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Non-smooth modelling of electrical systems using the flux approach

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Abstract

The non-smooth modelling of electrical systems, which allows for idealised switching components, is described using the flux approach. The formulations and assumptions used for non-smooth mechanical systems are adopted for electrical systems using the position–flux analogy. For the most important non-smooth electrical elements, like diodes and switches, set-valued branch relations are formulated and related to analogous mechanical elements. With the set-valued branch relations, the dynamics of electrical circuits are described as measure differential inclusions. For the numerical solution, the measure differential inclusions are formulated as a measure complementarity system and discretised with a difference scheme, known in mechanics as time-stepping. For every time-step a linear complementarity problem is obtained. Using the example of the DC–DC buck converter, the formulation of the measure differential inclusions, state reduction and their numerical solution using the time-stepping method is shown for the flux approach.

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Authors and Affiliations

  1. IMES, Center of Mechanics, ETH Zurich, CH-8092, Zurich, Switzerland

    Michael Möller & Christoph Glocker

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  1. Michael Möller
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  2. Christoph Glocker
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Correspondence to Michael Möller.

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Möller, M., Glocker, C. Non-smooth modelling of electrical systems using the flux approach. Nonlinear Dyn 50, 273–295 (2007). https://doi.org/10.1007/s11071-006-9157-2

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  • DOI: https://doi.org/10.1007/s11071-006-9157-2

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