Analysis of Relay Effect on Wireless Power Transfer
1
Sadegh Khaleghiand
2
Hamed Aliabadi,
1
Mahdi Zarif
1
Department of Electrical Engineering, Mashhad branch, Islamic Azad University, Mashhad, Iran
2
Department of Electrical Engineering, Neyshabur branch, Islamic Azad University, Neyshabur, Iran
Key
words: Witricity, Wireless Power Transfer, Magnetic Resonant Coupling.
Abstract: Witricity, the technology of wireless power transfer (WPT) over a limited distance via coupled magnetic
resonances in the non-radiative near-field, has been the center of researcher’s attention over the recent years.
As the main concern about this technology, there has been great effort to transfer electricity over longer
distances using resonant coil (Relay). However, despite all benefits and advantages of the resonant coils, they
bring about some undesirable effects on the system which have never been considered to date. This paper
provides an analysis on the results of a system with the resonant frequency of 2.8 MHZ.
1 INTRODUCTION
In 1889 wireless power transmission (WPT) was
demonstrated by Nikola Tesla. He succeeded to
transfer electricity to about a few miles. Wireless
power transfer-based on strong magnetic coupling,
known as witricity, has been considered by the MIT
university researchers in 2007 because of its
reasonable benefits and efficiency. The MIT
researchers successfully transferred about 60 Watt
over a distance of 7 feet (A. Tucker, 2013), (D.
Gallichi Nottiani, 2012), (F. Zhang, 2009). Thanks to
the recent significant progresses in this technology,
the witricity has extended its applications to many
other industries such as “feeding implant units” (X.
Liu, F. Zhang, 2009),” feeding Endoscopy Capsuls”,
by making them smaller and portable (free-motion)
(F. Tianjia Sun, 2007), charging Electric Vehicle
wirelessly ((S. Li, 2014), (S. Sabki, 2007)), robotic
industry, charging cell phones, wireless sensor
networks, and RFID technology (J. Wang, 2010).
In this paper we try to analyze the effect of
resonant coils on the transfer system. It will be
discussed in this paper that while these coils increase
the system efficiency, but they produce undesirable
effects on the transfer systems. One of the main topics
which has not yet been considered is mutual
inductance in receiving and sending systems by the
resonant relay.
This mutual inductance affects the main circuit
(sender and receiver) inductance according to the
position (location) of the resonant relay. Such
changes in the system inductance deteriorate the
resonant state of the system and weaken the
efficiency.
This issue needs even more attention when the
position of the resonant relay is not fixed and it moves
between the receiver and sender.
A transfer system with resonant frequency of 2.78
has been designed and analyzed in this paper. The
resonant frequency in each circuit is calculate using
1
2.
rp
p
p
f
L
C
π
=
1
2.
rs
s
s
f
L
C
π
=
1
2.
rt
tt
f
LC
π
=
(1)
To allow WPT the resonant frequency must be the
same in all the circuits.
Figure 1: Scheme of relayed witricity system.
Figure 2: Thevenin equivalent circuit model.
554
Zarif M., Aliabadi H. and Khaleghi S..
Analysis of Relay Effect on Wireless Power Transfer.
DOI: 10.5220/0005539005540557
In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), pages 554-557
ISBN: 978-989-758-122-9
Copyright
c
2015 SCITEPRESS (Science and Technology Publications, Lda.)
According to the coupling transformers principle, to
a have resonant circuit, the product of inductance and
capacitance in the circuits must be equal (T.
Mohamadi, 2011).
...
rp rs rt p p s s t t
f
ff LCLCLC
=
==⎯⎯→==
(2)
To solve and analyze the circuit, the KVL law is
applied to the Thevenin equivalent circuit of figure
2.
1
()
1, 2 1, 3
1
1
0()
2,1 2,3
0
1
()
3,1 3,2
R j lp jM jM
p
c
Ip
V
p
jM R j l jM I
s
ss
c
s
I
t
jM jM R R j lp
lt
c
t
ωω ω
ω
ωω ω
ω
ωω ω
ω
+− − −
=− +− −
−−++−
(3)
Where, IP is current in the primary circuit, is
denotes the current in the secondary circuit, It is
current in the receiver circuit, and R1, R2, R3 indicate
internal circuit resistances.
Due to the symmetric state of the system, i.e. M1,
2=M2, 1, M1, 3=M3, 1, and M2, 3=M3,2) and by
replacing the self-impedance with Z factor, the
following equation is obtained:
1,2 1,3
1
0
2,1 2,3
0
3,1 3,2
ZjMjM
I
p
V
p
jM Z jM I
s
s
I
t
jM jM Z
t
ωω
ωω
ωω
−−
=− −
−−
(4)
By solving equation (4), the current of each
circuit of each circuit is computed as:
22
..
2,3
.
1
22 2 22 3
.M . . . . . 2 . .
1,3 2, 3 1, 2 1, 2 1,3 2,3
ZZ M
pt
IV
p
ZZMZZZMiMMM
pp ptt
ω
ωω ω
+
=
++++
(5)
22
(.. ) . .
1, 2 2, 3 1, 3
.
1
22 2 22 3
.M . . . . . 2 . .
1, 3 2, 3 1, 2 1, 2 1, 3 2, 3
iZ M M M
t
IV
s
ZZMZZZMiMMM
pp ptt
ωω
ωω ω
−
=
++++
(6)
2
i( . . ) . .
1, 3 1, 2 2,3
.
1
22 2 22 3
.M . . . . . 2 . .
1, 3 2 ,3 1, 2 1, 2 1, 3 2, 3
ZM MM
p
IV
t
ZZMZZZMiMMM
pp ptt
ωω
ωω ω
−
=
++++
(7)
By calculating the current of the each coil, the produced and
consumed powers are obtained,
2
.
2
P
RI
s
s
=
,
.I
11
PV
p
=−
,
2
.
3
P
RI
L
t
=
(8)
Where, P1 is t power produced by his source. By
replacing the current in the equation (8) and
calculating the power for each circuit, the efficiency
of the whole system is obtained:
33
2
.
21 1
PP
P
PP P
η
==
(9)
2
2
i( . . ) . .
1, 3 1, 2 2, 3
..
1
22 2 22 3
.M . . . . . 2 . .
1, 3 2, 3 1, 2 1, 2 1,3 2 ,3
22
(. . )
2,3
2
.
1
22 2 22 3
.M . . . . . 2 . .
1, 3 2, 3 1, 2 1, 2 1, 3 2 ,3
ZM MM
p
VR
L
ZZMZZZMiMMM
pp ptt
ZZ M
pt
V
ZZMZZZMiMMM
pp ptt
ωω
ωω ω
η
ω
ωω ω
−
++++
=
−+
++++
(10)
(
)
(
)
2
2
.i( .. ) . .
1, 3 1, 2 2 , 3
22 22 2 22 3
(. . ) .M .. . .. 2 . .
2,3 1,3 2,3 1,2 1,2 1,3 2,3
RZM MM
Lp
ZZ M Z Z M ZZZ M iM M M
pt p p pt t
ωω
η
ωωω ω
−+
=
+++++
(11)
At the resonant frequency, the capacitive and
inductive parts of the circuit eliminate and the circuit
is purely resistive. Hence, the maximum efficiency is:
max:
:
f
r
r
ZR
pp
at f Z R
ss
ZRR
ttL
η
=
=⎯⎯⎯⎯→
=+
(12)
() ()()
max
2
2
.i( .. ) . .
1, 3 1,2 2 , 3
22 22 2 22 3
(. . ) .M .. . .. 2 . .
2,3 1,3 2,3 1,2 1,2 1,3 2, 3
RRM MM
p
L
R RR M R R M R RR RR M iMM M
pt p p pt tLLL
ωω
η
ωω ω ω
−+
=
++ + + +++ +
(13)
2 EXPERIMENTAL RESULTS
These tests are carried out on three different types of
topologies in witricity and results also show a clear
relationship and the validity between the theory and
the formulas have been obtained before. We have also
carried out a comparative study between the three
types of series, parallel and topology modify without
the resonant ring which can be found in each test in
terms of power quality the results of each methods.
By doing experimental tests on these three different
topologies mentioned before, as shown in figure 3.
These three types of topologies have just used in the
transmitter side of experiment. However, the
topology of the receiver is fixed in all three tests also
20 cm distance between transmitter and receiver is
considered and resonant ring moves between the two
parts(transmitter and receiver) which is shown by the
symbol d1 which mentioned in figure 2 and the results
of this experiment are clearly shown in figure 6. For
a comprehensive view on the issue, a comparative test
have done, without the existence of the resonant ring
this means that we change the distance between
transmitter and receiver (D in figure (2), From the
results it can be concluded that shown in Figure 7. It
should also be noted that the load resistance of 50
ohms is considered.
AnalysisofRelayEffectonWirelessPowerTransfer
555
Figure 3: Windings of the transmitter.
Figure 4: Receiver.
According to the equation (11), the resonant coupling
increases the efficiency allows power transfer over
longer distances. The effects of these coils on the
efficiency are demonstrated in figure 5.
Figure 5: Experimental results of relayed and conventional
witricity systems (F. Zhang, 2010).
In the next experiment according to the figure 2, we
settled the sender and the receiver windings, at a
distance of 20cm (D=20) and resonant ring will move
between the two windings. At first, we put the
Figure 6: Resonant ring impact on the efficiency of series,
parallel and modify windings.
resonant ring at the closest distance to the sender
windings (d1<1cm) and then we gradually increase
the distance and we calculate the efficiency during
these situations and as derived from the results,
proximity of resonant ring to each of the windings of
the sender and receiver will lead to There has been a
change in the parameters of the load and source which
these changes will lead to the withdrawal of the
resonant mode and it causes reducing the power
transfer efficiency.
The next test a wireless power transmission
system (WPT) with three different topologies for
transmitter, is analyzed and experimental tests shows
that the maximum power occurs at close distance
between transmitter and receiver. This experiment
carried out in the absence of receiver coil is placed in
the closest distance to the transmitter coil and the
distance increases gradually up to 40 cm. As figure 7
shows, using the modify form of winding will achieve
the greatest efficiency.
Figure 7: Comparisons between series, parallel and modify
windings (considering D in figure 2) as distance.
Experimental results show as that when we increase
the distance between receiver and sender into a point
that no more voltage is induced in receiver coil
(M1,3=0), a re-induction occurs at the receiver due to
entrance of resonate relay. In this experiment it was
noticed that when d1<d2, the efficiency increases. As
a notable point, when M1, 3≠0, (i.e. when we have
voltage on the receiver side even in the absence of
resonant relay), by the entrance of resonant relay to
the system, the inductive voltage increases as proved
by the experimental equations (11). However, it is
important not to reduce the values of d1, d2 too much.
If this happens, the system will be out of resonant
state due to the considerable changes in the
inductance of both receiver and sender (see equation
(3)).
ICINCO2015-12thInternationalConferenceonInformaticsinControl,AutomationandRobotics
556
3 CONCLUSIONS
In this paper, a WPT system with the resonant
frequency of 2.78 MHz, and circuit capacitance of
Cp= Cs=Ct=54.4 uF, and spiral coils with inductance
of LP, Ls, Lt=0.602 uH and capacitor capacity of 54.4
NF was designed and tested to investigate the effect
of resonant relay on the WPT efficiency
improvement. On this study, the position of the
resonant relay and its effect on the induced voltage as
well as the MPT efficiency of such a system was also
analyzed. Moreover, the limitation in choosing the
resonant relays positions was also provided. The
results of practical experiments on a system that has
been made, clearly showed that using the resonant
relay has been able to raise the voltage induction.
REFERENCES
A. Tucker , K. Warwick , W. Holderbaum, May 2013, “A
contribution to the wireless transmission of power”
Elsevier Ltd, Vol47, pp.235-242.
D. Gallichi Nottiani, F. Leccese, 2012 “A simpl metod for
calculating lumped parametrs of planar spiral coil for
wireless energy transfer” IEEE.
F. Zhang, S A. Hackworth, W. Fu, and M. Sunfhg, May
2010, ”The Relay Effect on Wireless Power Transfer
Using Witricity” 14th Biennial IEEE Conference,pp.1.
X. Liu, F. Zhang, S. A. Hackworth, R. Sclabassi and M.
Sun, April 2009, ”Wireless Power Transfer System
Design for Implanted and Wom Devices” IEEE 35th
Annual Northeast, pp. 1 - 2 . Tianjia Sun,
X. Xie, G. Li, Y. Gu, Y. Deng, and Z. Wang, NOVEMBER
2012.”A Two-Hop Wireless Power Transfer System
With an Efficiency-Enhanced Power Receiver for
Motion-Free Capsule Endoscopy Inspection” IEEE ,
VOL. 59, NO. 11.
S. Li, and C. Chris Mi, Apr 2014 ”Wireless Power Transfer
for Electric Vehicle Applications” IEEE Journal,
VOL.PP , NO.99,PP.1.
S. Sabki, Nadia Mei Lin Tan ”Wireless Power Transfer for
Electric Vehicle Applications” IEEE
J. Wang, Student Member, IEEE, S. L. Ho1, W. N. Fu, and
Mingui Sun, May 2010,”Finite Element Analysis and
Corresponding Experiments of Resonant Energy
Transmission for Wireless Transmission Devices Using
Witricity” 14th Biennial IEEE Conference,PP.1.
T. Mohamadi, July 2011 “Modeling and disining wireless
energi transfer circuit in high voltage based on
magnetic coupling” IEEE International Conference,
PP.1-4.
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