Typical models of the distribution system restoration process

TL;DR

This paper develops data-driven probabilistic models for the power distribution system restoration process, enabling more accurate resilience planning and decision-making through detailed stochastic modeling of restoration components.

Contribution

It introduces a comprehensive probabilistic modeling framework for distribution system restoration using outage data, including novel fits for restore time, duration, and first restore time.

Findings

Beta distribution best fits restore time progression

Total duration scales superlinearly with event size

Gamma model effectively describes time to first restore

Abstract

Accurate probabilistic modeling of the power system restoration process is essential for resilience planning, operational decision-making, and realistic simulation of resilience events. In this work, we develop data-driven probabilistic models of the restoration process using outage data from four distribution utilities. We decompose restoration into three components: normalized restore time progression, total restoration duration, and the time to first restore. The Beta distribution provides the best-pooled fit for restore time progression, and the Uniform distribution is a defensible, parsimonious approximation for many events. Total duration is modeled as a heteroskedastic Lognormal process that scales superlinearly with event size. The time to first restore is well described by a Gamma model for moderate and large events. Together, these models provide an end-to-end stochastic model for Monte Carlo simulation, probabilistic duration forecasting, and resilience planning that moves beyond summary statistics, enabling uncertainty-aware decision support grounded in utility data.