Complex behaviour of a simple partial-discharge modelH. Suzuki1, K. Aihara2, 3 and T. Okamoto4
1 Department of Mathematical Informatics, The University of Tokyo Tokyo 113-8656, Japan
2 Institute of Industrial Science, The University of Tokyo - Tokyo 153-8505, Japan
3 ERATO Aihara Complexity Modelling Project, JST - Kawaguchi 332-0012, Japan
4 Central Research Institute of Electric Power Industry - Kanagawa 240-0196, Japan
(Received 4 November 2003; accepted in final form 2 February 2004)
We examine the most simple and deterministic model of partial-discharge phenomena, or the three-capacitance equivalent circuit model with fixed parameter values. Although it is an old model proposed more than fifty years ago, here we show that its behaviour should be described with contemporary concepts of nonlinear dynamics such as devil's staircases and fractals. The model can be reduced to a class of piecewise isometries, termed double rotations. Because of the self-similar structure in the parameter space of double rotations, the average discharge rate of the three-capacitance model as a function of the applied voltage is very complex, resembling a devil's staircase, in spite of the simple appearance of the model. Our result provides comprehension of the dynamical complexity inherent in real partial-discharge phenomena.
05.45.Ac - Low-dimensional chaos.
05.45.Df - Fractals.
52.80.-s - Electric discharges.
© EDP Sciences 2004