机组组合问题的超立方锥松弛模型及其求解方法  

A Hyper-Cube Cone Relaxation Model and Solution for Unit Commitment

作　　者：杨林峰[1] 简金宝[2] 韩道兰[1] 郑海艳[1] 

机构地区：[1]广西大学,南宁530004 [2]玉林师范学院,玉林537000

出　　处：《电工技术学报》2013年第7期252-261,共10页Transactions of China Electrotechnical Society

基　　金：国家自然科学基金(71061002;71201049);广西自然科学基金(2011GXNSFD018022;2013GXNSFBA019246)资助项目

摘　　要：基于凸包变换和提升-投影锥(cone)松弛技术,在超立方(hyper-cube)空间内构造了计及爬坡约束机组组合(UC)问题的紧连续松弛(TCR)模型(HC-Cone-TCR),提出一种通过求解紧松弛模型从而获得UC问题次优解的新方法。将UC问题的混合整数规划(MIP)模型等价投影至超立方空间,再通过两次凸包变换,使得模型的直接连续松弛逐步变紧,进而获得UC问题的超立方混合整数规划模型(HC-MIP)。采用锥松弛技术,继续压缩HC-MIP的连续松弛问题可行域,获得UC问题的紧松弛模型HC-Cone-TCR。采用内点法求解该模型,并通过适当的启发式调整可获得UC问题的次优解。10～100机组24时段6个算例的仿真结果表明,所构造的HC-Cone-TCR模型是UC问题的一个好的紧连续松弛,基于该模型的UC问题直接求解方法,计算速度快,能获得高质量次优解,适合求解大规模UC问题。A new tighter continuous relaxation（TCR） model of the ramp rate constrained unit commitment（UC） problem in hyper-cube（HC） space is presented by integrating the techniques of convex hull transformation and lift-project cone relaxation. Named as HC-Cone-TCR, the proposed model can be solved directly to obtain the sub-optimal solutions of the UC problem. A hyper-cube mixed integer programming model（HC-MIP） of the UC problem is proposed by projecting the traditional MIP model to hyper-cube space and tightening it with the convex hull transformation technique. Based on the HC-MIP model and cone relaxation technique, the tighter continuous relaxation model（HC-Cone-TCR） of the UC problem is established. This model can be solved by interior point method, and the solutions can be corrected to be the sub-optimal solutions of the UC problem by heuristic methods. The simulation results for systems that range in size from 10 to 100 units and 24 hours show that the HC-Cone-TCR is a excellent tighter continuous relaxation of the UC problem 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 锥规划 凸包 紧松弛 

分 类 号：TM73[电气工程—电力系统及自动化]