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 C_rTX and C_rRX maximize the power transfer in the range of the switching frequency by introducing a negative reactance. The intermediate voltage V_mid 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.

Circuit model

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

Where:

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 Z₁₁, Z₂₂, and Z₁₂ of Equation 1 can be expressed as a function of Z_A, Z_B, and Z_C.

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 Z_A, Z_B, and Z_C 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:

• I_TX constant, with I_RX= 0
• I_RX constant, with I_TX= 0
• I_TX constant, with I_RX= –I_TX N₁/N₂

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

Resistances R_Ai, R_Bi, and R_Ci can be calculated by solving the following system of equations, where P_i‘, P_i”, and P_i”’ is the power dissipated on the i-th element in the above-mentioned cases.

For circuit operating with wider frequency range, the lumped model of Figure 4a can be used for Z_A or Z_C and the model of Figure 4b for Z_B.

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 P_i‘, P_i”, and P_i”’ referred to in the three-circuit condition previously defined.

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.

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).

References

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.