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Major Event Day Classification

Major Event Day Classification. Rich Christie University of Washington Distribution Design Working Group Webex Meeting October 26, 2001. Overview. MED definitions Proposed frequency criteria Bootstrap method of evaluation Probability distribution fitting method Comparison.

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Major Event Day Classification

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  1. Major Event Day Classification Rich Christie University of Washington Distribution Design Working Group Webex Meeting October 26, 2001 MED Classification

  2. Overview • MED definitions • Proposed frequency criteria • Bootstrap method of evaluation • Probability distribution fitting method • Comparison MED Classification

  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? MED Classification

  4. Existing MED Definition (P1366) • Reflects broad range of existing practice • Ambiguous: “catastrophic,” “reasonable” • 10% criterion inequitable • No one design limit • No standard event types 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. MED Classification

  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. MED Classification

  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) MED Classification

  7. Probability of Occurrence • Frequency of occurrence f is probability of occurrence p MED Classification

  8. Reliability Threshold • Find MED threshold R* from probability p and probability distribution • MEDs are days with reliability ri > R* MED Classification

  9. Reliability: SAIDI/day or CMI/day? • If total customers (NT) is constant, either one • If NT varies from year to year, SAIDI (SAIDI in mins) MED Classification

  10. Bootstrap Method • Sample distribution is best estimate of actual distribution • In N years of data, N·f worst days are MEDs • R* between best MED and worst non-MED ri • How much data? • More better • How much is enough? MED Classification

  11. Take daily reliability data (3 years worth) Bootstrap Example SAIDI in mins/day MED Classification

  12. Sort by reliability (descending) Bootstrap Example MED Classification

  13. Pick off worst N·f as Major Event Days Bootstrap Example N = 3 yrs f = 3/yr MED = 9 MEDs: 98: 2 99: 2 00: 5 R* = 2.19 to 3.00 MED Classification

  14. Bootstrap Results MED Classification

  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 3*365 existing samples? • What number of years of existing data maximizes this? MED Classification

  16. Bootstrap Data Size • Order statistics result, probability of exactly f new values in n new samples greater than k’th value of m samples • 5-10 years of data looks reasonable MED Classification

  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. MED Classification

  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* MED Classification

  19. Choosing a Distribution Type • Examine histogram • What does it look like? • What doesn’t it look like? • Make probability plots • Try different distributions • Parameters come out as side effect • Most linear plot is best distribution type MED Classification

  20. Examine Histogram • Not Gaussian (!) • Not too useful otherwise Data: 3 years, anonymous “Utility 2” MED Classification

  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 MED Classification

  22. Probability Plot for Gaussian Distribution • Not Gaussian (but we knew that) MED Classification

  23. Probability Plot for Log-Normal Distribution • Looks good for this data MED Classification

  24. Probability Plot for Weibull Distribution • Not as good as Log-Normal MED Classification

  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 MED Classification

  26. Some Other Suspects • Gamma distribution • Erlang distribution • Beta distribution • etc. MED Classification

  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 MED Classification

  28. Fit Process • Find R* from p Solve For R* given p MED Classification

  29. Fit Process • Or! F(r) is CDF of log-normal distn  is CDF of standard normal (Gaussian) distribution -1is NORMINV function in ExcelTM MED Classification

  30. Fit Process • What about ri = 0? • It’s a lumped probability p(0) = nz/n • Probability left under curve is 1-p(0) • Correct p to MED Classification

  31. Fit Results MED Classification

  32. Result Comparison Bootstrap MEDs in parentheses MED Classification

  33. Method Comparison • Bootstrap simpler • Bootstrap limits number of MEDs • Bootstrap can saturate - fit doesn’t • A good fit for most of the data may not be a good fit for the tails MED Classification

  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/christie/ MED Classification

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