考虑不确定因素的输电网灵活规划方法研究
|
摘要
电网规模的不断增大和电力系统的市场化改革给电网规划工作带来了很多的不确定性。传统确定性因素下的输电网规划方法得到的规划方案对未来年不确定性环境的适应性较低。本文基于灵活规划的思想,针对目前输电网灵活规划研究中存在的问题,着重研究了考虑不确定因素的系统安全性判定方法和系统性能评价指标,建立了适合不同要求的输电网灵活规划新模型,完善了考虑不确定因素的输电网灵活规划理论。其主要成果如下:
1)建立了区间最小切负荷模型,证明了该模型最优解的存在性,求解此模型能够精确求得区间负荷下区间最小切负荷量的全局最优解,为区间负荷下的电力系统安全性评估提供了新的思路。求解时将该模型分解为基于双层线性规划模型的区间至多切负荷模型和基于线性规划模型的区间至少切负荷模型两个子模型,分别求解两个子模型即可求得区间最小切负荷量的区间上下限值。
2)使用参数线性规划的相关理论,证明了区间至多切负荷量所对应负荷取值的负荷边界特性,利用此特性并结合双层线性规划理论,提出了改进的分支定界算法,可快速准确求得系统的区间至多切负荷量,大大缩短了区间不确定信息下系统安全性的判定时间。
3)建立了区间负荷下的输电网灵活规划模型,求解该模型得到满足区间负荷下系统安全性的输电网规划方案。结合区间最小切负荷的相关理论,使用改进的贪婪随机自适应搜索算法可快速有效的求解该模型。
4)建立了模糊负荷下基于可信性理论的输电网灵活规划模型,引入可信度指标来评价模糊不确定信息下系统的性能,该指标具有严格的数学基础和物理意义。证明了可信度指标等价定理,得到给定可信度指标下的等效区间输电网灵活规划模型,可直接使用区间输电网灵活规划理论对该模型进行分析求解。
5)建立了考虑线路负载率和可用传输能力的输电网灵活规划模型,通过引入线路负载率约束和可用传输能力约束来应对未来年负荷增长大小和地点的不确定性,新模型无需对未来年的不确定因素进行详细建模,易于求解并可处理系统中区域负荷增长的不确定性。
6)建立了考虑发电备用容量的输电网灵活规划模型,通过在模型中引入发电机故障约束和负荷增长约束,确保系统在出现发电机故障或负荷不确定性增长时,网络有足够的可用传输容量来传输系统中的发电备用以满足考虑不确定因素的系统安全性要求。
通过Garver-6节点系统和某实际地区77节点系统算例的分析和比较,说明了本文研究成果的可行性、有效性和适用范围。
The enlargement of power grid and revolution of power market bring many uncertainties into the transmission network expansion planning problem. The planning scheme solved by the traditional transmission expansion planning model under certain information doesn’t have enough adaptability for future uncertain environment. Based on the idea of transmission network flexible planning, this dissertation studies the safety evaluation index and method of the system considering uncertain factors, builds some new transmission network flexible planning models that can be used for different requirements under uncertain environment and perfects the transmission network flexible planning theory. The main results in this dissertation are as follows:
1) The interval minimum load cutting model is built and proved to have optimal solution. After solving this model, the precise global optimal solution of the interval minimum load cutting number can be gotten. The proposed interval analysis method starts a new way for the safety evaluation work of power system under interval information. When solving the interval planning model, it is decoupled into two sub-models that are solved separately. One is the interval most minimum load cutting model that is based on bilevel linear programming model, the other is the interval least minimum load cutting model that is based on linear programming model. After solving these two models, the upper and lower limits of the interval minimum load cutting number can be gotten.
2) Using parametric linear programming theory, the“load edges”characteristic existing in the interval most minimum load cutting problem is proved. Using this characteristic and combing the bilevel linear programming theory, the improved branch-and-bound algorithm is proposed. Using this algorithm, the interval most minimum load cutting number can be solved quickly and precisely, and the time to evaluate the safety of power system under interval information can be greatly reduced.
3) The transmission network flexible planning model under interval load is built. After solving this model, the planning scheme that is safe under interval load can be gotten. Combing the theory of interval minimum load cutting problem, the improved greedy randomized adaptive search procedure (GRASP) is used to solve this model. The improved GRASP is adaptive to solve the transmission network flexible planning model under uncertain information and improves a lot in calculation speed.
4) The transmission network flexible planning model based on credibility theory when the load is fuzzy uncertain is built. The credibility index, which has strict mathematic base and realistic physical meaning, is introduced to evaluate the performance of the system under fuzzy information. Furthermore, the equivalent credibility theorem is proposed and proved. By this theorem, the fuzzy planning model based on credibility theory can be converted into the equivalent interval planning model which can be solved much easier.
5) The transmission network flexible planning model considering the line loadability and zone available transfer capability is built. By including the line loadability constraint and zone available transfer capability constraint, the new planning model can better accommodate the load increasing magnitude uncertainty and location uncertainty.
6) The transmission network flexible planning model considering the power reserve is built. By including the constraints of generator failure and load increment, the planning scheme solved from the new model can make certain that it is able to transfer the power reserve to maintain the safety of the system when there are generator uncertain failure and load uncertain increment.
Analysis and comparison on the Garver 6-node system and a real 77-node system prove the feasibility, validity and applicability of returns of this dissertation.
1)建立了区间最小切负荷模型,证明了该模型最优解的存在性,求解此模型能够精确求得区间负荷下区间最小切负荷量的全局最优解,为区间负荷下的电力系统安全性评估提供了新的思路。求解时将该模型分解为基于双层线性规划模型的区间至多切负荷模型和基于线性规划模型的区间至少切负荷模型两个子模型,分别求解两个子模型即可求得区间最小切负荷量的区间上下限值。
2)使用参数线性规划的相关理论,证明了区间至多切负荷量所对应负荷取值的负荷边界特性,利用此特性并结合双层线性规划理论,提出了改进的分支定界算法,可快速准确求得系统的区间至多切负荷量,大大缩短了区间不确定信息下系统安全性的判定时间。
3)建立了区间负荷下的输电网灵活规划模型,求解该模型得到满足区间负荷下系统安全性的输电网规划方案。结合区间最小切负荷的相关理论,使用改进的贪婪随机自适应搜索算法可快速有效的求解该模型。
4)建立了模糊负荷下基于可信性理论的输电网灵活规划模型,引入可信度指标来评价模糊不确定信息下系统的性能,该指标具有严格的数学基础和物理意义。证明了可信度指标等价定理,得到给定可信度指标下的等效区间输电网灵活规划模型,可直接使用区间输电网灵活规划理论对该模型进行分析求解。
5)建立了考虑线路负载率和可用传输能力的输电网灵活规划模型,通过引入线路负载率约束和可用传输能力约束来应对未来年负荷增长大小和地点的不确定性,新模型无需对未来年的不确定因素进行详细建模,易于求解并可处理系统中区域负荷增长的不确定性。
6)建立了考虑发电备用容量的输电网灵活规划模型,通过在模型中引入发电机故障约束和负荷增长约束,确保系统在出现发电机故障或负荷不确定性增长时,网络有足够的可用传输容量来传输系统中的发电备用以满足考虑不确定因素的系统安全性要求。
通过Garver-6节点系统和某实际地区77节点系统算例的分析和比较,说明了本文研究成果的可行性、有效性和适用范围。
The enlargement of power grid and revolution of power market bring many uncertainties into the transmission network expansion planning problem. The planning scheme solved by the traditional transmission expansion planning model under certain information doesn’t have enough adaptability for future uncertain environment. Based on the idea of transmission network flexible planning, this dissertation studies the safety evaluation index and method of the system considering uncertain factors, builds some new transmission network flexible planning models that can be used for different requirements under uncertain environment and perfects the transmission network flexible planning theory. The main results in this dissertation are as follows:
1) The interval minimum load cutting model is built and proved to have optimal solution. After solving this model, the precise global optimal solution of the interval minimum load cutting number can be gotten. The proposed interval analysis method starts a new way for the safety evaluation work of power system under interval information. When solving the interval planning model, it is decoupled into two sub-models that are solved separately. One is the interval most minimum load cutting model that is based on bilevel linear programming model, the other is the interval least minimum load cutting model that is based on linear programming model. After solving these two models, the upper and lower limits of the interval minimum load cutting number can be gotten.
2) Using parametric linear programming theory, the“load edges”characteristic existing in the interval most minimum load cutting problem is proved. Using this characteristic and combing the bilevel linear programming theory, the improved branch-and-bound algorithm is proposed. Using this algorithm, the interval most minimum load cutting number can be solved quickly and precisely, and the time to evaluate the safety of power system under interval information can be greatly reduced.
3) The transmission network flexible planning model under interval load is built. After solving this model, the planning scheme that is safe under interval load can be gotten. Combing the theory of interval minimum load cutting problem, the improved greedy randomized adaptive search procedure (GRASP) is used to solve this model. The improved GRASP is adaptive to solve the transmission network flexible planning model under uncertain information and improves a lot in calculation speed.
4) The transmission network flexible planning model based on credibility theory when the load is fuzzy uncertain is built. The credibility index, which has strict mathematic base and realistic physical meaning, is introduced to evaluate the performance of the system under fuzzy information. Furthermore, the equivalent credibility theorem is proposed and proved. By this theorem, the fuzzy planning model based on credibility theory can be converted into the equivalent interval planning model which can be solved much easier.
5) The transmission network flexible planning model considering the line loadability and zone available transfer capability is built. By including the line loadability constraint and zone available transfer capability constraint, the new planning model can better accommodate the load increasing magnitude uncertainty and location uncertainty.
6) The transmission network flexible planning model considering the power reserve is built. By including the constraints of generator failure and load increment, the planning scheme solved from the new model can make certain that it is able to transfer the power reserve to maintain the safety of the system when there are generator uncertain failure and load uncertain increment.
Analysis and comparison on the Garver 6-node system and a real 77-node system prove the feasibility, validity and applicability of returns of this dissertation.
引文
[1]王锡凡.电力系统优化规划[M].北京:水利电力出版社,1990.
[2]程浩忠,张焰.电力网络规划的方法与应用[M].上海:科学技术出版社,2002.
[3]王锡凡.电力系统规划基础[M].北京:水利电力出版社,1994.
[4] Merrill H M,Wood A J.Risk and uncertainty in power system planning[J].Electric Power & Energy Systems,1991,13(2):81-90.
[5] T Tachikawa,H Kita,H Sugihara.A study of transmission planning under a deregulated environment in power system[C].IEEE International Conf. on Electric Utility Deregulation and Restructuring,2000,649-654.
[6]郑风雷,文福拴,吴复立.电力市场环境下的输电投资与扩展规划[J].电力系统自动化.2006,30(10):80-86.
[7]程浩忠,张焰,严正,等.电力系统规划[M].北京:中国电力出版社,2008.
[8]陈章潮,程浩忠,傅正财,等.城市电网规划与改造(第二版)[M].北京:中国电力出版社,2007.
[9] Haozhong Cheng,Haifeng Zhu,Mariesa L.Crow.Flexible method for power network planning using the unascertained number[J].Electric Power System Research,2004, 68(1):41-46.
[10]朱海峰.不确定性信息的电网灵活规划方法[D].上海交通大学博士学位论文,2000,8.
[11] B.G. Gorenstin,N.M. Campodonico,J.P. Costa.Power system expansion planning under uncertainty[J].IEEE Transactions on Power Systems,1993,8(1):129-136.
[12] Enrique , Crowilla , Peter Mrfner . Conflicting Objectives and Risk in Power System Planning[J].IEEE Transactions on Power Systems,1993,8(3):887-893.
[13]高赐威,程浩忠,王旭.考虑场景发生概率的柔性约束电网规划模型[J].中国电机工程学报,2004,24(11),34-38.
[14]朱海峰,程浩忠,张焰.考虑线路被选概率的电网灵活规划方法[J].电力系统自动化,2000, 24(17):20-24.
[15]程浩忠,朱海峰,马则良,等.基于等微增率准则的电网灵活规划方法[J].上海交通大学学报,2003,37(9):1351-1353.
[16]翟海保,程浩忠,陈春霖,等.基于最小期望悔值的电网灵活规划方法[J].上海交通大学学报,2005,39(Sup.1):27-30.
[17]刘铠滢,蔡述涛,张尧.基于风险评判的电网规划方法[J].中国电机工程学报,2007,27(22):69-73.
[18]麻常辉,薛禹胜,鲁庭瑞,等.输电规划方法的评述[J].电力系统自动化,2006,30 (12): 97-101.
[19] J.Choi,T.Tran,A.A.El-Keib.A method for transmission system expansion planning considering probabilistic reliability criteria[J].IEEE Transactions on Power Systems,2005,20(3):1606-1615.
[20]杨宁,文福拴.基于机会约束规划的输电系统规划方法[J].电力系统自动化,2004,28(14):23-27.
[21]杨宁,文福拴.计及风险约束的多阶段输电系统规划方法[J].电力系统自动化,2005,29(4):28-33.
[22]麻常辉,薛禹胜,王小英.基于静态和动态安全风险的输电规划—(二)计及注入功率的不确定性[J].电力系统自动化,2006,30(14):10-13.
[23] A. M. Leite da Silva,S. M. P. Ribeiro,R. N. Allan.Probabilistic load flow techniques applied to power system expansion planning[J].IEEE Transactions on Power Systems,1990,5(4):1047-1053.
[24]张焰.不确定性的长期电网规划方法研究[D].上海:上海交通大学博士学位论文,1998.
[25]张焰.电网规划中的模糊可靠性评估方法[J].中国电机工程学报,2000,20(11):77-80.
[26] I.J.Silva,M.J. Rider,R.Romero.Transmission network expansion planning considering uncertainty in demand[J].IEEE Transactions on Power Systems,2006,21(4):1565-1573.
[27]张洪明,廖培鸿.输电网规划的灰色模型及算法[J].上海交通大学学报,1995,29 (3):20- 26.
[28]邓聚龙.灰色系统的基本方法[M].武汉:华中理工大学出版社,1988.
[29]高赐威,程浩忠,王旭.盲信息的模糊评价模型在电网规划中的应用[J].中国电机工程学报,2004,24(9):24- 29.
[30]程浩忠,朱海峰,王建民.基于盲数BM模型的电网灵活规划方法[J].上海交通大学学报,2003,37(9):1347-1350.
[31]金华征,程浩忠,曾德君.基于集对分析的柔性电网规划方法[J].中国电机工程学报,2005,25(3):7-13.
[32]金华征,程浩忠,杨晓梅.基于联系数模型的电网灵活规划方法[J].中国电机工程学报,2006,26(12):16-20.
[33] A. Monticelli,A. S. Junior,M. V. F. Pereira.Interactive transmission network planning using a least-effort criterion[J].IEEE Transactions on Power Systems,1982,101(10):3919-3925.
[34] R.Villasana,L.Garver,S.J.Salon.Transmission network planning using linear planning[J].IEEE Transactions on Power Systems,1985,104(1):349-356.
[35] M. V. F. Pereira,L. M. V. G. Pinto.Application of sensitivity analysis of local supplying capability to interactive transmission expansion planning[J].IEEE Transactions on Power Systems,1985,104(1):381-389.
[36] R.Romero,C.Rocha,J.R.S.Mantovani.Constructive heuristic algorithm for the DC model in network transmission expansion planning[J].IEE Proc.-Gener. Transm. Distrib.,2005(2):277-282.
[37] S. Haffner,A. Monticelli,A. Garcia.Branch and bound algorithm for transmission system expansion planning using a transportation model[J].IEE Proc.-Gener. Transm. Distrib.,2000,147(3):149-156.
[38] L. Bahiense,G. C. Oliveira,M. Pereira.A mixed integer disjunctive model for transmission network expansion[J].IEEE Transactions on Power Systems,2001,16(3):560-565.
[39] R. Romero,A. Monticelli.A zero-one implicit enumeration method for optimizing investments in transmission expansion planning[J].IEEE Transactions on Power Systems,1994,129(3):1385-1391.
[40] Natalia Alguacil,Alexis L.Motto,Antonio J.Conejo.Transmission expansion planning:a mixed-integer LP approach[J].IEEE Transactions on Power Systems,2003,18(3):1070-1077.
[41] R.Romero,A.Monticelli.A hierarchical decomposition approach for transmission expansion planning[J].IEEE Transactions on Power Systems,1994,9(1):373-380.
[42] Silvio B,Mário V F P,Sérgio G.A New Benders Decomposition Approach to Solve Power Transmission Network Design Problems[J].IEEE Transactions on Power Systems,2001,16(2):235-240.
[43] R. Rornero,A. Monticelli. A.Garcia.Test systems and mathematical models for transmission network expansion planning[J].IEE proc.-gener. transm. Distrib,2002,149(1):27-36.
[44]邢文训,谢金星.现代优化计算方法[M].北京:清华大学出版社,1999.
[45] Edson Luiz da Silva,Hugo Alejandro Gil.Transmission Network Expansion Planning Under an Improved Genetic Algorithm[J].IEEE Transactions on Power Systems,2000,15(3):1169-1175.
[46] R. A. Gallego,A. Monticelli,R. Romero.Transmission system expansion planning by extended genetic algorithm[J].IEE proc.-gener. transm. Distrib.,1998,145(3):329-335.
[47]叶在福,单渊达.基于边界搜索策略的遗传算法在电网扩展规划中的应用[J].中国电机工程学报,2000,20(11):41-45.
[48]王秀丽,李淑慧,陈皓勇.基于非支配遗传算法及协同进化算法的多目标多区域电网规划[J].中国电机工程学报,2006,26(12):11-15.
[49]毛玉宾,王秀丽,王锡凡.多阶段输电网最优规划的遗传算法[J].电力系统自动化,1998, 22(12):13-5.
[50] Yi Wang,Haozhong Cheng,Chun Wang et al.Pareto optimality based multiobjective transmission planning[J].Electric Power Systems Research,2008,78(9):1619-1626.
[51] Romero R,Gallego R A,Monticelli A.Transmission system expansion planning by simulated annealing[J].IEEE Transaction on Power Systems,1996,11(1),364-369.
[52] Wen Fushuan,Chang C S.Transmission network optimal planning using the tabu search method[J].Electric Power Systems Research,1997,47(2):153-163.
[53] Ramon A,Gallego,Rubén Romero.Tabus earch algorithm for network synthesis[J].IEEETransaction on Power Systems,2000,15(2):490-495.
[54] Edson LS,Jorge MA,Gerson CO.Transmission network expansion planning under a tabu search approach[J].IEEE Transactions on Power Systems,2001,16(1):62-68.
[55] S.Binato,G..C.Oliveira,J.L.Araujo.A greedy randomized adaptive search procedure for transmission network expansion planning[J].IEEE Transactions on Power Systems,2001,16(2):247-253.
[56] Haroldo Faria,Jr Silvio Binato.Power Transmission Network Design by Greedy Randomized Adaptive Path Relinking[J].IEEE Transaction on Power Systems,2005,20(1),43-49.
[57]翟海保,程浩忠,陈春霖,等.基于改进蚁群算法的输电网络扩展规划[J].中国电力,2003,36(12):49-52.
[58] Dorigo M,Gambardella L M.Ant colony system:a cooperative learning approach to the traveling salesman problem[J].IEEE Transactions on Evolutionary Computation,1997,1(1):53-66.
[59] Dorigo M,Di Caro G,Stützle T.Ant algorithms[J].Future Generation Computer Systems,2000,16(8):5-7.
[60]翟海保,程浩忠,陈春霖,等.多阶段输电网络最优规划的并行蚁群算法[J].电力系统自动化,2004,28(20):37-42.
[61] Sensarma P S,Rahmani M,Carvalho A.A comprehensive method for optimal expansion planning using particle swarm optimization[C].Power Engineering Society Winter Meeting,2002,1317-1322.
[62] Kennedy J,Eberhart R.Particle swarm optimization[C].Proceedings of IEEE International Conference on Neural Networks,1995,1942-1948.
[63]金义雄,程浩忠,严健勇.改进粒子群算法及其在输电网规划中的应用[J].中国电机工程学报,2005,25(4):46-50.
[64]金义雄,程浩忠,严健勇.基于并行协同粒子群算法的多阶段电网规划[J].中国电机工程学报,2005,25(25):49-53.
[65] Galiana D,McGillis DT,Marin M.An expert systems in transmission planning[J].Proceedings of the IEEE,1992,80 (5):712- 726.
[66]石立宝,徐国禹.一种求解电网多目标模糊优化运行的自适应进化规划算法[J].中国电机工程学报,2001,21(3):53-61.
[67] Chun Wang,Haozhong Cheng.Optimization of network configuration in large distribution systems using plant growth simulation algorithm[J].IEEE Transactions on Power Systems,2008,23(1):119-126.
[68]胡泽春,王锡凡,张显,等.考虑线路故障的随机潮流[J].中国电机工程学报,2005,25(24):26-33.
[69]张焰,陈章潮.电网规划中的模糊潮流计算[J].电力系统自动化,1998,22(3):20-22.
[70] Wang Zian,Alvarado F L.Interval arithmetic in power flow analysis[J].IEEE Transactions on Power Systems,1992,7(3):1341-1349.
[71]朱海峰,程浩忠,张焰.利用盲数进行电网规划的潮流计算方法[J].中国电机工程学报,2000,21(8):74-78.
[72]郭永基著.电力系统可靠性分析[M].北京:清华大学出版社,2003.
[73]水利电力部.SD 131-84电力系统技术导则[M].北京:水利电力出版社,1984.
[74] Bracken J , McGill J T . Mathematical programs with optimization problems in the constraints[J].Operations Research,1973,21:37-44.
[75] Bard J F.Practical bilevel optimization:algorithms and applications[M].Dordrecht:Kluwer Academic Publishers,1998.
[76]刘红英.多层规划的理论与算法研究[D].西安:西安电子科技大学博士学位论文,2000.
[77] Zhongping Wang,Heng Fan,Shufen Wang.A bilevel programming model for the reactive power optimization[C].International Power Engineering Conference,2005,1265-1269.
[78] Bjondal M,Jornsten K.The deregulated electricity market viewed as a bilevel programming problem[J].Journal of Global Optimization,2005,33(3):465-475.
[79]范宏,程浩忠,严健勇,等.考虑经济性可靠性的输电网扩展规划的二层规划模型及混合算法[J].中国电机工程学报,2008,28(16):1-7.
[80] C. Shi,J. Lu,G. Zhang,Z. Hong.An extended Kth-best approach for linear bilevel programming[J].Applied Mathematics and Computation,2005,164(3):843-855.
[81] Shi Chenggen,Lu Jie,Zhang Guangquan.An extended Kuhn-Tucker approach for linear bilevel programming[J].Applied Mathematics and Computation,2005,162(1):51-63.
[82] C. Shi,J. Lu,G. Zhang,Z. Hong.An extended branch and bound algorithm for linear bilevel programming[J].Applied Mathematics and Computation,2006,180(2):529-537.
[83] D. J. White,G. Anandalingam.A penalty function approach for solving bi-level linear programs[J].Journal of Global Optimization,1993,3(4):397-419.
[84] Bard J , Moore J T . A branch and bound algorithm for the bilevel programming problem[J].SIAM Journal on Scientific and Statistical Computing,1990,11(2):281-292.
[85]龚怀云.应用泛函分析[M].西安:西安交通大学出版社,2001.
[86]王成山,郑海峰,谢莹华.计及分布式发电的配电系统随机潮流计算[J].电力系统自动化,2005,29(24):39-45.
[87]张焰,陈章潮.计及不确定性的模糊交流潮流计算方法研究[J].电网技术,1998,22(2):20-25.
[88]王守相,武志峰,王成山.计及不确定性的电力系统直流潮流的区间算法[J].电力系统自动化,2007,31(5):18-23.
[89]魏国华,王芬.线性规划[M].北京:高等教育出版社,1990.
[90]张永伍,余贻鑫,严雪飞.基于区间算法和范例学习的配电网网架规划[J].电力系统自动化,2005,29(17):40-44.
[91]孙洪波,徐国禹,秦翼鸿.电网规划的模糊随机优化模型[J].电网技术,1996,20(5):4-7.
[92] Liu B.Theory and practice of uncertain programming[M].Germany,Heidelberg:2002.
[93] Liu B,Liu Y K.Expected value of fuzzy variable and fuzzy expected value models[J].IEEE Transactions on Fuzzy Systems,2002,10(4):445-450.
[94]杨莉.基于可能性理论的发电公司报价策略研究[D].浙江:浙江大学博士学位论文,2003.
[95]冯永青,吴文传,张伯明,等.基于可信性理论的电力系统运行风险评估(一) [J].电力系统自动化,2006,30 (1):17-22.
[96]冯永青,吴文传,张伯明,等.基于可信性理论的电力系统运行风险评估(二) [J].电力系统自动化,2006,30 (2):11-15.
[97]冯永青,吴文传,张伯明,等.基于可信性理论的电力系统运行风险评估(三) [J].电力系统自动化,2006,30 (3):11-16.
[98]冯永青,吴文传,张伯明,等.基于可信性理论的水火电机组检修计划[J].中国电机工程学报,2006,26 (13):14-19.
[99]冯永青,吴文传,张伯明,等.基于可信性理论的输电网短期线路检修计划[J].中国电机工程学报,2007,27 (4):65-72.
[100]汪皓,吴文传,张伯明.基于可信性理论的模糊潮流方法[J].电力系统自动化,2007,31 (17):21-25.
[101]刘宝碇,赵瑞清.不确定数学规划方法[M].北京:清华大学出版社,2005.
[102] Liu Y K.Convergent result s about the use of fuzzy simulation in fuzzy optimization problems[J].IEEE Transactions on Fuzzy Systems,2006,14(2):295-304.
[103] Billinton R,Alland R N.Reliability evaluation of power systems[M].New York,USA,Plenum Press:1984.
[104]谭伦农,张保会.市场环境下的事故备用容量[J].中国电机工程学报,2002,22(11):54-58.
[105]孟祥星,韩学山.不确定性因素引起备用的探讨[J].电网技术,2005,29(1):30-34.
[106] Transmission Transfer Capability Task Force.Available transfer capability definition and determination[R].New Jersey:North American Electric Reliability Council,1996.
[107] G. Hamoud.Assessment of available transfer capability of transmission system[J].IEEE Transactions on Power Systems,2000,15(1):27-32.
[2]程浩忠,张焰.电力网络规划的方法与应用[M].上海:科学技术出版社,2002.
[3]王锡凡.电力系统规划基础[M].北京:水利电力出版社,1994.
[4] Merrill H M,Wood A J.Risk and uncertainty in power system planning[J].Electric Power & Energy Systems,1991,13(2):81-90.
[5] T Tachikawa,H Kita,H Sugihara.A study of transmission planning under a deregulated environment in power system[C].IEEE International Conf. on Electric Utility Deregulation and Restructuring,2000,649-654.
[6]郑风雷,文福拴,吴复立.电力市场环境下的输电投资与扩展规划[J].电力系统自动化.2006,30(10):80-86.
[7]程浩忠,张焰,严正,等.电力系统规划[M].北京:中国电力出版社,2008.
[8]陈章潮,程浩忠,傅正财,等.城市电网规划与改造(第二版)[M].北京:中国电力出版社,2007.
[9] Haozhong Cheng,Haifeng Zhu,Mariesa L.Crow.Flexible method for power network planning using the unascertained number[J].Electric Power System Research,2004, 68(1):41-46.
[10]朱海峰.不确定性信息的电网灵活规划方法[D].上海交通大学博士学位论文,2000,8.
[11] B.G. Gorenstin,N.M. Campodonico,J.P. Costa.Power system expansion planning under uncertainty[J].IEEE Transactions on Power Systems,1993,8(1):129-136.
[12] Enrique , Crowilla , Peter Mrfner . Conflicting Objectives and Risk in Power System Planning[J].IEEE Transactions on Power Systems,1993,8(3):887-893.
[13]高赐威,程浩忠,王旭.考虑场景发生概率的柔性约束电网规划模型[J].中国电机工程学报,2004,24(11),34-38.
[14]朱海峰,程浩忠,张焰.考虑线路被选概率的电网灵活规划方法[J].电力系统自动化,2000, 24(17):20-24.
[15]程浩忠,朱海峰,马则良,等.基于等微增率准则的电网灵活规划方法[J].上海交通大学学报,2003,37(9):1351-1353.
[16]翟海保,程浩忠,陈春霖,等.基于最小期望悔值的电网灵活规划方法[J].上海交通大学学报,2005,39(Sup.1):27-30.
[17]刘铠滢,蔡述涛,张尧.基于风险评判的电网规划方法[J].中国电机工程学报,2007,27(22):69-73.
[18]麻常辉,薛禹胜,鲁庭瑞,等.输电规划方法的评述[J].电力系统自动化,2006,30 (12): 97-101.
[19] J.Choi,T.Tran,A.A.El-Keib.A method for transmission system expansion planning considering probabilistic reliability criteria[J].IEEE Transactions on Power Systems,2005,20(3):1606-1615.
[20]杨宁,文福拴.基于机会约束规划的输电系统规划方法[J].电力系统自动化,2004,28(14):23-27.
[21]杨宁,文福拴.计及风险约束的多阶段输电系统规划方法[J].电力系统自动化,2005,29(4):28-33.
[22]麻常辉,薛禹胜,王小英.基于静态和动态安全风险的输电规划—(二)计及注入功率的不确定性[J].电力系统自动化,2006,30(14):10-13.
[23] A. M. Leite da Silva,S. M. P. Ribeiro,R. N. Allan.Probabilistic load flow techniques applied to power system expansion planning[J].IEEE Transactions on Power Systems,1990,5(4):1047-1053.
[24]张焰.不确定性的长期电网规划方法研究[D].上海:上海交通大学博士学位论文,1998.
[25]张焰.电网规划中的模糊可靠性评估方法[J].中国电机工程学报,2000,20(11):77-80.
[26] I.J.Silva,M.J. Rider,R.Romero.Transmission network expansion planning considering uncertainty in demand[J].IEEE Transactions on Power Systems,2006,21(4):1565-1573.
[27]张洪明,廖培鸿.输电网规划的灰色模型及算法[J].上海交通大学学报,1995,29 (3):20- 26.
[28]邓聚龙.灰色系统的基本方法[M].武汉:华中理工大学出版社,1988.
[29]高赐威,程浩忠,王旭.盲信息的模糊评价模型在电网规划中的应用[J].中国电机工程学报,2004,24(9):24- 29.
[30]程浩忠,朱海峰,王建民.基于盲数BM模型的电网灵活规划方法[J].上海交通大学学报,2003,37(9):1347-1350.
[31]金华征,程浩忠,曾德君.基于集对分析的柔性电网规划方法[J].中国电机工程学报,2005,25(3):7-13.
[32]金华征,程浩忠,杨晓梅.基于联系数模型的电网灵活规划方法[J].中国电机工程学报,2006,26(12):16-20.
[33] A. Monticelli,A. S. Junior,M. V. F. Pereira.Interactive transmission network planning using a least-effort criterion[J].IEEE Transactions on Power Systems,1982,101(10):3919-3925.
[34] R.Villasana,L.Garver,S.J.Salon.Transmission network planning using linear planning[J].IEEE Transactions on Power Systems,1985,104(1):349-356.
[35] M. V. F. Pereira,L. M. V. G. Pinto.Application of sensitivity analysis of local supplying capability to interactive transmission expansion planning[J].IEEE Transactions on Power Systems,1985,104(1):381-389.
[36] R.Romero,C.Rocha,J.R.S.Mantovani.Constructive heuristic algorithm for the DC model in network transmission expansion planning[J].IEE Proc.-Gener. Transm. Distrib.,2005(2):277-282.
[37] S. Haffner,A. Monticelli,A. Garcia.Branch and bound algorithm for transmission system expansion planning using a transportation model[J].IEE Proc.-Gener. Transm. Distrib.,2000,147(3):149-156.
[38] L. Bahiense,G. C. Oliveira,M. Pereira.A mixed integer disjunctive model for transmission network expansion[J].IEEE Transactions on Power Systems,2001,16(3):560-565.
[39] R. Romero,A. Monticelli.A zero-one implicit enumeration method for optimizing investments in transmission expansion planning[J].IEEE Transactions on Power Systems,1994,129(3):1385-1391.
[40] Natalia Alguacil,Alexis L.Motto,Antonio J.Conejo.Transmission expansion planning:a mixed-integer LP approach[J].IEEE Transactions on Power Systems,2003,18(3):1070-1077.
[41] R.Romero,A.Monticelli.A hierarchical decomposition approach for transmission expansion planning[J].IEEE Transactions on Power Systems,1994,9(1):373-380.
[42] Silvio B,Mário V F P,Sérgio G.A New Benders Decomposition Approach to Solve Power Transmission Network Design Problems[J].IEEE Transactions on Power Systems,2001,16(2):235-240.
[43] R. Rornero,A. Monticelli. A.Garcia.Test systems and mathematical models for transmission network expansion planning[J].IEE proc.-gener. transm. Distrib,2002,149(1):27-36.
[44]邢文训,谢金星.现代优化计算方法[M].北京:清华大学出版社,1999.
[45] Edson Luiz da Silva,Hugo Alejandro Gil.Transmission Network Expansion Planning Under an Improved Genetic Algorithm[J].IEEE Transactions on Power Systems,2000,15(3):1169-1175.
[46] R. A. Gallego,A. Monticelli,R. Romero.Transmission system expansion planning by extended genetic algorithm[J].IEE proc.-gener. transm. Distrib.,1998,145(3):329-335.
[47]叶在福,单渊达.基于边界搜索策略的遗传算法在电网扩展规划中的应用[J].中国电机工程学报,2000,20(11):41-45.
[48]王秀丽,李淑慧,陈皓勇.基于非支配遗传算法及协同进化算法的多目标多区域电网规划[J].中国电机工程学报,2006,26(12):11-15.
[49]毛玉宾,王秀丽,王锡凡.多阶段输电网最优规划的遗传算法[J].电力系统自动化,1998, 22(12):13-5.
[50] Yi Wang,Haozhong Cheng,Chun Wang et al.Pareto optimality based multiobjective transmission planning[J].Electric Power Systems Research,2008,78(9):1619-1626.
[51] Romero R,Gallego R A,Monticelli A.Transmission system expansion planning by simulated annealing[J].IEEE Transaction on Power Systems,1996,11(1),364-369.
[52] Wen Fushuan,Chang C S.Transmission network optimal planning using the tabu search method[J].Electric Power Systems Research,1997,47(2):153-163.
[53] Ramon A,Gallego,Rubén Romero.Tabus earch algorithm for network synthesis[J].IEEETransaction on Power Systems,2000,15(2):490-495.
[54] Edson LS,Jorge MA,Gerson CO.Transmission network expansion planning under a tabu search approach[J].IEEE Transactions on Power Systems,2001,16(1):62-68.
[55] S.Binato,G..C.Oliveira,J.L.Araujo.A greedy randomized adaptive search procedure for transmission network expansion planning[J].IEEE Transactions on Power Systems,2001,16(2):247-253.
[56] Haroldo Faria,Jr Silvio Binato.Power Transmission Network Design by Greedy Randomized Adaptive Path Relinking[J].IEEE Transaction on Power Systems,2005,20(1),43-49.
[57]翟海保,程浩忠,陈春霖,等.基于改进蚁群算法的输电网络扩展规划[J].中国电力,2003,36(12):49-52.
[58] Dorigo M,Gambardella L M.Ant colony system:a cooperative learning approach to the traveling salesman problem[J].IEEE Transactions on Evolutionary Computation,1997,1(1):53-66.
[59] Dorigo M,Di Caro G,Stützle T.Ant algorithms[J].Future Generation Computer Systems,2000,16(8):5-7.
[60]翟海保,程浩忠,陈春霖,等.多阶段输电网络最优规划的并行蚁群算法[J].电力系统自动化,2004,28(20):37-42.
[61] Sensarma P S,Rahmani M,Carvalho A.A comprehensive method for optimal expansion planning using particle swarm optimization[C].Power Engineering Society Winter Meeting,2002,1317-1322.
[62] Kennedy J,Eberhart R.Particle swarm optimization[C].Proceedings of IEEE International Conference on Neural Networks,1995,1942-1948.
[63]金义雄,程浩忠,严健勇.改进粒子群算法及其在输电网规划中的应用[J].中国电机工程学报,2005,25(4):46-50.
[64]金义雄,程浩忠,严健勇.基于并行协同粒子群算法的多阶段电网规划[J].中国电机工程学报,2005,25(25):49-53.
[65] Galiana D,McGillis DT,Marin M.An expert systems in transmission planning[J].Proceedings of the IEEE,1992,80 (5):712- 726.
[66]石立宝,徐国禹.一种求解电网多目标模糊优化运行的自适应进化规划算法[J].中国电机工程学报,2001,21(3):53-61.
[67] Chun Wang,Haozhong Cheng.Optimization of network configuration in large distribution systems using plant growth simulation algorithm[J].IEEE Transactions on Power Systems,2008,23(1):119-126.
[68]胡泽春,王锡凡,张显,等.考虑线路故障的随机潮流[J].中国电机工程学报,2005,25(24):26-33.
[69]张焰,陈章潮.电网规划中的模糊潮流计算[J].电力系统自动化,1998,22(3):20-22.
[70] Wang Zian,Alvarado F L.Interval arithmetic in power flow analysis[J].IEEE Transactions on Power Systems,1992,7(3):1341-1349.
[71]朱海峰,程浩忠,张焰.利用盲数进行电网规划的潮流计算方法[J].中国电机工程学报,2000,21(8):74-78.
[72]郭永基著.电力系统可靠性分析[M].北京:清华大学出版社,2003.
[73]水利电力部.SD 131-84电力系统技术导则[M].北京:水利电力出版社,1984.
[74] Bracken J , McGill J T . Mathematical programs with optimization problems in the constraints[J].Operations Research,1973,21:37-44.
[75] Bard J F.Practical bilevel optimization:algorithms and applications[M].Dordrecht:Kluwer Academic Publishers,1998.
[76]刘红英.多层规划的理论与算法研究[D].西安:西安电子科技大学博士学位论文,2000.
[77] Zhongping Wang,Heng Fan,Shufen Wang.A bilevel programming model for the reactive power optimization[C].International Power Engineering Conference,2005,1265-1269.
[78] Bjondal M,Jornsten K.The deregulated electricity market viewed as a bilevel programming problem[J].Journal of Global Optimization,2005,33(3):465-475.
[79]范宏,程浩忠,严健勇,等.考虑经济性可靠性的输电网扩展规划的二层规划模型及混合算法[J].中国电机工程学报,2008,28(16):1-7.
[80] C. Shi,J. Lu,G. Zhang,Z. Hong.An extended Kth-best approach for linear bilevel programming[J].Applied Mathematics and Computation,2005,164(3):843-855.
[81] Shi Chenggen,Lu Jie,Zhang Guangquan.An extended Kuhn-Tucker approach for linear bilevel programming[J].Applied Mathematics and Computation,2005,162(1):51-63.
[82] C. Shi,J. Lu,G. Zhang,Z. Hong.An extended branch and bound algorithm for linear bilevel programming[J].Applied Mathematics and Computation,2006,180(2):529-537.
[83] D. J. White,G. Anandalingam.A penalty function approach for solving bi-level linear programs[J].Journal of Global Optimization,1993,3(4):397-419.
[84] Bard J , Moore J T . A branch and bound algorithm for the bilevel programming problem[J].SIAM Journal on Scientific and Statistical Computing,1990,11(2):281-292.
[85]龚怀云.应用泛函分析[M].西安:西安交通大学出版社,2001.
[86]王成山,郑海峰,谢莹华.计及分布式发电的配电系统随机潮流计算[J].电力系统自动化,2005,29(24):39-45.
[87]张焰,陈章潮.计及不确定性的模糊交流潮流计算方法研究[J].电网技术,1998,22(2):20-25.
[88]王守相,武志峰,王成山.计及不确定性的电力系统直流潮流的区间算法[J].电力系统自动化,2007,31(5):18-23.
[89]魏国华,王芬.线性规划[M].北京:高等教育出版社,1990.
[90]张永伍,余贻鑫,严雪飞.基于区间算法和范例学习的配电网网架规划[J].电力系统自动化,2005,29(17):40-44.
[91]孙洪波,徐国禹,秦翼鸿.电网规划的模糊随机优化模型[J].电网技术,1996,20(5):4-7.
[92] Liu B.Theory and practice of uncertain programming[M].Germany,Heidelberg:2002.
[93] Liu B,Liu Y K.Expected value of fuzzy variable and fuzzy expected value models[J].IEEE Transactions on Fuzzy Systems,2002,10(4):445-450.
[94]杨莉.基于可能性理论的发电公司报价策略研究[D].浙江:浙江大学博士学位论文,2003.
[95]冯永青,吴文传,张伯明,等.基于可信性理论的电力系统运行风险评估(一) [J].电力系统自动化,2006,30 (1):17-22.
[96]冯永青,吴文传,张伯明,等.基于可信性理论的电力系统运行风险评估(二) [J].电力系统自动化,2006,30 (2):11-15.
[97]冯永青,吴文传,张伯明,等.基于可信性理论的电力系统运行风险评估(三) [J].电力系统自动化,2006,30 (3):11-16.
[98]冯永青,吴文传,张伯明,等.基于可信性理论的水火电机组检修计划[J].中国电机工程学报,2006,26 (13):14-19.
[99]冯永青,吴文传,张伯明,等.基于可信性理论的输电网短期线路检修计划[J].中国电机工程学报,2007,27 (4):65-72.
[100]汪皓,吴文传,张伯明.基于可信性理论的模糊潮流方法[J].电力系统自动化,2007,31 (17):21-25.
[101]刘宝碇,赵瑞清.不确定数学规划方法[M].北京:清华大学出版社,2005.
[102] Liu Y K.Convergent result s about the use of fuzzy simulation in fuzzy optimization problems[J].IEEE Transactions on Fuzzy Systems,2006,14(2):295-304.
[103] Billinton R,Alland R N.Reliability evaluation of power systems[M].New York,USA,Plenum Press:1984.
[104]谭伦农,张保会.市场环境下的事故备用容量[J].中国电机工程学报,2002,22(11):54-58.
[105]孟祥星,韩学山.不确定性因素引起备用的探讨[J].电网技术,2005,29(1):30-34.
[106] Transmission Transfer Capability Task Force.Available transfer capability definition and determination[R].New Jersey:North American Electric Reliability Council,1996.
[107] G. Hamoud.Assessment of available transfer capability of transmission system[J].IEEE Transactions on Power Systems,2000,15(1):27-32.