Download magnetic resonant co wireless power trans electric vehicle bat

MAGNETIC RESONANT COUPLINGS USED IN
WIRELESS POWER TRANSFER TO CHARGE THE
ELECTRIC VEHICLE BATTERIES
BATTERIES
Dragoş NICULAE
,,POLITEHNICA”Technical
University of Bucureşti
Lucia DUMITRIU
Mihai IORDACHE
Andrei ILIE
,,POLITEHNICA”Technical
University of Bucureşti
Lucian MANDACHE
University of Craiova
REZUMAT. În prezent aplicaţii precum reîncărcarea acumulatorilor autovehicolelor electrice au focalizat interesul cercetătorilor
spre transferul de putere prin inducţie. Transmisia fără conductoa
conductoare (wireless) a energiei electromagnetice este utilă în cazurile
în care reţeaua
reţeaua de conductoare este dificil sau chiar imposibil de realizat.
realizat. Transferul este eficient la o distanţă la care câmpul
electromagnetic este suficient de puternic pentru a asigura o putere
putere rezonabil
rezonabilă
ilă în circuitul de sarcină,
sarcină, ceea ce este posibil dacă
ambele circuite – emiţătorul şi receptorul - funcţionează la rezonanţă. Cei doi parametri care controlează valoarea puterii
transmise prin cuplaj magnetic şi randamentul transmisiei sunt frecvenţa şi coeficientul
coeficientul de cuplaj. Lucrarea este focalizată pe
calculul inductivităţii mutuale al sistemului wireless de care depinde ultimul parametru.
Cuvinte cheie:
cheie transfer de putere prin inducţie, reîncărcarea acumulatoarelor, vehicole electrice, inductivitate mutuală.
ABSTRACT. Nowadays applications
applications like recharging electric car batteries have focused the research on the wireless power transfer.
Wireless transmission is useful in cases when
when instantaneous or continuous energy is needed but interconnecting wires
wires are
inconvenient even impossible. The transfer is efficient over a distance at which the electromagnetic field is strong enough to
to allow a
reasonable power transfer, that is possible if both the emitter and the receiver achieve magnetic resonance. The two parameters
which control the amount of the transferred power by magnetic coupling and the transfer efficiency as well are the frequency and
the coupling coefficient. The paper is focused on the mutual inductance computation of the wireless system which control the last
parameter.
parameter.
Keywords:
Keywords wireless power transfer, battery recharging, electric vehicles, mutual inductance.
1. INTRODUCTION
One of the main issues regarding electric vehicles is
the process of automatically charging. The technology
of wireless power transfer (Witricity – from WIreless
elecTRICITY) provides large air gaps and large
amounts of power.
The antenna radiation technology is not suitable for
this application. The main reason is that the radiated
electromagnetic power is small, making this technology
more suitable to transfer information than power. Also,
in order to increase efficiency the antenna system
emission pattern must be oriented towards the receiver,
otherwise most of the power is radiated away and does
not reach the receiver antenna system. This technology
is affected by nearby or metal objects placed between
the emitter and receiver, which absorb the radiated
energy.
Because the physical principle behind the Witricity
concept relies on the fact that resonant objects
exchange energy efficiently, the simplest Witricity
system for power transfer consists in two circuits
(resonators) – Source (emitter) and Load (receiver) –
inductively coupled (Fig. 1).
The source (emitter) resonator emits a non-radiative
magnetic field oscillating at high frequencies, which
mediates an efficient power transfer to the load
(receiver) resonator.
In applications like light propagation in waveguides
or optical cavities, the Witricity concept is usualy
described by the coupled mode theory [1-3].
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An alternative theory is using of numerical methods
in order to solve the Maxwell equations which arise in
the study.
For the bigger power applications, like recharging of
the electric vehicle battery, because to perform wireless
power transfer RLC resonators are used, the circuit
theory can be applied as well [4].
 2
2

M = 4π Rr  − k  F −
k
k



E

(1)
in which R and r are the radiuses of the two circles,
k=
2 Rr
(2)
(R + r ) 2 + h 2
and h is the distance between their centers.
F and E are the complete elliptic integrals of the first
and the second kind. In general, elliptic integrals cannot
be expressed in terms of elementary functions. It can be
expressed as a power series.
Weinstein gives an expression for mutual inductance
of two coaxial circles in terms of the complementary
modulus k’:
Fig. 1. Wireless system foo recharging the electric vehicle battery.
From the reported researches’ results some remarks
have to be made:
The interaction between the source and device is
strong enough so that the interactions with nonresonant
objects can be neglected, and an efficient wireless
channel for power transmission is built.
Magnetic resonance is particularly suitable for
applications because, in general, the common materials
do not interact with magnetic fields.
It seems [5] that the power transfer is not visibly
affected when humans and various objects, such as
metals, wood, electronic devices, are placed between
the two coils at more then few centimetres from each of
them, even in cases where they completely obstruct the
line of sight between source and device.
Some materials (such as aluminium foil and
humans) just shift the resonant frequency, which can in
principle be easily corrected with a feedback circuit.
The two parameters which control the amount of the
transferred power by magnetic coupling and the transfer
efficiency as well are the frequency and the coupling
coefficient. In the following we shall develop a
computing procedure of the mutual inductance in
wireless systems which control the last parameter.
2. MUTUAL INDUCTANCE COMPUTATION
In order to compute the mutual inductance of the
various types of electric circuits occurring in practice,
many formulas have been developed.
The first and the most important formula to compute
the mutual inductance between two coaxial coils is the
elliptic integral formula given by Maxwell [6]:
 3 2 33 4 107 6

k' +
k ' +... ⋅
1 + k ' +
4
64
256




15


M = 4π Rr 
k '4 +  
1 +
4
⋅  log − 1 −  128
 

 
k '   185 6
k ' +...  

+
 1536
 

(3)
where k ' = 1 − k 2 .
Nagaoka has given formulas for the calculation of
the mutual inductance of coaxial circles, without using
the elliptic integral tables [7]. These formulas make use
of Jacobi’s q-series. The first formula is to be used
when the circles are not near each other and has the
following expression:
3
M = 16π 2 Rr q 2 (1 + ε ) ,
(4)
where
ε = 3q 4 − 4q 6 + 9q 8 − 12q 10 + ...
5
q=
l=
9
l
l
l
+ 2  + 15  + ...
2 2
2
(5)
1− k'
1+ k'
Nagaoka’s second formula is for coils which are
near each other and the expression is:
M = 4π Rr
1
2
2(1 − 2q1 )


1
2
 1 + 8q1 − 8q1 + ε1 log − 4
q1


[
]
(6)
where
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q1 =
l1 =
9
l1
l 
l 
+ 2 1  + 15 1  + ...
2
2
2
1− k
(7)
1+ k
ε1 = 32q13 − 40q14 + 48q15 − ...
Other formulas based on certain definite integrals of
Bessel functions or on elliptic integrals of the third kind
have been proposed by many authors.
To facilitate calculations in such problems, we have
implemented a procedure in Matlab based on Neumann
formula [8] :
M =
Φ 21 µ0
=
i1
4π
∫∫
C1C 2
dl1dl 2
R12
(8)
We have implemented the above expression in
Matlab using two grids for each coil – one of them
circumscribed and the other inscribed (Fig. 2); in this
way we can limited the values between a maximum and
a minimum, using a minimum mesh density.
Case 3
Case 4
To compute the integral in (8) we have used 50
points in the mesh construction for each coil. The
results of the analysis are presented in Table 2 together
with the values taken from the literature, for
comparison. In this table
Mp – is the value of the mutual inductance,
according to our procedure;
Mt – is the value of the mutual inductance, according
to the tables for elliptic integrals.
Using two identic coils (one connected to an
autotransformer at 50 Hz, the other connected two an
oscilloscope in order to measure the induced voltage)
we obtain the values presented in Table 3.
By means of simple formulas, we then calculate the
mutual inductance, having the current from primary
circuit and the voltage from the second one.
Mp – the value according to our procedure;
Mm – the value obtained by measurements;
Fig. 2. The two grids for each coil.
3. EXAMPLES
For comparison we have chosen from the literature
[6] four cases of mutual inductance, analytically
computed by means of various formulas, some of them
discussed in the precedent section. In Table 1 these
cases are presented.
Table 1. The theoretical cases
Case 1
Case 2
Fig. 3. The device for measurements and the electrical scheme.
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Table 2. The comparison of the results
x = 80 mm
R1 = 250 mm
R2 = 200 mm
x = 40 mm
R = 100 mm
Mp=1,352e-7H
Mt=1,351e-7H
Mp=2,893e-7H
Mt=2,9e-7H
Case 1
Case 2
r = 80 mm
R1 = 100 mm
R2 = 60 mm
cos θ = 0,7
r = 400 mm
R = 50 mm
cos θ = 0,4
Mp=-4,896e-11H
Mt=-4,9e-11H
Mp=2,44e-8H
Mt=2,32e-8H
Case 3
Case 4
Table 3. The values obtained by our computation procedure and the measurement results
x = 30 mm
R = 110 mm
x =30 mm
R = 110 mm
θ = 450
Mm=51,97e-6H
Mp=50,33e-6H
Case 1
Mm=17,61e-6H
Mp=17,01e-6H
x =100 mm
R = 110 mm
x =100 mm
R = 110 mm
θ =450
Case 3
4. CONCLUSIONS
Safe and accurate wireless power transfer remains a
challenge and a current research theme.
We have implemented a procedure to compute the
mutual inductance between two circular coils. The
computation results are in very good agreement with
the values reported in the technical literature.
We have built a device with two copper coils and a
system that allow us to place the two coils in various
positions and to make the measurements. The
differences between measured values and the values
obtained from software simulations could be explained
by means of apparatus tolerances and by the fact that in
our procedure we neglect the repartition of coil turns,
considering them concentrated in one turn.
As future papers and as a part of optimization
transfer process, we will enhance our procedure in order
to calculate the capacitance, allowing us to bring the
benefits of resonance in the process.
Mm=16,19e-6H
Mp=15,92e-6H
Case 2
Mm=14,73e-6H
Mp=16,52e-6H
Case 4
REFERENCE
[1] H.A. Haus and W. Huang, “Coupled-Mode Theory”,
Proc. of the IEEE, Vol. 79, No. 10, October 1991, pp.
1505-1518.
[2] R. A. Moffatt, Wireless Transfer of electric power, thesis
for Bachelor of Science in Physics - superviser M.
Soljačić, June 2009.
[3] T. Imura, H. Okabe, and Y. Hori, “Basic Experimental
Study on Helical Antennas of Wireless Power Transfer for
Electric Vehicles by using Magnetic Resonant Couplings”,
Proc. of Vehicle Power and Propulsion Conf., Sept. 2009,
IEEE Xplore, 4/10/2010, pp. 936-940.
[4] M. Iordache, Lucia Dumitriu, Teoria modernă a
circuitelor electrice, Vol.2, Editura ALL, 2000, ISBN
973-684-337-8.
[5] A. Kurs, Power transfer through strongly coupled
resonances, thesis for Master of Science in Physics superviser M. Soljačić, Sept. 2007.
[6] P.L. Kalantarov, L.A. Teitlin, Calculul inductantelor,
Editura Tehnica Bucuresti, 1958.
[7] E.B. Rosa, F.W. Grover, Formulas and tables for the
calculation of mutual and self-inductance, US
Government Printing Office Washington 1948.
[8] A. Timotin, V. Hortopan, A. Ifrim, M. Preda, Lectii de
Bazele Electrotehnicii, Editura Didactica si Pedagogica,
Bucuresti, 1970.
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