Welfare-maximizing transmission capacity expansion under uncertainty and imperfect competition

S. Wogrin*, D. Tejada-Arango, A. Downward, A. B. Philpott

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We apply the JuDGE optimization package to a multistage stochastic leader-follower model that determines a transmission capacity expansion plan to maximize expected social welfare of consumers and producers who act as Cournot oligopolists in each time period. The problem is formulated as a large-scale mixed integer programme and applied to a 5-bus instance over scenario trees of varying size. The computational effort required by JuDGE is compared with solving the deterministic equivalent mixed integer programme using a state-of-the-art integer programming package. This article is part of the theme issue 'The mathematics of energy systems'.

Original languageEnglish
Article number20190436
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2202
Publication statusPublished - 26 Jul 2021


  • bilevel programming
  • JuDGE
  • stochastic optimization
  • transmission expansion planning

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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