On Electricity Market Equilibria with Storage: Modeling, Uniqueness, and a Distributed ADMM

We consider spot-market trading of electricity including storage operators as additional agents besides producers and consumers. Storage devices allow for shifting produced electricity from one time period to a later one.
Due to this, multiple market equilibria may occur even if classical uniqueness
assumptions for the case without storage systems are satisfied. For models containing storage operators, we derive sufficient conditions that ensure uniqueness of generation and demand. We also prove uniqueness of the market equilibrium for the special case of a single storage operator. Nevertheless, in case of multiple storage operators, uniqueness fails to hold in general, which we
show by illustrative examples. We conclude the theoretical discussion with
a general ex-post condition for proving the uniqueness of a given solution.
In contrast to classical settings without storage systems, the computation of
market equilibria is much more challenging since storage operations couple all
trading events over time. For this reason, we propose a tailored parallel and
distributed alternating direction method of multipliers (ADMM) for efficiently
computing spot-market equilibria over long time horizons. We first analyze the
parallel performance of the method itself. Finally, we show that the parallel
ADMM clearly outperforms solving the respective problems directly and that
it is capable of solving instances with more than 42 million variables in less
than 13 minutes.