  Electricity market operators worldwide use mixed-integer linear programming
to solve the allocation problem in wholesale electricity markets. Prices are
typically determined based on the duals of relaxed versions of this
optimization problem. The resulting outcomes are efficient, but market
operators must pay out-of-market uplifts to some market participants and incur
a considerable budget deficit that was criticized by regulators. As the share
of renewables increases, the number of market participants will grow, leading
to larger optimization problems and runtime issues. At the same time,
non-convexities will continue to matter e.g., due to ramping constraints of the
generators required to address the variability of renewables or non-convex
curtailment costs. We draw on recent theoretical advances in the approximation
of competitive equilibrium to compute allocations and prices in electricity
markets using convex optimization. The proposed mechanism promises approximate
efficiency, no budget deficit, and computational tractability. We present
experimental results for this new mechanism in the context of electricity
markets, and compare the runtimes, the average efficiency loss of the method,
and the uplifts paid with standard pricing rules. We find that the computations
with the new algorithm are considerably fast for relevant problem sizes. In
general, the computational advantages come at the cost of efficiency losses and
a price markup for the demand side. Interestingly, both are small with
realistic problem instances. Importantly, the market operator does not incur a
budget deficit and the uplifts paid to market participants are significantly
lower compared to standard pricing rules.
