Pricing Economic Dispatch with AC Power Flow via Local Multipliers and Conic Relaxation

TL;DR

This paper investigates pricing mechanisms in AC power flow-based electricity markets, comparing local multipliers from nonconvex optimization with dual prices from SDP relaxations, and explores their properties and relationships.

Contribution

It introduces a novel comparison between local multipliers and SDP dual prices in AC power flow markets, revealing their equivalence and market implications.

Findings

SDP prices match distribution locational marginal prices in radial networks.

Relationships between local multipliers and SDP dual prices are established.

Numerical experiments validate theoretical insights.

Abstract

We analyze pricing mechanisms in electricity markets with AC power flow equations that define a nonconvex feasible set for the economic dispatch problem. Specifically, we consider two possible pricing schemes. The first among these prices are derived from Lagrange multipliers that satisfy Karush-Kuhn-Tucker conditions for local optimality of the nonconvex market clearing problem. The second is derived from optimal dual multipliers of the convex semidefinite programming (SDP) based relaxation of the market clearing problem. Relationships between these prices, their revenue adequacy and market equilibrium properties are derived and compared. The SDP prices are shown to equal distribution locational marginal prices derived with second-order conic relaxations of power flow equations over radial distribution networks. We illustrate our theoretical findings through numerical experiments.