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Consumer-based Carbon Costs: Integrating Consumer Carbon Preferences in Electricity Markets

Wenqian Jiang, Aditya Rangarajan, Line Roald

Abstract

An increasing share of consumers care about the carbon footprint of their electricity. This paper analyzes a method to integrate consumer carbon preferences in the electricity market-clearing by introducing consumer-based carbon costs and a carbon allocation mechanism. Specifically, consumers submit not only bids for power but also assign a cost to the carbon emissions incurred by their electricity use. The carbon allocation mechanism then assigns emissions from generation to consumers to minimize overall carbon costs. Our analysis starts from a previously proposed centralized market clearing formulation that maximizes social welfare under consideration of generation costs, consumer utility, and consumer carbon costs. We then derive an equivalent equilibrium formulation that incorporates a carbon allocation problem and gives rise to a set of carbon-adjusted electricity prices for both consumers and generators. We prove that the carbon-adjusted prices are higher for low-emitting generators and consumers with high carbon costs. Further, we prove that this new paradigm satisfies the same desirable market properties as standard electricity markets based on locational marginal prices, namely revenue adequacy and individual rationality, and demonstrate that a carbon tax on generators is equivalent to imposing a uniform carbon cost on consumers. Using a simplified three-bus system and the RTS-GMLC system, we illustrate that consumer-based carbon costs contribute to greener electricity market clearing both through generation redispatch and demand reductions.

Consumer-based Carbon Costs: Integrating Consumer Carbon Preferences in Electricity Markets

Abstract

An increasing share of consumers care about the carbon footprint of their electricity. This paper analyzes a method to integrate consumer carbon preferences in the electricity market-clearing by introducing consumer-based carbon costs and a carbon allocation mechanism. Specifically, consumers submit not only bids for power but also assign a cost to the carbon emissions incurred by their electricity use. The carbon allocation mechanism then assigns emissions from generation to consumers to minimize overall carbon costs. Our analysis starts from a previously proposed centralized market clearing formulation that maximizes social welfare under consideration of generation costs, consumer utility, and consumer carbon costs. We then derive an equivalent equilibrium formulation that incorporates a carbon allocation problem and gives rise to a set of carbon-adjusted electricity prices for both consumers and generators. We prove that the carbon-adjusted prices are higher for low-emitting generators and consumers with high carbon costs. Further, we prove that this new paradigm satisfies the same desirable market properties as standard electricity markets based on locational marginal prices, namely revenue adequacy and individual rationality, and demonstrate that a carbon tax on generators is equivalent to imposing a uniform carbon cost on consumers. Using a simplified three-bus system and the RTS-GMLC system, we illustrate that consumer-based carbon costs contribute to greener electricity market clearing both through generation redispatch and demand reductions.

Paper Structure

This paper contains 30 sections, 7 theorems, 30 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Carbon accounting under the GHG Protocol
  4. Carbon-Aware Load Shifting
  5. Carbon-Aware Electricity Market Clearing
  6. Our Contributions
  7. Electricity Market Clearing with Consumer-Based Carbon Cost
  8. Equivalent Equilibrium Formulation
  9. Optimality Conditions
  10. Dual problem
  11. KKT conditions
  12. Equilibrium Problem
  13. Carbon-Adjusted Prices
  14. Carbon-Adjusted Prices
  15. Ordering of Carbon-Adjustments
  16. ...and 15 more sections

Key Result

Theorem 4.2

For a set of generators $\mathcal{G}$ with increasing emission factors $e_{G,(1)} \leq e_{G,(2)} \leq \cdots \leq e_{G,(|\mathcal{G}|)}$, the corresponding generator carbon-adjustments will be decreasing, For a set of consumers $\mathcal{D}$ with decreasing carbon-costs $c_{D,(1)}\geq c_{D,(2)}\geq \cdots \geq c_{D,(|\mathcal{D}|)}$, the corresponding consumer carbon-adjustments will be increasin

Figures (5)

  • Figure 1: Impact of increasing carbon costs of Consumer 3 on market clearing results.
  • Figure 2: Relationship between the generator carbon-adjustments $\lambda_G$ and emission factors $e_G$ (left) and consumer carbon adjustments $\lambda_D$ and carbon costs $c_D$ (right).
  • Figure 3: Comparing carbon-adjusted and carbon-agnostic prices.
  • Figure 4: Changes in electricity prices with the introduction of carbon cost. Each circle represents a bus node, with color intensity representing standard (carbon-agnostic) LMPs. The squares connected to each node represent generators, where the color intensity reflects differences between generators' carbon-adjusted prices and standard LMP. Similarly, the triangles attached to each node represent consumers, with color intensity corresponding to their respective differences between consumers' carbon-adjusted prices and standard LMP. Congested transmission lines in carbon-aware case are highlighted by the red color (the uncongested lines are in gray).
  • Figure 5: Changes of Total carbon emissions, Total generation cost, and Total generation using yearly data for the RTS-GMLC system.

Theorems & Definitions (13)

  • Definition 4.1: Carbon-Adjusted Prices
  • Theorem 4.2: Ordering of Carbon-Adjustments
  • proof
  • Corollary 4.3
  • Corollary 4.4
  • Proposition 5.1
  • proof
  • Proposition 5.2
  • proof
  • Proposition 6.1: Equivalence to standard market clearing
  • ...and 3 more