Stability of supply function equilibria implications for daily versus hourly bids in a poolco market

Abstract

We consider a supply function model of a poolco electricity market where demand varies significantly over a time horizon such as a day and also has a small responsiveness to price. Although there are equilibria yielding prices at peak that are close to Cournot prices, it is known that the wider the range of demand uncertainty the narrower the range of such supply function equilibria. Here we show that such equilibria are also typically unstable and consequently would be difficult to sustain in practice. This strengthens the results of Green and Newbery by ruling out many equilibria that have high prices. We demonstrate this result both theoretically under somewhat restrictive assumptions and also numerically using both a three-firm example system and a five-firm example system having generation capacity constraints. Hence, this reinforces the conclusion that the market outcome is significantly influenced by a requirement that offers into the poolco be consistent over the time horizon. This result contrasts with markets where bids can be changed on an hourly basis, where Cournot prices are possible outcomes. The stability analysis has important policy implications for the design of day-ahead electricity markets. The stability perspective also provides a narrowing of the equilibrium selection that strengthens empirical analysis.