摘要
全国联网的实现使得机电暂态实时仿真变得更加困难。单一计算机的串行仿真难以实现这一目的,只有寄希望于并行计算。
本文首先用Newton-GMRES法求解电力系统暂态稳定计算的超大规模非线性方程组。该方法的外迭代为经典牛顿法,内迭代为用GMRES法不精确求解雅可比方程。在内迭代的每步只需用有限差分替代雅可比矩阵与向量的乘积运算,从而无需显式形成雅可比矩阵,且避免了雅可比矩阵的存储,因此能大大节省计算机内存,提高计算效率。在用GMRES法求解内迭代中的线性方程组前,先用稀疏近似逆预处理法对线性方程组的系数矩阵进行预处理,以降低系数矩阵的条件数,加快GMRES迭代收敛速度。
然后,本文提出了一种基于等值的机电暂态仿真并行异步新算法。其主要思想为：将原始网络分割为若干弱耦合的子系统。这些子系统在仿真的每一时步进行相互等值,各个子系统利用其他子系统传递来的等值信息进行独立迭代计算至收敛。在等值信息传递过程中,该算法使用了异步策略,即子系统在迭代计算过程中,随时监听其他子系统是否有新的等值信息传来,从而能够及时更新等值信息,加速迭代收敛。算例结果表明,该算法不仅具有较高的等值精度,而且具有较快的计算速度,已能够实现实时在线仿真计算。利用并行通信软件MPI中非阻塞通信可以将计算与通信重叠的特点实现的异步通信。
本文仿真基于的硬件设施是自己建立的一个6节点的小型PC集群。
本文的研究成果进一步丰富了电力系统机电暂态并行仿真计算方法,促进了电力系统机电暂态并行仿真计算的实用化进程。
The implementation of a national network makes real-time electromechanical transient simulation become more difficult. It is difficult to utilize serical simulation of a single computer to achieve this object, so we can only hope parallel computing.
Firstly, Newton-GMRES method is used in this paper to solve large-scale nonlinear equations of transient stability calculation of power system. The outer iteration of this method is the classical Newton method, and the inner iteration is using GMRES to solve Jacobi equations inexactly. In each inner iterative step, finite difference is used to replace the product operation of jacobian matrix and vector, so there is no need to form jacobian matrix explicitly, and avoid storing Jacobian matrix. This method can save computer memory greatly, and improve computational efficiency. Before using GMRES to solve the linear equations in the inner iteration, sparse approximate inverse method is used to precondition the coefficient matrix of the linear equations, which can reduce the conditional number of the coefficient matrix, and accelerate the convergent speed of GMRES.
Secondly, a new asynchronous parallel method based on equivalence is proposed for the parallel simulation of electromechanical transient. The general idea of this method is:The network is divided into several weak-coupling subsystems. In each simulation time step, each subsystem equivalence for each other, then utilizes the equivalent information from other subsystems to calculate independently until convergence. In the transferring process of equivalent information, the asynchronous strategy is used, that subsystems monitor that there is any new equivalent information coming from other subsystems or not at any time in the iterative process of calculation, which can update the equivalent information in time and speed up the convergence of iteration. The results of samples demonstrate that the new method not only has high equivalent accurancy, but also has a fast calculation speed. For some large-scale real systems, the on-line simulation will be realized. Communication and calculation to be carried out at the same time is the character of non-blocking communication, which is utilized to realize the asynchronous communication strategy in this thesis.
The simulation in this paper is based on a small 6-node PC cluster created by myself.
The achievements of this thesis enrich the parallel simulation methods of power system electromechanical transient and improve the utility progress of that.
引文
[1]IEEE Committee Report. Parallel processing in powre system computation. IEEE Transactions on Power Systems,1992,7(2):629-637
[2]韩祯祥,韩晓言.并行处理及其在电力系统中的应用.电网技术,1993,17(5)：1-8
[3]李亚楼,周孝信,吴中习.基于PC集群的电力系统机电暂态仿真并行算法.电网技术,2003,27(11)：6-12
[4]洪潮,单巍.在IBM-SP2上实现电力系统暂态稳定计算的一种并行算法.电力系统及其自动化学报,2001,13(1)：18-22
[5]韩晓言,韩祯祥.电力系统暂态稳定分析的并行算法研究.电力系统及其自动化学报,1995,7(3)：3-11
[6]薛巍,舒继武,严剑锋,等.基于集群机的大规模电力系统暂态过程并行仿真.中国电机工程学报,2003,23(8)：38-43
[7]王成山,张家安.改进的暂态稳定性分布式并行仿真算法.电力系统自动化,2003,27(19)：30-33
[8]王成山,张家安.基于支路分割和区域迭代的暂态稳定性仿真并行算法.电网技术,2004,28(1)：22-26
[9]Irving M R, Sterling M J H. Optimal network tearing using simulated annealing. IEE Proc-Gener.Transm.Distrib,1990,137(1):69-72
[10]Gomez A, Franquelo L G. A new contribution to the cluster problem. IEEE Transactions on Circuits and Systems,1987,34(5):546-552
[11]Chan K W, Dunn R W, Daniels A R. Efficient heuristic partitioning algorithm for parallel processing of large power systems network equations. IEE Proc-Gener. Transm.Distrib,1995,142(6):625-630
[12]Zhu N, Anjan B. A dynamic partitioning scheme for parallel transient stability analysis. IEEE Transactions on Power Systems,1992,7(2):940-946
[13]Ilic M, Crow M L, Pai M A. Transient stability simulation by waveform relaxation methods. IEEE Transactions on Power Systems,1987,2(4):943-952
[14]林济铿,李扬春,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.电工技术学报,2006,21(12)：47-53
[15]Crow M L, Ilic M, Pai M A. The parallel implementation of the waveform relaxation method for transient stability simulations. IEEE Transactions on Power Systems,1990,5(3):922-932
[16]Yao Linjiang, Richard M.M.Chen, Omar Wing. Convergence Analysis of Waveform Relaxation for Nonlinear Differential-Algebraic Equations of Index One. IEEE Transactions on Circuits and Systems,2000,47(11):1639-1645
[17]韩晓言,韩祯祥.电力系统暂态稳定分析的内在并行算法研究.中国电机工程学报,1997,171(3)：145-148
[18]Hou Lanjuan, Anjan B. Implementation of the waveform relaxation algorithm on a shared memory computer for the transient stability problem. IEEE Transactions on Power Systems,1997,12 (3):1053-1060
[19]胡博,周家启,刘洋,等.基于预条件处理GMRES的不精确牛顿法潮流计算.电工技术学报,2007,22(2)：98-104
[20]Dembo R S, Eisenstat S C, Steihaug T. Inexact Newton methods. SIAM J. Numer.Anal.,1982,19(1):400-408
[21]Rheinbolit W C. Methods for Solving Systems of Nonliner Equations. SIAM, Philadelphia,1998,10(4):205-210
[22]Knoll D A, Kenyes D E. Jacobian-free Newton-Krylov methods:A survey of approaches and applications. J.Comp.Phys,2004,8(5):357-397
[23]Chaniotis D, Pai M A. Iterative solver techniques in the dynamic simulation of Power Systems. In:Power Engineering Society Summer Meeting IEEE Structures. London,2000,609-613
[24]Pai M A, Sauer P W, Kulkami A Y. A preconditioned iterative solver for dynamic simulation of power systems. IEEE international Symposium on Circuits and Systems,1995,2(15):1279-1282
[25]陈颖,沈沉,梅生伟,等.基于Jacobian-Free Newton-GMRES(m)方法的电力系统分布式暂态仿真算法.电力系统自动化,2006,30(10)：12-16
[26]王锡凡.现代电力系统分析.北京：科学出版社,2003,294-295
[27]罗娜.半光滑方程组的牛顿类方法：[上海师范大学硕士学位论文].上海：上海师范大学,2007,4-6
[28]白中治,安恒斌.关于Newton-GMRES方法的有效变型与全局收敛性研究.数值计算与计算机应用,2005,12(4)：291-300
[29]李晓梅,吴建平.Krylov子空间方法及其并行计算.计算机科学,2005,32(1)：19-20,40
[30]Arnodi W E. The principle of minimized iterations in the solution of the matrix eigenvalue problem. Quart Appl Math,1951,9(4):17-29
[31]张海燕,闵涛,刘相国.GMRES(m)算法在离散不适定问题中的应用.Science and Technology Review,2007,25(13):54-59
[32]赵丽萍,舒期梁,刘伟浩.GMRES算法及其加速收敛现象分析.福建电脑,2006,4(4)：126-128
[33]张键飞,姜弘道.适合于求解边界元方程组的GMRES算法的实用化和并行化研究.计算力学学报,2004,21(5)：620-624
[34]李晓华,厉吉文,张林鑫,等.潮流计算雅克比矩阵预处理方法的比较研究.电力系统保护与控制,2005,33(15)：33-36
[35]蔡大用,陈玉荣.用不完全LU分解预处理的不精确潮流计算方法.电力系统自动化,2002,26(8)：11-14
[36]汪芳宗,何一帆,叶婧.基于稀疏近似逆预处理的牛顿-广义极小残余潮流计算方法.电网技术,2008,32(14)：50-53
[37]Wang F Z. Parallel-in-time relaxed Newton method for transient stability analysis. IEE Proceedings-Generation Transmission and Distributions,1998,145(2): 155-159
[38]苏敏.逆矩阵求法的进一步研究.河南纺织高等专科学校学报,2004,16(2)：28-30
[39]易大义,沈云宝,李有法.计算方法.杭州：浙江大学出版社,2002,220-223
[40]苏德富,梁正友.并行计算技术及其应用.重庆：重庆大学出版社,2007,239-243
[41]I eNet.架设基于LINUX的服务器集群.http://itpapers.zdnet.com.cn/itpaper/detail/2/12402.shtml,2008-3-20
[42]陈科.FORTRAN完全自学手册.北京：机械工业出版社,2009,2-16
[43]张武生,薛巍,李建江,等.MPI并行程序设计实例教程.北京：清华大学出版社,2009,1-4
[44]李晓梅,吴建平.数值并行算法与软件.北京：科学出版社,2007,209
[45]都志辉.高性能计算并行编程技术—MPI并行程序设计.北京：清华大学出版社,2001,19-191
[46]张伯明,陈寿明,严正.高等电力网络分析.北京：清华大学出版社,2007,140-158
[47]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.电力系统自动化,2003,27(19)：6-10
[48]徐箭,陈允平.基于改进通信算法的暂态稳定并行仿真.中国电机工程学报,2006,26(15)：12-18
[49]Chan K W, Dun R W, Daniels A R. Efficient heuristic partitioning algorithm for parallel processing of large power systems network equations. IEE Proceeding-Generation, Transmission and Distribution,1995,142(6):625-630
[50]Ning Zhu, Anjan Bose. A dynamic partitioning scheme for parallel transient stability analysis. IEEE Transactions on Power Systems,1992,7(2):940-946
[51]陈亚民.电力系统计算程序及其计算.北京：水利电力出版社,1995,147-233
[52]I eNet. IBM HPC刀片集群解决方案.http://itpapers.zdnet.com.cn/itpaper/detail/3/20962.shtml,2008-3-20