Numerical analysis of a system of wireless energy transfer via resonance of magnetic induction

In the early 19th century Nikola Tesla, the inventor well known for his contribution for the development of the present day alternating current system gave rise to the idea of wireless electricity, however it was short lived and sparks insignificant interest to the then society. In 2007, physicist at Massachusetts Institute of Technology (MIT) has demonstrated an efficient scheme of wireless energy transfer via magnetic induction at resonance frequency. The literature has reported several methods to optimize the power delivery and efficiency; as well as theories to explain the behavior of the wireless energy transfer system. However, most of them are based on the Coupled Mode Theory (which was put forward by the MIT physicist),and the Impedance Analysis Model. There are some limitations imposed by these theories,the Coupled Mode Theory despite being widely accepted in the literature are unfamiliar to electrical engineers, in that it introduces variables that does not directly correlate to variables accustomed to electrical engineers, as a result an ample time had to be spent to understand the theory. While the Impedance Analysis is more familiar and simpler, it only solves the system in the frequency domain and does not explain the system relationship to time; thus it only considers the steady state condition and does not provide the transient behavior. This thesis fills the gap by providing a set of numerical equations to solve the currents of a two-coil Wireless Energy Transfer via Resonance of Magnetic Induction in the time domain from an initial condition to a steady state condition by using variables familiar to electrical engineers;with the objective of obtaining the conditions for that maximizes the efficiency and power delivery. The behavior of the system is governed by variables defined by the values of the system’s circuit components, and relationship between these variables is investigated by solving the ordinary differential equations of the system’s current and providing both the analytical and the numerical solution to the differential equation problem. It was found that,analytical solution of the system’s current in the time domain results in a very long algebraic expression, while the numerical solution produces equation much shorter in length. Analysis is done on the numerical solution by simulating the equation in MATLAB programming. The hardware was constructed to test the validity of the numerical solutions to the equations presented. The data presented shows an agreeable result between the hardware and the equation based simulation. Result of analyses performed found that there exist unsymmetrically between the lower resonant frequency and the upper resonant frequency at high coupling coefficient. It was also found that there exist several load and frequency conditions that give peak power delivery in over-coupled mode. Moreover, a theoretical analysis performed suggest that efficiency at very low coupling coefficient could be maximize by optimizing the ratio self-inductance to the series capacitance in conjunction with a correct terminated load, as such it was shown that efficiency of 55% is obtainable at a very low coupling coefficient of 0.005. Finally, this thesis also provides a set of equations to calculate the mutual inductance and magnetic field of the system’s coil; this is done by applying the Biot-Savart equation to perform finite element calculation.

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