Properties of oligopolistic market equilibria in linearized DC power networks with arbitrage and supply function conjectures

We present mathematical models for a power market on a linearized DC network with affine demand. The models represent the conjecture that each power generating company may hold regarding how rival firms will change their outputs if prices change. The classic Cournot model is a special case of this conjecture. The models differ in how arbitrage is handled, and their formulations give rise to nonlinear mixed complementarity problems. In the Stackelberg version, the generators anticipate how arbitrage would affect prices at different locations, and therefore treat the arbitrage amounts as decision variables in their profit maximization problems. In the other version, arbitrage is exogenous to the firms. We show that solutions to the latter model are also solutions to the Stackelberg model. We also demonstrate existence and uniqueness properties for the exogenous arbitrage model.