Bilevel programming applied to power system vulnerability analysis under multiple contingencies

• Published in: IET generation, transmission & distribution Vol. 4; no. 2; pp. 178 - 190
• Main Author: Arroyo, J.M.
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering & Technology 01.02.2010
• Subjects: Computer programs; Contingency; Equivalence; Mathematical models; Operators; Optimization; Outages; Programming
• ISSN: 1751-8687; 1751-8695
• DOI: 10.1049/iet-gtd.2009.0098

This study examines, the use of bilevel programming to analyse the vulnerability of power systems under multiple contingencies. One of the main purposes of this study, is to explain the state of the art of the subject matter. A minimum vulnerability model and a maximum vulnerability model are presented and discussed. In both models, the upper-level optimisation determines a set of simultaneous outages in the transmission network, whereas the lower-level optimisation models, the reaction of the system operator against the outages identified in the upper level. The system operator reacts by minimising the system load shed through an optimal operation of the power system. Two solution approaches for the resulting mixed-integer, non-linear bilevel programs are analysed and compared. The first approach is based on the application of Karush-Kuhn-Tucker optimality conditions, whereas the second procedure relies on duality theory. This study shows, that both approaches are essentially equivalent from a rigorous mathematical viewpoint; however, the second method is more suitable for off-the-shell, branch-and-cut software as corroborated by numerical simulations.