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.

中文翻译：

---

通过分布稳健优化解决机组组合中有条件和相关的风力发电预测误差

本文对具有随机风力发电的日提前机组承诺问题进行了研究，该研究通过分布稳健的优化方法考虑了有条件的和相关的风力发电预测误差。首先，为了捕获随机风电预测误差的特征，利用最小绝对收缩和选择算子（Lasso）来开发鲁棒的条件误差估计器，而使用无偏估计器来获得协方差矩阵。然后使用条件误差和协方差矩阵来构造增强的歧义集。其次，我们开发了具有随机变量多面体支持的两阶段分布鲁棒单位承诺模型的等效混合整数半定规划（MISDP）公式。进一步，为了有效解决此问题，介绍了一种新颖的切割平面算法，该算法利用了从第二阶段半定规划（SDP）问题中识别出的极值分布。最后，数值案例研究表明，该模型在捕获风力发电时空相关性，经济效率和调度决策的鲁棒性方面具有优势。