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## Statistical Methods of Classifying Major Event Days in Distribution Systems

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### July 22, 2002. MED Classification. 3. Major Event Days. Reliability measured in SAIDI/day ... Long tail in historical data has more effect on 3s and bootstrap ... – PowerPoint PPT presentation

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Title: 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

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

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?

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

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

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

7
Three Sigma Theory
• 3s assumes SAIDI is normally distributed

8
Three Sigma Theory
• Expected MEDs depend on multiple (k 3), not
average (µ) or standard deviation (s)

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
10
Two Point Five Beta (2.5ß)
• 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.
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.
• Calculate the average (a) and standard deviation
(ß) of the logs
• Calculate threshold(EXP function)

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

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

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 Rs to most recent year of present data
to find MEDs

15
Comparison of Methods
16
Example 7
Long tail in historical data has more effect on
3s and bootstrap (B3) methods.
17
Comparison of Methods
Complexity
Equity
Robustness
High
No
Low
3s
Vary with size, avg
Fairly Low
High
Yes
2.5ß
Med
Yes
Medium
B3
Saturation problem
Harder to explain
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!)