高水电比重系统电力电量平衡混合整数二次规划模型及算法研究
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摘要
清洁能源战略的提出凸显了高水电比重系统电力电量平衡以及调度优化方案研究的重要性。该文基于水文特征和水电站发电特性拟合出水电转换曲线的分段线性函数;并通过引入0-1辅助变量,计及水与电的相互关联作用、水与电各自在地域上与时间上的耦合关系、水电与火电的协调调峰能力以及水电机组的振荡区间等约束,提出互斥技术和权值技术构建含六类0-1变量的混合整数二次规划(mixed integer quadratic programming,MIQP)模型。最后提出动态启发式算法(dynamic heuristic algorithm,DHA)和有效集割平面算法(active set cutting plane method,ASCPM),借助混合整数规划求解器对某测试系统进行验证,结果表明,所提模型及算法能够有效地处理高水电比重系统电力电量平衡问题并获得机组调度优化方案。
Clean energy strategy presented highlights the importance of the system's power balance and scheduling optimization studies with high proportion of hydropower. Based on the hydrological characteristic and hydropower generation characteristic, hydropower conversion curve's piecewise linear function was fit. By introducing auxiliary 0-1 variables, this paper proposed two methods, that were repulsion technique and right valuation technique, to build a mixed integer quadratic programming(MIQP) model containing six kinds of 0-1 variables, which considered the connection of water and electricity, water and electricity coupling relationship respectively in geography and time, hydropower and thermal power's coordination peaking capacity as well as hydropower units' oscillation interval constraints. Finally, adopt dynamic heuristics algorithm(DHA) and active set cutting plane method(ASCPM) with the mixed integer programming solver for a test system to verify the model. The simulation results demonstrate the model and algorithm proposed is capable of handling high proportion of hydropower's system power balance problem and gets the scheduling optimization plan effectively.
Clean energy strategy presented highlights the importance of the system's power balance and scheduling optimization studies with high proportion of hydropower. Based on the hydrological characteristic and hydropower generation characteristic, hydropower conversion curve's piecewise linear function was fit. By introducing auxiliary 0-1 variables, this paper proposed two methods, that were repulsion technique and right valuation technique, to build a mixed integer quadratic programming(MIQP) model containing six kinds of 0-1 variables, which considered the connection of water and electricity, water and electricity coupling relationship respectively in geography and time, hydropower and thermal power's coordination peaking capacity as well as hydropower units' oscillation interval constraints. Finally, adopt dynamic heuristics algorithm(DHA) and active set cutting plane method(ASCPM) with the mixed integer programming solver for a test system to verify the model. The simulation results demonstrate the model and algorithm proposed is capable of handling high proportion of hydropower's system power balance problem and gets the scheduling optimization plan effectively.
引文
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[14]黎静华,韦化.求解机组组合问题的邻域搜索法[J].中国电机工程学报,2008,28(13):33-40.Li Jinghua,Wei Hua.Unit commitment via local search point method[J].Proceedings of the CSEE,2008,28(13):33-40(in Chinese).
[15]孙力勇,张焰,蒋传文.基于矩阵实数编码遗传算法求解大规模机组组合问题[J].中国电机工程学报,2006,26(2):82-87.Sun Liyong,Zhang Yan,Jiang Chuanwen.A solution to the unit commitment problem based on matrix real-coded genetic algorithm[J].Proceedings of the CSEE,2006,26(2):82-87(in Chinese).
[16]吴小珊,张步涵,袁小明,等.求解含风电场的电力系统机组组合问题的改进量子离散粒子群优化方法[J].中国电机工程学报,2013,33(4):45-52.Wu Xiaoshan,Zhang Buhan,Yuan Xiaoming,et al.Solutions to unit commitment problems in power systems with wind farms using advanced quantuminspired binary PSO[J].Proceedings of the CSEE,2013,33(4):45-52(in Chinese).
[17]侯贸军,罗春辉,隗霖捷,等.基于微分进化算法的水火电短期优化调度的研究[J].电力系统保护与控制,2015,43(9):54-61.Hou Maojun,Luo Chunhui,Wei Linjie1,et al.Study on short-term hydrothermal scheduling based on differential evolution[J].Power System Protection and Control,2015,43(9):54-61(in Chinese).
[18]Ostrowski J,Anjos M F,Vannelli A.Tight mixed integer linear programming formulations for the unit commitment problem[J].IEEE Transactions on Power Systems,2012,27(1):39-46.
[19]Carrion M,Arroyo J M.A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem[J].IEEE Transactions on Power Systems,2006,21(3):1371-1378.
[20]Chang G,Aganagic M,Waight J,et al.Experiences with mixed integer linear programming based approaches on short-term hydro scheduling[J].IEEE Transactions on Power Systems,2001,16(4):743–749.
[21]李庆杨,王能超,易大义.数值分析[M].北京:清华大学出版社,2008.Li Qingyang,Wang Nengchao,Yi Dayi.Numerical analysis[M].Beijing:Tsinghua University Press,2008(in Chinese).
[22]邓俊,韦化,黎静华,等.一种含四类0-1变量的机组组合混合整数线性规划模型[J].中国电机工程学报,2015,35(11):2770-2778.Deng Jun,Wei Hua,Li Jinghua,et al.A mixed-integer linear programming model using four sets of binary variables for the unit commitment problem[J].Proceedings of the CSEE,2015,35(11):2770-2778(in Chinese).
[23]韩明.概率论与数理统计[M].上海:同济大学出版社,2013.Han Ming.Probability theory and mathematical statistics[M].Shanghai:Tongji University Press,2013(in Chinese).
[24]任煜峰.水轮发电机组值班[M].北京:中国电力出版社,2003.Ren Yufeng.Hydro-generating unit on duty[M].Beijing:China Power Press,2003(in Chinese).
[25]申建建,武新宇,程春田,等.大规模水电站群短期优化调度方法II:高水头多振动区问题[J].水利学报,2011,42(10):1168-1176.Shen Jianjian,Wu Xinyu,Cheng Chuntian,et al.Short-term optimal operation methods of large-scale hydropower plants II:solution method for high-head generating units with multi-vibration zone[J].Hydraulic Engineering,2011,42(10):1168-1176(in Chinese).
[26]李文武,郑俊,吴稀西,等.考虑振动区的水电机组组合优化研究[J].水电能源科学,2012,30(9):122-124.Li wen Wu,Zheng Jun,Wu Xixi,et al.Unit commitment of hydro power station considering vibration zone[J].Water Resources and Power,2012,30(9):122-124(in Chinese).
[27]IBM Corp.IBM ILOG CPLEX optimizer V12.5[R/OL].[2013-08-01].http://www-01.ibm.com/softwar e/commerce/optimization/cplex-optimizer/.
[28]许丹,夏少连,丁强,等.基于启发式混合整数规划法求解大规模机组组合问题[J].电力系统保护与控制,2012,40(21):1-6.Xu Dan,Xia Shaolian,Ding Qiang,et al.Fast unit commitment based on heuristic mixed integer programming[J].Power System Protection and Control,2012,40(21):1-6(in Chinese).
[29]陈宝林.最优化理论与算法[M].北京:清华大学出版社,2005.Chen Baolin.Optimization theory and algorithms[M].Beijing:Tsinghua University Press,2005(in Chinese).
[30]Kazarlis S A,Bakirtzis A G,Petridis V.A genetic algorithm solution to the unit commitment problem[J].IEEE Transactions on Power Systems,1996,11(1):83-92.
[2]周之豪.水利水能规划[M].北京:中国水利电力出版社,1986.Zhou Zhihao.Water conservancy planning[M].Beijing:China Water Power Press,1986(in Chinese).
[3]张勇传.水电站经济运行原理[M].北京:中国水利水电出版社,1998.Zhang Yongzhuan.Hydropower economic operation principle[M].Beijing:China Water Power Press,1998(in Chinese).
[4]叶秉如.水资源系统优化规划和调度[M].北京:中国水利水电出版社,2001.Ye Bingru.Water system optimization planning and scheduling[M].Beijing:China Water Power Press,2001(in Chinese).
[5]丁军威,胡旸,夏清,等.竞价上网中的水电优化运行[J].电力系统自动化,2002,27(3):19-23.Ding Junwei,Hu Yang,Xia Qing,et al.Hydro power optmization in competition with thermal generation[J].Automation of Electric Power Systems,2002,27(3):19-23(in Chinese).
[6]郭壮志,吴杰康,孔繁镍.基于仿电磁学算法和数据包络分析的水火电力系统多目标优化调度[J].中国电机工程学报,2013,33(4):53-61.Guo Zhuangzhi,Wu Jiekang,Kong Fannie.Multiobjective optimization scheduling for hydrothermal power systems based on electromagnetism-like mechanism and data envelopment analysis[J].Proceedings of the CSEE,2013,33(4):53-61(in Chinese).
[7]Alberto B,Claudia D A,Andrea L,et al.An MILP approach for short-term hydro scheduling and unit commitment with head-dependent reservoir[J].IEEE Transactions on Power systems,2008,23(3):1115-1124.
[8]Lisias V L A,Mohammad E K,Mohammad S,et al.Risk-constrained coordination of cascaded hydro units with variable wind power generation[J].IEEE Transactions on Sustainable Energy,2012,3(3):359-368.
[9]Gary W C,Mohamed A,James G W,et al.Experiences with mixed integer linear programming based approaches on short-term hydro scheduling[J].IEEE Transactions on Power Systems,2001,16(4):743-749.
[10]全然,简金宝,韦化.基于特殊有效不等式求解机组组合问题的内点割平面法[J].中国电机工程学报,2011,31(19):51-59.Quan Ran,Jian Jinbao,Wei Hua.An interior-point cutting plane method for unit commitment based on special valid inequalities[J].Proceedings of the CSEE,2011,31(19):51-49(in Chinese).
[11]杨林峰,简金宝,郑海艳.求解机组组合问题的次超立方紧混合整数规划广义割平面法[J].中国电机工程学报,2013,33(1):99-108.Yang Linfeng,Jian Jinbao,Zheng Haiyan.A sub hyper-cube tight mixed integer programming extended cutting plane method for unit commitment[J].Proceedings of the CSEE,2013,31(1):99-108(in Chinese).
[12]Ongsakul W,Petcharaks N.Unit commitment by enhanced adaptive Lagrangian relaxation[J].IEEE Trans.on Power Systems,2004,19(1):620-628.
[13]黎静华,韦化,夏小琴.求解机组组合问题的改进模式搜索算法[J].中国电机工程学报,2011,31(28):33-41.Li Jinghua,Wei Hua,Xia Xiaoqin.Improved general pattern search filter algorithm for unit commitment problems[J].Proceedings of the CSEE,2011,31(28):33-41(in Chinese).
[14]黎静华,韦化.求解机组组合问题的邻域搜索法[J].中国电机工程学报,2008,28(13):33-40.Li Jinghua,Wei Hua.Unit commitment via local search point method[J].Proceedings of the CSEE,2008,28(13):33-40(in Chinese).
[15]孙力勇,张焰,蒋传文.基于矩阵实数编码遗传算法求解大规模机组组合问题[J].中国电机工程学报,2006,26(2):82-87.Sun Liyong,Zhang Yan,Jiang Chuanwen.A solution to the unit commitment problem based on matrix real-coded genetic algorithm[J].Proceedings of the CSEE,2006,26(2):82-87(in Chinese).
[16]吴小珊,张步涵,袁小明,等.求解含风电场的电力系统机组组合问题的改进量子离散粒子群优化方法[J].中国电机工程学报,2013,33(4):45-52.Wu Xiaoshan,Zhang Buhan,Yuan Xiaoming,et al.Solutions to unit commitment problems in power systems with wind farms using advanced quantuminspired binary PSO[J].Proceedings of the CSEE,2013,33(4):45-52(in Chinese).
[17]侯贸军,罗春辉,隗霖捷,等.基于微分进化算法的水火电短期优化调度的研究[J].电力系统保护与控制,2015,43(9):54-61.Hou Maojun,Luo Chunhui,Wei Linjie1,et al.Study on short-term hydrothermal scheduling based on differential evolution[J].Power System Protection and Control,2015,43(9):54-61(in Chinese).
[18]Ostrowski J,Anjos M F,Vannelli A.Tight mixed integer linear programming formulations for the unit commitment problem[J].IEEE Transactions on Power Systems,2012,27(1):39-46.
[19]Carrion M,Arroyo J M.A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem[J].IEEE Transactions on Power Systems,2006,21(3):1371-1378.
[20]Chang G,Aganagic M,Waight J,et al.Experiences with mixed integer linear programming based approaches on short-term hydro scheduling[J].IEEE Transactions on Power Systems,2001,16(4):743–749.
[21]李庆杨,王能超,易大义.数值分析[M].北京:清华大学出版社,2008.Li Qingyang,Wang Nengchao,Yi Dayi.Numerical analysis[M].Beijing:Tsinghua University Press,2008(in Chinese).
[22]邓俊,韦化,黎静华,等.一种含四类0-1变量的机组组合混合整数线性规划模型[J].中国电机工程学报,2015,35(11):2770-2778.Deng Jun,Wei Hua,Li Jinghua,et al.A mixed-integer linear programming model using four sets of binary variables for the unit commitment problem[J].Proceedings of the CSEE,2015,35(11):2770-2778(in Chinese).
[23]韩明.概率论与数理统计[M].上海:同济大学出版社,2013.Han Ming.Probability theory and mathematical statistics[M].Shanghai:Tongji University Press,2013(in Chinese).
[24]任煜峰.水轮发电机组值班[M].北京:中国电力出版社,2003.Ren Yufeng.Hydro-generating unit on duty[M].Beijing:China Power Press,2003(in Chinese).
[25]申建建,武新宇,程春田,等.大规模水电站群短期优化调度方法II:高水头多振动区问题[J].水利学报,2011,42(10):1168-1176.Shen Jianjian,Wu Xinyu,Cheng Chuntian,et al.Short-term optimal operation methods of large-scale hydropower plants II:solution method for high-head generating units with multi-vibration zone[J].Hydraulic Engineering,2011,42(10):1168-1176(in Chinese).
[26]李文武,郑俊,吴稀西,等.考虑振动区的水电机组组合优化研究[J].水电能源科学,2012,30(9):122-124.Li wen Wu,Zheng Jun,Wu Xixi,et al.Unit commitment of hydro power station considering vibration zone[J].Water Resources and Power,2012,30(9):122-124(in Chinese).
[27]IBM Corp.IBM ILOG CPLEX optimizer V12.5[R/OL].[2013-08-01].http://www-01.ibm.com/softwar e/commerce/optimization/cplex-optimizer/.
[28]许丹,夏少连,丁强,等.基于启发式混合整数规划法求解大规模机组组合问题[J].电力系统保护与控制,2012,40(21):1-6.Xu Dan,Xia Shaolian,Ding Qiang,et al.Fast unit commitment based on heuristic mixed integer programming[J].Power System Protection and Control,2012,40(21):1-6(in Chinese).
[29]陈宝林.最优化理论与算法[M].北京:清华大学出版社,2005.Chen Baolin.Optimization theory and algorithms[M].Beijing:Tsinghua University Press,2005(in Chinese).
[30]Kazarlis S A,Bakirtzis A G,Petridis V.A genetic algorithm solution to the unit commitment problem[J].IEEE Transactions on Power Systems,1996,11(1):83-92.