基于Adomian分解方法的暂态稳定并行仿真研究
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摘要
针对目前大规模电力系统难以实现快速实时仿真的问题,提出了一种基于Adomian分解方法的暂态稳定仿真并行算法。首先,在考虑节点权重的同时,采用METIS将大系统拆分成若干子系统,然后采用波形松弛方法对系统进行并行求解。为加速各子系统的迭代过程,所有状态变量经过隐式梯形积分格式差分化后,采用基于Adomian分解的迭代算法配合非诚实牛顿算法进行了求解;为了进一步提高波形松弛法的整体收敛性,同时还使用了窗口方法、预处理方法与波形预测方法;最后,采用2 383节点和12685节点两个算例进行了测试,发电机采用复杂模型,同时考虑励磁调速系统,并通过共享内存的并行环境加以实现。测试研究结果表明,上述算法可以取得较为理想的收敛速度和并行加速比,同时实现了上万节点的超实时仿真。
Aiming at the problem that fast simulation for large-scale power systems is hard to realize,a parallel transient stability simulation based on Adomian decomposition method was presented. First of all,a power system described by large-scale differential-algebraic equations( DAE) was decomposed into several subsystems by METIS with the weight of all nodes taken into consideration. Waveform relaxation method was adopted for parallel implementation and all subsystems were solved using Adomian decomposition method combined with very dishonest newton( VDHN) method independently after the state variables were discretized by implicit-trapezoidal rule. Moreover,to accelerate convergence of the system,windowing,preconditioning and waveform prediction were adopted. Finally,the proposed algorithm was verified by two large-scale test cases with 2 383 buses and 12 685 buses and complex model was adopted for generators as well as the exciting and governing systems. The parallel efficiency was further improved by a shared-memory parallel environment. The results indicate that the proposed method achieves in increasing convergence speed and parallel speedup effectively,and super real-time simulation is realized.
Aiming at the problem that fast simulation for large-scale power systems is hard to realize,a parallel transient stability simulation based on Adomian decomposition method was presented. First of all,a power system described by large-scale differential-algebraic equations( DAE) was decomposed into several subsystems by METIS with the weight of all nodes taken into consideration. Waveform relaxation method was adopted for parallel implementation and all subsystems were solved using Adomian decomposition method combined with very dishonest newton( VDHN) method independently after the state variables were discretized by implicit-trapezoidal rule. Moreover,to accelerate convergence of the system,windowing,preconditioning and waveform prediction were adopted. Finally,the proposed algorithm was verified by two large-scale test cases with 2 383 buses and 12 685 buses and complex model was adopted for generators as well as the exciting and governing systems. The parallel efficiency was further improved by a shared-memory parallel environment. The results indicate that the proposed method achieves in increasing convergence speed and parallel speedup effectively,and super real-time simulation is realized.
引文
[1]刘振亚.中国电力与能源[M].北京:中国电力出版社,2012:345.
[2]赵志奇,王建全.隐式精细积分算法在电力系统暂态稳定分析中的应用[J].机电工程,2012,29(5):580-583.
[3]武同心,吕晓祥,王建全.Duhamel数值积分算法在电力系统暂态稳定分析中的应用[J].机电工程,2013,30(6):741-745.
[4]FABOZZI D,CHIEH A S,HAUT B,et al.Accelerated and localized newton schemes for faster dynamic simulation of large power systems[J].IEEE Transactions on Pouer Systens,2013,28(4):4936-4947.
[5]QUANYUAN J,HAN J.OpenMP-based parallel transient stability simulation for large-scale power systems[J].Science China:Technological Sciences,2012(10):2837-2846.
[6]HONG C.Implementation of parallel-in-time newton method for transient stability analysis on a message passing multiComputer[C]//Internation al Conferen ce on Power Syztem Teehnology,2002:1239-1243.
[7]洪潮.电力系统暂态稳定计算的一种时间并行算法[J].电网技术,2003(4):31-35.
[8]ILIC'-SPONG M,CROW M L,PAI M A.Transient stability simulation by waveform relaxation methods[J].Power Systems,IEEE Transactions on,1987,2(4):943-949.
[9]薛巍,舒继武,严剑峰,等.基于集群机的大规模电力系统暂态过程并行仿真[J].中国电机工程学报,2003,23(8):38-43.
[10]林济铿,李杨春,罗萍萍,等.波形松弛法的电力系统暂态稳定性并行仿真计算[J].电工技术学报,2006,21(12):47-53,65.
[11]王锡凡,方万良,杜正春.现代电力系统分析[M].北京:科学出版社,2003.
[12]ADOMIAN G,RACH R.On the solution of algebraic equations by the decomposition method[J].Journal of Mathematical Analysis and Applications,1985,105(1):141-166.
[13]ABBASBANDY S.Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method[J].Applied Mathematics and Computation,2003,145(2-3):887-893.
[14]NOOR M A.New family of iterative methods for nonlinear equations[J].Applied Mathematics and Computation,2007(190):553-558.
[15]CHUN C.Iterative methods improving newton's method by the decomposition method[J].Computers&Mathematics with Applications,2005,50(10-12):1559-1568.
[16]BABOLIAN E,BIAZAR J.Solution of nonlinear equations by modified adomian decomposition method[J].Applied Mathematics and Computation,2002,132(1):167-172.
[17]蒋耀林.波形松弛方法[M].北京:科学出版社,2009.
[18]PRUVOST F,LAURENT-GENGOUX P,MAGOULES F,et al.Accelerated waveform relaxation methods for power systems[C]//2011 International collferen on Electrical and Cohtrol Enginering,2011:2877-2888.
[19]舒继武,薛巍,郑纬民.一种电力系统暂态稳定并行计算的优化分区策略[J].电力系统自动化,2003(19):6-10.
[20]ZECEVIC A I,GACIC N.A partitioning algorithm for the parallel solution of differential-algebraic equations by waveform relaxation[J].Circuits and Systems I:Fundamental Theory and Applications,IEEE Transactions on,1999,46(4):421-434.
[21]GEORGE K V K.METIS:A Software Package for Partitioning Unstructured Graphs,Partitioning Meshes,and Computing Fill-Reducing Orderings of Sparse Matrices Version4[M].1998.
[22]BARBARA C G J A R.Using OpenMP:Portable Shared Memory Parallel Programming[M].Cambridge,MAL:MIT Press,2007.
[23]DAVO T A,NATARAJAN E P.Algorithm 907:KLU a direct sparse solver for circuit simulation problems[J].ACM Transactions on Mathematical Software,2010,3(37):1-17.
[24]ZIMMERMAN R D,MURILLO S X,NCHEZ C E,et al.MATPOWER:steady-state operations,planning,and analysis tools for power systems research and education[J].Power Systems,IEEE Transactions on,2011,26(1):12-19.
[25]JIWU S,WEI X,WEIMIN Z.A parallel transient stability simulation for power systems[J].Power Systems,IEEE Transactions on,2005,20(4):1709-1717.
[26]HOU L,BOSE A.Implementation of the waveform relaxation algorithm on a shared memory computer for the transient stability problem[J].Power Systems,IEEE Transactions on,1997,12(3):1053-1060.
[2]赵志奇,王建全.隐式精细积分算法在电力系统暂态稳定分析中的应用[J].机电工程,2012,29(5):580-583.
[3]武同心,吕晓祥,王建全.Duhamel数值积分算法在电力系统暂态稳定分析中的应用[J].机电工程,2013,30(6):741-745.
[4]FABOZZI D,CHIEH A S,HAUT B,et al.Accelerated and localized newton schemes for faster dynamic simulation of large power systems[J].IEEE Transactions on Pouer Systens,2013,28(4):4936-4947.
[5]QUANYUAN J,HAN J.OpenMP-based parallel transient stability simulation for large-scale power systems[J].Science China:Technological Sciences,2012(10):2837-2846.
[6]HONG C.Implementation of parallel-in-time newton method for transient stability analysis on a message passing multiComputer[C]//Internation al Conferen ce on Power Syztem Teehnology,2002:1239-1243.
[7]洪潮.电力系统暂态稳定计算的一种时间并行算法[J].电网技术,2003(4):31-35.
[8]ILIC'-SPONG M,CROW M L,PAI M A.Transient stability simulation by waveform relaxation methods[J].Power Systems,IEEE Transactions on,1987,2(4):943-949.
[9]薛巍,舒继武,严剑峰,等.基于集群机的大规模电力系统暂态过程并行仿真[J].中国电机工程学报,2003,23(8):38-43.
[10]林济铿,李杨春,罗萍萍,等.波形松弛法的电力系统暂态稳定性并行仿真计算[J].电工技术学报,2006,21(12):47-53,65.
[11]王锡凡,方万良,杜正春.现代电力系统分析[M].北京:科学出版社,2003.
[12]ADOMIAN G,RACH R.On the solution of algebraic equations by the decomposition method[J].Journal of Mathematical Analysis and Applications,1985,105(1):141-166.
[13]ABBASBANDY S.Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method[J].Applied Mathematics and Computation,2003,145(2-3):887-893.
[14]NOOR M A.New family of iterative methods for nonlinear equations[J].Applied Mathematics and Computation,2007(190):553-558.
[15]CHUN C.Iterative methods improving newton's method by the decomposition method[J].Computers&Mathematics with Applications,2005,50(10-12):1559-1568.
[16]BABOLIAN E,BIAZAR J.Solution of nonlinear equations by modified adomian decomposition method[J].Applied Mathematics and Computation,2002,132(1):167-172.
[17]蒋耀林.波形松弛方法[M].北京:科学出版社,2009.
[18]PRUVOST F,LAURENT-GENGOUX P,MAGOULES F,et al.Accelerated waveform relaxation methods for power systems[C]//2011 International collferen on Electrical and Cohtrol Enginering,2011:2877-2888.
[19]舒继武,薛巍,郑纬民.一种电力系统暂态稳定并行计算的优化分区策略[J].电力系统自动化,2003(19):6-10.
[20]ZECEVIC A I,GACIC N.A partitioning algorithm for the parallel solution of differential-algebraic equations by waveform relaxation[J].Circuits and Systems I:Fundamental Theory and Applications,IEEE Transactions on,1999,46(4):421-434.
[21]GEORGE K V K.METIS:A Software Package for Partitioning Unstructured Graphs,Partitioning Meshes,and Computing Fill-Reducing Orderings of Sparse Matrices Version4[M].1998.
[22]BARBARA C G J A R.Using OpenMP:Portable Shared Memory Parallel Programming[M].Cambridge,MAL:MIT Press,2007.
[23]DAVO T A,NATARAJAN E P.Algorithm 907:KLU a direct sparse solver for circuit simulation problems[J].ACM Transactions on Mathematical Software,2010,3(37):1-17.
[24]ZIMMERMAN R D,MURILLO S X,NCHEZ C E,et al.MATPOWER:steady-state operations,planning,and analysis tools for power systems research and education[J].Power Systems,IEEE Transactions on,2011,26(1):12-19.
[25]JIWU S,WEI X,WEIMIN Z.A parallel transient stability simulation for power systems[J].Power Systems,IEEE Transactions on,2005,20(4):1709-1717.
[26]HOU L,BOSE A.Implementation of the waveform relaxation algorithm on a shared memory computer for the transient stability problem[J].Power Systems,IEEE Transactions on,1997,12(3):1053-1060.