输电检修与机组组合联合的区间鲁棒优化决策
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摘要
在设备实施状态检修背景下,输电设备检修与机组组合容易产生矛盾,尤其是风电等可再生能源接入所产生的剧烈不确定性使这一矛盾更加突出。为此,该文以区间不确定集描述电网各母线上负荷或风电的不确定性,建立了输电设备检修与机组组合联合的区间鲁棒优化决策模型。从该模型出发,提出了以奔德斯(Benders)分解协调为核心的求解框架,其中以输电设备检修和机组组合联合决策为主问题,依据电网潮流可行性和电网潮流最优性的条件,引入奔德斯可行割和最优割,借助拉格朗日松弛技术(Lagrangian relaxation technique)使分解协调迭代格式得以有效进行,最终驱使主问题趋向潮流可行到最优,完成优化决策。其中,为提升优化算法计算效率,引入主问题中设备检修和机组启停变动情景下的发电与负荷平衡(单母线模型)的经济调度最小运行成本以减小主问题目标与子问题目标衔接的间隙,并促使其以最小的迭代次数趋向最优解;其次,针对电网潮流可行性及最优性校验遭遇的max-min复杂模型,提出一定主问题解条件下,依据对偶原理和区间不确定集特点使其转换为易于求解的混合整数线性规划模型的方法,并给出应用模式识别加速这一校验过程的基本流程。最后,以简单6节点和IEEE118节点算例系统验证了该文模型和方法的有效性。
In the background of equipment condition-based maintenance, contradictions are easily introduced between transmission maintenance scheduling and unit commitment, especially with a high level of uncertainty due to the wind power integration. To meet this challenge, this paper modeled the uncertainty of nodal demands and wind power generations through the interval uncertainty set, and then proposed a robust optimization decision model to solve the coordination of transmission maintenance scheduling with unit commitment in the presence of interval uncertainty. According to the proposed model, a solution framework based on Benders decomposition and coordination strategy was proposed, in which the master problem applied the Lagrangian relaxation technique to obtain optimal hourly results for transmission maintenance scheduling and unit commitment in several iterations by adding the Benders cuts constructed on the basis of the feasible or optimal conditions of the power flow sub-problems. Furthermore, the proposed approach introduced additional constraints that were associated with the minimum operating cost of single-bus economic dispatch varying with transmission maintenance and unit commitment schedule into the master problem to decrease the gap between the master problem and sub-problems for accelerating the convergence of the optimal results, and also used the principle of duality and the characteristic of interval uncertainty set to covert the intractable max-min models of the feasible and optimal power flow sub-problems into tractable mix integer linear programming models, in which pattern recognition algorithm was applied to improve efficiency. Case studies with the six-bus system and the IEEE 118-bus test system were used to exhibit the effectiveness of the proposed scheduling approach.
In the background of equipment condition-based maintenance, contradictions are easily introduced between transmission maintenance scheduling and unit commitment, especially with a high level of uncertainty due to the wind power integration. To meet this challenge, this paper modeled the uncertainty of nodal demands and wind power generations through the interval uncertainty set, and then proposed a robust optimization decision model to solve the coordination of transmission maintenance scheduling with unit commitment in the presence of interval uncertainty. According to the proposed model, a solution framework based on Benders decomposition and coordination strategy was proposed, in which the master problem applied the Lagrangian relaxation technique to obtain optimal hourly results for transmission maintenance scheduling and unit commitment in several iterations by adding the Benders cuts constructed on the basis of the feasible or optimal conditions of the power flow sub-problems. Furthermore, the proposed approach introduced additional constraints that were associated with the minimum operating cost of single-bus economic dispatch varying with transmission maintenance and unit commitment schedule into the master problem to decrease the gap between the master problem and sub-problems for accelerating the convergence of the optimal results, and also used the principle of duality and the characteristic of interval uncertainty set to covert the intractable max-min models of the feasible and optimal power flow sub-problems into tractable mix integer linear programming models, in which pattern recognition algorithm was applied to improve efficiency. Case studies with the six-bus system and the IEEE 118-bus test system were used to exhibit the effectiveness of the proposed scheduling approach.
引文
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[11]Wang Yifei,Li Zhiyi,Shahidehpour M,et al.Stochastic co-optimization of midterm and short-term maintenance outage scheduling considering covariates in power systems[J].IEEE Transactions on Power Systems,2016,31(6):4795-4805.
[12]陈建华,吴文传,张伯明,等.安全性与经济性协调的鲁棒区间风电调度方法[J].中国电机工程学报,2014,34(7):1033-1040.Chen Jianhua,Wu Wenchuan,Zhang Boming,et al.Arobust interval wind power dispatch method considering the tradeoff between security and economy[J].Proceedings of the CSEE,2014,34(7):1033-1040(in Chinese).
[13]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):134-141,148.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):134-141,148(in Chinese).
[14]于丹文,杨明,韩学山,等.计及风电概率分布特征的鲁棒实时调度方法[J].中国电机工程学报,2017,37(3):727-737.Yu Danwen,Yang Ming,Han Xueshan,et al.Robust real-time dispatch considering probabilistic distribution of wind generation[J].Proceedings of the CSEE,2017,37(3):727-737(in Chinese).
[15]汲国强,吴文传,张伯明.考虑风电不确定性的机组检修鲁棒优化方法[J].中国电机工程学报,2015,35(12):2919-2926.Ji Guoqiang,Wu Wenchuan,Zhang Boming.Robust optimization method of generator maintenance schedule considering wind power integration[J].Proceedings of the CSEE,2015,35(12):2919-2926(in Chinese).
[16]Bertsimas D,Litvinov E,Sun X A,et al.Adaptive robust optimization for the security constrained unit commitment problem[J].IEEE Transactions on Power Systems,2013,28(1):52-63.
[17]Boyd S,Vandenberghe L.Convex optimization[M].New York:Cambridge University Press,2004:215-227.
[18]Nocedal J,Wright S J.Numerical optimization[M].2nd ed.New York:Springer,2006:30-37.
[19]Fu Yong,Li Zuyi,Shahidehpour M,et al.Coordination of midterm outage scheduling with short-term securityconstrained unit commitment[J].IEEE Transactions on Power Systems,2009,24(4):1818-1830.
[2]Marwali M K C,Shahidehpour S M.Integrated generation and transmission maintenance scheduling with network constraints[J].IEEE Transactions on Power Systems,1998,13(3):1063-1068.
[3]丁明,冯永青.发输电设备联合检修安排模型及算法研究[J].中国电机工程学报,2004,24(5):18-23.Ding Ming,Feng Yongqing.Research on the modeling and algorithm to global generator and transmission maintenance scheduling[J].Proceedings of the CSEE,2004,24(5):18-23(in Chinese).
[4]方陈,夏清,胡朝阳,等.月度发输电检修一体优化方法[J].电力系统自动化,2011,35(11):50-54,92.Fang Chen,Xia Qing,Hu Chaoyang,et al.Integrated generation and transmission monthly maintenance scheduling method[J].Automation of Electric Power Systems,2011,35(11):50-54,92(in Chinese).
[5]冯永青,吴文传,张伯明,等.基于可信性理论的输电网短期线路检修计划[J].中国电机工程学报,2007,27(4):65-71.Feng Yongqing,Wu Wenchuan,Zhang Boming,et al.Short-term transmission line maintenance scheduling based on credibility theory[J].Proceedings of the CSEE,2007,27(4):65-71(in Chinese).
[6]Fu Yong,Shahidehpour M,Li Zuyi.Security-constrained optimal coordination of generation and transmission maintenance outage scheduling[J].IEEE Transactions on Power Systems,2007,22(3):1302-1313.
[7]李本新,韩学山.发输电检修与机组组合联合决策的Benders分解方法[J].电工技术学报,2015,30(3):224-231.Li Benxin,Han Xueshan.Benders decomposition algorithm to coordination of generation and transmission maintenance scheduling with unit commitment[J].Transactions of China Electrotechnical Society,2015,30(3):224-231(in Chinese).
[8]Birge J R,Louveaux F.Introduction to stochastic programming[M].2nd ed.New York:Springer,2011.
[9]Ben-Tal A,El Ghaoui L,Nemirovski A.Robust optimization[M].Princeton,NJ,USA:Princeton University Press,2009.
[10]Wu Lei,Shahidehpour M,Fu Yong.Security-constrained generation and transmission outage scheduling with uncertainties[J].IEEE Transactions on Power Systems,2010,25(3):1674-1685.
[11]Wang Yifei,Li Zhiyi,Shahidehpour M,et al.Stochastic co-optimization of midterm and short-term maintenance outage scheduling considering covariates in power systems[J].IEEE Transactions on Power Systems,2016,31(6):4795-4805.
[12]陈建华,吴文传,张伯明,等.安全性与经济性协调的鲁棒区间风电调度方法[J].中国电机工程学报,2014,34(7):1033-1040.Chen Jianhua,Wu Wenchuan,Zhang Boming,et al.Arobust interval wind power dispatch method considering the tradeoff between security and economy[J].Proceedings of the CSEE,2014,34(7):1033-1040(in Chinese).
[13]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):134-141,148.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):134-141,148(in Chinese).
[14]于丹文,杨明,韩学山,等.计及风电概率分布特征的鲁棒实时调度方法[J].中国电机工程学报,2017,37(3):727-737.Yu Danwen,Yang Ming,Han Xueshan,et al.Robust real-time dispatch considering probabilistic distribution of wind generation[J].Proceedings of the CSEE,2017,37(3):727-737(in Chinese).
[15]汲国强,吴文传,张伯明.考虑风电不确定性的机组检修鲁棒优化方法[J].中国电机工程学报,2015,35(12):2919-2926.Ji Guoqiang,Wu Wenchuan,Zhang Boming.Robust optimization method of generator maintenance schedule considering wind power integration[J].Proceedings of the CSEE,2015,35(12):2919-2926(in Chinese).
[16]Bertsimas D,Litvinov E,Sun X A,et al.Adaptive robust optimization for the security constrained unit commitment problem[J].IEEE Transactions on Power Systems,2013,28(1):52-63.
[17]Boyd S,Vandenberghe L.Convex optimization[M].New York:Cambridge University Press,2004:215-227.
[18]Nocedal J,Wright S J.Numerical optimization[M].2nd ed.New York:Springer,2006:30-37.
[19]Fu Yong,Li Zuyi,Shahidehpour M,et al.Coordination of midterm outage scheduling with short-term securityconstrained unit commitment[J].IEEE Transactions on Power Systems,2009,24(4):1818-1830.