Logarithmic resilience risk metrics that address the huge variations in blackout cost

Paper: arXiv 2505.12016

Authors: Arslan Ahmad, Ian Dobson

Abstract

Resilience risk metrics must address the customer cost of the largest blackouts of greatest impact. However, there are huge variations in blackout cost in observed distribution utility data that make it impractical to properly estimate the mean large blackout cost and the corresponding risk. These problems are caused by the heavy tail observed in the distribution of customer costs. To solve these problems, we propose resilience metrics that describe large blackout risk using the mean of the logarithm of the cost of large-cost blackouts, the slope index of the heavy tail, and the frequency of large-cost blackouts.

Complexity vs Empirical Score

• Math Complexity: 5.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper applies heavy-tailed distribution theory and Hill estimators to power grid resilience data, proposing log-transformed risk metrics (ALEC/ALCRI) to resolve infinite mean/variance issues. It evaluates empirical outage data across five US utilities with sound statistical testing, though it is cut off slightly at the end.

Research Flowchart

  flowchart TD
    A[Goal: Measure resilience risk despite huge blackout cost variations] --> B[Input: Observed distribution utility outage & cost data]
    B --> C[Analyze Empirical Data: Identify heavy-tailed cost distribution]
    C --> D[Identify Issue: Standard mean cost estimation fails due to extreme variance]
    D --> E[Formulate Logarithmic Resilience Metrics]
    E --> F[Calculate Components: Log-mean cost, heavy-tail slope index, & blackout frequency]
    F --> G[Outcome: Accurate, stable metrics for high-impact resilience risk]