A Software-Based Approach to wireless transfer of electricity

Wireless power transfer (WPT) is a process that has been known for quite some time, dating back to the invention of the Tesla coil. Due to some valuable benefits (lack of cables and connectors, as well as high isolation between power transmitter and receiver), this technology plays a relevant role today in applications such as EV charging, phone charging, medical devices, and more.1,2 Based on the standard or on the inductive coupling process, WPT needs to achieve a high level of efficiency, minimizing the power losses.

This article suggests an innovative software-based approach to the modeling of WPT circuits. By extracting the equivalent circuit for a given positioning of the coils, an accurate estimation of the power losses can be provided. In particular, the model can estimate the type of loss (conduction, eddy current, or core) and where it has originated (TX/RX winding or TX/RX core). Loss analysis is essential for designing the shape and structure of the coils and for predicting which parts of the system will produce more heat during the charge. The software model will represent all power losses as power dissipated by resistors belonging to the modeled circuit. The results of the proposed approach have been validated by comparing the predicted loss with the measurements conducted on a 10-W WPT system, considering both alignment and misalignment condition of the coils. Read the original article

The block diagram of a classical WPT system for phone-battery charging is shown in Figure 1. The transmitter includes the DC/AC inverter and the TX coil, whereas the receiver includes the RX coil, the AC/DC rectifier, and other conversion systems for the battery charger. Capacitors CrTX and CrRX maximize the power transfer in the range of the switching frequency by introducing a negative reactance. The intermediate voltage Vmid is usually regulated through a low-bandwidth control loop, which wirelessly transmits the feedback signal to the transmitter. This, in turn, can adjust the target voltage by changing the switching frequency or the phase shift of the TX full-bridge. In this circuit, losses are mainly due to the copper and core losses of the TX and RX coils.

A Software-Based Approach to Wireless Power Transfer Modeling
Figure 1: Block diagram of a wireless phone charger

Circuit model

The following relations describe the voltage and current characteristics of the transmitting and receiving coils:

A Software-Based Approach to Wireless Power Transfer Modeling


A Software-Based Approach to Wireless Power Transfer Modeling

The corresponding model is shown in Figure 2, where N1 and N2 are, respectively, the number of turns on the TX and RX coils. The three impedances Z11Z22, and Z12 of Equation 1 can be expressed as a function of ZAZB, and ZC.

A Software-Based Approach to Wireless Power Transfer Modeling
A Software-Based Approach to Wireless Power Transfer Modeling
A Software-Based Approach to Wireless Power Transfer Modeling
A Software-Based Approach to Wireless Power Transfer Modeling
Figure 2: Circuit model for the TX and RX coils

All above-mentioned impedances are a function of frequency, and their values can be determined either through direct measurements or predicted by software simulation. At a given frequency ω, each impedance ZAZB, and ZC can be replaced by the series connection of a resistor and an inductor. The dissipation on all these resistors represents the total loss in the system at the given frequency.

The following approach is based on the finite element method (FEM) simulation of three electric working conditions and on the calculation of the loss of any i-th element by using an FEM analysis tool:

  • ITX constant, with IRX= 0
  • IRX constant, with ITX= 0
  • ITX constant, with IRX= –ITX N1/N2

Considering the elements connected in series, the circuit of Figure 2 becomes the model shown in Figure 3.

A Software-Based Approach to Wireless Power Transfer Modeling
Figure 3: Circuit model with series connection

Resistances RAiRBi, and RCi can be calculated by solving the following system of equations, where PiPi, and Pi”’ is the power dissipated on the i-th element in the above-mentioned cases.

A Software-Based Approach to Wireless Power Transfer Modeling

For circuit operating with wider frequency range, the lumped model of Figure 4a can be used for ZA or ZC and the model of Figure 4b for ZB.

A Software-Based Approach to Wireless Power Transfer Modeling
Figure 4: Equivalent circuit for wider frequency range

Software model

The losses present in the circuit of Figure 1 are mainly due to eddy-current copper losses concentrated on the receiver side. In the circuit model of Figure 3, eddy-current losses are represented by resistors. FEM software can predict the losses in different positions, applying the three above-mentioned conditions. For coils, FEM simulation is usually conducted using either Litz wires (which involve high-complexity geometry with a lot of parameters to be considered) or tools like FastHenry3 (wherein the geometry is approximated by a set of current wires).

In our case, a hybrid approach has been chosen,4 providing a clear circuit interpretation but also exploiting the flexibility of FEM analysis to accurately represent the geometry. The software can be broken down into three main steps:

  1. Geometry generation of the Litz wire. The model of the TX and RX coils is based on the discretization of the Litz wire strand as a single wire coupled with the others with a given resistance.
  2. Calculation of the coupling at strand level. After this step, all the coupling calculated allows for creation of a coupling circuit, as shown in Figure 5.
  3. Extraction of the electrical model. Using the equivalent circuit of Figure 5, the software calculates the losses PiPi, and Pi”’ referred to in the three-circuit condition previously defined.
A Software-Based Approach to Wireless Power Transfer Modeling
Figure 5: Electrical equivalent model of the coupling of each strand

Experimental results

The measurement setup shown in Figure 6 has been used to determine the TX and RX coil impedance, where the distance between coils can be modified using motorized linear, rotary, and goniometric stages. The expected results produced by software algorithms are checked against the actual results measured by impedance/vector network analyzer BODE100. Figure 7 shows a comparison of these results between real measurements and software circuit simulation.

A Software-Based Approach to Wireless Power Transfer Modeling
Figure 6: Measurement setup
A Software-Based Approach to Wireless Power Transfer Modeling
Figure 7: Model and measure comparison

The proposed software-based modeling approach for a WPT circuit provides a precise estimation of the losses, their types (eddy current, conduction, and core), and their location (TX/RX core or TX/RX windings).


1Collins, L. (2007). “Cut the cord.” Electronic Systems and Software, Vol. 5, No. 6, pp. 42–46.

2Kim et al. (2015).

Energy Conversion Congress and Exposition (ECCE), Montreal, Quebec, pp. 3087–3091, doi: 10.1109/ECCE.2015.7310092.

3Kamon et al. (1994). “FastHenry: A Multipole-Accelerated 3-D Inductance Extraction Program.” IEEE Transactions on Microwave Theory and Techniques, Vol. 42, No. 9, pp. 1750–1758.

4Bettini et al. (2017). “A Volume Integral Formulation for Solving Eddy Current Problems on Polyhedral Meshes.” IEEE Transactions on Magnetics, Vol. 53, No. 6, pp. 1–4, Art No. 7204904.

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