Stability of supply function equilibrium in electricity markets under piecewise linear function perturbations

Abstract

The supply function equilibrium model has been used widely to study strategic behavior and market power in electricity markets. However, theoretically there exists a continuum of supply function equilibria, which limits the predictive value of this model. We refine the supply function equilibria by a stability analysis. The local behavior of supply function equilibrium under small perturbations in the form of piecewise linear functions is analyzed. We demonstrate the effectiveness of this method through a symmetric example, and find out that the stable supply function equilibria set that survive piecewise linear function perturbations is significantly smaller than the set of all theoretical SFEs. On the other hand, since practically any form of perturbation function can be reasonably approximated by some piecewise linear perturbation function, if some of the supply functions do not behave chaotically under piecewise linear function perturbations, it suggests that they are likely to be sustainable in reality. This stability analysis method is not limited to symmetric models, and is applicable to asymmetric supply function equilibrium models as well.