Polynomial time algorithms and extended formulations for unit commitment problems
Yongpei Guan,
Kai Pan and
Kezhuo Zhou
IISE Transactions, 2018, vol. 50, issue 8, 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(T3)$\mathcal {O}(T^3)$ 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)$\mathcal {O}(T)$ time) and stochastic (i.e., O(N)$\mathcal {O}(N)$ 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 original mixed-integer linear programs as linear programs. Similarly, physical meanings of the decision variables are explored to show the insights of the new modeling approach.
Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (6)
Downloads: (external link)
http://hdl.handle.net/10.1080/24725854.2017.1397303 (text/html)
Access to full text is restricted to subscribers.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:taf:uiiexx:v:50:y:2018:i:8:p:735-751
Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/uiie20
DOI: 10.1080/24725854.2017.1397303
Access Statistics for this article
IISE Transactions is currently edited by Jianjun Shi
More articles in IISE Transactions from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().