Quantifying resilience for distribution system customers with SALEDI

TL;DR

The paper tackles the instability of SAIDI when major blackout days occur and proposes SALEDI, a log-transformed resilience index derived from large-event CMIp data. SALEDI decomposes into annual large-event frequency $f_{\rm large}$ and the Average Large Event Duration $ALED$, giving $SALEDI = f_{\rm large} \cdot ALED$; the tail of large-event magnitudes is modeled as a Pareto with slope $\alpha$, with $ALED$ estimating $\alpha^{-1}$ and linking to CVAR concepts. The method is validated on outage data from five utilities, with a principled threshold selection for large events via Clauset’s method and practical guidance that 2–5 years of data suffice for stable estimates. The authors clarify the distinct roles of SAIDI and SALEDI, provide area interpretations of tail metrics, and discuss extrapolation for unobserved extremes to quantify resilience risk. Overall, SALEDI emerges as a practical, interpretable resilience index for distribution systems that complements traditional reliability metrics and supports risk-aware investment and operational decisions.

Abstract

The impact of routine smaller outages on distribution system customers in terms of customer minutes interrupted can be tracked using conventional reliability indices. However, the customer minutes interrupted in large blackout events are extremely variable, and this makes it difficult to quantify the customer impact of these extreme events with resilience metrics. We solve this problem with the System Average Large Event Duration Index SALEDI that logarithmically transforms the customer minutes interrupted. We explain how this new resilience metric works, compare it with alternatives, quantify its statistical accuracy, and illustrate its practical use with standard outage data from five utilities.

Figures (6)

• Figure 1: Annual fluctuations in SAIDI with and without major event days, and resilience indices SALEDI (with log) and SPLEDI (without log) for utility 4.
• Figure 2: Tracking SALEDI over years. For each utility, a sliding window of duration $n_{\rm year}$ is used.
• Figure 3: Exceedance functions $\overline{F}(M)$ for all events of utilities 1-5; log-log plot
• Figure 4: Tails of the exceedance functions of Fig. \ref{['fig:exceedance']} with normalized event CMIp $P=M/M_{\rm large}$ on the horizontal axis with a log scale.
• Figure 5: Plot (a) shows on a log-log plot the idealized Pareto probability exceedance function \ref{['powerlaw']} of the normalized CMIp $M/M_{\rm large}$ for the large event tail. The slope magnitude $\alpha$ characterizes the tail. In this plot $\alpha=0.8<1$ so that the mean ${\rm E}P$ is infinite. Plot (b) applies a logarithm to the same normalized CMIp by relabeling the horizontal axis. Since plot (b) is an exceedance function that is the same straight line of slope magnitude $\alpha$ but now on a log plot, the log-transformed data $X=\ln P$ is an exponential distribution of rate $\alpha$ and finite mean $1/\alpha$. Plot (c) is the same as plot (b) but now on a linear plot. The area under plot (c) is the ALED metric. Plot (d) is the same as plot (c) except that the vertical axis is rescaled to show a frequency exceedance function with annual large event frequency $f_{\rm large}$. The area under plot (d) is SALEDI = $f_{\rm large}$ ALED.