We present an empirical analysis of a supply function equilibrium model in the Texas spot electricity market. We derive conditions for optimal bidding behavior in a spot market with ex ante bilaterally contracted sales. By estimating costs, we are able to derive a set of ex post-and ex ante-optimal supply functions and use a non-parametric behavioral model to compare our theoretically optimal supply functions to actual offers made. Our results show that with the exception of the largest generators, firms make offers with markups and markdowns far in excess of what a model of profit-maximizing behavior suggests.

We present an empirical analysis of a supply function equilibrium model in the Texas spot electricity market. We derive condititions for optimal bidding behavior in a spot market with ex ante bilaterally contracted sales. By using generation cost information, we are able to derive a set of ex post- and ex ante-optimal supply functions and use a nonparametric model of firm behavior to compare our theoretically-optimal supply functions to actual offers made in years 2002 and 2003. Our results show that with markups and markdowns far in excess of what a model of profit-maximizing behavior suggests. For small generators, municipalities, and cogenerators we find evidence suggesting these firms may be acting to exclude themselves from the market by economically witholding their generation.By using partial-linear behavior model we demonstrate some learning effects to have taken place during the first quarter of 2002.

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 give a numerical example for a special case and examine the effect of the equilibrium bidding behavior on the generators' total revenues and on the energy payments.

Many wholesale electricity markets call on the independent system operator (ISO) to determine day-ahead schedules for generators based on a centralized unit commitment. Up until recently, the Lagrangian relaxation (LR) algorithm was the only practical means of solving an ISO-scale unit commitment problem, and it was the solution technique used by most ISOs. Johnson et al. [1] demonstrate, however, that equity, incentive, and efficiency issues will arise from use of LR solutions, because different commitments that are similar in terms of total system costs can result in different surpluses to individual units. Recent advances in computing capabilities and optimization algorithms now make solution of the mixed-integer programming (MIP) formulation by means of branch and bound (B&B) tractable, often with optimality gaps smaller than those of LR algorithms, which has led some ISOs to adopt B&B algorithms and others proposing to do so.

With the move towards B&B, one obvious question is whether the use of MIP will eliminate or reduce the issues with LR raised by Johnson et al. Using actual market data from an ISO, we demonstrate that both LR and MIP solutions will suffer the same equity issues, unless the ISO unit commitment problems can be solved to complete optimality within the allotted timeframe—which is beyond current computational capabilities. Our results further demonstrate that the size of the payoff deviations are not monotone in the size of the optimality gap, meaning smaller optimality gaps from B&B will not necessarily mitigate the issues Johnson et al. raise. We show that the use of “make-whole” payments, which ensure units recover any startup and no-load costs not recovered by inframarginal energy rents, can help to reduce surplus volatility and differences to some extent.