Directly Constraining Marginal Prices
  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. 
Kyri Baker
math.OC