Robust Cournot-Bertrand Equilibria on Power Networks

We present a convex model describing risk-averse strategies for electricity producers in congested electricity networks. Extending prior work on Cournot-Bertrand equilibria in Poolco-style spot markets with locational marginal pricing, we propose a formulation which integrates uncertainty through robust convex optimization. We find that producers uniformly benefit from robust strategies under small uncertainty intervals, and explore the impacts of congestion and network effects on strategic behavior. We demonstrate our results on a simple example and explore the impacts of robust strategies on social welfare, finding that these risk-averse strategies reduce welfare by restricting output and increasing prices. By formulating the equilibrium conditions as a convex optimization problem, we are able to scale our results to large networks and accommodate many sources of uncertainty.