IEEE Power & Energy Magazine - May/June 2018 - 45

table 1. Summary statistics of daily SAIDI values of a local distribution company, 2008-2016.
Original

Simplified Beta

IEEE Beta

Year

Sum

Max

Days

Sum

Max

Days

Threshold

Sum

Max

Days

2008

12.2

271

5.7

270

1.31

1.9

266

2009

10.0

221

5.4

220

1.31

3.4

216

2010

22.4

232

4.7

231

1.47

3.1

230

2011

2447

1793.0

224

3.3

216

1.44

3.3

216

2012

105

56.7

215

6.4

214

1.81

3.4

213

2013

7.5

216

6.3

215

1.77

4.0

214

2014

14.4

186

4.9

185

1.81

4.9

185

2015

214

133.6

205

4.2

202

1.95

4.2

202

2016

167

91.2

194

5.1

191

2.09

7.3

192

Trend

−26.0

−0.1

2.8

Notes
Original: statistics derived from the original data without taking out major event days.
Simplified Beta: statistics derived from the sample data with major event days excluded using the simplified Beta method.
IEEE Beta: statistics derived from the sample data with major event days excluded using the Beta method of IEEE Standard 1366.
Sum: annual SAIDI (in minutes) calculated as the sum of daily SAIDI values.
Max: maximum daily SAIDI (in minutes) during the period being included in the calculation.
Days: number of days being included in the calculation.
Threshold: a rolling number (a + 2.5b) by year used to exclude major event days as guided by IEEE Standard 1366.
Trend: the trend (in minutes/year) of annual SAIDI during the nine-year period.

original daily saiDi value (in minutes) is gone after taking
the log transformation. twenty days of the nine-year period
fall beyond 2.5 standard deviations. We denote this method
of calculating the threshold based on the entire data set (a
nine-year period in this case) as the simplified Beta method.
We also did the exact calculation as guided by the Beta
method of ieee standard 1366, resulting in a rolling threshold (e.g., a + 2.5b) calculated once a year based on the five
most recent years of historical values of daily saiDi values.
When fewer than five years of data is available, the entire
history was used. for instance, to calculate the threshold for
2011, we used three years of history (2008-2010).
table 1 lists the sum and maximum of daily saiDi values and the number of days with interruptions for each
year based on the three methods. We also calculate the
trends of the annual saiDi (sum of the daily saiDi values by
year). When the major event days are not excluded in the
annual saiDi calculation, the reliability shows a very strong
decreasing trend (−26 min/year). on the other hand, the simplified Beta method shows a flat trend (−0.1 min/year), while
the ieee Beta method presents a moderate increasing trend
(2.8 min/year). again, due to the lack of weather input in the
calculation of either method, the trend resulting from each
one does not indicate the improvement or degradation of this
lDc's daily operations.
the surge of outages in 2011 was due to a major hurricane. although other hurricanes affected the region during
may/june 2018

the nine-year period, some of which also resulted in extended
interruptions, none were as damaging to the power grid as
the one in 2011. Because of this surge, the major event day
threshold was bumped up to 1.81 in 2012. according to the
Beta method, this surge stays in the calculation of a and b
for five years, so the thresholds of 2012-2016 are higher than
those of 2008-2011. the aforementioned strong increasing
trend in the annual saiDi calculated using the Beta method
is largely due to this step-up in the threshold for major event
day. this effect was also mentioned in ieee standard 1366
as an ongoing work "undertaken to develop objective methods for identifying and processing catastrophic events (to
eliminate the noted effect on the reliability trend)."
figure 1 shows a more detailed view of the daily saiDi
data. part (a) shows the daily saiDi values of the entire
nine-year period (2008-2016), where the surge in 2011
makes the other days look like a flat line. part (b) excludes
the top 20 days with the highest daily saiDi values. the
line plot of the remaining days does not show any obvious
seasonal patterns either. Note that the distribution of the
log-transformed daily saiDi values does not pass commonly used normality tests, such as shapiro-Wilk, anderson-Darling, and Kolmogorov-smirnov. simply speaking,
the daily saiDi values of this lDc do not follow a lognormal distribution. in practice, among the lDcs we work
with, we can hardly find any that have the daily saiDi following a lognormal distribution. in the remaining part of
ieee power & energy magazine

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