Study On Bifurcation, Chaos And Its Applications In Power Electronic Circuits

Bifurcation and chaos phenomena have been widely known in many practical circuits, such as Wien bridge circuit, radar antenna, phase-locked loops, DC/DC converters and so on. Due to numerous varieties and topologies, nonlinear circuits have redundant bifurcation patterns leading to chaos. In this dissertation, with the assistance of Twin-T circuit and memristor based chaotic circuit (MCC), bifurcation and chaos in several typical digitally controlled power electronic circuits are discussed. Additionally, chaos is applied to power electronic circuits for the sake of improving the system performance.Twin-T circuit is widely used in oscillators and notch filter due to its outstanding frequency-selecting ability. A new chaotic Twin-T circuit is designed in this dissertation by connecting a light-emitting diode to the junction of two capacitors in the original circuit topology. The bifurcation diagrams are drawn, which shows clearly that the output voltage evolved to chaos through period-adding bifurcation as the control signal strength coefficient increases.Memristor is regarded as the forth basic element except for resistor, capacitor and inductor. By replacing the nonlinear element in Chua's circuit with memristor, MCC system is obtained. Bifurcation behavior and double-scroll strange attractor are studied by means of numerical methods such as bifurcation diagram, the largest Lyapunov exponent, power spectrum, etc. A chaos controller which includes a Twin-T notch filter and a voltage-current interface circuit is designed to adjust MCC from chaos to period in this dissertation. By modifying MCC system with an inductor and a negative conductance, a new five order hyperchaotic circuit is achieved.It has been validated that bifurcation and chaos are common phenomena in power electronic converters. However, the bifurcation phenomena in digitally controlled converter involving with time delay and quantization error is rarely concerned. In this dissertation, the bifurcation phenomenon of a digitally proportional-integral (PI) controlled synchronous buck converter (SBC) is investigated by making use of z-domain small signal model. In addition, the limit cycle is estimated by taking into account the dynamic gain caused by quantization effect on the basis of describing function.Switched reluctance drive (SRD) can also be regarded as a converter circuit including a particular moving component. Based on the assumption that phase inductance is independent of phase current, the comparison of bifurcation behaviors between analogly and digitally controlled SRD are presented. Additionally, a new nonlinear model on the basis of exponential function is designed and brought to analyze the bifurcate and chaotic behaviors in SRD system by the aid of bifurcation diagram and power spectrum. In many cases, the topology as well as mathematic describing equations of a circuit is of impossibility to characterize by reason of the complex. In this dissertation, a time series sampled from MCC is used to testify the validation of phase space reconstruction technique. Additionally, a fuzzy controlled SRD simulation model is built based on MATLAB Simulink environment. The calculation results of fractal dimension and the largest Lyapunov exponent demonstrate that in a wide parameter region, digitally controlled SRD behaves in chaotic oscillation.MCC is introduced as signal source to carry out the chaotic frequency spreading strategy for digitally controlled SBC. In accordance with the conclusion that fuzzy controlled SRD system can operate in a wide region chaotically, a chaotic frequency spreading strategy is designed by taking feedback acceleration as chaotic signal. In addition, the frequency spectrum of filter capacitor in SRD operated under the condition that different single phase faults come forth in the converter is analyzed. Single fault diagnosis of converter in SRD system is implemented on the strength of chaotic invariant extracted from detailed filter capacitor voltage.