  We consider the problem of co-optimized energy-reserve market clearing with
state-of-charge (SoC) dependent bids from battery storage participants. While
SoC-dependent bidding accurately captures storage's degradation and opportunity
costs, such bids result in a non-convex optimization in the market clearing
process. More challenging is the regulation reserve capacity clearing, where
the SoC-dependent cost is uncertain as it depends on the unknown regulation
trajectories ex-post of the market clearing. Addressing the nonconvexity and
uncertainty in a multi-interval co-optimized real-time energy-reserve market,
we introduce a simple restriction on the SoC-dependent bids along with a robust
optimization formulation, transforming the non-convex market clearing under
uncertainty into a standard convex piece-wise linear program and making it
possible for large-scale storage integration. Under reasonable assumptions, we
show that SoC-dependent bids yield higher profit for storage participants than
that from SoC-independent bids. Numerical simulations demonstrate a 28%-150%
profit increase of the proposed SoC-dependent bids compared with the
SoC-independent counterpart.
