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Effects of binary variables in mixed integer linear programming based unit commitment in large-scale electricity markets

机译：电力市场中基于混合整数线性规划的二元变量对机组承诺的影响

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Mixed integer linear programming is one of the main approaches used to solve unit commitment problems. Due to the computational complexity of unit commitment problems, several researches remark the benefits of using less binary variables or relaxing them for the branch-and-cut algorithm. However, integrality constraints relaxation seems to be case dependent because there are many instances where applying it may not improve the computational burden. In addition, there is a lack of extensive numerical experiments evaluating the effects of the relaxation of binary variables in mixed integer linear programming based unit commitment. Therefore, the primary purpose of this work is to analyze the effects of binary variables and compare different relaxations, supported by extensive computational experiments. To accomplish this objective, two power systems are used for the numerical tests: the IEEE118 test system and a very large scale real system. The results suggest that a direct link between the relaxation of binary variables and computational burden cannot be easily assured in the general case. Therefore, relaxing binary variables should not be used as a general rule-of-practice to improve computational burden, at least, until each particular model is tested under different load scenarios and formulations to quantify the final effects of binary variables on the specific UC implementation. The secondary aim of this work is to give some preliminary insight into the reasons that could be supporting the binary relaxation in some UC instances. (C) 2018 Elsevier B.V. All rights reserved.
机译：混合整数线性规划是用于解决单元承诺问题的主要方法之一。由于单位承诺问题的计算复杂性，一些研究指出使用较少的二进制变量或将其放宽用于分支剪切算法的好处。但是，完整性约束松弛似乎取决于大小写，因为在许多情况下应用它可能不会改善计算负担。此外，在基于混合整数线性规划的单元承诺中，缺乏广泛的数值实验来评估二进制变量的松弛效果。因此，这项工作的主要目的是分析二进制变量的影响，并在广泛的计算实验的支持下比较不同的松弛。为了实现此目标，两个电源系统用于数值测试：IEEE118测试系统和超大规模实测系统。结果表明，在一般情况下，二进制变量的松弛与计算负担之间的直接联系不容易得到保证。因此，至少在直到每个特定模型在不同的负载场景和公式下进行测试以量化二进制变量对特定UC实施的最终影响之前，放松二进制变量不应被用作改善计算负担的一般惯例。 。这项工作的次要目的是对可能支持某些UC实例中的二进制松弛的原因提供一些初步的见解。 （C）2018 Elsevier B.V.保留所有权利。

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