Past Event: Babuška Forum

A Convex Primal Formulation for Convex Hull Pricing

Ross Baldick, Professor, Department of Electrical & Computer Engineering, UT Austin

Abstract

In certain electricity markets, because of non-convexities that arise from their operating characteristics, generators that follow the independent system operator’s (ISO’s) decisions may fail to recover their cost through sales of energy at locational marginal prices. The ISO makes discriminatory side payments to incentivize the compliance of generators. Convex hull pricing is a uniform pricing scheme that minimizes these side payments. The Lagrangian dual problem of the unit commitment problem has been solved in the dual space to determine convex hull prices. However, this approach is computationally expensive. We propose a polynomially-solvable primal formulation for the Lagrangian dual problem. This formulation explicitly describes for each generating unit the convex hull of its feasible set and the convex envelope of its cost function. We cast our formulation as a second-order cone program when the cost functions are quadratic, and a linear program when the cost functions are piecewise linear. A 96-period 76-unit transmission-constrained example is solved in less than fifteen seconds on a personal computer. Bio Dr. Ross Baldick is a Professor in the Department of Electrical & Computer Engineering at The University of Texas at Austin and holds the Leland Barclay Fellowship in Engineering. He earned his Ph.D. in electrical engineering from the University of California, Berkeley in 1990. He joined the faculty of The University of Texas at Austin in 1994. He won a National Science Foundation Young Investigator Award that same year. Dr. Baldick is a Fellow of the IEEE and the recipient of the 2015 IEEE PES Outstanding Power Engineering Educator Award. His research is related to analysis of restructured electricity markets and electric transmission and very large-scale integration circuit analysis. His current research is focused on optimization, economic theory, and statistical analysis applied to electric power system operations.