基于改进的Benders分解与透视割平面的机组组合算法

Unit commitment algorithm based on improved Benders decomposition and perspective cut

经典的Benders分解法（BDM）将问题分解为主问题与子问题2个简单的形式进行求解,由于主问题是一个混合整数问题,其求解是BDM中最费时的部分。基于改进的BDM与透视割平面（PC）,提出一种求解火电机组组合（UC）问题的新算法。首先结合覆盖不等式提出改进的松弛型BDM;然后借助于PC和线性化技术建立UC问题的近似混合整数线性规划（MILP）模型;最后利用松弛型BDM求解该模型。包含10~1000台机组的多个系统24时段的测试结果以及与其他方法的比较说明所提算法是有效的。

Classical BDM（Benders Decomposition Method） decomposes a problem into master problem and sub-problem in simple form and solves them. As the master problem is a mixed integer problem,to solve it is the most time-consuming part of BDM. In order to solve the UC（Unit Commitment） problem of thermal power,an algorithm based on improved BDM and PC（Perspective Cut） is proposed. Combined with the cover inequality,an improved relaxed BDM is proposed and,based on PC and linearization technique,an approximate MILP（Mixed Integer Linear Programming） model is established. The UC problem is then solved by the relaxed BDM. The test results of 24-period,10~1000-unit systems and the comparison between two methods prove the proposed algorithm effective.