  The marginal price of electricity traditionally depends on the dual variables
associated with relevant optimization goals. Particularly, in the optimal power
flow realm, prices represent the cost of supplying an additional unit of power
at each bus; for the economic dispatch case, dual variables represent the cost
of supplying an additional unit of power to the whole system. Dual variables
are useful for many additional tasks, including the analysis of system
congestion and the determination of the cost of load adjustments. In this
letter, departing from conventional optimal power flow analysis, it is shown
how constraints on relevant dual variables affect the prices of electricity,
allowing for market settings and demand response programs that accept bids and
caps on individual prices.
