电力电缆温度场及载流量计算方法研究
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摘要
随着电气设备容量的扩大和社会对电力需求的日益增长,对输电线路的可靠性要求也不断提高。在电能的传输过程中,电力电缆作为主要载体被广泛的使用。由于在敷设过程中选用理论数据设计电缆回路,使得电缆回路的理论载流量和实际运行中表现出的载流量有较大的差异,如何对现有运行电缆的载流量在不同条件下的变化情况进行分析,对于提高电缆的容量利用率,准确快速的计算其载流量对电力系统安全、可靠、高效地运行有着很重要的意义。
电缆绝缘层的工作温度不能超过其耐热寿命允许值。由于影响电缆散热的可变因素很多,仅按规程法确定载流量无法满足需要。为保证电缆安全、有效地运行,采用数值计算方法精确模拟地下电缆的散热特性具有重要的工程实际意义。
本文在理解温度场的基础上,将地下电缆温度场归结为二维热传导问题,建立了地下电缆的温度场的控制方程、影响范围以及边界的边界条件。对二维传热方程组使用有限元法进行离散。使用有限元分析软件COMSOL作为软件平台,建立了各种敷设形式的地下电缆温度场的模型,结合双点弦截的迭代方法快速准确的计算各种地下电缆的最大载流量,对比规则和不规则排列情况下地下电缆的温度场分布,并详尽的分析了各种因素对地下电缆载流量的影响,为地下电缆安全、可靠地运行提供保障。
同时,建立了地下电缆的电场模型,得出电缆电场的分布,与温度场得出的数据进行比较,分析两者间的数值关系。计算结果表明电缆的温度场与电场之间呈近似的线性关系。为更好对地下电缆的运行状态进行监测提供了新的思路。
With the increase of electrical equipments’capacity and the growing electricity demand of society, the reliability requirement of transmission line is required higher and higher. In the process of power transmission, power cables are widely used as the main carrier for power transmission. In the cable laying process, the data are selected to design cable circuit, which leads to the cable circuit’s theoretical and practical carrying capacity have a great difference. So how to analyze the carrying capacity of present running cables under various conditions is very important to improve cables’capacity utilization rate, to calculate its carrying capacity rapidly and accurately, to guarantee the power system safety, reliability and high efficiency.
The operating temperature of the cable insulation layer should not exceed the allowable values of its heat-resistant life. It will not meet the demand if the carrying capacity is only determined by rules because of excessive variable factors that affect the heat dissipation of cables. To ensure the cable safety and operation effectiveness, the use of accurate numerical method to simulate the heat dissipation characteristics of underground cables has great practical significance.
On the basis of temperature field, in this paper, the temperature field of underground cables was treated as two-dimensional heat conduction problem, the control equation, area and the boundary condition of the temperature field of the underground cable were established. The finite element method was used to discrete the two-dimensional heat transfer equations. The finite element analysis software COMSOL was used as a software platform to build the various forms of laying underground cable models of temperature field, at the same time,using the dual-point secant method to calculate the underground cables ampacity rapidly and accurately , comparing to the rules and irregularity the rules of underground cables with the temperature distribution, and detailed analysis of the various factors on the impact of ampacity for protecting the safety and reliable operation of underground cables was given.
At the same time, the electric field model of underground cables was established to obtain the the distribution of electric field and the the data was compared with the data from the temperature field to analyze the numerical relationship. The computa- tional results showed that the temperature field is linear with the electric field. The conclusion provide new solution for the state monitoring of the underground cables.
电缆绝缘层的工作温度不能超过其耐热寿命允许值。由于影响电缆散热的可变因素很多,仅按规程法确定载流量无法满足需要。为保证电缆安全、有效地运行,采用数值计算方法精确模拟地下电缆的散热特性具有重要的工程实际意义。
本文在理解温度场的基础上,将地下电缆温度场归结为二维热传导问题,建立了地下电缆的温度场的控制方程、影响范围以及边界的边界条件。对二维传热方程组使用有限元法进行离散。使用有限元分析软件COMSOL作为软件平台,建立了各种敷设形式的地下电缆温度场的模型,结合双点弦截的迭代方法快速准确的计算各种地下电缆的最大载流量,对比规则和不规则排列情况下地下电缆的温度场分布,并详尽的分析了各种因素对地下电缆载流量的影响,为地下电缆安全、可靠地运行提供保障。
同时,建立了地下电缆的电场模型,得出电缆电场的分布,与温度场得出的数据进行比较,分析两者间的数值关系。计算结果表明电缆的温度场与电场之间呈近似的线性关系。为更好对地下电缆的运行状态进行监测提供了新的思路。
With the increase of electrical equipments’capacity and the growing electricity demand of society, the reliability requirement of transmission line is required higher and higher. In the process of power transmission, power cables are widely used as the main carrier for power transmission. In the cable laying process, the data are selected to design cable circuit, which leads to the cable circuit’s theoretical and practical carrying capacity have a great difference. So how to analyze the carrying capacity of present running cables under various conditions is very important to improve cables’capacity utilization rate, to calculate its carrying capacity rapidly and accurately, to guarantee the power system safety, reliability and high efficiency.
The operating temperature of the cable insulation layer should not exceed the allowable values of its heat-resistant life. It will not meet the demand if the carrying capacity is only determined by rules because of excessive variable factors that affect the heat dissipation of cables. To ensure the cable safety and operation effectiveness, the use of accurate numerical method to simulate the heat dissipation characteristics of underground cables has great practical significance.
On the basis of temperature field, in this paper, the temperature field of underground cables was treated as two-dimensional heat conduction problem, the control equation, area and the boundary condition of the temperature field of the underground cable were established. The finite element method was used to discrete the two-dimensional heat transfer equations. The finite element analysis software COMSOL was used as a software platform to build the various forms of laying underground cable models of temperature field, at the same time,using the dual-point secant method to calculate the underground cables ampacity rapidly and accurately , comparing to the rules and irregularity the rules of underground cables with the temperature distribution, and detailed analysis of the various factors on the impact of ampacity for protecting the safety and reliable operation of underground cables was given.
At the same time, the electric field model of underground cables was established to obtain the the distribution of electric field and the the data was compared with the data from the temperature field to analyze the numerical relationship. The computa- tional results showed that the temperature field is linear with the electric field. The conclusion provide new solution for the state monitoring of the underground cables.
引文
[1]郑肇骥,王明.高压电缆线路[M].北京:水利水电出版社,1983.107～111
[2] International Electrotechnical Commission.IEC 60287-1.Calculation of currentrating part 1:(100%load factor)and calculation of losses[S].2001
[3]李熙谋.不同敷设条件下电缆载流量的校正和实用算法[J].电力建设,1997,(5):1～7
[4]杨泽亮,侯志云,何杰.封闭空间电缆群散热的实验研究[J].华南理工大学学报,1996,25(6):85～90
[5]孟凡凤,李香龙,王颂等.电缆群直埋敷设散热的试验研究[J],绝缘材料,2007,40(1):58～60
[6] E.Tarasiewicz,E.Kuffel,S.Grzybowski.Calculations of temperature distrib-utions within cable trench backfill and the surrounding soil[J].IEEE Transacti-ons on Apparatus and Systems,1985,3(8):1973～1977
[7] G.J.Anders.Power cable thermal analysis with considerations of heat and mois-ture transfer in the soil[J].IEEE Trans.on Power Delivery,1988,3(4):1280～1285
[8]李志坚,张东斐,曹慧玲等.地下埋设电缆温度场和载流量的数值计算[J].高电压技术,2004,30(6):27～30
[9]李雯靖,李志坚,高捷.直埋地下电缆温度场和载流量的数值计算[J].天津电力技术,2003,2:59～61
[10] W.L.Black and Sang-il Park.Emergency ampacities of direct buried three phase underground cable systems[J].IEEE Trans.on Power Apparatus and Systems,1983,5(7):2124～2132
[11] Saleeby,K.E.,Black,W.Z.,and Hartley,J.G..Effective thermal resistancefor power cables buried in thermal backfill[J].IEEE Trans.1979,PAS-98(6):2201～2208
[12] W.K.Chow and K.C.Chan.Computer simulation of the thermal environmentinside a 275-kV underground electric cable tunnel[J].ASHRAE Transactions:Research 3718:277～284
[13]陶文铨.数值传热学[M].西安:西安交通大学出版社,1995.86～90
[14]陶文铨.计算传热学的近代进展[M].北京:科学出版社,2001.60～77
[15] Kellow,M.A.,A numerical procedure for the calculation of the temperature rise and ampacity of underground cables[J].IEEE Trans.1981,PAS-100(7):3322～3330
[16] K.Khanafer,K.Vafai.Effective boundary conditions for buoyancy driven flowsand heat transfer in fully open-ended two-dimensional enclosures[J].International Journal of Heat and Mass Transfer,2002,45(2)
[17]曹惠玲,王增强,李雯靖等.坐标组合法对直埋电缆与土壤界面温度场的数值计算[J].电工技术学报,2003:59～63
[18] Hiranandani,A.Calculation of conductor temperatures and ampacity of cable systems using a generalized finite difference model[J].IEEE PES:323～329
[19] Anders,G.J.,M.Chaaban,N.Bedard,R.W.Ganton.New approach to ampacity evaluation of cables in ducts using finite element technique[J].IEEE Trans-actions on Power Delivery,1987,2(3):969～975
[20]孟凡凤,李香龙,徐燕飞等.地下直埋电缆温度场和载流量的数值计算[J].绝缘材料,2006,39(4):59～61
[21] Gela G,Dai J J.Calculation of thermal fields of underground cables using the boundary element method[J].IEEE Transactions on Power Delivery,1988,5(3):1341～1347
[22]丁丽娟,程杞元.数值计算方法[M].北京:北京理工大学出版社,2005.267～274
[23] Hanna M A,Chikhani A Y,Salama M.M.A,Thermal analysis of power cablesin multi-layered soil—Part 1:Theoretical model[J].IEEE Trans.on PowerDelivery,1993,8:761～771
[24] Hanna M A,Chikhani A Y,Salama M.M.A.Thermal analysis of power cables in multi-layered soil—Part 2:Practical Considerations[J].IEEE Trans.on Power Delivery,1993,8:772～777
[25] Hanna M A,Chikhani A Y,Salama M.M.A.Thermal analysis of power cables in multi-layered soil,Part3:Case of Two Cables in a Trench[J].IEEE Trans Power Delivery,1994,9:572～577
[26] Carlos Gaggido,Antonio F.Otero,and Jose cidras.Theoretical model to calculate steady state and transient smpacity and temperature in buried cables[J].IEEE Trans.on Power Delivery,2003,18(3):667～677
[27]牛海清,王晓兵,蚁泽沛等.110kV单芯电缆金属护套环流计算与试验研究[J].高电压技术,2005,31(8):15~17
[28]赵建华,袁宏永,范维澄等.基于表面温度场的电缆线芯温度在线诊断研究[J].中国电机工程学报,1999,19(11):52~54
[29]成永红,谢恒,衣立东.基于热效应的电力电缆及其终端在线检测技术[J].高电压技术,1999,25(3):4~6
[30]贾欣,曹晓珑,喻明.单芯电缆计及护套环流时载流量的计算[J].高电压技术,2001,27(1):25~26
[31]刘毅刚,罗俊华.电缆导体温度实时计算的数学方法[J].高电压技术,2005,31(5):52~54
[32]王增强,曹惠玲.预埋管地下电缆温度场和载流量的数值计算[J].河北工业大学学报.2003,32(3):103~107
[33]孟凡凤,梁永春,李彦明.交联电缆额定载流量计算的软件实现[J].高压电器,2006,42(3):194~195
[34]杨小静,马国栋.电力电缆载流量计算视窗化[J].电线电缆,2002,(2):36~40
[35]苏巍,明安持.多回路电缆布置优化的研究[J].高电压技术,2006,32(11):64～66
[36]葛新石,叶宏译.传热和传质基本原理(第六版) [M].北京:化学工业出版社,2007
[37]赵镇南。传热学[M]。北京:高等教育出版社[M],2002
[38]杨世铭著.传热学基础(机械热加工类专业适用) [M].北京:高等教育出版社,1991.
[39]梁永春,李彦明,柴进爱等地下电缆群稳态温度场和载流量计算新方法[J],电工技术学报,2007,22(8)185~189;
[40]马国栋.电线电缆载流量[M],北京:中国电力出版社,2003
[41]王勖成编著,有限单元法[M],北京:清华大学出版社,2003
[42]关正西,强洪夫译.有限元分析的概念与应用[M],西安:西安交通大学出版社2007
[43]王崧,刘丽娟,董春敏等译.有限元分析——ansys理论与应用(第三版)[M],北京:电子工业出版社,2008
[44]杨大地,涂光裕编.数值分析.重庆:重庆大学出版社,1998.+
[45]孙志忠,袁慰平,闻震初编著.数值分析,南京:东南大学出版社,2002
[46]夏新民主编.电力电缆选型与敷设,北京:化学工业出版社,2008
[47]王增强.地下电缆温度场和载流量的数值模拟(D).河北:河北工业大学,2001.
[48]王春江,电线电缆手册[M],北京:机械工业出版社,2008
[49]孙敏,孙亲锡等,工程电磁场基础[M],北京:科学技术出版社,2001
[50]贾起民,郑永令等,电磁学(第二版)[M],北京:高等教育出版社,2001
[2] International Electrotechnical Commission.IEC 60287-1.Calculation of currentrating part 1:(100%load factor)and calculation of losses[S].2001
[3]李熙谋.不同敷设条件下电缆载流量的校正和实用算法[J].电力建设,1997,(5):1～7
[4]杨泽亮,侯志云,何杰.封闭空间电缆群散热的实验研究[J].华南理工大学学报,1996,25(6):85～90
[5]孟凡凤,李香龙,王颂等.电缆群直埋敷设散热的试验研究[J],绝缘材料,2007,40(1):58～60
[6] E.Tarasiewicz,E.Kuffel,S.Grzybowski.Calculations of temperature distrib-utions within cable trench backfill and the surrounding soil[J].IEEE Transacti-ons on Apparatus and Systems,1985,3(8):1973～1977
[7] G.J.Anders.Power cable thermal analysis with considerations of heat and mois-ture transfer in the soil[J].IEEE Trans.on Power Delivery,1988,3(4):1280～1285
[8]李志坚,张东斐,曹慧玲等.地下埋设电缆温度场和载流量的数值计算[J].高电压技术,2004,30(6):27～30
[9]李雯靖,李志坚,高捷.直埋地下电缆温度场和载流量的数值计算[J].天津电力技术,2003,2:59～61
[10] W.L.Black and Sang-il Park.Emergency ampacities of direct buried three phase underground cable systems[J].IEEE Trans.on Power Apparatus and Systems,1983,5(7):2124～2132
[11] Saleeby,K.E.,Black,W.Z.,and Hartley,J.G..Effective thermal resistancefor power cables buried in thermal backfill[J].IEEE Trans.1979,PAS-98(6):2201～2208
[12] W.K.Chow and K.C.Chan.Computer simulation of the thermal environmentinside a 275-kV underground electric cable tunnel[J].ASHRAE Transactions:Research 3718:277～284
[13]陶文铨.数值传热学[M].西安:西安交通大学出版社,1995.86～90
[14]陶文铨.计算传热学的近代进展[M].北京:科学出版社,2001.60～77
[15] Kellow,M.A.,A numerical procedure for the calculation of the temperature rise and ampacity of underground cables[J].IEEE Trans.1981,PAS-100(7):3322～3330
[16] K.Khanafer,K.Vafai.Effective boundary conditions for buoyancy driven flowsand heat transfer in fully open-ended two-dimensional enclosures[J].International Journal of Heat and Mass Transfer,2002,45(2)
[17]曹惠玲,王增强,李雯靖等.坐标组合法对直埋电缆与土壤界面温度场的数值计算[J].电工技术学报,2003:59～63
[18] Hiranandani,A.Calculation of conductor temperatures and ampacity of cable systems using a generalized finite difference model[J].IEEE PES:323～329
[19] Anders,G.J.,M.Chaaban,N.Bedard,R.W.Ganton.New approach to ampacity evaluation of cables in ducts using finite element technique[J].IEEE Trans-actions on Power Delivery,1987,2(3):969～975
[20]孟凡凤,李香龙,徐燕飞等.地下直埋电缆温度场和载流量的数值计算[J].绝缘材料,2006,39(4):59～61
[21] Gela G,Dai J J.Calculation of thermal fields of underground cables using the boundary element method[J].IEEE Transactions on Power Delivery,1988,5(3):1341～1347
[22]丁丽娟,程杞元.数值计算方法[M].北京:北京理工大学出版社,2005.267～274
[23] Hanna M A,Chikhani A Y,Salama M.M.A,Thermal analysis of power cablesin multi-layered soil—Part 1:Theoretical model[J].IEEE Trans.on PowerDelivery,1993,8:761～771
[24] Hanna M A,Chikhani A Y,Salama M.M.A.Thermal analysis of power cables in multi-layered soil—Part 2:Practical Considerations[J].IEEE Trans.on Power Delivery,1993,8:772～777
[25] Hanna M A,Chikhani A Y,Salama M.M.A.Thermal analysis of power cables in multi-layered soil,Part3:Case of Two Cables in a Trench[J].IEEE Trans Power Delivery,1994,9:572～577
[26] Carlos Gaggido,Antonio F.Otero,and Jose cidras.Theoretical model to calculate steady state and transient smpacity and temperature in buried cables[J].IEEE Trans.on Power Delivery,2003,18(3):667～677
[27]牛海清,王晓兵,蚁泽沛等.110kV单芯电缆金属护套环流计算与试验研究[J].高电压技术,2005,31(8):15~17
[28]赵建华,袁宏永,范维澄等.基于表面温度场的电缆线芯温度在线诊断研究[J].中国电机工程学报,1999,19(11):52~54
[29]成永红,谢恒,衣立东.基于热效应的电力电缆及其终端在线检测技术[J].高电压技术,1999,25(3):4~6
[30]贾欣,曹晓珑,喻明.单芯电缆计及护套环流时载流量的计算[J].高电压技术,2001,27(1):25~26
[31]刘毅刚,罗俊华.电缆导体温度实时计算的数学方法[J].高电压技术,2005,31(5):52~54
[32]王增强,曹惠玲.预埋管地下电缆温度场和载流量的数值计算[J].河北工业大学学报.2003,32(3):103~107
[33]孟凡凤,梁永春,李彦明.交联电缆额定载流量计算的软件实现[J].高压电器,2006,42(3):194~195
[34]杨小静,马国栋.电力电缆载流量计算视窗化[J].电线电缆,2002,(2):36~40
[35]苏巍,明安持.多回路电缆布置优化的研究[J].高电压技术,2006,32(11):64～66
[36]葛新石,叶宏译.传热和传质基本原理(第六版) [M].北京:化学工业出版社,2007
[37]赵镇南。传热学[M]。北京:高等教育出版社[M],2002
[38]杨世铭著.传热学基础(机械热加工类专业适用) [M].北京:高等教育出版社,1991.
[39]梁永春,李彦明,柴进爱等地下电缆群稳态温度场和载流量计算新方法[J],电工技术学报,2007,22(8)185~189;
[40]马国栋.电线电缆载流量[M],北京:中国电力出版社,2003
[41]王勖成编著,有限单元法[M],北京:清华大学出版社,2003
[42]关正西,强洪夫译.有限元分析的概念与应用[M],西安:西安交通大学出版社2007
[43]王崧,刘丽娟,董春敏等译.有限元分析——ansys理论与应用(第三版)[M],北京:电子工业出版社,2008
[44]杨大地,涂光裕编.数值分析.重庆:重庆大学出版社,1998.+
[45]孙志忠,袁慰平,闻震初编著.数值分析,南京:东南大学出版社,2002
[46]夏新民主编.电力电缆选型与敷设,北京:化学工业出版社,2008
[47]王增强.地下电缆温度场和载流量的数值模拟(D).河北:河北工业大学,2001.
[48]王春江,电线电缆手册[M],北京:机械工业出版社,2008
[49]孙敏,孙亲锡等,工程电磁场基础[M],北京:科学技术出版社,2001
[50]贾起民,郑永令等,电磁学(第二版)[M],北京:高等教育出版社,2001