Game-theoretic robust energy coordination for a neighbourhood of smart homes

Scalable coordination algorithms for neighbourhoods of households featuring electric vehicles (EVs) and embedded renewable generation are required in order to achieve safe and efficient operation of local distribution networks without excessive centralization of control decisions. This paper presents a non-cooperative algorithm to coordinate multi-period EV charging amidst uncertainty affecting both the charging dynamics and the intermittent renewable energy supply. The strategy space includes not only nominal EV charging plans, but also a causal system of linear responses to the forecast errors of renewable infeeds. In a setting where the price of electricity from the main grid has a fixed component and a component that depends on the aggregate purchase requirements of the neighbourhood, we prove a condition under which convergence to the unique Nash equilibrium of the associated game is guaranteed. The algorithm relies on an update rule known as the Krasnoselskij iteration, and the convergence proof is based on the non-expansivity property of an associated operator. We demonstrate the algorithm for a group of 100 households.