Cutting planes for the multistage stochastic unit commitment problem

Jiang, Ruiwei; Guan, Yongpei; Watson, Jean -Paul

doi:10.1007/s10107-015-0971-5

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. As a result, our computational results verify the effectiveness of the proposed approach.

Authors:

Jiang, Ruiwei ^[1]; Guan, Yongpei ^[2]; Watson, Jean -Paul ^[3]

Univ. of Michigan, Ann Arbor, MI (United States)
Univ. of Florida, Gainesville, FL (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Wed Apr 20 00:00:00 EDT 2016

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1062274

Alternate Identifier(s):: OSTI ID: 1332947

Report Number(s):: SAND-2012-9093J; SAND-2016-11112J
Journal ID: ISSN 0025-5610; PII: 971

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Mathematical Programming

Additional Journal Information:: Journal Volume: 157; Journal Issue: 1; Journal ID: ISSN 0025-5610

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 29 ENERGY PLANNING, POLICY, AND ECONOMY; security-constrained unit commitment; stochastic programming; cutting planes; sequence independent lifting; 96 KNOWLEDGE MANAGEMENT AND PRESERVATION

Citation Formats


                    Jiang, Ruiwei, Guan, Yongpei, and Watson, Jean -Paul. Cutting planes for the multistage stochastic unit commitment problem.  United States: N. p., 2016. 
Web.  doi:10.1007/s10107-015-0971-5.

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                    Jiang, Ruiwei, Guan, Yongpei, & Watson, Jean -Paul. Cutting planes for the multistage stochastic unit commitment problem.  United States.  https://doi.org/10.1007/s10107-015-0971-5

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                    Jiang, Ruiwei, Guan, Yongpei, and Watson, Jean -Paul. Wed .  
"Cutting planes for the multistage stochastic unit commitment problem".  United States.  https://doi.org/10.1007/s10107-015-0971-5.  https://www.osti.gov/servlets/purl/1062274.

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@article{osti_1062274,

  title        = {Cutting planes for the multistage stochastic unit commitment problem},

  author       = {Jiang, Ruiwei and Guan, Yongpei and Watson, Jean -Paul},

  abstractNote = {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. As a result, our computational results verify the effectiveness of the proposed approach.},

  doi          = {10.1007/s10107-015-0971-5},

  journal      = {Mathematical Programming},

  number       = 1,

  volume       = 157,

  place        = {United States},

  year         = {Wed Apr 20 00:00:00 EDT 2016},

  month        = {Wed Apr 20 00:00:00 EDT 2016}

}

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Large-scale unit commitment under uncertainty: an updated literature survey
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Title: Cutting planes for the multistage stochastic unit commitment problem

Abstract

Citation Formats

A scenario decomposition algorithm for 0–1 stochastic programs journal, November 2013

A finite branch-and-bound algorithm for two-stage stochastic integer programs journal, June 2004

Wind Power Forecasting in U.S. Electricity Markets journal, April 2010

Dual decomposition in stochastic integer programming journal, February 1999

Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods journal, February 2009

A polyhedral study of production ramping journal, June 2015

A polyhedral study of the semi-continuous knapsack problem journal, June 2012

Household response to dynamic pricing of electricity: a survey of 15 experiments journal, August 2010

Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs journal, November 2012

Sequence Independent Lifting in Mixed Integer Programming journal, January 2000

An optimization-based method for unit commitment journal, February 1992

Cutting Planes for Multistage Stochastic Integer Programs journal, April 2009

A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem journal, March 2005

The Value of Multistage Stochastic Programming in Capacity Planning Under Uncertainty journal, August 2009

The complexity of cover inequality separation journal, August 1998

An algorithm for the construction of convex hulls in simple integer recourse programming journal, December 1996

The integer L-shaped method for stochastic integer programs with complete recourse journal, April 1993

Progressive hedging and tabu search applied to mixed integer (0,1) multistage stochastic programming journal, January 1996

Lifting, superadditivity, mixed integer rounding and single node flow sets revisited journal, May 2007

A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems journal, June 2004

Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse journal, February 2010

Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem journal, February 2012

Reserve Requirements for Wind Power Integration: A Scenario-Based Stochastic Programming Framework journal, November 2011

Lifting inequalities: a framework for generating strong cuts for nonlinear programs journal, May 2008

The C3 Theorem and a D2 Algorithm for Large Scale Stochastic Mixed-Integer Programming: Set Convexification journal, April 2005

Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming journal, July 2005

Unit commitment literature synopsis journal, January 1994

A stochastic model for the unit commitment problem journal, January 1996

A transmission-constrained unit commitment method in power system scheduling journal, January 1999

Security-Constrained Unit Commitment With Volatile Wind Power Generation journal, August 2008

A Chance-Constrained Two-Stage Stochastic Program for Unit Commitment With Uncertain Wind Power Output journal, February 2012

Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation journal, January 1995

Reliability unit commitment in ERCOT conference, January 2006

Valid Inequalities and Superadditivity for 0–1 Integer Programs journal, February 1977

Stochastic Security-Constrained Unit Commitment journal, May 2007

Large-scale unit commitment under uncertainty: an updated literature survey journal, September 2018

A finite $$\epsilon $$-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables journal, August 2019

Modeling and Solution Techniques Used for Hydro Generation Scheduling journal, July 2019

A scenario decomposition algorithm for 0–1 stochastic programs
journal, November 2013

A finite branch-and-bound algorithm for two-stage stochastic integer programs
journal, June 2004

Wind Power Forecasting in U.S. Electricity Markets
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Dual decomposition in stochastic integer programming
journal, February 1999

Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods
journal, February 2009

A polyhedral study of production ramping
journal, June 2015

A polyhedral study of the semi-continuous knapsack problem
journal, June 2012

Household response to dynamic pricing of electricity: a survey of 15 experiments
journal, August 2010

Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs
journal, November 2012

Sequence Independent Lifting in Mixed Integer Programming
journal, January 2000

An optimization-based method for unit commitment
journal, February 1992

Cutting Planes for Multistage Stochastic Integer Programs
journal, April 2009

A branch-and-cut algorithm for the stochastic uncapacitated lot-sizing problem
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The Value of Multistage Stochastic Programming in Capacity Planning Under Uncertainty
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The complexity of cover inequality separation
journal, August 1998

An algorithm for the construction of convex hulls in simple integer recourse programming
journal, December 1996

The integer L-shaped method for stochastic integer programs with complete recourse
journal, April 1993

Progressive hedging and tabu search applied to mixed integer (0,1) multistage stochastic programming
journal, January 1996

Lifting, superadditivity, mixed integer rounding and single node flow sets revisited
journal, May 2007

A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems
journal, June 2004

Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse
journal, February 2010

Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem
journal, February 2012

Reserve Requirements for Wind Power Integration: A Scenario-Based Stochastic Programming Framework
journal, November 2011

Lifting inequalities: a framework for generating strong cuts for nonlinear programs
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The C3 Theorem and a D2 Algorithm for Large Scale Stochastic Mixed-Integer Programming: Set Convexification
journal, April 2005

Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming
journal, July 2005

Unit commitment literature synopsis
journal, January 1994

A stochastic model for the unit commitment problem
journal, January 1996

A transmission-constrained unit commitment method in power system scheduling
journal, January 1999

Security-Constrained Unit Commitment With Volatile Wind Power Generation
journal, August 2008

A Chance-Constrained Two-Stage Stochastic Program for Unit Commitment With Uncertain Wind Power Output
journal, February 2012

Short-term generation scheduling with transmission and environmental constraints using an augmented Lagrangian relaxation
journal, January 1995

Reliability unit commitment in ERCOT
conference, January 2006

Valid Inequalities and Superadditivity for 0–1 Integer Programs
journal, February 1977

Stochastic Security-Constrained Unit Commitment
journal, May 2007

Large-scale unit commitment under uncertainty: an updated literature survey
journal, September 2018

A finite $$\epsilon $$-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables
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Modeling and Solution Techniques Used for Hydro Generation Scheduling
journal, July 2019