Abstract
The paper deals with processes analysis in circuits of converter working on a time-varying load. A control of inverter and load switches are realised by signals with incommensurable frequencies. Processes in such a system are described by differential equations with periodical coefficients. Steady-state periodic solutions can be obtained by the extension of ordinary differential equations with one independent time variable into partial differential equations with two independent variables of time. These equations are solved by use of the Galerkin method with trigonometric basis and weight functions. The results of calculations of the steady-state process for a buck-boost converter are presented in form of the double Fourier series. They are compared with results obtained in the way of numerical calculation of differential equations for a transient process. Extended equations are also solved by a generalized state-space averaging method. A balance of active power in circuits of converter with the time-varying load is shown.
Highlights
DC converters are used to energy supply of loads with constant and varied structure
If DC converter works on a varied load, the processes in the circuit are described by differential equations with periodic coefficients
The aim of this paper is to present methods based on the differential equations extension and on use of the Galerkin method [12]
Summary
If DC converter works on a varied load, the processes in the circuit are described by differential equations with periodic coefficients. Processes in such a system can be analysed using analytical and numerical methods [1]–[7]. An extension of differential equation is shown in [10] and an approximation of solutions in [9] It should be mentioned, that in case of incommensurable frequencies, state-space average models cannot be used. In order to simplify a calculation procedure of processes it is expedient to use both tools, i.e. the extension of differential equations and the approximation of solutions [11]. Results of calculations are compared with results obtained by a numerical method
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