Stability analysis of a model for the market dynamics of a smart grid

We consider the dynamics of a smart grid system characterized by widespread distributed generation and storage devices. We assume that agents are free to trade electric energy over the network and we focus on the emerging market dynamics. We consider three different models for the market dynamics for which we present a stability analysis. We see that stability depends on the specific form of the market dynamics and it may depend on the structure of the underlying network topology. We run numerical simulations that confirm our theoretical predictions. As an example, we test our model for the market dynamics over a real network topology, namely, the Tramway 11 Feeder from New Mexico´s power network.