  Electricity markets typically clear in two stages: a day-ahead market and a
real-time market. In this paper, we propose market mechanisms for a two-stage
multi-interval electricity market with energy storage, generators, and demand
uncertainties. We consider two possible mixed bidding strategies: storage first
bids cycle depths in the day ahead and then charge-discharge power bids in the
real-time market for any last-minute adjustments. While the first strategy only
considers day-ahead decisions from an individual participant's perspective as
part of their individual optimization formulation, the second strategy accounts
for both the market operator's and participants' perspectives. We demonstrate
that the competitive equilibrium exists uniquely for both mechanisms. However,
accounting for the day-ahead decisions in the bidding function has several
advantages. Numerical experiments using New York ISO data provide bounds on the
proposed market mechanism.
