Welfare-maximizing transmission capacity expansion under uncertainty

Abstract

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’.

Introduction: the mathematics of energy systems

“…The paper by Wogrin et al [8] addresses the problem of the stochastic optimization of transmission capacity expansion to maximize the expected total social welfare of consumers and producers. A very interesting feature of the model is that it allows generators to be modelled with behaviour between perfectly competitive and Cournot players, with the potential to also study the implications of such behaviour if it evolves randomly over time, for example in response to evolving regulatory mechanisms.…”