Journal of Electromagnetic Analysis and Applications, 2013, 5, 312-315 Published Online July 2013 (
Finite Element Assisted Numerical Comparison of Single
and Two Phase Inductively Coupled Power Transfer
Pratik Raval#, Dariusz Kacprzak, Aiguo Patrick Hu
Department of Electrical and Computer Engineering, The University of Auckland, Auckland, New Zealand.
Received May 13th, 2013; revised June 13th, 2013; accepted June 21st, 2013
Copyright © 2013 Pratik Raval et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Inductively coupled power transfer systems (ICPT) are becoming ubiquitous in industry. Many such systems are excited
with single or multi-phase input current. This leads to increased complexity in comparing such systems when solely
using the magnetic frequency analysis. This paper utilizes modern finite element method analysis software to propose a
novel software methodology for the numerical comparison of single and two phase ICPT systems as demonstrated on a
three dimensional (3D) battery charging system. The sinusoidal magnetic frequency response of a single phase system
is compared to the magnetic transient response of a multi-phase cu rrent system by u se of a novel software methodology
proposed in this paper. This consists of a transient response analysis to determine compute the resulting magnetic re-
sponse over the duration of an input current period on the two phase system. The resulting non-sinusoidal response is
then integrated over a whole period to extract the root-mean-square value for comparison with that of a single phase
system across a 3D cubic power zone.
Keywords: Finite Element Method; Electromagnetics; Magnetics; Induction; Wireless-Power-Transfer
1. Introduction
The technique termed inductively coupled power transfer
(ICPT) is a wireless-power-transfer technique that trans-
fers power across an air-gap by means of magnetic in-
duction [1]. This technique removes the inconveniences
caused from physical wires by providing power in hard
to reach places where conventional direct electrical con-
nections are inconven ient, hazardou s, or impossible, low-
ers maintenance requirements as there is less wear and
tear from wet, dirty, moisturized and hazardous envi-
ronments, and provides enhanced safety as it is free of
sparking and can be used in potentially explosive atmos-
pheres and supports freedom of mechanical movement of
any load(s) as opposed to a localized load(s). Naturally,
this has led to many ICPT applications including mono-
rail systems [2,3], people mover or transportation appli-
cations such electric cars, trains and buses [4], biomedi-
cal implantation and more recently low power consumer
battery charging applications [5]. However, a majority of
current such applications largely only support unidirec-
tional and/or bidirectional load movement. That is, there
is no support for three-dimensional (3D) load movement
along orthogonal axes. This is due to a lack of generation
of an omnidirectional primary link that provides a 3D
power transfer window. This paper uses the developed
3D cage—like primary magnetic structures that compose
a unique 3D ICPT system. Furthermore, depending on the
application requirements, the primary AC excitation cur-
rents in these systems may be applied as single or multi-
phase. For analysis, such excitation of primary currents
must be numerically computed using advanced modern
finite element method (FEM) analysis software as in [6].
The FEM software being used is JMAG designer.
This paper proposes a methodology for the numerical
comparison of a single and two phase 3D battery charg-
ing ICPT system in terms of the resulting magnetic field.
2. Proposed ICPT System
The battery charging system operating at 155 kHz is il-
lustrated in Figure 1. The power converter inverts a DC
input to distribute an A C power transfer window through
the primary track coils. Typically, the power converter
*The author declares no conflict of interest.
#Corresponding author.
Copyright © 2013 SciRes. JEMAA
Finite Element Assisted Numerical Comparison of Single and Two Phase Inductively
Coupled Power Transfer Systems 313
Figure 1. Battery charging ICPT system.
may consist of a p rimary compensation network with the
purpose of providing a resonant AC current. This current
is fed into the primary magnetic winding structure. The
objective of the primary magnetic structure is to distrib-
ute magneto-motive force (MMF) uniformly throughout
the entire cubic power transfer volume. The secondary
magnetic structure, often termed a pick-up, induces an
AC voltage. This voltage is often weak and noisy. So,
typically pick-up compensator networks are used to make
the induced signal stronger. The result is rectified before
operating a load. The presented single and two phase
systems are excited with an equivalent ampere-turns ratio
[7]. This ensures that an equal MMF is input in ampere
current-turns to produce the same magnetic flux density
within a pre-defined cubic power transfer volume of
1920 cm3. The only differences between the two systems
presented next are the orientatio n of the primary winding
structures and the input phase of the primary excitation
3. Single Phase System
The single phase system is shown in Figure 2. This sys-
tem consists of several over-layed planar rectangular
winding structures that are vertically displaced. This gen-
erates a predominant normal or vertical component in
magnetic flux density. The winding structures are sur-
rounded by a ferromagnetic material casing. This ferrite
material acts as a magnetic circuit with three main func-
tions. Firstly, to provide a low magnetic reluctance path-
way to the magnetic flux vectors to guide the flux
through the ferrite and then disperse the field back into
the intended power zone. Secondly, to confine the mag-
netic flux thereby reducing the flux vectors leaked out-
wards in an effort to reduce flux leakage so as to reduce
Figure 2. Single phase system (Left) and MFD vectors
potentially harmful electromagnetic interference. Thirdly,
to enhance the field with a high relative permeability of
1200. In this single phase system, the AC sinusoidal ex-
citation primary currents are applied simultaneously and
in phase to the primary track coils. This produces a net
vertically directed with the simulated magnetic flux den-
sity (MFD) distribution vectors also shown in Figur e 2.
4. Two Phase System
The two phase system is shown in Figure 3. This system
consists of two Helmholtz coil pairs along orthogonal
axes. The first Helmholtz coil pair is input with an AC
sinusoidal primary current that is in phase but of opposite
polarity. The second Helmholtz coil pair is similarly in-
put with AC sinusoidal primary current that has a 90 de-
grees phase difference to the current applied in the first
Helmholtz coil pair. That is, the primary currents are
applied sequentially and in phase quadrature to parallel
but adjacent coil windings so as to produce an elliptical
rotating magnetic field resulting from fields
0B and
90B. The resulting winding structures are su rrounded
by ferromagnetic material casing. In this case, the ferrite
acts as an electromagnetic attractor that essentially at-
tracts the flux from unlike magnetic poles. This aids the
propagation of the magnetic field from one side of the
box to the other that in essence distributes the flux
throughout the 3D cubic power transfer volume. The
resulting instantan eous MFD distribution vectors are also
shown in Figure 3.
5. System Comparison
The numerically computed parameter of comparison
MS is shown below. This is defined as the root-
mean-square (RMS) value of the averaged magnitude
magnetic flux density
Bavg throughout the cubic
intended power zone and N is the number of steps in the
transient response. The intended power region to com-
puting the cubic average is illustrated in Figure 4.
vg (1)
For a single phase system,
B is readily derived
Copyright © 2013 SciRes. JEMAA
Finite Element Assisted Numerical Comparison of Single and Two Phase Inductively
Coupled Power Transfer Systems
Figure 3. Two phase system (Left) and MFD vectors (Right).
Figure 4. Intended powe r zone : Cubic volume.
via the simulated magnetic frequency responses instant-
taneous peak due to the sinusoidal nature. However, for a
two phase system this parameter is no longer sinusoidal
so a transient response system model as a simulation
methodology is developed as in Figure 5. Firstly, a tran-
sient response analysis is performed on the two phase
model consisting of 400 steps corresponding to time in-
tervals of 32.25805 ns. Next, the cubic averaged MFD is
computed in the cubic volume. Finally, an RMS integra-
tor is performed on the resulting signal, shown in Figure
6, to attain the parameter of comparison
The resulting comparison of B.
MS is shown in Table
1. This result shows that the single phase system is 5.8%
more efficient at distributing the MMF throughout the
intended cubic power transfer volume. It is expected that
this novel numerical FEM computable comparison tech-
nique may be applied to other ICPT systems and multi-
phase systems. More specifically, this methodology of
comparison overcomes a limitation in the FEM software
by manual determination of the net peak electromagnetic
wave in a multi-phase system that exhibits a non-sinu-
soidal response over a 3D power transfer volume.
6. Conclusion
This paper has proposed a novel FEM software method-
ology for the numerical comparison of single and two
Figure 5. Two phase system software methodology.
Figure 6. Transient Response of Two Phase System.
Table 1. Comparison of single and two phase ICPT sys-
ICPT systems input current phase:
Single phase 33.590
Two phase 31.745
phase ICPT systems via a transient response analysis
where the resulting signal is not of sinusoidal nature over
a 3D power transfer volume in terms of a performance
governing metric.
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Finite Element Assisted Numerical Comparison of Single and Two Phase Inductively
Coupled Power Transfer Systems
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