Relationship of fast‐scale and slow‐scale instabilities in switching circuit with multiple inputs

Abstract

SummaryPower converter circuits, such as current‐controlled or voltage‐controlled converters and inverters often have multiple inputs in the controller. The multiple inputs cause high‐frequency and low‐frequency oscillations. In earlier studies, the characteristics of circuits in fast‐scale and slow‐scale dynamics have been investigated. However, in many cases, circuits with multiple inputs have three or more dimensional topology which makes detailed analysis difficult. In this paper, we analyze a simple interrupted electric circuit in order to understand essential characteristics of fast‐scale and slow‐scale dynamics. The advantage of this simple interrupted circuit is that it is possible to derive a 1‐dimensional map, which facilitates rigorous studies. Based on the structure of the return map and the characteristic multiplier, we explain the characteristics of the system. We report the occurrence of pitchfork, period doubling, and border collision bifurcations in slow scale, and period doubling bifurcation in fast scale. We found that local bifurcation, which appears in fast‐scale dynamics, does not significantly affect the global behavior of the system while instabilities in the slow‐scale dynamics strongly affect the system behavior. Copyright © 2016 John Wiley & Sons, Ltd.