An inductive system for wireless power transfer is technically and
commercially very interesting way of transmitting electrical energy. Also in
company Kolektor Sikom, PE Magma we develop systems for inductive wireless
power transfer to charge portable devices in the automotive industry, medicine and
other market interesting areas.
Doctoral dissertation describes the numerical modeling of the inductive system
for wireless power transfer, which consists of the transmitter and the receiver coil
with ferrite cores. Inductive wireless power transfer can be resonant or non-resonant.
Since the company Kolektor Sikom, PE Magma has been focused on production of
coils with ferrite cores we analyze in detail non-resonant transfer while for
applications in power electronics resonant transfer is also relevant. Also, most
interesting market applications for charging portable devices use small distances in
the range of a few millimeters, where non-resonant transfer is comparable with the
In the literature, inductive systems mainly consist of a transmitter and receiver
coils without ferrite cores. Such simple systems, can be analyzed by analytical or
empirical equations. In order to improve inductive wireless power transfer, ferrite
cores are also used that in parallel also serve as a magnetic shield against magnetic
fields from the transmitter and receiver coils. However, due to the complex geometry
of the ferrite cores and nonlinear properties of the ferrite material the analytical
approach is no longer possible. It is therefore essential to use finite element software
for numerical modeling of the inductive system with ferrite cores. Studies, which
describe the inductive system with numerical modeling also use simplified models
which do not describe the influence of all parameters.
The aim of this work was to build numerical models: which describe, evaluate
and analyze the impact of position between the transmitter and receiver coils with
ferrite cores, to specify ferrite materials from the relative permeability and magnetic
shield, to consider the impact of copper foil on the magnetic shield, to find the
optimal shape of the ferrite cores, to calculate inductance of coils with ferrite cores,
to examine the effect of assembled ferrite plates, to determine the losses in different
coils made from litz wires, to evaluate the losses in ferrite cores, and finally to
analyze the impact of the heating on transmitter and receiver coils with ferrite cores.
Numerical models are also compared with the measurements.
In the introductory chapters an inductive system for wireless power transfer is
presented, which consists of transmitter and receiver coils. Inductive system is
presented through various equations and parameters: the coupling coefficient, quality
factor and efficiency. A comparison between inductive resonant and non-resonant
wireless power transfer is also presented. Furthermore, the parameters inductance
and ohmic resistance are defined. Inductance is presented from theoretical and
empirical methods, where also an overview of the literature for inductance
calculations of different authors is presented. The ohmic resistance consists of pure
ohmic resistance, resistance due to skin and proximity effect.
Further, the materials and methods are explained. The calculations of
numerical models were made in the programming environments Comsol
Multiphysics and Ansoft Maxwell. Characteristics of ferrite materials in the models
were selected on the basis of realistic materials that can be used or are used for such
industrial applications. Finally, the measuring methods and measuring instruments
which were used for verification of simulations in programming environments are
In the 5. Results and discussion chapter results of numerical models which
analyzed the effects of different geometries and parameters are presented: the
coupling coefficient k, the inductance L, the quality factor Q and magnetic shielding.
All these parameters have an impact on the performance and characteristics of an
inductive system for wireless power transfer. The impact of varying position on
coupling coefficient is presented in example of geometry with transmitter and
receiver coil with additional ferrite cores in horizontal direction, vertical direction
and angle of rotation between coils. It has been found that by increasing the distances
in the vertical and horizontal direction and by increasing the angle between coils the
coupling coefficient k decreases. Additionally, values of self and mutual inductances
of coils with ferrite cores are compared between each other and also the effect of
negative coupling coefficient k is explained.
From the view of the coupling coefficient k and magnetic shielding the
parameterization of various ferrite materials with increasing the relative permeability
was also made for the specific geometry of the inductive system. It has been found
that using materials with higher relative permeability does not significantly improve
the value of coupling coefficient k and magnetic shielding. Futhermore, the copper
foil added on ferrite core significantly improves magnetic shielding.
Furthermore, ferrite cores, which are used in inductive system are of different
shapes: ferrite pots, ferrite plates, the E-core and the U-core. In a serial production of
inductive components consumption of ferrite material is of great importance.
Therefore, optimization of the inductive system made of coils with ferrite cores
which were made from ferrite bars was analyzed. We obtained that to reach high
value of coupling coefficient k it is important to select a higher number of ferrite
bars. This results in less material used and also less weight of a ferrite core. In
addition, higher number of ferrite bars provide sufficient magnetic shielding. Further,
it has been found that the effect of the angle between ferrite bars on the transmitter
and receiver side on the overall coupling coefficient is smaller in the case of higher
number of ferrite bars.
The inductance of coils with ferrite cores as presented in the literature, is
primarily based on analytical and empirical equations for coils without ferrite cores.
Therefore, a new inductance factor was defined which allows faster and simplified
calculation of inductance of coils with ferrite cores in numerical models.
Due to the limitations in manufacturing larger ferrite plates in serial production
also the possibility of making through stacking was analyzed. The larger ferrite plate
is therefore made from small ferrite plates where it is necessary to choose some
compromise between the size of an air gap and the number of ferrite plates. Stacking
of ferrite plates does not deteriorate significantly the coupling coefficient k and
Moreover, it is very important to determine the losses in the coils and in ferrite
cores. The coil, which is used in high frequency range above 100 kHz, is made of
litz wire which consists of number of smaller strands. For the determination of losses
in coils, which are made of litz wire, more air coils with the different number of turns
and strands were analyzed. It was concluded that coil made of litz wire represents
very complex structure in numerical models, since it is made of the large number of
twisted strands. In addition, the geometry of litz wire is not uniquely determined and
known as it is very dependent on the manufacturing process. It has been found that
due to the complex structure of litz wire in high frequencies, it is better to make a
real coil and to make measurements of resistivity or to use resistivity formulas and
thus losses from the literature. Further, there was performed at certain geometry also
the calculation of the quality factor Q of the two coils with the addition of ferrite
cores. The losses in ferrite cores were determined through numerical models and
catalogue data of ferrite manufacturer. In the analysis of losses in the inductive
system, it has been found that the dominant losses are in the coils and not in the
ferrite cores. Both calculated losses in coils and ferrite cores were then inserted also
in a thermal model. It was found that the accurate knowledge of the losses in ferrite
cores, which are usually derived from catalogue data of material, does not
significantly contribute to improve the accuracy of the models.
All analyzes and calculations of different impacts and parameters on inductive
system were made through simulations in different numerical models in the
programming environments which are based on finite element method. Results of
specific numerical models were compared to experimentally obtained values. The
development of numerical models provides a detailed insight into the functioning of
the inductive system made of transmitter and receiver coils with ferrite cores from
view of electromagnetic and thermal phenomena. Developed numerical models will
contribute to a faster and better design of an inductive system for wireless power