How good are supply function equilibrium models: an empirical analysis of the ERCOT balancing market

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. Copyright Springer Science+Business Media, LLC 2007Electricity markets, Supply function equilibrium, ERCOT, Market power,

Microstructure and Strengthening Mechanisms in an Ultrafine Grained Al-Mg-Sc Alloy Produced by Powder Metallurgy

Additions of Sc to an Al-Mg matrix were investigated, paying particular attention to the influence of Al3Sc precipitates and other dispersoids, as well as grain size, on mechanical behavior. Prior studies have shown that Sc significantly increases the strength of coarse-grained Al-Mg alloys. Prompted by these findings, we hypothesized that it would be of fundamental and technological interest to study the behavior of Sc additions to an ultrafine-grained (UFG) microstructure (e.g., 100\u27s nm). Accordingly, we investigated the microstructural evolution and mechanical behavior of a cryomilled ultrafine grained Al-5Mg-0.4Sc (wt pct) and compared the results to those of an equivalent fine-grained material (FG) produced by powder metallurgy. Experimental materials were consolidated by hot isostatic pressing (HIP\u27ing) followed by extrusion or dual mode dynamic forging. Under identical processing conditions, UFG materials generate large Al3Sc precipitates with an average diameter of 154 nm and spaced approximately 1 to 3 μm apart, while precipitates in the FG materials have a diameter of 24 nm and are spaced 50 to 200 nm apart. The strengthening mechanisms are calculated for all materials and it is determined that the greatest strengthening contributions for the UFG and FG materials are Mg-O/N dispersion strengthening and precipitate strengthening, respectively