求解机组组合问题的次超立方紧混合整数规划广义割平面法  

A Sub Hyper-cube Tight Mixed Integer Programming Extended Cutting Plane Method for Unit Commitment

作　　者：杨林峰[1] 简金宝[2] 郑海艳[1] 韩道兰[1] 

机构地区：[1]广西大学,广西壮族自治区南宁市530004 [2]玉林师范学院,广西壮族自治区玉林市537000

出　　处：《中国电机工程学报》2013年第1期99-108,共10页Proceedings of the CSEE

基　　金：国家自然科学基金项目(71061002);广西自然科学基金项目(2011GXNSFD018022);广西高校人才小高地创新团队资助计划~~

摘　　要：为改进机组组合(unit commitment,UC)问题的求解效率,基于超立方(hyper-cube,HC)投影,构造了计及爬坡约束UC问题的次超立方混合整数规划(sub HC mixed integer programming,SHC-MIP)模型,并基于该模型和广义割平面(extended cutting plane,ECP)技术,提出一种新的求解UC问题的确定性方法(SHC-MIP-ECP)。该方法首先利用超立方投影将UC问题的混合整数规划(mixed integerprogramming,MIP)模型等价投影为具有更紧连续松弛的SHC-MIP模型。然后采用ECP方法产生序列混合整数线性规划来求解SHC-MIP模型。10—100机组24时段等7个算例的仿真结果表明:利用ECP方法求解UC问题的2种模型时,SHC-MIP能比MIP获得质量更好的次优解;此外,所提方法计算速度快,适合求解大规模UC问题。In order to improve the efficiency of solving unit commitment （UC） problem, a novel sub hyper-cube mixed integer programming （SHC-MIP） model of the ramp rate constrained UC problem is presented by using the technique of hyper-cube （HC） projection, and a new deterministic method is presented for solving UC problem based on the proposed model and extended cutting plane （ECP） method. Named as SHC-MIP-ECP, the proposed method involves reformulating the UC problem into a tight SHC-MIP model with HC projection, and applying ECP method to solve SHC-MIP by a sequence of mixed integer linear programming. The simulation results for 7 systems that range in size from 10 to 100 units and 24 hours show that the SHC-MIP model can get better sub-optimal solutions of the UC problem than the traditional mixed integer programming （MIP） when ECP method is used, and the proposed method is very promising for large scale UC problems due to its excellent performance and results.

关 键 词：机组组合 爬坡约束 超立方投影 混合整数规划 广义割平面 

分 类 号：TM71[电气工程—电力系统及自动化]