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Competitive Equilibrium for Electricity Markets with Spatially Flexible Loads

Nan Gu, Junjie Qin

TL;DR

Electrification of transport and large-scale computing creates spatially flexible loads that couple power grids with transportation and datacenter networks. The authors formulate a generalized competitive equilibrium (GCE) that captures bidirectional price–demand interactions via locational marginal prices and FL responses, derive conditions for existence, uniqueness, and efficiency, and extend the framework to multiple FL systems. They provide an optimization-based characterization of GCE, show how it reduces informational and computational burdens, and demonstrate via NYISO case studies that FLs mutually influence grid operations and each other’s welfare. The results quantify when selfish FL behavior aligns with or deviates from social welfare and illustrate how increased spatial flexibility generally improves system performance, with clear implications for market design and infrastructure coordination.

Abstract

Electric vehicle charging and geo-distributed datacenters introduce spatially flexible loads (FLs) that couple power, transportation, and datacenter networks. These couplings create a closed-loop feedback between locational marginal prices (LMPs) and decisions of the FL systems, challenging the foundations of conventional competitive equilibrium (CE) in electricity markets. This paper studies a notion of generalized competitive equilibrium (GCE) that aims to capture such price-demand interactions across the interconnected infrastructures. We establish structural conditions under which the GCE preserves key properties of the conventional CE, including existence, uniqueness, and efficiency, without requiring detailed knowledge of decision processes for individual FL systems. The framework generalizes to settings where the grid is coupled with multiple FL systems. Stylized examples and case studies on the New York ISO grid, coupled with the Sioux Falls transportation and distributed datacenter networks, demonstrate the use of our theoretical framework and illustrate the mutual influence among the grid and the studied FL systems.

Competitive Equilibrium for Electricity Markets with Spatially Flexible Loads

TL;DR

Electrification of transport and large-scale computing creates spatially flexible loads that couple power grids with transportation and datacenter networks. The authors formulate a generalized competitive equilibrium (GCE) that captures bidirectional price–demand interactions via locational marginal prices and FL responses, derive conditions for existence, uniqueness, and efficiency, and extend the framework to multiple FL systems. They provide an optimization-based characterization of GCE, show how it reduces informational and computational burdens, and demonstrate via NYISO case studies that FLs mutually influence grid operations and each other’s welfare. The results quantify when selfish FL behavior aligns with or deviates from social welfare and illustrate how increased spatial flexibility generally improves system performance, with clear implications for market design and infrastructure coordination.

Abstract

Electric vehicle charging and geo-distributed datacenters introduce spatially flexible loads (FLs) that couple power, transportation, and datacenter networks. These couplings create a closed-loop feedback between locational marginal prices (LMPs) and decisions of the FL systems, challenging the foundations of conventional competitive equilibrium (CE) in electricity markets. This paper studies a notion of generalized competitive equilibrium (GCE) that aims to capture such price-demand interactions across the interconnected infrastructures. We establish structural conditions under which the GCE preserves key properties of the conventional CE, including existence, uniqueness, and efficiency, without requiring detailed knowledge of decision processes for individual FL systems. The framework generalizes to settings where the grid is coupled with multiple FL systems. Stylized examples and case studies on the New York ISO grid, coupled with the Sioux Falls transportation and distributed datacenter networks, demonstrate the use of our theoretical framework and illustrate the mutual influence among the grid and the studied FL systems.

Paper Structure

This paper contains 42 sections, 10 theorems, 57 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Contributions and Paper Organization
  3. Related Literature
  4. Unified Framework
  5. Models of Generators and Stationary Loads
  6. Model of Spatially Flexible Loads
  7. Economic Dispatch
  8. Classical and Generalized Competitive Equilibrium
  9. General Results
  10. Grid Coupled with Single FL System
  11. Generalization to Multiple Independent FL Systems
  12. Coupled Power and Transportation Networks
  13. Elements of the FL System for Electrified Transportation
  14. Collective decision model
  15. FL decisions
  16. ...and 27 more sections

Key Result

Theorem 1

A triple $(\mathbf{g},\mathbf{s},\boldsymbol{\lambda})$ is a GCE if and only if it is a primal-dual optimal solution to the following optimization:

Figures (7)

  • Figure 1: Closed-loop feedback between the grid and FL system. See Section \ref{['sec:general:nfl']} for the extension to multiple FL systems.
  • Figure 2: Coupled transportation and 2-bus power system.
  • Figure 3: Coupled data center and 2-bus power system.
  • Figure 4: Impact of FL parameters on generation cost.
  • Figure 5: Travel cost under increasing EV and datacenter loads.
  • ...and 2 more figures

Theorems & Definitions (23)

  • Definition 1: Classical CE given FL Profile
  • Definition 2: Generalized CE
  • Theorem 1: Structural Characterization for GCE
  • Corollary 1: Existence and Uniqueness of GCE
  • Lemma 1: Structural Characterization for SWM
  • Corollary 2: Efficiency of the GCE
  • Definition 3: Stacked FL Representation for Multiple Systems
  • Theorem 2: GCE with Multiple Independent FL Systems
  • Lemma 2: Equivalence of UE and Best-Response Model
  • Lemma 3: Comparison of $(\mathrm{P}_{\mathrm{GCE}})$ and $(\mathrm{P}_{\mathrm{SWM}})$
  • ...and 13 more