July 22, 2002MED Classification1 Statistical Methods of Classifying Major Event Days in Distribution Systems Rich Christie University of Washington PES SM 2002 Panel July 22, 2002

MED Classification2 Overview Major Event Days (MEDs) Classification Methods –Three Sigma (3σ) –Two Point Five Beta (2.5β) –Bootstrap (B3) Comparison with example Conclusion

July 22, 2002MED Classification3 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?

July 22, 2002MED Classification4 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

July 22, 2002MED Classification5 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

July 22, 2002MED Classification6 Three Sigma Method Assemble 3-5 years of daily SAIDI values Calculate the average (μ) and standard deviation (σ) (spreadsheet functions) Calculate threshold

July 22, 2002MED Classification7 Three Sigma Theory 3σ assumes SAIDI is normally distributed

July 22, 2002MED Classification8 Three Sigma Theory Expected MEDs depend on multiple (k = 3), not average (μ) or standard deviation (σ)

July 22, 2002MED Classification9 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

July 22, 2002MED Classification10 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.

July 22, 2002MED Classification11 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)

July 22, 2002MED Classification12 Why 2.5? Expect 2.3 MEDs/year Distribution Design Working Group members like 2.5 better than 2 or 3.

July 22, 2002MED Classification13 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*

July 22, 2002MED Classification14 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

July 22, 2002MED Classification15 Comparison of Methods

July 22, 2002MED Classification16 Example 7 Long tail in historical data has more effect on 3σ and bootstrap (B3) methods.

July 22, 2002MED Classification17 Comparison of Methods 3σ 2.5β B3 ComplexityEquityRobustness Low High Fairly Low Med No Yes Vary with size, avg Saturation problem Medium Harder to explain High

July 22, 2002MED Classification18 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!)