Numerical modeling of transient and steady-state modes in the operation of pulsed DC-DC voltage converters


Аuthors

Tarasov D. Y.1*, Sukhomlino G. L.1**, Mikhailov V. V.2***

1. Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia
2. Leonov Moscow Region University of Technology, Korolev, Moscow Region, Russia

*e-mail: tarasovdu@bmstu.ru
**e-mail: sukhomlinov@bmstu.ru
***e-mail: mo_techuniv@mosreg.ru

Abstract

It is noted in the introductory part of the article that approaches based on application of the powerful commercial software such as MATLAB/Simulink are widely employed in the research works of the design organizations associated with the various types of the switched-mode DC-DC voltage converters development. At the same time, the trend associated with development of simpler computing tools, which can be relied upon not only while conducting specific computational studies of the said converters, but also for reliability confirming of the results obtained based on this software as well, is still being called for. The purpose of the article consists in describing one of the like type of computational tools based on the numerical integration method and designed for studying transient and steady state operation modes of the converters under discussion.

The article points out that systems of differential equations describing the dynamics of the switched-mode DC-DC voltage converters are characterized by the presence of specifics associated with abrupt changes of their parameters in time initiated by switching by pulse-width modulators with a given clock frequency f and a period T = 1/f. With reference to the work of one of the co-authors of the article, dealt with the numerical solution of dynamics problems of the electro-mechanical systems with discontinuous features (such as dry friction), the authors note that a simple and effective way of numerical implementation in such cases is application of an unconditionally computationally stable implicit Euler scheme when integrating over time.

The main content of the article deals with the description of the said approach in relation to the numerical simulation of transients in the operation of a buck switched-mode DC-DC voltage converter. The article presents a design diagram of the converter and corresponding dynamics problem is formulated in the form of a system of the two first-order differential equations (with respect to the inductor current i and the load voltage U) with discontinuous features. The algorithm of the numerical solution, implemented in the form of a program in the Fortran language, is recounted. The article presents the results of computations performed by this program related to the transient operation modes of the two concrete buck converters. These results fidelity is confirmed by comparison with the simulation results available in the open sources, performed in the MATLAB/Simulink. The article points at the option of the proposed model application (accounting for the discontinuous specifics) in the version corresponding to the so-called “continuous” or “averaged” model. On the example of the transient process computing for one of the considered buck converters performed with “discontinuous” and “continuous” versions of the developed computational model the article demonstrates that computational results of these versions are in good agreement with each other.

The final part of the article contains conclusions on the research performed. It is noted here that the article presents (based on the implicit Euler scheme implementation) an approach to the numerical modeling of transients of the switched-mode DC-DC voltage converters operation, with account for discontinuous features in the formulation of differential equations describing dynamics of such devices. Transients of two options of the DC-DC buck voltage converters (described in literature) were subjected to the numerical analysis. Fidelity of the numerical simulation results has been confirmed by practical concurrence with the results of computer modeling and physical experiment available in the literature. Capabilities of the continuous version of the developed computational model for solving problems of dynamics of the buck switched-mode DC-DC voltage converters have been demonstrated.

Keywords:

pulsed DC-DC voltage converter, differential equations with discontinuous singularities, implicit Euler scheme of numerical integration

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