基于整数规划的供电系统检修计划优化方法
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摘要
科学、合理、实用的检修计划有利于提高电力系统运行的可靠性，能够提高电力企业的现代化管理水平和经济效益。本文在研究供电系统检修计划制定现状的基础上，通过分析供电系统检修计划优化问题的多目标性、随机性、关系复杂性等特点，提出了一种以停电损失的负荷最小为目标的整数规划模型。
本文的数学模型根据检修操作的同时性、顺序性和互斥性要求，建立了约束条件；然后对模型进行加速改进，即首先处理等式约束来降低维数，并对设备按照重要性等级和影响的负荷大小进行排序，通过这样的处理，有效的减少了枚举的次数；最后应用枚举法，得到全局最优解。通过算例验证了该方法的实用性和有效性。
采用本文提出的优化方法，使编制出的检修计划更合理，提高了电力系统供电的安全性和可靠性，保证节约人力、物力，减少检修所造成的损失。
The scientific, rational and practical maintenance scheduling are helpful to improve the stability of the power system operation and improve the modernization level and profit efficiency of the enterprises. The optimization of maintenance scheduling in power supply system has the traits, such as multiple goals, highly randomicity, complex restriction relation, etc. By analyzing these problems and on basis of studying the current situation of the maintenance scheduling design, an optimization method has been presented in this paper. The goal function is the minimal power cutting lost load.
The optimal solution can be got by Integer Programming module. The module’s restriction can be established by the synchronous, mutually exclusive and ordinal need. Then an accelerated amelioration has acted on the module, which firstly reduce dimension by dealing with equation restriction, then sort the equipments by their voltage grade and related cutting lost load. By these the amount of enumerating can be reduced effectively. Lastly the global optimized solution can be got by enumerating. The practicality and efficiency of the method had been proved by the example.
With the optimized method in this paper, it can make the plan more rational, decrease the loss of power cut, improve the safety and reliability of power supply system and enhance the economical efficiency and social efficiency of the enterprises. A useful attempt is made in this thesis to digitalize the production and operation of power supply enterprises.
本文的数学模型根据检修操作的同时性、顺序性和互斥性要求，建立了约束条件；然后对模型进行加速改进，即首先处理等式约束来降低维数，并对设备按照重要性等级和影响的负荷大小进行排序，通过这样的处理，有效的减少了枚举的次数；最后应用枚举法，得到全局最优解。通过算例验证了该方法的实用性和有效性。
采用本文提出的优化方法，使编制出的检修计划更合理，提高了电力系统供电的安全性和可靠性，保证节约人力、物力，减少检修所造成的损失。
The scientific, rational and practical maintenance scheduling are helpful to improve the stability of the power system operation and improve the modernization level and profit efficiency of the enterprises. The optimization of maintenance scheduling in power supply system has the traits, such as multiple goals, highly randomicity, complex restriction relation, etc. By analyzing these problems and on basis of studying the current situation of the maintenance scheduling design, an optimization method has been presented in this paper. The goal function is the minimal power cutting lost load.
The optimal solution can be got by Integer Programming module. The module’s restriction can be established by the synchronous, mutually exclusive and ordinal need. Then an accelerated amelioration has acted on the module, which firstly reduce dimension by dealing with equation restriction, then sort the equipments by their voltage grade and related cutting lost load. By these the amount of enumerating can be reduced effectively. Lastly the global optimized solution can be got by enumerating. The practicality and efficiency of the method had been proved by the example.
With the optimized method in this paper, it can make the plan more rational, decrease the loss of power cut, improve the safety and reliability of power supply system and enhance the economical efficiency and social efficiency of the enterprises. A useful attempt is made in this thesis to digitalize the production and operation of power supply enterprises.
引文
[1] 董雷,鲍海,齐郑,张粒子.一种供电系统检修计划自动制定系统的设计方法.现代电力,2001年8月
[2] 杨澎,陈少华.制定大规模发电机组检修计划的整数规划法.华南师范大学学报（自然科学版）,1997（3）
[3] 王剑峰,顾新建,高国宁.电网调度计划编制方法的研究和应用.中国电力,1997年9月
[4] 全宏兴,刘俊勇.发电机组检修计划的可靠性和经济性研究.四川电力技术,2001年第5期
[5] 杨丽君,孟子川,孙丽杰.发电机组状态技术.黑龙江电力,2000年10月
[6] 杨杰.以可靠性为中心的检修在电力系统中的应用.山西电力技术, 1999年10月
[7] 丁明,冯永青.发电机组检修计划的可靠性和经济性研究.中国电力,2001年第7期
[8] Luonan CHEN, et al. Power Arrival Evaluation of Bulk System Including Network Constrains Based on Linear Programming Approach. IEEE Trans on Power System, Vol.6, No.1,Feb.1991:37-42
[9] Luonan CHEN, Junichi TOYODA. Optimal Generating Unit Maintenance Scheduling for Multi-Area System with Network Constraints. IEEE Trans on Power System Vol.6, No.3, Aug.1991:1168-1174
[10] L.N.CHEN, J.TOYODA. Power Maintenance Scheduling Based on Two Level Hierarchical Structure to Equal Incremental Risk. IEEE Trans on Power System, Vol.5, No.4, November.1990:1510-1516
[11]Debabrata Chattopadhyay. A Practical Maintenance Scheduling Program:Mathematical Maintenance Scheduling Program:Mathematical Modle and Case Study. IEEE Trans on Power System, Vlo.13, No.4, Nov. 1998:1475-1479.
[12] H.H.Zurn,V.H.Quintana. Generator Maintenance Scheduling via Successive Approximation Dynamic Programming. IEEE Trans on Power Apparatus and System, Vol.Pas-94,March/April 1975:665-671
[13] Zia Yamayee,Kathleen Sidenblad. A Computationally Efficient:Optimal Maintenance Scheduling Method. IEEE Trans on Power Apparatus and System, Vol.Pas-102, No.2, Feb.1983:330-338
[14] Lucia Munoz Moro, Andres Ramos. Goal Programming Approach to Maintenance Scheduling of Generating Unit in Large Scale Power System. IEEE Trans on Power System, Vol.14, No.3, Aug.1999:1021-1027
[15] 陈竟成,于尔铿,刘广一,周京阳,李小彬,李永生.检修计划新模型与算法的研究.电网技术,1997年11月
[16] A flexible unit maintenance scheduling using fuzzy 0-1 integer programming Rong-Ceng Leou Shih-An Yih Power Engineering Society Summer Meeting [J]. IEEE Volume: 4 , July 2000, 2551 –2555.
[17] G.T,Egan,et al. An Experimental Method of Determination of Optimal Maintenance Schedules in Power System Using the Branch and Bound Technique. IEEE Trans on Man and Cybernetics, Vol.SMC-6, No.8,Aug.1976:538-547
[18]Rana Mukerji,John H.Parker. Power Plan Maintenance Scheduling: Optimizing Economics and Relibility. IEEE Trans on Power Sysrem, Vol.6,No.2,May 1991:476-483
[19] D. Chattopadhyay,et al. A System Approach to Least-cost Maintenance Scheduling for an Interconnected Power System. IEEE Trans on Power Sysrem, Vol.10, No.4, November 1995:2002-2007
[20] J.F.Dopazo,H.M.Merrill. Optimal Generator Maintenance Scheduling Using Integer Programming. IEEE Trans on Power Apparatus and System, Vol.Pas-94,September/October,1975:1537-1545
[21] J.C.Kohli,et al. Optimal Preventive and Corrective Maintenance Scheduling in Power System-Model and Technique of Analysis. IEEE PES Winter meeting,New York,N.Y.January 26-31,1975:C75 146-6
[22] 卢开澄.单目标、多目标与整数规划.清华大学出版社,1999
[23] 朱道立.大系统优化理论与应用.上海交通大学出版社,1987
[24] J.Yellen,et al. A Decomposition Approach to Unit Maintenance Scheduling. IEEE Trans on Power System, Vol.7, No.2, May 1992:726-733
[25] T.M Al-khamis,et al. Unit Maintenance Scheduling with Fuel Constraints.IEEE Trans on Power System,Vol.7,No.2,May 1992:110-115
[26] E.L.Silva,M.Morozowski,et al. Transmission Constrained Maintenance Scheduling of Generating Units: a Stochastic Programming Approach. IEEE Trans on Power System, Vol.10, No.2, May 1995:695-701
[27] M.K.C.Marwali,S.M.Shahodehpour,V.C.Ramesh. A Decompositon Approach to Generation Maintenance Scheduling with Network Constraints. APC
Proc., Vol.59-I, April 1997:110-115
[28] M.K.C.Marwali,S.M.Shahodehpour,V.C.Ramesh. Integrated Generation and Transmission Maintenance Scheduling with Network Constraints. IEEE Trans on Power System, Vol.13, No.3, Aug. 1998:1063-1068
[29] M.K.C.Marwali,S.M.Shahodehpour. Integrated Generation and Transmission Maintenance Scheduling with Network Constraints. PICA Proc. Paper., No.185,May 1997
[30] M.K.C.Marwali,S.M.Shahodehpour. Long-term Transmission and Generation Maintenance Scheduling with Network, Fuel and Emission Constraints. IEEE Trans on Power System, Vol.14, No.3, Aug. 1999:1160-1165
[31] 王智敏.基于整数规划法的供电检修计划编制方法研究.华北电力大学,2002
[32] 孙洪波.电力网络规划.重庆大学出版社,1996
[33] 周明,孙树栋.遗传算法原理及应用.国防工业出版社,1999
[34] 陈少华,杨澎.遗传算法在火力发电机组检修计划中的应用.武汉水利电力大学学报,1999年10月
[35] G.Bretthauer, et al. Integrated Maintenance Scheduling System for Electrical Energy System. IEEE Trans on Power Delivery, Vol.13, No.2, April 1998:655-660
[36] 刑文训 谢尽兴 现代优化计算方法 清华大学出版社 1999
[37] Hyunchul Kim, Yasuhiro Hayashi, Koichi Nara. An Algorithm for Thermal Unit Maintenance Scheduling through Combined Use of GA SA and TS. IEEE Trans on Power System, Vol.12, No.1, February 1997:329-335
[38] Fabrice Fourcade,Thierry Eve,Thierry Socroun. Improving Lagrangian of Pressurized Water Reactor Outage. IEEE Trans on Power System, Vol.12, No.2, May 1997:919-925
[39] K,Kawahara, et al. A Proposal of a Supporting Expert System for Outage Planning of Electric Power Facilities Retainning High Power Supply Reliability(Part I: Outline of a Supporting System and Outage Work Allocation Based on Indices). IEEE Trans on Power System, Vol.13, No.4, Nov.1998:1453-1458
[40] K,Kawahara, et al. A Proposal of a Supporting Expert System for Outage Planning of Electric Power Facilities Retainning High Power Supply
Reliability(Part II: Knowledge Processing and Simulation Results). IEEE Trans on Power System, Vol.13, No.4, Nov.1998:1459-1465
[41] 马仲蕃.线性整数规划的数学基础.科学出版社,1998
[42] 胡运权,郭耀煌.运筹学教程,清华大学出版社,2000
[43] 李维铮,郭耀煌等.运筹学.清华大学出版社,1985
[44] 唐焕文，秦学志.实用最优化方法. 大连理工大学出版社,2000
[45] 何仰赞等.电力系统分析,华中理工大学出版社,1995.
[46] 陈衍.电力系统稳态分析.水利电力出版社,1995.
[47] 诸骏伟主编.电力系统分析（上册）.中国电力出版社,1998.
[48] 郑人杰等.软件工程概论.清华大学出版社,1998
[2] 杨澎,陈少华.制定大规模发电机组检修计划的整数规划法.华南师范大学学报（自然科学版）,1997（3）
[3] 王剑峰,顾新建,高国宁.电网调度计划编制方法的研究和应用.中国电力,1997年9月
[4] 全宏兴,刘俊勇.发电机组检修计划的可靠性和经济性研究.四川电力技术,2001年第5期
[5] 杨丽君,孟子川,孙丽杰.发电机组状态技术.黑龙江电力,2000年10月
[6] 杨杰.以可靠性为中心的检修在电力系统中的应用.山西电力技术, 1999年10月
[7] 丁明,冯永青.发电机组检修计划的可靠性和经济性研究.中国电力,2001年第7期
[8] Luonan CHEN, et al. Power Arrival Evaluation of Bulk System Including Network Constrains Based on Linear Programming Approach. IEEE Trans on Power System, Vol.6, No.1,Feb.1991:37-42
[9] Luonan CHEN, Junichi TOYODA. Optimal Generating Unit Maintenance Scheduling for Multi-Area System with Network Constraints. IEEE Trans on Power System Vol.6, No.3, Aug.1991:1168-1174
[10] L.N.CHEN, J.TOYODA. Power Maintenance Scheduling Based on Two Level Hierarchical Structure to Equal Incremental Risk. IEEE Trans on Power System, Vol.5, No.4, November.1990:1510-1516
[11]Debabrata Chattopadhyay. A Practical Maintenance Scheduling Program:Mathematical Maintenance Scheduling Program:Mathematical Modle and Case Study. IEEE Trans on Power System, Vlo.13, No.4, Nov. 1998:1475-1479.
[12] H.H.Zurn,V.H.Quintana. Generator Maintenance Scheduling via Successive Approximation Dynamic Programming. IEEE Trans on Power Apparatus and System, Vol.Pas-94,March/April 1975:665-671
[13] Zia Yamayee,Kathleen Sidenblad. A Computationally Efficient:Optimal Maintenance Scheduling Method. IEEE Trans on Power Apparatus and System, Vol.Pas-102, No.2, Feb.1983:330-338
[14] Lucia Munoz Moro, Andres Ramos. Goal Programming Approach to Maintenance Scheduling of Generating Unit in Large Scale Power System. IEEE Trans on Power System, Vol.14, No.3, Aug.1999:1021-1027
[15] 陈竟成,于尔铿,刘广一,周京阳,李小彬,李永生.检修计划新模型与算法的研究.电网技术,1997年11月
[16] A flexible unit maintenance scheduling using fuzzy 0-1 integer programming Rong-Ceng Leou Shih-An Yih Power Engineering Society Summer Meeting [J]. IEEE Volume: 4 , July 2000, 2551 –2555.
[17] G.T,Egan,et al. An Experimental Method of Determination of Optimal Maintenance Schedules in Power System Using the Branch and Bound Technique. IEEE Trans on Man and Cybernetics, Vol.SMC-6, No.8,Aug.1976:538-547
[18]Rana Mukerji,John H.Parker. Power Plan Maintenance Scheduling: Optimizing Economics and Relibility. IEEE Trans on Power Sysrem, Vol.6,No.2,May 1991:476-483
[19] D. Chattopadhyay,et al. A System Approach to Least-cost Maintenance Scheduling for an Interconnected Power System. IEEE Trans on Power Sysrem, Vol.10, No.4, November 1995:2002-2007
[20] J.F.Dopazo,H.M.Merrill. Optimal Generator Maintenance Scheduling Using Integer Programming. IEEE Trans on Power Apparatus and System, Vol.Pas-94,September/October,1975:1537-1545
[21] J.C.Kohli,et al. Optimal Preventive and Corrective Maintenance Scheduling in Power System-Model and Technique of Analysis. IEEE PES Winter meeting,New York,N.Y.January 26-31,1975:C75 146-6
[22] 卢开澄.单目标、多目标与整数规划.清华大学出版社,1999
[23] 朱道立.大系统优化理论与应用.上海交通大学出版社,1987
[24] J.Yellen,et al. A Decomposition Approach to Unit Maintenance Scheduling. IEEE Trans on Power System, Vol.7, No.2, May 1992:726-733
[25] T.M Al-khamis,et al. Unit Maintenance Scheduling with Fuel Constraints.IEEE Trans on Power System,Vol.7,No.2,May 1992:110-115
[26] E.L.Silva,M.Morozowski,et al. Transmission Constrained Maintenance Scheduling of Generating Units: a Stochastic Programming Approach. IEEE Trans on Power System, Vol.10, No.2, May 1995:695-701
[27] M.K.C.Marwali,S.M.Shahodehpour,V.C.Ramesh. A Decompositon Approach to Generation Maintenance Scheduling with Network Constraints. APC
Proc., Vol.59-I, April 1997:110-115
[28] M.K.C.Marwali,S.M.Shahodehpour,V.C.Ramesh. Integrated Generation and Transmission Maintenance Scheduling with Network Constraints. IEEE Trans on Power System, Vol.13, No.3, Aug. 1998:1063-1068
[29] M.K.C.Marwali,S.M.Shahodehpour. Integrated Generation and Transmission Maintenance Scheduling with Network Constraints. PICA Proc. Paper., No.185,May 1997
[30] M.K.C.Marwali,S.M.Shahodehpour. Long-term Transmission and Generation Maintenance Scheduling with Network, Fuel and Emission Constraints. IEEE Trans on Power System, Vol.14, No.3, Aug. 1999:1160-1165
[31] 王智敏.基于整数规划法的供电检修计划编制方法研究.华北电力大学,2002
[32] 孙洪波.电力网络规划.重庆大学出版社,1996
[33] 周明,孙树栋.遗传算法原理及应用.国防工业出版社,1999
[34] 陈少华,杨澎.遗传算法在火力发电机组检修计划中的应用.武汉水利电力大学学报,1999年10月
[35] G.Bretthauer, et al. Integrated Maintenance Scheduling System for Electrical Energy System. IEEE Trans on Power Delivery, Vol.13, No.2, April 1998:655-660
[36] 刑文训 谢尽兴 现代优化计算方法 清华大学出版社 1999
[37] Hyunchul Kim, Yasuhiro Hayashi, Koichi Nara. An Algorithm for Thermal Unit Maintenance Scheduling through Combined Use of GA SA and TS. IEEE Trans on Power System, Vol.12, No.1, February 1997:329-335
[38] Fabrice Fourcade,Thierry Eve,Thierry Socroun. Improving Lagrangian of Pressurized Water Reactor Outage. IEEE Trans on Power System, Vol.12, No.2, May 1997:919-925
[39] K,Kawahara, et al. A Proposal of a Supporting Expert System for Outage Planning of Electric Power Facilities Retainning High Power Supply Reliability(Part I: Outline of a Supporting System and Outage Work Allocation Based on Indices). IEEE Trans on Power System, Vol.13, No.4, Nov.1998:1453-1458
[40] K,Kawahara, et al. A Proposal of a Supporting Expert System for Outage Planning of Electric Power Facilities Retainning High Power Supply
Reliability(Part II: Knowledge Processing and Simulation Results). IEEE Trans on Power System, Vol.13, No.4, Nov.1998:1459-1465
[41] 马仲蕃.线性整数规划的数学基础.科学出版社,1998
[42] 胡运权,郭耀煌.运筹学教程,清华大学出版社,2000
[43] 李维铮,郭耀煌等.运筹学.清华大学出版社,1985
[44] 唐焕文，秦学志.实用最优化方法. 大连理工大学出版社,2000
[45] 何仰赞等.电力系统分析,华中理工大学出版社,1995.
[46] 陈衍.电力系统稳态分析.水利电力出版社,1995.
[47] 诸骏伟主编.电力系统分析（上册）.中国电力出版社,1998.
[48] 郑人杰等.软件工程概论.清华大学出版社,1998