Fractional Calculus and Its Application in Capacitance Modeling of Power Converter

Accurate modeling is the key technology of power electronics system. Traditional integer order equivalent models capture the power converter dynamics with limited knowledge, which neglects the fact that the capacitor and the inductor are fractional in nature. Firstly, several definition forms of fractional calculus commonly used in engineering field are given. And explanations on the geometric and physical meanings of fractional calculus are discussed. Then, the application feasibility of fractional calculus modeling for power electronics converter is discussed. A fractional calculus modeling method for power electronics converters is proposed. The fractional capacitance models of several power electronics systems are built. The integer order model and the fractional order model of the power electronics systems are compared and analyzed. The advantages and disadvantages of fractional calculus modeling for different converter objects are presented by the simulation results. Also, the application necessity and validity of the fractional order modeling method for converter field are verified.