Accurate Symbolic Steady State Modeling of Buck Converter

Abstract

Steady state analysis is fundamental to any electric and electronic circuit design. Buck converter is one of most popular power electronics circuit and has been analyzed in various situations. Although the behavior of buck converters can be understood approximately by the well-known state space averaging method, little is known in the sense of detailed behavior or exact solution to equations. In this paper a steady state analysis of buck converter is proposed which allows the exact calculation of steady state response. Our exact solution is expressed as a Fourier series. Our result is compared with numerical calculation to be verified. Our method copes with more complicated problems such as describing average power and root-mean-square power that are most critical issues in power electronics circuit.Copyright c 2017 Institute of Advanced Engineering and Science.All rights reserved.Corresponding Author: Ichijo Hodaka Department of Environmental Robotics, University of Miyazaki 1-1, Gakuen Kibanadai-nishi, Miyazaki, 889-2192, Japan Phone: +81 985 587 352 E-mail: hijhodaka[at]cc.miyazaki-u.ac.jp INTRODUCTIONAn analysis of steady-state response of a system is important key in circuit design and control, included dc-dc converter. In convential method, the steady state of dc-dc converter is assumed as the constant value. Many researches based on state space averaging method and high switching frequency assumption observe steady state response [1,2,3,4,5]. The method gives simple way to analyze but some ripples are undescribed clearly. The power electronic handbook approximate linear ripple to analyze dc-dc converter more accurately [6]. The approximation may be correct if the switching frequency is high. Since there are some limitation in component, some high frequency is not always reached.The importance of accurate steady-state analysis has already noticed in many researches [7,8,9,10,11,12]. A significant part of the design of circuits requires the simulation of the steady-state response. Parameters such as the gain, harmonic distortion and the input and output impedances are studied in the steady-state mode of operation [7]. Using conventional time-stepping simulations and waiting-time for possible steady state is often not practical because in most cases the time constants of the modes are much larger than the switching period [8]. In conventional method of dc-dc converter analysis, steady state ripple values are negligible, compared to the steady state values themselves. Switching power converters are inherently nonlinear and consequently it is very difficult to calculate the root-mean-square (RMS) values of the state variable ripple. These RMS values are important in order to calculate the current stresses of the different power converter devices as well as to filter design in order to meet the given specifications [9]. Though power electronic handbook [6] shows the RMS calculation using approximation linear ripple, the result is not absolutely correct due to linear approximation. In order to achieve a ...

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