Generation bidding game with flexible demand

With the onset of large numbers of plug-in electric and hybrid-electric vehicles, requiring overnight charging ahead of the morning commute, a significant portion of electricity demand will be somewhat flexible and accordingly may be responsive to changes in electricity spot prices. For such a responsive demand idealized, we consider a deregulated electricity marketplace wherein the grid (ISO, retailer-distributor) accepts bids per-unit supply from generators (simplified herein neither to consider start-up/ramp-up expenses nor day-ahead or shorter-term load following) which are then averaged (by supply allocations via an economic dispatch) to a common “clearing” price borne by customers (irrespective of variations in transmission/distribution or generation prices), i.e., the ISO does not compensate generators based on their marginal costs. Rather, the ISO provides sufficient information for generators to sensibly adjust their bids. For a generation duopoly with neither transmission capacity bounds nor constraints, there are a surprising plurality of Nash equilibria under quadratic generation costs. In this paper, we explore transmission costs and constraints for any number of generators, and simplify our numerical study by taking the power flow problem only as a “commodity” flow. Notwithstanding our idealizations, we consider a complex dispatch problem the retailer/grid must solve for a demand that depends on the dispatch [19] here through the clearing price, and moreover the grid needs to inform the generators of the sensitivity of their allocation to small changes in their prices.