IEEE Power & Energy Magazine - May/June 2018 - 47

may/june 2018

scenarios. the red line in the middle connects the median
(normalized) values of the nine years within each group.
taking the first three-year training period (2008-2010) for
example, each of the corresponding nine dots represents the
predicted saiDi values if those three years were experiencing
the same weather as one of the nine-year period (2008-2016).
the red dot in the middle is the median value that can be used
to indicate the daily operations during this three-year period
normalized based on nine years of weather history. overall, the
slopes from the dashed lines range from −0.1 to −1 min/year. in
other words, given the same weather from any year of the nineyear period, the weather-related saiDi of this utility shows a
decreasing trend from 2008 to 2016. the normalized curve
has a slope of −0.7 min/year, indicating weather-normalized
improvement of the weather-related saiDi at this lDc.
have utility operations been improving over the last nine
years? at this stage, we have answered the question for the
weather-related outages, which assemble the largest share of the
total saiDi for the small lDc in this case study. since weather

Calibration Results of
Daily SAIDI (in Minutes) Prediction Model
25
20
15
10
5

2008 2009 2010 2011 2012 2013 2014 2015 2016
Actual (Slope = -0.8 min/year)
Predicted (Slope = -0.4 min/year)

figure 3. The calibration results of the model that predicts
the weather-related daily SAIDI.

A Probabilistic View of
Weather-Related SAIDI (in Minutes)
25
20
15
10

-2
01
6

20
14

-2
01
5

20
13

-2
01
4

20
12

-2
01
3

20
11

-2
01
2

-2
01
1

20
10

20
09

-2
01
0

20
08

variables: temperature, dew-point temperature, heat index,
feels-like temperature (the combination of the heat index
and the wind-chill factor), wind chill, wind-chill energy, wet
bulb temperature, relative humidity, wind speed, speed gust,
and precipitation. to match them up with the daily saiDi
data, we convert the original records of the first ten weather
variables to daily values by taking the maximum, mean, and
minimum of the hourly values. for precipitation, we sum up
the hourly records by day to obtain the daily precipitation.
in addition, we include four dummy variables to describe the
weather events of the day, such as fog, rain, snow, and thunderstorm. in total, we use 37 candidate-independent variables to build a model that predicts the dependent-variable,
weather-related daily saiDi.
We use the regression procedure of the sas stat package to conduct the model selection process. after trying several different options, such as forward selection, backward
elimination, stepwise, maximum R 2 improvement, adjusted
R 2 selection, and mallows' C p selection, we select the following 11 variables: maximum dew-point temperature, minimum dew-point temperature, daily precipitation, average
relative humidity, average speed gust, minimum speed gust,
thunderstorm, maximum wind chill, average wind chill, average wind speed, and minimum wind speed.
calibrating this model using the 3,268 days of historical
data, we obtain predicted values of the weather-related daily
saiDi for the lDc. figure 3 shows the annual aggregates
of the actual and predicted saiDi values. Both saiDi
curves show a decreasing trend, with the slope of −0.8 and
−0.4 min/year for the actual and predictive saiDi, respectively. as mentioned earlier, the slope of the actual saiDi
curve indicates the trend of customer experience regarding
interruptions rather than the improvement of daily operations.
alternatively, one could assume that the lDc has engaged in
relatively consistent daily operational practices over the nineyear period. under this assumption, the decreasing slope
indicates that the weather, rather than improved operational
practices, has contributed to the trend of increased reliability
over the nine-year period.
however, maintaining constant daily operational practices
over a long period (i.e., nine years) is quite a strong assumption. Whether the utility has improved its daily operations is
the question we have been trying to answer. to further investigate this issue, we conduct a simulation to offer a probabilistic view of the weather-related saiDi. We first shrink the
training period to three years. We then fit the same 11-variable
model using the three-year training data and predict the daily
saiDi values of the nine-year period. By repeating this training window on a rolling basis, we can obtain seven groups
of predicted saiDi profiles, where each group includes nine
years of predicted daily saiDi values representing three years
of operational practice under nine different years of weather
scenarios from 2008 to 2016. figure 4 shows the annual
aggregates of the predicted saiDi values that are caused by
weather. the nine dashed lines represent the nine weather

figure 4. A probabilistic view of the weather-related SAIDI
over a nine-year period.
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