Statistical Methods of Classifying Major Event Days in Distribution Systems

1. Statistical Methods of Classifying Major Event Days in Distribution Systems Rich Christie University of Washington PES SM 2002 Panel July 22, 2002 MED Classification

2. Overview • Major Event Days (MEDs) • Classification Methods • Three Sigma (3σ) • Two Point Five Beta (2.5β) • Bootstrap (B3) • Comparison with example • Conclusion MED Classification

3. Major Event Days • Reliability measured in SAIDI/day • Some days, reliability is a whole lot worse than other days - Major Event Day (MED) • How can MEDs be identified? MED Classification

4. Classification • Need to classify MEDs the day they occur • Threshold R* on SAIDI/day • Classification should be fair for different utilities • Classification should be unambiguous • Reliability is a statistical process • Classification should be statistical MED Classification

5. Three Sigma (3σ) • Familiar concepts of average (μ) and standard deviation (σ) of daily reliability • More standard deviations above average means fewer values • 3σ a common threshold for exceptional values MED Classification

6. Three Sigma Method • Assemble 3-5 years of daily SAIDI values • Calculate the average (μ) and standard deviation (σ) (spreadsheet functions) • Calculate threshold MED Classification

7. Three Sigma Theory • 3σ assumes SAIDI is normally distributed MED Classification

8. Three Sigma Theory • Expected MEDs depend on multiple (k = 3), not average (μ) or standard deviation (σ) MED Classification

9. Three Sigma Problem • Daily reliability is NOT normally distributed Histogram of three years of daily SAIDI data from anonymous Utility 2 supplied by the Distribution Design Working Group MED Classification

10. Two Point Five Beta (2.5β) • The natural logs (ln) of daily reliability are normally distributed Histogram of the natural logs of three years of daily SAIDI data from anonymous Utility 2 supplied by the Distribution System Design Working Group. MED Classification

11. Two Point Five Beta Method • Assemble 3-5 years of daily SAIDI values • Take the natural log of each value. For SAIDI = 0, use lowest non-zero SAIDI in data set. (Spreadsheet function) • Calculate the average (α) and standard deviation (β) of the logs • Calculate threshold(EXP function) MED Classification

12. Why 2.5? • Expect 2.3 MEDs/year • Distribution Design Working Group members like 2.5 better than 2 or 3. MED Classification

13. Bootstrap Method (B3) • Decide on desired expected MEDs/year (3) • Assemble 3-5 years of daily SAIDI values • Sort in descending order • Calculate expected MEDs in data (years * MED/year, e.g. 3 years, 3/year = 9 MEDs) • SAIDI of last MED is threshold R* MED Classification

14. Comparison of Methods • Three example data sets (2,6,7) from different anonymous utilities • Use three (or less) years of “historical” data to calculate thresholds • Apply R*s to most recent year of “present” data to find MEDs MED Classification

15. Comparison of Methods MED Classification

16. Example 7 Long tail in historical data has more effect on 3σ and bootstrap (B3) methods. MED Classification

17. Comparison of Methods Complexity Equity Robustness No High Low 3σ Vary with size, avg Fairly Low High Yes 2.5β Med Medium Yes B3 Saturation problem Harder to explain MED Classification

18. Conclusion • Two Point Five Beta method best reflects nature of daily reliability (log-normal). • Factor of 2.5 arrived at by consensus in Distribution Design Working Group (subject to change!) MED Classification