黄艳玲　司马文霞　杨　鸣　杨　庆　袁　涛

(输配电装备及系统安全与新技术国家重点实验室(重庆大学)　重庆　400044)



实测铁磁谐振时间序列的非线性动力学分析

黄艳玲司马文霞杨鸣杨庆袁涛

(输配电装备及系统安全与新技术国家重点实验室(重庆大学)重庆400044)

摘要在仅有实测单一电压时间序列的情况下，为准确识别出电力系统铁磁谐振类型，运用坐标延迟方法重构与原系统拓扑意义上等价的相空间。采用相平面、庞加莱截面和关联维数3种基于重构相空间的非线性动力学分析工具表达电压时间序列的运动特征，由此识别其所属的铁磁谐振类型。对3例典型的中性点不接地系统电磁式电压互感器铁磁谐振实测时间序列进行了动力学特征分析。其中两例时间序列的相平面轨迹、庞加莱截面均呈现周期运动特性，关联维数估计值分别为1.015 0±0.003 9、1.006 1±0.000 6，由此判别它们作周期运动；另一例时间序列的相平面轨迹、庞加莱截面均未呈现周期或准周期运动特性，关联维数估计值为2.300 2±0.061 2，由此判别其作混沌运动。实测电压时间序列受到多种因素的影响，综合以上3种分析方法所表达的特征，对所发生的铁磁谐振类型作出的判断更准确和更有说服力。

关键词：铁磁谐振时间序列非线动力学相空间重构关联维数电磁式电压互感器

Nonlinear Dynamic Analysis of the Measured Ferroresonance Time Series

HuangYanlingSimaWenxiaYangMingYangQingYuanTao

(State Key Laboratory of Power Transmission Equipment and System Safety and New Technology Chongqing UniversityChongqing400044China)

AbstractWith 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.

Keywords：Ferroresonance，time series，nonlinear dynamics，phase space construction，correlation dimension，inductive voltage transformer

0引言

铁磁谐振是一种复杂的电现象，它可能发生在由电力变压器或电磁式电压互感器(PT)及带铁心的电抗器等非线性电感元件与电容元件构成的回路中[1]。……