  We examine the problem of clearing day-ahead electricity market auctions
where each bidder, whether a producer or consumer, can specify a minimum profit
or maximum payment condition constraining the acceptance of a set of bid curves
spanning multiple time periods in locations connected through a transmission
network with linear constraints. Such types of conditions are for example
considered in the Spanish and Portuguese day-ahead markets. This helps
describing the recovery of start-up costs of a power plant, or analogously for
a large consumer, utility reduced by a constant term. A new market model is
proposed with a corresponding MILP formulation for uniform locational price
day-ahead auctions, handling bids with a minimum profit or maximum payment
condition in a uniform and computationally-efficient way. An exact
decomposition procedure with sparse strengthened Benders cuts derived from the
MILP formulation is also proposed. The MILP formulation and the decomposition
procedure are similar to computationally-efficient approaches previously
proposed to handle so-called block bids according to European market rules,
though the clearing conditions could appear different at first sight. Both
solving approaches are also valid to deal with both kinds of bids
simultaneously, as block bids with a minimum acceptance ratio, generalizing
fully indivisible block bids, are but a special case of the MP bids introduced
here. We argue in favour of the MP bids by comparing them to previous models
for minimum profit conditions proposed in the academic literature, and to the
model for minimum income conditions used by the Spanish power exchange OMIE.
