Joint Energy and Reserves Auction with Opportunity Cost Payment for Reserves

System operators in the electricity industry are required to procure reserve capacity to deal with unanticipated outages, demand shocks, and transmission constraints. One traditional method of procuring reserves is through a separate capacity auction with two-part bids. We analyze an alternative scheme whereby reserves are procured through the energy market using only energy bids, and capacity payments are made based on a generator's implied opportunity cost. By using the revelation principle, we are able to derive the equilibrium bidding function in this market and show that generators have a clear incentive to understate their costs in order to capture higher capacity rents. We then show that in spite of making energy payments based on the marginally procured unit, the expected energy costs under our scheme are bounded by that of a disjoint auction. We then give a numerical example for a special case of uniform demand distributions.