基于块广义向后差分方法的高压输电线路电磁暂态数值计算方法
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摘要
为了避免高压输电线路电磁暂态仿真计算中的数值振荡问题,采用块边界值方法计算输电线路电磁暂态数值。首先将输电线路电报方程经空间离散转化为关于时间的一元微分方程组,建立输电线路电磁暂态数值计算的一阶数学模型。进而采用块边界值方法,利用L-稳定的2到3阶的块广义向后差分公式求解该初值问题得到空间离散点处时域数值解。采用简单的RL串联电路及单相输电线路空载合闸过电压计算2个仿真算例,与临界阻尼调整法作对比测试。仿真结果表明,新方法无需检测突变过程,可采用较大的时间积分步长,有效避免数值振荡问题,适合用于输电线路电磁暂态的数值计算。
In order to avoid the problem of numerical oscillation in the electromagnetic transient(EMT) simulation of high voltage overhead transmission line,the paper uses block boundary value method to make the EMT numerical calculation for the transmission line. Firstly, the telegraph equation of the transmission line is discretized and transformed into differential equations with one unknown in spatial domain. Accordingly, the first-order mathematical model of the EMT numerical calculation is established for the transmission line. Then the initial value problem is solved by the block boundary value method. Actually, two-order and three-order block generalized backward differentiation formulae(BGBDF), which are L-stable numerical method, are used to obtain the time domain numerical solutions of the spatial discrete points. A simple RL series circuit and the overvoltage of single-phase transmission line when no-load closing is studied by the BGBDF and critical damping adjustment(CDA) method. The numerical results show that the BGBDF can take bigger time step and avoid the numerical oscillation problem without detecting the mutation process. It is suitable for the numerical calculation of electromagnetic transient simulation for the high-voltage overhead transmission line.
In order to avoid the problem of numerical oscillation in the electromagnetic transient(EMT) simulation of high voltage overhead transmission line,the paper uses block boundary value method to make the EMT numerical calculation for the transmission line. Firstly, the telegraph equation of the transmission line is discretized and transformed into differential equations with one unknown in spatial domain. Accordingly, the first-order mathematical model of the EMT numerical calculation is established for the transmission line. Then the initial value problem is solved by the block boundary value method. Actually, two-order and three-order block generalized backward differentiation formulae(BGBDF), which are L-stable numerical method, are used to obtain the time domain numerical solutions of the spatial discrete points. A simple RL series circuit and the overvoltage of single-phase transmission line when no-load closing is studied by the BGBDF and critical damping adjustment(CDA) method. The numerical results show that the BGBDF can take bigger time step and avoid the numerical oscillation problem without detecting the mutation process. It is suitable for the numerical calculation of electromagnetic transient simulation for the high-voltage overhead transmission line.
引文
[1] LIN J, MARTI J R. Implementation of the CDA procedure in the EMTP[J]. IEEE Transactions on Power Systems,1990, 5(2):394-402.
[2]王成山,李鹏,王立伟.电力系统电磁暂态仿真算法研究进展[J].电力系统自动化. 2009, 33(7):97-103.WANG Chengshan, LI Peng, WANG Liwei. Progresses on algorithm of electromagnetic transient simulation for electric power system[J]. Automation of Electric Power Systems, 2009, 33(7):97-103.
[3]杜向楠,徐波,郭志全,等.一种基于关联矩阵的配电网在线行波故障定位方法[J].智慧电力,2017,45(10):61-65.DU Xiangnan, XU Bo, GUO Zhiquan, et al. Traveling wave fault online location method for distribution network based on incidence matrix[J]. Smart Power,2017,45(10):61-65.
[4]陈洁羽,谈震,贺晓,等.传统选相元件在风电集中接入系统中的应用研究[J].智慧电力,2018, 46(5):27-32.CHEN Jieyu, TAN Zhen, HE Xiao, et al. Application of traditional phase selector in wind power centralized access system[J].Smart Power, 2018,46(5):27-32.
[5]王大鹏,魏佩瑜,王婧,等.输电线路暂态计算与分析方法的发展与展望[J].继电器,2007, 35(6):10-15.WANG Dapeng, WEI Peiyu, WANG Jing, et al.Development and prospect of transmission line analysis and calculation theories[J]. Relay, 2007, 35(6):10-15.
[6] PAUL C R. Incorporation of terminal constraints in the FDTD analysis of transmission lines[J]. IEEE Transactions on Electromagnetic Compatibility, 1994, 36(2):85-91.
[7] MARTI J R, LIN J M. Suppression of numericaloscillations in the EMTP[J]. IEEE Power Engineering Review, 1989, 9(5):71-72.
[8] CANGELLARIS A C, PASHA S, PRINCE J L, et al. A new discrete transmission line model for passive model order reduction and macromodeling of high-speed interconnections[J]. IEEE Transactions on Advanced Packaging, 1999,22(3):356-364.
[9] XU Q W, LI Z F, WANG J, et al. Modeling of transmission lines by the differential quadrature method[J]. IEEE Microwave and Guided Wave Letters, 1999, 9(4):145-147.
[10] LU Y, JIANG Y L. Symplectic schemes for telegraph equations[J]. Journal of Computational Mathematics,2016,34(3):285-299.
[11] NODA T, TAKENAKA K, INOUE T. Numerical integration by the 2-stage diagonally implicit RungeKutta method for electromagnetic transient simulations[J].IEEE Transactions on Power Delivery, 2009,24(1):390-399.
[12] BRUGNANO L, TRIGIANTE D. Boundary value methods:the third way between linear multistep and Runge-Kutta methods[J].Computers&Mathematics with Applications, 1998, 36(10):269-284.
[13] BRUGNANO L, TRIGIANTE D. Solving differential problems by multistep initial and boundary value methods[M].Amsterdam:Gordon and Breach, 1998.
[14] SULTAN M, REEVE J, ADAPA R. Combined transient and dynamic analysis of HVDC and FACTS systems[J].IEEE Transactions on Power Delivery, 1998, 13(4):1271-1 277.
[15] WANG C, FU X, LI P, et al. Multiscale simulation of power system transients based on the matrix exponential function[J]. IEEE Transactions on Power Systems, 2017,32(3):1913-1926.
[16]商莹,于玉铭,邹振宇,等.非线性电路暂态仿真中消除数值振荡的改进方法[J].电力系统保护与控制,2011, 39(7):142-146.SHANG Ying, YU Yuming, ZOU Zhenyu, et al. An advanced method of non-linear circuit eliminating numerical oscillation in electromagnetic transient simulation[J].Power System Protection and Control, 2011, 39(7):142-146.
[17]张伟,曹良,崔健,等.基于模糊控制与扩张状态观测器的VSG电压治理策略[J].供用电,2018,35(12):1-7+49.ZHANG Wei, CAO Liang, CUI Jian, et al. VSG voltage management strategy based on fuzzy control and extended state observer[J]. Distribution&Utilization, 2018, 35(12):1-7+49.
[18]姬煜轲,许建中,徐延明,等.无插值仿真平台中抑制数值振荡的阻尼电路设计方法[J].电力自动化设备,2016,36(7):143-149.JI Yuke, XU Jianzhong, XU Yanming, et al. Design of damping circuit for depressing numerical oscillation in interpolation-free simulation environment[J]. ElectricPower Automation Equipment, 2016,36(7):143-149.
[2]王成山,李鹏,王立伟.电力系统电磁暂态仿真算法研究进展[J].电力系统自动化. 2009, 33(7):97-103.WANG Chengshan, LI Peng, WANG Liwei. Progresses on algorithm of electromagnetic transient simulation for electric power system[J]. Automation of Electric Power Systems, 2009, 33(7):97-103.
[3]杜向楠,徐波,郭志全,等.一种基于关联矩阵的配电网在线行波故障定位方法[J].智慧电力,2017,45(10):61-65.DU Xiangnan, XU Bo, GUO Zhiquan, et al. Traveling wave fault online location method for distribution network based on incidence matrix[J]. Smart Power,2017,45(10):61-65.
[4]陈洁羽,谈震,贺晓,等.传统选相元件在风电集中接入系统中的应用研究[J].智慧电力,2018, 46(5):27-32.CHEN Jieyu, TAN Zhen, HE Xiao, et al. Application of traditional phase selector in wind power centralized access system[J].Smart Power, 2018,46(5):27-32.
[5]王大鹏,魏佩瑜,王婧,等.输电线路暂态计算与分析方法的发展与展望[J].继电器,2007, 35(6):10-15.WANG Dapeng, WEI Peiyu, WANG Jing, et al.Development and prospect of transmission line analysis and calculation theories[J]. Relay, 2007, 35(6):10-15.
[6] PAUL C R. Incorporation of terminal constraints in the FDTD analysis of transmission lines[J]. IEEE Transactions on Electromagnetic Compatibility, 1994, 36(2):85-91.
[7] MARTI J R, LIN J M. Suppression of numericaloscillations in the EMTP[J]. IEEE Power Engineering Review, 1989, 9(5):71-72.
[8] CANGELLARIS A C, PASHA S, PRINCE J L, et al. A new discrete transmission line model for passive model order reduction and macromodeling of high-speed interconnections[J]. IEEE Transactions on Advanced Packaging, 1999,22(3):356-364.
[9] XU Q W, LI Z F, WANG J, et al. Modeling of transmission lines by the differential quadrature method[J]. IEEE Microwave and Guided Wave Letters, 1999, 9(4):145-147.
[10] LU Y, JIANG Y L. Symplectic schemes for telegraph equations[J]. Journal of Computational Mathematics,2016,34(3):285-299.
[11] NODA T, TAKENAKA K, INOUE T. Numerical integration by the 2-stage diagonally implicit RungeKutta method for electromagnetic transient simulations[J].IEEE Transactions on Power Delivery, 2009,24(1):390-399.
[12] BRUGNANO L, TRIGIANTE D. Boundary value methods:the third way between linear multistep and Runge-Kutta methods[J].Computers&Mathematics with Applications, 1998, 36(10):269-284.
[13] BRUGNANO L, TRIGIANTE D. Solving differential problems by multistep initial and boundary value methods[M].Amsterdam:Gordon and Breach, 1998.
[14] SULTAN M, REEVE J, ADAPA R. Combined transient and dynamic analysis of HVDC and FACTS systems[J].IEEE Transactions on Power Delivery, 1998, 13(4):1271-1 277.
[15] WANG C, FU X, LI P, et al. Multiscale simulation of power system transients based on the matrix exponential function[J]. IEEE Transactions on Power Systems, 2017,32(3):1913-1926.
[16]商莹,于玉铭,邹振宇,等.非线性电路暂态仿真中消除数值振荡的改进方法[J].电力系统保护与控制,2011, 39(7):142-146.SHANG Ying, YU Yuming, ZOU Zhenyu, et al. An advanced method of non-linear circuit eliminating numerical oscillation in electromagnetic transient simulation[J].Power System Protection and Control, 2011, 39(7):142-146.
[17]张伟,曹良,崔健,等.基于模糊控制与扩张状态观测器的VSG电压治理策略[J].供用电,2018,35(12):1-7+49.ZHANG Wei, CAO Liang, CUI Jian, et al. VSG voltage management strategy based on fuzzy control and extended state observer[J]. Distribution&Utilization, 2018, 35(12):1-7+49.
[18]姬煜轲,许建中,徐延明,等.无插值仿真平台中抑制数值振荡的阻尼电路设计方法[J].电力自动化设备,2016,36(7):143-149.JI Yuke, XU Jianzhong, XU Yanming, et al. Design of damping circuit for depressing numerical oscillation in interpolation-free simulation environment[J]. ElectricPower Automation Equipment, 2016,36(7):143-149.
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