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考虑风功率预测条件误差和时空关联性的分布鲁棒机组组合模型及算法

Addressing the Conditional and Correlated Wind Power Forecast Errors in Unit Commitment by Distributionally Robust Optimization

摘要:本文研究含随机风电的机组组合问题, 基于分布鲁棒优化提出了考虑风功率预测的条件误差和误差时空相关性的建模及优化方法. 首先, 为了量化计算风功率的预测误差, 用Lasso(最小绝对值收敛和选择算子)训练得到鲁棒的条件误差估计器;为了获取风功率预测误差的时空关联信息, 通过无偏估计从历史数据得到误差的协方差矩阵. 用所得的条件误差和协方差矩阵构造了改进的风功率预测误差的概率分布模糊集. 其次, 在多面体支撑集上建立了风功率预测误差的随机量, 构建了两阶段分布鲁棒机组组合模型, 并提出了与该模型等效的混合整数半正定规划模型. 再次, 提出了从第二阶段半正定优化问题辨识极限分布的方法, 并提出了利用极限分布求解两阶段分布鲁棒机组组合问题的高效割平面算法. 最后, 进行数值实验, 验证了所提模型在应对风功率预测误差的时空关联性方面的能力和优势, 验证了模型决策方案的经济性和鲁棒性.

英文摘要:In this paper, a study of the day-ahead unit commitment problem with stochastic wind power generation is presented, which considers conditional and correlated wind power forecast errors through a distributionally robust optimization approach. Firstly, to capture the characteristics of random wind power forecast errors, the least absolute shrinkage and selection operator (Lasso) is utilized to develop a robust conditional error estimator, while an unbiased estimator is used to obtain the covariance matrix. The conditional error and the covariance matrix are then used to construct an enhanced ambiguity set. Secondly, we develop an equivalent mixed integer semidefinite programming (MISDP) formulation of the two-stage distributionally robust unit commitment model with a polyhedral support of random variables. Further, to efficiently solve this problem, a novel cutting plane algorithm that makes use of the extremal distributions identified from the second-stage semidefinite programming (SDP) problems is introduced. Finally, numerical case studies show the advantage of the proposed model in capturing the spatiotemporal correlation in wind power generation, as well as the economic efficiency and robustness of dispatch decisions.

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[V2] 2022-08-07 13:16:07 chinaXiv:202208.00027V2 下载全文
[V1] 2022-08-04 09:49:18 chinaXiv:202208.00027v1 查看此版本 下载全文
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