基于特殊有效不等式求解机组组合问题的内点割平面法  

An Interior-point Cutting Plane Method for Unit Commitment Based on Special Valid Inequalities

作　　者：全然[1] 简金宝[1] 韦化[1] 杨林峰[1] 

机构地区：[1]广西大学,广西壮族自治区南宁市530004

出　　处：《中国电机工程学报》2011年第19期51-59,共9页Proceedings of the CSEE

基　　金：国家自然科学基金项目(71061002;50867001);高等学校博士学科点专项科研基金资助项目(20070593002;20060593002)~~

摘　　要：基于特殊的有效不等式(valid inequalities,VIs),提出一种求解计及爬坡约束机组组合(unit commitment,UC)问题的内点割平面法。采用线性化技术将UC问题转化为一个混合整数二次规划(mixed integer quadratic programming,MIQP)。根据UC问题约束的特点,产生3种特殊的VIs,即覆盖不等式(cover inequalities,CIs)、提升覆盖不等式(lifted cover inequalities,LCIs)和广义流覆盖不等式(generalized flow cover inequalities,GFCIs),进而将其作为割平面,建立求解MIQP的内点割平面法。100机组24时段等6个系统的仿真结果表明,产生CIs、LCIs和GFCIs的方法快速有效,所提内点割平面法具有良好的收敛性和稳定性,能有效处理爬坡约束,与其他多种方法相比较,获得了更好的数值结果。An interior-point cutting plane method based on special valid inequalities （VIs） was presented for solving the ramp rate constrained unit commitment （UC） problem. The proposed method uses the linearization technique to get a mixed integer quadratic programming （MIQP） formulation for the UC problem. With the characteristics of the constraints of the UC problem, the presented approach yields three classes of special Vls, i.e., cover inequalities （Cls）, lifted cover inequalities （LCIs） and generalized flow cover inequalities （GFCIs）. Then, using CIs, LCIs and GFCIs as cutting planes, an interior-point cutting plane method was proposed to solve the MIQP. The simulation results for six systems up to 100 units and 24 hours show that the methods for generating CIs, LCIs and GFCIs are quick and efficient, and that the interior-point cutting plane method has good convergence and stability properties and can handle the ramp rate constraints efficiently. Furthermore, the proposed algorithm provides better results than many other existing algorithms.

关 键 词：电力系统 机组组合 内点割平面法 有效不等式 覆盖不等式 提升覆盖不等式 广义流覆盖不等式 

分 类 号：TM71[电气工程—电力系统及自动化]