实测铁磁谐振时间序列的非线性动力学分析

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Abstract With only a single voltage time series recorded in fact,for accurately identifying the ferroresonance types,the delay coordinates method was applied to obtain the reconstructed phase space that is topologically equivalent to the phase space of the original system.Nonlinear dynamics methods based on the reconstructed phase space,e.g.phase plane,Poincaré section and correlation dimension,were used to express the dynamic characteristics of the time series and identify the type of ferroresonance based on them.The nonlinear dynamic characteristics analysis was conducted to 3 typical cases of measured time series of ferroresonance occurred in inductive voltage transformer in isolated neutral system.The phase plane trajectories and Poincaré sections of two time series cases of them show periodic motion characteristics,their correlation dimension estimation values respectively are 1.015 0±0.003 9,1.006 1±0.000 6;therefore their motion modes were identified as fundamental mode and subharmonic mode.The phase plane trajectory and Poincaré section of another time series case do not show periodic or quasiperiodic motion characteristics,its correlation dimension estimation value is 2.300 2±0.061 2;therefore its motion mode was identified as chaotic mode.The measured voltage time series is affected by many factors,the identification result of ferroresonance mode occurred is more accurate and convictive through synthesizing the features characterized by the above 3 analysis methods.

Key words： Ferroresonance time series nonlinear dynamics phase space construction correlation dimension inductive voltage transformer

Received: 04 March 2015 Published: 16 March 2016

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TM864

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	Huang Yanling
	Sima Wenxia
	Yang Ming
	Yang Qing
	Yuan Tao

Cite this article:

Huang Yanling,Sima Wenxia,Yang Ming等. Nonlinear Dynamic Analysis of the Measured Ferroresonance Time Series[J]. Transactions of China Electrotechnical Society, 2016, 31(5): 126-134.

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https://dgjsxb.ces-transaction.com/EN/ OR https://dgjsxb.ces-transaction.com/EN/Y2016/V31/I5/126

[1] Emin Z,Al Zahawi B A T,Auckland D W,et al.Ferroresonance in electromagnetic voltage transformers:a study based on nonlinear dynamics[J].IEE Proceedings-Generation,Transmission and Distribution,1997,144(4):383-387.
[2] Mork B A,Stuehm D L.Application of nonlinear dynamics and chaos to ferroresonance in distribution systems[J].IEEE Transactions on Power Delivery,1994,9(2):1009-1017.
[3] 周丽霞,尹忠东,郑立.配网PT铁磁谐振机理与抑制的试验研究[J].电工技术学报,2007,22(5):153-158.
Zhou Lixia,Yin Zhongdong,Zheng Li.Research on principle of PT resonance in distribution power system and its suppression[J].Transactions of China Electrotechnical Society,2007,22(5):153-158.
[4] 张博,鲁铁成,杜晓磊.中性点接地系统铁磁谐振非线性动力学分析[J].高电压技术,2007,33(1):31-35.
Zhang Bo,Lu Tiecheng,Du Xiaolei.Nonlinear dynamic analysis of ferroresonance in neutral-grounded power system[J].High Voltage Engineering,2007,33(1):31-35.
[5] Val E M,Dudurych I,Redfern M A.Characterization of ferroresonant modes in HV substation with CB grading capacitors[J].Electric Power Systems Research,2007,77(11):1506-1513.
[6] Araujo A E A,Soudack A C,Marti J R.Ferroresonance in power systems:chaotic behaviour[J].Generation,Transmission and Distribution,IEE Proceedings C,1993,140(3):237-240.
[7] Emin Z,Al Zahawi B A T,Yu K T,et al.Quantification of the chaotic behavior of ferroresonant voltage transformer circuits[J].Circuits and Systems I:Fundamental IEEE Transactions on Theory and Applications,2001,48(6):757-760.
[8] Mozaffari S,Henschel S,Soudack A C.Chaotic ferroresonance in power transformers[J].IEE Proceedings-Generation,Transmission and Distribution,1995,142(3):247-250.
[9] Kieny C.Application of the bifurcation theory in studying and understanding the global behavior of a ferroresonant electric power circuit[J].IEEE Transactions on Power Delivery,1991,6(2):866-872.
[10]司马文霞,郑哲人,杨庆,等.用参数不匹配混沌系统的脉冲同步方法抑制铁磁谐振过电压[J].电工技术学报,2012,27(6):218-225.
Sima Wenxia,Zheng Zheren,Yang Qing,et al.Suppressing the ferroresonance overvoltage by impulsive synchronization of chaotic systems with parameter mismatched[J].Transactions of China Electrotechnical Society,2012,27(6):218-225.
[11]Takens F.Detecting strange attractors in turbulence[M]//Lecture Notes in Mathematica.Berlin:Springer Press,1981:366-381.
[12]Packard N H,Crutchfield J P,Farmer J D,et al.Geometry from a time series[J].Physical Review Letters,1980,45:712-715.
[13]行鸿彦,龚平,徐伟.嵌入窗方法确定混沌系统重构参数的仿真研究[J].系统仿真学报,2013,25(6):1219-1225.
Xing Hongyan,Gong Ping,Xu Wei.Simulation research of chaos system reconstruction parameters based on embedded window[J].Journal of System Simulation,2013,25(6):1219-1225.
[14]Albano A M,Muench J,Schwartz C,et al.Singular-value decomposition and the Grassberger-Procaccia algorithm[J].Physical Review A,1988,38(6):3017-3026.
[15]Fraser A M,Swinney H L.Independent coordinates for strange attractors from mutual information[J].Physical Review A,1986,33(2):1134-1440.
[16]Grassberger P,Procaccia I.Measuring the strangeness of strange attractors[J].Physica D Nonlinear Phenomena,1983,9(1/2):189-208.
[17]Broomhead D S,King G P.Extracting qualitative dynamics from experimental data[J].Physica D,1986,20(2/3):217-236.
[18]Kennel M B,Brown R,Abarbanel H D I.Determining embedding dimension for phase-space reconstruction using a geometrical construction[J].Physical Review A,1992,45(6):3403-3411.
[19]Cao L Y.Practical method for determining the minimum embedding dimension of a scalar time series[J].Physica D,1997,110(1/2):43-50.
[20]Kugiumtzis D.State space reconstruction parameters in the analysis of chaotic time series—the role of the time window length[J].Physica D:Nonlinear Phenomena,1996,95(1):13-28.
[21]Kim H S,Eykholt R,Salas J D.Nonlinear dynamics,delay times,and embedding windows[J].Physica D:Nonlinear Phenomena,1999,127(1/2):48-60.
[22]Otani M,Jones A.Automated embedding and creep phenomenon in chaotic time series[EB/OL].http://users.cs.cf.ac.uk/Antonia.J.Jones/UnpublishedPapers/Creep.pdf/,2000-10-14/2011-03-15.
[23]Franca L,Savi M A.Distinguishing periodic and chaotic time series obtained from an experimental nonlinear pendulum[J].Nonlinear Dynamics,2001,26(3):253-271.
[24]刘秉正,彭建华.非线性动力学[M].北京:高等教育出版社,2005.
[25]Grassberge P,Procaccia I.Characterization of strange attractors[J].Physical Review Letters,1983,50(5):346-349.
[26]Kantz H,Schreiber T.Nonlinear time series analysis[M].Cambridge:Cambridge University Press,1997.
[27]张雨.时间序列的混沌和符号分析及实践[M].长沙:国防科技大学出版社,2007.
[28]Theiler J.Efficient algorithm for estimating the correlation dimension from a set of discrete points[J].Physical Review A,1987,36(9):4456-4462.
[29]Grassberger P.An Optimized box-assisted algorithm for fractal dimensions[J].Physics Letters A,1990,148(1/2):63-68.
[30]Schreiber T.Efficient neighbor searching in nonlinear time-series analysis[J].International Journal of Bifurcation and Chaos,1995,5(2):349-358.
[31]杜林,李欣,司马文霞,等.110 kV变电站过电压在线监测系统及其波形分析[J].高电压技术,2012,38(3):535-543.
Du Lin,Li Xin,Sima Wenxia,et al.Overvoltage on-line monitoring system for 110 kV substation and its waveforms analysis[J].High Voltage Engineering,2012,38(3):535-543.