Using optimization models and techniques to implement electricity auctions

Optimization models and techniques for two different bid format auctions are analyzed in this paper. The first model is the simple-bids auction in which participants only submit the offered power quantity and its unitary price. The second model deals with a multi-part bids auction in which bidders submit both a startup and variable cost coefficient. An optimization model that describes the simple-bids auction is formulated and the conditions under which multiple primal solutions exist are described. Using duality theory, the authors prove that Lagrange multipliers can be used to set the market price and that, in the absence of degeneracy, they reflect marginal pricing. They briefly describe the pros and cons of using simplex and interior-point methods to solve the optimization model. For the multi-part bids auction, they find that, in the absence of duality gap, Lagrange multipliers used as market prices lead to the recovery of all the costs submitted by the scheduled bidders. When a duality gap exists, the dual variables do not recover all the costs; even more, the cost not recovered is equal to the magnitude of the duality gap. The authors describe the conditions under which certain type of multiple primal solutions can be identified. The use of a direct and a Lagrangian-relaxation based technique to solve the auction are also briefly discussed