城市输电网最大供电能力改进Benders算法
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摘要
考虑静态电压稳定约束的城市输电网最大供电能力(total supply capability,TSC)问题是一类大规模、高维度、多约束、非凸、非线性优化问题。为了快速、准确地求解TSC问题,该文应用Benders分解法并对其进行改进,提出了"多级分层,逐批选取,变速反馈"的策略。首先,将子问题按照越限情况分为若干层,层级越高,子问题越限故障越严重;其次,在最高层级中选取一批有代表性的子问题形成反馈集,最后,将反馈集中子问题Benders割约束进行变速处理后反馈给主问题。该文对MATPOWER4节点、IEEE30节点、IEEE118节点算例进行了仿真计算,结果表明该文策略相比现有文献策略,在计算结果和计算速度方面均有提高。
The total supplying capability(TSC) problem with system voltage stability constraints of city transmission network is a large-scale, high-dimensional, multi-constrained,non-convex and nonlinear problem. To solve the TSC problem rapidly and exactly, an improved Benders decomposition method was proposed, applying the proposed "multi-layer stratify, batch filtering, shifting feedback" strategy. Firstly, the subproblems were classified into four layers. The higher the level, the more serious the subproblem was. Secondly, a feedback set consisting of a batch of representative subproblems were selected from the highest layer. Finally, the shifted Benders cuts were generated and added to the master problem. The MATPOWER 4-bus system, IEEE 30-bus system and 118-bus system were simulated, and the results show the proposed method outperforms the previous methods on both the solution quality and solving time.
The total supplying capability(TSC) problem with system voltage stability constraints of city transmission network is a large-scale, high-dimensional, multi-constrained,non-convex and nonlinear problem. To solve the TSC problem rapidly and exactly, an improved Benders decomposition method was proposed, applying the proposed "multi-layer stratify, batch filtering, shifting feedback" strategy. Firstly, the subproblems were classified into four layers. The higher the level, the more serious the subproblem was. Secondly, a feedback set consisting of a batch of representative subproblems were selected from the highest layer. Finally, the shifted Benders cuts were generated and added to the master problem. The MATPOWER 4-bus system, IEEE 30-bus system and 118-bus system were simulated, and the results show the proposed method outperforms the previous methods on both the solution quality and solving time.
引文
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[21]默哈莫德·夏班,刘皓明,李卫星,等.静态安全约束下基于Benders分解算法的可用传输容量计算[J].中国电机工程学报,2003,23(8):7-11.Mohamed S,Liu Haoming,Li Weixing,et al.ATCcalculation with static security constraints using Benders decomposition[J].Proceedings of the CSEE,2003,23(8):7-11(in Chinese).
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[23]邹晓松,罗先觉.多预想事故静态电压稳定预防控制阻塞管理方法[J].电网技术,2010,34(2):143-148.Zou Xiaosong,Luo Xianjue.A congestion management method based on preventive controls for voltage stability considering multi contingency[J].Power System Technology,2010,34(2):143-148(in Chinese).
[24]潘雄,徐国禹.基于最优潮流并计及静态电压稳定性约束的区域间可用输电能力计算[J].中国电机工程学报,2004,24(12):86-91.Pan Xiong,Xu Guoyu.OPF based ATC calculation with static voltage stability constraints[J].Proceedings of the CSEE,2004,24(12):86-91(in Chinese).
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[26]李杰,罗滇生,李帅虎,等.Benders算法在发电机无功储备管理中的应用[J].电力系统及其自动化学报,2016,28(7):83-88.Li Jie,Luo Diansheng,Li Shuaihu,et al.Application of Benders algorithm to reactive power reserve management of generators[J].Proceedings of the CSU-EPSA,2016,28(7):83-88(in Chinese).
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[2]王成山,王兴刚,魏炜.输电系统可用输电能力研究[J].电力系统及其自动化学报,2005,17(5):42-49.Wang Chengshan,Wang Xinggang,Wei Wei.Study on available transfer capability of power systems[J].Proceeding of the CUS-EPSA,2005,17(5):42-49(in Chinese).
[3]张曦,刘友波,吕林,等.计及高压配电网负荷转供的城市220 kV片区电网供电能力分析[J].电网技术,2017,41(5):1612-1618.Zhang Xi,Liu Youbo,LüLin,et al.Total supply capability analysis of urban 220 kV area power system considering load transfer capability of HV distribution network[J].Power System Technology,2017,41(5):1612-1618(in Chinese).
[4]张曦,吕林,金勇,等.基于高压配电网变电单元分组重构的城市电网输电阻塞管控模型及算法[J].中国电机工程学报,2016,36(20):5403-5413.Zhang Xi,LüLin,Jin Yong,et al.Congestion mitigation model and algorithm for urban power grids considering reconfigurability of high-voltage distribution transformer unit groups[J].Proceedings of the CSEE,2016,36(20):5403-5413(in Chinese).
[5]Luo Fengzhang,Wang Chengshan,Xiao Jun,et al.Rapid evaluation method for power supply capability of urban distribution system based on N-1 contingency analysis of main-transformers[J].International Journal of Electrical Power&Energy Systems,2010,32(10):1063-1068.
[6]葛少云,韩俊,刘洪,等.计及主变过载和联络容量约束的配电系统供电能力计算方法[J].中国电机工程学报,2011,31(25):97-103.Ge Shaoyun,Han Jun,Liu Hong,et al.Power supply capability determination considering constraints of transformer overloading and tie-line capacity[J].Proceedings of the CSEE,2011,31(25):97-103(in Chinese).
[7]葛少云,赵浛,雷显荣,等.高中压配电系统供电能力评估与分析[J].天津大学学报:自然科学与工程技术版,2017,50(7):739-747.Ge Shaoyun,Zhao Han,Lei Xianrong,et al.Evaluation and analysis of load supply capability of high-medium voltage distribution system[J].Journal of Tianjin University:Science and Technology,2017,50(7):739-747(in Chinese).
[8]肖峻,刘世嵩,李振生,等.基于潮流计算的配电网最大供电能力模型[J].中国电机工程学报,2014,34(31):5516-5524.Xiao Jun,Liu Shisong,Li Zhensheng,et al.Model of total supply capability for distribution network based on power flow calculation[J].Proceedings of the CSEE,2014,34(31):5516-5524(in Chinese).
[9]王成山,李慧聪,魏炜,等.考虑电压稳定性约束的输电能力综合计算[J].电力自动化设备,2004,24(1):9-13.Wang Chengshan,Li Huicong,Wei Wei,et al.Integrative computation of transfer capability with voltage stability constrain[J].Electric Power Automation Equipment,2004,24(1):9-13.
[10]罗钢,石东源,蔡德福,等.计及相关性的含风电场电力系统概率可用输电能力快速计算[J].中国电机工程学报,2014,34(7):1024-1032.Luo Gang,Shi Dongyuan,Cai Defu,et al.Fast calculation of probabilistic available transfer capability considering correlation in wind power integrated systems[J].Proceedings of the CSEE,2014,34(7):1024-1032(in Chinese).
[11]卢志刚,陈伟坤,张晓辉,等.城市电网输配全局最大供电能力分析[J].电网技术,2015,39(6):1623-1630.Lu Zhigang,Chen Weikun,Zhang Xiaohui,et al.Global maximum power supply capability analysis of city power grid[J].Power System Technology,2015,39(6):1623-1630(in Chinese).
[12]刘皓明,倪以信,吴军基,等.计算电网可用输电能力的方法述评[J].继电器,2003,31(10):45-50.Liu Haoming,Ni Yixin,Wu Junji,et al.Review of available transfer capability calculation in electricity market[J].Relay,2003,31(10):45-50(in Chinese).
[13]王成山,王兴刚.考虑静态电压稳定约束并计及负荷和发电机出力不确定性因素的概率最大输电能力快速计算[J].中国电机工程学报,2006,26(16):46-51.Wang Chengshan,Wang Xinggang.Fast calculation of probabilistic total transfer capability considering static voltage stability constraints and the uncertainties of load and generator output[J].Proceedings of the CSEE,2006,26(16):46-51(in Chinese).
[14]王成山,王兴刚,张沛.考虑静态电压稳定约束并计及设备故障概率的TTC快速计算[J].中国电机工程学报,2006,26(19):7-12.Wang Chengshan,Wang Xinggang,Zhang Pei.Fast calculation of probabilistic total transfer capability considering static voltage stability constraints and the probability of device contingencies[J].Proceedings of the CSEE,2006,26(19):7-12(in Chinese).
[15]Aman M M,Jasmon G B,Bakar A H A,et al.Optimum network reconfiguration based on maximization of system loadability using continuation power flow theorem[J].International Journal of Electrical Power&Energy Systems,2014,54:123-133.
[16]王成山,魏伟.一种改进的步长控制连续性潮流计算方法[J].电工技术学报,2004,19(2):58-63.Wang Chengshan,Wei Wei.An improved continuation method with controlled step size[J].Transactions of China Electrotechnical Society,2004,19(2):58-63(in Chinese).
[17]汪峰,白晓民.基于最优潮流方法的传输容量计算研究[J].中国电机工程学报,2002,22(11):35-40.Wang Feng,Bai Xiaomin.OPF based transfer capability calculation[J].Proceedings of the CSEE,2002,22(11):35-40(in Chinese).
[18]王成山,魏炜.联营体模式下考虑静态电压稳定性约束的阻塞管理[J].电工技术学报,2005,20(3):53-57.Wang Chengshan,Wei Wei.Congestion management with voltage stability considered in pool power market[J].Transactions of China Electrotechnical Society,2005,20(3):53-57(in Chinese).
[19]晏鸣宇,何宇斌,文劲宇,等.考虑柔性交流输电系统设备控制的校正型安全约束最优潮流[J].电力系统自动化,2017,41(12):63-69.Yan Mingyu,He Yubin,Wen Jinyu.Corrective security-constrained optimal power flow with control of flexible AC transmission system devices[J].Automation of Electric Power Systems,2017,41(12):63-69(in Chinese).
[20]张立志,赵冬梅.考虑FACTS配置的电网输电能力计算[J].电网技术,2007,31(7):26-31.Zhang Lizhi,Zhao Dongmei.Calculation of power network available transfer capability considering optimal mounted positions of FACTS devices[J].Power System Technology,2007,31(7):26-31(in Chinese).
[21]默哈莫德·夏班,刘皓明,李卫星,等.静态安全约束下基于Benders分解算法的可用传输容量计算[J].中国电机工程学报,2003,23(8):7-11.Mohamed S,Liu Haoming,Li Weixing,et al.ATCcalculation with static security constraints using Benders decomposition[J].Proceedings of the CSEE,2003,23(8):7-11(in Chinese).
[22]荆朝霞,王宏益,吴青华.220 kV电网供电能力计算的改进Benders分解法[J].中国电机工程学报,2017,37(17):4893-4900.Jing Zhaoxia,Wang Hongyi,Wu Qinghua.Modified Benders decomposition method for total supplying capability calculation of 220kV power grid[J].Proceedings of the CSEE,2017,37(17):4893-4900(in Chinese).
[23]邹晓松,罗先觉.多预想事故静态电压稳定预防控制阻塞管理方法[J].电网技术,2010,34(2):143-148.Zou Xiaosong,Luo Xianjue.A congestion management method based on preventive controls for voltage stability considering multi contingency[J].Power System Technology,2010,34(2):143-148(in Chinese).
[24]潘雄,徐国禹.基于最优潮流并计及静态电压稳定性约束的区域间可用输电能力计算[J].中国电机工程学报,2004,24(12):86-91.Pan Xiong,Xu Guoyu.OPF based ATC calculation with static voltage stability constraints[J].Proceedings of the CSEE,2004,24(12):86-91(in Chinese).
[25]Geoffrion A M.Generalized Benders decomposition[J].Journal of Optimization Theory and Applications,1972,10(4):237-260.
[26]李杰,罗滇生,李帅虎,等.Benders算法在发电机无功储备管理中的应用[J].电力系统及其自动化学报,2016,28(7):83-88.Li Jie,Luo Diansheng,Li Shuaihu,et al.Application of Benders algorithm to reactive power reserve management of generators[J].Proceedings of the CSU-EPSA,2016,28(7):83-88(in Chinese).
[27]王斌,夏叶,夏清,等.基于Benders分解法的交直流互联电网安全约束经济调度[J].中国电机工程学报,2016,36(6):1588-1595.Wang Bin,Xia Ye,Xia Qing,et al.Security-constrained economic dispatch with AC/DC interconnection system based on Benders decomposition method[J].Proceedings of the CSEE,2016,36(6):1588-1595(in Chinese).
[28]钟世民,韩学山,刘道伟,等.计及校正控制的安全约束最优潮流的奔德斯分解算法[J].中国电机工程学报,2011,31(1):65-71.Zhong Shimin,Han Xueshan,Liu Daowei,et al.Benders decomposition algorithm for corrective securityconstrained optimal power flow[J].Proceedings of the CSEE,2011,31(1):65-71(in Chinese).
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