Methods, apparatus, and systems for clearing a forward capacity auction

A method for clearing a forward capacity auction, comprising:

• solving an initial bid cost minimization problem based on bids and offers received in the auction to provide a price-quantity set (Po, Qo) that includes zonal price-quantity pairs for each zone that satisfy a market equilibrium condition;
• determining if Q0 is a feasible solution for a consumer payment minimization problem;
• if Q0 is a feasible solution, then:
• performing market clearing post processing for the price-quantity set (Po, Qo);
• and
• outputting final clearing results for the auction;
• if Q0 is not a feasible solution, then:
• obtaining an benchmark solution for a consumer payment minimization problem based on the bids and offers received in the auction;
• calculating at least one zonal price ceiling;
• selecting a limited number of lumpy offers and price levels for enumeration;
• generating at least one feasible price/quantity combination for the bids and offers which are based on the selected lumpy offers and price levels and are constrained by the at least one zonal price ceiling;
• calculating a consumer payment for each of the generated price/quantity combinations;
• comparing a smallest of the consumer payments with a consumer payment calculated for the initial benchmark solution;
• if the smallest consumer payment is less than the consumer payment for the initial benchmark solution, then:
• resetting the benchmark solution to correspond to the smallest consumer payment;
• performing market clearing post processing for the reset benchmark solution;
• and
• outputting final clearing results for the auction.