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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. Lastly, 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.

Authors:
 [1];  [2];  [3]
  1. Univ. of Michigan, Ann Arbor, MI (United States)
  2. Univ. of Florida, Gainesville, FL (United States)
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
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) (SC-21)
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.
Jiang, Ruiwei, Guan, Yongpei, & Watson, Jean -Paul. Cutting planes for the multistage stochastic unit commitment problem. United States. doi:10.1007/s10107-015-0971-5.
Jiang, Ruiwei, Guan, Yongpei, and Watson, Jean -Paul. Wed . "Cutting planes for the multistage stochastic unit commitment problem". United States. doi:10.1007/s10107-015-0971-5. https://www.osti.gov/servlets/purl/1062274.
@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. Lastly, 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.},
doi = {10.1007/s10107-015-0971-5},
journal = {Mathematical Programming},
number = 1,
volume = 157,
place = {United States},
year = {2016},
month = {4}
}

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