考虑风场高维相依性的电网动态经济调度优化算法
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摘要
大规模风电并网给电力系统的调度运行带来了巨大的挑战.本文提出改进的二阶段带补偿随机优化算法,用于考虑风场出力高维相依性的电网动态经济调度问题求解.首先,利用Copula函数描述多风场出力的高维相依性,获得多风场出力的联合分布;随后,引入二阶段带补偿随机优化算法解耦求解动态经济调度模型中的常规变量与随机变量;求解过程中,针对补偿费用期望值的计算受限于相依性风场维数,且对迭代方向指导不明确,导致算法收敛耗时长的问题,引入基于整体最小二乘的递推动态多元线性回归法对二阶段带补偿随机优化算法进行改进,通过补偿费用期望值的动态更新,促使两阶段模型的迭代求解快速收敛,克服了传统随机优化方法的"维数灾"弊端,使该算法能够用于考虑风场高维相依性的电网动态经济调度模型求解.最后利用IEEE 118节点系统和某省级实际电网系统验证了所提算法的有效性和实用性.
Large-scale wind power connected to power grid has brought great challenges to power system scheduling operation. In this paper, an improved two-stage compensation stochastic optimization algorithm is proposed to solve the dynamic economic dispatching problem considering the high-dimensional correlation of multiple wind farms. Firstly,Copula function is used to describe the correlation of high-dimensional wind farms, and the joint distribution of wind output is obtained. Secondly, a two-stage compensation stochastic optimization algorithm is proposed to decouple the conventional and stochastic variables in the dynamic economic scheduling model solving. The calculation of the expected value of compensation cost is usually limited by the dimension of the correlated wind farms, and the direction of the iterative is not clear enough to lead the convergence, all this lead to long computation time consumed. So the recursive dynamic multivariable linear regression method based on global least squares is introduced to improve the proposed algorithm. By dynamic updating of compensation penalty expectation, computation time is greatly shortened. This improved two-stage compensation algorithm proposed in this paper overcomes the dimensional disaster of the traditional stochastic optimization method, and is capable of solving the dynamic economic dispatching problem considering the high-dimensional correlation of multiple wind farms. Finally, the practicability and efficiency of the proposed algorithm is verified by the examples of IEEE 118 system and an actual provincial system.
Large-scale wind power connected to power grid has brought great challenges to power system scheduling operation. In this paper, an improved two-stage compensation stochastic optimization algorithm is proposed to solve the dynamic economic dispatching problem considering the high-dimensional correlation of multiple wind farms. Firstly,Copula function is used to describe the correlation of high-dimensional wind farms, and the joint distribution of wind output is obtained. Secondly, a two-stage compensation stochastic optimization algorithm is proposed to decouple the conventional and stochastic variables in the dynamic economic scheduling model solving. The calculation of the expected value of compensation cost is usually limited by the dimension of the correlated wind farms, and the direction of the iterative is not clear enough to lead the convergence, all this lead to long computation time consumed. So the recursive dynamic multivariable linear regression method based on global least squares is introduced to improve the proposed algorithm. By dynamic updating of compensation penalty expectation, computation time is greatly shortened. This improved two-stage compensation algorithm proposed in this paper overcomes the dimensional disaster of the traditional stochastic optimization method, and is capable of solving the dynamic economic dispatching problem considering the high-dimensional correlation of multiple wind farms. Finally, the practicability and efficiency of the proposed algorithm is verified by the examples of IEEE 118 system and an actual provincial system.
引文
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[4]SHAHIRINIA A H,SOOFI E S,YU D C.Probability distributions of outputs of stochastic economic dispatch.International Journal of Electrical Power&Energy Systems,2016,81:308-316.
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[8]ZHANG Menglin,AI Xiaomeng,WEN Jinyu.Economic dispatch for power system integrated with wind power using stackelberg game.Control Theory&Applications,2018,35(5):653-661.(仉梦林,艾小猛,文劲宇.含风电电力系统的主从博弈经济调度.控制理论与应用,2018,35(5):653-661.)
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[10]NIKNAM T,AZIZIPANAH-ABARGHOOSE R,ROOSTA A.Reserve constrained dynamic economic dispatch:A new fast selfadaptive modified firefly algorithm.IEEE Systems Journal,2012,6(4):635-646.
[11]LIU S D,JIAN J B,WANG Y Y,et al.A robust optimization approach to wind farm diversification.International Journal of Electrical Power&Energy Systems,2013,53(53):409-415.
[12]ALVARO L,XU A S.Adaptive robust optimization with dynamic uncertainty sets for multi-period economic dispatch under significant wind.IEEE Transactions on Power Systems,2015,30(4):1702-1713.
[13]TAHER N,HASSAN D M,MAJID N.A new fuzzy adaptive particle swarm optimization for non-smooth economic dispatch.Energy,2010,35(4):1764-1778.
[14]NIKNAM T,GOLESTANEH.Enhanced adaptive particle swarm optimization algorithm for dynamic economic dispatch of units considering valve-point effects and ramp rates.IET Generation,Transmission&Distribution,2012,6(5):424-435.
[15]CHEN Yuanyuan.Implementation of”energy-saving generation dispatching measures(trial)”.China Environment News,2007-08-20(003).(陈媛媛.《节能发电调度办法(试行)》实施.中国环境报,2007-08-20(003).)
[16]XIE Min,ZHU Yanhan,WU Yaxiong,et al.Application of ordinal optimization theory in solving large-scale unit commitment.Control Theory&Applications,2016,33(4):542-551.(谢敏,诸言涵,吴亚雄,等.序优化理论在大规模机组组合求解中的应用.控制理论与应用,2016,33(4):542-551.)
[17]FARHAT I A,EL-HAWARY M E.Dynamic adaptive bacterial foraging algorithm for optimum economic dispatch with valve-point effects and wind power.IET Generation,Transmission&Distribution,2010,4(9):989-999.
[18]SUN Mingsheng,GE Yanxiang.Sulfur dioxide emissions trading system and its application in shandong province.Shandong:Shandong Agricultural University,2010.(孙明晟,葛颜祥.二氧化硫排放权交易制度及其在山东省的应用研究.山东:山东农业大学,2010.)
[19]LING H.Dependence patterns across financial markets:a mixed copula approach.Applied Financial Economics,2006,16(10):717-729.
[20]KAUT M,STEIN W W.Shape-based scenario generation using copulas.Computational Management Science,2011,8(1/2):181-199.
[21]LEHMANN E L.Nonparametrics:statistical methods based on ranks.International Biometric Society,1976,32(2):287-317.
[22]ROGER B.An Introduction to Copulas.New York:Springer Series in Statistics,1999.
[23]DANTZIG G B.Linear programming under uncertainty.Management Science,1955,1(2):197-206.
[24]KALL P.Stochastic Linear Programming.Berlin Heidelberg:Springer,1976.
[25]TOUTOUNIAN F,KARIMI S.Global least squares method(GlLSQR)for solving general linear systems with several right-hand sides.Applied Mathematics and Computation,2006,178(2):452-460.
[26]ZHEN Guoping,ZHAO Liqiang,YU Baiyin,et al.A recurrence algorithm and error analysis in parameter estimate of multivariate linear regression.College Mathematics,2007,23(3):78-82.(郑国萍,赵立强,俞百印,等.多元线性回归模型参数估计的递推算法及误差分析.大学数学,2007,23(3):78-82.)
[27]REN Minghui,LIU Lifang,MEI Hanfei.Editing program with monte-carlo method for calculating multiple integral.Journal of Hunan University of Arts and Science(Natural Science),2011,23(4):1-2.(任明慧,刘丽芳,梅汉飞.多重积分的蒙特卡罗算法编程.湖南文理学院学报(自然科学版),2011,23(4):1-2.)
[28]RADELJAK K,PETRA.Scenario method in spatial research and planning.Croatian Geographical Bulletin,2016,78(1):45-71.
[2]LEE T Y.Optimal spinning reserve for a wind-thermal power system using EIPSO.IEEE Transactions on Power Systems,2007,22(4):1612-1621.
[3]WANG J,SHAHIDEHPOUR M,LI Z.Security-constrained unit commitment with volatile wind power generation.IEEE Transactions on Power Systems,2008,22(4):1319-1327.
[4]SHAHIRINIA A H,SOOFI E S,YU D C.Probability distributions of outputs of stochastic economic dispatch.International Journal of Electrical Power&Energy Systems,2016,81:308-316.
[5]SUN Yuanzhang,WU Jun,LI Guojie,et al.Dynamic economic dispatch considering wind power penetration based on wind speed forecasting and stochastic programming.Proceedings of the CSEE,2009,29(4):41-47.(孙元章,吴俊,李国杰,等.基于风速预测和随机规划的含风电场电力系统动态经济调度.中国电机工程学报,2009,29(4):41-47.)
[6]MALCOLM S A,ZENIOSS A.Robust optimization for power systems capacity expansion under uncertainty.Journal of the Operational Research Society,1994,45(9):1040-1049.
[7]ZHANG M H,GUAN Y P.Two-stage Robust Unit Commitment Problem.Tempe,AZ,USA:Arizona State University,2009.
[8]ZHANG Menglin,AI Xiaomeng,WEN Jinyu.Economic dispatch for power system integrated with wind power using stackelberg game.Control Theory&Applications,2018,35(5):653-661.(仉梦林,艾小猛,文劲宇.含风电电力系统的主从博弈经济调度.控制理论与应用,2018,35(5):653-661.)
[9]WU W C,CHEN J H,ZHANG B M,et al.A robust wind power optimization method for look-ahead power dispatch.IEEE Transactions on Sustainable Energy,2014,5(2):507-515.
[10]NIKNAM T,AZIZIPANAH-ABARGHOOSE R,ROOSTA A.Reserve constrained dynamic economic dispatch:A new fast selfadaptive modified firefly algorithm.IEEE Systems Journal,2012,6(4):635-646.
[11]LIU S D,JIAN J B,WANG Y Y,et al.A robust optimization approach to wind farm diversification.International Journal of Electrical Power&Energy Systems,2013,53(53):409-415.
[12]ALVARO L,XU A S.Adaptive robust optimization with dynamic uncertainty sets for multi-period economic dispatch under significant wind.IEEE Transactions on Power Systems,2015,30(4):1702-1713.
[13]TAHER N,HASSAN D M,MAJID N.A new fuzzy adaptive particle swarm optimization for non-smooth economic dispatch.Energy,2010,35(4):1764-1778.
[14]NIKNAM T,GOLESTANEH.Enhanced adaptive particle swarm optimization algorithm for dynamic economic dispatch of units considering valve-point effects and ramp rates.IET Generation,Transmission&Distribution,2012,6(5):424-435.
[15]CHEN Yuanyuan.Implementation of”energy-saving generation dispatching measures(trial)”.China Environment News,2007-08-20(003).(陈媛媛.《节能发电调度办法(试行)》实施.中国环境报,2007-08-20(003).)
[16]XIE Min,ZHU Yanhan,WU Yaxiong,et al.Application of ordinal optimization theory in solving large-scale unit commitment.Control Theory&Applications,2016,33(4):542-551.(谢敏,诸言涵,吴亚雄,等.序优化理论在大规模机组组合求解中的应用.控制理论与应用,2016,33(4):542-551.)
[17]FARHAT I A,EL-HAWARY M E.Dynamic adaptive bacterial foraging algorithm for optimum economic dispatch with valve-point effects and wind power.IET Generation,Transmission&Distribution,2010,4(9):989-999.
[18]SUN Mingsheng,GE Yanxiang.Sulfur dioxide emissions trading system and its application in shandong province.Shandong:Shandong Agricultural University,2010.(孙明晟,葛颜祥.二氧化硫排放权交易制度及其在山东省的应用研究.山东:山东农业大学,2010.)
[19]LING H.Dependence patterns across financial markets:a mixed copula approach.Applied Financial Economics,2006,16(10):717-729.
[20]KAUT M,STEIN W W.Shape-based scenario generation using copulas.Computational Management Science,2011,8(1/2):181-199.
[21]LEHMANN E L.Nonparametrics:statistical methods based on ranks.International Biometric Society,1976,32(2):287-317.
[22]ROGER B.An Introduction to Copulas.New York:Springer Series in Statistics,1999.
[23]DANTZIG G B.Linear programming under uncertainty.Management Science,1955,1(2):197-206.
[24]KALL P.Stochastic Linear Programming.Berlin Heidelberg:Springer,1976.
[25]TOUTOUNIAN F,KARIMI S.Global least squares method(GlLSQR)for solving general linear systems with several right-hand sides.Applied Mathematics and Computation,2006,178(2):452-460.
[26]ZHEN Guoping,ZHAO Liqiang,YU Baiyin,et al.A recurrence algorithm and error analysis in parameter estimate of multivariate linear regression.College Mathematics,2007,23(3):78-82.(郑国萍,赵立强,俞百印,等.多元线性回归模型参数估计的递推算法及误差分析.大学数学,2007,23(3):78-82.)
[27]REN Minghui,LIU Lifang,MEI Hanfei.Editing program with monte-carlo method for calculating multiple integral.Journal of Hunan University of Arts and Science(Natural Science),2011,23(4):1-2.(任明慧,刘丽芳,梅汉飞.多重积分的蒙特卡罗算法编程.湖南文理学院学报(自然科学版),2011,23(4):1-2.)
[28]RADELJAK K,PETRA.Scenario method in spatial research and planning.Croatian Geographical Bulletin,2016,78(1):45-71.