  This paper finds near equilibrium prices for electricity markets with
nonconvexities due to binary variables, in order to reduce the market
participants' opportunity costs, such as generators' unrecovered costs. The
opportunity cost is defined as the difference between the profit when the
instructions of the market operator are followed and when the market
participants can freely make their own decisions based on the market prices. We
use the minimum complementarity approximation to the minimum total opportunity
cost (MTOC) model, from previous research, with tests on a much more realistic
unit commitment (UC) model than in previous research, including features such
as reserve requirements, ramping constraints, and minimum up and down times.
The developed model incorporates flexible price responsive demand, as in
previous research, but since not all demand is price responsive, we consider
the more realistic case that total demand is a mixture of fixed and flexible.
Another improvement over previous MTOC research is computational: whereas the
previous research had nonconvex terms among the objective function's continuous
variables, we convert the objective to an equivalent form that contains only
linear and convex quadratic terms in the continuous variables. We compare the
unit commitment model with the standard social welfare optimization version of
UC, in a series of sensitivity analyses, varying flexible demand to represent
varying degrees of future penetration of electric vehicles and smart
appliances, different ratios of generation availability, and different values
of transmission line capacities to consider possible congestion. The minimum
total opportunity cost and social welfare solutions are mostly very close in
different scenarios, except in some extreme cases.
