Symbolic analysis method and apparatus of fractional order switching converter under continuous current mode

Abstract

The present invention discloses a symbolic analysis method and apparatus of a fractional order switching converter operating under continuous current mode. On the basis of the harmonic balance principle, the method converts a process of solving non-integer-order calculus operation into a processing of matrix operation and linear equation group solution by converting state variable fractional order differential operation in the converter into differential operators and combining all of the differential operators into a diagonal semiotic matrix. Compared with an existing analysis method of establishing an Oustaloup filter approximate model in Matlab / Simulink which is frequently used for a fractional order switching converter, the method can analytically analyze state variable ripple peak-to-peak values of the converter and the influence of order change of an energy storage element on the working condition of the converter, can rapidly obtain analytical solution of a steady state period of state variables, and can also be used for analyzing harmonic components of the state variables.

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 and device for fractional-order switching converters working in current continuous mode. 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 "Podlubny I.Fractional Differential Equations[M].San Diego:Academic Press,1999,Chap.2."It i...

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Problems solved by technology

According to this idea, the existing technology (such as reference 1 "Wang Faqiang, Ma Xikui. Modeling and analysis of Boost converter in inductor current discontinuous mode based on fractional calculus [J]. Chinese Science: Technical Science, 2013, 43(4), pp.368-374", etc.) studied the fractional-order switching converters in the inductor current discontinuous 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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