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The switching behavior of power converters with "ideal" electronic devices (EDs) makes it difficult to define a switched model that describes the dynamics of the converter in all possible operating conditions, i.e., a "complete" model. Indeed, simplifying assumptions on the sequences of modes are usually adopted, also in order to obtain averaged models and discrete-time maps. In this paper, we show how the complementarity framework can be used to represent complete switched models of a wide class of power converters, with EDs having characteristics represented by piecewise-affine (even complicated) relations. The model equations can be written in an easy and compact way without the enumeration of all converter modes, eventually formalizing the procedure to an algorithm. The complementarity model can be used to perform transient simulations and time-domain analysis. Mathematical tools coming from nonlinear programming allow to simulate numerically the transient behavior of even complex power converters. Also rigorous time-domain analysis is possible without excluding pathological situations like, for instance, inconsistent initial conditions and simultaneous switchings. Basic converter topologies are used as examples to show the construction procedure for the complementarity models and their usefulness for simulating the dynamic evolution also for nontrivial operating conditions.

This paper studies linear passive electrical networks with ideal switches. We employ the so-called linear switched systems framework in which these circuits can be analyzed for any given switch configuration. After providing a complete characterization of admissible inputs and consistent initial states with respect to a switch configuration, the paper introduces a new state reinitialization rule that is based on energy minimization at the time of switching. This new rule is proven to be equivalent to the classical methods of Laplace transform and charge/flux conservation principle. Also we illustrate the new rule on typical examples that have been treated in the literature.Index Terms-Consistent initial conditions, energy-based jump rule, state discontinuities, state jump, switched networks.

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Çamlıbel, Mehmet Kanat (Dogus Author) -- Göknar, İzzet Cem (Dogus Author) -- Conference full title: 2008 IEEE International Symposium on Circuits and Systems : Seattle, WA, 18 - 21 May 2008In this paper, the objects of study are electrical networks consisting of passive elements, independent sources, and ideal switches. We study the discontinuities in state variable that are caused by the switching behavior. The main contribution of the paper is to present an energy-based state jump rule that is equivalent to those based on charge/flux conservation principle and Laplace transform. The advantage of the proposed rule lies in the fact that one can explicitly compute the state jump

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