October 26, 2001MED Classification1 Major Event Day Classification Rich Christie University of Washington Distribution Design Working Group Webex Meeting October 26, 2001

MED Classification2 Overview MED definitions Proposed frequency criteria Bootstrap method of evaluation Probability distribution fitting method Comparison

October 26, 2001MED Classification3 Major Event Days Some days, reliability r i is a whole lot worse than other days –r i 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?

October 26, 2001MED Classification4 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.

October 26, 2001MED Classification5 10% Criterion AB 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.

October 26, 2001MED Classification6 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)

October 26, 2001MED Classification7 Probability of Occurrence Frequency of occurrence f is probability of occurrence p

October 26, 2001MED Classification8 Reliability Threshold Find MED threshold R* from probability p and probability distribution MEDs are days with reliability r i > R*

October 26, 2001MED Classification9 Reliability: SAIDI/day or CMI/day? If total customers ( N T ) is constant, either one If N T varies from year to year, SAIDI (SAIDI in mins)

October 26, 2001MED Classification10 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 r i How much data? –More better –How much is enough?

October 26, 2001MED Classification11 Bootstrap Example Take daily reliability data (3 years worth) SAIDI in mins/day

October 26, 2001MED Classification12 Bootstrap Example Sort by reliability (descending)

October 26, 2001MED Classification13 Bootstrap Example Pick off worst N·f 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

October 26, 2001MED Classification14 Bootstrap Results

October 26, 2001MED Classification15 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?

October 26, 2001MED Classification16 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

October 26, 2001MED Classification17 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.

October 26, 2001MED Classification18 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*

October 26, 2001MED Classification19 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

October 26, 2001MED Classification20 Examine Histogram Not Gaussian (!) Not too useful otherwise Data: 3 years, anonymous “Utility 2”

October 26, 2001MED Classification21 Probability Plot Order samples: e.g. r i = {2, 5, 7, 12} Probability of next sample having a value less than 5 is Given a distribution, can find a random variable value x k (p k ) (p k is area under curve to left of x k ) If plot of r k vs x k is linear, distribution is good fit

October 26, 2001MED Classification22 Probability Plot for Gaussian Distribution Not Gaussian (but we knew that)

October 26, 2001MED Classification23 Probability Plot for Log-Normal Distribution Looks good for this data

October 26, 2001MED Classification24 Probability Plot for Weibull Distribution Not as good as Log-Normal

October 26, 2001MED Classification25 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

October 26, 2001MED Classification26 Some Other Suspects Gamma distribution Erlang distribution Beta distribution etc.

October 26, 2001MED Classification27 Fit Process Find log-normal parameters (  and  are not mean and standard deviation!) Example:  = -3.4  = 1.95 Leave out r i = 0, but count how many

October 26, 2001MED Classification28 Fit Process Find R* from p Solve For R* given p

October 26, 2001MED Classification29 Fit Process Or! F(r) is CDF of log-normal distn  is CDF of standard normal (Gaussian) distribution  -1 is NORMINV function in Excel TM

October 26, 2001MED Classification30 Fit Process What about r i = 0? –It’s a lumped probability p(0) = n z /n –Probability left under curve is 1-p(0) –Correct p to

October 26, 2001MED Classification31 Fit Results

October 26, 2001MED Classification32 Result Comparison Bootstrap MEDs in parentheses

October 26, 2001MED Classification33 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

October 26, 2001MED Classification34 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: