电力市场条件下可用传输能力的研究
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摘要
在电力市场环境下，输电领域的改革要求输电网的所有权者必须向电网的所有用户平等地提供输电服务，充分利用现有的输电网络资源。这样，如何快速有效地计算输电系统可用传输能力非常必要。本文首先总结了输电网可用传输能力研究的历史及现状，介绍了最大可用传输能力、输电可靠性裕度、容量效益裕度等与ATC计算相关的概念，分析了影响ATC计算的各种不确定因素。然后，比较分析了现有基于确定性模型的ATC典型计算方法的优缺点。
传统的最优潮流法计算ATC时，必须假设所有的最优化参数在整个供电区和受电区间可以集中分配。在非集中性的环境中，这种假设通常得不到满足，因而，传统的最优潮流法就不能计算ATC。本文提出了一种基于传输的考虑安全约束的最优潮流数学模型，考虑了系统的电压安全约束、线路热极限约束以及稳定性安全约束，采用先进的约束变尺度最优化方法求解ATC。本文所提出的方法仅仅假设优化参数在选定的供电区和受电区可以集中分配，在非集中性的网络结构中假设也可以得到满足，所以该方法在非集中性环境也同样适合计算输电网络的ATC。同时，所提方法还可以任意的调整供电区的有功出力以及受电区负荷的有功和无功功率，相对于连续潮流法和反复潮流法只能按照某确定的步长进行调整而言，是有广泛应用前景的好方法。
最后利用MATLAB工具制作了仿真分析程序，对典型的传输系统进行分析计算，充分证明了该方法的有效性。
Under the condition of power market environment, the reform in transmission area requires the right of a transmission provider to supply all the transmission customers equally, so as to take full advantages of transmission sources of power system. Thus, it is necessary to calculate ATC(Available Transfer Capability)fast and correctly. Firstly the full presentation of historic and recent research achievement of ATC is given, definition about calculation of ATC is introduced, including definition of Total Transfer Capability Transmission Reliability Margin Capacity Benefit Margin etc. Then, Several typical ATC calculating methods on the basis of determinable model are compared.
Conventional security constrained optimal power flow methods maximize the transfer capability between two control areas assuming all OPFrOptimized parameters can be centrally dispatched, In the decentralized environment, usually this assumption cannot be satisfied, so they are not suitable for TTC(Total Transfer Capability) calculation. To overcome the deficiency of the conventional SCOPF, a transfer-based SCOPF model is presented in the paper, considering voltage limits thermal limits and stability limits. Sequential constrained variable metric programming is used in the optimal power flow (OPF) to calculate TTC. It assumes that only all OPF-optimized parameters involving the selected source and sink area can be dispatched, which can be satisfied in decentralized structure. It can also adjust the real power output at the source area, the real and active load at the sink area in any way, while RPF and CPF adjusts those in a fixed incremental step. TSCOPF is a good method to use in the future application.
Lastly, A program for simulation and calculation is developed using toolbox of MATLAB and an example of calculation is given.
传统的最优潮流法计算ATC时，必须假设所有的最优化参数在整个供电区和受电区间可以集中分配。在非集中性的环境中，这种假设通常得不到满足，因而，传统的最优潮流法就不能计算ATC。本文提出了一种基于传输的考虑安全约束的最优潮流数学模型，考虑了系统的电压安全约束、线路热极限约束以及稳定性安全约束，采用先进的约束变尺度最优化方法求解ATC。本文所提出的方法仅仅假设优化参数在选定的供电区和受电区可以集中分配，在非集中性的网络结构中假设也可以得到满足，所以该方法在非集中性环境也同样适合计算输电网络的ATC。同时，所提方法还可以任意的调整供电区的有功出力以及受电区负荷的有功和无功功率，相对于连续潮流法和反复潮流法只能按照某确定的步长进行调整而言，是有广泛应用前景的好方法。
最后利用MATLAB工具制作了仿真分析程序，对典型的传输系统进行分析计算，充分证明了该方法的有效性。
Under the condition of power market environment, the reform in transmission area requires the right of a transmission provider to supply all the transmission customers equally, so as to take full advantages of transmission sources of power system. Thus, it is necessary to calculate ATC(Available Transfer Capability)fast and correctly. Firstly the full presentation of historic and recent research achievement of ATC is given, definition about calculation of ATC is introduced, including definition of Total Transfer Capability Transmission Reliability Margin Capacity Benefit Margin etc. Then, Several typical ATC calculating methods on the basis of determinable model are compared.
Conventional security constrained optimal power flow methods maximize the transfer capability between two control areas assuming all OPFrOptimized parameters can be centrally dispatched, In the decentralized environment, usually this assumption cannot be satisfied, so they are not suitable for TTC(Total Transfer Capability) calculation. To overcome the deficiency of the conventional SCOPF, a transfer-based SCOPF model is presented in the paper, considering voltage limits thermal limits and stability limits. Sequential constrained variable metric programming is used in the optimal power flow (OPF) to calculate TTC. It assumes that only all OPF-optimized parameters involving the selected source and sink area can be dispatched, which can be satisfied in decentralized structure. It can also adjust the real power output at the source area, the real and active load at the sink area in any way, while RPF and CPF adjusts those in a fixed incremental step. TSCOPF is a good method to use in the future application.
Lastly, A program for simulation and calculation is developed using toolbox of MATLAB and an example of calculation is given.
引文
[1] 李国庆，王成山，余贻鑫．电力系统区域间功率交换能力研究综述[J]．中国电机工程学报，2001，21(4)：20-24
[2] North American Electricity Reliability Council. Transmission transfer capability: a reference documents for calculating and reporting the electric power transfer capability of interconnected electric systems[R]. Technical Report, NERC, 1995,23-25
[3] Federal Energy Regulatory Commission. Open access same-time information system formerly real-time information networks and standards of conduct [R]. Washington: Federal Energy Regulatory Commission, 1996,34-38
[4] Available Transfer Capability Definition and Determination. Available transfer capability definition and determination: a reference document prepared by TTC task force[R]. New Jersey: North American Electric Reliability Council, 1996,30-35
[5] Heydt G T, Katz B M. A stochastic model in simultaneous interchange capacity calculations[J]. IEEE Trans on Power Apparatus and Systems, 1975, 94(2),350-359
[6] PJM Transmission Reliability Task Force. Bulk power area reliability evaluation considering probabilistic transfer capability[J]. IEEE Trans on Power Apparatus and Systems, 1982, 101(9): 3551-3562
[7] Lauby M G, Douda J H, Polesky R W, et al. The procedure used in the probabilistic transfer capability analysis of the MAPP region bulk transmission system[J]. IEEE Trans on Power Apparatus and Systems, 1985, 1104(11): 3013-3019
[8] EPRI Report. Simultaneous transfer capability project: direction for software development[R]. Final Report to RP3140-1,1991,19-23
[9] Sandrin P, Dubost L, Feltin L. Evaluation of transfer capability between interconnected utilities[C]. Proceedings of the 11th Power System Computation Conference, Avignon, France August 30～September 3, 1993, 981-985
[10] Feng Xia, Sakis A P, Meliopoulos. A methodology for probabilistic simultaneous transfer capability analysis[J]. IEEE Trans on Power Systems, 1996, 11(3): 1269-1278
[11] Sakis A P, Meliopoulos, Feng Xia. Simultaneous transfer capability analysis; a probabilistic approach[C]. Proceedings of the 11th Power system Conference, Avignon, France, 1993, 569-576
[12] Mello J C O, Melo A C G, Granville S. Simultaneous transfer capability assessment by combining interior point and monte carlo simultation[J]. IEEE Trans on Power Systems, 1997, 12(2): 736-742
[13] Landgren G L, Terhune H L, Angel R K. Transmission interchange capability analysis by computer[J]. IEEE Trans on Power Apparatus and Systems, 1972, 91(6): 2405-2414
[14] Landgren G L, Anderson S W. Simultaneous power interchange capability analysis[J].IEEE Trans on power Apparatus and Systems, 1973,92(6): 1973-1986.
[15] Landgren G L, Anderson S W. Maximized transmission grid loading using linear programming[C]. IEEE Tutorial Course, 76 CH 1107-2-PWR, 1976, 101-105
[16] Garver L L, Van Horne P R, Wirgau K A. Load supplying capability of generation-transmission networks[J]. IEEE Trans on Power Apparatus and Systems; 1979, 98(3): 957-962
[17] Pereira M V F, Pinto L M V G. Application of sensitivity analysis of supplying capability to interactive transmission expansion planning[J].IEEE Trans on Power Apparatus and Systems,1985, 104(2): 381-389
[18] Alvarado F L, Jung T H. Direct detection of voltage collapse conditions[C]. Proc. of Eng. Found Conference on Bulk Power System Voltage Phenomena-Voltage Stability and Security Potosi, Mich., Sept. 1998, 5.23-5.38
[19] Canizares C A, Alvarado F L. Point of collapse and continuation methods for large AC/DC system[J]. IEEE Trans on Power Systems, 1993, 8(1): 1-8
[20] Ajjarapn V, Christy C. The continuation power flow: a tool for steady state voltage stability analysis[J]. IEEE Trans on Power Systems, 1992, 7(1): 416-423
[21] Flatabo N, Ognedal R, Carlsen T. Voltage stability condition in a power transmission system calculated by sensitivity analysis[J]. IEEE Trans on Power Systems, 1990, 5(4): 1286-1293
[22] Lemaitre C, Tesseton J-P, J-M, et al, An indicator of the risk of voltage profile instability for real-time control applications[J]. IEEE Trans on Power Systems, 1990,5(1): 154-161
[23] Tamura Y, Mori H, Iwamoto S. Relationship between voltage instability and multiple load flow solutions in electric power systems[J]. IEEE Trans on PAS, 1983,102(5): 1115-1125
[24] Iba K, Suzuki H, Egava M, et al. Calculation of critical loading condition with nose curve using homotopy continuation method[J]. IEEE Trans on Power Systems, 1991, 6(2): 584-593
[25] Kwatny H G, et al. Loss of steady state stability and voltage collapse in electric power systems[C]. Proc of 24th Conf. On Decision and Control, Ft. Lauderdale, fl, 1985, 804-811
[26] Begovic M M, Chao X Y, Meliopoulos A P. Voltage stability margin enhancement via optimal power flow[R]. NSF International Workshop on Bulk Power System Voltage Phenomena- 1991: Voltage stability and Security, Deep Creek, MD, 1991, 233-236
[27] Austria R R, Reppen N D, Uhrin J A, et al. Applications of the optimal power flow to analysis of voltage collapse limited power transfer[R]. NSF International Workshop on Bulk Power System Voltage Phenomena-1991, Voltage stability and Security, Deep Creek, MD, 1991, 503-509
[28] Carpentier J, Girard R, Seano E. Voltage collapse proximity indixators computed from an optimal power flow[C]. Proc.of 8th Pscc conference, Helsinik, 1984
[29] Sauer P W, Demaree K D, Pai M A. Stability limited load supply and interchange capability[J]. IEEE Trans on Power Apparatus and Systems, 1983, 102(11): 3637-3643
[30] 刘肇旭，童建中．暂态稳定约束的电网供电能力的计算方法[J]．中国电机工程学报，1987，7(3)：18-23
[31] 于尔铿，韩放，谢开等．电力市场．北京：中国电力出版社，1998，56-58
[32] 于尔铿，刘广一，周京阳等，能量管理系统(EMS)．北京：科学出版社，2001，71-73
[33] 赵遵廉，辛耀中，郭国川等．电力市场运营系统．北京：中国电力出版社，2001，103-104
[34] 姚建刚，电力市场运营．北京：高等教育出版社，2001，57-58
[35] H. Chiang, A. J. Fluech, K. S. Shah, and N. Balu. CPFLOW: A practical tool for tracing power system steady-state stationary behavior due to load and generation variations[J]. IEEE Trans. Power Syst., 1995,10:623-634
[36] 李国庆．基于连续型方法的大型互联电力系统区域间输电能力的研究[D]．天津：天津大学，1998，27-29
[37] 王成山，李国庆，余贻鑫等．电力系统区域间功率交换能力的研究(一)：连续型方法的基本理论及应用[J]．电力系统自动化，1999，23(3)：23-26．
[38] 王成山，李国庆，余贻鑫等．电力系统区域间功率交换能力的研究(二)：计算区域间最大交换功率的模型与算法[J]．电力系统自动化，1999，23(4)：5-9
[39] M. H. Gravener, C. Nwankpa, and I. Yeoh. ATC computational issues, n Proc,32nd Hawaii Int. Conf. Syst. Sci,1999,71-73
[40] X..Luo.A.D.Patton, and C. Singh. Real power transfer capability calculations using multi-layer feed-forward neural networks. IEEE Trans.Power Syst., 2000, 15: 903-908
[41] Sauer P W. Technical challenges of computing Available Transfer Capability (ATC) in electric power systems [A]. System Sciences. Proceedings of HICSS-30 International conference on[C]. Havaii: institute of Electrical and Electronics Engineers, 1997, 7-10
[42] Corniere B, Martin L, Vitet S, et al. Assessment of the congestion cost and the risk of curtailment associated with Available Transfer Capability (ATC)[A]. IEEE PES. Conference Proceeding on 2000 Power Engineering society Winter Meeting [C]. Singapore: Institute of Electrical and Electronics Engineers, 2000, 891-896
[43] M. Gravener and C. Nwankpa. Available transfer capability and first order sensitivity. IEEE Trans. Power Syst, 1999, 14:512-518
[44] Xiao Y, Song Y H. Available Transfer Capability evaluation by stochastic programming[J]. IEEE Power Engineering Review, 2000, 20(9): 50-52
[45] Xiao Y, Song Y H, Sun Y Z. A hybrid stochastic approach to available transfer capability evaluation [J]. IEE Proceeding Generation, Transmission and Distribution, 2001, 148(5): 420-426
[46] Xia F, Meliopoulos A P S. A methodology for probabilistic simultaneous transfer capability analysis [J]. IEEE Trans.on Power System, 1996, 11(3): 1269-1278.
[47] Mello J C O, Melo A C G, Granville S. Simultaneous transfer capability assessment by combining interior point methods and monte carlo simulation[J]. IEEE Trans.on Power Systems, 1997, 12(2): 736-742
[48] Tsai C Y, Lu C N. Bootstrap application in ATC estimation[J]. IEEE Power Engineering Review, 2001, 21(2): 40-42
[49] Qu Y, Singh C. Assessment of available transfer capability and margins[J].IEEE Trans. On Power Systems, 2002, 17(2): 463-468
[50] 周家启等译．电力系统可靠性评估．重庆：科学技术文献出版社重庆分社，1986，31-41
[51] Vojdani A R. Computing available transmission capability using trace[Z].[s.1]: EPRI Power System Planning &Operation News, 1995, 12-14
[52] Hamoud G. Assessment of available transfer capability of transmission system[J].IEEE Trans.on Power Sytems, 2000,15(1): 27-32
[53] Ejebe G C, Waight J G, Sanots-Nieto M,et.al.Available transfer capability calculations [J]. IEEE TRNS.on Power Systems, 1998, 13(4): 1521-1527
[54] 王锡凡等．现代电力系统分析．北京：科学出版社，2003，155-157
[55] 张伯明，陈寿孙．高等电力网络分析．北京：清华大学出版社，1999，187-189
[56] Grijalva S, Sauer P W. Reactive power considerations in ATC computation[J]. Decision Support Systems, 2001, 30(3): 327-340
[57] X..Luo.A.D.Patton, and C. Singh. Quickprop algorithm for transfer capability calculations[A]. IEEE PES. Conference Proceedings on 1999 Power Engineering Society Winter Meeting[C]. New York: Institute of Electrical and Electronics Engineers, 1999, 1075-1077
[58] Shaaban M, Ni Y X, Wu F. Total transfer capability calculations for competitive power networks using genetic algorithms [A]. IEEE, IEE. Proceedings of Institute of Electrical and Electronics Engineerings, 2000, 114-118
[59] 郭耀煌等．运筹学与工程系统分析[M]．北京：中国建筑工业出版社，1986，176-179
[60] 陈宝林．最优化理论与算法．北京：清华大学出版社，2002，508-527
[61] 粟塔山，彭维杰，周作益，曾之华．最优化计算原理与算法程序设计[M]．长沙：国防科技大学出版社，2001
[62] 李涛，贺勇军，刘志俭．Matlab工具箱应用指南—应用数学篇．北京：电子工业出版社，2000，202-249
[2] North American Electricity Reliability Council. Transmission transfer capability: a reference documents for calculating and reporting the electric power transfer capability of interconnected electric systems[R]. Technical Report, NERC, 1995,23-25
[3] Federal Energy Regulatory Commission. Open access same-time information system formerly real-time information networks and standards of conduct [R]. Washington: Federal Energy Regulatory Commission, 1996,34-38
[4] Available Transfer Capability Definition and Determination. Available transfer capability definition and determination: a reference document prepared by TTC task force[R]. New Jersey: North American Electric Reliability Council, 1996,30-35
[5] Heydt G T, Katz B M. A stochastic model in simultaneous interchange capacity calculations[J]. IEEE Trans on Power Apparatus and Systems, 1975, 94(2),350-359
[6] PJM Transmission Reliability Task Force. Bulk power area reliability evaluation considering probabilistic transfer capability[J]. IEEE Trans on Power Apparatus and Systems, 1982, 101(9): 3551-3562
[7] Lauby M G, Douda J H, Polesky R W, et al. The procedure used in the probabilistic transfer capability analysis of the MAPP region bulk transmission system[J]. IEEE Trans on Power Apparatus and Systems, 1985, 1104(11): 3013-3019
[8] EPRI Report. Simultaneous transfer capability project: direction for software development[R]. Final Report to RP3140-1,1991,19-23
[9] Sandrin P, Dubost L, Feltin L. Evaluation of transfer capability between interconnected utilities[C]. Proceedings of the 11th Power System Computation Conference, Avignon, France August 30～September 3, 1993, 981-985
[10] Feng Xia, Sakis A P, Meliopoulos. A methodology for probabilistic simultaneous transfer capability analysis[J]. IEEE Trans on Power Systems, 1996, 11(3): 1269-1278
[11] Sakis A P, Meliopoulos, Feng Xia. Simultaneous transfer capability analysis; a probabilistic approach[C]. Proceedings of the 11th Power system Conference, Avignon, France, 1993, 569-576
[12] Mello J C O, Melo A C G, Granville S. Simultaneous transfer capability assessment by combining interior point and monte carlo simultation[J]. IEEE Trans on Power Systems, 1997, 12(2): 736-742
[13] Landgren G L, Terhune H L, Angel R K. Transmission interchange capability analysis by computer[J]. IEEE Trans on Power Apparatus and Systems, 1972, 91(6): 2405-2414
[14] Landgren G L, Anderson S W. Simultaneous power interchange capability analysis[J].IEEE Trans on power Apparatus and Systems, 1973,92(6): 1973-1986.
[15] Landgren G L, Anderson S W. Maximized transmission grid loading using linear programming[C]. IEEE Tutorial Course, 76 CH 1107-2-PWR, 1976, 101-105
[16] Garver L L, Van Horne P R, Wirgau K A. Load supplying capability of generation-transmission networks[J]. IEEE Trans on Power Apparatus and Systems; 1979, 98(3): 957-962
[17] Pereira M V F, Pinto L M V G. Application of sensitivity analysis of supplying capability to interactive transmission expansion planning[J].IEEE Trans on Power Apparatus and Systems,1985, 104(2): 381-389
[18] Alvarado F L, Jung T H. Direct detection of voltage collapse conditions[C]. Proc. of Eng. Found Conference on Bulk Power System Voltage Phenomena-Voltage Stability and Security Potosi, Mich., Sept. 1998, 5.23-5.38
[19] Canizares C A, Alvarado F L. Point of collapse and continuation methods for large AC/DC system[J]. IEEE Trans on Power Systems, 1993, 8(1): 1-8
[20] Ajjarapn V, Christy C. The continuation power flow: a tool for steady state voltage stability analysis[J]. IEEE Trans on Power Systems, 1992, 7(1): 416-423
[21] Flatabo N, Ognedal R, Carlsen T. Voltage stability condition in a power transmission system calculated by sensitivity analysis[J]. IEEE Trans on Power Systems, 1990, 5(4): 1286-1293
[22] Lemaitre C, Tesseton J-P, J-M, et al, An indicator of the risk of voltage profile instability for real-time control applications[J]. IEEE Trans on Power Systems, 1990,5(1): 154-161
[23] Tamura Y, Mori H, Iwamoto S. Relationship between voltage instability and multiple load flow solutions in electric power systems[J]. IEEE Trans on PAS, 1983,102(5): 1115-1125
[24] Iba K, Suzuki H, Egava M, et al. Calculation of critical loading condition with nose curve using homotopy continuation method[J]. IEEE Trans on Power Systems, 1991, 6(2): 584-593
[25] Kwatny H G, et al. Loss of steady state stability and voltage collapse in electric power systems[C]. Proc of 24th Conf. On Decision and Control, Ft. Lauderdale, fl, 1985, 804-811
[26] Begovic M M, Chao X Y, Meliopoulos A P. Voltage stability margin enhancement via optimal power flow[R]. NSF International Workshop on Bulk Power System Voltage Phenomena- 1991: Voltage stability and Security, Deep Creek, MD, 1991, 233-236
[27] Austria R R, Reppen N D, Uhrin J A, et al. Applications of the optimal power flow to analysis of voltage collapse limited power transfer[R]. NSF International Workshop on Bulk Power System Voltage Phenomena-1991, Voltage stability and Security, Deep Creek, MD, 1991, 503-509
[28] Carpentier J, Girard R, Seano E. Voltage collapse proximity indixators computed from an optimal power flow[C]. Proc.of 8th Pscc conference, Helsinik, 1984
[29] Sauer P W, Demaree K D, Pai M A. Stability limited load supply and interchange capability[J]. IEEE Trans on Power Apparatus and Systems, 1983, 102(11): 3637-3643
[30] 刘肇旭，童建中．暂态稳定约束的电网供电能力的计算方法[J]．中国电机工程学报，1987，7(3)：18-23
[31] 于尔铿，韩放，谢开等．电力市场．北京：中国电力出版社，1998，56-58
[32] 于尔铿，刘广一，周京阳等，能量管理系统(EMS)．北京：科学出版社，2001，71-73
[33] 赵遵廉，辛耀中，郭国川等．电力市场运营系统．北京：中国电力出版社，2001，103-104
[34] 姚建刚，电力市场运营．北京：高等教育出版社，2001，57-58
[35] H. Chiang, A. J. Fluech, K. S. Shah, and N. Balu. CPFLOW: A practical tool for tracing power system steady-state stationary behavior due to load and generation variations[J]. IEEE Trans. Power Syst., 1995,10:623-634
[36] 李国庆．基于连续型方法的大型互联电力系统区域间输电能力的研究[D]．天津：天津大学，1998，27-29
[37] 王成山，李国庆，余贻鑫等．电力系统区域间功率交换能力的研究(一)：连续型方法的基本理论及应用[J]．电力系统自动化，1999，23(3)：23-26．
[38] 王成山，李国庆，余贻鑫等．电力系统区域间功率交换能力的研究(二)：计算区域间最大交换功率的模型与算法[J]．电力系统自动化，1999，23(4)：5-9
[39] M. H. Gravener, C. Nwankpa, and I. Yeoh. ATC computational issues, n Proc,32nd Hawaii Int. Conf. Syst. Sci,1999,71-73
[40] X..Luo.A.D.Patton, and C. Singh. Real power transfer capability calculations using multi-layer feed-forward neural networks. IEEE Trans.Power Syst., 2000, 15: 903-908
[41] Sauer P W. Technical challenges of computing Available Transfer Capability (ATC) in electric power systems [A]. System Sciences. Proceedings of HICSS-30 International conference on[C]. Havaii: institute of Electrical and Electronics Engineers, 1997, 7-10
[42] Corniere B, Martin L, Vitet S, et al. Assessment of the congestion cost and the risk of curtailment associated with Available Transfer Capability (ATC)[A]. IEEE PES. Conference Proceeding on 2000 Power Engineering society Winter Meeting [C]. Singapore: Institute of Electrical and Electronics Engineers, 2000, 891-896
[43] M. Gravener and C. Nwankpa. Available transfer capability and first order sensitivity. IEEE Trans. Power Syst, 1999, 14:512-518
[44] Xiao Y, Song Y H. Available Transfer Capability evaluation by stochastic programming[J]. IEEE Power Engineering Review, 2000, 20(9): 50-52
[45] Xiao Y, Song Y H, Sun Y Z. A hybrid stochastic approach to available transfer capability evaluation [J]. IEE Proceeding Generation, Transmission and Distribution, 2001, 148(5): 420-426
[46] Xia F, Meliopoulos A P S. A methodology for probabilistic simultaneous transfer capability analysis [J]. IEEE Trans.on Power System, 1996, 11(3): 1269-1278.
[47] Mello J C O, Melo A C G, Granville S. Simultaneous transfer capability assessment by combining interior point methods and monte carlo simulation[J]. IEEE Trans.on Power Systems, 1997, 12(2): 736-742
[48] Tsai C Y, Lu C N. Bootstrap application in ATC estimation[J]. IEEE Power Engineering Review, 2001, 21(2): 40-42
[49] Qu Y, Singh C. Assessment of available transfer capability and margins[J].IEEE Trans. On Power Systems, 2002, 17(2): 463-468
[50] 周家启等译．电力系统可靠性评估．重庆：科学技术文献出版社重庆分社，1986，31-41
[51] Vojdani A R. Computing available transmission capability using trace[Z].[s.1]: EPRI Power System Planning &Operation News, 1995, 12-14
[52] Hamoud G. Assessment of available transfer capability of transmission system[J].IEEE Trans.on Power Sytems, 2000,15(1): 27-32
[53] Ejebe G C, Waight J G, Sanots-Nieto M,et.al.Available transfer capability calculations [J]. IEEE TRNS.on Power Systems, 1998, 13(4): 1521-1527
[54] 王锡凡等．现代电力系统分析．北京：科学出版社，2003，155-157
[55] 张伯明，陈寿孙．高等电力网络分析．北京：清华大学出版社，1999，187-189
[56] Grijalva S, Sauer P W. Reactive power considerations in ATC computation[J]. Decision Support Systems, 2001, 30(3): 327-340
[57] X..Luo.A.D.Patton, and C. Singh. Quickprop algorithm for transfer capability calculations[A]. IEEE PES. Conference Proceedings on 1999 Power Engineering Society Winter Meeting[C]. New York: Institute of Electrical and Electronics Engineers, 1999, 1075-1077
[58] Shaaban M, Ni Y X, Wu F. Total transfer capability calculations for competitive power networks using genetic algorithms [A]. IEEE, IEE. Proceedings of Institute of Electrical and Electronics Engineerings, 2000, 114-118
[59] 郭耀煌等．运筹学与工程系统分析[M]．北京：中国建筑工业出版社，1986，176-179
[60] 陈宝林．最优化理论与算法．北京：清华大学出版社，2002，508-527
[61] 粟塔山，彭维杰，周作益，曾之华．最优化计算原理与算法程序设计[M]．长沙：国防科技大学出版社，2001
[62] 李涛，贺勇军，刘志俭．Matlab工具箱应用指南—应用数学篇．北京：电子工业出版社，2000，202-249