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Measuring outage resilience in a distribution system with the number of outages in large events

Arslan Ahmad, Ian Dobson

Abstract

We develop LENORI, a Large Event Number of Outages Resilience Index measuring distribution system resilience with the number of forced line outages observed in large extreme events. LENORI is calculated from standard utility outage data. The statistical accuracy of LENORI is ensured by taking the logarithm of the outage data. A related Average Large Event Number of Outages metric ALENO is also developed, and both metrics are applied to a distribution system to quantify the power grid strength relative to the extreme events stressing the grid. The metrics can be used to track resilience and quantify the contributions of various types of hazards to the overall resilience.

Measuring outage resilience in a distribution system with the number of outages in large events

Abstract

We develop LENORI, a Large Event Number of Outages Resilience Index measuring distribution system resilience with the number of forced line outages observed in large extreme events. LENORI is calculated from standard utility outage data. The statistical accuracy of LENORI is ensured by taking the logarithm of the outage data. A related Average Large Event Number of Outages metric ALENO is also developed, and both metrics are applied to a distribution system to quantify the power grid strength relative to the extreme events stressing the grid. The metrics can be used to track resilience and quantify the contributions of various types of hazards to the overall resilience.
Paper Structure (14 sections, 19 equations, 2 figures, 4 tables)

This paper contains 14 sections, 19 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Literature review
  3. Utility data, outages, and events
  4. Defining LENORI and ALENO
  5. LENORI and ALENO in more depth
  6. Probability mass function of number of outages
  7. Linear approximation to the power law tail
  8. Log transformation converts heavy tail to light tail
  9. Required number of large events and metric variability
  10. Variability of LENORI with no logarithm
  11. Large event threshold $N_{\rm L}$
  12. Results
  13. Discussion of Heavy Tails
  14. Conclusion

Figures (2)

  • Figure 1: Log-log plot of probability mass function of number of outages.
  • Figure 3: Plot (a) shows on a log-log plot the idealized Pareto probability mass function \ref{['powerlaw']} of the event number of outages $N$ for the large event tail $N\ge N_{\rm L}=10$. The tail index $\alpha$ characterizes the tail since the slope magnitude of the tail is $\alpha+1$. Plot (b) applies a logarithm to the same number of outages data as plot (a) by relabeling the horizontal axis. Since plot (b) is a probability mass function that is the same straight line of slope magnitude $\alpha+1$ but now on a log plot, the log-transformed data $X=\ln N$ is a light-tailed distribution similar to an exponential distribution with parameter $\alpha+1$ and mean ALENO$+b$, where $b=\ln(N_{\rm L}-0.5)$. Plot (c) is the same as plot (b) but now on a linear plot. Plot (d) is the same as plot (c) except that the vertical axis is rescaled to show frequency. The annual large event frequency is $f_{\rm large}$. The mean of the frequency function is LENORI$+bf_{\rm large}$.