| Fractional calculus has been developed for hundreds of years,and has been increasingly used in engineering in recent decades..Study have shown that fractional derivative have an advantage in describing some material and system with memory and genetic characteristics,and more accurate in the field of fluid mechanics.With the deepening of research,scientist introduced the fractional model into the field of circuit and system,expanded the integer order model of the capacitive inductance to the fractional order model,and studies the fractional model describing the device.Based on the fractional characteristics of inductance and capacitance devices,the fractional calculus is introduced into the modeling and control method of power filter.The influence of the fractional order of the circuit component on the filter effect and the stability of the control system is studied.First,this paper summarized the theory of fractional calculus in the progress of circuit,capacitance inductance of fractional characteristics,study the fractional order circuit model of the device.The mathematical model and circuit model of fractional inductance and capacitance are given.The circuit approximation simulation of the 0.9 capacitor is carried out.The simulation and experiment of voltage and current relationship are carried out.Secondly,the fractional order LCL filter is studied.The fractional order model of the filter circuit is established,and the influence of the order number on the transfer function and resonance frequency is analyzed.Based on this,the fractional order model of active filter containing LCL filter is derived.The transfer function of the output current to the input voltage and the duty cycle is established,and the fractional current closed-loop control is introduced.The stability of the fractional-order control system is analyzed.The difference between the fractional-order control and the integer-order control is compared,and the system of fractional order parameter influence on control effect. |
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