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Regularized MIP Model for Integrating Energy Storage Systems and Its Application for Solving a Trilevel Interdiction Problem.

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Title: Regularized MIP Model for Integrating Energy Storage Systems and Its Application for Solving a Trilevel Interdiction Problem.
Authors: Han, Dahye1 (AUTHOR) dahye.han@gatech.edu, Jiang, Nan2 (AUTHOR) nanjiang@cornell.edu, Dey, Santanu S.1 (AUTHOR) santanu.dey@isye.gatech.edu, Xie, Weijun1 (AUTHOR) wxie@gatech.edu
Source: INFORMS Journal on Computing. May/Jun2026, Vol. 38 Issue 3, p729-744. 16p.
Subject Terms: *Battery storage plants, *Mathematical optimization, *Linear programming, Mixed integer linear programming, Energy storage
Abstract: In modeling battery energy storage systems (BESS) in power systems, binary variables are used to represent the complementary nature of charging and discharging. A conventional approach for these BESS optimization problems is to relax binary variables and convert the problem into a linear program. However, such linear programming relaxation models can yield unrealistic fractional solutions, such as simultaneous charging and discharging. In this paper, we develop a regularized mixed-integer programming (MIP) model for the optimal power flow (OPF) problem with BESS. We prove that, under mild conditions, the proposed regularized model admits a zero integrality gap with its linear programming relaxation; hence, it can be solved efficiently. By studying the properties of the regularized MIP model, we show that its optimal solution is also near optimal to the original OPF problem with BESS, thereby providing a valid and tight upper bound for the OPF problem with BESS. The use of the regularized MIP model allows us to solve a trilevel min - max - min network contingency problem, which is otherwise intractable to solve. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: N. Jiang (as a graduate student at the Georgia Institute of Technology) and W. Xie were supported in part by the National Science Foundation [Grant 2246414] and the Office of Naval Research [Grant N00014-24-1-2066]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0771) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2024.0771). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]
Copyright of INFORMS Journal on Computing is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="AR" term="%22Han%2C+Dahye%22">Han, Dahye</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> dahye.han@gatech.edu</i><br /><searchLink fieldCode="AR" term="%22Jiang%2C+Nan%22">Jiang, Nan</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> nanjiang@cornell.edu</i><br /><searchLink fieldCode="AR" term="%22Dey%2C+Santanu+S%2E%22">Dey, Santanu S.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> santanu.dey@isye.gatech.edu</i><br /><searchLink fieldCode="AR" term="%22Xie%2C+Weijun%22">Xie, Weijun</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wxie@gatech.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22INFORMS+Journal+on+Computing%22">INFORMS Journal on Computing</searchLink>. May/Jun2026, Vol. 38 Issue 3, p729-744. 16p.
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  Data: *<searchLink fieldCode="DE" term="%22Battery+storage+plants%22">Battery storage plants</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br />*<searchLink fieldCode="DE" term="%22Linear+programming%22">Linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Mixed+integer+linear+programming%22">Mixed integer linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+storage%22">Energy storage</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: In modeling battery energy storage systems (BESS) in power systems, binary variables are used to represent the complementary nature of charging and discharging. A conventional approach for these BESS optimization problems is to relax binary variables and convert the problem into a linear program. However, such linear programming relaxation models can yield unrealistic fractional solutions, such as simultaneous charging and discharging. In this paper, we develop a regularized mixed-integer programming (MIP) model for the optimal power flow (OPF) problem with BESS. We prove that, under mild conditions, the proposed regularized model admits a zero integrality gap with its linear programming relaxation; hence, it can be solved efficiently. By studying the properties of the regularized MIP model, we show that its optimal solution is also near optimal to the original OPF problem with BESS, thereby providing a valid and tight upper bound for the OPF problem with BESS. The use of the regularized MIP model allows us to solve a trilevel min - max - min network contingency problem, which is otherwise intractable to solve. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: N. Jiang (as a graduate student at the Georgia Institute of Technology) and W. Xie were supported in part by the National Science Foundation [Grant 2246414] and the Office of Naval Research [Grant N00014-24-1-2066]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0771) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2024.0771). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of INFORMS Journal on Computing is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1287/ijoc.2024.0771
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        Text: English
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        PageCount: 16
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      – SubjectFull: Battery storage plants
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Linear programming
        Type: general
      – SubjectFull: Mixed integer linear programming
        Type: general
      – SubjectFull: Energy storage
        Type: general
    Titles:
      – TitleFull: Regularized MIP Model for Integrating Energy Storage Systems and Its Application for Solving a Trilevel Interdiction Problem.
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            NameFull: Han, Dahye
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            NameFull: Jiang, Nan
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            NameFull: Dey, Santanu S.
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              M: 05
              Text: May/Jun2026
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              Y: 2026
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