CET FEA transportation

Contactless Energy Transfer Systems Finite Elements Modeling with Flux

Vincent Marché


Contactless energy transfer (CET) systems are used in many industrial sectors. These include conveyors, trolleys, storage and retrieval units, baggage handling,

Contactless Energy Transfert FEA Iron core coreless CET coils

Figure 1: Iron core and coreless CET coils (Pavol Bauer, TU Delft).

battery charging stations, mobile phones and medical implants.
The energy transfer model is quite similar to a conventional transformer, except for the weak coupling between the primary and secondary windings and partial or non-existent ferromagnetic closing paths. Inductive coupling is commonly used in a range from a few mW to a few hundred kW.
Figure 1 shows a schematic view of a transmission and reception antenna for an electric car battery charging device, modeled in Flux 3D software. The transmitting coil is stationary and fed by a high frequency switching power source. The reception antenna is inductively coupled to the transmission antenna and supplies electric power storage (battery or supercapacitors). The operational frequency is above the audible range but remains below 100 kHz to limit switching losses in the power source. Resonant circuits are used on the primary and secondary sides to boost transmitted power and minimize voltage and current in the device. Total efficiency is usually above 90%.

Contactless Energy Transfert FEA coreless CET coils with ferrite back

Figure 2: Schematic view of a coreless CET coils with ferrite back yokes.

The upper CET configurations in figure 1 use a soft ferrite yoke while the lower ones build up an ironless transformer.

The left hand side models can be investigated via a 2D axisymmetric model while the right hand side models require 3D analysis. A hybrid model can also consist of an air coil and back yokes made of ferrite disks (fig. 2). In this model, the ferrite yokes comprise a full disk (shown in light blue and dark blue over 180°) or sectors. The emitting and receiving coils are shown in yellow and red colours.



Contactless Energy Transfert FEA Flux Ferrite saturation temperature losses field density

From coupling coefficient depending on alignment to losses and global power balance computation, from magnetic field density analysis to saturation of ferrites prediction through temperature distribution study, Flux FEA enables complete design and optimization of contactless energy transfer systems.


Contactless energy transfer system simulation and 2D FEM analysis

For battery charging devices, the distance between the coils may be substantial (typically 100 mm) and misalignments between transmitting and receiving antenna must be addressed. Due to the large airgap between the primary and secondary windings, mutual inductance is low compared to leakage inductances. Therefore the magnetizing current is high and generates excessive Joule losses.

A popular solution is to use a resonant circuit based on additional capacitors connected in series or parallel with the primary and secondary windings. The equivalent circuit for a compensated CET device supplied by a three phase rectifier and feeding a battery via an H-bridge is shown in figure 3. The equivalent circuit of the coupled antennas is inside the yellow box.
A simple CET model comprises primary and secondary linear inductances (L1 and L2), a mutual inductance and winding resistances. Due to the high supply frequency (25 to 60 kHz), the coils will be Litz wires which, despite the low fill factor, dramatically reduce eddy current and proximity effect losses in the windings. The external capacitors C1 and C2 are used to build up a resonant circuit. The primary and secondary resonance frequencies are usually equal and can be approximately defined by:

CET formula

L1 is the primary inductance and L2 the secondary inductance.
C1 and C2 are capacitors connected in series with the primary and secondary phases.

The model shown in figure 3 may be efficiently used in a system simulation software such as  Activate to optimize device performances (choice of operational frequency, switching losses, number of turns, influence of load variation). The CET lumped circuit model does not include additional losses within the CET system (ferrite hysteresis losses, losses in the housing or in shielding plates). If such phenomena need to be integrated into the model, it is possible to conduct a co-simulation between Portunus and Flux® using a macro model of the CET.
The lumped circuit model shown in figure 3 would be replaced by a component describing the FEM model of the transformer.
This model is solved using Flux® and coupled to a circuit defined under Activate. This method is more accurate as it takes into account any iron saturation and other complex physical phenomena. It is however more time-consuming, especially if the FEM model is three-dimensional.


“Contactless energy transfer offer cost reductions in energy transfer, compact design, maintenancefree equipment, versatility and greater reliability.”


A dynamic simulation using the lumped circuit model of the antennas requires good knowledge of winding inductances. These can be derived from an AC harmonic analysis with Flux® 2D or Flux® 3D. To determine the primary inductance L1, the primary winding is supplied with AC current. The primary inductance L1 and the coupling inductance M are easily derived from the coupled fluxes. The same procedure is applied to the secondary winding to derive the secondary inductance L2. This model is valid for CET devices without ferrite or with linear ferrite permeability and without conducting regions (shielding plates for instance). Due to the large airgaps, the assumption on the linear behaviour of the system is often valid.
Figure 4 shows an academic case of a CET device exhibiting transmission and reception coils, ferrite back yokes and aluminium shielding above the moving coil. The CET device was modeled with Flux® 2D using a current source on the primary side, series compensation capacitors and a resistive load. The primary and secondary capacitors were determined using the classical formula mentioned above in order to satisfy a resonance frequency of 40 kHz. It is worth mentioning that the formula does not take into account ferrite losses or losses in housing or shielding plates. The flux lines are displayed in figure 4 for a resistive load at resonance frequency. We notice that the upper shielding preents the flux lines from extending out of the CET environment.

Contactless Energy Transfert FEA flux lines harmonic analysis

Figure 4: Flux lines in a CET device AC Harmonic analysis with Flux 2D.

Figure 5 shows a 3D view of the power in a resistive load vs. operational frequency and load resistance. The computation is made on a 2D model. The resonance frequency is relatively constant when the load changes. Airgap variations can however create a drift on the resonance frequency and a fixed or variable frequency control must be decided depending on the working environment.

Contactless Energy Transfert FEA Transmitted power vs. operational frequency F and load

Figure 5: Transmitted power vs. operational frequency F and load resistance RL.

The output power takes ferrite losses into account via complex permeability and its dependence over the supply frequency. Also, eddy currents are assumed to flow in an aluminium shielding plate (upper region). The transmitted power calculation is based on a constant copper and ferrite temperature. The maximum transmitted power will however be limited by losses in the coils and in the ferrite, as well as the current density in the coils. The temperature distribution in the device can also be determined using the thermal analysis application of Flux® .
Flux’s parametric solver can furthermore be used to assess various configurations. Also, the influence of the number of primary and secondary turns, resonance capacitances or saturation can be investigated. The designer can make use of Flux’s parametric solver to determine the influence of key parameters. These include resonance frequency for a rated load, variations of transmitted power vs. airgap, device efficiency, influence of number of turns, power factor, etc.


3D finite element method analysis

3D FEM analysis is compulsory for some design cases: investigation of antenna misalignment, use of rectangular coils or ferrite yokes containing sectors. Low penetration depth in conducting regions can make the simulation very tedious and requires extensive computation time. Flux® 3D provides some interesting features to conduct studies on CET devices. Nonmeshed coils are superposed to the finite element domain and need not be meshed. They can help model very complicated coil shapes, provided that eddy current and proximity effects are neglected. Furthermore, non-linear surfacic impedances are available for AC analysis. They efficiently model conducting regions where penetration depth is low vs. region depth. On the other hand, lossy ferrites are modeled using complex permeabilities depending on operational frequency.

Contactless energy transfert

Figure 6: Flux lines distribution in a CET device (AC Harmonic analysis with Flux 3D).

Figure 6 shows a case where sectored ferrite yokes are used. In this case only the primary winding is supplied with a current source at 40 kHz. Thin aluminium shielding plates are inserted below the emitting antenna and above the receiving antenna. The ferrite yokes are modeled as magnetic conducting regions. Due to the high frequencies and low penetration depth in the aluminium, a volumic meshing of the shielding plates would require a larger number of meshes. These regions tend to be modeled in Flux® 3D via surfacic impedances (boundary condition on the region surface). This allows a coarse discretisation of the shielding plates as the magnetic field is only computed on the surface.
The device’s ferrite yokes each comprise nine ferrite sectors. The symmetry of the domain means that the study can be limited to a 40° sector. Also, the device model is included in an ‘infinite  region’ while the magnetic field is assumed to expand out of the airgap. This feature allows assessment of the influence of the charging device on electronic components or optimizes shielding to limit the field radiated within the car body.

Figure 6 shows flux density magnitude in the ferrite blocs. It should be noted that saturation flux density in MnZn ferrites hardly exceeds 0.5 T and that Curie temperature is around 220°C. Therefore it is strongly recommended to check losses in this region and to assess their influence on ferrite temperature.


Fig 7: Current density distribution in the CET shielding plates (AC Harmonic analysis with Flux 3D).

Figure 7 shows loss density in the aluminium shielding plates in this configuration. The use of ferrite sectors instead of a ferrite disk can be justified on cost, but the design must be carefully assessed in order to avoid hot points in the shielding plates. Even if symmetry conditions are applied, a 3D transient analysis of a CET device is quite time-consuming. It should therefore be used for AC analysis or at the final validation stage if transient analysis is required. Numerous tests might be necessary to assess the influence of misalignment and variable airgap over the transmitted power, the amount of losses in the car body, near-field radiation, etc. AC analysis of a single configuration takes a few minutes’ calculation time. On the other hand, the optimization of a 3D CET device may require hundreds of parametric computations. This is where the use of the optimization tool HyperStudy can dramatically reduce computation time. The user can set a set of constraints (coil volume, maximum current density, maximum airgap, coil shape,…) and objective functions (transmitted power, robustness vs. misalignment, power factor) and search for optimum configurations.


Contactless Energy Transfert Radiation Hazard and standards respect studies in FEKO

Radiation Hazard and standards respect studies in FEKO



Depending on the configuration of the CET device, a 2D or a 3D FEM analysis might be required to assess device performances. This can be conducted using various strategies. Based on a simple model of the device (self and mutual inductances between emitting and receiving antenna, coil resistances), fast prediction of system behaviour and switching losses can be achieved using the system simulation software solidThinking Activate. The lumped circuit model of the CET must beforehand be determined under Flux®. It can be easily and accurately derived from an AC harmonic analysis. For a more sophisticated approach, it is interesting to rely on a co-simulation model where the CET device is modeled under Flux® and the circuit defined under Activate. This strategy allows any saturation and hysteresis losses in the ferrites to be predicted along with eddy current losses in the housing and shielding plates. This procedure provides accurate results for the system’s dynamic behaviour but at a higher computation-time cost.

Contactless Energy Transfert System Optimization

HyperStudy design exploration, study and exploration environement enables to efficiently define new optimized systems, for instance to optimize energy transfert and reduce ferrite shielding parts weight, with constrains on the induction and dimensions.

In order to assess the efficiency of the system, it is also possible to rely on a full FEM analysis with Flux®. Additionally, the parametric solver allows various configurations to be investigated, resonance frequency variation vs. different parameters to be determined (coil shape, airgap, misalignment, load resistance) and necessary modifications to be made to achieve the system requirements. Moreover, FEKO – Altair solution for HF electromagnetic studies – will enable complementary studies for radiation hazard and standards respect, like ICNIRP restictions.
A novel approach might also include the HyperStudy optimization tool. Searching several hundred configurations to find the most suitable one can be tedious, and sometimes impossible when relying on parametric analysis.  HyperStudy allows an intelligent choice of a preferred solution to be made using surface responses and various types of deterministic and stochastic optimization algorithms.

Learn more about Flux , FEKO and HyperStudy


We specially thank Dr. Taghezout – APPLIED MAGNETICS who help writing this article.

Vincent Marché

About Vincent Marché

Vincent Marché graduated first in electronics, and then went on to refine his skills at business school. After more than 10 years in the industry, working on product marketing and sales of sensors, switches and electronic devices, he fell into a melting pot called electrical engineering simulation. Supporting FluxTM electromagnetic simulation software since 2009, he is passionate about the large fields of applications addressed by simulation tools and the application expertise of the users. He is constantly looking for solutions that address the innovation needs of electrical engineers. Since the recent acquisition of Cedrat by Altair, he manages the promotion of electromagnetic applications, electrical engineering and e-Mobility.