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

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 main...

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Veröffentlicht in:Journal of combinatorial optimization Jg. 44; H. 3; S. 1511 - 1536
Hauptverfasser: Lu, Cheng, Deng, Zhibin, Fang, Shu-Cherng, Jin, Qingwei, Xing, Wenxun
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.10.2022
Springer Nature B.V
Schlagworte:
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
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-019-00489-9