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Electricity Market-Clearing With Extreme Events

Tomas Tapia, Zhirui Liang, Charalambos Konstantinou, Yury Dvorkin

TL;DR

This work addresses the persistent risk of extreme events in electricity markets by introducing an extreme reserve and two Large Deviation Theory–based market formulations (LDT-CC-ED and LDT-WCC-ED) that co-optimize energy and two reserve types. It provides tractable reformulations, a cutting-plane solution approach for the LDT-WCC-ED, and derives marginal prices for energy, regular reserve, and extreme reserve, proving competitive equilibrium and cost-recovery properties. Case studies on a single-node example and the 8-zone ISO-NE system demonstrate that LDT-based designs better hedge tail risks and can reduce expected operating costs and volatility compared with conventional CC-based scheduling. The framework supports network-constrained extensions (LMP-like pricing and location-specific reserves) and highlights practical considerations for implementing extreme-reserve markets in renewable-dominated power systems.

Abstract

Extreme events jeopardize power network operations, causing beyond-design failures and massive supply interruptions. Existing market designs fail to internalize and systematically assess the risk of extreme and rare events. Efficiently maintaining the reliability of renewable-dominant power systems during extreme weather events requires co-optimizing system resources, while differentiating between large/rare and small/frequent deviations from forecast conditions. To address this gap in both research and practice, we propose managing the uncertainties associated with extreme weather events through an additional reserve service, termed extreme reserve. The procurement of extreme reserve is co-optimized with energy and regular reserve using a large deviation theory chance-constrained (LDT-CC) model, where LDT offers a mathematical framework to quantify the increased uncertainty during extreme events. To mitigate the high additional costs associated with reserve scheduling under the LDT-CC model, we also propose an LDT model based on weighted chance constraints (LDT-WCC). This model prepares the power system for extreme events at a lower cost, making it a less conservative alternative to the LDT-CC model. The proposed market design leads to a competitive equilibrium while ensuring cost recovery. Numerical experiments on an illustrative system and a modified 8-zone ISO New England system highlight the advantages of the proposed market design.

Electricity Market-Clearing With Extreme Events

TL;DR

This work addresses the persistent risk of extreme events in electricity markets by introducing an extreme reserve and two Large Deviation Theory–based market formulations (LDT-CC-ED and LDT-WCC-ED) that co-optimize energy and two reserve types. It provides tractable reformulations, a cutting-plane solution approach for the LDT-WCC-ED, and derives marginal prices for energy, regular reserve, and extreme reserve, proving competitive equilibrium and cost-recovery properties. Case studies on a single-node example and the 8-zone ISO-NE system demonstrate that LDT-based designs better hedge tail risks and can reduce expected operating costs and volatility compared with conventional CC-based scheduling. The framework supports network-constrained extensions (LMP-like pricing and location-specific reserves) and highlights practical considerations for implementing extreme-reserve markets in renewable-dominated power systems.

Abstract

Extreme events jeopardize power network operations, causing beyond-design failures and massive supply interruptions. Existing market designs fail to internalize and systematically assess the risk of extreme and rare events. Efficiently maintaining the reliability of renewable-dominant power systems during extreme weather events requires co-optimizing system resources, while differentiating between large/rare and small/frequent deviations from forecast conditions. To address this gap in both research and practice, we propose managing the uncertainties associated with extreme weather events through an additional reserve service, termed extreme reserve. The procurement of extreme reserve is co-optimized with energy and regular reserve using a large deviation theory chance-constrained (LDT-CC) model, where LDT offers a mathematical framework to quantify the increased uncertainty during extreme events. To mitigate the high additional costs associated with reserve scheduling under the LDT-CC model, we also propose an LDT model based on weighted chance constraints (LDT-WCC). This model prepares the power system for extreme events at a lower cost, making it a less conservative alternative to the LDT-CC model. The proposed market design leads to a competitive equilibrium while ensuring cost recovery. Numerical experiments on an illustrative system and a modified 8-zone ISO New England system highlight the advantages of the proposed market design.
Paper Structure (25 sections, 5 theorems, 39 equations, 6 figures, 4 tables, 1 algorithm)

This paper contains 25 sections, 5 theorems, 39 equations, 6 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation and Scope
  3. Literature Review
  4. Contributions
  5. Benchmark Models
  6. CC-ED: Chance-Constrained Economic Dispatch Model
  7. From CCs to Weighted Chance Constraints (WCCs)
  8. Proposed Formulations under Extreme Events
  9. LDT-CC-ED: ED with Large Deviation Theory CCs
  10. Reformulations of LDT-CC-ED
  11. LDT-WCC-ED: A Relaxation of LDT-CC-ED
  12. Reformulations of LDT-WCC-ED
  13. Prices for Energy, Regular Reserve, and Extreme Reserve
  14. Market-Clearing Based on LDT-CC-ED
  15. Market-Clearing Based on LDT-WCC-ED
  16. ...and 10 more sections

Key Result

Proposition 1

(Pricing based on LDT-CC-ED) The optimal values of $\pi$, $\rho$, and $\chi$ based on LDT-CC are given by:

Figures (6)

  • Figure 1: Operation regimes under uncertainty with regular (red) and LDT (yellow) chance constraints.
  • Figure 2: Comparison of benchmark (CC), the proposed model (LDT-CC), and its relaxation (LDT-WCC).
  • Figure 3: Illustrative single-node system.
  • Figure 4: 8-zones ISO New England system Krishnamurthy2016ISONEData.
  • Figure 5: Energy dispatch, regular and extreme reserve comparison.
  • ...and 1 more figures

Theorems & Definitions (11)

  • Proposition 1
  • proof
  • Theorem 1
  • proof
  • Remark 1
  • Proposition 2
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • ...and 1 more