Typical models of the distribution system restoration process

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 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.