Tight Relaxation Method for Unit Commitment Problem Using Reformulation and Lift-and-Project

• Published in: IEEE transactions on power systems Vol. 30; no. 1; pp. 13 - 23
• Main Authors: Yang, Linfeng, Jian, Jinbao, Zhu, Yunan, Dong, Zhaoyang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Computer simulation; Heuristic; Integer programming; Lift-and-project; Linear programming; Mathematical models; Programming; reformulation; relaxation; Relaxation methods; Scheduling; Simulation; Solvers; Spinning; Strengthening; tightness; Time factors; Unit commitment; Vectors
• ISSN: 0885-8950; 1558-0679
• DOI: 10.1109/TPWRS.2014.2326920

This paper presents a novel method to solve the unit commitment (UC) problem by solving a sequence of increasingly tight continuous relaxations based on the techniques of reformulation and lift-and-project (L&P). After projecting the power output of unit onto [0, 1], the continuous relaxation of the UC problem can be tightened with the reformulation techniques. Then, a tighter model which is called L&P-TMIP is established by strengthening the continuous relaxation of the feasible region of the tight UC problem iteratively using L&P. High-quality suboptimal solutions can be obtained from the solutions of the relaxation for this tight model. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the proposed tight relaxation method is competitive with general-purpose mixed integer programming solvers based methods for large-scale UC problems due to the excellent performance and the good quality of the solutions it generates.