Abstract
The paper deals with processes analysis in inverter circuits. These processes are described by differential equations with periodical coefficients. Since control signals and voltages operating in an inverter circuit are independent theirs frequencies are often incommensurable. In order to obtain steady-state periodic solutions ordinary differential equations with one independent time variable are expanded into partial differential equations with two independent variables of time. Obtained partial differential equations with periodical coefficients are transformed into equations with constant coefficients by using the Lyapunov transformation. Since these equations are defined in the domain of two time variables theirs solutions are determined by using the two dimensional Laplace transform. After solving differential equations a steady-state solution is given in the form of the double Fourier series. Frequency responses are defined as functions of Fourier coefficients dependent on control signal and power voltage frequencies. Results of calculations of frequency responses for a buck-boost inverter are presented.Ref. 11, fig. 7.<
Highlights
The analysis of transient and steady-state processes in periodic time-varying circuits a difficult task connected with necessity to take into account element models, control signals and power sources
In periodic time-varying circuits this method can not be used since processes in such circuits are described by differential equations with periodically variable coefficients
The aim of this article is to find steady-state processes in an inverter circuit worked with incommensurable signal frequencies and analyze frequency responses
Summary
The analysis of transient and steady-state processes in periodic time-varying circuits a difficult task connected with necessity to take into account element models, control signals and power sources. For linear circuits there are different analysis methods among which it should be noted the frequency response method [1]. In periodic time-varying circuits this method can not be used since processes in such circuits are described by differential equations with periodically variable coefficients. Processes in such circuits can be analysed by different method [2, 3, 4, 5] in case these circuits are controlled by signals with the same or proportional frequencies. In the domain of one time variable one cannot find periodic steady-state behaviour
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