基波铁磁谐振频繁发生于电力系统中，严重威胁电力系统的安全稳定运行。首先利用理论分析方法研究了典型铁磁谐振电路的基波铁磁谐振，用非线性曲线描述了非线性电感的饱和特性，并考虑了回路电阻对谐振的影响；在仅考虑基波分量的情况下，根据理论推导结果得出系统各参数对铁磁谐振的影响，并给出了各参数导致系统发生谐振的临界值求解方法；最后利用实验验证了理论分析中电源电压对铁磁谐振影响的正确性。研究结果表明：该方法能够很好地分析基波铁磁谐振及其影响因素，铁心损耗越小，电源电压越高，回路电阻越小，回路电容越小，系统发生谐振的可能性越大。

Fundamental frequency ferroresonance frequently occurs in power system and the overvoltage and overcurrent caused by ferroresonance seriously threatens secure and stable operation of power system. In this paper, firstly the fundamental frequency ferroresonance in typical ferroresonance circuit is theoretically analyzed and the saturation characteristic of nonlinear inductance is described by nonlinear curve and the influence of circuit resistance is taken into account; considering fundamental component merely and according to the theoretical derivation, the influence of system parameters on ferroresonance is obtained and an approach to solve the critical value under which the ferroresonance occurs is given; finally through experimental verification, the inference form theoretical analysis that the source voltage impacts ferroresonance is validated. Research results show that the proposed method can analyze fundamental frequency ferroresonance and related influencing factors well; the smaller the core loss, the higher the source voltage, the smaller the circuit capacitance and resistance, the more possible the fundamental frequency ferroresonance happens.

[1] 袁毅．一起变电所母线电压互感器铁磁谐振事故的分析[J]．电网技术，1999，23(6)：68-69． Yuan Yi．Analysis of a resonance fault of potential transformer for substation busbar[J]．Power System Technology，1999，23(6)： 68-69(in Chinese)． [2] 杨秋霞，宗伟，田璧元．基于小波分析的铁磁谐振检测[J]．电网技术，2001，25(11)：55-57． Yang Qiuxia，Zong Wei，Tian Biyuan．Detection of ferromagnetic resonance based on wavelet analysis[J]．Power System Technology， 2001，25(11)：55-57(in Chinese)． [3] 刘凡，司马文霞，孙才新，等．基于常值脉冲法的铁磁谐振过电压混沌抑制[J]．电网技术，2006，30(3)：57-61． Liu Fan，Sima Wenxia，Sun Caixin，et al．Controlling chaos in ferroresonance overvoltage based on constant pulse method[J]．Power System Technology，2006，30(3)：57-61(in Chinese)． [4] 周浩，余宇红，张利庭，等．10 kV配电网铁磁谐振消谐措施的仿真比较研究[J]．电网技术，2005，29(22)：24-34． Zhou Hao，Yu Yuhong，Zhang Liting，et al．Comparative study on ferroresonance elimination measures in 10 kV power distribution system by simulation method[J]．Power System Technology，2005， 29(22)：24-34(in Chinese)． [5] 金秋生．农村电力网产生铁磁谐振的机理及防范措施[J]．电网技术，2001，25(6)：61-63． Jin Qiusheng．Mechanism of ferro-magnetic resonance ocurred in rural power system and its countermeasures[J]．Power System Technology，2001，25(6)：61-63(in Chinese)． [6] Piasecki W，Florkowski M，Fulczyk M，et al．Mitigating ferroresonance in voltage transformers in ungrounded MV networks [J]．IEEE Trans on Power Delivery，2007，22(4)：2362-2369． [7] Barbisio E，Bottauscio O，Chiampi M，et al．Experimental and modeling analysis of ferroresonant electric circuits[J]．Journal of Magnetism and Magnetic Materials，2007，31(6)：299-301． [8] Tokic A，Madzarevic V，Uglesic I．Numerical calculations of three-phase transformer transients[J]．IEEE Trans on Power Delivery，2005，20(4)：2493-2500． [9] 李云阁，施围．应用解析法分析中性点接地系统中的工频铁磁谐振：非线性电感工频励磁特性的求取[J]．中国电机工程学报，2003，23(10)：94-98． Li Yunge，Shi Wei．Study of fundamental ferroresonance on neutral-grounded systems by using analytical method-solution to the power frequency excitation characteristic of nonlinear inductors [J]．Proceedings of the CSEE，2003，23(10)：94-98(in Chinese)． [10] 李云阁，施围．应用解析法分析中性点接地系统中的工频铁磁谐振：谐振判据和消谐措施[J]．中国电机工程学报，2003，23(9)：141-145． Li Yunge，Shi Wei．Study of fundamental ferroresonance on neutral-grounded systems by using analytical method-criterion and elimination[J]．Proceedings of the CSEE，2003，23(9)：141-145(in Chinese)． [11] 张博，鲁铁成，杜晓磊．中性点接地系统基频铁磁谐振及其实验分析[J]．高压电器，2006，42(2)：47-50． Zhang Bo，Lu Tiecheng，Du Xiaolei．Analysis of the fundamental ferroresonance of neutral grounded power system and the experimental validation[J]．High Voltage Apparatus，2006，42(2)：47-50(in Chinese)． [12] 张博，鲁铁成，杜晓磊．电力系统基频铁磁谐振谐波平衡分析[J]．高电压技术，2006，32(1)：94-96． Zhang Bo，Lu Tiecheng，Du Xiaolei．Analysis of harmonic balance based fundamental resonance of the ferroresonance circuit in power system[J]．High Voltage Engineering，2006，32(1)：94-96(in Chinese)． [13] 李云阁，施围，秦睿，等．消除中性点接地系统铁磁谐振新方法[J]．电工电能新技术，2002，21(4)：58-63． Li Yunge，Shi Wei，Qin Rui，et al．Novel scheme for suppressing ferroresonance on neutral-grounded systems[J]．Advanced Technology of Electrical Engineering and Energy，2002，21(4)：58-63(in Chinese)． [14] 刘凡，孙才新，司马文霞，等．铁磁谐振过电压混沌振荡的理论研究[J]．电工技术学报，2006，21(2)：103-107． Liu Fan，Sun Caixin，Sima Wenxia，et al．Theoretical analysis of chaotic oscillation of ferroresonance overvoltage in power systems [J]．Transactions of China Electrotechnical Society，2006，21(2)：103-107(in Chinese)． [15] 刘东晖，夏承铨，史可琴，等．混沌振荡与真空断路器动作特性之间相互作用的研究[J]．电工电能新技术，2007，26(3)：15-19． Liu Donghui，Xia Chengquan，Shi Keqin，et al．Research on interaction between operation of high voltage circuit breaker and chaotic oscillation[J]．Advanced Technology of Electrical Engineering and Energy，2007，26(3)：15-19(in Chinese)． [16] Sowa，P，Walczak J，Pasko M．Evaluation of the influence of the chaotic ferroresonance in transformer on the power system work conditions[C]．Electrotechnical Conference，Israel，1998． [17] Marti J R．Ferroresonance in power systems：fundamental solutions [J]．IEE Proceedings-C，1991，138(4)：321-329．