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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 [Formula: see text]-[Formula: see text]-[Formula: see text] 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/ .
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Efficient Nested Simulation Experiment Design via the Likelihood Ratio Method
In the nested simulation literature, a common assumption is that the experimenter can choose the number of outer scenarios to sample. This paper considers the case when the experimenter is given a fixed set of outer scenarios from an external entity. We propose a nested simulation experiment design that pools inner replications from one scenario to estimate another scenario’s conditional mean via the likelihood ratio method. Given the outer scenarios, we decide how many inner replications to run at each outer scenario as well as how to pool the inner replications by solving a bilevel optimization problem that minimizes the total simulation effort. We provide asymptotic analyses on the convergence rates of the performance measure estimators computed from the optimized experiment design. Under some assumptions, the optimized design achieves [Formula: see text] mean squared error of the estimators given simulation budget [Formula: see text]. Numerical experiments demonstrate that our design outperforms a state-of-the-art design that pools replications via regression. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the National Science Foundation [Grant CMMI-2045400] and the Natural Sciences and Engineering Research Council of Canada [Grant RGPIN-2018-03755]. 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.2022.0392 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0392 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
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- Award ID(s):
- 2246281
- PAR ID:
- 10525457
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- INFORMS Journal on Computing
- ISSN:
- 1091-9856
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/ijoc.2022.0392
