基于改进临界阻尼调整法的电磁暂态仿真算法
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摘要
数值振荡是基于Dommel算法的电磁暂态数字仿真中存在的突出问题。文中提出了一种改进临界阻尼调整法以解决数值振荡问题。受临界阻尼调整法启发,采用一类新的低阶、L-稳定的线性多步法,并联合隐式梯形积分法形成该算法。该方法在网络突变时刻采用4步新线性多步法进行数值积分,而在正常情况下依然使用隐式梯形积分法进行计算。针对典型电磁暂态算例,对比分析了4步新线性多步法与临界阻尼调整法在不同时间尺度下的仿真特性,结果表明改进临界阻尼调整法可以完全消除数值振荡,且比传统临界阻尼调整法具有更高的计算精度。
Numerical oscillation is a prominent problem in electromagnetic transient simulation based on Dommel algorithm. An improved critical damping adjustment(ICDA) method is proposed to solve the numerical oscillation problem. Inspired by the critical damping adjustment method, a new class of low-order and L-stable linear multi-step method combined with the implicit trapezoidal integration method is used to form ICDA. Specifically, ICDA uses a four-step new linear multistep method to perform numerical integration at the time of network abrupt change, and still uses the implicit trapezoidal integration method for calculation in normal conditions. The simulation characteristics of the four-step new linear multistep method and the ICDA method at different time scales are compared and analyzed for typical electromagnetic transient examples. The results show that the ICDA method can completely eliminate the numerical oscillation and has higher computation accuracy than the traditional critical damping adjustment method.
Numerical oscillation is a prominent problem in electromagnetic transient simulation based on Dommel algorithm. An improved critical damping adjustment(ICDA) method is proposed to solve the numerical oscillation problem. Inspired by the critical damping adjustment method, a new class of low-order and L-stable linear multi-step method combined with the implicit trapezoidal integration method is used to form ICDA. Specifically, ICDA uses a four-step new linear multistep method to perform numerical integration at the time of network abrupt change, and still uses the implicit trapezoidal integration method for calculation in normal conditions. The simulation characteristics of the four-step new linear multistep method and the ICDA method at different time scales are compared and analyzed for typical electromagnetic transient examples. The results show that the ICDA method can completely eliminate the numerical oscillation and has higher computation accuracy than the traditional critical damping adjustment method.
引文
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[21]迟永宁,舒德兀,张春朋,等.交流弱电网中用于抑制数值振荡的变参数有理分式拟合算法[J].电网技术,2016,40(6):1792-1796.CHI Yongning,SHU Dewu,ZHANG Chunpeng,et al.Aparameterized rational-fraction fitting algorithm for numerical oscillation suppression in weak AC grid[J].Power System Technology,2016,40(6):1792-1796.
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[2]舒德兀,张树卿,姜齐荣.基于指数项有理分式拟合的网络差分化算法及其适用性分析[J].电力系统自动化,2016,40(10):103-109.SHU Dewu,ZHANG Shuqing,JIANG Qirong.Network differencing algorithm based on rational approximation of exponential and its applicability analysis[J].Automation of Electric Power Systems,2016,40(10):103-109.
[3]MARTI J R,LIN J.Suppression of numerical oscillation in the EMTP[J].IEEE Transactions on Power Systems,1989,4(2):739-747.
[4]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.
[5]WANG F Z,YANG M.Fast electromagnetic transient simulation for over-voltages of transmission line by high order Radau method and V-transformation[J].IET Generation,Transmission&Distribution,2016,10(14):3639-3645.
[6]汪芳宗,王永,宋墩文,等.基于矩阵对角化的电磁暂态时间并行计算方法[J].电网技术,2017,41(8):2521-2527.WANG Fangzong,WANG Yong,SONG Dunwen,et al.Parallel-in-time algorithm for electromagnetic transient numerical simulation based on matrix diagonalization[J].Power System Technology,2017,41(8):2521-2527.
[7]NODA T,TAKENAKA K,INOUE T.Numerical integration by the 2-stage diagonally implicit Runge-Kutta method for electromagnetic transient simulations[J].IEEE Transactions on Power Delivery,2009,24(1):390-399.
[8]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.
[9]LIN J,MARTI J R.Implementation of the CDA procedure in the EMTP[J].IEEE Transactions on Power Systems,1990,5(2):394-402.
[10]杨萌,汪芳宗.基于2级3阶单对角隐式Runge-Kutta法的电磁暂态计算方法[J].电力系统保护与控制,2017,45(6):68-73.YANG Meng,WANG Fangzong.2-stage 3-order diagonally implicit Runge-Kutta method for electromagnetic transient calculation[J].Power System Protection and Control,2017,45(6):68-73.
[11]NODA T,KIKUMA T,YONEZAWA R.Supplementary techniques for 2S-DIRK-based EMT simulations[J].Electric Power Systems Research,2014,115:87-93.
[12]王永,张磊,叶婧,等.基于3步4阶隐式泰勒级数法的电磁暂态数值计算方法[J].电力系统保护与控制,2018,46(11):8-13.WANG Yong,ZHANG Lei,YE Jing,et al.Electromagnetic transient numerical calculation method based on 3-step 4-order implicit Taylor series method[J].Power System Protection and Control,2018,46(11):8-13.
[13]赵金利,刘君陶,李鹏,等.面向指数积分方法的电磁暂态仿真GPU并行算法[J].电力系统自动化,2018,42(6):113-119.DOI:10.7500/AEPS20170821009.ZHAO Jinli,LIU Juntao,LI Peng,et al.GPU based parallel algorithm oriented to exponential integration method for electromagnetic transient simulation[J].Automation of Electric Power Systems,2018,42(6):113-119.DOI:10.7500/AEPS 20170821009.
[14]陈颖,宋炎侃,黄少伟,等.基于GPU的大规模配电网电磁暂态并行仿真技术[J].电力系统自动化,2017,41(19):82-88.DOI:10.7500/AEPS20170109016.CHEN Ying,SONG Yankan,HUANG Shaowei,et al.GPU-based techniques of parallel electromagnetic transient simulation for large-scale distribution network[J].Automation of Electric Power Systems,2017,41(19):82-88.DOI:10.7500/AEPS20170109016.
[15]舒德兀,张春朋,姜齐荣,等.电力电子仿真中开关时刻自校正插值算法[J].电网技术,2016,40(5):1455-1461.SHU Dewu,ZHANG Chunpeng,JIANG Qirong,et al.Aswitching point self-correction interpolation algorithm for power electronic simulations[J].Power System Technology,2016,40(5):1455-1461.
[16]GEAR C W.Numerical initial value problems in ordinary differential equations[M].New Jersey,USA:Prentice Hall,1971.
[17]BELLMAN R,CASTI J.Differential quadrature and longterm integration[J].Journal of Mathematical Analysis and Applications,1971,34(2):235-238.
[18]WANG F,WANG Y.A coupled pseudospectral-differential quadrature method for a class of hyperbolic telegraph equations[J/OL].Mathematical Problems in Engineering[2017-12-20].https://www.hindawi.com/journals/mpe/2017/90138261.
[19]DAHLQUIST G G.A special stability problem for linear multistep methods[J].Bit Numerical Mathematics,1963,3(1):27-43.
[20]袁兆鼎,费景高,刘德贵.刚性常微分方程初值问题的数值解法[M].北京:科学出版社,1987.YUAN Zhaoding,FEI Jinggao,LIU Degui.Numerical solution of the initial value problem of stiff ordinary differential equations[M].Beijing:Science Press,1987.
[21]迟永宁,舒德兀,张春朋,等.交流弱电网中用于抑制数值振荡的变参数有理分式拟合算法[J].电网技术,2016,40(6):1792-1796.CHI Yongning,SHU Dewu,ZHANG Chunpeng,et al.Aparameterized rational-fraction fitting algorithm for numerical oscillation suppression in weak AC grid[J].Power System Technology,2016,40(6):1792-1796.
[22]SHU D,ZHANG S,XIE X,et al.Hybrid method for numerical oscillation suppression based on rational-fraction approximations to exponential functions[J].IET Generation,Transmission&Distribution,2016,10(11):2825-2832.
[23]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.
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