暂态稳定计算中网络节点编号优化算法的研究
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摘要
大规模交直流联合运行的电力系统的形成,对电力系统暂态稳定分析速度提出更高的要求。暂态稳定性的快速正确评估,对于电力系统的安全稳定运行具有重要的意义。目前广泛采用数值积分法对预想事故进行暂态稳定性分析,这种方法的主要缺点是计算速度慢。在电力系统暂态稳定计算中,大量的计算量存在于网络方程中的矩阵运算,深入研究电力系统暂态稳定计算中节点编号的优化以提高计算速度是本论文的主要研究内容。
本文首先分析了稀疏技术在电力系统网络计算中的应用以及各种已有稀疏矩阵节点编号和稀疏矢量节点编号方法的特点、效率及其存在的问题。根据节点优化编号本质上属于组合优化的特点,提出了基于粒子群优化算法的节点优化编号方案。在不同规模的系统上证明了算法的有效性,并以该算法的结果作为近似最优解,与传统的各节点编号算法进行比较,说明了对于大规模电网各传统节点编号算法还有待改进。同时,指出了当系统网络结构或独立矢量、解矢量发生局部变化时,对基于粒子群优化的最优节点编号作局部修正仍然是比较好的近似最优解。文中还指出了暂态稳定计算中,网络方程独立矢量中仅发电机节点的注入电流为非零元,解矢量也只需要得到发电机节点电压的特点,根据这个特点,提出了在独立矢量和解矢量确定的情况下的MSNOL、MD-MSL1、MD-ML1、MD-MNPS等节点编号优化算法,并与其他算法得到的结果进行了比较,证实了这些算法的有效性。最后,提出可将改进的节点编号优化算法应用于网络的分区中,说明了基于因子树的网络分割方案,将节点编号优化方案用于优化平衡分区的计算负荷及在分区中进一步减少前代回代计算量。
As the scale of the interconnection of power systems is enlarging increasingly, the requirement for faster electromechanical transient simulation is more urgent. The main analysis method of transient stability is numerical integration. Though lots of methods were presented so far, none of them is fast and reliable enough for practical use. The application of sparsity technology evidently makes the matrix calculation of power system more efficient. The main works of this paper focus on the electrical network node ordering in transient stability solution.
The paper firstly analyzes the characteristic and efficiency of the node ordering algorithms that already presented recently. A new method of node ordering that based on swarm particle optimization was proposed and its efficiency had been demonstrated by simulation tests of different systems. And the results of the node ordering algorithm based on PSO and the traditional method are being compared, which demonstrate that the efficiency of the traditional node ordering method has to be improved. According to the characteristic of network equation, some improvement of the traditional node ordering is proposed in the event that independent vector and solution vector are determined. Test result on many power systems indicates that the methods proposed like MSNOL、MD-MSL1、MD-ML1、MD-MNPS have effective performance. These methods are then used in network partition that based on factorization path tree partitioning, to assess the partitioning scheme in the original algorithm of factorization path tree partitioning to make the distribution of computing load between each processor more reasonable.
本文首先分析了稀疏技术在电力系统网络计算中的应用以及各种已有稀疏矩阵节点编号和稀疏矢量节点编号方法的特点、效率及其存在的问题。根据节点优化编号本质上属于组合优化的特点,提出了基于粒子群优化算法的节点优化编号方案。在不同规模的系统上证明了算法的有效性,并以该算法的结果作为近似最优解,与传统的各节点编号算法进行比较,说明了对于大规模电网各传统节点编号算法还有待改进。同时,指出了当系统网络结构或独立矢量、解矢量发生局部变化时,对基于粒子群优化的最优节点编号作局部修正仍然是比较好的近似最优解。文中还指出了暂态稳定计算中,网络方程独立矢量中仅发电机节点的注入电流为非零元,解矢量也只需要得到发电机节点电压的特点,根据这个特点,提出了在独立矢量和解矢量确定的情况下的MSNOL、MD-MSL1、MD-ML1、MD-MNPS等节点编号优化算法,并与其他算法得到的结果进行了比较,证实了这些算法的有效性。最后,提出可将改进的节点编号优化算法应用于网络的分区中,说明了基于因子树的网络分割方案,将节点编号优化方案用于优化平衡分区的计算负荷及在分区中进一步减少前代回代计算量。
As the scale of the interconnection of power systems is enlarging increasingly, the requirement for faster electromechanical transient simulation is more urgent. The main analysis method of transient stability is numerical integration. Though lots of methods were presented so far, none of them is fast and reliable enough for practical use. The application of sparsity technology evidently makes the matrix calculation of power system more efficient. The main works of this paper focus on the electrical network node ordering in transient stability solution.
The paper firstly analyzes the characteristic and efficiency of the node ordering algorithms that already presented recently. A new method of node ordering that based on swarm particle optimization was proposed and its efficiency had been demonstrated by simulation tests of different systems. And the results of the node ordering algorithm based on PSO and the traditional method are being compared, which demonstrate that the efficiency of the traditional node ordering method has to be improved. According to the characteristic of network equation, some improvement of the traditional node ordering is proposed in the event that independent vector and solution vector are determined. Test result on many power systems indicates that the methods proposed like MSNOL、MD-MSL1、MD-ML1、MD-MNPS have effective performance. These methods are then used in network partition that based on factorization path tree partitioning, to assess the partitioning scheme in the original algorithm of factorization path tree partitioning to make the distribution of computing load between each processor more reasonable.
引文
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13.Yue Yuan,J.K.,Hiroshi Sasaki,A Solution of Optimal Power Flow with Multicontingency Transient Stability Constrains.IEEE Trans.on Power System,2003.18(3):p.1094-1102.
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16.洪潮,沈俊明,电力系统暂态稳定计算的一种空间并行算法.电网技术,2000.24(5):p.20-25.
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30.A.Gomez.,L.G.Franquelo.,Node Ordering Algorithm for Sparse Vector Method Improvement.IEEE Trans,1988.PWRS-3(3).
31.R.Betancourt.,An Efficent tleuristic Ordering Alorgrithm for Partial Matrix Refactorization.IEEE Trans,1988.PWRS-3(3).
32.A.Gomez,L.G..Franquelo,An Efficient Ordering Algorithm to Improve Sparse Vector Mothdods.IEEE Trans,1988.PWRS-3.
33.Enns,M.,W.Tinney,F.,and L.Alvarando.,Sparse Matrix Inverse Factors.IEEE Trans on Power Apparatus and Systems,1900.5(2):p.466-473.
34.F.L.Alvarado,D.C.Yu,R.Betancourt,Partioned Sparse A-1Methods.IEEE Trans.on Power System,1900.5(2):p.452-459.
35.Chun-liang,L.,C.Nan-ming.,Sparse Vector Method Implument Via Minimum Inverse Fill-in Odering.IEEE Transachons on Power Systems,1993.8(1):p.239-245.
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42.薛巍,舒继武,王心丰,电力系统暂态稳定仿真并行算法的研究进展.系统仿真学报,2002.14(2):p.177-182.
43.杨建林,电力系统暂态稳定空间并行仿真.2006,天津大学.
44.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):p.6-10.
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50.Angeline,P.J.Using selection to improve particle swarm optimization,in Proc IEEE Int Conf on Evolutionary Computation.1998.Anchorage.
51.Shi,Y.,Eberbart.Fuzzy adaptive Partiele swarmopimization.in ProeeedingsoftheIEEECongressonEvolutionaryComputation.2001.Seoul,Korea.
52.Angeline,P.Using Selection to Improve Particle Swarm Optimization.in Proc.of IEEE Intl.Conf,on Evolutionary Computation.May 1998.Anchorage.
53.Lovb jerg,M.,T.Rasmussen,K.,and T.Krink.Hybrid Particle Swarm Optimization with Breeding and Subpopulations.in Proc of the third Genetic and Evolutionary Computation Conference.2001.
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2.郭永基,加强电力系统可靠性的研究和应用-北美东部大停电的思考.电力系统自动化,2003.28(18).
3.黄家裕,电力系统数字仿真.2003,北京:中国电力出版社.
4.袁季修,电力系统安全稳定控制.1996,北京:中国电力出版社.
5.Definations,I.T.F.o.T.a.,Proposed terms and definations for power system stability.IEEE Trans,1982.PAS-101(7).
6.王锡凡,现代电力系统分析.2003,北京:科学出版社.
7.Maria G.A.,T.C.,Kim J.,Hybrid Transient Stability,IEEE Trans.on Power System.9,1990.2:p.384-393.
8.倪以信,姚良忠,蔡译祥,直接暂态稳定分析综合法.中国电机工程学报,1992.12(6):p.63-68.
9.Dommel H W,S.N.,Fast transient stability solutions.IEEE Trans.on Power Apparatus and System,1972.91(3):p.1643-1650.
10.Xia D,G.H.,On line Transient Stability Decomposition-Aggredation and High Order Derivatives.IEEE Trans.on Power System,,1983.102(7):p.2038-2046.
11.郭志忠,柳焯,快速高阶Taylor级数法暂态稳定计算.中国电机工程学报,1991.11(3):p.9-15.
12.Sergio Bruno,M.L.S.,Unified Power Plow Controllers for Secrurity Constrained Transmission Management.IEEE Trans.on Power System,2004.19(1):p.418-426.
13.Yue Yuan,J.K.,Hiroshi Sasaki,A Solution of Optimal Power Flow with Multicontingency Transient Stability Constrains.IEEE Trans.on Power System,2003.18(3):p.1094-1102.
14.汪芳宗,电力系统并行计算.1998,北京:中国电力出版社.
15.苏新民,毛承雄,陆继,电力系统并行仿真的PVM实现.电力系统及其自动化学报,2002.14(1):p.5-9.
16.洪潮,沈俊明,电力系统暂态稳定计算的一种空间并行算法.电网技术,2000.24(5):p.20-25.
17.朱凌志,安宁,基于二维链表的稀疏矩阵在潮流计算中的应用.电网技术,2005. 29(8):p.51-55.
18.徐得超,李亚楼,吴中信,稀疏技术在电力系统状态估计中的应用.电网技术,2007.31(8):p.32-36.
19.M.H.M.Vale,D.M.F.,E.Kaszkurewicz.Electrical power network decomposition for parallel computations,in Proceeding of the IEEE Symposium on circuits and systems.May 1992.San Diego,CA.
20.Banerjee P,J.M.H.,Sargent J.S.,Parallel simulated annealing algoritluns for cell placement on hypercube muhiprocessors.IEEETrans.on Parallel and Distributed Systems,1990.1(1):p.91-106.
21.Chan K W,D.R.W.,Daniels A R.,Efficient heuristic partitioning algorithm for parallel processing of large power systems network equation.IEEE Proceedings-Generation Transmission and Distribution,1995.142(6):p.625-630.
22.张伯明,陈寿孙,严正,高等电力网络分析,ed.2.2007,北京:清华大学出版社.
23.陈珩,电力系统稳态分析.1995,北京:中国电力出版社.
24.Tinney,W.F.,Walker,J W,Direct solutions of sparse network equations by optimally ordered triangular factorization.Proc.of the IEEE,1967.55(11):p.1801-1809.
25.吴际舜,电力系统稳态分析的计算机方法.1992,上海:上海交通大学出版社.
26.W.F.Tinney,V.Brandwajn,S.M.Chen,Sparse Vector Methods.IEEE Trans,1985.PAS-104(2).
27.N.Sato,W.F.Tinney,Techniques for Exploiting the Sparsity of the Network Admttance Matrix.IEEE Trans,1968.PAS-82(12).
28.TINNEY,W.,J.WALKER,Direct solutions of sparse network equations by optimally ordered triangular factorization.Proceedings of the IEEE,1967.55(11):p.1801-1809.
29.Alasco,B.Stott,W.Tinney,Sparsity oriented compensation methodsfor modified network solutions.IEEE Trans on Power Apparatus and Systems,1983.102(5):p.1050-1060.
30.A.Gomez.,L.G.Franquelo.,Node Ordering Algorithm for Sparse Vector Method Improvement.IEEE Trans,1988.PWRS-3(3).
31.R.Betancourt.,An Efficent tleuristic Ordering Alorgrithm for Partial Matrix Refactorization.IEEE Trans,1988.PWRS-3(3).
32.A.Gomez,L.G..Franquelo,An Efficient Ordering Algorithm to Improve Sparse Vector Mothdods.IEEE Trans,1988.PWRS-3.
33.Enns,M.,W.Tinney,F.,and L.Alvarando.,Sparse Matrix Inverse Factors.IEEE Trans on Power Apparatus and Systems,1900.5(2):p.466-473.
34.F.L.Alvarado,D.C.Yu,R.Betancourt,Partioned Sparse A-1Methods.IEEE Trans.on Power System,1900.5(2):p.452-459.
35.Chun-liang,L.,C.Nan-ming.,Sparse Vector Method Implument Via Minimum Inverse Fill-in Odering.IEEE Transachons on Power Systems,1993.8(1):p.239-245.
36.Kron,G.,Diakoptics-a piecewise solution of large scale systems.1957-1958,London:Elect J.
37.Happ,H.H.,Piecewise methods and applications to power system.1970:John Wiley &Sons Inc.
38.Wu,F.F.,Solution of large scale networks by Tearing.IEEE trans on circuits and Systems,1976.CAS(23):p.706-713.
39.张伯明,张海波,多控制中心之间分解协调计算模式研究.中国电机工程学报,2006.26(22):p.1-5.
40.薛巍,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):p.38-43.
41.杨晓东,基于组件树模型和双向迭代技术的暂态稳定仿真方法研究.2006,天津大学.
42.薛巍,舒继武,王心丰,电力系统暂态稳定仿真并行算法的研究进展.系统仿真学报,2002.14(2):p.177-182.
43.杨建林,电力系统暂态稳定空间并行仿真.2006,天津大学.
44.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):p.6-10.
45.Eberhart,R.C.and J.Kennedy.A new optimizer using particles swarm theory.in Proc.Sixth International Symposium on Micro Machine and Human Science.1995.Nagoya,Japan:IEEE Service Center.
46.Kennedy,J.,R.C.Eberhart,and Particle Swarm optimization,in Proceedings of IEEE International Conference on Neural Networks,N.Piscataway,Editor.1995,IEEE service center,p.1942-1948.
47.Shi,Y.H.,R.C.Eberhart.A Modified Particle Swarm Optimizer.in IEEE International conference of Evolutionary Computation.1998.Anchorage,Alaska.
48.Suganthan,P.N.Particle swarm optimiser with neighbourhood operator,in Proc of the Congress on Evolutionary Computation.1999.Washington DC.
49.高尚,蚁群算法理论、应用及其与其它算法的混合.2005,南京理工大学:南京.
50.Angeline,P.J.Using selection to improve particle swarm optimization,in Proc IEEE Int Conf on Evolutionary Computation.1998.Anchorage.
51.Shi,Y.,Eberbart.Fuzzy adaptive Partiele swarmopimization.in ProeeedingsoftheIEEECongressonEvolutionaryComputation.2001.Seoul,Korea.
52.Angeline,P.Using Selection to Improve Particle Swarm Optimization.in Proc.of IEEE Intl.Conf,on Evolutionary Computation.May 1998.Anchorage.
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