Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be e...

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Bibliographic Details
Published in:Sustainable Energy, Grids and Networks Vol. 40; no. C; p. 101563
Main Authors: Liu, Jian, Wunsch, Donald C., Wang, Siyuan, Bo, Rui
Format: Journal Article
Language:English
Published: Netherlands Elsevier Ltd 01.12.2024
Elsevier
Subjects:
Branch and bound
Economic dispatch
Lagrangian function
Parametric analysis for MILP
Transmission planning
Unit commitment
Economic dispatch
Branch and bound
Transmission planning
Lagrangian function
Parametric analysis for MILP
Unit commitment
ISSN:2352-4677, 2352-4677
Online Access:Get full text
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Summary:Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. We compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.
Bibliography:EE0008781
USDOE Office of Energy Efficiency and Renewable Energy (EERE)
USDOE Office of Energy Efficiency and Renewable Energy (EERE), Renewable Power Office. Water Power Technologies Office
ISSN:2352-4677
2352-4677
DOI:10.1016/j.segan.2024.101563