含抽水蓄能电网安全约束机组组合问题的混合整数线性规划算法
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摘要
抽水蓄能机组的投运对电网发电调度计划的制定具有很大影响,建立了含抽水蓄能机组电网的安全约束机组组合模型。以考虑了抽水蓄能机组启停费用的所有机组总运行费用为目标函数,根据抽水蓄能机组的不同运行工况给出旋转备用容量的解析表达式,同时在系统功率平衡约束中考虑了网络损耗的影响,并考虑了抽水蓄能机组的运行调度约束及网络安全约束。为了保证模型求解的可靠性和提高模型求解的计算效率,将目标函数进行分段线性化,并根据抽水蓄能机组的运行特点将其旋转备用容量约束等价转化为线性表达式。同时采用一种动态分段线性化方法近似逼近网络损耗,从而将机组组合模型转化为混合整数线性规划模型,并采用成熟的数学优化求解器CPLEX进行求解。对某实际23机306节点电网算例的计算结果表明,所提出的混合整数线性规划调度模型的网损逼近效果合理正确,算法求解速度快,具有较好的工程实用价值。
The operation of Pumped Storage Hydro(PSH) units has great influence on the compilation of generation scheduling of power grid, a security constrained unit commitment model of power grid with PSH units is established. In the model, total operation cost of all units which includes the start up/stop down cost of PSH units is considered as the objective function, an analytical expression of the spinning reserve capacity of PSH units is given according to different operation conditions, and the network loss is considered in the power balance constraint of the system, the operation scheduling constraints of PSH units and the network security constraints are also considered. In order to ensure the reliability and improve the calculation efficiency of model solution, the objective function is piecewise linearized and the spinning reserve capacity constraint of PSH units is equivalently transformed into a linear expression according to their operation characteristics. Meanwhile, a dynamic piecewise linearization method is adopted to approximate the network loss, so that the unit commitment model is transformed into a Mixed Integer Linear Programming(MILP) model, which can be solved by using the mature mathematical optimization solver CPLEX. Test results on an actual power grid of 23 units and 306 buses demonstrate that the approximation effect of network loss in the proposed MILP model is reasonable and correct, and the proposed algorithm is fast and has good practical value in engineering.
The operation of Pumped Storage Hydro(PSH) units has great influence on the compilation of generation scheduling of power grid, a security constrained unit commitment model of power grid with PSH units is established. In the model, total operation cost of all units which includes the start up/stop down cost of PSH units is considered as the objective function, an analytical expression of the spinning reserve capacity of PSH units is given according to different operation conditions, and the network loss is considered in the power balance constraint of the system, the operation scheduling constraints of PSH units and the network security constraints are also considered. In order to ensure the reliability and improve the calculation efficiency of model solution, the objective function is piecewise linearized and the spinning reserve capacity constraint of PSH units is equivalently transformed into a linear expression according to their operation characteristics. Meanwhile, a dynamic piecewise linearization method is adopted to approximate the network loss, so that the unit commitment model is transformed into a Mixed Integer Linear Programming(MILP) model, which can be solved by using the mature mathematical optimization solver CPLEX. Test results on an actual power grid of 23 units and 306 buses demonstrate that the approximation effect of network loss in the proposed MILP model is reasonable and correct, and the proposed algorithm is fast and has good practical value in engineering.
引文
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[5]李晓磊,周京阳,于尔铿,等.基于动态搜索线性混合整数法的机组组合新算法[J].电力系统自动化,2008,32(21):18-21.LI Xiaolei,ZHOU Jingyang,YU Erkeng,et al.Linear mixed integer programming algorithm for unit commitment based on dynamic search[J].Automation of Electric Power Systems,2008,32(21):18-21.
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[10]吕翔,刘国静,周莹.含抽水蓄能的风水火联合机组组合研究[J].电力系统保护与控制,2017,45(12):35-43.LüXiang,LIU Guojing,ZHOU Ying.Research on combined unit commitment of wind power-hydro power-t hermal power for the power system with pumped hydro storage[J].Power System Protection and Control,2017,45(12):35-43.
[11]徐飞,陈磊,金和平,等.抽水蓄能与风电的联合优化运行建模及应用分析[J].电力系统自动化,2013,37(1):149-154.XU Fei,CHEN Lei,JIN Heping,et al.Modeling and application analysis of optimal joint operational of pumped storage power station and wind power[J].Automation of Electric Power Systems,2013,37(1):149-154.
[12]黄庶,林舜江,刘明波.含风电场和抽水蓄能电站的多目标安全约束动态优化调度[J].中国电机工程学报,2016,36(1):112-121.HUANG Shu,LIN Shunjiang,LIU Mingbo.Multiobjective security constrained dynamic optimal dispatch with wind farms and pumped storage stations[J].Proceedings of the CSEE,2016,36(1):112-121.
[13]全然,张健,史志鸿.求解含风电场机组组合问题的透视割平面邻域搜索算法[J].电力系统保护与控制,2017,45(14):26-31.QUAN Ran,ZHANG Jian,SHI Zhihong.A perspective cut neighborhood search method for unit commitment with volatile wind power[J].Power System Protection and Control,2017,45(14):26-31.
[14]瞿寒冰,朱英刚,尹茂林,等.计及风电并网的机组组合方法研究[J].电力系统保护与控制,2017,45(16):95-98.QU Hanbing,ZHU Yinggang,YIN Maolin,et al.Study on the unit commitment considering wind power paralleling in the power system[J].Power System Protection and Control,2017,45(16):95-98.
[15]AI Qian,FAN Songli,PIAO Longjian.Optimal scheduling strategy for virtual power plants based on credibility theory[J].Protection and Control of Modern Power Systems,2016,1(1):48-55.DOI:10.1186/s41601-016-0017-x.
[16]娄素华,余欣梅,熊信艮,等.电力系统机组启停优化问题的改进DPSO算法[J].中国电机工程学报,2005,25(8):30-35.LOU Suhua,YU Xinmei,XIONG Xinyin,et al.Unit commitment using improved discrete particle swarm optimization algorithm[J].Proceedings of the CSEE,2005,25(8):30-35.
[17]吴金华,吴耀武,熊信艮,等.机组优化组合问题的随机tabu搜索算法[J].电网技术,2003,27(10):35-38.WU Jinhua,WU Yaowu,XIONG Xinyin,et al.Random tabu search with simulated annealing approach for the unit commitment problem[J].Power System Technology,2003,27(10):35-38.
[18]ALGUACIL N,CONEJO A J.Multiperiod optimal power flow using Benders decomposition[J].IEEETransactions on Power Systems,2000,15(1):196-201.
[19]MOTTO A L,GALIANA F D.Network-constrained multiperiod auction for a pool-based electricity market[J].IEEE Transactions on Power Systems,2002,17(3):646-653.
[20]DOS SANTOS T N,DINIZ A L.A dynamic piecewise linear model for DC transmission losses in optimal scheduling problems[J].IEEE Transactions on Power Systems,2011,26(2):508-519.
[21]MA H L,SHAHIDEHPOUR S M.Transmissionconstrained unit commitment based on Benders decomposition[J].International Journal of Electrical Power&Energy Systems,1998,20(4):287-294.
[22]赵燃,康重庆,刘梅,等.面向节能发电调度的母线负荷预测平台[J].中国电力,2009,42(6):32-36.ZHAO Ran,KANG Chongqing,LIU Mei,et al.The platform of bus load forecasting for energy-conservation based generation dispatching[J].Electric Power,2009,42(6):32-36.
[23]谢毓广.计及网络安全约束和风力发电的机组组合问题的研究[D].上海:上海交通大学,2011.XIE Yuguang.Research on the unit commitment problem with security-constraints and wind power[D].Shanghai:Shanghai Jiao Tong University,2011.
[2]杨明,杨毅刚.用大系统分解与协调理论研究电力系统的最优机组组合[J].中国电机工程学报,1989,9(3):51-58.YANG Ming,YANG Yigang.Using large scale system decomposition and coordination theory to research optimal unit commitment of large electric power system[J].Proceedings of the CSEE,1989,9(3):51-58.
[3]ZHAI Qiaozhu,GUAN Xiaohong,CUI Jian.Unit commitment with identical units successive subproblem solving method based on Lagrangian relaxation[J].IEEETransactions on Power Systems,2002,17(4):1250-1257.
[4]FAN J Y,ZHANG L,MCDONALD J D.Enhanced techniques on sequential unit commitment with interchange transactions[J].IEEE Transactions on Power Systems,1996,11(1):1131-1138.
[5]李晓磊,周京阳,于尔铿,等.基于动态搜索线性混合整数法的机组组合新算法[J].电力系统自动化,2008,32(21):18-21.LI Xiaolei,ZHOU Jingyang,YU Erkeng,et al.Linear mixed integer programming algorithm for unit commitment based on dynamic search[J].Automation of Electric Power Systems,2008,32(21):18-21.
[6]CARRIóN M,JOSéM.A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem[J].IEEE Transactions on Power Systems,2006,21(3):1371-1378.
[7]KHODAYAR M E,ABREU L,SHAHIDEHPOUR M.Transmission-constrained intrahour coordination of wind and pumped-storage hydro units[J].IET Generation,Transmission,and Distribution,2013,7(7):755-765.
[8]JIANG Ruiwei,WANG Jianhui,GUAN Yongpei.Robust unit commitment with wind power and pumped storage hydro[J].IEEE Transactions on Power Systems,2012,27(2):800-810.
[9]胡泽春,丁华杰,孔涛.风电-抽水蓄能联合日运行优化调度模型[J].电力系统自动化,2012,36(2):36-41.HU Zechun,DING Huajie,KONG Tao.A joint daily operational optimization model for wind power and pumped-storage plant[J].Automation of Electric Power Systems,2012,36(2):36-41.
[10]吕翔,刘国静,周莹.含抽水蓄能的风水火联合机组组合研究[J].电力系统保护与控制,2017,45(12):35-43.LüXiang,LIU Guojing,ZHOU Ying.Research on combined unit commitment of wind power-hydro power-t hermal power for the power system with pumped hydro storage[J].Power System Protection and Control,2017,45(12):35-43.
[11]徐飞,陈磊,金和平,等.抽水蓄能与风电的联合优化运行建模及应用分析[J].电力系统自动化,2013,37(1):149-154.XU Fei,CHEN Lei,JIN Heping,et al.Modeling and application analysis of optimal joint operational of pumped storage power station and wind power[J].Automation of Electric Power Systems,2013,37(1):149-154.
[12]黄庶,林舜江,刘明波.含风电场和抽水蓄能电站的多目标安全约束动态优化调度[J].中国电机工程学报,2016,36(1):112-121.HUANG Shu,LIN Shunjiang,LIU Mingbo.Multiobjective security constrained dynamic optimal dispatch with wind farms and pumped storage stations[J].Proceedings of the CSEE,2016,36(1):112-121.
[13]全然,张健,史志鸿.求解含风电场机组组合问题的透视割平面邻域搜索算法[J].电力系统保护与控制,2017,45(14):26-31.QUAN Ran,ZHANG Jian,SHI Zhihong.A perspective cut neighborhood search method for unit commitment with volatile wind power[J].Power System Protection and Control,2017,45(14):26-31.
[14]瞿寒冰,朱英刚,尹茂林,等.计及风电并网的机组组合方法研究[J].电力系统保护与控制,2017,45(16):95-98.QU Hanbing,ZHU Yinggang,YIN Maolin,et al.Study on the unit commitment considering wind power paralleling in the power system[J].Power System Protection and Control,2017,45(16):95-98.
[15]AI Qian,FAN Songli,PIAO Longjian.Optimal scheduling strategy for virtual power plants based on credibility theory[J].Protection and Control of Modern Power Systems,2016,1(1):48-55.DOI:10.1186/s41601-016-0017-x.
[16]娄素华,余欣梅,熊信艮,等.电力系统机组启停优化问题的改进DPSO算法[J].中国电机工程学报,2005,25(8):30-35.LOU Suhua,YU Xinmei,XIONG Xinyin,et al.Unit commitment using improved discrete particle swarm optimization algorithm[J].Proceedings of the CSEE,2005,25(8):30-35.
[17]吴金华,吴耀武,熊信艮,等.机组优化组合问题的随机tabu搜索算法[J].电网技术,2003,27(10):35-38.WU Jinhua,WU Yaowu,XIONG Xinyin,et al.Random tabu search with simulated annealing approach for the unit commitment problem[J].Power System Technology,2003,27(10):35-38.
[18]ALGUACIL N,CONEJO A J.Multiperiod optimal power flow using Benders decomposition[J].IEEETransactions on Power Systems,2000,15(1):196-201.
[19]MOTTO A L,GALIANA F D.Network-constrained multiperiod auction for a pool-based electricity market[J].IEEE Transactions on Power Systems,2002,17(3):646-653.
[20]DOS SANTOS T N,DINIZ A L.A dynamic piecewise linear model for DC transmission losses in optimal scheduling problems[J].IEEE Transactions on Power Systems,2011,26(2):508-519.
[21]MA H L,SHAHIDEHPOUR S M.Transmissionconstrained unit commitment based on Benders decomposition[J].International Journal of Electrical Power&Energy Systems,1998,20(4):287-294.
[22]赵燃,康重庆,刘梅,等.面向节能发电调度的母线负荷预测平台[J].中国电力,2009,42(6):32-36.ZHAO Ran,KANG Chongqing,LIU Mei,et al.The platform of bus load forecasting for energy-conservation based generation dispatching[J].Electric Power,2009,42(6):32-36.
[23]谢毓广.计及网络安全约束和风力发电的机组组合问题的研究[D].上海:上海交通大学,2011.XIE Yuguang.Research on the unit commitment problem with security-constraints and wind power[D].Shanghai:Shanghai Jiao Tong University,2011.