Construction Of Fractional Order Transformer And Modeling Analysis Of Fractional Order Flyback Converter

Fractional calculus is more accurate in describing the true characteristics of objects,and it can increase the flexibility and freedom of circuit design.Therefore,in recent years,fractional calculus has been widely used in the engineering field.Components such as inductors,capacitors,coupled inductors,and transformers are common components of DC-DC converters,and recent studies have shown that they all exhibit fractional characteristics.Only the fractional model of the component can describe the real relationship between voltage and current.Therefore,fractional-order inductor and fractional-order capacitor are used in the research of fractional-order DC-DC converter to analyze the real characteristics of the converter.However,due to the lack of circuit models and construction methods for fractional coupled inductors and fractional transformers,there are few studies on fractional-order DC-DC converters with fractional-order coupled inductors and fractional-order transformers.In this paper,under the condition of full coupling and the same order,the fractional-order transformer circuit model is derived based on the fractional-order coupled inductance model.Moreover,in order to realize the fractional-order transformer,the fractional-order transformer construction circuit is proposed and verified by experiments.Finally,the fractional-order flyback converter with the fractional-order transformer and the fractional-order capacitor is proposed,and simulations and experiments are carried out by using the proposed construction circuit.The specific work of this paper is as follows:1.The basic definition of fractional calculus,Laplace transform,basic properties and the basic characteristics of the fractional-order capacitor and the fractional-order inductor are introduced.The process of using the Oustaloup rational approximation algorithm to obtain the approximate circuit of the fractional-order capacitor and the fractional-order inductor is introduced in detail.And the simulation of the fractional-order capacitor and the fractionalorder inductor is carried out.2.In order to realize the fractional-order transformer element,the construction circuit of the fractional-order transformer is proposed.Firstly,under the condition of full coupling and the same order,the fractional-order transformer circuit model is derived based on the fractionalorder coupled inductance model.Meanwhile the open-circuit impedance characteristics and load impedance characteristics of fractional order transformer are studied.Then,in order to realize and apply the fractional-order transformer,the construction circuit of fractional-order transformer is proposed and the construction steps are summarized.Finally,the fractional-order transformers with different orders are constructed.The rationality and feasibility of the constructed circuit are verified by simulations and experiments.3.The fractional-order flyback converter circuit model is proposed based on the fractionalorder transformer and fractional-order capacitor model.The state space averaging method and the switch network averaging method are respectively used to obtain the model of the fractionalorder flyback converter in continuous conduction mode.Finally,the experiment of the fractional-order flyback converter is carried out by using the proposed constructed fractionalorder transformer.The simulation and experimental results show that the order of fractionalorder elements has a great influence on the characteristics of the converter.Moreover the fractional-order flyback converter can achieve smaller voltage overshoot,shorter transition time and higher design freedom.