Modeling of Processes on the Basis of State Space Averaging in Boost Converter With Magnetically Coupled Elements

Abstract

The features of the state-space average method using Lagrange's theorems for calculation of processes in the boost converter with magnetically coupled elements (with autotransformer connection of inductors) in continuous currents mode are considered. A mathematical model of the converter based on relative variables has been developed, which makes it possible to calculate processes in a wide range of parameters taking into account the degree of magnetic coupling between inductive elements, including the definition of constant and pulsating components. It is shown that to obtain a complete system of the algebraic equations as a mathematical model of converters, which provides its single solution, it is advisable to additionally use the ratio according to energy balance in reactive elements in a steady state at the operation intervals of the converter during commutation period. The boundary dependences of boost converter parameters with magnetically coupled elements between the modes of discontinuous and continuous currents are calculated. The relative characteristics of the converter have been studied, which demonstrate the influence of imperfection of the magnetic coupling in the regulation zone of the relative duration value of switching interval. Ref. 21, fig. 6.