  This paper focuses on the operation of an electricity market that accounts
for participants that bid at a sub-minute timescale. To that end, we model the
market-clearing process as a dynamical system, called market dynamics, which is
temporally coupled with the grid frequency dynamics and is thus required to
guarantee system-wide stability while meeting the system operational
constraints. We characterize participants as price-takers who rationally update
their bids to maximize their utility in response to real-time schedules of
prices and dispatch. For two common bidding mechanisms, based on quantity and
price, we identify a notion of alignment between participants' behavior and
planners' goals that leads to a saddle-based design of the market that
guarantees convergence to a point meeting all operational constraints. We
further explore cases where this alignment property does not hold and observe
that misaligned participants' bidding can destabilize the closed-loop system.
We thus design a regularized version of the market dynamics that recovers all
the desirable stability and steady-state performance guarantees. Numerical
tests validate our results on the IEEE 39-bus system.
