Semidefinite relaxation and generalised benders decomposition to solve the transmission expansion network and reactive power planning

This study presents a methodology to solve simultaneously the alternating current (AC) transmission network expansion and reactive power planning problems, considering multiple stages and operating conditions. A mixed-integer non-linear programming model for the proposed planning problem is presente...

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Veröffentlicht in:IET generation, transmission & distribution Jg. 14; H. 11; S. 2160 - 2168
Hauptverfasser: Alvarez, Erik F, Paredes, Miguel, Rider, Marcos J
Format: Journal Article
Sprache:Englisch
Veröffentlicht: The Institution of Engineering and Technology 05.06.2020
Schlagworte:
AC power flow
alternating current transmission network expansion
Garver 6‐bus system
generalised Benders decomposition
IEEE 118‐bus system
investment cost
load flow
lower‐level problems
minimisation
mixed‐integer linear programming problem
multistage expansion
power transmission planning
reactive power
reactive power planning problems
Research Article
semidefinite relaxation
semidefinite structures
transmission expansion network
upper‐level problem
Garver 6-bus system
multistage expansion
AC power flow
generalised Benders decomposition
lower-level problems
upper-level problem
transmission expansion network
mixed-integer linear programming problem
investment cost
semidefinite relaxation
reactive power planning problems
reactive power
power transmission planning
alternating current transmission network expansion
minimisation
semidefinite structures
load flow
IEEE 118-bus system
ISSN:1751-8687, 1751-8695
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Beschreibung
Zusammenfassung:This study presents a methodology to solve simultaneously the alternating current (AC) transmission network expansion and reactive power planning problems, considering multiple stages and operating conditions. A mixed-integer non-linear programming model for the proposed planning problem is presented and rewritten with semidefinite structures. Then, the generalised Benders decomposition is used to separate the overall problem into an upper-level (master) problem and several lower-level (slaves) problems. The master problem is a mixed-integer linear programming problem that optimises the investment cost and constraints of the multistage expansion. Each slave problem minimises the operating costs associated with each stage and operating condition (normal operation or contingency), considering the AC power flow via semidefinite relaxation. With the proposed methodology, the global optimality of generalised Benders decomposition can be preserved due to the use of semidefinite relaxation in each slave problem. Garver's 6-bus system and an IEEE 118-bus system are used to show the precision and convergence to near-global optimal solutions with small relaxation gaps through the proposed approach.
ISSN:1751-8687
1751-8695
DOI:10.1049/iet-gtd.2019.0331