双绕组电力变压器梯形网络频率响应的矩阵算法
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摘要
针对双绕组电力变压器梯形网络的仿真软件建模的非完整性以及现存等效电路频率响应算法多变量求解的低效率,围绕一种电力变压器绕组高频等效模型频率响应的矩阵计算方法开展研究,基于等效电路的拓扑结构,给出了利用阻抗支路矩阵和导纳支路矩阵来完整表示该等效电路的方法。其次,通过矩阵运算,推导了阻抗支路电流、导纳支路电流以及节点电压列向量之间的关系,进而求解节点电压列向量,获得等效电路的频率响应。最后,将矩阵算法与基于电路仿真得到的频响曲线进行比较,结果表明,曲线相关系数较大,吻合程度很高,对于不含高幅值谐振峰(-500dB以上)的曲线,相关系数为10,即两者完全吻合,而矩阵算法的计算耗时少于电路仿真运算。上述分析表明,在保证仿真模型完整性和精确性的同时,提出的矩阵算法由于仅有两次矩阵取逆运算且求取的未知量较少,具有良好的计算效率及计算精度。
To improve the incomplete transformer winding model in the circuit simulation software or the low efficiency of frequency response calculation due to many unknowns in the existing algorithm,a research on a matrix algorithm to calculate the frequency response of the equivalent ladder network for double-winding transformer is conducted.Following the equivalent circuit topology,the model is completely described by the impedance branch matrix and the admittance branch matrix.By means of matrix operation,the relationships of the column vectors of impedance branch current and admittance branch current with nodal voltage are obtained.The frequency response of the equivalent circuit model is calculated by solving the nodal voltage column vector.A comparison between the simulated results of matrix algorithm and those obtained by circuit simulation indicates that the correlation coefficient(CC)becomes greater showing good agreement between them.The curves without high amplitude resonance peaks(above-500 dB)coincide perfectly with a CC of 10.The matrix algorithm takes less calculation time than simulation software.Ensuring the integrality and precision of the simulation model,the proposed algorithm is endowed with good computational accuracy and efficiency due to only twicematrix inversions and less unknowns to be solved.
To improve the incomplete transformer winding model in the circuit simulation software or the low efficiency of frequency response calculation due to many unknowns in the existing algorithm,a research on a matrix algorithm to calculate the frequency response of the equivalent ladder network for double-winding transformer is conducted.Following the equivalent circuit topology,the model is completely described by the impedance branch matrix and the admittance branch matrix.By means of matrix operation,the relationships of the column vectors of impedance branch current and admittance branch current with nodal voltage are obtained.The frequency response of the equivalent circuit model is calculated by solving the nodal voltage column vector.A comparison between the simulated results of matrix algorithm and those obtained by circuit simulation indicates that the correlation coefficient(CC)becomes greater showing good agreement between them.The curves without high amplitude resonance peaks(above-500 dB)coincide perfectly with a CC of 10.The matrix algorithm takes less calculation time than simulation software.Ensuring the integrality and precision of the simulation model,the proposed algorithm is endowed with good computational accuracy and efficiency due to only twicematrix inversions and less unknowns to be solved.
引文
[1]WANG M,VANDERMAAR A J,SRIVASTAVA K D.Review of condition assessment of power transformers in service[J].IEEE Electrical Insulation Magazine,2002,18(6):12-25.
[2]刘勇,杨帆,张凡,等.检测电力变压器绕组变形的扫频阻抗法研究[J].中国电机工程学报,2015,35(17):4505-4516.LIU Yong,YANG Fan,ZHANG Fan,et al.Study on sweep frequency impedance to detect winding deformation within power transformer[J].Proceedings of the CSEE,2015,35(17):4505-4516.
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[4]张凡,汲胜昌,祝令瑜,等.短路冲击下变压器振动频响函数研究[J].西安交通大学学报,2017,51(2):97-103,154.ZHANG Fan,JI Shengchang,ZHU Lingyu,et al.Frequency response function of short circuit viberation for power transformer[J].Journal of Xi’an Jiaotong University,2017,51(2):97-103,154.
[5]REYKHERDT A A,DAVYDOV V.Case studies of factors influencing frequency response analysis measurements and power transformer diagnostics[J].IEEE Electrical Insulation Magazine,2011,27(1):22-30.
[6]RYDER S A.Diagnosing transformer faults using frequency response analysis[J].IEEE Electrical Insulation Magazine,2003,19(2):16-22.
[7]KIM J W,PARK B,JEONG S,et al.Fault diagnosis of a power transformer using an improved frequencyresponse analysis[J].IEEE Transactions on Power Delivery,2005,20(1):169-178.
[8]王曙鸿,张海军.一种基于模型修正的变压器绕组变形定量诊断方法:CN105180792A[P].2015-07-01.
[9]ABU-SIADA A,HASHEMNIA N,ISLAM S,et al.Understanding power transformer frequency response analysis signatures[J].IEEE Electrical Insulation Magazine,2013,29(3):48-56.
[10]BJERKAN E.High frequency modeling of power transformers[D].Trondheim,Norwegian:Norwegian University of Science and Technology,2005:192-195.
[11]SHABESTARY M M,GHANIZADEH A J,GHAREHPETIAN G B,et al.Ladder network parameters determination considering nondominant resonances of the transformer winding[J].IEEE Transactions on Power Delivery,2014,29(1):108-117.
[12]RASHTCHI V,RAHIMPOUR E,REZAPOUR E M.Using agenetic algorithm for parameter identification of transformer RLCM model[J].Electrical Engineering,2006,88(5):417-422.
[13]ABEYWICKRAMA N,SERDYUK Y V,GUBANSKI S M.High-frequency modeling of power transformers for use in frequency response analysis(FRA)[J].IEEE Transactions on Power Delivery,2008,23(4):2042-2049.
[14]SHINTEMIROV A,TANG W H,WU Q H.A hybrid winding model of disc-type power transformers for frequency response analysis[J].IEEE Transactions on Power Delivery,2009,24(2):730-739.
[15]张震.变压器绕组变形检测装置的研究[D].沈阳:沈阳工业大学,2013:18-27.
[16]陈晓晗.基于有限元法的电力变压器绕组变形检测与识别的仿真研究[D].重庆:重庆大学,2015:42-55.
[17]ABEYWICKRAMA K B,SERDYUK Y V,GUBANSKI S M.Exploring possibilities for characterization of power transformer insulation by frequency response analysis(FRA)[J].IEEE Transactions on Power Delivery,2006,21(3):1375-1382.
[18]朱明林.频响分析法及其模型辨识检测和诊断变压器绕组变形的研究[D].上海:上海交通大学,2001:12-20.
[19]PODOLTSEV A D,NILANGA K G,ABEYWICKRAMA K B,et al.Multiscale computations of parameters of power transformer windings at high frequencies:part I Small-scale level[J].IEEE Transactions on Magnetics,2007,43(11):3991-3998.
[20]PODOLTSEV A D,ABEYWICKRAMA K B,SERDYUK Y V,et al.Multiscale computations of parameters of power transformer windings at high frequencies:part II Large-scale level[J].IEEE Transactions on Magnetics,2007,43(12):4076-4082.
[21]武剑利.频响分析法检测变压器绕组变形的理论研究[D].武汉:武汉大学,2004:21-22.
[2]刘勇,杨帆,张凡,等.检测电力变压器绕组变形的扫频阻抗法研究[J].中国电机工程学报,2015,35(17):4505-4516.LIU Yong,YANG Fan,ZHANG Fan,et al.Study on sweep frequency impedance to detect winding deformation within power transformer[J].Proceedings of the CSEE,2015,35(17):4505-4516.
[3]朱叶叶,汲胜昌,张凡,等.电力变压器振动产生机理及影响因素研究[J].西安交通大学学报,2015,49(6):115-125.ZHU Yeye,JI Shengchang,ZHANG Fan,et al.Vibration mechanism and influence factors in power transformers[J].Journal of Xi’an Jiaotong University,2015,49(6):115-125.
[4]张凡,汲胜昌,祝令瑜,等.短路冲击下变压器振动频响函数研究[J].西安交通大学学报,2017,51(2):97-103,154.ZHANG Fan,JI Shengchang,ZHU Lingyu,et al.Frequency response function of short circuit viberation for power transformer[J].Journal of Xi’an Jiaotong University,2017,51(2):97-103,154.
[5]REYKHERDT A A,DAVYDOV V.Case studies of factors influencing frequency response analysis measurements and power transformer diagnostics[J].IEEE Electrical Insulation Magazine,2011,27(1):22-30.
[6]RYDER S A.Diagnosing transformer faults using frequency response analysis[J].IEEE Electrical Insulation Magazine,2003,19(2):16-22.
[7]KIM J W,PARK B,JEONG S,et al.Fault diagnosis of a power transformer using an improved frequencyresponse analysis[J].IEEE Transactions on Power Delivery,2005,20(1):169-178.
[8]王曙鸿,张海军.一种基于模型修正的变压器绕组变形定量诊断方法:CN105180792A[P].2015-07-01.
[9]ABU-SIADA A,HASHEMNIA N,ISLAM S,et al.Understanding power transformer frequency response analysis signatures[J].IEEE Electrical Insulation Magazine,2013,29(3):48-56.
[10]BJERKAN E.High frequency modeling of power transformers[D].Trondheim,Norwegian:Norwegian University of Science and Technology,2005:192-195.
[11]SHABESTARY M M,GHANIZADEH A J,GHAREHPETIAN G B,et al.Ladder network parameters determination considering nondominant resonances of the transformer winding[J].IEEE Transactions on Power Delivery,2014,29(1):108-117.
[12]RASHTCHI V,RAHIMPOUR E,REZAPOUR E M.Using agenetic algorithm for parameter identification of transformer RLCM model[J].Electrical Engineering,2006,88(5):417-422.
[13]ABEYWICKRAMA N,SERDYUK Y V,GUBANSKI S M.High-frequency modeling of power transformers for use in frequency response analysis(FRA)[J].IEEE Transactions on Power Delivery,2008,23(4):2042-2049.
[14]SHINTEMIROV A,TANG W H,WU Q H.A hybrid winding model of disc-type power transformers for frequency response analysis[J].IEEE Transactions on Power Delivery,2009,24(2):730-739.
[15]张震.变压器绕组变形检测装置的研究[D].沈阳:沈阳工业大学,2013:18-27.
[16]陈晓晗.基于有限元法的电力变压器绕组变形检测与识别的仿真研究[D].重庆:重庆大学,2015:42-55.
[17]ABEYWICKRAMA K B,SERDYUK Y V,GUBANSKI S M.Exploring possibilities for characterization of power transformer insulation by frequency response analysis(FRA)[J].IEEE Transactions on Power Delivery,2006,21(3):1375-1382.
[18]朱明林.频响分析法及其模型辨识检测和诊断变压器绕组变形的研究[D].上海:上海交通大学,2001:12-20.
[19]PODOLTSEV A D,NILANGA K G,ABEYWICKRAMA K B,et al.Multiscale computations of parameters of power transformer windings at high frequencies:part I Small-scale level[J].IEEE Transactions on Magnetics,2007,43(11):3991-3998.
[20]PODOLTSEV A D,ABEYWICKRAMA K B,SERDYUK Y V,et al.Multiscale computations of parameters of power transformer windings at high frequencies:part II Large-scale level[J].IEEE Transactions on Magnetics,2007,43(12):4076-4082.
[21]武剑利.频响分析法检测变压器绕组变形的理论研究[D].武汉:武汉大学,2004:21-22.