Projected mixed integer programming formulations for unit commitment problem

Linfeng Yang; Jinbao Jian; Yuanyuan Wang; Zhaoyang Dong

doi:10.1016/j.ijepes.2014.12.054

Projected mixed integer programming formulations for unit commitment problem

Linfeng Yang
, Jinbao Jian^*
, Yuanyuan Wang
, Zhaoyang Dong

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

33 Citations (Scopus)

Abstract

The thermal unit commitment (UC) problem is a large-scale mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. This paper presents a projected reformulation for UC problem. After projecting the power output of unit onto [0,1], a novel MIQP reformulation, denoted as P-MIQP, can be formed. The obtained P-MIQP is tighter than traditional MIQP formulation of UC problem. And the reduced problem of P-MIQP, which is eventually solved by solvers such as CPLEX, is compacter than that of traditional MIQP. In addition, two mixed integer linear programming (MILP) formulations can be obtained from traditional MIQP and our P-MIQP of UC by replacing the quadratic terms in the objective functions with a sequence of piece-wise perspective-cuts. Projected MILP is also tighter and compacter than the traditional MILP due to the same reason of MIQP. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the projected reformulation yields tight and compact mixed integer programming UC formulations, which are competitive with currently traditional ones. © 2014 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	195-202
Journal	International Journal of Electrical Power and Energy Systems
Volume	68
DOIs	https://doi.org/10.1016/j.ijepes.2014.12.054
Publication status	Published - Jun 2015
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Compact
Mixed integer programming
Project
Tight
Unit commitment

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@article{57da5d4363904f6dba5229fb96567c12,

title = "Projected mixed integer programming formulations for unit commitment problem",

abstract = "The thermal unit commitment (UC) problem is a large-scale mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. This paper presents a projected reformulation for UC problem. After projecting the power output of unit onto [0,1], a novel MIQP reformulation, denoted as P-MIQP, can be formed. The obtained P-MIQP is tighter than traditional MIQP formulation of UC problem. And the reduced problem of P-MIQP, which is eventually solved by solvers such as CPLEX, is compacter than that of traditional MIQP. In addition, two mixed integer linear programming (MILP) formulations can be obtained from traditional MIQP and our P-MIQP of UC by replacing the quadratic terms in the objective functions with a sequence of piece-wise perspective-cuts. Projected MILP is also tighter and compacter than the traditional MILP due to the same reason of MIQP. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the projected reformulation yields tight and compact mixed integer programming UC formulations, which are competitive with currently traditional ones. {\textcopyright} 2014 Elsevier Ltd. All rights reserved.",

keywords = "Compact, Mixed integer programming, Project, Tight, Unit commitment",

author = "Linfeng Yang and Jinbao Jian and Yuanyuan Wang and Zhaoyang Dong",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].",

year = "2015",

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doi = "10.1016/j.ijepes.2014.12.054",

language = "English",

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pages = "195--202",

journal = "International Journal of Electrical Power and Energy Systems",

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TY - JOUR

T1 - Projected mixed integer programming formulations for unit commitment problem

AU - Yang, Linfeng

AU - Jian, Jinbao

AU - Wang, Yuanyuan

AU - Dong, Zhaoyang

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2015/6

Y1 - 2015/6

N2 - The thermal unit commitment (UC) problem is a large-scale mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. This paper presents a projected reformulation for UC problem. After projecting the power output of unit onto [0,1], a novel MIQP reformulation, denoted as P-MIQP, can be formed. The obtained P-MIQP is tighter than traditional MIQP formulation of UC problem. And the reduced problem of P-MIQP, which is eventually solved by solvers such as CPLEX, is compacter than that of traditional MIQP. In addition, two mixed integer linear programming (MILP) formulations can be obtained from traditional MIQP and our P-MIQP of UC by replacing the quadratic terms in the objective functions with a sequence of piece-wise perspective-cuts. Projected MILP is also tighter and compacter than the traditional MILP due to the same reason of MIQP. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the projected reformulation yields tight and compact mixed integer programming UC formulations, which are competitive with currently traditional ones. © 2014 Elsevier Ltd. All rights reserved.

AB - The thermal unit commitment (UC) problem is a large-scale mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. This paper presents a projected reformulation for UC problem. After projecting the power output of unit onto [0,1], a novel MIQP reformulation, denoted as P-MIQP, can be formed. The obtained P-MIQP is tighter than traditional MIQP formulation of UC problem. And the reduced problem of P-MIQP, which is eventually solved by solvers such as CPLEX, is compacter than that of traditional MIQP. In addition, two mixed integer linear programming (MILP) formulations can be obtained from traditional MIQP and our P-MIQP of UC by replacing the quadratic terms in the objective functions with a sequence of piece-wise perspective-cuts. Projected MILP is also tighter and compacter than the traditional MILP due to the same reason of MIQP. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the projected reformulation yields tight and compact mixed integer programming UC formulations, which are competitive with currently traditional ones. © 2014 Elsevier Ltd. All rights reserved.

KW - Compact

KW - Mixed integer programming

KW - Project

KW - Tight

KW - Unit commitment

UR - https://www.scopus.com/pages/publications/84920730723

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84920730723&origin=recordpage

U2 - 10.1016/j.ijepes.2014.12.054

DO - 10.1016/j.ijepes.2014.12.054

M3 - RGC 21 - Publication in refereed journal

SN - 0142-0615

VL - 68

SP - 195

EP - 202

JO - International Journal of Electrical Power and Energy Systems

JF - International Journal of Electrical Power and Energy Systems

ER -

Projected mixed integer programming formulations for unit commitment problem

Abstract

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Research Keywords

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