Fast computation of global solutions to the single-period unit commitment problem

• Published in: Journal of combinatorial optimization Vol. 44; no. 3; pp. 1511 - 1536
• Main Authors: Lu, Cheng, Deng, Zhibin, Fang, Shu-Cherng, Jin, Qingwei, Xing, Wenxun
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2022; Springer Nature B.V
• Subjects: Algorithms; Combinatorics; Convex and Discrete Geometry; Electricity; Global optimization; Lower bounds; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Mixed integer; Operations Research/Decision Theory; Optimization; Quadratic programming; Solvers; Theory of Computation; Unit commitment; 90C20; Mixed-integer pogramming; 90C27; Quadratic programming; Branch-and-bound algorithm; 90C11
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-019-00489-9

The single-period unit commitment problem has significant applications in electricity markets. An efficient global algorithm not only provides the optimal schedule that achieves the lowest cost, but also plays an important role for deriving the market-clearing price. As of today, the problem is mainly solved by using a general-purpose mixed-integer quadratic programming solver such as CPLEX or Gurobi. This paper proposes an extremely efficient global optimization algorithm for solving the problem. We propose a conjugate function based convex relaxation and design a special dual algorithm to compute a tight lower bound of the problem in O ( n log n ) complexity. Then, a branch-and-bound algorithm is designed for finding a global solution to the problem. Computational experiments show that the proposed algorithm solves test instances with 500 integer variables in less than 0.01 s, whereas current state-of-the-art solvers fail to solve the same test instances in one hour. This superior performance of the proposed algorithm clearly indicates its potential in day-ahead and real-time electricity markets.