Report 1994-13

Circuits in Power Electronics

J. Waldvogel

Abstract: The dynamics of circuits in power electronics may often be modelled by means of systems of linear differential equations with piecewise constant coefficients and sinusoidal inhomogeneities. The Static Var (Volt-Ampere reactive) Compensator (SVC, a device for power network control) is a representative example. Initial value problems of this type may be handled by means of the matrix exponential, whereas the construction of periodic solutions is in itself a linear problem. The linear algebra package MATLAB is ideally suited for numerically performing the above mentioned tasks, including stability analysis and spectral analysis of periodic solutions. This paper begins with the description of the engineering background and a brief outline of the well known mathematical theory. Then a transparent, but efficient program capable of generating, plotting and analyzing periodic solutions is presented and documented.

Keywords: circuit, exponential matrix, linear differential equation, MATLAB, periodic solution, piecewise constant coefficients, power electronics

Paper: Available as PDF (178 KB) or as hardcopy to order reports@sam.math.ethz.ch.

Publishing information: Solving Problems in Scientific Computing using Maple and MATLAB. Editors: W. Gander, J. Hrebicek. Springer Verlag, second edition, (1995), pp. 299-311