Electricity Market Dynamics as Smooth Games: Organizing Gradient-Based Learners and Identifying Instabilities

Abstract

Wide-spread adoption of machine learning and distributed energy production has the potential to fundamentally change behaviours of energy markets. In practice, along with the benefits, previously unseen instabilities have begun emerging in markets currently embracing these technologies. In this report we study electricity markets as dynamical systems arising in smooth games, where energy consumers are modelled as gradient-based learners who interact on a graph through distributed energy producers. We give simple examples of how instabilities can arise even when the consumers’ local objectives seem reasonable and how these instabilities can be remedied. Drawing insights from these examples, we begin developing a general model of optimization-driven electricity market dynamics and give conditions for ensuring local Nash equilibria of the system are stable fixed points of the dynamics. Our results demonstrate how models of electricity market dynamics might be used for deriving formal guarantees in order to stabilize markets and enact regulatory policies in the face of market shocks.