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Title: Polynomial time algorithms and extended formulations for unit commitment problems
Authors: Guan, YP
Pan, K 
Zhou, KZ
Issue Date: 2018
Source: IISE transactions, 2018, v. 50, no. 8, p. 735-751
Abstract: Recently, increasing penetration of renewable energy generation has created challenges for power system operators to perform efficient power generation daily scheduling, due to the intermittent nature of the renewable generation and discrete decisions of each generation unit. Among all aspects to be considered, a unit commitment polytope is fundamental and embedded in the models at different stages of power system planning and operations. In this article, we focus on deriving polynomial-time algorithms for the unit commitment problems with a general convex cost function and piecewise linear cost function, respectively. We refine an O(T-3) time, where T represents the number of time periods, algorithm for the deterministic single-generator unit commitment problem with a general convex cost function and accordingly develop an extended formulation in a higher-dimensional space that can provide an integral solution, in which the physical meanings of the decision variables are described. This means the original problem can be solved as a convex program instead of a mixed-integer convex program. Furthermore, for the case in which the cost function is piecewise linear, by exploring the optimality conditions, we derive more efficient algorithms for both deterministic (i.e., O(T) time) and stochastic (i.e., O(N) time, where N represents the number of nodes in the stochastic scenario tree) single-generator unit commitment problems. We also develop the corresponding extended formulations for both deterministic and stochastic single-generator unit commitment problems that solve the originalmixed-integer linear programs as linear programs. Similarly, physical meanings of the decision variables are explored to show the insights of the new modeling approach.
Keywords: Unit commitment
Polynomial-time algorithm
Integral formulation
Publisher: Taylor & Francis
Journal: IISE transactions 
ISSN: 2472-5854
EISSN: 2472-5862
DOI: 10.1080/24725854.2017.1397303
Rights: © 2018 “IISE”
This is an Accepted Manuscript of an article published by Taylor & Francis in IISE Transactions on 26 Jan 2018 (Published online), available online: http://www.tandfonline.com/10.1080/24725854.2017.1397303.
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