Supply Function Equilibrium in a Constrained Transmission System

This article characterizes a supply function equilibrium in an auction market constrained by limited capacities of links in a transportation network and limited input/output capacities of participants. The formulation is adapted to a wholesale spot market for electricity managed by the operator of the transmission system. The results are derived using the calculus of variations to obtain the Euler conditions and the transversality conditions that characterize a Nash equilibrium in an auction in which bids are as supply functions, and quantities and payments are based either on nodal prices or pay-as-bid.