电流控制型DC-DC级联系统大信号稳定性关键问题研究
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摘要
随着电子信息技术和新能源技术的不断发展,直流分布式电源系统以其独特的优势受到学术界的热切关注,并广泛应用于电动汽车、计算机系统、医疗电子设备以及电信行业等领域。在带来诸多好处的同时,庞大的规模及复杂的结构不仅使系统的稳定性问题凸显,还给稳定性设计带来了很大的难度,若想将其作为整体进行稳定性分析几乎不可能。针对这一重要学术难题,国内外学术界从直流分布式电源系统最基本的连接形式——级联系统入手,基于小信号分析方法取得了一定的理论成果,但仅限于对系统稳态工作点附近的稳定性情况进行研究,不适用于大信号扰动的情况。因此,为全面分析系统的稳定性,深入理解和改善系统在大信号扰动下的运行情况,提高系统的可靠性,极有必要从大信号角度出发,结合非线性理论建立相应的研究方法对级联系统稳定性进行分析。本文从大信号的研究角度出发,结合回转器理论和相关的非线性研究方法对DC-DC级联系统大信号稳定性问题进行了深入探讨,主要包含以下内容：
在对现有大信号模型进行对比研究的基础上,本文基于回转器理论为电流模式控制型DC-DC变流器建立了统一的大信号模型。该模型克服了现有大信号模型复杂、难以应用于理论分析的缺点,实现了降阶,输入-输出表达式简单,且仅采用单环反馈即可实现电流模式控制的功能,为后续理论分析提供了便利。由于回转器理论的基础是能量守恒定律,故该模型具有普适性,仅需修改一个参数的数值即可实现对不同拓扑变流器的建模分析。在较好地反映原变流器大信号特性的同时,该模型还能够正确反映系统在平衡点附近的小信号特性。模型的简便性、普适性、结构统一性和完备性为理论分析系统稳定性奠定了良好的基础,也为解析形式大信号稳定性判据的提出提供了可能。
在DC-DC级联系统稳定性分析方面,本文采用李雅普诺夫线性化方法及混合势函数理论分别对级联系统的小信号和大信号稳定性进行了探讨。出于简化分析的目的,采用回转器统一大信号模型和恒功率负载分别对系统中的源、负载变流器进行替代。基于该简化级联系统及李雅普诺夫线性化方法,本文提出了解析形式的小信号稳定性判据。该判据仅需较少的参数即可对稳定性情况进行判断,避免了复杂的阻抗计算过程。同时,本文基于混合势函数理论得到了级联系统在大信号扰动下保持稳定运行所需满足的充分条件,即解析形式的大信号稳定性判据。由于分析时基于相同的简化系统模型,故可将大、小信号判据合二为一,得到了级联系统的统一稳定性判据。当该判据成立时,系统在大、小信号扰动下均能稳定运行,从而使设计过程得以简化。同时,本文对负载变流器响应速度较慢、不具备等效为恒功率负载条件的级联系统稳定性也进行了研究,并得到了相似的结论。为方便应用,仍可采用上述统一稳定性判据对该类级联系统进行分析。
本文第四章将提出的回转器统一大信号模型和级联系统大信号稳定性理论研究成果应用于直流母线补偿技术领域,提出了一种直流母线电压补偿控制策略。该策略从大信号的研究角度出发,根据级联系统的具体情况对其进行补偿。且该策略由混合势函数理论的稳定性定理推导得出,从理论上保证了加入补偿装置后整个系统在大信号扰动下的稳定性。此外,该控制策略还具有一定的普适性,能够达到较好的补偿效果。
With the development of electronic and renewable energy technique, DC distribution power system (DPS) becomes more and more attractive due to its unique advantages, and it has been widely used in the fields of electric vehicles, computer systems, medical electronic equipment, telecommunications industry, etc. The DC DPS has provided lots of benefits, but also negative factors. Increasingly larger size and complex structure not only highlights the stability issue, but also brings great difficulty for stability design. It is almost impossible to take the DC DPS as a whole for stability analysis. For this important issue, researches and analysis starts with cascaded system which is the most basic connection form of distributed architecture, and some useful theoretical achievements have been made based on small-signal analysis method. But the conclusions are only suitable to analyze the stability around equilibrium point, and will be invalid when large-signal disturbance occurs. Therefore, in order to analyze comprehensively, get in-depth understanding of system operation under large-signal disturbance, and improve system reliability, it is necessary to establish appropriate research methods based on nonlinear theory for large-signal stability analysis. This dissertation investigated and analyzed the large signal stability issue of DC-DC cascaded system in depth based on gyrator theory and relevant nonlinear analysis methods, which mainly contains the contents as below.
Based on the comparative study of the existing large-signal model, this dissertation proposes a unified large signal model for current-mode controlled DC-DC converter based on the gyrator theory. The proposed model overcomes the shortcomings of existing large-signal models, such as complicated and difficult to be adopted for theoretical analysis. It is order-reduced, and the input-output expression is simple. Only single feedback loop is needed to achieve current mode control function, and it provides convenience for theoretical analysis. Because the gyrator theory is based on the energy conservation law, the proposed large-signal model is generalized and can be applied to all the basic topologies by modifying only one parameter in the model.In addition to reflect large-signal properties of original converter well, this model also includes all the small-signal information around the equilibrium point. Due to the characteristic of simplicity, generalization, structural uniformity, and completeness, this model provides foundation and possibility for theoretical analysis, and analytical large-signal stability criterion could be derived based on it.
For the stability analysis of DC-DC cascaded system, this dissertation investigates the small-signal and large-signal stability of DC-DC cascaded system based on Lyapunov linearization method and mixed potential theory. To simplify the analysis, the proposed gyrator large-signal model is employed for simplifying the source converter, and the load converter is simplified as a constant power load (CPL). An analytical small-signal stability criterion is obtained based on this simplified system and Lyapunov linearization method. With the proposed criterion, the small-signal stability of system can be judged based on few parameters without complex input-output impedance calculation. Furthermore, the sufficient condition for stable operation of system under large-signal disturbance is proposed based on the mixed potential theory. It is also the analytical large-signal stability criterion for DC-DC cascaded system. Based on the same simplified system model, the proposed small-and large-signal criteria can be combined to derive a general stability criterion. When it holds, the system can work stable under both small-signal and large-signal disturbance, and the design process is simplified. Meanwhile, this dissertation also investigates the cascaded system in which the response speed of load converter is not so fast that it can not be simplified by CPL. Similar conclusion is derived. For convenience of application, the general stability criterion mentioned above can still be used to analyze the stability for this kind of system.
Based on the proposed gyrator large-signal model and theoretical reseach results of large-signal stability analysis for cascaded system, chapter4of this dissertation studies the compensation methodology of DC bus voltage, and proposes a compensation control law for voltage bus conditioner (VBC). Effective compensation can be done based on the parameters of source and load converters. Meanwhile, the proposed control law is derived from the stability theorem of mixed potential theory, so the stability of cascaded system with VBC under large-signal disturbance is guaranteed theoretically. Besides, the proposed control law is universal, and the compensation result is satisfied.
在对现有大信号模型进行对比研究的基础上,本文基于回转器理论为电流模式控制型DC-DC变流器建立了统一的大信号模型。该模型克服了现有大信号模型复杂、难以应用于理论分析的缺点,实现了降阶,输入-输出表达式简单,且仅采用单环反馈即可实现电流模式控制的功能,为后续理论分析提供了便利。由于回转器理论的基础是能量守恒定律,故该模型具有普适性,仅需修改一个参数的数值即可实现对不同拓扑变流器的建模分析。在较好地反映原变流器大信号特性的同时,该模型还能够正确反映系统在平衡点附近的小信号特性。模型的简便性、普适性、结构统一性和完备性为理论分析系统稳定性奠定了良好的基础,也为解析形式大信号稳定性判据的提出提供了可能。
在DC-DC级联系统稳定性分析方面,本文采用李雅普诺夫线性化方法及混合势函数理论分别对级联系统的小信号和大信号稳定性进行了探讨。出于简化分析的目的,采用回转器统一大信号模型和恒功率负载分别对系统中的源、负载变流器进行替代。基于该简化级联系统及李雅普诺夫线性化方法,本文提出了解析形式的小信号稳定性判据。该判据仅需较少的参数即可对稳定性情况进行判断,避免了复杂的阻抗计算过程。同时,本文基于混合势函数理论得到了级联系统在大信号扰动下保持稳定运行所需满足的充分条件,即解析形式的大信号稳定性判据。由于分析时基于相同的简化系统模型,故可将大、小信号判据合二为一,得到了级联系统的统一稳定性判据。当该判据成立时,系统在大、小信号扰动下均能稳定运行,从而使设计过程得以简化。同时,本文对负载变流器响应速度较慢、不具备等效为恒功率负载条件的级联系统稳定性也进行了研究,并得到了相似的结论。为方便应用,仍可采用上述统一稳定性判据对该类级联系统进行分析。
本文第四章将提出的回转器统一大信号模型和级联系统大信号稳定性理论研究成果应用于直流母线补偿技术领域,提出了一种直流母线电压补偿控制策略。该策略从大信号的研究角度出发,根据级联系统的具体情况对其进行补偿。且该策略由混合势函数理论的稳定性定理推导得出,从理论上保证了加入补偿装置后整个系统在大信号扰动下的稳定性。此外,该控制策略还具有一定的普适性,能够达到较好的补偿效果。
With the development of electronic and renewable energy technique, DC distribution power system (DPS) becomes more and more attractive due to its unique advantages, and it has been widely used in the fields of electric vehicles, computer systems, medical electronic equipment, telecommunications industry, etc. The DC DPS has provided lots of benefits, but also negative factors. Increasingly larger size and complex structure not only highlights the stability issue, but also brings great difficulty for stability design. It is almost impossible to take the DC DPS as a whole for stability analysis. For this important issue, researches and analysis starts with cascaded system which is the most basic connection form of distributed architecture, and some useful theoretical achievements have been made based on small-signal analysis method. But the conclusions are only suitable to analyze the stability around equilibrium point, and will be invalid when large-signal disturbance occurs. Therefore, in order to analyze comprehensively, get in-depth understanding of system operation under large-signal disturbance, and improve system reliability, it is necessary to establish appropriate research methods based on nonlinear theory for large-signal stability analysis. This dissertation investigated and analyzed the large signal stability issue of DC-DC cascaded system in depth based on gyrator theory and relevant nonlinear analysis methods, which mainly contains the contents as below.
Based on the comparative study of the existing large-signal model, this dissertation proposes a unified large signal model for current-mode controlled DC-DC converter based on the gyrator theory. The proposed model overcomes the shortcomings of existing large-signal models, such as complicated and difficult to be adopted for theoretical analysis. It is order-reduced, and the input-output expression is simple. Only single feedback loop is needed to achieve current mode control function, and it provides convenience for theoretical analysis. Because the gyrator theory is based on the energy conservation law, the proposed large-signal model is generalized and can be applied to all the basic topologies by modifying only one parameter in the model.In addition to reflect large-signal properties of original converter well, this model also includes all the small-signal information around the equilibrium point. Due to the characteristic of simplicity, generalization, structural uniformity, and completeness, this model provides foundation and possibility for theoretical analysis, and analytical large-signal stability criterion could be derived based on it.
For the stability analysis of DC-DC cascaded system, this dissertation investigates the small-signal and large-signal stability of DC-DC cascaded system based on Lyapunov linearization method and mixed potential theory. To simplify the analysis, the proposed gyrator large-signal model is employed for simplifying the source converter, and the load converter is simplified as a constant power load (CPL). An analytical small-signal stability criterion is obtained based on this simplified system and Lyapunov linearization method. With the proposed criterion, the small-signal stability of system can be judged based on few parameters without complex input-output impedance calculation. Furthermore, the sufficient condition for stable operation of system under large-signal disturbance is proposed based on the mixed potential theory. It is also the analytical large-signal stability criterion for DC-DC cascaded system. Based on the same simplified system model, the proposed small-and large-signal criteria can be combined to derive a general stability criterion. When it holds, the system can work stable under both small-signal and large-signal disturbance, and the design process is simplified. Meanwhile, this dissertation also investigates the cascaded system in which the response speed of load converter is not so fast that it can not be simplified by CPL. Similar conclusion is derived. For convenience of application, the general stability criterion mentioned above can still be used to analyze the stability for this kind of system.
Based on the proposed gyrator large-signal model and theoretical reseach results of large-signal stability analysis for cascaded system, chapter4of this dissertation studies the compensation methodology of DC bus voltage, and proposes a compensation control law for voltage bus conditioner (VBC). Effective compensation can be done based on the parameters of source and load converters. Meanwhile, the proposed control law is derived from the stability theorem of mixed potential theory, so the stability of cascaded system with VBC under large-signal disturbance is guaranteed theoretically. Besides, the proposed control law is universal, and the compensation result is satisfied.
引文
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