On Mixed-Integer Programming Formulations for the Unit Commitment Problem
Abstract
We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved—and in the process, we identify a new state-of-the-art UC formulation.
- Authors:
-
[1];
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Discrete Math & Optimization
- Univ. of Tennessee, Knoxville, TN (United States). Industrial and Systems Engineering
- Sandia National Lab. (SNL-CA), Livermore, CA (United States). Data Science & Cyber Analytics
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE Office of Electricity (OE); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1670724
- Report Number(s):
- SAND-2019-13440J
Journal ID: ISSN 1091-9856; 681098
- Grant/Contract Number:
- AC04-94AL85000; SC0018175; NA0003525
- Resource Type:
- Accepted Manuscript
- Journal Name:
- INFORMS Journal on Computing
- Additional Journal Information:
- Journal Volume: 32; Journal Issue: 4; Journal ID: ISSN 1091-9856
- Publisher:
- INFORMS
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Knueven, Bernard, Ostrowski, James, and Watson, Jean-Paul. On Mixed-Integer Programming Formulations for the Unit Commitment Problem. United States: N. p., 2020.
Web. doi:10.1287/ijoc.2019.0944.
Knueven, Bernard, Ostrowski, James, & Watson, Jean-Paul. On Mixed-Integer Programming Formulations for the Unit Commitment Problem. United States. https://doi.org/10.1287/ijoc.2019.0944
Knueven, Bernard, Ostrowski, James, and Watson, Jean-Paul. Thu .
"On Mixed-Integer Programming Formulations for the Unit Commitment Problem". United States. https://doi.org/10.1287/ijoc.2019.0944. https://www.osti.gov/servlets/purl/1670724.
@article{osti_1670724,
title = {On Mixed-Integer Programming Formulations for the Unit Commitment Problem},
author = {Knueven, Bernard and Ostrowski, James and Watson, Jean-Paul},
abstractNote = {We provide a comprehensive overview of mixed-integer programming formulations for the unit commitment (UC) problem. UC formulations have been an especially active area of research over the past 12 years due to their practical importance in power grid operations, and this paper serves as a capstone for this line of work. We additionally provide publicly available reference implementations of all formulations examined. We computationally test existing and novel UC formulations on a suite of instances drawn from both academic and real-world data sources. Driven by our computational experience from this and previous work, we contribute some additional formulations for both generator production upper bounds and piecewise linear production costs. By composing new UC formulations using existing components found in the literature and new components introduced in this paper, we demonstrate that performance can be significantly improved—and in the process, we identify a new state-of-the-art UC formulation.},
doi = {10.1287/ijoc.2019.0944},
journal = {INFORMS Journal on Computing},
number = 4,
volume = 32,
place = {United States},
year = {Thu Jun 25 00:00:00 EDT 2020},
month = {Thu Jun 25 00:00:00 EDT 2020}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
A State Transition MIP Formulation for the Unit Commitment Problem
journal, January 2018
- Atakan, Semih; Lulli, Guglielmo; Sen, Suvrajeet
- IEEE Transactions on Power Systems, Vol. 33, Issue 1
Analyzing valid inequalities of the generation unit commitment problem
conference, March 2009
- Hedman, Kory W.; O'Neill, Richard P.; Oren, Shmuel S.
- 2009 IEEE/PES Power Systems Conference and Exposition (PSCE)
MIP formulation improvement for large scale security constrained unit commitment with configuration based combined cycle modeling
journal, July 2017
- Chen, Yonghong; Wang, Fengyu
- Electric Power Systems Research, Vol. 148
Tighter Approximated MILP Formulations for Unit Commitment Problems
journal, February 2009
- Frangioni, A.; Gentile, C.; Lacalandra, F.
- IEEE Transactions on Power Systems, Vol. 24, Issue 1
A tight MIP formulation of the unit commitment problem with start-up and shut-down constraints
journal, April 2016
- Gentile, C.; Morales-España, G.; Ramos, A.
- EURO Journal on Computational Optimization, Vol. 5, Issue 1-2
The summed start-up costs in a unit commitment problem
journal, March 2016
- Brandenberg, René; Huber, Matthias; Silbernagl, Matthias
- EURO Journal on Computational Optimization, Vol. 5, Issue 1-2
Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem
journal, November 2013
- Morales-Espana, ; Latorre, Jesus M.; Ramos, Andres
- IEEE Transactions on Power Systems, Vol. 28, Issue 4
Perspective cuts for a class of convex 0–1 mixed integer programs
journal, July 2005
- Frangioni, A.; Gentile, C.
- Mathematical Programming, Vol. 106, Issue 2
The IEEE Reliability Test System: A Proposed 2019 Update
journal, January 2020
- Barrows, Clayton; Preston, Eugene; Staid, Andrea
- IEEE Transactions on Power Systems, Vol. 35, Issue 1
Improving Large Scale Day-Ahead Security Constrained Unit Commitment Performance
journal, November 2016
- Chen, Yonghong; Casto, Aaron; Wang, Fengyu
- IEEE Transactions on Power Systems, Vol. 31, Issue 6
Accelerating NCUC Via Binary Variable-Based Locally Ideal Formulation and Dynamic Global Cuts
journal, September 2016
- Wu, Lei
- IEEE Transactions on Power Systems, Vol. 31, Issue 5
Incorporating Fuel Constraints and Electricity Spot Prices into the Stochastic Unit Commitment Problem
journal, April 2000
- Takriti, Samer; Krasenbrink, Benedikt; Wu, Lilian S. -Y.
- Operations Research, Vol. 48, Issue 2
Modified orbital branching for structured symmetry with an application to unit commitment
journal, September 2014
- Ostrowski, James; Anjos, Miguel F.; Vannelli, Anthony
- Mathematical Programming, Vol. 150, Issue 1
Pyomo — Optimization Modeling in Python
book, January 2017
- Hart, William E.; Laird, Carl D.; Watson, Jean-Paul
- Springer Optimization and Its Applications
Improving Accuracy and Efficiency of Start-Up Cost Formulations in MIP Unit Commitment by Modeling Power Plant Temperatures
journal, July 2016
- Silbernagl, Matthias; Huber, Matthias; Brandenberg, Rene
- IEEE Transactions on Power Systems, Vol. 31, Issue 4
A Convex Primal Formulation for Convex Hull Pricing
journal, September 2017
- Hua, Bowen; Baldick, Ross
- IEEE Transactions on Power Systems, Vol. 32, Issue 5
Stochastic Lagrangian Relaxation Applied to Power Scheduling in a Hydro-Thermal System under Uncertainty
journal, January 2000
- Nowak, Matthias P.; Römisch, Werner
- Annals of Operations Research, Vol. 100, Issue 1/4, p. 251-272
Locally ideal formulations for piecewise linear functions with indicator variables
journal, November 2013
- Sridhar, Srikrishna; Linderoth, Jeff; Luedtke, James
- Operations Research Letters, Vol. 41, Issue 6
The Unit Commitment Problem With AC Optimal Power Flow Constraints
journal, November 2016
- Castillo, Anya; Laird, Carl; Silva-Monroy, Cesar A.
- IEEE Transactions on Power Systems, Vol. 31, Issue 6
A novel projected two-binary-variable formulation for unit commitment in power systems
journal, February 2017
- Yang, Linfeng; Zhang, Chen; Jian, Jinbao
- Applied Energy, Vol. 187
Exploiting Identical Generators in Unit Commitment
journal, July 2018
- Knueven, Ben; Ostrowski, Jim; Watson, Jean-Paul
- IEEE Transactions on Power Systems, Vol. 33, Issue 4
An Application of Mixed-Integer Programming Duality to Scheduling Thermal Generating Systems
journal, December 1968
- Muckstadt, John; Wilson, Richard
- IEEE Transactions on Power Apparatus and Systems, Vol. PAS-87, Issue 12
The Ramping Polytope and Cut Generation for the Unit Commitment Problem
journal, November 2018
- Knueven, Ben; Ostrowski, Jim; Wang, Jianhui
- INFORMS Journal on Computing, Vol. 30, Issue 4
Optimal Self-Scheduling of a Thermal Producer in Short-Term Electricity Markets by MILP
journal, November 2010
- Simoglou, Christos K.; Biskas, Pandelis N.; Bakirtzis, Anastasios G.
- IEEE Transactions on Power Systems, Vol. 25, Issue 4
Optimal response of a thermal unit to an electricity spot market
journal, January 2000
- Arroyo, J. M.; Conejo, A. J.
- IEEE Transactions on Power Systems, Vol. 15, Issue 3
Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem
journal, February 2012
- Ostrowski, James; Anjos, Miguel F.; Vannelli, Anthony
- IEEE Transactions on Power Systems, Vol. 27, Issue 1
Polynomial time algorithms and extended formulations for unit commitment problems
journal, January 2018
- Guan, Yongpei; Pan, Kai; Zhou, Kezhuo
- IISE Transactions, Vol. 50, Issue 8
Pyomo: modeling and solving mathematical programs in Python
journal, August 2011
- Hart, William E.; Watson, Jean-Paul; Woodruff, David L.
- Mathematical Programming Computation, Vol. 3, Issue 3
Tight and Compact MILP Formulation of Start-Up and Shut-Down Ramping in Unit Commitment
journal, May 2013
- Morales-Espana, German; Latorre, Jesus M.; Ramos, Andres
- IEEE Transactions on Power Systems, Vol. 28, Issue 2
Tight MIP formulations for bounded up/down times and interval-dependent start-ups
journal, October 2016
- Queyranne, Maurice; Wolsey, Laurence A.
- Mathematical Programming, Vol. 164, Issue 1-2
A polyhedral study of production ramping
journal, June 2015
- Damcı-Kurt, Pelin; Küçükyavuz, Simge; Rajan, Deepak
- Mathematical Programming, Vol. 158, Issue 1-2
Integer Programming Approach to the Problem of Optimal Unit Commitment with Probabilistic Reserve Determination
journal, November 1978
- Dillon, T. S.; Edwin, K. W.; Kochs, H. -D.
- IEEE Transactions on Power Apparatus and Systems, Vol. PAS-97, Issue 6
Works referencing / citing this record:
The impacts of convex piecewise linear cost formulations on AC optimal power flow
journal, October 2021
- Coffrin, Carleton; Knueven, Bernard; Holzer, Jesse
- Electric Power Systems Research, Vol. 199
A New Affinely Adjustable Robust Model for Security Constrained Unit Commitment under Uncertainty
journal, April 2021
- Sierra-Aguilar, Juan Esteban; Marín-Cano, Cristian Camilo; López-Lezama, Jesús M.
- Applied Sciences, Vol. 11, Issue 9