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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| Published in: | Journal of combinatorial optimization Vol. 44; no. 3; pp. 1511 - 1536 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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Springer US
01.10.2022
Springer Nature B.V |
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| ISSN: | 1382-6905, 1573-2886 |
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| Abstract | 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
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n
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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. |
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| AbstractList | 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. 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(nlogn) 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. |
| Author | Deng, Zhibin Lu, Cheng Fang, Shu-Cherng Jin, Qingwei Xing, Wenxun |
| Author_xml | – sequence: 1 givenname: Cheng surname: Lu fullname: Lu, Cheng organization: School of Economics and Management, North China Electric Power University – sequence: 2 givenname: Zhibin orcidid: 0000-0003-0563-5841 surname: Deng fullname: Deng, Zhibin email: zhibindeng@ucas.edu.cn organization: School of Economics and Management, University of Chinese Academy of Sciences, Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences – sequence: 3 givenname: Shu-Cherng surname: Fang fullname: Fang, Shu-Cherng organization: Department of Industrial and Systems Engineering, North Carolina State University – sequence: 4 givenname: Qingwei surname: Jin fullname: Jin, Qingwei organization: Department of Management Science and Engineering, Zhejiang University – sequence: 5 givenname: Wenxun surname: Xing fullname: Xing, Wenxun organization: Department of Mathematical Sciences, Tsinghua University |
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| References_xml | – volume: 164 start-page: 269 year: 2005 end-page: 285 ident: CR12 article-title: Efficient market-clearing prices in markets with nonconvexities publication-title: Eur J Oper Res doi: 10.1016/j.ejor.2003.12.011 – year: 1979 ident: CR5 publication-title: Computers and intractability: a guide to the theory of NP-completeness – year: 1970 ident: CR16 publication-title: Convex analysis doi: 10.1515/9781400873173 – volume: 106 start-page: 403 year: 2006 end-page: 421 ident: CR1 article-title: New algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds publication-title: Math Program doi: 10.1007/s10107-005-0595-2 – volume: 18 start-page: 452 year: 2003 end-page: 459 ident: CR4 article-title: Reconciling social welfare, agent profits, and consumer payments in electricity pools publication-title: IEEE Trans Power Syst doi: 10.1109/TPWRS.2003.810676 – year: 2001 ident: CR11 publication-title: Electric power system applications of optimization (Power Engineering (Willis)) – volume: 46 start-page: 321 year: 1990 end-page: 328 ident: CR14 article-title: An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds publication-title: Math Program doi: 10.1007/BF01585748 – volume: 27 start-page: 1334 year: 2012 end-page: 1342 ident: CR17 article-title: Pricing non-convexities in an electricity pool publication-title: IEEE Trans Power Syst doi: 10.1109/TPWRS.2012.2184562 – volume: 27 start-page: 525 year: 2016 end-page: 543 ident: CR8 article-title: Optimal hour-ahead bidding in the real-time electricity market with battery storage using approximate dynamic programming publication-title: INFORMS J Comput doi: 10.1287/ijoc.2015.0640 – ident: CR13 – year: 2004 ident: CR15 publication-title: Variational analysis. 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| SubjectTerms | 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 |
| Title | Fast computation of global solutions to the single-period unit commitment problem |
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