On Locational Marginal Emissions in Electricity Markets: A Two-Layered Dispatch Mechanism and Its Fundamental Theorems

TL;DR

This paper introduces a two-layered dispatch mechanism for real-time electricity markets that incorporates carbon emissions into economic dispatch, establishing fundamental theorems and validating the approach with case studies.

Contribution

It develops a novel two-layered dispatch framework that defines locational marginal emissions and proves their fundamental properties and system-wide consistency.

Findings

LMEs satisfy welfare economics theorems

Decentralized carbon profit maximization aligns with system dispatch

LME-based carbon accounting ensures total emissions match physical emissions

Abstract

We propose a market design for real-time electricity markets that utilizes a two-layered dispatch mechanism to systematically incorporate carbon accounting into grid operations. In this mechanism, ``dispatch'', the centralized allocation of generation resources to meet system load, is executed via a hierarchical structure where the first layer minimizes financial costs to maintain economic efficiency, while the second layer minimizes system emissions strictly within the set of cost-optimal solutions. We define locational marginal emissions (LMEs) as the marginal rate of system emissions derived from the dual variables of the two-layered formulation. Unlike standard marginal prices which correspond to right-hand-side constraint relaxations, LMEs must account for the requirement of economic optimality which introduces demand parameters into the problem's constraint structure. Under the framework, we establish that LMEs satisfy properties analogous to the first and second fundamental theorems of welfare economics. We prove that (1) decentralized ``carbon profit'' maximization by individual grid entities guarantees a system-wide emission profile consistent with the economic dispatch, and (2) any optimal low-carbon economic dispatch is supported by a corresponding set of LME signals acting as a decentralized equilibrium. Furthermore, we establish a general carbon accounting theorem, called the Carbon Footprint Theorem, showing that these market-consistent LMEs ensure the sum of carbon accounts across all grid components (loads, generators, transmission, and storage) equals the total physical carbon emissions. This completes the theoretical foundation of the LME. Finally, we investigate and validate the empirical properties of LMEs and LME-based carbon accounting through case studies on a realistic Texas grid model.