分类： 动力与电气工程 >> 电气工程 分类： 数学 >> 控制和优化 提交时间： 2022-08-07
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.
分类： 核科学技术 >> 核科学与技术 提交时间： 2023-08-27
摘要： Intensity-modulated particle therapy (IMPT) with carbon ions is comparatively susceptible to various uncertainties caused by breathing motion, including range, setup, and target positioning uncertainties. To determine relative biological effectiveness-weighted dose (RWD) distributions that are resilient to these uncertainties, the reference phase-based four-dimensional (4D) robust optimization (RP-4DRO) and each phase-based 4D robust optimization (EP-4DRO) method in carbon-ion IMPT treatment planning were evaluated and compared. Based on RWD distributions, 4DRO methods were compared with 4D conventional optimization using planning target volume (PTV) margins (PTV-based optimization) to assess the effectiveness of the robust optimization methods. Carbon-ion IMPT treatment planning was conducted in a cohort of five lung cancer patients. The results indicated that the EP-4DRO method provided better robustness (P=0.080) and improved plan quality (P=0.225) for the clinical target volume (CTV) in the individual respiratory phase when compared with the PTV-based optimization. Compared with the PTV-based optimization, the RP-4DRO method ensured the robustness (P = 0.022) of the dose distributions in the reference breathing phase, albeit with a slight sacrifice of the target coverage (P=0.450). Both 4DRO methods successfully maintained the doses delivered to the organs at risk (OARs) below tolerable levels, which were lower than the doses in the PTV-based optimization (P<0.05). Furthermore, the RP-4DRO method exhibited significantly superior performance when compared with the EP-4DRO method in enhancing overall OAR sparing in either the individual respiratory phase or reference respiratory phase (P<0.05). In general, both 4DRO methods outperformed the PTV-based optimization in terms of OAR sparing and robustness.
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