  This paper proposes a market mechanism for multi-interval electricity markets
with generator and storage participants. Drawing ideas from supply function
bidding, we introduce a novel bid structure for storage participation that
allows storage units to communicate their cost to the market using
energy-cycling functions that map prices to cycle depths. The resulting
market-clearing process--implemented via convex programming--yields
corresponding schedules and payments based on traditional energy prices for
power supply and per-cycle prices for storage utilization. We illustrate the
benefits of our solution by comparing the competitive equilibrium of the
resulting mechanism to that of an alternative solution that uses prosumer-based
bids. Our solution shows several advantages over the prosumer-based approach.
It does not require a priori price estimation. It also incentivizes
participants to reveal their truthful cost, thus leading to an efficient,
competitive equilibrium. Numerical experiments using New York Independent
System Operator (NYISO) data validate our findings.
