A Convex Primal Formulation for Convex Hull Pricing

TL;DR

This paper introduces a polynomially-solvable primal formulation for convex hull pricing in electricity markets, enabling efficient computation of prices that minimize side payments despite non-convexities.

Contribution

It presents a new primal formulation explicitly describing convex hulls and envelopes, cast as SOCP or LP, significantly reducing computational complexity.

Findings

Solved a 96-period, 76-unit example in under 15 seconds

Formulation is polynomially solvable and applicable to quadratic and piecewise linear costs

Reduces computational cost compared to traditional dual approaches

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. Discriminatory side payments are made by the ISO 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 used to determine convex hull prices. However, this approach is computationally expensive. In this paper, 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.