Research Of The Nonlinear Dynamic Characteristics Of DC-DC Switching Converters

DC-DC switching converters have very ultra-intensive applications. They are typical switching systems with strong nonlinear and time-varying characteristics, and exhibit abundant nonlinear behaviors, such as various types of bifurcation and chaos under certain operational conditions. With the development of the power electronics, the requirement of their stability, reliability and economy is increasing. Therefore, it is very necessary and significant that the nonlinear behaviors, characteristics and physical mechanism are investigated so that the nonlinear behaviors are better understood, their operation mechanism is deeply revealed, and their designs are further optimized. Furthermore, it is beneficial to exploit the research field of power electronics, promote the further development of the power electronics, and enrich the contents and the methods of the nonlinear science for them to be researched.On the basis of the theory of the nonlinear dynamic system, a theoretical and experimental investigation of the nonlinear dynamic characteristics of the DC-DC switching converters are deeply made from the following five aspects:their modeling, research of their nonlinear behavior, investigation of the mechanism of their nonlinear behavior, study of the dynamic characteristics of the DC-DC converter in maximum power point tracking (MPPT) for photovoltaic power system. The main works and contributions are as follows:1) Modeling of the DC-DC switching converters is made. A new modeling method is proposed, in which the advantages of the three-terminal switching modeling method, switching network averaging modeling method and the energy conservation modeling methods are combined. The equivalent circuit model is established, in which the parasitic components, such as the on-resistance of the transistor, the forward resistance and built-in voltage of the diode, the equivalent series resistance of the inductance and capacitor and the magnetized inductance of transformer are considered. The DC and small signal circuit model are derived based on it. The theoretical analysis and simulation research of the steady-state and dynamical characteristics are made according to the model. The obtained results show that the equivalent series resistance of the capacitor and MOSFET delay effect have great influence on the high frequency characteristics of the converters, and the other parasitic components have mainly influence on the low frequency characteristics. The method is characteristics of high precision and small computing quantity.2) Research of the nonlinear behaviors in DC-DC switching converters is performed. The period-doubling bifurcation, tangential bifurcation, chaos and intermittent chaos are studied deeply. Theoretically, the first and the third discrete iterative maps of the converters are derived, and it is proved that the necessary conditions leading to period-doubling bifurcation and tangential bifurcation in converter under some conditions can be satisfied. An analysis of the evolution of period-doubling bifurcation, tangential bifurcation, chaos and intermittent chaos is performed by graph method. A detail discussion of the relationship of the critical value causing period-doubling bifurcation and the circuit parameters is conducted.3) Investigation of the mechanism of the nonlinear behavior is done. Based on the nonlinear dynamic theory, investigation of the mechanism of period-doubling bifurcation, tangential bifurcation, chaos and intermittent chaos are made. Their physical mechanisms are revealed. That is, under some operational conditions, when some circuit parameters, such as reference current and voltage feedback factor, are equal to some critical values, the catastrophe of the number and the stability of the discrete iterative map solutions happens so that the conditions resulting in period-doubling bifurcation and tangential bifurcation are satisfied, the behaviors occur. With the continuous variation of the circuit parameter, the catastrophe of the number and the stability of the map solutions will also take place, thus leading to bifurcating continuously, and the system eventually approaches to chaos. The reasons that the intermittent chaos happens is that before the tangential bifurcation takes place, when some parameters are equal to their critical values, the long-time regular behavior and the sporadic short-time irregular behavior carry out alternatively and randomly. In other words, it is the approximate period motion with occasional irregular behavior.4) Analysis of the dynamical characteristics of DC-DC Converter in maximum power point tracking (MPPT) for photovoltaic (PV) power system is performed. Based on the nonlinear dynamic system theory, the model of the discrete iterative map of the interleaved Boost converter (ILBC) in MPPT is derived. The study of the dynamical characteristics is made by bifurcation diagrams, time-domain waveforms and phase trajectories in the terms of the model, and the comparison between the interleaved Boost converter and the parallel-connected Boost converter (PCBC) is performed. Both the simulation and experiment results show that compared with the PCBC, the ILBC is larger in the stable-domain, smaller in inductor current ripple and capacitance voltage ripple and smaller in variation range of inductor current and capacitance voltage. Thus, the ILBC is more suitable than the PCBC in MPPT for PV generation.5) Experiments are done. The experiments of the nonlinear behaviors such as period-doubling bifurcation, tangential bifurcation, chaos and intermittent chaos in DC-DC switching converters have been done. In addition, the experiments of the interleaved boost converter in MPPT for PV power system are performed. The experimental results fit the theoretical analysis quite well, thus validating the correctness of the theory.