计及过程安全性的配电网重构开关顺序优化
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摘要
配电网重构过程应采用合理、可靠的开关操作顺序以避免对配电网的稳定运行产生冲击。采用改进的二进制粒子群算法求取配电网重构解集,对迭代过程中的无效粒子进行随机性的坐标修正,提升搜索效率;提出配电网重构实施过程合环、解环应满足的安全性约束,并应用戴维南等效模型计算合环冲击电流;提出用于求解计及过程安全性的配电网重构开关顺序的递归算法,搜索过程遵循贪心策略;针对递归过程中的无效中间解,以二进制编码方式记录,避免重复计算。IEEE 33节点系统、PG&E 69节点系统算例结果验证了所提方法的有效性。
Rational and reliable switch operation sequence should be adopted in the process of distribution network reconfiguration to avoid impact on the stable operation of distribution network. An improved binary particle swarm optimization algorithm is used to obtain the solution set of distribution network reconfiguration,and the coordinates of invalid particles in the iterative process are modified randomly to improve the search efficiency. The safety constraints should be satisfied during loop closing and unwinding in distribution network reconfiguration are proposed,and Thevenin equivalent model is applied to calculate the surge current due to closing loop. A recursive algorithm is proposed for solving the switch sequence of distribution network reconfiguration with the consideration of process safety,and the greedy strategy is followed in the search process. The invalid intermediate solutions in the recursive process are recorded with binary coding to avoid repeated calculation. Case results of IEEE 33-bus and PG&E 69-bus systems verify the effectiveness of the proposed method.
Rational and reliable switch operation sequence should be adopted in the process of distribution network reconfiguration to avoid impact on the stable operation of distribution network. An improved binary particle swarm optimization algorithm is used to obtain the solution set of distribution network reconfiguration,and the coordinates of invalid particles in the iterative process are modified randomly to improve the search efficiency. The safety constraints should be satisfied during loop closing and unwinding in distribution network reconfiguration are proposed,and Thevenin equivalent model is applied to calculate the surge current due to closing loop. A recursive algorithm is proposed for solving the switch sequence of distribution network reconfiguration with the consideration of process safety,and the greedy strategy is followed in the search process. The invalid intermediate solutions in the recursive process are recorded with binary coding to avoid repeated calculation. Case results of IEEE 33-bus and PG&E 69-bus systems verify the effectiveness of the proposed method.
引文
[1] BARAN M E,WU F F.Network reconfiguration in distribution systems for loss reduction and load balancing[J].IEEE Transactions on Power Delivery,1989,4(4):1401-1407.
[2] SARMA N D R,PRAKASA R K S.A new 0-1 integer programming method of feeder reconfiguration for loss minimization in distribution systems[J].Electric Power Systems Research,1995,33(2):125-131.
[3] 刘柏私,谢开贵,周家启.配电网重构的动态规划算法[J].中国电机工程学报,2005,25(9):29-34.LIU Bosi,XIE Kaigui,ZHOU Jiaqi.Electrical distribution networks reconfiguration using dynamic programming[J].Proceedings of the CSEE,2005,25(9):29-34.
[4] SHIRMOHAMMADI D,HONG H W.Reconfiguration of electric dis-tribution networks for resistive line losses reduction[J].IEEE Tran-sactions on Power Delivery,1989,4(2):1492-1498.
[5] 邓佑满,张伯明,相年德.配电网络重构的改进最优流模式算法[J].电网技术,1995,19(7):47-50.DENG Youman,ZHANG Boming,XIANG Niande.An improved optimal flow pattern algorithm for distribution network reconfiguration[J].Power System Technology,1995,19(7):47-50.
[6] 刘蔚,韩祯祥.基于最优流法和遗传算法的配电网重构[J].电网技术,2004,28(19):29-33.LIU Wei,HAN Zhenxiang.Distribution network reconfiguration ba-sed on optimal flow pattern algorithm and genetic algorithm[J].Power System Technology,2004,28(19):29-33.
[7] 毕鹏翔,刘健,张文元.配电网络重构的改进支路交换法[J].中国电机工程学报,2001,21(8):98-103.BI Pengxiang,LIU Jian,ZHANG Wenyuan.A refined branch exchan-ge algorithm for distribution networks reconfiguration[J].Procee-dings of the CSEE,2001,21(8):98-103.
[8] 张剑,何怡刚.基于无向图所有生成树的网络重构遗传算法[J].电力自动化设备,2017,37(5):136-141.ZHANG Jian,HE Yigang.Genetic algorithm based on all spanning trees of undirected graph for distribution network reconfiguration[J].Electric Power Automation Equipment,2017,37(5):136-141.
[9] 麻秀范,张粒子.基于十进制编码的配网重构遗传算法[J].电工技术学报,2004,19(10):65-69.MA Xiufan,ZHANG Lizi.Distribution network reconfiguration based on genetic algorithm using decimal encoding[J].Transactions of China Electrotechnical Society,2004,19(10):65-69.
[10] 余贻鑫,段刚.基于最短路算法和遗传算法的配电网络重构[J].中国电机工程学报,2000,20(9):44-49.YU Yixin,DUAN Gang.Shortest path algorithm and genetic algorithm based distribution system reconfiguration[J].Proceedings of the CSEE,2000,20(9):44-49.
[11] DE BRAZ H D M,DE BENEMAR A S.Distribution network reconfiguration using genetic algorithms with sequential encoding:subtractive and additive approaches[J].IEEE Transactions on Power Systems,2011,26(2):582-593.
[12] 蒙文川,邱家驹.基于免疫算法的配电网重构[J].中国电机工程学报,2006,26(17):25-29.MENG Wenchuan,QIU Jiaju.An artificial immune algorithm to distribution network reconfiguration[J].Proceedings of the CSEE,2006,26(17):25-29.
[13] 林济铿,王旭东,陈云山,等.基于可行解搜索和自适应免疫算法的配网重构[J].天津大学学报,2008,41(12):1505-1511.LIN Jikeng,WANG Xudong,CHEN Yunshan,et al.Distribution net-work reconfiguration based on feasible solution search and adaptive immune algorithm[J].Journal of Tianjin University,2008,41(12):1505-1511.
[14] 余建明,张凡.基于改进免疫遗传算法的配电网重构[J].电网技术,2009,33(19):100-105.YU Jianming,ZHANG Fan.Distribution network reconfiguration ba-sed on improved immune genetic algorithm[J].Power System Technology,2009,33(19):100-105.
[15] 李樊,刘天琪,江东林.采用改进免疫算法的多目标配电网重构[J].电网技术,2011,35(7):134-138.LI Fan,LIU Tianqi,JIANG Donglin.Distribution network reconfiguration with multi-objective based on improved immune algorithm[J].Power System Technology,2011,35(7):134-138.
[16] 许立雄,吕林,刘俊勇.基于改进粒子群优化算法的配电网络重构[J].电力系统自动化,2006,30(7):27-30.XU Lixiong,Lü Lin,LIU Junyong.Modified particle swarm optimization for reconfiguration of distribution network[J].Automation of Electric Power Systems,2006,30(7):27-30.
[17] 李振坤,陈星莺,余昆,等.配电网重构的混合粒子群算法[J].中国电机工程学报,2008,28(31):35-41.LI Zhenkun,CHEN Xingying,YU Kun,et al.Hybrid particle swarm optimization for distribution network reconfiguration[J].Procee-dings of the CSEE,2008,28(31):35-41.
[18] WU W C,TSAI M S.Application of enhanced integer coded particle swarm optimization for distribution system feeder reconfiguration[J].IEEE Transactions on Power Systems,2011,26(3):1591-1599.
[19] 刘健,石晓军,程红丽,等.配电网大面积断电供电恢复及开关操作顺序生成[J].电力系统自动化,2008,32(2):76-79,83.LIU Jian,SHI Xiaojun,CHENG Hongli,et al.Restoration for large area blackout of distribution network and switching operation sequence management[J].Automation of Electric Power Systems,2008,32(2):76-79,83.
[20] 马静,许东,王增平.基于加权理想点法的配网故障供电恢复策略[J].电力自动化设备,2014,34(2):61-67.MA Jing,XU Dong,WANG Zengping.Power restoration strategy ba-sed on weighted ideal point method for distribution network[J].Electric Power Automation Equipment,2014,34(2):61-67.
[21] 徐玉琴,张丽,王增平,等.基于多智能体遗传算法并考虑分布式电源的配电网大面积断电供电恢复算法[J].电工技术学报,2010,25(4):135-141.XU Yuqin,ZHANG Li,WANG Zengping,et al.Algorithm of service restoration for large area blackout in distribution network with distributed generators[J].Transactions of China Electrotechnicl Society,2010,25(4):135-141.
[22] 朱海南,刘玉田.考虑线路投入顺序的网架重构机组恢复多目标优化[J].电力系统自动化,2014,38(16):53-59.ZHU Hainan,LIU Yutian.Multi-objective optimization of unit restoration during network reconstruction considering line restoration sequence[J].Automation of Electric Power Systems,2014,38(16):53-59.
[23] 张璨,林振智,文福拴,等.基于后悔思想的网络重构两步策略[J].电力系统自动化,2013,37(8):46-52,75.ZHANG Can,LIN Zhenzhi,WEN Fushuan,et al.A two-stage stra-tegy for network reconfiguration based on concept of regret[J].Automation of Electric Power Systems,2013,37(8):46-52,75.
[24] 秦福欣,王建学,王秀丽.考虑输电元件损坏概率的电力网架时序恢复策略优化[J].电网技术,2017,41(1):137-145.QIN Fuxin,WANG Jianxue,WANG Xiuli.Time sequence restoration optimization strategy of network considering power components' damage probability[J].Power System Technology,2017,41(1):137-145.
[25] 甘国晓,王主丁,李瑞,等.配电网合环冲击电流计算方法及其简化计算公式[J].电力系统自动化,2014,38(20):115-120.GAN Guoxiao,WANG Zhuding,LI Rui,et al.Methods and simplified formulas for calculating surge currents from loop closing in distribution networks[J].Automation of Electric Power Systems,2014,38(20):115-120.
[26] 葛少云,李晓明.基于戴维南等值的配电网合环冲击电流计算[J].电力系统及其自动化学报,2007,19(6):124-127.GE Shaoyun,LI Xiaoming.Study on surge current due to closing loop in distribution network based on Thevenin's equivalent[J].Proceedings of the CSU-EPSA,2007,19(6):124-127.
[27] 刘健,孙泉,张小庆,等.配电网合环分析与合环条件判断[J].电力系统自动化,2014,38(11):130-135.LIU Jian,SUN Quan,ZHANG Xiaoqing,et al.Analysis on and criteria for loop closing operation for distribution grids[J].Automation of Electric Power Systems,2014,38(11):130-135.
[28] LEE R C T,TSENG S S,CHANG R C,等.算法设计与分析导论[M].王卫东,译.北京:机械工业出版社,2008:40-41.
[29] KENNEDY J,EBERHART R.Particle swarm optimization[C]//IEEE Conference on Neural Networks.Perth,Australia:[s.n.],1995:1942-1948.
[30] KENNEDY J,EBERHART R C.A discrete binary version of the particle swarm algorithm[C]//International Conference on System,Man and Cybernetics.Orlando,USA:[s.n.],1997:4104-4108.
[31] 张伯明.高等电力网络分析[M].北京:清华大学出版社,2007:35-36.
[32] 李光琦.电力系统暂态分析[M].北京:中国电力出版社,2007:15-16.
[2] SARMA N D R,PRAKASA R K S.A new 0-1 integer programming method of feeder reconfiguration for loss minimization in distribution systems[J].Electric Power Systems Research,1995,33(2):125-131.
[3] 刘柏私,谢开贵,周家启.配电网重构的动态规划算法[J].中国电机工程学报,2005,25(9):29-34.LIU Bosi,XIE Kaigui,ZHOU Jiaqi.Electrical distribution networks reconfiguration using dynamic programming[J].Proceedings of the CSEE,2005,25(9):29-34.
[4] SHIRMOHAMMADI D,HONG H W.Reconfiguration of electric dis-tribution networks for resistive line losses reduction[J].IEEE Tran-sactions on Power Delivery,1989,4(2):1492-1498.
[5] 邓佑满,张伯明,相年德.配电网络重构的改进最优流模式算法[J].电网技术,1995,19(7):47-50.DENG Youman,ZHANG Boming,XIANG Niande.An improved optimal flow pattern algorithm for distribution network reconfiguration[J].Power System Technology,1995,19(7):47-50.
[6] 刘蔚,韩祯祥.基于最优流法和遗传算法的配电网重构[J].电网技术,2004,28(19):29-33.LIU Wei,HAN Zhenxiang.Distribution network reconfiguration ba-sed on optimal flow pattern algorithm and genetic algorithm[J].Power System Technology,2004,28(19):29-33.
[7] 毕鹏翔,刘健,张文元.配电网络重构的改进支路交换法[J].中国电机工程学报,2001,21(8):98-103.BI Pengxiang,LIU Jian,ZHANG Wenyuan.A refined branch exchan-ge algorithm for distribution networks reconfiguration[J].Procee-dings of the CSEE,2001,21(8):98-103.
[8] 张剑,何怡刚.基于无向图所有生成树的网络重构遗传算法[J].电力自动化设备,2017,37(5):136-141.ZHANG Jian,HE Yigang.Genetic algorithm based on all spanning trees of undirected graph for distribution network reconfiguration[J].Electric Power Automation Equipment,2017,37(5):136-141.
[9] 麻秀范,张粒子.基于十进制编码的配网重构遗传算法[J].电工技术学报,2004,19(10):65-69.MA Xiufan,ZHANG Lizi.Distribution network reconfiguration based on genetic algorithm using decimal encoding[J].Transactions of China Electrotechnical Society,2004,19(10):65-69.
[10] 余贻鑫,段刚.基于最短路算法和遗传算法的配电网络重构[J].中国电机工程学报,2000,20(9):44-49.YU Yixin,DUAN Gang.Shortest path algorithm and genetic algorithm based distribution system reconfiguration[J].Proceedings of the CSEE,2000,20(9):44-49.
[11] DE BRAZ H D M,DE BENEMAR A S.Distribution network reconfiguration using genetic algorithms with sequential encoding:subtractive and additive approaches[J].IEEE Transactions on Power Systems,2011,26(2):582-593.
[12] 蒙文川,邱家驹.基于免疫算法的配电网重构[J].中国电机工程学报,2006,26(17):25-29.MENG Wenchuan,QIU Jiaju.An artificial immune algorithm to distribution network reconfiguration[J].Proceedings of the CSEE,2006,26(17):25-29.
[13] 林济铿,王旭东,陈云山,等.基于可行解搜索和自适应免疫算法的配网重构[J].天津大学学报,2008,41(12):1505-1511.LIN Jikeng,WANG Xudong,CHEN Yunshan,et al.Distribution net-work reconfiguration based on feasible solution search and adaptive immune algorithm[J].Journal of Tianjin University,2008,41(12):1505-1511.
[14] 余建明,张凡.基于改进免疫遗传算法的配电网重构[J].电网技术,2009,33(19):100-105.YU Jianming,ZHANG Fan.Distribution network reconfiguration ba-sed on improved immune genetic algorithm[J].Power System Technology,2009,33(19):100-105.
[15] 李樊,刘天琪,江东林.采用改进免疫算法的多目标配电网重构[J].电网技术,2011,35(7):134-138.LI Fan,LIU Tianqi,JIANG Donglin.Distribution network reconfiguration with multi-objective based on improved immune algorithm[J].Power System Technology,2011,35(7):134-138.
[16] 许立雄,吕林,刘俊勇.基于改进粒子群优化算法的配电网络重构[J].电力系统自动化,2006,30(7):27-30.XU Lixiong,Lü Lin,LIU Junyong.Modified particle swarm optimization for reconfiguration of distribution network[J].Automation of Electric Power Systems,2006,30(7):27-30.
[17] 李振坤,陈星莺,余昆,等.配电网重构的混合粒子群算法[J].中国电机工程学报,2008,28(31):35-41.LI Zhenkun,CHEN Xingying,YU Kun,et al.Hybrid particle swarm optimization for distribution network reconfiguration[J].Procee-dings of the CSEE,2008,28(31):35-41.
[18] WU W C,TSAI M S.Application of enhanced integer coded particle swarm optimization for distribution system feeder reconfiguration[J].IEEE Transactions on Power Systems,2011,26(3):1591-1599.
[19] 刘健,石晓军,程红丽,等.配电网大面积断电供电恢复及开关操作顺序生成[J].电力系统自动化,2008,32(2):76-79,83.LIU Jian,SHI Xiaojun,CHENG Hongli,et al.Restoration for large area blackout of distribution network and switching operation sequence management[J].Automation of Electric Power Systems,2008,32(2):76-79,83.
[20] 马静,许东,王增平.基于加权理想点法的配网故障供电恢复策略[J].电力自动化设备,2014,34(2):61-67.MA Jing,XU Dong,WANG Zengping.Power restoration strategy ba-sed on weighted ideal point method for distribution network[J].Electric Power Automation Equipment,2014,34(2):61-67.
[21] 徐玉琴,张丽,王增平,等.基于多智能体遗传算法并考虑分布式电源的配电网大面积断电供电恢复算法[J].电工技术学报,2010,25(4):135-141.XU Yuqin,ZHANG Li,WANG Zengping,et al.Algorithm of service restoration for large area blackout in distribution network with distributed generators[J].Transactions of China Electrotechnicl Society,2010,25(4):135-141.
[22] 朱海南,刘玉田.考虑线路投入顺序的网架重构机组恢复多目标优化[J].电力系统自动化,2014,38(16):53-59.ZHU Hainan,LIU Yutian.Multi-objective optimization of unit restoration during network reconstruction considering line restoration sequence[J].Automation of Electric Power Systems,2014,38(16):53-59.
[23] 张璨,林振智,文福拴,等.基于后悔思想的网络重构两步策略[J].电力系统自动化,2013,37(8):46-52,75.ZHANG Can,LIN Zhenzhi,WEN Fushuan,et al.A two-stage stra-tegy for network reconfiguration based on concept of regret[J].Automation of Electric Power Systems,2013,37(8):46-52,75.
[24] 秦福欣,王建学,王秀丽.考虑输电元件损坏概率的电力网架时序恢复策略优化[J].电网技术,2017,41(1):137-145.QIN Fuxin,WANG Jianxue,WANG Xiuli.Time sequence restoration optimization strategy of network considering power components' damage probability[J].Power System Technology,2017,41(1):137-145.
[25] 甘国晓,王主丁,李瑞,等.配电网合环冲击电流计算方法及其简化计算公式[J].电力系统自动化,2014,38(20):115-120.GAN Guoxiao,WANG Zhuding,LI Rui,et al.Methods and simplified formulas for calculating surge currents from loop closing in distribution networks[J].Automation of Electric Power Systems,2014,38(20):115-120.
[26] 葛少云,李晓明.基于戴维南等值的配电网合环冲击电流计算[J].电力系统及其自动化学报,2007,19(6):124-127.GE Shaoyun,LI Xiaoming.Study on surge current due to closing loop in distribution network based on Thevenin's equivalent[J].Proceedings of the CSU-EPSA,2007,19(6):124-127.
[27] 刘健,孙泉,张小庆,等.配电网合环分析与合环条件判断[J].电力系统自动化,2014,38(11):130-135.LIU Jian,SUN Quan,ZHANG Xiaoqing,et al.Analysis on and criteria for loop closing operation for distribution grids[J].Automation of Electric Power Systems,2014,38(11):130-135.
[28] LEE R C T,TSENG S S,CHANG R C,等.算法设计与分析导论[M].王卫东,译.北京:机械工业出版社,2008:40-41.
[29] KENNEDY J,EBERHART R.Particle swarm optimization[C]//IEEE Conference on Neural Networks.Perth,Australia:[s.n.],1995:1942-1948.
[30] KENNEDY J,EBERHART R C.A discrete binary version of the particle swarm algorithm[C]//International Conference on System,Man and Cybernetics.Orlando,USA:[s.n.],1997:4104-4108.
[31] 张伯明.高等电力网络分析[M].北京:清华大学出版社,2007:35-36.
[32] 李光琦.电力系统暂态分析[M].北京:中国电力出版社,2007:15-16.
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