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计及灵活资源日内调节离散性的日前两阶段分布鲁棒机组组合——基于L1范数Wasserstein模糊集的稀疏建模与求解方法

Day-Ahead Network-Constrained Unit Commitment Considering Distributional Robustness and Intraday Discreteness: A Sparse Solution Approach

摘要:快速启停发电机组等具备强调节能力的设备是保证高比例可再生能源电力系统经济可靠运行的重要灵活资源.通过在电力系统的日前发电计划优化或现货市场出清中构建风电的不确定性模型、快速启停机组日内含离散决策量的运行模型, 本文基于Wasserstein概率分布模糊集建立了含混合整数追索问题的日前两阶段分布鲁棒机组组合优化模型. 为高效计算所建立模型的最优解, 本文提出了两个可行的算法框架. 其中第一个算法用有限多个离散的事件来逼近并最终等效刻画风电出力的连续支撑集, 另一个算法则利用了由子程序辨识得到的风电出力极端概率分布来更新日前机组开停机方案. 两个算法都依赖于经典的嵌套列和约束生成法(the nested column-and-constraint generation method, nested GCG). 本文的理论和计算分析表明, 得益于L1范数Wasserstein距离的稀疏特性, 连续支撑集可以由相对较少的离散事件等效表征,而极限分布同样具有稀疏性. 稀疏性带来的缩减效应使得两个算法均能够高效处理含混合整数追索的两阶段分布鲁棒优化问题. 本文的数值实验表明, 精确考虑快速启停机组的日内离散行为有益于得到更具鲁棒性和经济性的日前机组开停机方案; 此外, 分布鲁棒优化在样本外测试中能够可靠和经济地应对风电出力的不确定性.

英文摘要:Quick-start generation units are critical devices and flexible resources to ensure a high penetration level of renewable energy in power systems. By considering the wind uncertainty, and both binary and continuous decisions of quick-start units within the intraday dispatch, we develop a Wasserstein-metric-based distributionally robust optimization model for the day-ahead network-constrained unit commitment (NCUC) problem with mixed integer recourse. We propose two feasible frameworks for solving the optimization problem. One approximates the continuous support of random wind power with finitely many events, the other leverages the extremal distributions instead. Both solution frameworks rely on the classic nested column-and-constraint generation (CCG) method. It is shown that due to the sparsity of L1-norm Wasserstein metric, the continuous support of wind power generation could be represented by a discrete one with a small number of events, and the extremal distributions rendered are sparse as well. With this reduction, the distributionally robust NCUC model with complicated mixed-integer recourse problems can be efficiently handled by both solution frameworks. Numerical studies are carried out, demonstrating that the model considering quick-start generation units ensures unit commitment (UC) schedules to be more robust and cost effective, and the distributionally robust optimization method captures the wind uncertainty well in terms of out-of-sample tests.

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[V2] 2022-08-07 13:27:42 chinaXiv:202208.00026V2 下载全文
[V1] 2022-08-04 19:39:07 chinaXiv:202208.00026v1 查看此版本 下载全文
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