一种混沌分析与抑制方法及在电力系统铁磁谐振中的应用研究
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摘要
对非线性系统行为的分析与判定,是一项具有科学意义和工程背景的重要课题。如何判定这些系统复杂行为和产生机制,是十分艰巨的。其中,混沌的解析预测、混沌的抑制、高维系统混沌分析等一直是现代科学研究的热点。电力系统的铁磁谐振常常表现为高维非线性系统的混沌行为,产生很高的内部过电压,对电力系统的安全稳定运行有着很大威胁。因此对电力系统混沌铁磁谐振的分析、预测及抑制的研究具有重要的理论与实际意义。
本文提出了一种新的消除混沌的分析方法:排除分析法。该方法的基本思想是对于系统可能出现的四种稳态解即常数解(平衡解)、周期解、拟周期解和混沌解中,如果排除混沌以外的其他解的存在区域,就可以得到系统出现混沌的解析条件。此方法适用于任何维数的自治和非自治系统,分析过程相对简单。
在建立混沌排除分析法的基础上,将这一方法应用到电力系统混沌铁磁谐振和Van der pol—Duffing方程的分析中,得到了判断其出现混沌的新解析条件。所有结论均用实例进行验证,表明结果是正确的。通过与Melnikov等方法比较,提出的排除分析法比经典方法精确的多,适应范围更加广泛。
为了消除混沌和谐振,本文提出了一种消除谐振和混沌的方法。该方法的基本思想是如果系统存在一个非混沌或者非谐振的正常解,并且系统具有唯一的稳态,则此时对应的条件就是系统不发生谐振或混沌的条件。是一种新的消除混沌和谐振的方法。
根据提出的唯一稳态消谐法对中性点接地电力系统的零序消谐、单相铁磁谐振、中性点不接地系统的消除谐振条件进行了分析,得到了相应的消谐条件,并用数值模拟或实验数据进行验证,证明了方法的有效性。
The analysis and determining of non-linear system behaviour is an important scientific subject with engineering background. How to determine the behaviour and mechanism is an arduous subject. Among them, the chaos analysis and repression for high order non-linear system has been a hot spot in modern science.
The ferroresonanc of the power system often presents the high order non-linear chaos behavious and produce very high inner overvoltage which will bring a big harm to the safe and stable operation of power system. So, study on analysis and repression of chaos ferroresonance of power system is of great theoretical and practical importance.
For analying the chaos in high order systems and improve the methods for analytic prediction of chaos, in this paper, a new analytical method for predictiing chaos i.e the exclusion method is presented. Its basic idea is that for any systems, there are only four sorts of different solutions of steady states, they are constant solutions, periodic solutions, quasi periodic solutions and chaotic solutions. If the parameter space corresponding to the solutions except chaotic solutions is excluded, the remained parameter spaces are only the areas corresponding to chaotic solutions, and the analytical conditions for the chaotic solutions is obtained. The exclusion method has been applied to both autonomous systems and non-autonomous systems with any degrees, and the analysis process is relatively simple.
This exclusion method of chaos has been applied to analyze the ferroresonance problem in power system and to solve the Van der pol-Duffing equation. The analytical conditions for the two cases are obtained, the conclusions are proved by practical examples and numerical simulation. Compared with classical Melnikov method, the new method is much more accurate and has much better adaptation for different conditions.
A new method for eliminating the chaos ferroresonance is presented. Its basic idea is that if there is a normal solution for the system, and the steady state of system is unique solution, then the corresponding conditions are the conditions for elimina-ting the ferroresonance and chaos.
The method has been applied to those single phase power system, neutral grounding power system and neutral non-grounding power system for eliminating chaos and ferroresonance, the corresponding conditions are obtained, and those conclusions are proved by practical examples and numerical simulation.
本文提出了一种新的消除混沌的分析方法:排除分析法。该方法的基本思想是对于系统可能出现的四种稳态解即常数解(平衡解)、周期解、拟周期解和混沌解中,如果排除混沌以外的其他解的存在区域,就可以得到系统出现混沌的解析条件。此方法适用于任何维数的自治和非自治系统,分析过程相对简单。
在建立混沌排除分析法的基础上,将这一方法应用到电力系统混沌铁磁谐振和Van der pol—Duffing方程的分析中,得到了判断其出现混沌的新解析条件。所有结论均用实例进行验证,表明结果是正确的。通过与Melnikov等方法比较,提出的排除分析法比经典方法精确的多,适应范围更加广泛。
为了消除混沌和谐振,本文提出了一种消除谐振和混沌的方法。该方法的基本思想是如果系统存在一个非混沌或者非谐振的正常解,并且系统具有唯一的稳态,则此时对应的条件就是系统不发生谐振或混沌的条件。是一种新的消除混沌和谐振的方法。
根据提出的唯一稳态消谐法对中性点接地电力系统的零序消谐、单相铁磁谐振、中性点不接地系统的消除谐振条件进行了分析,得到了相应的消谐条件,并用数值模拟或实验数据进行验证,证明了方法的有效性。
The analysis and determining of non-linear system behaviour is an important scientific subject with engineering background. How to determine the behaviour and mechanism is an arduous subject. Among them, the chaos analysis and repression for high order non-linear system has been a hot spot in modern science.
The ferroresonanc of the power system often presents the high order non-linear chaos behavious and produce very high inner overvoltage which will bring a big harm to the safe and stable operation of power system. So, study on analysis and repression of chaos ferroresonance of power system is of great theoretical and practical importance.
For analying the chaos in high order systems and improve the methods for analytic prediction of chaos, in this paper, a new analytical method for predictiing chaos i.e the exclusion method is presented. Its basic idea is that for any systems, there are only four sorts of different solutions of steady states, they are constant solutions, periodic solutions, quasi periodic solutions and chaotic solutions. If the parameter space corresponding to the solutions except chaotic solutions is excluded, the remained parameter spaces are only the areas corresponding to chaotic solutions, and the analytical conditions for the chaotic solutions is obtained. The exclusion method has been applied to both autonomous systems and non-autonomous systems with any degrees, and the analysis process is relatively simple.
This exclusion method of chaos has been applied to analyze the ferroresonance problem in power system and to solve the Van der pol-Duffing equation. The analytical conditions for the two cases are obtained, the conclusions are proved by practical examples and numerical simulation. Compared with classical Melnikov method, the new method is much more accurate and has much better adaptation for different conditions.
A new method for eliminating the chaos ferroresonance is presented. Its basic idea is that if there is a normal solution for the system, and the steady state of system is unique solution, then the corresponding conditions are the conditions for elimina-ting the ferroresonance and chaos.
The method has been applied to those single phase power system, neutral grounding power system and neutral non-grounding power system for eliminating chaos and ferroresonance, the corresponding conditions are obtained, and those conclusions are proved by practical examples and numerical simulation.
引文
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