A Symbolic Analysis Method for Inductive Current Discontinuous Mode Fractional Order Switching Converter

Abstract

The invention discloses an inductance current interrupted mode fractional order switch converter symbol analysis method combining a harmonic wave balance principle; the method converts differential operation relating to status variable fractional order in a converter into differential operators, and combines all differential operators into an opposite angle symbol matrix, thus converting a non-integer order calculus operation solving process into a matrix operation and linear equation (group) solving process. Compared with a conventional normal analysis method, aiming at the fractional order switch converter, of building an Oustaloup filter approximation model in a Matlab / Simulink, the novel method can parse and analyze converter status variable ripple peak-to-peak value size and influences on converter work status by energy storage element order changes, can fast obtain a status variable stable state periodic analytic solution, and can parse status variable harmonic wave components.

Description

technical field [0001] The invention relates to the field of modeling and analysis of fractional-order switching converters, in particular to a symbolic analysis method for fractional-conduction-conduction mode (DCM, Discontinuous-conduction Mode) switching converters. Background technique [0002] In the past, the commonly used modeling and analysis methods for switching converters include: models based on state space averaging, discrete iterative mapping models, piecewise linear models based on circuit principles (KCL, KVL), and methods that combine harmonic balance and disturbance methods, etc. The analysis objects of these methods are integer-order switching converters, that is, the capacitors and inductors in the converter are all integer-order components. However, the existing reference 1 "Westerlund S. Dead Matter Has Memory![ M].Kalmar,Sweden:Causal Consulting,2002,Chap.7."And reference 2 "PodlubnyI.Fractional Differential Equations[M].San Diego:Academic Press,1999,C...

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Problems solved by technology

According to this idea, existing technologies (such as reference 4 "Wang Faqiang, Ma Xikui. Fractional-order modeling and simulation analysis of Boost converter under inductor current continuous mode [J]. Acta Physica Sinica, 2011, 60(7). 070506- 1–070506-8”, etc.) studied the fractional-order switching converters in the inductor current continuous and pseudo-continuous operating modes, image 3 and Figure 4 are separately passed figure 1 and figure 2 The capacitor voltage and inductor current waveforms obtained by the model established in , the existing technology is to show the operating characteristics of the fractional-order switching converter by building a modular model in Matlab / Simulink, and show the steady state by means of simulated waveforms The ripple of the converter state variable; this method cannot obtain the steady-state periodic analytical solution of the state variable, and it is difficult to analytically analyze the peak-to-peak value of the ripple

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