分层土壤接地格林函数的多精度多分辨率计算
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摘要
广域系统电磁兼容问题研究采用的大地模型具有分层多和参数差异大的特点,传统数值方法求解接地格林函数时面临严重的数值奇异问题。结合理论推导和数值计算提出格林函数的多精度多分辨率求解方案:利用多精度计算库GMP直接求解积分核函数,从而有效避免一般方法求解失败的问题,并结合解析解验证方法的有效性;提出多分辨率计算方法实现格林函数积分核函数的全积分域复镜像重构,并推导计算误差上限的理论公式,证明多精度多分辨率方法的准确性。最后,针对某分层大地模型,采用多精度多分辨率法求解地表电位分布,并与改进高阶复镜像法进行性能对比,全面验证该文方法的先进性。
For electromagnetic compatibility of wide-area system, the layers and parameters of soil models are so sophisticated that traditional numerical methods fail to compute the Green's function with serious numerical singularity issues.A multi-precision-resolution solution was proposed in combination with theoretical derivation and numerical calculation to handle with these problems. Firstly, using the multi-precision computation library GMP to solve the integral kernel directly, which can effectively avoid general methods that lead to failure. Also, this method was verified analytically.Secondly, a multi-resolution method was proposed to reconstruct the integral kernel function in Green's function along the integral domain by complex images. Then the theoretical calculation formula of the upper error has been derived, and the accuracy of the multi-precision-resolution method has been proven. Finally, for a model of layered earth,the multi-precision-resolution computation was used to solve the earth surface potential distribution, and its performance was compared with that of a modified high-order complex image method(HOCIM), which fully verifies the advancement of this method.
For electromagnetic compatibility of wide-area system, the layers and parameters of soil models are so sophisticated that traditional numerical methods fail to compute the Green's function with serious numerical singularity issues.A multi-precision-resolution solution was proposed in combination with theoretical derivation and numerical calculation to handle with these problems. Firstly, using the multi-precision computation library GMP to solve the integral kernel directly, which can effectively avoid general methods that lead to failure. Also, this method was verified analytically.Secondly, a multi-resolution method was proposed to reconstruct the integral kernel function in Green's function along the integral domain by complex images. Then the theoretical calculation formula of the upper error has been derived, and the accuracy of the multi-precision-resolution method has been proven. Finally, for a model of layered earth,the multi-precision-resolution computation was used to solve the earth surface potential distribution, and its performance was compared with that of a modified high-order complex image method(HOCIM), which fully verifies the advancement of this method.
引文
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[23]阮羚,徐碧川,全江涛,等.用于土壤分层电阻率模型反演的人工蜂群结合混沌搜索算子及混沌算法[J].高电压技术,2015,41(1):42-48.Ruan Ling,Xu Bichuan,Quan Jiangtao,et al.Artificial colony algorithm combined with chaotic search operator and chaotic pool used for resistivity model inversion of layered soil[J].High Voltage Engineering,2015,41(1):42-48(in Chinese).
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[31]Hajiaboli A,Fortin S,Dawalibi F P.Numerical techniques for the analysis of HVDC sea electrodes[J].IEEETransactions on Industry Applications,2015,51(6):5175-5181.
[32]Fortin S,Mitskevitch N,Dawalibi F P.Analysis of grounding systems in horizontal multilayer soils containing finite heterogeneities[J].IEEE Transactions on Industry Applications,2015,51(6):5095-5100.
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[2]刘连光,姜克如,李洋,等.直流接地极近区三维大地电阻率模型建立方法[J].中国电机工程学报,2018,38(6):1622-1630.Liu Lianguang,Jiang Keru,Li Yang,et al.Threedimensional earth resistivity structure modelling around dc ground electrode[J].Proceedings of the CSEE,2018,38(6):1622-1630(in Chinese).
[3]王晓希,阮羚,文习山,等.基于深层大地电阻率的直流偏磁电流特征分析[J].高电压技术,2015,41(5):1536-1543.Wang Xiaoxi,Ruan Ling,Wen Xishan,et al.Characteristics analysis of DC-bias currents considering deep-earth resistivity[J].High Voltage Engineering,2015,41(5):1536-1543(in Chinese).
[4]曹方圆,孟晓波,廖永力,等.直流接地极对埋地金属管道影响的电路模型及应用[J].电网技术,2016,40(10):3258-3264.Cao Fangyuan,Meng Xiaobo,Liao Yongli,et al.Circuit model and application for influence of DC ground electrode on buried metal pipelines[J].Power System Technology,2016,40(10):3258-3264(in Chinese).
[5]白锋,陆家榆,林珊珊,等.特高压交直流输电线路同走廊正常运行时对邻近埋地油气管道的电磁影响分析[J].电网技术,2016,40(11):3609-3614.Bai Feng,Lu Jiayu,Lin Shanshan,et al.Analysis of electromagnetic effect of UHV AC and DC transmission lines in same corridor in normal operation on adjacent petroleum&gas pipelines[J].Power System Technology,2016,40(11):3609-3614(in Chinese).
[6]张威.钢筋混凝土结构轨道交通杂散电流腐蚀损伤机理[D].哈尔滨:哈尔滨工业大学,2017.Zhang Wei.Corrosion damage mechamism of reinforced concrete structures caused by the stray current of rail transit system[D].Harbin:Harbin Institute of Technology,2017(in Chinese).
[7]刘颖熙.城市轨道交通杂散电流动态分布及泄漏监测研究[D].徐州:中国矿业大学,2017.Liu Yingxi.Research on the dynamic distribution and leakage monitoring of stray current in urban rail transit[D].Xuzhou:China University of Mining&Technology,2017(in Chinese).
[8]Pan Zhuohong,Zhang Lu,Wang Xiaomao,et al.HVDCground return current modeling in AC systems considering mutual resistances[J].IEEE Transactions on Power Delivery,2016,31(1):165-173.
[9]黄义隆,张波,国建宝,等.改善直流电流地中分布的接地极互联技术研究[J].电网技术,2017,41(4):1338-1344.Huang Yilong,Zhang Bo,Guo Jianbao,et al.Research on improving DC current distribution in earth by interconnecting DC grounding electrodes[J].Power System Technology,2017,41(4):1338-1344(in Chinese).
[10]文习山,刘晨蕾,李伟,等.考虑深层大地电阻率的电网广域直流电流分布数值计算[J].高电压技术,2017,43(7):2331-2339.Wen Xishan,Liu Chenlei,Li Wei,et al.Computation for wide-area direct current distribution of power grids considering deep earth resistivity[J].High Voltage Engineering,2017,43(7):2331-2339(in Chinese).
[11]何金良,曾嵘.电力系统接地技术[M].北京:科学出版社,2007:209-2013,217-222.He Jinliang,Zeng Rong.Grounding technology of power system[M].Beijing:Science Press,2007:209-213,217-222(in Chinese).
[12]Tsiamitros D A,Papagiannis G K,Dokopoulos P S.Earth return impedances of conductor arrangements in multilayer soils-Part I:Theoretical model[J].IEEETransactions on Power Delivery,2008,23(4):2392-2400.
[13]司马文霞,艾琳丰,袁涛,等.土壤介电频变特性试验研究及其对接地极冲击特性的影响[J].中国电机工程学报,2015,35(16):4247-4253.Sima Wenxia,Ai Linfeng,Yuan Tao,et al.Experimental study on the frequency characteristic of soil permittivity and the influence on impact characteristics of grounding electrode[J].Proceedings of the CSEE,2015,35(16):4247-4253(in Chinese).
[14]张占龙,许晓,刘成,等.一种多频扫描式杆塔接地电阻的测量方法[J].中国电机工程学报,2015,35(19):5078-5086.Zhang Zhanlong,Xu Xiao,Liu Cheng,et al.Amulti-frequency sweeping method of measuring tower grounding resistance[J].Proceedings of the CSEE,2015,35(19):5078-5086(in Chinese).
[15]Yuan Tao,Bai Yang,Sima Wenxia,et al.Grounding resistance measurement method based on the fall of potential curve test near current electrode[J].IEEETransactions on Power Delivery,2017,32(4):2005-2012.
[16]Li Wei,Pan Zhuohong,Lu Hailiang,et al.Influence of deep earth resistivity on HVDC ground-return currents distribution[J].IEEE Transactions on Power Delivery,2017,32(4):1844-1851.
[17]杨娜,陈煜,潘卓洪,等.准东--皖南±1100kV特高压直流输电工程受端电网的直流偏磁影响预测及治理[J].电网技术,2018,42(2):380-386.Yang Na,Chen Yu,Pan Zhuohong,et al.Influence prediction and suppression research of DC bias in Eastern Junggar-Southern Anhui±1100kV UHVDC receiving-end grid[J].Power System Technology,2018,42(2):380-386(in Chinese).
[18]孟晓波,廖永力,李锐海,等.金属管道受入地电流影响的抑制措施研究[J].南方电网技术,2015,9(2):62-67.Meng Xiaobo,Liao Yongli,Li Ruihai,et al.Research on repressive measures of the influence of the ground return current on the metallic pipeline[J].Southern Power System Technology,2015,9(2):62-67(in Chinese).
[19]唐波,张小武,葛光祖,等.特高压直流输电线路与接地极对地电场观测的干扰[J].高电压技术,2013,39(12):2951-2959.Tang Bo,Zhang Xiaowu,Ge Guangzu,et al.Interference on geoelectric field observation from UHVDC power lines and its ground electrode[J].High Voltage Engineering,2013,39(12):2951-2959(in Chinese).
[20]正霖.滨海环境下杂散电流对砂浆中钢筋的电化学腐蚀行为研究[D].深圳:深圳大学,2016.Pu Zhenglin.Study on the electrochemical corrosion behaviour of reinforcement by stray current in mortar in the coastal environment[D].Shenzhen:Shenzhen University,2016(in Chinese).
[21]程明,唐强,魏德军,等.高压直流接地极干扰区埋地钢质油气管道的综合防护[J].天然气工业,2015,35(9):105-111.Cheng Ming,Tang Qiang,Wei Dejun,et al.Comprehensive protection of buried steel pipelines at HVDC earthed electrode interference area[J].Natural Gas Industry,2015,35(9):105-111(in Chinese).
[22]何为,张瑞强,杨帆,等.变电站内水平多层土壤参数反演[J].中国电机工程学报,2014,34(33):5964-5973.He Wei,Zhang Ruiqiang,Yang Fan,et al.Parameter estimation of horizontal multi-layer earth in substation[J].Proceedings of the CSEE,2014,34(33):5964-5973(in Chinese).
[23]阮羚,徐碧川,全江涛,等.用于土壤分层电阻率模型反演的人工蜂群结合混沌搜索算子及混沌算法[J].高电压技术,2015,41(1):42-48.Ruan Ling,Xu Bichuan,Quan Jiangtao,et al.Artificial colony algorithm combined with chaotic search operator and chaotic pool used for resistivity model inversion of layered soil[J].High Voltage Engineering,2015,41(1):42-48(in Chinese).
[24]Southey R D,Siahrang M,Fortin S,et al.Using fall-ofpotential measurements to improve deep soil resistivity estimates[J].IEEE Transactions on Industry Applications,2015,51(6):5023-5029.
[25]张瑞强,何为,李羿,等.基于正逆问题分析方法的变电站接地网研究综述[J].中国电机工程学报,2014,34(21):3548-3560.Zhang Ruiqiang,He Wei,Li Yi,et al.Studies on substation ground grids from the perspective of primary and inverse problems[J].Proceedings of the CSEE,2014,34(21):3548-3560(in Chinese).
[26]潘文霞,柴守江,刘铜锤,等.双层土壤中接地网接地电阻短距离测量方法研究[J].中国电机工程学报,2017,37(S1):211-217.Pan Wenxia,Chai Shoujiang,Liu Tongchui,et al.Research on short distance measurement method of grounding resistance of grounding grids in double layer soil[J].Proceedings of the CSEE,2017,37(S1):211-217(in Chinese).
[27]Wang Yu,Pan Zhuohong,Zha Zhipeng,et al.Numerical simulation and field test of the transient temperature rise of HVDC grounding electrodes[J].IEEE Transactions on Power Delivery,2018,33(1):22-31.
[28]Ma J,Dawalibi F P,Daily W K.Analysis of grounding systems in soils with hemispherical layering[J].IEEETransactions on Power Delivery,1993,8(4):1773-1781.
[29]Zhao Huiliang,Fortin S,Dawalibi F P.Analysis of grounding systems including freely oriented plates of arbitrary shape in multilayer soils[J].IEEE Transactions on Industry Applications,2015,51(6):5189-5197.
[30]Hajiaboli A,Fortin S,Dawalibi F P,et al.Analysis of grounding systems in the vicinity of hemispheroidal heterogeneities[J].IEEE Transactions on Industry Applications,2015,51(6):5070-5077.
[31]Hajiaboli A,Fortin S,Dawalibi F P.Numerical techniques for the analysis of HVDC sea electrodes[J].IEEETransactions on Industry Applications,2015,51(6):5175-5181.
[32]Fortin S,Mitskevitch N,Dawalibi F P.Analysis of grounding systems in horizontal multilayer soils containing finite heterogeneities[J].IEEE Transactions on Industry Applications,2015,51(6):5095-5100.
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