Fabrication Of Fractance And Modeling Analysis Of Fractional Order DC-DC Converter

Fractional calculus has had a profound impact on the system modeling and analysis in various fields since its introduction.Inductors and capacitors with fractional nature are important components of DC-DC converters,and their electrical properties which are related with fractional order can have a significant effect on the modeling and analysis.However,the research literature about fractional-order DC-DC converters is still very scarce,especially using the actual fractional-order elements is rarely reported.Therefore,this paper discusses the construction steps and synthesis methods of fractance,and constructs the actual fractance approximation circuit.Then,two typical fractional-order DC-DC converters are modeled and analysed by the Equivalent Small Parameter Method(ESPM)which is suitable for strong nonlinear system analysis.The steady-state periodic solutions of state variables of are obtained in the form of analytical expressions which can accurately reflect the influence of component order.And ESPM has the advantages of clear physical meaning and high precision.The paper mainly completed the following work:(1)The theoretical basis and commonly used approximation algorithm of fractional-order component construction are introduced.And based on the Brune synthesis method,a passive fractance synthesis method suitable for 0-1 order is designed with the concept of minimum function.It can be combined with various algorithms for fractional element approximation circuit structure.Based on this method,the approximation circuit of fractional capacitance and fractional inductance is constructed,and the simulation analysis and experimental verification are carried out.(2)The nonlinear mathematical model of the fractional-order Z-source converter running in the current continuous mode(CCM)and the fractional-order Boost converter running in the current discontinuous mode(DCM)are established.And get their approximate analytic expressions of steady-state periodic solutions for state variables with ESPM.And then discuss the influence of fractional-order on the harmonics of state variables.The proposed method is proved to effective when compared its result with numerical simulation and circuit simulation.(3)Based on the fractional capacitance and inductance approximation circuit,an experimental circuit of fractional-order DCM-Boost converter is constructed.The experimental results are in well agreement with the results of the ESPM,which shows that the ESPM is effective and accurate in analyzing the fractional-order DC-DC converters.