Research On Fractional-order Circuits And Fractional-Order Electromagnetics Applied In Resonant Wireless Power Transmisson Model

The natural characteristics and dynamic behaviors of numerous physical objects can be described precisely and reasonably by the theory of fractional calculus. More flexible and effective modeling methods can be obtained with the help of fractional-order differential equations. Thus, fractional calculus has been being applied in many engineering fields such as materialogy, physics, informatics, bioscience, economics, electromagnetics and so on. As a research hotspot recently, much exciting progress has been made on the resonant wireless power transmisson technology. However, the related researches still remain uncomprehensive. Few researches has concentrated on the electromagnetic performances from the perspective of fractional calculus. Therefore, it is not only of theoretical significance, but also of practical value to study the resonant wireless power transmisson as well as the electromagnetic field with the tool of fractional calculus. In this paper, characteristics of several basic fractional-order circuits are analyzed. On this basis, a fractional-order resonance transmission model is established in order to describe the inherent fractional-order electromagnetic properties precisely. The main contents of the paper are presented as follows:The impedance constitute of the fractioanl-order RLβ and RCα series circuit is considered. The influences on frequency responses made by orders of fractances are illustrated. Compared to integral-order conditions, the impedance performances are more flexible and the phase ranges double which mean more convenient for circuit design.The frequency performances of the fractioanl-order RLβCα series circuit which contains two fractances are studied. Considering whether R is zero or not, the influences on impedance performances made by orders of fractances are discussed. The frequency conditions which meet different impedance performances are calculated when R ? 0 and the sensitivity informations are obtained when R ? 0. Compared to integral-order conditions, the changes of magnitudes are more flexible and the scopes of phases are determined by orders.The features of the fractioanl-order mutual inductance circuit are analyzed. The frequency responses of its impedance matrix are illustrated. As the order of self-inductance changes, pure imaginary impedance only exist in self-inductance and the order of mutual-inductance can be obtained with the order of self-inductance in a certain frequency.A circuit model of fractioanl-order resonant wireless power transmisson is established. The loop currents and the resonance frequencies are derived with the method used for the fractional-order circuits. The changing trend of the magnetic flux between the two coupling coils is analyzed from the perspective of circuit. The vector forms of the fractional-order maxwell’s equations are derived from the perspective of space. When integer order is considered, the classical results can be recovered. The solutions of the fractional-order passive wave equations are obtained from the perspective of time. As a result, the relationship between the accompanying electromagnetic field and the differential order is obtained.It is demonstrated that the degree of freedom for model design with fractional-order circuits and fractional-order electromagnetics is increased which means more flexibility and more generality than traditional integral-order conditions.