DC-DC开关变换器的非线性动力学特性研究
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摘要
DC-DC开关变换器具有极其广泛的用途。它们是一类典型的强非线性时变系统,在一定的工作条件下呈现出丰富的非线性现象,如各种类型的分岔、混沌等。随着电力电子技术的发展,对其在稳定性、可靠性、经济性等多方面性能的要求不断提高。因此,深入研究其非线性现象、特性及产生机制,对于深刻认识这类开关变换器,揭示这些非线性现象产生的本质,进而优化这类变换器的设计都具有十分重要的现实意义。同时,对于拓展电力电子学的研究领域,促进电力电子学的进一步发展,丰富非线性科学的研究内容也具有重要的理论意义。
本文以非线性动力学理论为基础,从DC-DC开关变换器的建模、非线性现象分析、非线性现象机理研究、光伏发电最大功率点跟踪中DC-DC开关变换器的动力学特性、实验验证等五个方面对DC-DC开关变换器的非线性动力学特性进行了深入的理论和实验研究。本文主要研究工作和取得的研究成果包括：
1) DC-DC开关变换器的建模。结合三端器件开关模型法、开关网络平均模型法及能量守恒法的特点,提出了一种新的建模方法。建立了包含功率开关管的导通电阻、二极管的正向电阻和正向压降、电感和电容的等效串联电阻、变压器的激磁电感等寄生参数的等效电路模型,在此基础上导出其相应的DC和交流小信号电路模型。根据该模型,对其稳态和动态特性进行了深入的理论分析和仿真研究。结果表明,输出电容的等效串联电阻和MOSFET延迟效应对变换器的高频特性有较大的影响,功率开关管的导通电阻、二极管的正向导通电阻、电感等效串联电阻影响其低频特性。该方法具有精度高、计算量小的优点。
2) DC-DC开关变换器的非线性现象研究。本文重点研究了倍周期分岔、切分岔、混沌和阵发混沌这些非线性现象。从理论上,导出变换器的一次和三次离散迭代映射方程,论证了变换器在一定条件下满足产生倍周期分岔和切分岔所需的条件,采用图解的方法分析了倍周期分岔、切分岔、混沌和阵发混沌的演化过程,详细讨论了变换器产生倍周期分岔的临界值与电路参数的关系。
3)DC-DC开关变换器的非线性现象机理研究。根据非线性动力学原理,分析了变换器倍周期分岔、切分岔、混沌和阵发混沌现象产生的机理,揭示了这种非线性现象的物理本质。其物理本质是：在一定的工作条件下,当变换器的某些电路参数(如参考电流,电压反馈系数)等于某一临界值时,系统离散迭代映射方程的解的数目和稳定性会发生突变,使得倍周期分岔和切分岔的条件得以满足,从而引起倍周期分岔和切分岔现象。随着电路参数的不断变化,方程的解的数目和稳定性也在不断地突变,导致系统不断地发生分岔现象,最终趋向混沌运动状态。而在发生切分岔之前,当某些参数有变化达到某一临界阈值时,长时间的规则行为与相对短时间的突发不规则运动之间随机地交替出现,也就是带有偶发不规则运动的近似周期运动,由此产生阵发混沌现象。
4)光伏发电最大功率点跟踪(Maximum Power Point Ttracking, MPPT)中DC-DC开关变换器的动力学特性分析。建立了光伏发电MPPT交错并联boost变换器的离散迭代映射模型,在此基础上采用分岔图、时域波形图、相轨迹图方法,研究了其动力学特性,在变换器的稳定域、输入电感电流和输出电容电压的纹波、变化幅度等方面进行详细的讨论,并与普通boost变换器进行比较。研究结果表明,在相同电路参数的情况下,与一般boost变换器相比,交错并联boost变换器的稳定域更大,电感电流和电容电压的纹波小、变化幅度小,更适用于光伏发电MPPT。
5)实验。我们对DC-DC开关变换器电路中的倍周期分岔、切分岔、阵发混沌、混沌等非线性现象以及光伏发电MPPT中交错并联boost变换器进行了较全面的实验研究。实验结果与理论分析相符合,验证了本文理论分析的正确性。
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.
本文以非线性动力学理论为基础,从DC-DC开关变换器的建模、非线性现象分析、非线性现象机理研究、光伏发电最大功率点跟踪中DC-DC开关变换器的动力学特性、实验验证等五个方面对DC-DC开关变换器的非线性动力学特性进行了深入的理论和实验研究。本文主要研究工作和取得的研究成果包括：
1) DC-DC开关变换器的建模。结合三端器件开关模型法、开关网络平均模型法及能量守恒法的特点,提出了一种新的建模方法。建立了包含功率开关管的导通电阻、二极管的正向电阻和正向压降、电感和电容的等效串联电阻、变压器的激磁电感等寄生参数的等效电路模型,在此基础上导出其相应的DC和交流小信号电路模型。根据该模型,对其稳态和动态特性进行了深入的理论分析和仿真研究。结果表明,输出电容的等效串联电阻和MOSFET延迟效应对变换器的高频特性有较大的影响,功率开关管的导通电阻、二极管的正向导通电阻、电感等效串联电阻影响其低频特性。该方法具有精度高、计算量小的优点。
2) DC-DC开关变换器的非线性现象研究。本文重点研究了倍周期分岔、切分岔、混沌和阵发混沌这些非线性现象。从理论上,导出变换器的一次和三次离散迭代映射方程,论证了变换器在一定条件下满足产生倍周期分岔和切分岔所需的条件,采用图解的方法分析了倍周期分岔、切分岔、混沌和阵发混沌的演化过程,详细讨论了变换器产生倍周期分岔的临界值与电路参数的关系。
3)DC-DC开关变换器的非线性现象机理研究。根据非线性动力学原理,分析了变换器倍周期分岔、切分岔、混沌和阵发混沌现象产生的机理,揭示了这种非线性现象的物理本质。其物理本质是：在一定的工作条件下,当变换器的某些电路参数(如参考电流,电压反馈系数)等于某一临界值时,系统离散迭代映射方程的解的数目和稳定性会发生突变,使得倍周期分岔和切分岔的条件得以满足,从而引起倍周期分岔和切分岔现象。随着电路参数的不断变化,方程的解的数目和稳定性也在不断地突变,导致系统不断地发生分岔现象,最终趋向混沌运动状态。而在发生切分岔之前,当某些参数有变化达到某一临界阈值时,长时间的规则行为与相对短时间的突发不规则运动之间随机地交替出现,也就是带有偶发不规则运动的近似周期运动,由此产生阵发混沌现象。
4)光伏发电最大功率点跟踪(Maximum Power Point Ttracking, MPPT)中DC-DC开关变换器的动力学特性分析。建立了光伏发电MPPT交错并联boost变换器的离散迭代映射模型,在此基础上采用分岔图、时域波形图、相轨迹图方法,研究了其动力学特性,在变换器的稳定域、输入电感电流和输出电容电压的纹波、变化幅度等方面进行详细的讨论,并与普通boost变换器进行比较。研究结果表明,在相同电路参数的情况下,与一般boost变换器相比,交错并联boost变换器的稳定域更大,电感电流和电容电压的纹波小、变化幅度小,更适用于光伏发电MPPT。
5)实验。我们对DC-DC开关变换器电路中的倍周期分岔、切分岔、阵发混沌、混沌等非线性现象以及光伏发电MPPT中交错并联boost变换器进行了较全面的实验研究。实验结果与理论分析相符合,验证了本文理论分析的正确性。
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.
引文
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