns N
Coil turnsWire
N diameter
Wire diameter
Frequency f
Frequency f
Inner resistance R
Inner resistance R
Value
20 cmValue
16 cm20 cm
10 16 cm
2 mm 10
73 kHz2 mm
73 kHz
0.05 Ω
0.05 Ω
A 3 mm thick and 30 cm long square plate made of aluminum is used in the simulation. The
A
mm thick and
30atcm
plate
made ofdielectric
aluminum
is used
the
electric3conductivity
is set
3.5long
× 107square
S/m and
the relative
constant
as in
well
as simulation.
the relative
The electric conductivity is set at 3.5 ˆ 107 S/m and the relative dielectric constant as well as the
relative magnetic permeability is 1. The system is driven by a source working at 73 kHz so that a
compensated capacitor of 120 nF is chosen.
Energies 2016, 9, 576
8 of 16
magnetic permeability is 1. The system is driven by a source working at 73 kHz so that a
of 120 nF is chosen.
8 of 16
To validate the theoretical and simulating results, experimental prototype using the receiving
coil and the metal plate introduced above is designed and displayed in Figure 5b. The values of
To validate the theoretical and simulating results, experimental prototype using the receiving coil
receiving coil inductance measured by theoretical calculations according to Equation (8), and by
and the
metal
Energies
2016,plate
576 introduced above is designed and displayed in Figure 5b. The values of8receiving
16
COMSOL,
by 9,experimental
calculations are 40.67, 39.938, and 40.68 μH, respectively. The of
deviation
coil inductance measured by theoretical calculations according to Equation (8), and by COMSOL,
between
the simulation is
value
andsystem
the theoretical
value
is 0.03%
while
the
deviation
between
magnetic permeability
1. The
is and
driven
by µH,
a source
workingThe
at deviation
73 kHz sobetween
that a the
by experimental
calculations are
40.67,
39.938,
40.68
respectively.
the compensated
measured capacitor
value and
the
theoretical
value
is
1.8%,
and
both
deviations
demonstrate
of 120 nF is chosen.
simulation value and the theoretical
value is 0.03% while the deviation between the measured value
acceptable
To precision.
validate the theoretical and simulating results, experimental prototype using the receiving
and the theoretical value is 1.8%, and both deviations demonstrate acceptable precision.
Theoretical
calculation,
simulation
andis experimental
measurement
are 5b.
employed
to quantify
coil
and the metal
plate introduced
above
designed and displayed
in Figure
The values
of
Theoretical
calculation,
simulation
and
experimental
measurement
are
employed
to quantify
receiving
coil
inductance
measured
by
theoretical
calculations
according
to
Equation
(8),
and
by
the influence of the metal plate on the receiving coil inductance is specifically displayed in Figure 6.
the influence
ofbythe
metal platecalculations
on the receiving
coil
inductance
is μH,
specifically
displayed
in Figure 6.
experimental
are 40.67,
39.938,
40.68
respectively.
The deviation
TheCOMSOL,
metal plate
is
placed at different
distances
from
theand
receiving
coil.
Both the simulation
and the
The metal
plate
issimulation
placed at value
different
distances
from value
the receiving
coil.
Both
the
simulation
and the
between
the
and
the
theoretical
is
0.03%
while
the
deviation
between
experimental results validate the correctness of theoretical analysis. It also indicates that the farther
experimental
resultsvalue
validate
correctness
theoretical
analysis.both
It also indicatesdemonstrate
that the farther
the measured
and the
theoretical ofvalue
is 1.8%,
the metal
plate is moved
awaythe
from
the receiving coil,
the lessand
influencedeviations
it brings about.
acceptable
the metal
plate precision.
is moved away from the receiving coil, the less influence it brings about.
compensated
Energies
2016, 9, 576capacitor
Inductance(μH)
Inductance(μH)
Theoretical calculation, simulation and experimental measurement are employed to quantify
the influence of the metal plate on the receiving coil inductance is specifically displayed in Figure 6.
The metal plate is placed at different distances from the receiving coil. Both the simulation and the
experimental results validate the correctness of theoretical analysis. It also indicates that the farther
the metal plate is moved away from the receiving coil, the less influence it brings about.
Cal.result
Distance from the coil of the metal plate(cm)
Figure
Effect
of different
distances
between
the receiving
coil and coil
the metal
platemetal
on theplate
coil inductance.
Figure6. 6.
Effect
of different
distances
between
the receiving
and the
on the
coil inductance.
Cal.result
In this paper, the metal plate is placed near the receiving coil. Considering the distance between
the coil of the metal plate(cm)
the metal plate and the transmittingDistance
coil isfrom
large
enough (d ≥ 6 cm), the influence of the metal plate on
In this paper, the metal plate is placed near the receiving coil. Considering the distance between
Figure 6. Effect
of different
distances on
between
the receiving
and analysis.
the metal plate
on the that
coil inductance.
the transmitting
coil
can be ignored
the basis
of the coil
above
It shows
neglecting M13 is
the metal plate and the transmitting coil is large enough (d ě 6 cm), the influence of the metal
reasonable. If we replace the aluminum plate with a copper one, we can get the same results.
plate on In
thethis
transmitting
coilplate
can isbeplaced
ignored
the basiscoil.
of Considering
the above analysis.
shows that
paper, the metal
near on
the receiving
the distanceItbetween
Consequently,
non-ferromagnetic
materials
with
different electric
conductivities
have the same
neglecting
M
is
reasonable.
If
we
replace
the
aluminum
plate
with
a
copper
one,
we
the metal 13
plate and the transmitting coil is large enough (d ≥ 6 cm), the influence of the metal plate can
on get
influences on coil parameters.
the same
results. Consequently,
non-ferromagnetic
different
electric
conductivities
the transmitting
coil can be ignored
on the basis ofmaterials
the above with
analysis.
It shows
that neglecting
M13 is have
Based on If
theweprototype
shown in Figure 5b, the effect of frequency on the inductance of the
reasonable.
the aluminum plate with a copper one, we can get the same results.
the same
influences
onreplace
coil parameters.
receiving
coil is analyzed
and illustrated
in Figure
7, whichelectric
shows the changing cure
of
receiving
Consequently,
materials
with 5b,
different
have
thethe
same
Based
on thenon-ferromagnetic
prototype shown
in Figure
the effect ofconductivities
frequency on
the
inductance
coil’s
inductance
vs.
frequency
measured
by
a
Vector
Network
Analyzer
(Rohde
&
Schwarz
influences
on coil
of the
receiving
coilparameters.
is analyzed and illustrated in Figure 7, which shows the changing cure
Technology
Germany).
It can
be 5b,
seen
when
the distance
between
the of
metal
BasedCo,
on Munich,
the prototype
shown in
Figure
thethat
effect
of frequency
on the
inductance
the plate
of the receiving coil’s inductance vs. frequency measured by a Vector Network Analyzer
coil is analyzed
and illustrated
Figure
7, which shows
the changing
cure of the receiving
andreceiving
the receiving
coil is fixed,
receivingincoil’s
inductance
remains
almost unchanged
regardless of
(Rohde & Schwarz Technology Co, Munich, Germany). It can be seen that when the distance between
coil’s inductance
by proportional
a Vector Network
Schwarz
frequency
variation. vs.
Thefrequency
influencemeasured
is inversely
to theAnalyzer
distance (Rohde
between&the
metal plate
the metal
plate and
the
receiving
coil isItfixed,
receiving
coil’s
inductance
remains
almost
unchanged
Technology
Co,
Munich,
Germany).
can
be
seen
that
when
the
distance
between
the
metal
plate
and the receiving coil, which can be clarified by the fact that a smaller d leads to a larger ΔL.
regardless
frequency
The influence
is inversely
proportional
to the distance
between
and theofreceiving
coilvariation.
is fixed, receiving
coil’s inductance
remains
almost unchanged
regardless
of
the metal
platevariation.
and the The
receiving
coil,
which can
be clarified
by distance
the fact between
that a smaller
d leads
frequency
influence
is inversely
proportional
to the
the metal
plate to a
largerand
∆L.the receiving coil, which can be clarified by the fact that a smaller d leads to a larger ΔL.
Figure 7. Effect of frequency on inductance parameters of the receiving coil.
Figure 7. Effect of frequency on inductance parameters of the receiving coil.
Figure 7. Effect of frequency on inductance parameters of the receiving coil.
Energies 2016, 9, 576
Energies 2016, 9, 576
Energies 2016, 9, 576
9 of 16
9 of 16
9 of 16
3.3.
Simulation and
and Experimental
Experimental Research
3.3. Simulation
Research of
of WPT
WPT System
System with
with aa Single-Side
Single-Side Metal
Metal Plate
Plate
3.3. Simulation and Experimental Research of WPT System with a Single-Side Metal Plate
On the basis
basis of
of the
the analysis
analysisabove,
above,our
ourexperimental
experimentalprototype
prototypewith
witha asingle-side
single-side
metal
plate
metal
plate
is
On the basis
of the analysis
above,
our
experimental
prototype
withofathe
single-side
metalcoil
plate
is
is
constructed
as
shown
in
Figure
8.
In
this
prototype,
the
parameters
transmitting
and
constructed as shown in Figure 8. In this prototype, the parameters of the transmitting coil and those
constructed
as
shown
in
Figure
8.
In
this
prototype,
the
parameters
of
the
transmitting
coil
and
those
those
the receiving
coilas
areshown
as shown
in Table
1. The
metal
plate
introducedininSection
Section3.2
3.2isis used.
used.
of theofreceiving
coil are
in Table
1. The
metal
plate
introduced
of the receiving
are as shown
in Table
1. The metal
plate introduced in Section 3.2 is used.
According
to the coil
simulation
result and
the experimental
measurement
results shown in Figure 8 as
According
to the(12),
simulation
result and
the experimental
results
shown
in Figure
8 as
well
as Equation
the relationship
between
the mutualmeasurement
inductance and
the metal
plate
distance
is
well
as
Equation
(12),
the
relationship
between
the
mutual
inductance
and
the
metal
plate
distance
is
calculated and displayed in Figure 9.
calculated and displayed in Figure 9.
DC power
DC power
Control Circuit
Control Circuit
Aluminum plate
Aluminum plate
Load
Load
Inverter
Inverter
Transmitting coil
Transmitting coil
(a)
(a)
Receiving coil
Receiving coil
(b)
(b)
Figure 8.
8. (a) Simulation
model; (b)
(b) Experiment model.
model.
Figure
Figure 8. (a)
(a) Simulation
Simulation model;
model; (b) Experiment
Experiment model.
4
4
3.5
3.5
3
3
No metal plate
No metal plate
Calculated value
Calculated value
mutual
inductance(μH)
mutual
inductance(μH)
2.5
2.5
2
2
1.5
1.5
Experiment value
Experiment value
simulation value
simulation value
1
1
0.5
0.5
0
00
0
1
2
3
4
5
6
7
8
1 The distance
2
5
7 plate(cm)
8
of3between4the receiving
coil6 and metal
9
9
10
10
The distance of between the receiving coil and metal plate(cm)
Figure 9. Effect of metal plate’s distance on the mutual inductance between coils.
Figure 9.
9. Effect
Effect of
of metal
metal plate’s
plate’s distance
distance on
on the
the mutual
mutual inductance
inductance between
between coils.
coils.
Figure
The distance of 0 cm in Figure 9 indicates that the metal plate does not exist. The experimental
The distance of 0 cm in Figure 9 indicates that the metal plate does not exist. The experimental
measurements
areof
also
included
here,
presenting
a consistent
result.does
A larger
distance
to
The distance
0 cm
in Figure
9 indicates
that
the metal plate
not exist.
The contributes
experimental
measurements are also included here, presenting a consistent result. A larger distance contributes to
a larger mutualare
inductance
between
transmitting
coil and result.
the receiving
coil,
which contributes
indicates a
measurements
also included
here,the
presenting
a consistent
A larger
distance
a larger mutual inductance between the transmitting coil and the receiving coil, which indicates a
smaller
influence
the metal between
plate on the transmitting
system. This coil
is why
gap is usually
set between
the
to
a larger
mutualof
inductance
andan
theairreceiving
coil, which
indicates
a
smaller influence of the metal plate on the system. This is why an air gap is usually set between the
receiving
coil and of
thethe
EVs
chassis
toon
enhance
PTE for
charging
smaller
influence
metal
plate
the system.
This
is why EVs.
an air gap is usually set between the
receiving coil and the EVs chassis to enhance PTE for charging EVs.
The coil
changes
of EVs
transferred
and
PTE
accordance
receiving
and the
chassis topower
enhance
PTE
for in
charging
EVs. to distance variations can be
The changes of transferred power and PTE in accordance to distance variations can be
measured on the basis of Figure 8b. In the experiment, the distance between the transmitting coil and
measured on the basis of Figure 8b. In the experiment, the distance between the transmitting coil and
the receiving coil remains at 6 cm. A system with no ferrite cores or metal materials is used to power
the receiving coil remains at 6 cm. A system with no ferrite cores or metal materials is used to power
Energies 2016, 9, 576
10 of 16
The changes of transferred power and PTE in accordance to distance variations can be measured
on
the
basis of Figure 8b. In the experiment, the distance between the transmitting coil and
the
Energies 2016, 9, 576
10 of 16
receiving coil remains at 6 cm. A system with no ferrite cores or metal materials is used to power a load
of
2 Ω, of
and
theand
transferred
power power
and theand
PTE
are
10 W
80%
respectively,
which which
are taken
the
a load
2 Ω,
the transferred
the
PTE
areand
10 W
and
80% respectively,
areas
taken
reference
values
to
normalize
the
performance
of
a
system
with
a
metal
plate,
as
displayed
in
Figure
as the reference values to normalize the performance of a system with a metal plate, as displayed10.
in
Similar
to Figure
theFigure
metal 9,
plate
not used
theused
distance
0 cm.
It can be
Figure 10.
Similar9, to
theismetal
platewhen
is not
whenisthe
distance
is 0concluded
cm. It canthat
be
there
is a continuous
in both transferred
and PTE when
theand
distance
increases.
In other
concluded
that thereincrease
is a continuous
increase inpower
both transferred
power
PTE when
the distance
words,
the In
effect
of words,
the metal
declining.
metal plate
is placed
at a distance
1.5 cm
increases.
other
theplate
effectis of
the metalWhen
platethe
is declining.
When
the metal
plate is of
placed
at
away
from
the
receiving
coil
(quite
close
to
the
receiving
coil),
transferred
power
is
extremely
low
a distance of 1.5 cm away from the receiving coil (quite close to the receiving coil), transferred power
due
to the influences
metal
plate, while,
PTEplate,
is approximately
3.2%,
can be mainly
is extremely
low dueoftothe
the
influences
of the the
metal
while, the PTE
is which
approximately
3.2%,
caused
by the
fact that
the existence
of that
the metal
plate leads
tometal
the detuning
of the
receiving
coil.
which can
be mainly
caused
by the fact
the existence
of the
plate leads
to the
detuning
of
This
would
definitely
have
an
adverse
influence
on
system
operations
and
exacerbate
system
the receiving coil. This would definitely have an adverse influence on system operations and
performance.
Therefore,
in orderTherefore,
to addressinthis
problem,
WPTthis
systems
withWPT
a single-side
metala
exacerbate system
performance.
order
to address
problem,
systems with
plate
shouldmetal
be improved
and optimized.
single-side
plate should
be improved and optimized.
1
No metal plate
0.8
P/P0
0.6
η/η0
0.4
0.2
0
0
1
2
3
4
5
6
7
8
9
10
The distance of between the receiving coil and metal plate(cm)
Figure 10.
10. Effect
Effect of
of metal
metal plate‘s
plate‘s distance
distance on
on transferred
transferred power
power and
and PTE
PTE of
of systems.
systems.
Figure
4. Performance
4.
Performance Improvement
Improvement of
of WPT
WPT System
System with
with aa Single-Side
Single-Side Metal
Metal Plate
Plate
4.1. Application
Application of
of Ferrite
Ferrite Cores
Cores and
and Its
Its Effect
Effect on
on the
the Receiving
Receiving Coil
Coil
4.1.
The metal
metal plate
plate is
is supposed
supposed to
to absorb
absorb the
the magnetic
magnetic field
field so
so the
the coil
coil inductance
inductance decreases
decreases
The
accordingly. As
As aa result,
result, itit is
is necessary
necessary to
to reduce
reduce the
the effect
effect of
of the
the metal
metal plate
plate on
on coils
coils by
by limiting
limiting the
the
accordingly.
electromagnetic
field
intensity.
Several
ferrite
cores
are
placed
between
the
receiving
coil
and
the
electromagnetic field intensity. Several ferrite cores are placed between the receiving coil and the metal
metal
plate,
through
which
the
electromagnetic
field
in
a
close
region
can
be
enhanced.
As
a
result,
plate, through which the electromagnetic field in a close region can be enhanced. As a result, the
the leakage
is reduced
both self-inductance
mutual are
inductance
increased.
leakage
field isfield
reduced
and bothand
self-inductance
and mutualand
inductance
increased.are
Nevertheless,
Nevertheless,
the
use
of
ferrite
cores
produces
power
loss
due
to
eddy
current.
The
power
loss to
is
the use of ferrite cores produces power loss due to eddy current. The power loss is proportional
2
2
proportional
to electric
σ and frequency
f . Consequently,
materialsare
with
small
electric
conductivity
σ and conductivity
frequency f . Consequently,
materials
with small conductivity
preferred
conductivity
are The
preferred
improve
The
ferrite
used in
the paper
a DMR95
Mn-Zn
to
improve PTE.
ferritetocores
usedPTE.
in the
paper
arecores
a DMR95
Mn-Zn
with are
specific
dimensions
3@100 kHz,
3 @100
with
specific
dimensions
of 7 standard
cm × 2 cmpower
× 0.5 cm.
standard
power
loss
is 300
of
7 cm
ˆ 2 cm
ˆ 0.5 cm. The
lossThe
is 300
mW/cm
kHz,
200mW/cm
mT, much
smaller
200 mT, much smaller than that of metal materials whose conductivity is 3500–4500@(80–120 kHz).
As a result, power loss caused by the eddy current is extremely low.
According to Figure 5a, the COMSOL simulation model of a system consisting of a receiving
coil, a metal plate and ferrite cores placed between them is shown in Figure 11. The magnetic field
Energies 2016, 9, 576
11 of 16
than that of metal materials whose conductivity is 3500–4500@(80–120 kHz). As a result, power loss
caused by the eddy current is extremely low.
According
Energies
2016, 9, 576to Figure 5a, the COMSOL simulation model of a system consisting of a receiving
11coil,
of 16
Energies 2016, 9, 576
11 of 16
a metal
plate and ferrite cores placed between them is shown in Figure 11. The magnetic field intensity
intensity
at the
ofisthe
coil is displayed.
The distance
between
the metal
platethe
andreceiving
the receiving
at
the center
of center
the coil
displayed.
The distance
between
the metal
plate and
coil
intensity at the center of the coil is displayed. The distance between the metal plate and the receiving
1.5and
cm the
andexcitation
the excitation
current
is 1 A.
iscoil
1.5iscm
current
is 1 A.
coil is 1.5 cm and the excitation current is 1 A.
①
①
Aluminum plate
Aluminum plate
⑥
⑥
⑤
⑤
③
③
φ
φ
eddy current loss
eddy current loss
Ferrite cores
Ferrite cores
φa
φa
Coils
Coils
④
④
(a)
(a)
②
②
(b)
(b)
Figure11.
11.System
Systemmodel
modelwith
withferrite
ferritecores:
cores:(a)
(a)2D
2Dmodel;
model;(b)
(b)3D
3Dsimulation
simulationmodel.
model.
Figure
Figure 11.
System model
with ferrite
cores: (a)
2D model;
(b) 3D
simulation model.
When ferrite cores are not used, the magnetic field intensity is around 25 μT as shown in
When
ferrite
cores
are not
the magnetic
field intensity
is aroundis25around
µT as shown
12. in
When
ferrite
cores
areused,
not used,
the magnetic
field intensity
25 μTinasFigure
shown
Figure 12. With the increase in the number of ferrite cores, the magnetic field intensity increases
With
the increase
theincrease
numberin
of the
ferrite
cores,ofthe
magnetic
obviously,
to
Figure
12. Withinthe
number
ferrite
cores,field
the intensity
magneticincreases
field intensity
increases
obviously, to about 39 μT by 56% when six ferrite cores are used. Since self-inductance of the coil is
about
39 µT by
when
sixby
ferrite
cores are
the coil is proportional
obviously,
to 56%
about
39 μT
56% when
six used.
ferriteSince
cores self-inductance
are used. Since of
self-inductance
of the coil is
proportional to the magnetic field intensity, so the application of the ferrite cores is a feasible way to
to proportional
the magnetictofield
intensity, field
so the
application
ofapplication
the ferrite cores
a feasible
way
to enhance
the magnetic
intensity,
so the
of the is
ferrite
cores is
a feasible
way to
enhance the self-inductance.
theenhance
self-inductance.
the self-inductance.
(a)
(a)
(b)
(b)
Figure 12. (a) Magnetic field distribution; (b) Magnetic changing curve vs. numbers of ferrite cores.
Figure
Magnetic
field
distribution;
Magnetic
changing
curve
numbers
of ferrite
cores.
Figure
12.12.
(a)(a)
Magnetic
field
distribution;
(b)(b)
Magnetic
changing
curve
vs.vs.
numbers
of ferrite
cores.
According to the analytical results above, the simulation and experimental results of the
According to the analytical results above, the simulation and experimental results of the
relationship
between
coil’s self-inductance
andthe
thesimulation
number of and
ferrite
cores when the
metal
According
to thethe
analytical
results above,
experimental
results
ofplate
the
relationship between the coil’s self-inductance and the number of ferrite cores when the metal plate
is not used are
illustrated
in Figure
13, which and
shows
moreofferrite
a larger
relationship
between
the coil’s
self-inductance
thethat
number
ferritecores
corescontribute
when the to
metal
platecoil
is
is not used are illustrated in Figure 13, which shows that more ferrite cores contribute to a larger coil
inductance.
Six
ferrite
cores,
whose
sequence
numbers
represent
different
locations,
are
used
as
not used are illustrated in Figure 13, which shows that more ferrite cores contribute to a larger coil
inductance. Six ferrite cores, whose sequence numbers represent different locations, are used as
shown in Figure
11a, cores,
and the
inductance
is increased
to 46 μH different
by 15%. It
should be
that
there
inductance.
Six ferrite
whose
sequence
numbers represent
locations,
arenoted
used as
shown
shown in Figure 11a, and the inductance is increased to 46 μH by 15%. It should be noted that there
is
only
one
ferrite
core
in
each
location,
for
example,
sequence
⑤
represents
that
a
ferrite
core
in Figure 11a, and the inductance is increased to 46 µH by 15%. It should be noted that there is onlyis
is only one ferrite core in each location, for example, sequence ⑤ represents that a ferrite core is
placed
at the
5 represents that a ferrite core is placed at the
one
ferrite
coreposition
in each ⑤.
location, for example, sequence placed at the position ⑤.
If the
5 power loss is ignored, the results in Figures 6 and 13 demonstrate that proper distribution
position
.
If the power loss is ignored, the results in Figures 6 and 13 demonstrate that proper distribution
of ferrite
cores can
increase
while 6the
plate has that
an adverse
impact on of
it.
If the power
loss is
ignored,the
theinductance
results in Figures
andmetal
13 demonstrate
proper distribution
of ferrite cores can increase the inductance while the metal plate
has an adverse impact on it.
0.5, the
According
to
the
resonant
frequency
determined
by
f
=
1/2π(LC)
use
of
ferrite
cores
which
ferrite cores can increase the inductance while the metal plate has an adverse
impact on it. According
According to the resonant frequency determined by0.5f = 1/2π(LC)0.5, the use of ferrite cores which
leads
to the increase
in inductance
in a decrease
resonant
frequency.
the
to
the resonant
frequency
determinedalso
by f results
= 1/2π(LC)
, the useofofthe
ferrite
cores which
leadsOn
to the
leads to the increase in inductance also results in a decrease of the resonant frequency. On the
contrary, the metal plate which results in the decrease in inductance increases the resonant
contrary, the metal plate which results in the decrease in inductance increases the resonant
frequency. As a consequence, the proper distribution of a number of ferrite cores is able to eliminate
frequency. As a consequence, the proper distribution of a number of ferrite cores is able to eliminate
the influence brought by the metal plate completely, which is vital to system stability. The metal
the influence brought by the metal plate completely, which is vital to system stability. The metal
plate is placed at a distance of 1.5 cm apart from the receiving coil, and the ferrite cores are added
plate is placed at a distance of 1.5 cm apart from the receiving coil, and the ferrite cores are added
one by one in the sequence as illustrated by Figure 11, the simulation results and the measured
one by one in the sequence as illustrated by Figure 11, the simulation results and the measured
Energies 2016, 9, 576
12 of 16
Coil inductance(μH)
increase in inductance also results in a decrease of the resonant frequency. On the contrary, the metal
plate which results in the decrease in inductance increases the resonant frequency. As a consequence,
the proper distribution of a number of ferrite cores is able to eliminate the influence brought by the
metal plate completely, which is vital to system stability. The metal plate is placed at a distance of
1.5 cm apart from the receiving coil, and the ferrite cores are added one by one in the sequence as
Energies 2016, 9, 576
12 of 16
illustrated by Figure 11, the simulation results and the measured results are tabulated in Table 2.
①②③
④⑤
①②
①②③
④⑤⑥
①②③
Exp. result
Sim. result
Number of magnetic cores
Figure
Figure13.
13.Effect
Effectof
offerrite
ferritecores
coreson
oninductance
inductanceparameters
parametersof
ofthe
thereceiving
receivingcoil.
coil.
Table
Table2.
2.Receiving
Receivingcoil’s
coil’sparameter
parametervariation.
variation.
Coil Inductance (μH)
Resonant Frequency (kHz)
Coil Inductance (µH)
Resonant Frequency (kHz)
Ferrite
Cores
Simulation
Measured
Simulation
Measured
Ferrite Cores
Simulation Values
Simulation
Values
Measured
ValuesMeasured Values
Values
Values
Values Values
23.401
94.98
94.7594.75
None None
23.401
23.42 23.42
94.98
①
28.48
86.09
85.9785.97
1
28.48
28.56 28.56
86.09
①②
1 2
30.57
83.08
83.0183.01
30.57
30.59 30.59
83.08
1 2 3 4 ①②③④
34.25
34.17 34.17
78.51
34.25
78.51
78.3978.39
1 2 3 4 ①②③④⑤
5
35.76
35.20
76.83
35.76
35.20
76.83
76.8276.82
1 2 3 4 ①②③④⑤⑥
5 6
39.65
40.04
72.96
39.65
40.04
72.96
72.9572.95
The
further validate
validatethe
thefeasibility
feasibilityofofoffsetting
offsettingthe
theinfluence
influence
a metal
plate
The results
results in
in Table
Table 22 further
ofof
a metal
plate
by
by
using
ferrite
cores.
It should
be noted
the needed
ferrite
coresinchanges
in
using
ferrite
cores.
It should
be noted
that thethat
needed
number number
of ferrite of
cores
changes
accordance
accordance
with the
distancebetween
variations
the metal
plate
and the
receiving coil.
with the distance
variations
thebetween
metal plate
and the
receiving
coil.
4.2.Comparative
ComparativeExperiments
Experimentson
onPerformance
PerformanceofofSystems
Systemswith
withand
andwithout
without Ferrite
Ferrite Cores
Cores
4.2.
Systemperformance
performanceenhancement
enhancementby
byusing
usingmagnetic
magneticmaterials
materials(ferrites)
(ferrites)isisfurther
furtherinvestigated.
investigated.
System
thetransferred
transferredpower
powerand
andthe
thePTE
PTEare
areset
setas
asbenchmarks
benchmarkswhen
whenthe
thesystem
systemhas
hasno
nometal
metalor
orferrite
ferrite
IfIfthe
materialbetween
betweentwo
twocoils
coilsand
andin
insurrounding
surroundingareas,
areas,by
bynormalizing
normalizingmeasured
measuredresults
resultsfor
foraasecond
second
material
time, we can
curve
of PTE
andand
that that
of transferred
powerpower
in accordance
to the distance
time,
can get
getthe
thevariation
variation
curve
of PTE
of transferred
in accordance
to the
betweenbetween
the metalthe
plate
andplate
the receiving
coil as shown
Figurein14.
distance
metal
and the receiving
coil asinshown
Figure 14.
According to Figure
thethe
increase
of ferrite
cores,cores,
the influence
of metalofplate
on plate
receiving
According
Figure14,
14,with
with
increase
of ferrite
the influence
metal
on
coils
is
weakened,
and
the
optimum
is
achieved
in
a
certain
condition.
When
the
optimal
state
receiving coils is weakened, and the optimum is achieved in a certain condition. When the optimalis
reached,
the enhancement
effect of effect
ferriteof
cores
on the
inductance
of receiving
and the
weakening
state
is reached,
the enhancement
ferrite
cores
on the inductance
of coil
receiving
coil
and the
effect of metal
plate
on receiving
offset coils
each offset
other,each
and the
system
is insystem
a resonance
again.
weakening
effect
of metal
plate oncoils
receiving
other,
and the
is in a state
resonance
Suchagain.
as Figure
1.5 cm, is
the
cores isofabout
for a5–6;
distance
state
Such14,
as when
Figurethe
14, distance
when theisdistance
1.5number
cm, theofnumber
cores 5–6;
is about
for a
of 3.5 cm,
is about is
4–5;
for a4–5;
distance
of 6cm, the
number
is about is
3–4.
When
number
distance
ofthe
3.5 number
cm, the number
about
for a distance
of 6cm,
the number
about
3–4.the
When
the
of cores of
is optimal,
the influence
of metal of
plate
on plate
receiving
coils can coils
be basically
offset. Atoffset.
this time,
number
cores is optimal,
the influence
metal
on receiving
can be basically
At
transferred
power andpower
PTE had
90% in the
presence
ofpresence
metal plate.
Of course,
is course,
difficult
this
time, transferred
andreturned
PTE hadtoreturned
to 90%
in the
of metal
plate.itOf
therebecause
are losses
in both
the metal
plate
the plate
ferriteand
cores,
as
ittoisrecover
difficultcompletely,
to recover because
completely,
there
are losses
in both
theand
metal
the such
ferrite
eddy current
or current
hysteresis
etc. With the
increase
in the
of in
ferrite
cores, theofeffect
of
cores,
such asloss
eddy
lossloss,
or hysteresis
loss,
etc. With
thenumber
increase
the number
ferrite
cores, the effect of ferrite cores on a receiving coil plays a major role, which sets WPT systems in a
state of disharmony, so the transferred power and PTE of WPT systems are decreased again. When
the transmission distance is 6cm, the system input voltage, output voltage and current waveforms
are shown in Figure 15.
Energies 2016, 9, 576
13 of 16
ferrite cores on a receiving coil plays a major role, which sets WPT systems in a state of disharmony,
so the transferred power and PTE of WPT systems are decreased again. When the transmission distance
is Energies
6cm, the
system
2016,
9, 576 input voltage, output voltage and current waveforms are shown in Figure1315.
of 16
1
1
Optimum cores number
P/P0
0.8
0.8
Optimum cores number
0.6
η/η0
0.6
P/P0
η/η0
0.4
0.4
0.2
0.2
0
0
0
1
2
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
Number of magnetic cores
Number of magnetic cores
(a)
(b)
Optimum cores number
P/P0
η/η0
Number of magnetic cores
(c)
Figure 14. Experimental results: (a) The distance between metal plate and receiving coil is 3.5 cm;
Figure
14.distance
Experimental
(a) The
metal
plate
and receiving
coil isplate
3.5 cm;
(b) The
betweenresults:
metal plate
and distance
receiving between
coil is 6 cm;
(c) The
distance
between metal
(b)and
Thereceiving
distancecoil
between
metal
plate
and
receiving
coil
is
6
cm;
(c)
The
distance
between
metal
plate
is 1.5 cm.
Energies 2016, 9, x
14 of 16
and receiving coil is 1.5 cm.
(a)
(b)
(a)
(b)
Figure 15. Cont.
Energies 2016, 9, 576
14 of 16
(a)
(b)
(c)
(d)
Figure
When
metal
plate
is 6cm
away
the receiving
coil, input
current-voltage
and
Figure
15.15.
When
thethe
metal
plate
is 6cm
away
fromfrom
the receiving
coil, input
current-voltage
and output
output current-voltage waveforms vary with different numbers of cores: (a) without cores; (b) with 8
current-voltage waveforms vary with different numbers of cores: (a) without cores; (b) with 8 cores;
cores; (c) with 6 cores; (d) with 3 cores.
(c) with 6 cores; (d) with 3 cores.
In summary, the aforementioned results demonstrate that by using a strong magnetic
In summary,
the aforementioned
demonstrate
that by coil
using
a strong magnetic
conductive
conductive
material
placed between results
metal objects
and receiving
reasonably,
we can reduce
the
material
and
receiving
coilmaximize
reasonably,
we can reduce the effect of metal
effect ofplaced
metal between
objects onmetal
WPTobjects
systems
effectively
and
PTE.
objects on WPT systems effectively and maximize PTE.
5. Discussion
5. Discussion
Problems caused by metal materials have to be tackled to guarantee applications of WPT
Problemsin caused
by metal
materials
to smart-phones,
be tackled to intelligent
guaranteehousehold
applications
of WPT
technology
many fields,
such as
charginghave
for EVs,
appliances,
technology
in
many
fields,
such
as
charging
for
EVs,
smart-phones,
intelligent
household
appliances,
other relevant industries and so on. The magnetic field caused by metals results in a decrease of
other
relevant
industriesInand
so on. the
Themodeling
magneticand
fieldanalysis
caused in
bysuch
metals
results in a decrease
of system
system
performance.
addition,
a complicated
environment
are
performance.
In addition,
and analysis
in such afield,
complicated
environment
hard
hard to implement
sincethe
it modeling
includes coupling
of magnetic
electric field
and heatare
field.
to Researches
implementaddressing
since it includes
coupling
of magnetic
field, electric
fieldintends
and heat
Researches
these issues
are still
at the beginning.
The paper
to field.
improve
PTE of
WPT systems
in still
the environment
with The
metal
materials
and
thePTE
influence
these
addressing
theseworking
issues are
at the beginning.
paper
intends
to reduce
improve
of WPTofsystems
metal materials
on system performance.
working
in the environment
with metal materials and reduce the influence of these metal materials on
be more specific, a non-ferromagnetic metal plate is used in this paper to simulate the
systemTo
performance.
working
environment
metal materials.
A basic
analysis
completed
and corresponding
To be more
specific, awith
non-ferromagnetic
metal
plate is
used inisthis
paper to simulate
the working
solutions towith
improve
are proposed.
High-frequency
magnetic
conductive materials
areto
environment
metal PTE
materials.
A basic analysis
is completed
and corresponding
solutions
employed
and
the
system
performance
is
obviously
enhanced
by
their
proper
distribution,
which
improve PTE are proposed. High-frequency magnetic conductive materials are employed and the
provides
a feasibleis way
to tackle
problems
in aproper
WPT distribution,
system withwhich
a single
side ametal
plate.
system
performance
obviously
enhanced
by their
provides
feasible
way
Meanwhile,
quantitative
analysis
is
not
carried
out
due
to
the
complexity
of
the
system
working
in is
to tackle problems in a WPT system with a single side metal plate. Meanwhile, quantitative analysis
environment with metal materials, so simulation combined with experimental verification is
notthe
carried
out due to the complexity of the system working in the environment with metal materials,
widely used in the paper, causing difficulties in system design. Moreover, the use of magnetic
so simulation combined with experimental verification is widely used in the paper, causing difficulties
in system design. Moreover, the use of magnetic materials increases the overall costs. The compromise
between reducing expenses and developing technology to improve system performance is what we
need to consider in future research. Anyway, the performance improvement of WPT systems working
in the environment with metal materials is of great significance to promote the wide applications of
WPT technology.
6. Conclusions
This paper studies the effect of non-ferromagnetic metal plates on resonant WPT systems, and
establishes an impedance model containing metal plates. Through comparing the model calculation
results, the simulation results and the experimental results, which are in accord with each other,
we verify the correctness of the model. When a non-ferromagnetic metal material exists around coils,
the intrinsic resonant frequency is lowered, and the effect caused by the metal material around the
coil produces eddy current loss, which is not conducive to the effective transmission of the energy
Energies 2016, 9, 576
15 of 16
system. Therefore this paper uses the magnetic characteristics of the magnetic material, and rebuilds
the circulation channel for magnetic field between the metal plate and coils, thus weakening its effect
on the coils. By means of theoretical analysis and experiment, this paper proves the correctness of
this approach.
The performance improvement of WPT systems with metal is not only a complicated math
problem, but also a key problem which needs to be solved urgently practical application. This paper
only investigates systems with non-ferromagnetic metal plates, but our research results provide
certain reference values in irregular metal system modeling, and a feasible solution to improve system
performance in the metal environment.
Acknowledgments: This work was supported in part by National Nature Science Youth Foundation of China
(No. 51507032), Nature Science Youth Foundation of Jiangsu Province (No. BK20150617), the Fundamental
Research Funds for the Central Universities, and Science and Technique Project Funds of State Grid Jiangsu
Electric Power Company (No. J2016021).
Author Contributions: Linlin Tan designed the model and performed the calculations and experiments.
Linlin Tan, Xueliang Huang and Jiacheng Li proposed the research topic and analyzed the data. Chen Chen,
Jinpeng Guo, and Changxin Yan helped write part of the simulation programs. All authors contributed to the
writing of the manuscript, and have read and approved the final manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
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