Major Event Day Classification

1
Major Event Day Classification

• Rich Christie
• University of Washington
• Distribution Design Working Group Webex Meeting
• October 26, 2001

2
Overview

• MED definitions
• Proposed frequency criteria
• Bootstrap method of evaluation
• Probability distribution fitting method
• Comparison

3
Major Event Days

• Some days, reliability ri is a whole lot worse
  than other days
• ri is SAIDI/day, actually unreliabilty
• Usual cause is severe weather hurricanes,
  windstorms, tornadoes, earthquakes, ice storms,
  rolling blackouts, terrorist attacks
• These are Major Event Days (MED)
• Problem Exactly which days are MED?

4
Existing MED Definition (P1366)
Designates a catastrophic event which exceeds
reasonable design or operational limits of the
electric power system and during which at least
10 of the customers within an operating area
experience a sustained interruption during a 24
hour period.

• Reflects broad range of existing practice
• Ambiguous catastrophic, reasonable
• 10 criterion inequitable
• No one design limit
• No standard event types

5
10 Criterion
A
B
Same geographic phenomenon (e.g. storm track)
affects more than 10 of B, less than 10 of A.
Should be a major event for both, or neither -
inequitable to larger utility.
6
Proposed Frequency Criteria

• Utilities could agree, with regulators, on
  average frequency of MEDs, e.g. on average, 3
  MEDs/year
• Quantitative
• Equitable to different sized utilities
• Easy to understand
• Consistent with design criteria (withstand 1 in N
  year events)

7
Probability of Occurrence

• Frequency of occurrence f is probability of
  occurrence p

8
Reliability Threshold

• Find MED threshold R from probability p and
  probability distribution

• MEDs are days with reliability ri gt R

9
Reliability SAIDI/day or CMI/day?
(SAIDI in mins)

• If total customers (NT) is constant, either one
• If NT varies from year to year, SAIDI

10
Bootstrap Method

• Sample distribution is best estimate of actual
  distribution
• In N years of data, Nf worst days are MEDs
• R between best MED and worst non-MED ri
• How much data?
• More better
• How much is enough?

11
Bootstrap Example

• Take daily reliability data (3 years worth)

SAIDI in mins/day
12
Bootstrap Example

• Sort by reliability (descending)

13
Bootstrap Example

• Pick off worst Nf as Major Event Days

N 3 yrs f 3/yr MED 9
MEDs 98 2 99 2 00 5
R 2.19 to 3.00
14
Bootstrap Results
15
Bootstrap Data Size Issue

• How many years of data?
• New data revises MEDs
• Ideally, one new year should cause f new MEDs
  (i.e. 3, in example with f 3 MED/yr)
• What is probability of exactly 3 new values in
  365 new samples greater than the 9th largest
  value in 3365 existing samples?
• What number of years of existing data maximizes
  this?

16
Bootstrap Data Size

• Order statistics result, probability of exactly f
  new values in n new samples greater than kth
  value of m samples

• 5-10 years of data looks reasonable

17
Bootstrap Characteristics

• Fast
• Easy
• Intuitive
• Saturates
• e.g. if f 3 and one year has the 30 highest
  values, need 11 years of data before any other
  year has an MED, or exceptional year must roll
  out of data set.

18
Probability Distribution Fitting

• Should be immune to saturation
• Process
• Choose a probability distribution type
• Fit data to distribution
• Calculate R from fitted distribution and p
• Find MEDs from R

19
Choosing a Distribution Type

• Examine histogram
• What does it look like?
• What doesnt it look like?
• Make probability plots
• Try different distributions
• Parameters come out as side effect
• Most linear plot is best distribution type

20
Examine Histogram
Data 3 years, anonymous Utility 2

• Not Gaussian (!)
• Not too useful otherwise

21
Probability Plot

• Order samples e.g. ri 2, 5, 7, 12
• Probability of next sample having a value less
  than 5 is
• Given a distribution, can find a random variable
  value xk(pk) (pk is area under curve to left of
  xk)
• If plot of rk vs xk is linear, distribution is
  good fit

22
Probability Plot for Gaussian Distribution

• Not Gaussian (but we knew that)

23
Probability Plot for Log-Normal Distribution

• Looks good for this data

24
Probability Plot for Weibull Distribution

• Not as good as Log-Normal

25
Stop at Log-Normal

• Good fit
• Computationally tractable
• Pragmatically important that method be accessible
  to typical utility engineer
• Weak theoretical reasons to go with log-normal
• Loosely, normal process with lower limit has
  log-normal distribution

26
Some Other Suspects

• Gamma distribution
• Erlang distribution
• Beta distribution
• etc.

27
Fit Process

• Find log-normal parameters
• (? and ? are not mean and standard deviation!)

Example ? -3.4 ? 1.95
Leave out ri 0, but count how many
28
Fit Process

• Find R from p

Solve
For R given p
29
Fit Process

• Or!

F(r) is CDF of log-normal distn
? is CDF of standard normal (Gaussian)
distribution
?-1 is NORMINV function in ExcelTM
30
Fit Process

• What about ri 0?
• Its a lumped probability p(0) nz/n
• Probability left under curve is 1-p(0)
• Correct p to

31
Fit Results
32
Result Comparison
Bootstrap MEDs in parentheses
33
Method Comparison

• Bootstrap simpler
• Bootstrap limits number of MEDs
• Bootstrap can saturate - fit doesnt
• A good fit for most of the data may not be a good
  fit for the tails

34
Conclusion

• Frequency criteria (MEDs/year) is at root of work
• Two methods to classify MEDs based on frequency -
  strengths and weaknesses
• Reliability distributions may not all be log
  normal
• White paper and spreadsheet at
  http//www.ee.washington.edu/people/faculty/christ
  ie/