Typical models of the distribution system restoration process

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.

Figures (7)

• Figure 1: Variation of Event Restoration Duration with Event Size (log-log scale).
• Figure 2: Empirical CCDF of Event Restoration Duration $D$ of events with $n \geq 2$. The straight line shows a Pareto fit to the distribution tail starting at $D^{\rm cutoff}$.
• Figure 3: Variation of Time To First Restore with Event Size (log-log scale).
• Figure 4: Quantile–quantile plots comparing empirical normalized restore times $\Delta r_i$ (Utility 1, events with $n \geq 30$) against candidate distributions.
• Figure 5: Example event restore process. Empirical outage and restore processes are compared with fitted restore time process models.