Can we prevent the gaming of ramp constraints?

Some electric power markets allow bidders to specify constraints on ramp rates for increasing or decreasing power production. We show in a small example that a bidder could use an overly restrictive constraint to increase profits, and explore the cause by visualizing the feasible region from the linear program corresponding to the power auction. We propose three penalty approaches to discourage bidders from such a tactic: two based on the duality theory of linear programming (LP) and the other based on social cost differences caused by ramp constraints. We evaluate the approaches using a simplified scaled model of the California power system, with actual 2001 California demand data.