隨機參數激勵下的風力發(fā)電及轉子系統(tǒng)穩(wěn)定性與Hopf分岔分析
發(fā)布時間：2019-06-08 19:05
【摘要】：電能對人類社會的重要性不言而喻,它支撐著如今的電氣化、網絡信息化時代。但是隨著人們對化石燃料、煤炭能源的肆意開采,傳統(tǒng)能源逐漸消耗殆盡,而且傳統(tǒng)能源的使用造成的環(huán)境污染和溫室效應等問題的嚴重性遠遠甚于能源缺乏的危機。所以在未來發(fā)展的計劃中,開發(fā)新型可再生能源便是全世界各個國家最重要的戰(zhàn)略方向。新型的可再生能源有風能、太陽能、光能等,而在這其中,對于風能的開發(fā)應用最為廣泛,其相關技術也日趨成熟。在我國大地上隨處可見風力發(fā)電群,依托一些地區(qū)特殊的氣候環(huán)境,風力發(fā)電的發(fā)展非常迅速。但是目前來說,風力發(fā)電還不是我國主要的電力輸出來源,依然未能擺脫對傳統(tǒng)能源依賴,究其原因還是風力發(fā)電項目的開發(fā)技術需進一步完善,比如,如何保證風力發(fā)電有穩(wěn)定的電力輸出,如何降低風力發(fā)電項目建設過程中的成本等。而要使得風力發(fā)電系統(tǒng)有穩(wěn)定的電力輸出,既要考慮自然風的不確定性,隨機性。本文即是針對風能利用的主要設備風力發(fā)電機進行了研究,由于轉子系統(tǒng)連接結構復雜,自身材質的不均質性,以及受到隨機風力的影響,會導致轉子系統(tǒng)的不確定性,運用非線性隨機動力學系統(tǒng)理論,詳細的研究了風電轉子系統(tǒng)的動力學行為,主要內容如下:1.詳述了有關風力發(fā)電系統(tǒng)的研究動態(tài),和高速轉子-軸承系統(tǒng)的國內外研究背景,綜述了本文的研究目的。然后敘述了非線性隨機動力學的基本理論、具體概念和主要內容。2.研究了一個具有隨機風力擾動下的風力發(fā)電系統(tǒng)的穩(wěn)定性及Hopf分岔,將系統(tǒng)受到的內部因素與外部隨機風力影響用高斯白噪聲代替。運用隨機平均原理,將擬哈密頓系統(tǒng)收斂于一個一維伊藤隨機擴散過程,然后運用最大李雅普諾夫指數法,來判斷系統(tǒng)的局部穩(wěn)定性,得到系統(tǒng)局部穩(wěn)定的條件。然后通過FPK方程之解,即平穩(wěn)概率密度來模擬系統(tǒng)發(fā)生Hopf分岔。3.研究了一個具有隨機參激的高速轉子-軸承系統(tǒng)的穩(wěn)定性及Hopf分岔,運用隨機非線性動力學擬不可積哈密頓系統(tǒng)理論,將系統(tǒng)漸近收斂于一個一維伊藤微分方程,在運用最大李雅普諾夫指數分析局部穩(wěn)定性后,通過伊藤隨機微分方程的奇異邊界理論,得到了系統(tǒng)保證全局穩(wěn)定性的條件,并通過平穩(wěn)概率密度函數和聯合概率密度函數,模擬系統(tǒng)由穩(wěn)定到發(fā)生Hopf分岔的過程。4.研究了一個四維轉子-系統(tǒng)的隨機穩(wěn)定性及Hopf分岔,對于四維隨機非線性系統(tǒng)來說,也可以運用擬不可積哈密頓系統(tǒng)理論進行分析,將四維系統(tǒng)運用隨機平均原理,依概率1弱收斂于一個一維隨機擴散過程。但是在計算漂移擴散指數的時候,為了避免計算多重積分,引入了極坐標變換,得到伊藤隨機微分方程。然后分析其局部穩(wěn)定性及全局穩(wěn)定性,并且模擬系統(tǒng)發(fā)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.
【學位授予單位】：蘭州交通大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175;TM614
本文編號：2495503
[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.
【學位授予單位】：蘭州交通大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175;TM614
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