SPWM单相逆变器的建模与瞬态分析
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摘要
本文建立了SPWM单相逆变器系统的非线性数学模型,通过引入双重傅里叶变换描述非线性开关函数,将等效小参量法拓展到逆变器的瞬态分析中,得到了该系统状态变量的瞬态解析解。该方法弥补了状态空间平均法无法分析纹波的特点,同时相比于广义平均法更加简便。仿真结果验证了该方法的准确性。所得结果均为符号表达式,可为工程设计提供理论指导,并可以进一步应用于系统的非线性特性与稳定性分析。
In this paper, a nonlinear mathematical model of SPWM single-phase inverter system is established. By introducing the double-Fourier transform to describe the nonlinear switching function, the equivalent small parameter(ESP) method is extended to the transient analysis of the inverter, and the system Transient Analytical Solutions of State Variables. This method makes up the characteristics of state space averaging(SSA) method that cannot analyze the ripple, and it is more convenient than the generalized average method. The simulation results verify the accuracy of the method. The results are symbolic expressions, which can provide theoretical guidance for engineering design and can be further applied to the nonlinear characteristics and stability analysis of the system.
In this paper, a nonlinear mathematical model of SPWM single-phase inverter system is established. By introducing the double-Fourier transform to describe the nonlinear switching function, the equivalent small parameter(ESP) method is extended to the transient analysis of the inverter, and the system Transient Analytical Solutions of State Variables. This method makes up the characteristics of state space averaging(SSA) method that cannot analyze the ripple, and it is more convenient than the generalized average method. The simulation results verify the accuracy of the method. The results are symbolic expressions, which can provide theoretical guidance for engineering design and can be further applied to the nonlinear characteristics and stability analysis of the system.
引文
[1]张友军.DC/AC逆变器技术及其应用综述[J].电气开关,2004,06:18-22.
[2]R.D.Middlebrook and S.Cuk,“A general unified approach to modelling switching-converter power stages,”1976 IEEE Power Electronics Specialists Conference,Cleveland,OH,1976,pp.18-34.
[3]V.Vorperian,R.Tymerski and F.C.Y.Lee,“Equivalent circuit models for resonant and PWM switches,”in IEEE Transactions on Power Electronics,vol.4,no.2,pp.205-214,Apr 1989.
[4]A.F.Witulski and R.W.Erickson,“Small signal ac equivalent circuit modelling of the series resonant converter,”1987 IEEE Power Electronics Specialists Conference,Blacksburg,VA,USA,1987,pp.693-704.
[5]X.Liu;A.M.Cramer;F.Pan,“Generalized Average Method for Time-Invariant Modeling of Inverters,”in IEEE Transactions on Circuits and Systems I:Regular Papers,vol.PP,no.99,pp.1-12
[6]丘水生.开关功率变换器符号分析方法的原理[J].电子学报,1997,01:5-10.
[7]刘永迪,李虹,张波,郑琼林,游小杰.基于双重傅里叶级数的混沌SPWM频谱量化分析[J].物理学报,2014,07:68-77.
[8]林波涛,丘水生.适于瞬态分析的等效小参量法及其在PWM开关变换器中的应用[J].电子科学学刊,1997,(05):649-657.
[2]R.D.Middlebrook and S.Cuk,“A general unified approach to modelling switching-converter power stages,”1976 IEEE Power Electronics Specialists Conference,Cleveland,OH,1976,pp.18-34.
[3]V.Vorperian,R.Tymerski and F.C.Y.Lee,“Equivalent circuit models for resonant and PWM switches,”in IEEE Transactions on Power Electronics,vol.4,no.2,pp.205-214,Apr 1989.
[4]A.F.Witulski and R.W.Erickson,“Small signal ac equivalent circuit modelling of the series resonant converter,”1987 IEEE Power Electronics Specialists Conference,Blacksburg,VA,USA,1987,pp.693-704.
[5]X.Liu;A.M.Cramer;F.Pan,“Generalized Average Method for Time-Invariant Modeling of Inverters,”in IEEE Transactions on Circuits and Systems I:Regular Papers,vol.PP,no.99,pp.1-12
[6]丘水生.开关功率变换器符号分析方法的原理[J].电子学报,1997,01:5-10.
[7]刘永迪,李虹,张波,郑琼林,游小杰.基于双重傅里叶级数的混沌SPWM频谱量化分析[J].物理学报,2014,07:68-77.
[8]林波涛,丘水生.适于瞬态分析的等效小参量法及其在PWM开关变换器中的应用[J].电子科学学刊,1997,(05):649-657.