Cutting planes for the multistage stochastic unit commitment problem

Ruiwei Jiang, Yongpei Guan, Jean Paul Watson

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use to enhance the reliability unit commitment process for day-ahead power system operations. In our approach, we first develop a deterministic equivalent formulation for the problem, which leads to a large-scale mixed-integer linear program. Then, we verify that the turn on/off inequalities provide a convex hull representation of the minimum-up/down time polytope under the stochastic setting. Next, we develop several families of strong valid inequalities mainly through lifting schemes. In particular, by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes, we obtain strong valid inequalities for the ramping and general load balance polytopes. Finally, branch-and-cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem. Our computational results verify the effectiveness of the proposed approach.

Original languageEnglish (US)
Pages (from-to)121-151
Number of pages31
JournalMathematical Programming
Volume157
Issue number1
DOIs
StatePublished - May 1 2016
Externally publishedYes

Fingerprint

Unit Commitment
Cutting Planes
Valid Inequalities
Lifting Scheme
Coal
Power System
Cost effectiveness
Verify
Chemical reactions
Electricity Market
Branch-and-cut
Load Balance
Cost-effectiveness
Renewable Energy
Integer Program
System Reliability
Polytopes
Polytope
Linear Program
Convex Hull

Keywords

  • Cutting planes
  • Security-constrained unit commitment
  • Sequence independent lifting
  • Stochastic programming

ASJC Scopus subject areas

  • Mathematics(all)
  • Software

Cite this

Cutting planes for the multistage stochastic unit commitment problem. / Jiang, Ruiwei; Guan, Yongpei; Watson, Jean Paul.

In: Mathematical Programming, Vol. 157, No. 1, 01.05.2016, p. 121-151.

Research output: Contribution to journalArticle

Jiang, Ruiwei ; Guan, Yongpei ; Watson, Jean Paul. / Cutting planes for the multistage stochastic unit commitment problem. In: Mathematical Programming. 2016 ; Vol. 157, No. 1. pp. 121-151.
@article{d309a4d3321b425bb25ee9066d0390e4,
title = "Cutting planes for the multistage stochastic unit commitment problem",
abstract = "As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use to enhance the reliability unit commitment process for day-ahead power system operations. In our approach, we first develop a deterministic equivalent formulation for the problem, which leads to a large-scale mixed-integer linear program. Then, we verify that the turn on/off inequalities provide a convex hull representation of the minimum-up/down time polytope under the stochastic setting. Next, we develop several families of strong valid inequalities mainly through lifting schemes. In particular, by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes, we obtain strong valid inequalities for the ramping and general load balance polytopes. Finally, branch-and-cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem. Our computational results verify the effectiveness of the proposed approach.",
keywords = "Cutting planes, Security-constrained unit commitment, Sequence independent lifting, Stochastic programming",
author = "Ruiwei Jiang and Yongpei Guan and Watson, {Jean Paul}",
year = "2016",
month = "5",
day = "1",
doi = "10.1007/s10107-015-0971-5",
language = "English (US)",
volume = "157",
pages = "121--151",
journal = "Mathematical Programming",
issn = "0025-5610",
publisher = "Springer-Verlag GmbH and Co. KG",
number = "1",

}

TY - JOUR

T1 - Cutting planes for the multistage stochastic unit commitment problem

AU - Jiang, Ruiwei

AU - Guan, Yongpei

AU - Watson, Jean Paul

PY - 2016/5/1

Y1 - 2016/5/1

N2 - As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use to enhance the reliability unit commitment process for day-ahead power system operations. In our approach, we first develop a deterministic equivalent formulation for the problem, which leads to a large-scale mixed-integer linear program. Then, we verify that the turn on/off inequalities provide a convex hull representation of the minimum-up/down time polytope under the stochastic setting. Next, we develop several families of strong valid inequalities mainly through lifting schemes. In particular, by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes, we obtain strong valid inequalities for the ramping and general load balance polytopes. Finally, branch-and-cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem. Our computational results verify the effectiveness of the proposed approach.

AB - As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use to enhance the reliability unit commitment process for day-ahead power system operations. In our approach, we first develop a deterministic equivalent formulation for the problem, which leads to a large-scale mixed-integer linear program. Then, we verify that the turn on/off inequalities provide a convex hull representation of the minimum-up/down time polytope under the stochastic setting. Next, we develop several families of strong valid inequalities mainly through lifting schemes. In particular, by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes, we obtain strong valid inequalities for the ramping and general load balance polytopes. Finally, branch-and-cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem. Our computational results verify the effectiveness of the proposed approach.

KW - Cutting planes

KW - Security-constrained unit commitment

KW - Sequence independent lifting

KW - Stochastic programming

UR - http://www.scopus.com/inward/record.url?scp=84964409197&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964409197&partnerID=8YFLogxK

U2 - 10.1007/s10107-015-0971-5

DO - 10.1007/s10107-015-0971-5

M3 - Article

AN - SCOPUS:84964409197

VL - 157

SP - 121

EP - 151

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1

ER -