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Is Locational Marginal Price All You Need for Locational Marginal Emission?

Xuan He, Danny H. K. Tsang, Yize Chen

Abstract

Growing concerns over climate change call for improved techniques for estimating and quantifying the greenhouse gas emissions associated with electricity generation and transmission. Among the emission metrics designated for power grids, locational marginal emission (LME) can provide system operators and electricity market participants with valuable information on the emissions associated with electricity usage at various locations in the power network. In this paper, by investigating the operating patterns and physical interpretations of marginal emissions and costs in the security-constrained economic dispatch (SCED) problem, we identify and draw the exact connection between locational marginal price (LMP) and LME. Such interpretation helps instantly derive LME given nodal demand vectors or LMP, and also reveals the interplay between network congestion and nodal emission pattern. Our proposed approach helps reduce the computation time of LME by an order of magnitude compared to analytical approaches, while it can also serve as a plug-and-play module accompanied by an off-the-shelf market clearing and LMP calculation process.

Is Locational Marginal Price All You Need for Locational Marginal Emission?

Abstract

Growing concerns over climate change call for improved techniques for estimating and quantifying the greenhouse gas emissions associated with electricity generation and transmission. Among the emission metrics designated for power grids, locational marginal emission (LME) can provide system operators and electricity market participants with valuable information on the emissions associated with electricity usage at various locations in the power network. In this paper, by investigating the operating patterns and physical interpretations of marginal emissions and costs in the security-constrained economic dispatch (SCED) problem, we identify and draw the exact connection between locational marginal price (LMP) and LME. Such interpretation helps instantly derive LME given nodal demand vectors or LMP, and also reveals the interplay between network congestion and nodal emission pattern. Our proposed approach helps reduce the computation time of LME by an order of magnitude compared to analytical approaches, while it can also serve as a plug-and-play module accompanied by an off-the-shelf market clearing and LMP calculation process.

Paper Structure

This paper contains 18 sections, 2 theorems, 14 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Security-Constrained Economic Dispatch Model
  4. LMP and LME via Sensitivity Analysis
  5. Critical Region Projection-based LMEs
  6. Affine Policy in Critical Load Regions
  7. Mapping from Load to LME and LMP
  8. Mapping from LMP to LME
  9. Case Study
  10. Benchmark Methods
  11. Implicit Function (IF)-based LME
  12. Finite Difference (FD)-based LME
  13. Simulation Setup
  14. Computation Efficiency Analysis
  15. Robustness Analysis on Load Perturbations
  16. ...and 3 more sections

Key Result

Lemma 1

For a feasible $\boldsymbol{l}_\mathbf{c} \in \mathcal{L}$, in the neighborhood of the KKT point [$\mathbf{x}_\mathbf{c}, \mathbf{\lambda}_\mathbf{c}$], a first-order approximation of decision variable $\mathbf{x}$ and the Lagrange multiplier $\boldsymbol{\lambda}$ is, where and $Y$ is a null matrix of dimension ($g\times n$).

Figures (5)

  • Figure 1: Illustration of the mappings of Load-LME and LMP-LME via critical region projection, which helps us derive LME for given SCED instances.
  • Figure 2: Computation efficiency results. Reported time is averaged over 1000 samples with standard deviation shown as error bars. The y-axis is of logscale.
  • Figure 3: Robustness Analysis for 118-bus system.
  • Figure 4: LME and LMP in different critical regions of the 14-bus system. Negative LME are observed in Critical Region 1.
  • Figure 5: Calculation time of Load-based and LMP-based LME mappings.

Theorems & Definitions (4)

  • Lemma 1
  • Definition 1
  • Theorem 1
  • proof