A New Chaos Analysis Method: Exclusion Analysis Method and its Application: Simulation and Comparison

Abstract:

In this paper, a new analytical analysis method for chaos: exclusion method is used to analyze ferro-resonance in power system. Its basic idea is that for any systems, there are only four different solution types, that is, constant solutions (equilibrium solutions), periodic solutions, almost periodic solutions and chaotic solutions. If the parameter spaces corresponding to the solutions except chaotic solutions are excluded, the remaining parameter spaces are only the scopes corresponding to chaotic solutions, and then the analytical conditions for the chaotic solutions are obtained. This new method has been applied to the chaos analysis of vibrations equation and electronic circuit successfully. The analytical conditions for chaotic ferro-resonance solutions are obtained for the first time in a recently published paper and the conclusions are proved correct theoretically. In this paper, the resulted conditions are simulated numerically and compared with the Melnikov method to identify the efficiency of the exclusion analysis method. Compared with classical Melnikov method, the conclusion of this article shows that the new method is much more accurate than previous analytical method and is suitable for the system with any degree, especially for high dimensions system.

• Periodical: Advanced Materials Research (Volumes 490-495)
• Pages: 46-50
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.490-495.46
• Online since: March 2012
• Authors: Ping Feng, Wei Jun Wang, Yang Jia, Bo Sun, Er Zhi Wang, Gang Chen
• Keywords: Chaos, Duffing Equation, Exclusion Analysis Method, Ferro-Resonance, Melnikov Method, Power System

References

[1] Feng Ping, Wang Erzhi，Exclusion analysis method and its application to chaotic vibration equatiion, Journal of Lanzhou University of Technology, Dec., 2009, Vol25, No. 6, pp.84-88.

[2] Feng, Ping, Research on the chaotic analysis and suppressing methods and its application in ferro-resonance in power system, Doctoral Dissertation, 2009. 07. Shenyang University of Technology, Shenyang P.R. China.

[3] Feng Ping, Wang Erzhi , Exclusion analysis method and its application to the analysis of chaotic electronic circuit., Journal of Natural Science of Hunan Normal University , Jun. 2010, Vol33, No. 2, pp.48-53.

[4] Wojciech P. Mitigating ferroresonance in voltage transformers [J]. IEEE Transactions on Power Delivery, 2007, 22(4): 657-662.

[5] Feng Ping, Wang Erzhi, Wang Weijun etc. A New Chaotic Analysis Method: Exclusion Analysis Method and Its Application in Ferro-resonance in Power System , Interantiional conferenc on Computer and Electrical and engery, Nov. 2011, Chengdu ,P.R. China.

[6] Liu Fan, Sun Caixin, Sima tec. The theoretical analysis on chaotic ferroresonance overvoltage, Trans. Of China Electrotechnical Society. 2006, 21(17): 103-107.