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Enhancing Electricity-System Resilience with Adaptive Robust Optimization and Conformal Uncertainty Characterization

Shuyi Chen, Shixiang Zhu, Ramteen Sioshansi

TL;DR

This work tackles the resilience of electricity systems to extreme weather by formulating a tri-level robust-optimization problem that tightly couples proactive hardening, adversarial disruptions, and reactive responses. It introduces distribution-free, spatio-temporal uncertainty sets constructed via conformal prediction, providing finite-sample coverage guarantees and region-specific bounds that adapt to heterogeneity. By reformulating the tri-level model into a bi-level program through duality and solving with Benders decomposition, the approach delivers scalable, provably convergent solutions. Numerical experiments on synthetic data and a real Massachusetts case study show that joint proactive-reactive planning with conformal-prediction uncertainty sets outperforms traditional robust and two-stage methods, especially under tight budgets and extreme events.

Abstract

Extreme weather is straining electricity systems, exposing the limitations of reactive responses, and prompting the need for proactive resilience planning. Most existing approaches to enhance electricity system resilience employ simplified uncertainty models and decouple proactive and reactive decisions. This paper proposes a novel tri-level optimization model that integrates proactive actions, adversarial disruptions, and reactive responses. Conformal prediction is used to construct distribution-free system-disruption uncertainty sets with coverage guarantees. The tri-level problem is solved by using duality theory to derive a bi-level reformulation and employing Bender's decomposition. Numerical experiments demonstrate that our approach outperforms conventional robust and two-stage methods.

Enhancing Electricity-System Resilience with Adaptive Robust Optimization and Conformal Uncertainty Characterization

TL;DR

This work tackles the resilience of electricity systems to extreme weather by formulating a tri-level robust-optimization problem that tightly couples proactive hardening, adversarial disruptions, and reactive responses. It introduces distribution-free, spatio-temporal uncertainty sets constructed via conformal prediction, providing finite-sample coverage guarantees and region-specific bounds that adapt to heterogeneity. By reformulating the tri-level model into a bi-level program through duality and solving with Benders decomposition, the approach delivers scalable, provably convergent solutions. Numerical experiments on synthetic data and a real Massachusetts case study show that joint proactive-reactive planning with conformal-prediction uncertainty sets outperforms traditional robust and two-stage methods, especially under tight budgets and extreme events.

Abstract

Extreme weather is straining electricity systems, exposing the limitations of reactive responses, and prompting the need for proactive resilience planning. Most existing approaches to enhance electricity system resilience employ simplified uncertainty models and decouple proactive and reactive decisions. This paper proposes a novel tri-level optimization model that integrates proactive actions, adversarial disruptions, and reactive responses. Conformal prediction is used to construct distribution-free system-disruption uncertainty sets with coverage guarantees. The tri-level problem is solved by using duality theory to derive a bi-level reformulation and employing Bender's decomposition. Numerical experiments demonstrate that our approach outperforms conventional robust and two-stage methods.
Paper Structure (16 sections, 2 theorems, 34 equations, 8 figures, 4 tables, 2 algorithms)

This paper contains 16 sections, 2 theorems, 34 equations, 8 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Model Formulation
  3. Tri-Level Model
  4. Constructing $\Omega(w)$ via Conformal Prediction
  5. Model Benchmarking
  6. Solution Strategy
  7. Continuous Reformulation of Recourse Problem
  8. Combining Middle and Lowest Levels of (\ref{['equ:solution:continuous:objFunc']})
  9. Benders's Decomposition of (\ref{['equ:solution:combine:final:objFunc']})--(\ref{['equ:solution:combine:final:proactive:binary']})
  10. Example
  11. Data Simulation
  12. Results
  13. Case Study
  14. Data
  15. Results
  16. ...and 1 more sections

Key Result

Lemma 1

The definition of $\Omega(w)$ in (equ:model:predict:cons:nature), its construction by Algorithm alg:model:predict, and the observations in $\mathcal{M}$ being exchangable ensure that chance constraint (equ:model:optimization:cons:nature) is satisfied, regardless of the distribution of $u$.

Figures (8)

  • Figure 1: Difference in (\ref{['equ:model:benchmark:bilevel']}) vis-à-vis tri-level model for example in Section \ref{['sec:example']} as $\chi$ is varied.
  • Figure 2: Difference in (\ref{['equ:model:benchmark:bilevel']}) vis-à-vis tri-level model for example in Section \ref{['sec:example']} as $n$ is varied.
  • Figure 3: Difference in (\ref{['equ:model:benchmark:bilevel']}) vis-à-vis tri-level model for example in Section \ref{['sec:example']} as $B$ is varied.
  • Figure 4: Difference in (\ref{['equ:model:benchmark:bilevel']}) vis-à-vis tri-level model for example in Section \ref{['sec:example']} as $C$ is varied.
  • Figure 5: Total wall-clock time of Algorithm \ref{['alg:solution:benders']} for example in Section \ref{['sec:example']} as $n$ is varied.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Lemma 1
  • Lemma 2