Abstract
The concept of Wireless Power Transfer (WPT) was first introduced by Nikola Tesla in the 19th century. Since then, significant progress has been made in this field. WPT techniques include Radio Frequency, Capacitive coupling, and Inductive coupling. Applications of WPT are diverse, some are biomedical implants that greatly improve the quality of life for individuals with chronic health conditions, enabling them to live more independently and comfortably. Some are electric vehicle charging, which could greatly increase their practicality and convenience, helping integrate them into the market. A popular market is consumer electronics, such as portable chargers, NFC, and RFID. Today, we see advancement even in public and avionic transportation. Even though, the efficient transfer of power on the order of tens of watts remains a challenging task that academia and industry are attempting to address.
One promising method of WPT is Resonant Inductive Coupling Power Transfer (RICT), which was demonstrated by MIT researchers in 2007 [1]. They were able to wirelessly deliver 60W at 40% efficiency to a light bulb located 2 meters from the power source. Due to its simplicity, safety, high efficiency, and power transfer capabilities, RICT is widely researched and used in various applications. WPT systems require control algorithms to maintain maximum efficiency and power delivery as the load and distance between the transmitter and receiver change.
Analysis
Consider a simple 2-coil wireless power transfer (WPT) system with its equivalent circuit shown in the figure below. The discussed system is the called a Series-Series compensated RICT system. In order to simplify the analysis, we modeled both sides’ loss with resistors R1 and R2. Losses may be input source resistance, DC/AC inverter losses, magnetic material loss, capacitors’ ESR, and coils’ series resistance.
We use Kirchhoff voltage law on both sides and get the system equations, which are
We can use these equations and redraw the electrical circuit to get an equivalent circuit
We want to present a qualitative analysis, hence we select C1=C2 and L1=L2. The system is resonating at an angular frequency of ω0 = 1/√LC.
In resonance, the impedance of the compensation capacitors and the coils' self-inductances cancel each other. We redraw the electrical circuit at resonance, and receive a circuit which is fairly simple and easy to analyze.
We analyze this circuit and after some tedious algebra we get
An exemplary plot of the efficiency as a function of the load is shown below, for two different coupling coefficients
All of the above shows that for every coupling coefficient, there exist one load at which we get peak efficiency. We can also deduce that knowing the optimal load is critical at low coupling applications. After some more tedious algebra we get it's expression
Summary
Wireless power transfer (WPT) systems are used in power delivery applications where a physical link between the power source and the load is impossible. A key parameter in a WPT system is the coupling coefficient, which quantifies the magnetic coupling between the transmitter and receiver. Knowing the coupling coefficient is cruical to maximizing efficiency, since the optimal load depends on it.
References:
[1] Andr´e Kurs & Aristeidis Karalis & Robert Moffatt & J. D. Joannopoulos, Peter Fisher, and Marin Soljaˇci´c. “Wireless Power Transfer via Strongly Coupled Magnetic Resonances”. In: Science 317 (2007), pp. 83–86.
[2] Borenstein, Shay et al. “Maximum Efficiency Point Tracking for Wireless Power Transfer Systems Using Additional Winding / Shay Borenstein ; [Supervision: Yoash Levron].” Technion - Israel Institute of Technology, 2024. Print.
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