计及负荷和调配时间不确定性的防灾应急电源优化配置
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摘要
为最大限度地降低自然灾害可能导致的停电损失,合理配置防灾应急电源至关重要。现有的关于防灾应急电源的研究大多侧重于优化调度城市区域中已有的防灾应急电源,而应该如何对防灾应急电源进行合理配置则研究较少,且没有系统考虑用户负荷及因交通拥堵、道路破坏等引起的应急电源调配时间不确定性的影响。在此背景下,建立了计及负荷和调配时间不确定性的防灾应急电源优化配置模型,并以最大化城市区域的社会效益为优化目标。采用径向区间数的形式(即区间数的两端设定相应的波动半径)来更合理地描述调配时间的不确定性,并将其转化为悲观子模型和乐观子模型,之后分别采用鲁棒优化方法求解。最后,用算例说明了所述模型和方法的基本特征。
It is crucial to appropriately allocate emergency power sources for reducing the outage cost to the greatest extent in emergency circumstances.Existing publications on emergency power sources are focused on optimal scheduling of emergency power sources in urban areas,while less attention has been paid to reasonable allocations of emergency power sources and the impacts of uncertain load demands and dispatching time periods of emergency power sources caused by some factors such as traffic jam and road damage have not yet been addressed.Given this background,an optimization model for allocating emergency power sources is presented with uncertain load demands and dispatching time periods considered,with an objective of maximizing the social welfare.The well-established radial interval represented by the fluctuation radius for the boundaries of an interval value is employed to more appropriately characterize the uncertainties involved.The optimization model is next transformed into a pessimistic sub-model and an optimistic sub-model for speeding the solving process,and each of the submodels is then solved by a robust optimization method.Finally,case studies are served for demonstrating the developed model and method for allocating emergency power sources.
It is crucial to appropriately allocate emergency power sources for reducing the outage cost to the greatest extent in emergency circumstances.Existing publications on emergency power sources are focused on optimal scheduling of emergency power sources in urban areas,while less attention has been paid to reasonable allocations of emergency power sources and the impacts of uncertain load demands and dispatching time periods of emergency power sources caused by some factors such as traffic jam and road damage have not yet been addressed.Given this background,an optimization model for allocating emergency power sources is presented with uncertain load demands and dispatching time periods considered,with an objective of maximizing the social welfare.The well-established radial interval represented by the fluctuation radius for the boundaries of an interval value is employed to more appropriately characterize the uncertainties involved.The optimization model is next transformed into a pessimistic sub-model and an optimistic sub-model for speeding the solving process,and each of the submodels is then solved by a robust optimization method.Finally,case studies are served for demonstrating the developed model and method for allocating emergency power sources.
引文
[1]林伟芳,孙华东,汤涌,等.巴西“11·10”大停电事故分析及启示[J].电力系统自动化,2010,34(7):1-5.LIN Weifang,SUN Huadong,TANG Yong,et al.Analysis and lessons of the blackout in Brazil power grid on November 10,2009[J].Automation of Electric Power Systems,2010,34(7):1-5.
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[5]YU Wenjie,XUE Y,LUO Jianbo,et al.An UHV grid security and stability defense system:considering the risk of power system communication[J].IEEE Transactions on Smart Grid,2016,7(1):491-500.
[6]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[J].电力系统自动化,2003,27(19):1-5.GUO Yongji.To focus on improving power system reliability—a pondering over the East North-America major blackout[J].Automation of Electric Power Systems,2003,27(19):1-5.
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[9]赵炜炜,张建华,尚敬福,等.电网大面积停电应急评价指标体系及其应用[J].电力系统自动化,2008,32(20):27-31.ZHAO Weiwei,ZHANG Jianhua,SHANG Jingfu,et al.Power system large scale blackout emergency evaluation index system and its application[J].Automation of Electric Power Systems,2008,32(20):27-31.
[10]王宏,林振智,文福拴,等.计及负荷停电风险的电力应急服务的最优选址[J].电力自动化设备,2013,33(12):73-78.WANG Hong,LIN Zhenzhi,WEN Fushuan,et al.Optimal siting of power emergency service station considering outage risk of loads[J].Electric Power Automation Equipment,2013,33(12):73-78.
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[12]周莉梅,范明天,张祖平.基于重要用户的应急电源优化配置[J].电力系统自动化,2007,31(6):99-102.ZHOU Limei,FAN Mingtian,ZHANG Zuping.Optimal allocation of emergency power supplies for urban important customers[J].Automation of Electric Power Systems,2007,31(6):99-102.
[13]张爱国,郝建刚,唐志芳,等.考虑综合负荷重要性的移动应急电源容量优化分配[J].电网技术,2008,32(2):86-89.ZHANG Aiguo,HAO Jiangang,TANG Zhifang,et al.The allocation scheme of mobile emergency generator considering the loads importance[J].Power System Technology,2008,32(2):86-89.
[14]王宏,林振智,文福拴,等.城市移动应急电源的优化调度[J].电力系统自动化,2014,38(3):123-129.DOI:10.7500/AEPS20130220002.WANG Hong,LIN Zhenzhi,WEN Fushuan,et al.Optimal scheduling of urban mobile emergency power sources[J].Automation of Electric Power Systems,2014,38(3):123-129.DOI:10.7500/AEPS20130220002.
[15]倪程捷,房鑫炎,赵文恺,等.基于图论的移动应急电源孤岛划分及最优接入点搜索[J].电力系统自动化,2015,39(6):34-40.DOI:10.7500/AEPS20140626001.NI Chengjie,FANG Xinyan,ZHAO Wenkai,et al.Island partitioning and optimal connecting point search of mobile emergency power source based on graph theory[J].Automation of Electric Power Systems,2015,39(6):34-40.DOI:10.7500/AEPS20140626001.
[16]胡启洲,张卫华.区间数理论的研究及其应用[M].北京:科学出版社,2010.
[17]TAN Q,HUANG G H,CAI Y P.Radial interval chanceconstrained programming for agricultural non-point source water pollution control under uncertainty[J].Agricultural Water Management,2011,98(10):1595-1606.
[18]MOORE R E.Methods and applications of interval analysis[M].Philadelphia,USA:SIAM Press,1995.
[19]毛安家,熊超中,张粒子,等.基于改进Tobit模型的负荷停电损失估算方法[J].电力系统自动化,2010,34(9):29-33.MAO Anjia,XIONG Chaozhong,ZHANG Lizi,et al.A customer’s outage cost assessment approach based on the improved Tobit model[J].Automation of Electric Power Systems,2010,34(9):29-33.
[20]宋春丽,刘涤尘,吴军,等.基于差异化全寿命周期成本的电网规划经济性评估方法[J].电网技术,2013,37(7):1849-1855.SONG Chunli,LIU Dichen,WU Jun,et al.An economic assessment of power system planning based on differentiated life cycle cost[J].Power System Technology,2013,37(7):1849-1855.
[21]CHINNECK J W,RAMADAN K.Linear programming with interval coefficients[J].Journal of the Operational Research Society,2000,51(2):209-220.
[22]LI Mian,GABRIEL S A,SHIM Y,et al.Interval uncertaintybased robust optimization for convex and non-convex quadratic programs with applications in network infrastructure planning[J].Networks and Spatial Economics,2011,11(1):159-191.
[23]SOU K C,SANDBERG H,JOHANSSON K H.Computing critical k-tuples in power networks[J].IEEE Transactions on Power Systems,2012,27(3):1511-1520.
[2]毛安家,张戈力,吕跃春,等.2011年9月8日美墨大停电事故的分析及其对我国电力调度运行管理的启示[J].电网技术,2012,36(4):74-78.MAO Anjia,ZHANG Geli,LYuechun,et al.Analysis on large-scale blackout occurred in South America and North Mexico interconnected power grid on Sept.8,2011and lessons for electric power dispatching in China[J].Power System Technology,2012,36(4):74-78.
[3]薛禹胜.时空协调的大停电防御框架:(一)从孤立防线到综合防御[J].电力系统自动化,2006,30(1):8-16.XUE Yusheng.Space-time cooperative framework for defending blackouts:PartⅠfrom isolated defense lines to coordinated defending[J].Automation of Electric Power Systems,2006,30(1):8-16.
[4]薛禹胜.时空协调的大停电防御框架:(三)各道防线内部的优化和不同防线之间的协调[J].电力系统自动化,2006,30(3):1-10.XUE Yusheng.Space-time cooperative framework for defending blackouts:PartⅢoptimization and coordination of defenselines[J].Automation of Electric Power Systems,2006,30(3):1-10.
[5]YU Wenjie,XUE Y,LUO Jianbo,et al.An UHV grid security and stability defense system:considering the risk of power system communication[J].IEEE Transactions on Smart Grid,2016,7(1):491-500.
[6]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[J].电力系统自动化,2003,27(19):1-5.GUO Yongji.To focus on improving power system reliability—a pondering over the East North-America major blackout[J].Automation of Electric Power Systems,2003,27(19):1-5.
[7]田世明,陈希,朱朝阳,等.电力应急管理平台研究[J].电网技术,2008,32(1):26-30.TIAN Shiming,CHEN Xi,ZHU Chaoyang,et al.Study on electric power emergency management platform[J].Power System Technology,2008,32(1):26-30.
[8]刘思革,范明天,张祖平,等.城市电网应急能力评估技术指标的研究[J].电网技术,2007,31(22):17-20.LIU Sige,FAN Mingtian,ZHANG Zuping,et al.A prospective research on technical assessment indices of emergency management capability in urban power network[J].Power System Technology,2007,31(22):17-20.
[9]赵炜炜,张建华,尚敬福,等.电网大面积停电应急评价指标体系及其应用[J].电力系统自动化,2008,32(20):27-31.ZHAO Weiwei,ZHANG Jianhua,SHANG Jingfu,et al.Power system large scale blackout emergency evaluation index system and its application[J].Automation of Electric Power Systems,2008,32(20):27-31.
[10]王宏,林振智,文福拴,等.计及负荷停电风险的电力应急服务的最优选址[J].电力自动化设备,2013,33(12):73-78.WANG Hong,LIN Zhenzhi,WEN Fushuan,et al.Optimal siting of power emergency service station considering outage risk of loads[J].Electric Power Automation Equipment,2013,33(12):73-78.
[11]梁博淼,王宏,林振智,等.电力系统应急服务多点最优选址规划[J].电力系统自动化,2014,38(18):40-45.DOI:10.7500/AEPS20131101007.LIANG Bomiao,WANG Hong,LIN Zhenzhi,et al.Optimal siting of power emergency multi-point service provisions[J].Automation of Electric Power Systems,2014,38(18):40-45.DOI:10.7500/AEPS20131101007.
[12]周莉梅,范明天,张祖平.基于重要用户的应急电源优化配置[J].电力系统自动化,2007,31(6):99-102.ZHOU Limei,FAN Mingtian,ZHANG Zuping.Optimal allocation of emergency power supplies for urban important customers[J].Automation of Electric Power Systems,2007,31(6):99-102.
[13]张爱国,郝建刚,唐志芳,等.考虑综合负荷重要性的移动应急电源容量优化分配[J].电网技术,2008,32(2):86-89.ZHANG Aiguo,HAO Jiangang,TANG Zhifang,et al.The allocation scheme of mobile emergency generator considering the loads importance[J].Power System Technology,2008,32(2):86-89.
[14]王宏,林振智,文福拴,等.城市移动应急电源的优化调度[J].电力系统自动化,2014,38(3):123-129.DOI:10.7500/AEPS20130220002.WANG Hong,LIN Zhenzhi,WEN Fushuan,et al.Optimal scheduling of urban mobile emergency power sources[J].Automation of Electric Power Systems,2014,38(3):123-129.DOI:10.7500/AEPS20130220002.
[15]倪程捷,房鑫炎,赵文恺,等.基于图论的移动应急电源孤岛划分及最优接入点搜索[J].电力系统自动化,2015,39(6):34-40.DOI:10.7500/AEPS20140626001.NI Chengjie,FANG Xinyan,ZHAO Wenkai,et al.Island partitioning and optimal connecting point search of mobile emergency power source based on graph theory[J].Automation of Electric Power Systems,2015,39(6):34-40.DOI:10.7500/AEPS20140626001.
[16]胡启洲,张卫华.区间数理论的研究及其应用[M].北京:科学出版社,2010.
[17]TAN Q,HUANG G H,CAI Y P.Radial interval chanceconstrained programming for agricultural non-point source water pollution control under uncertainty[J].Agricultural Water Management,2011,98(10):1595-1606.
[18]MOORE R E.Methods and applications of interval analysis[M].Philadelphia,USA:SIAM Press,1995.
[19]毛安家,熊超中,张粒子,等.基于改进Tobit模型的负荷停电损失估算方法[J].电力系统自动化,2010,34(9):29-33.MAO Anjia,XIONG Chaozhong,ZHANG Lizi,et al.A customer’s outage cost assessment approach based on the improved Tobit model[J].Automation of Electric Power Systems,2010,34(9):29-33.
[20]宋春丽,刘涤尘,吴军,等.基于差异化全寿命周期成本的电网规划经济性评估方法[J].电网技术,2013,37(7):1849-1855.SONG Chunli,LIU Dichen,WU Jun,et al.An economic assessment of power system planning based on differentiated life cycle cost[J].Power System Technology,2013,37(7):1849-1855.
[21]CHINNECK J W,RAMADAN K.Linear programming with interval coefficients[J].Journal of the Operational Research Society,2000,51(2):209-220.
[22]LI Mian,GABRIEL S A,SHIM Y,et al.Interval uncertaintybased robust optimization for convex and non-convex quadratic programs with applications in network infrastructure planning[J].Networks and Spatial Economics,2011,11(1):159-191.
[23]SOU K C,SANDBERG H,JOHANSSON K H.Computing critical k-tuples in power networks[J].IEEE Transactions on Power Systems,2012,27(3):1511-1520.