计及N-k网络安全约束的二阶段鲁棒机组组合
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摘要
为提高调度决策的安全性以增强其应对偶发线路故障扰动的能力,文中提出一种计及N-k网络安全约束的二阶段鲁棒机组组合模型。首先,介绍了2种当前研究中采用的N-k不确定集合,并对集合特点进行了阐述;其次,基于2种N-k不确定集合,构建了一般形式的二阶段鲁棒机组组合模型。其中,第一阶段为线路故障前的机组启停决策;第二阶段为观测到线路故障最坏情况下的经济调度决策。所提模型可采用列与约束生成(C&CG)算法将第一阶段、第二阶段问题分别对应转化为主问题与子问题进行迭代求解,并且运用对偶原理和线性化技术,可将主问题与子问题均转化为混合整数线性规划(MILP)模型。最后,通过对IEEE 14节点及IEEE 118节点系统的测试分析,验证了所提模型的有效性。
In order to improve the security of scheduling decision and enhance its ability to deal with occasional line contingencies, a two-stage robust unit commitment model considering N-k network security constraints is proposed. Firstly, two kinds of N-k uncertainty sets used in the current research are introduced, and the characteristics of the set are described. Secondly, based on the two kinds of N-k uncertainty sets, a general form of two-stage robust unit commitment model is constructed. The formulation is divided into two stages, where the first stage is the unit commitment decision before the line contingency, and the second stage is the economic dispatching decision as the worst case of line contingencies are observed. The first and second stage problems are reformulated into a master problem and sub-problem, respectively, So that the column-and-constraint generation(C&CG) algorithm can be used to solve the proposed two-stage unit commitment model in an iterative manner. By using linearization techniques and duality theory, both the master problem and the sub-problem can be converted into mixed integer linear programming(MILP). Finally, the validity of the proposed model was verified by the calculation and analysis of the IEEE 14 bus and IEEE 118 bus systems.
In order to improve the security of scheduling decision and enhance its ability to deal with occasional line contingencies, a two-stage robust unit commitment model considering N-k network security constraints is proposed. Firstly, two kinds of N-k uncertainty sets used in the current research are introduced, and the characteristics of the set are described. Secondly, based on the two kinds of N-k uncertainty sets, a general form of two-stage robust unit commitment model is constructed. The formulation is divided into two stages, where the first stage is the unit commitment decision before the line contingency, and the second stage is the economic dispatching decision as the worst case of line contingencies are observed. The first and second stage problems are reformulated into a master problem and sub-problem, respectively, So that the column-and-constraint generation(C&CG) algorithm can be used to solve the proposed two-stage unit commitment model in an iterative manner. By using linearization techniques and duality theory, both the master problem and the sub-problem can be converted into mixed integer linear programming(MILP). Finally, the validity of the proposed model was verified by the calculation and analysis of the IEEE 14 bus and IEEE 118 bus systems.
引文
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[10]梁捷.基于禁忌动态规划的含电动汽车机组组合研究[J].电力工程技术,2018,37(2):67-72.LIANG Jie.Research on the unit commitment of electric vehicle based on tuba-dynamic programming[J].Electric Power Engineering Technology,2018,37(2):67-72.
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[14]PENG X,JIRUTITIJAROEN P.An adjustable robust optimization approach for unit commitment under outage contingencies[C]∥2012 Power and Energy Society General Meeting,San Diego,CA,USA:8p,2012.
[15]PENG X,JIRUTITIJAROEN P.Two-stage adjustable robust optimisation for unit commitment under uncertainty[J].IETGeneration Transmission&Distribution,2014,8(3):573-582.
[16]WANG Q,WATSON J P,GUAN Y.Two-stage robust optimization for N-k contingency-constrained unit commitment[J].IEEE Transactions on Power Systems,2013,28(3):2366-2375.
[17]CHEN L Y,FAN N,PINAR A,et al.Contingency-constrained unit commitment with post-contingency corrective recourse[J].Annals of Operations Research,2017,249(1-2):381-407.
[18]刁浩然,杨明,韩学山,等.电力设备停运概率的非精确条件估计[J].中国电机工程学报,2016,36(19):5134-5144.DIAO Haoran,YANG Ming,HAN Xueshan,et al.Imprecise estimation for conditional outage probabilities of power components[J].Proceedings of the CSEE,2016,36(19):5134-5144.
[19]ZENG B,ZHAO L.Solving two-stage robust optimization problems using a column-and-constraint generation method[J].Operations Research Letters,2013,41(5):457-461.
[20]于丹文,杨明,翟鹤峰,等.鲁棒优化在电力系统调度决策中的应用研究综述[J].电力系统自动化,2016,40(7):134-143,148.YU Danwen,YANG Ming,ZHAI Hefeng,et al.An overview of robust optimization used for power system dispatch and decision-making[J].Automation of Electric Power Systems,2016,40(7):134-143,148.
[21]STREET A,MOREIRA A,ARROYO J M.Energy and reserve scheduling under a joint generation and transmission security criterion:an adjustable robust optimization approach[J].IEEEtransactions on Power Systems,2014,29(1):3-14.
[22]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.
[23]TRIEBEL H.Interpolation theory,function spaces,differential operators[M].Amsterdam,The Netherlands:NorthHolland,1978.
[24]李利利,丁恰,涂孟夫,等.机组组合问题的仿射可调整鲁棒优化模型与算法[J].电力工程技术,2017,36(3):33-37.LI Lili,DING Qia,TU Mengfu,et al.Affinely adjustable robust optimization model and algorithm for unit commitment problem[J].Electric Power Engineering Technology,2017,36(3):33-37.
[25]FERNANDEZ-BLANCO R,DVORKIN Y,ORTEGA-VAZQUE-Z M A.Probabilistic security-constrained unit commitment with generation and transmission contingencies[J].IEEE Transactions on Power Systems,2017,32(1):228-239.
[26]LOTFIOU A,SHAHIDEHP M,FU Y,et al.Security-constrained unit commitment with AC/DC transmission systems[J].IEEE Transactions on Power Systems,2010,25(1):531-542.
[27]WANG J,SHAHIDEHPOUR M,LI Z.Security-constrained unit commitment with volatile wind power generation[J].IEEETransactions on Power Systems,2008,23(3):1319-1327.
[2]VAIMAN,BELL,CHEN,et al.Risk assessment of cascading outages:methodologies and challenges[J].IEEE Transactions on Power Systems,2012,27(2):631-641.
[3]陈丰,林成虎,奚建飞,等.供电可靠性管理应用架构设计及关键技术实现[J].广东电力,2017,30(7):126-130.CHEN Feng,LIN Chenghu,XI Jianfei,et al.Design on power supply reliability management application structure and realization of key technology[J].Guangdong Electric Power,2017,30(7):126-130.
[4]汪洋,夏清,康重庆.考虑电网N-1闭环安全校核的最优安全发电计划[J].中国电机工程学报,2011,31(10):39-45.WANG Yang,XIA Qing,KANG Chongqing.Optimal security constrained generation scheduling considering closed-loop N-1security correction[J].Proceedings of the CSEE,2011,31(10):39-45.
[5]张国华,张建华,杨志栋,等.电力系统N-K故障的风险评估方法[J].电网技术,2009,33(5):17-21.ZHANG Guohua,ZHANG Jianhua,YANG Zhidong,et al.Risk assessment method of power system N-K contingencies[J].Power System Technology,2009,33(5):17-21.
[6]李扬,苏慧玲.N-k故障下影响电力系统脆弱性的关键线路研究[J].电力自动化设备,2015,35(3):60-67.LI Yang,SU Huiling.Critical line affecting power system vulnerability under N-k contingency condition[J].Electric Power Automation Equipment,2015,35(3):60-67.
[7]CHE Liang,LIU Xuan,WEN Yunfeng,et al.A mixed integer programming model for evaluating the hidden probabilities of N-k Line contingencies in smart grids[J].IEEE Transactions on Smart Grid,2019,10(1):1036-1045.
[8]刘国静,李娟,谈健,等.基于两层规划的电力系统N-K故障分析方法[J].电力工程技术,2018,37(1):40-44.LIU Guojing,LI Juan,TAN Jian,et al.N-K fault analysis method for power systems based on two-level programming[J].Electric Power Engineering Technology,2018,37(1):40-44.
[9]陈皓勇,王锡凡.机组组合问题的优化方法综述[J].电力系统自动化,1999,23(4):51-56.CHEN Haoyong,WANG Xifan.A survey of optimization-based methods for unit commitment[J].Automation of Electric Power Systems,1999,23(4):51-56.
[10]梁捷.基于禁忌动态规划的含电动汽车机组组合研究[J].电力工程技术,2018,37(2):67-72.LIANG Jie.Research on the unit commitment of electric vehicle based on tuba-dynamic programming[J].Electric Power Engineering Technology,2018,37(2):67-72.
[11]马留洋,孟安波,胡函武.基于离散纵横交叉算法的含风电电力系统机组组合优化[J].广东电力,2018,31(2):38-44.MA Liuyang,MENG Anbo,HU Hanwu.Optimization on power system unit commitment with wind power based on discrete crisscross algorithm[J].Guangdong Electric Power,2018,31(2):38-44.
[12]王民量,张伯明.考虑机组爬坡速度和网络安全的经济调度新算法[J].电力系统自动化,2000,24(10):14-20.WANG Minliang,ZHANG Boming,XIA Qing,et al.A novel economic dispatching algorithm with unit ramp rate and network security constraints[J].Automation of Electric power systems,2000,24(10):14-20.
[13]STREET A,OLIVEIRA F,ARROYO J M.Contingency-constrained unit commitment with N-K security criterion:a robust optimization approach[J].IEEE Transactions on Power Systems,2011,26(3):1581-1590.
[14]PENG X,JIRUTITIJAROEN P.An adjustable robust optimization approach for unit commitment under outage contingencies[C]∥2012 Power and Energy Society General Meeting,San Diego,CA,USA:8p,2012.
[15]PENG X,JIRUTITIJAROEN P.Two-stage adjustable robust optimisation for unit commitment under uncertainty[J].IETGeneration Transmission&Distribution,2014,8(3):573-582.
[16]WANG Q,WATSON J P,GUAN Y.Two-stage robust optimization for N-k contingency-constrained unit commitment[J].IEEE Transactions on Power Systems,2013,28(3):2366-2375.
[17]CHEN L Y,FAN N,PINAR A,et al.Contingency-constrained unit commitment with post-contingency corrective recourse[J].Annals of Operations Research,2017,249(1-2):381-407.
[18]刁浩然,杨明,韩学山,等.电力设备停运概率的非精确条件估计[J].中国电机工程学报,2016,36(19):5134-5144.DIAO Haoran,YANG Ming,HAN Xueshan,et al.Imprecise estimation for conditional outage probabilities of power components[J].Proceedings of the CSEE,2016,36(19):5134-5144.
[19]ZENG B,ZHAO L.Solving two-stage robust optimization problems using a column-and-constraint generation method[J].Operations Research Letters,2013,41(5):457-461.
[20]于丹文,杨明,翟鹤峰,等.鲁棒优化在电力系统调度决策中的应用研究综述[J].电力系统自动化,2016,40(7):134-143,148.YU Danwen,YANG Ming,ZHAI Hefeng,et al.An overview of robust optimization used for power system dispatch and decision-making[J].Automation of Electric Power Systems,2016,40(7):134-143,148.
[21]STREET A,MOREIRA A,ARROYO J M.Energy and reserve scheduling under a joint generation and transmission security criterion:an adjustable robust optimization approach[J].IEEEtransactions on Power Systems,2014,29(1):3-14.
[22]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.
[23]TRIEBEL H.Interpolation theory,function spaces,differential operators[M].Amsterdam,The Netherlands:NorthHolland,1978.
[24]李利利,丁恰,涂孟夫,等.机组组合问题的仿射可调整鲁棒优化模型与算法[J].电力工程技术,2017,36(3):33-37.LI Lili,DING Qia,TU Mengfu,et al.Affinely adjustable robust optimization model and algorithm for unit commitment problem[J].Electric Power Engineering Technology,2017,36(3):33-37.
[25]FERNANDEZ-BLANCO R,DVORKIN Y,ORTEGA-VAZQUE-Z M A.Probabilistic security-constrained unit commitment with generation and transmission contingencies[J].IEEE Transactions on Power Systems,2017,32(1):228-239.
[26]LOTFIOU A,SHAHIDEHP M,FU Y,et al.Security-constrained unit commitment with AC/DC transmission systems[J].IEEE Transactions on Power Systems,2010,25(1):531-542.
[27]WANG J,SHAHIDEHPOUR M,LI Z.Security-constrained unit commitment with volatile wind power generation[J].IEEETransactions on Power Systems,2008,23(3):1319-1327.