A Linear and Scalable Cutting-Plane Algorithm for Electricity Pricing

TL;DR

This work tackles price formation under the nonconvex AC-OPF by proposing a linear cutting-plane approach that outer-approximates the Jabr SOC relaxation. The Cutting-Plane Pricing Algorithm (CPPA) builds a tight linear relaxation $ ext{Q}^{CP}$ via dynamically generated linear cuts, enabling pricing under Convex Hull (CH) or Integer Programming (IP) rules with runtimes comparable to DC-OPF. Across a 617-bus network and very large grids (≥15,000 buses), CPPA yields price signals very close to the Jabr SOC and significantly lower redispatch costs than DC, with strong scalability when using warm-starts. The method provides a practical, scalable path to accurate AC-feasible pricing in large-scale electricity markets, balancing model fidelity and computational tractability.

Abstract

We propose a linear cutting-plane pricing algorithm tailored for large-scale electricity markets, addressing nonconvexities arising from the Alternating Current Optimal Power Flow equations. We benchmark our algorithm against a Direct Current (DC) approximation and the Jabr Second-Order Cone (SOC) relaxation under both the Integer Programming and Convex Hull pricing rules. We provide numerical results for a small (617-bus) and three large ($\geq 15,000$-bus) networks. Our algorithm yields price signals very close to the Jabr SOC, with computation times comparable to DC once we allow for warm-starts, including scenarios with line contingencies.

Figures (1)

• Figure 1: Average price distance $\delta$ for CP and DC to Jabr SOC