UC问题的高维三周期局部理想MIP公式
High Dimensional Three-Periods Locally Ideal MIP Formulations for the UC Problem
摘要：
火电机组组合问题通常可以归结为一个混合整数二次规划问题，特别是对于大规模的火电机组组合问题，其求解效率很低。更紧密的特征减少了搜索空间，因此，作为一个自然的结果，显着减少了计算负担。在文献中，许多收紧的单一单位与部分约束的配方报道，没有介绍他们是如何推导出来的。在本文中，一个系统的方法来制定严格的配方。其思想是在高维空间中引入更多的新变量来捕获单个单元在三个周期内的所有状态，然后利用这些状态变量系统地推导出UC中约束子集的三个周期的局部理想表达式。同时，利用这些新的状态变量的线性相关关系，保持了所得到的公式的紧凑性。基于这种方法，我们提出了两个更紧密的模型，即3 P-HD和3 P-HD-Pr。所提出的模型和其他四个国家的最先进的模型进行了测试，在51个实例，包括42个现实的实例和9个8单元为基础的实例，在24小时的调度期内，系统范围从10到1080发电机组。仿真结果表明，我们提出的MIQP UC公式是最紧密的，可以最有效地解决。采用分段逼近技术对二次型运营费用函数进行逼近后，六个UC MIQP公式可近似为六个相应的混合整数线性规划（MILP）公式。我们的实验表明，所提出的3 P-HD和3 P-HD-Pr MILP配方在紧密性和溶解时间方面也表现得最好。
英文摘要：
The thermal unit commitment (UC) problem often can be formulated as a mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. The tighter characteristic reduces the search space, therefore, as a natural conse-quence, significantly reduces the computational burden. In the literature, many tightened formulations for single units with parts of constraints were reported without presenting how they were derived. In this paper, a sys-tematic approach is developed to formulate the tight formulations. The idea is using more new variables in high dimension space to capture all the states for single units within three periods, and then, using these state variables systematic derive three-periods locally ideal expressions for a subset of the constraints in UC. Meanwhile, the linear dependence relations of those new state variables are leveraged to keep the compactness of the obtained formulations. Based on this approach, we propose two tighter models, namely 3P-HD and 3P-HD-Pr. The proposed models and other four state-of-the-art models were tested on 51 instances, including 42 realistic instances and 9 8-unit-based instances, over a scheduling period of 24 h for systems ranging from 10 to 1080 generating units. The simulation results show that our proposed MIQP UC formulations are the tightest and can be solved most efficiently. After using piecewise technique to approxi-mate the quadratic operational cost function, the six UC MIQP formulations can be approximated by six corre-sponding mixed-integer linear programming (MILP) formulations. Our experiments show that the proposed 3P-HD and 3P-HD-Pr MILP formulations also perform the best in terms of tightness and solution times.
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