IEEE Power & Energy Magazine - May/June 2018 - 44

to measure and communicate reliability, utility stakeholders often use reliability indices as a good measure of utility
system health. Just as many complex systems have their own
level of health measurements, reliability indices let everyone
know if the utility system is getting better or worse over time.
reliability indices help power engineers and other operations personnel see and show the interconnected nature of
the many independent system components that make up an
electric distribution system. to quantify the level of system
reliability, power engineers have adopted and invented many
reliability indices.
a commonly used index for power distribution systems is
system average interruption Duration index (saiDi), which
indicates the total interruption duration for the average customer during a predefined period. the formula to calculate
the index is
SAIDI =

Sum of all Customer Interuption Durations
.
Total Number of Customers Served

the numerator can be thought of as the total number of outage minutes experienced by all customers for a predefined
period, which is typically one year. saiDi is commonly
given in minutes and, generally speaking, represents the
average outage minutes experienced for a customer connected to the utility's system. Daily and monthly saiDi values may be used for a more detailed and timely analysis of
system reliability. it should be noted that some utilities do
not have enough outages to calculate a saiDi for every day
in the year.
a high saiDi value indicates poor system reliability.
although saiDi, together with many other reliability indices, can be used to describe customer experience, it does
not offer many actionable insights into the daily operations
of utilities. this is because the saiDi calculation is significantly impacted by severe weather conditions that take out
large numbers of customers for an extended period of time.
let's consider two power companies, P1 and P2, each serving
1 million customers. P1 had 50,000 customers who experienced
300 6-min interruptions within one year. the annual saiDi value
of P1 can be calculated as 6 # 300 # 50,000/1,000,000 =
90 min . P2 was hit by a major hurricane that caused a systemwide outage of 90 min, while no other interruptions occurred during the year. the annual saiDi value of P2 would be
90 # 1 # 1,000,000/1,000,000 = 90 min.
although both companies share exactly the same saiDi
value, the potential and strategy for them to improve their
reliability can be quite different. P1 can improve its daily
operations to reduce the number of interruptions and the
duration of each interruption. on the other hand, the major
hurricane that hit P2 could be a rare event that is out of anyone's control. if P2 chose to do exactly the same practice
as before but did not experience another major hurricane in
the next year, its saiDi value would be very small, indicating a very good reliability. if P2 chose to improve its storm
44

ieee power & energy magazine

restoration practice, the duration of the interruption caused
by a similar hurricane could be shortened.

The Beta Method
from IEEE Standard 1366
to study major events separately from daily operations and
to reveal trends in daily operations that can be hidden by the
statistical effect of major events, the ieee Working Group
on Distribution reliability included the section "major event
Day classification" in ieee standard 1366, IEEE Guide for
Electric Power Distribution Reliability Indices. according
to this standard, the daily saiDi value is assumed to follow a log-normal distribution. after taking the natural logarithm transformation of the daily saiDi values, the days
falling beyond the 2.5 standard deviations to the right of the
mean are classified as major event days. the mean and standard deviation are denoted by a and b, respectively. this
method is also known as the Beta method, the 2.5 b method,
or ieee 2.5 Beta.
to appeal to a broad audience, the Beta method keeps
its simplicity by avoiding any predictive modeling effort in
the saiDi reporting process other than taking the logarithm
transformation and calculating the mean and standard deviation. the Beta method is better at "revealing trends in daily
operations that would be hidden by the large statistical effect
of major events" than the original all-inclusive saiDi calculation. however, due to the exclusion of weather information,
it is unable to answer some important and frequently asked
what-if questions, such as "What would be the saiDi values if the weather this year was the same as last year?" consequently, the Beta method has limited capability to reveal
trends in reliability, including any improvement or degradation that could be hidden by weather conditions not classified
as major events. moreover, the assumption that daily saiDi
always follows the lognormal distribution is yet to be verified.
have utility operations been improving over the last few
years? the power industry has been trying to answer this
question since the late 20th century. While ieee standard
1366 has made great progress by bringing a simple tool to
the reporting process, there is still a long way to go. in this
article, we will demonstrate a predictive modeling approach
that can provide a probabilistic view of reliability indices to
help further reveal a utility's reliability trend. the case study
is based on a small local distribution company (lDc) in the
united states.

Descriptive Outage
and Reliability Analytics
the lDc serves approximately 30,000 customers. the case
study uses nine years of outage information collected from
this lDc. interruptions occurred in 1,964 of the 3,288 days
covered by the data set. after taking the log transformation
on the daily saiDi values, we obtain the mean (a) of these
nine years of log transformed daily saiDi values as −2.80
with a standard deviation (b) 1.88. Note that the unit of the
may/june 2018



Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - May/June 2018

Contents
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IEEE Power & Energy Magazine - May/June 2018 - Cover3
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