Fairly Extreme: Minimizing Outages Equitably

TL;DR

This paper introduces two methods to incorporate fairness into power grid outage minimization, ensuring equitable distribution of outages among customers, with extensive computational validation of their effectiveness.

Contribution

It proposes a novel $ ext{ extsterling}$-fairness concept and modifies existing optimization models to incorporate fairness through objective adjustment and a second-order cone constraint.

Findings

Both methods effectively incorporate fairness in outage minimization.

The $ ext{ extsterling}$-fairness approach is flexible and can be integrated into various optimization problems.

Computational case studies demonstrate the practical benefits of the proposed methods.

Abstract

This paper focuses on the problem of minimizing the outages due to extreme events on the power grid equitably among all customers of the grid. The paper presents two ways of incorporating fairness into the existing formulations that seek to minimize the total outage in the power grid. The first method is motivated by existing literature on incorporating fairness in optimization problems and this is done by modifying the problem's objective function. The second method introduces a novel notion of fairness, termed $\varepsilon$-fairness, that can be incorporated into existing problem formulations through a single second-order cone constraint. Both these methods are very general and can be used to incorporate fairness in existing planning and operational optimization problems in the power grid and beyond. Extensive computational case studies that examine the effectiveness of both these methods to characterize fairness is presented followed by conclusions and ways forward.