随机参数激励下的风力发电及转子系统稳定性与Hopf分岔分析

发布时间：2019-06-08 19:05

【摘要】：电能对人类社会的重要性不言而喻,它支撑着如今的电气化、网络信息化时代。但是随着人们对化石燃料、煤炭能源的肆意开采,传统能源逐渐消耗殆尽,而且传统能源的使用造成的环境污染和温室效应等问题的严重性远远甚于能源缺乏的危机。所以在未来发展的计划中,开发新型可再生能源便是全世界各个国家最重要的战略方向。新型的可再生能源有风能、太阳能、光能等,而在这其中,对于风能的开发应用最为广泛,其相关技术也日趋成熟。在我国大地上随处可见风力发电群,依托一些地区特殊的气候环境,风力发电的发展非常迅速。但是目前来说,风力发电还不是我国主要的电力输出来源,依然未能摆脱对传统能源依赖,究其原因还是风力发电项目的开发技术需进一步完善,比如,如何保证风力发电有稳定的电力输出,如何降低风力发电项目建设过程中的成本等。而要使得风力发电系统有稳定的电力输出,既要考虑自然风的不确定性,随机性。本文即是针对风能利用的主要设备风力发电机进行了研究,由于转子系统连接结构复杂,自身材质的不均质性,以及受到随机风力的影响,会导致转子系统的不确定性,运用非线性随机动力学系统理论,详细的研究了风电转子系统的动力学行为,主要内容如下:1.详述了有关风力发电系统的研究动态,和高速转子-轴承系统的国内外研究背景,综述了本文的研究目的。然后叙述了非线性随机动力学的基本理论、具体概念和主要内容。2.研究了一个具有随机风力扰动下的风力发电系统的稳定性及Hopf分岔,将系统受到的内部因素与外部随机风力影响用高斯白噪声代替。运用随机平均原理,将拟哈密顿系统收敛于一个一维伊藤随机扩散过程,然后运用最大李雅普诺夫指数法,来判断系统的局部稳定性,得到系统局部稳定的条件。然后通过FPK方程之解,即平稳概率密度来模拟系统发生Hopf分岔。3.研究了一个具有随机参激的高速转子-轴承系统的稳定性及Hopf分岔,运用随机非线性动力学拟不可积哈密顿系统理论,将系统渐近收敛于一个一维伊藤微分方程,在运用最大李雅普诺夫指数分析局部稳定性后,通过伊藤随机微分方程的奇异边界理论,得到了系统保证全局稳定性的条件,并通过平稳概率密度函数和联合概率密度函数,模拟系统由稳定到发生Hopf分岔的过程。4.研究了一个四维转子-系统的随机稳定性及Hopf分岔,对于四维随机非线性系统来说,也可以运用拟不可积哈密顿系统理论进行分析,将四维系统运用随机平均原理,依概率1弱收敛于一个一维随机扩散过程。但是在计算漂移扩散指数的时候,为了避免计算多重积分,引入了极坐标变换,得到伊藤随机微分方程。然后分析其局部稳定性及全局稳定性,并且模拟系统发生的Hopf分岔。
[Abstract]:The importance of electric energy to human society is self-evident, which supports the age of electrification and network information. However, with the wanton exploitation of fossil fuels and coal energy, the traditional energy is gradually consumed, and the environmental pollution caused by the use of traditional energy and Greenhouse Effect are far more serious than the crisis of lack of energy. Therefore, in the future development plan, the development of new renewable energy is the most important strategic direction of all countries in the world. The new renewable energy sources are wind energy, solar energy, light energy and so on, among which, the development and application of wind energy is the most extensive, and its related technologies are becoming more and more mature. Wind power generation groups can be seen everywhere in our country. Relying on the special climate environment in some areas, the development of wind power generation is very rapid. However, at present, wind power is not the main source of power output in our country, and it is still unable to get rid of its dependence on traditional energy. The reason is that the development technology of wind power project needs to be further improved, for example, How to ensure the stable power output of wind power generation, how to reduce the cost in the construction process of wind power generation project, and so on. In order to make the wind power generation system have stable power output, we should consider the uncertainty and randomness of natural wind. In this paper, the main equipment wind turbine for wind energy utilization is studied. Because of the complex connection structure of rotor system, the heterogeneity of its own material, and the influence of random wind force, it will lead to the uncertainty of rotor system. Based on the theory of nonlinear stochastic dynamic system, the dynamic behavior of wind power rotor system is studied in detail. The main contents are as follows: 1. The research trends of wind power generation system and the research background of high speed rotor-bearing system at home and abroad are described in detail, and the research purpose of this paper is summarized. Then the basic theory, concrete concept and main content of nonlinear stochastic dynamics are described. The stability and Hopf bifurcation of a wind power generation system with random wind disturbance are studied. The internal factors and external random wind influence of the system are replaced by Gaussian white noise. By using the principle of random average, the quasi-Hamilton system is converged to a one-dimensional Ito random diffusion process, and then the maximum Lyapunov index method is used to judge the local stability of the system, and the conditions for the local stability of the system are obtained. Then the Hopf bifurcation of the system is simulated by the solution of the FPK equation, that is, the stationary probability density. The stability and Hopf bifurcation of a high speed rotor-bearing system with random parameter excitation are studied. by using the theory of stochastic nonlinear dynamic quasi-inintegrable Hamilton system, the system converges asymptotically to a one-dimensional Ito differential equation. After analyzing the local stability by using the maximum Leonov index, the conditions for ensuring the global stability of the system are obtained by using the singular boundary theory of Ito stochastic differential equations, and the stationary probability density function and the joint probability density function are used to guarantee the global stability of the system. The process from stability to Hopf bifurcation is simulated. 4. The random stability and Hopf bifurcation of a four-dimensional rotor-system are studied. for the four-dimensional stochastic nonlinear system, the quasi-inintegrable Hamilton system theory can also be used to analyze the four-dimensional system, and the four-dimensional system can be analyzed by using the stochastic average principle. According to probability 1, it converges weakly to a one-dimensional random diffusion process. However, in order to avoid calculating multiple integral, polar coordinate transformation is introduced to obtain Ito stochastic differential equation when calculating drift diffusion index. Then the local stability and global stability are analyzed, and the Hopf bifurcation of the system is simulated.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175;TM614

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