计及风电时间相关性的鲁棒机组组合
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摘要
鲁棒优化是解决大规模新能源接入后电力系统调度的重要手段。相比于基于场景的随机规划、带有风险约束的机组组合等,鲁棒机组组合的结果往往偏于保守。鲁棒优化的保守性直接受到不确定集合的影响。研究了风电预测误差时间相关特点,提出了基于自相关性的时间相关性约束。并利用不确定集合的离散性特点,将该约束近似简化为可以用于实际鲁棒优化问题的线性约束。在列与限制生成(C&CG)算法的基础上,改进了Bender’s分解后子问题的求解算法,提出了一种适合离散型不确定集合的鲁棒优化求解方法。最后,以真实风电数据进行了大量的仿真实验。结果表明,提出的算法能够在不影响机组组合可靠性的前提下,降低鲁棒优化保守性。
Robust optimization(RO)is an important tool to solve dispatch problem for power system with large scale renewable energy.Comparing with stochastic optimization and risk-constrained unit commitment,over-conservativeness is a major shortcoming for RO.The conservativeness of RO is directly infected by uncertainty set.The temporal correlation characteristics of wind farm output are studied and a time-correlation constraint based on Pearson correlation coefficient is established.Then,the constraint is simplified and applied in robust unit commitment(RUC)by using discrete characteristics of uncertainty set.The solution of sub problem in Bender's decomposition is improved.Based on column and constraint generation algorithm,a new solution for RO with discrete uncertainty set is developed.Numerical experiments are performed with the actual data of wind farms.The results show that the proposed algorithm can improve RUC performance without jeopardize system robustness.
Robust optimization(RO)is an important tool to solve dispatch problem for power system with large scale renewable energy.Comparing with stochastic optimization and risk-constrained unit commitment,over-conservativeness is a major shortcoming for RO.The conservativeness of RO is directly infected by uncertainty set.The temporal correlation characteristics of wind farm output are studied and a time-correlation constraint based on Pearson correlation coefficient is established.Then,the constraint is simplified and applied in robust unit commitment(RUC)by using discrete characteristics of uncertainty set.The solution of sub problem in Bender's decomposition is improved.Based on column and constraint generation algorithm,a new solution for RO with discrete uncertainty set is developed.Numerical experiments are performed with the actual data of wind farms.The results show that the proposed algorithm can improve RUC performance without jeopardize system robustness.
引文
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[2]国家发展和改革委员会能源研究所.中国风电发展路线图2050[R].2011.Energy Research Institute National Development and Reform Commission Renewable Energy.Wind power development roadmap of China for 2050[R].2011.
[3]ZHANG Y,WANG J,WANG X.Review on probabilistic forecasting of wind power generation[J].Renewable and Sustainable Energy Reviews,2014,32:255-270.
[4]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.
[5]WEI W,LIU F,MEI S,et al.Robust energy and reserve dispatch under variable renewable generation[J].IEEE Transactions on Smart Grid,2015,6(1):369-380.
[6]WEI W,LIU F,MEI S W.Dispatchable region of the variable wind generation[J].IEEE Transactions on Power Systems,2015,30(5):2755-2765.
[7]ZHAO C,GUAN Y.Unified stochastic and robust unit commitment[J].IEEE Transactions on Power Systems,2013,28(3):3353-3361.
[8]AN Y,ZENG B.Exploring the modeling capacity of two-stage robust optimization:variants of robust unit commitment model[J].IEEE Transactions on Power Systems,2015,30(1):109-122.
[9]WANG C,LIU F,WANG J,et al.Risk-based admissibility assessment of wind generation integrated into a bulk power system[J].IEEE Transactions on Sustainable Energy,2016,7(1):325-336.
[10]SOYSTER A L.Technical note—convex programming with set-inclusive constraints and applications to inexact linear programming[J].Operations Research,1973,21(5):1154-1157.
[11]BEN-TAL A,GORYASHKO A,GUSLITZER E,et al.Adjustable robust solutions of uncertain linear programs[J].Mathematical Programming,2004,99(2):351-376.
[12]BEN-TAL A,NEMIROVSKI A.Robust optimization—methodology and applications[J].Mathematical Programming,2002,92(3):453-480.
[13]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.
[14]ZHANG N,KANG C,XIA Q,et al.Modeling conditional forecast error for wind power in generation scheduling[J].IEEE Transactions on Power Systems,2014,29(3):1316-1324.
[15]张宁,康重庆.风电出力分析中的相依概率性序列运算[J].清华大学学报(自然科学版),2012,52(5):704-709.ZHANG Ning,KANG Chongqing.Dependent probabilistic sequence operations for wind power output analyses[J].Journal of Tsinghua University(Science and Technology),2012,52(5):704-709.
[16]蔡菲,严正,赵静波,等.基于Copula理论的风电场间风速及输出功率相依结构建模[J].电力系统自动化,2013,37(17):9-16.CAI Fei,YAN Zheng,ZHAO Jingbo,et al.Dependence structure models for wind speed and wind power among different wind farms based on Copula theory[J].Automation of Electric Power Systems,2013,37(17):9-16.
[17]汤雪松,殷明慧,邹云.考虑风速相关性的风电穿透功率极限的改进计算[J].电网技术,2015,39(2):420-425.TANG Xuesong,YIN Minghui,ZOU Yun.An improved method to calculate wind power penetration limit considering wind speed correlation[J].Power System Technology,2015,39(2):420-425.
[18]SOMAN S S,ZAREIPOUR H,MALIK O,et al.A review of wind power and wind speed forecasting methods with different time horizons[C]//Proceedings of the North American Power Symposium(NAPS),September 26-28,2010,Arlington,USA.
[19]HOCAOGLU F O,GEREK O N,KURBAN M.The effect of Markov chain state size for synthetic wind speed generation[C]//Proceedings of the 10th International Conference on Probabilistic Methods Applied to Power Systems,May 25-29,2008,Rincon,Puerto Rico.
[20]BEL G,CONNAUGHTON C P,TOOTS M,et al.Grid-scale fluctuations and forecast error in wind power[J].Physics,2016,18:023015.
[21]JABR R A.Adjustable robust OPF with renewable energy sources[J].IEEE Transactions on Power Systems,2013,28(4):4742-4751.
[22]Transnet BW公司.德国巴登-符腾堡州风电预测数据.[EB/OL].[2018-01-01].https://www.transnetbw.com/en.Transnet BW.Wind power forecast data for BadenWürttemberg,Germany[EB/OL].[2018-01-01].https://www.transnetbw.com/en.
[23]WOLSEY L.Integer programming[M].New York:Wiley Inter-Science,1998.
[24]伊利诺伊理工大学.IEEE标准测试模型[EB/OL].[2014-10-01].http://motor.ece.iit.edu/data/.Illinois Institute of Technology.IEEE standard test model[EB/OL].[2014-10-01].http://motor.ece.iit.edu/data/.
[25]LOFBERG J.YALMIP:a toolbox for modeling and optimization in MATLAB[C]//IEEE International Symposium on Computer Aided Control Systems Design,September 2-4,2004,New Orleans,USA:284-289.