  A power market with non-convexities may not have an equilibrium price for
power that provides economic stability of the centralized dispatch outcome. In
this case, the market players are entitled to receive the uplift payments that
compensate the economic profit lost when following the centralized dispatch. We
consider a special class of the (possibly non-linear) redundant constraints
that are redundant not only on the feasible set of the centralized dispatch
optimization problem (and, therefore, do not change the centralized dispatch
outcome) but also on the larger set obtained when the power balance constraint
is relaxed. We show that the Lagrangian relaxation of these redundant
constraints may reduce the uplift payments without changing the duality gap.
For any given market price (or a pricing algorithm that sets the producer
revenue as a function of its output volume) in a uninode multi-period power
market with fixed load, we explicitly construct a family of the redundant
constraints that do not change the maximum profit of the producer and result in
zero uplift payment. We show that the introduction and subsequent Lagrangian
relaxation of just one redundant constraint in the centralized dispatch problem
suffice to eliminate the uplift payments for all the producers. In the case of
the convex hull pricing method, the introduction of these redundant constraints
affects neither the duality gap nor the market price for power. The results can
be straightforwardly generalized to a power market with the price-sensitive
load.
