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Reliability

447

mission-caused interruptions). Both are done for the same reasons as storm

exclusions: neither scheduled interruptions nor transmission-caused inter-

ruptions reﬂect the normal operating performance of the distribution system.

The IEEE working group appears to favor a statistical approach to classi-

fying major events (Christie, 2002). An argument against this approach is

that major substation or transmission outages can be “major events” and get

excluded from indices. From the customer point of view, major event or no

major event, an interruption is still a loss of production or a spoiled inventory

or a loss of productivity or a missed football game. For this reason, some

regulators hesitate to allow exclusions.

During storm days, the interruption durations increase exponentially. Fig-

ure 9.5 shows probability distributions of the daily SAIDI based on data

from four utilities. The plot is on a log-normal scale: the x-axis shows SAIDI

for each day on a log scale, and the y-axis shows the probability on a normal-

distribution scale. On this plot, data with a log-normal distribution comes

out as a straight line. Most of the utility data ﬁts a log-normal distribution.

But, two of the utilities are even more skewed than a log-normal distribution

indicates — at these utilities, storm days have even more customer-minutes

FIGURE 9.4

Distribution of utility indices with and without excluding storms. (Data from [EEI, 1999].)

storms

excluded

storms

included

0 1 2 3 4

storms

excluded

storms

included

0 2 4 6 8 10 12

100

SAIFI, events/year

Percent of utility indices

exceeding the x-axis value

100

SAIDI, hours/year

Percent of utility indices

exceeding the x-axis value

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interrupted. At one of these utilities, 0.2% of the days contributed 40% of

the SAIDI index (over a 7-year period). During the worst year at this utility,

70% of SAIDI for that year happened because of three storms (impacting 5

days total). If we have one day with a SAIDI of over 100 min (the value for

a whole year at some utilities), it is going to be a long year. Figure 9.6 again

emphasizes how skewed the probability distribution of reliability data is.

The average is much higher than the median, and the extreme days heavily

inﬂuence the average.

Weather, even if it does not reach the level of “major event,” plays a major

role in reliability. Weather varies considerably from year to year — these

weather variations directly affect reliability indices. Bad lightning years or

excessively hot years worsen the indices.

Monitoring by Ontario Hydro Technologies in Ontario, Canada, gives

some insight into storm durations and failure rates (CEA 160 D 597, 1998).

In a mild to moderate lightning area, 20% of the interruptions occurred

during storm periods and 15% in the 24 h following a storm. The study area

had an average of 25 storm days per year and 73 storm hours per year.

Therefore, about 35% of outages occur in 7% of the time in a year (and 20%

in 0.8% of the time). The study found an interruption rate during storms of

10 to 20 times the non-storm rate.

FIGURE 9.5

SAIDI per day probability distributions for four utilities.

0.01 0.1 1.0 10.0 100.0

0.1

1.0

5.0

10.0

20.0

50.0

80.0

90.0

95.0

99.0

99.9

0.1

1.0

5.0

10.0

20.0

50.0

80.0

90.0

95.0

99.0

99.9

0.1

1.0

5.0

10.0

20.0

50.0

80.0

90.0

95.0

99.0

99.9

0.1

1.0

5.0

10.0

20.0

50.0

80.0

90.0

95.0

99.0

99.9

SAIDI/day, minutes

Percent of days

exceeding the x-axis value

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Reliability

449

Faults and interruptions have signiﬁcant year-to-year variation because

weather conditions vary signiﬁcantly. Just as severe storm patterns vary,

normal storm frequencies and durations vary. Consider the thunderstorm

duration plot in Figure 9.7. Over this 30-year period in Tampa, FL (a very

high lightning area), some years had less than 80 h of storms, and a couple

of years had more than 240 h. These are not “severe events,” just variations

in the normal weather patterns. These storm variations translate into varia-

tions in the number of faults and in the reliability indices. Even in areas with

FIGURE 9.6

SAIDI per day probability density at one utility.

FIGURE 9.7

Thunderstorm duration by year for Tampa, Florida. (Data from [MacGorman et al., 1984].)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.5 1.0 1.5 2.0

SAIDI per day in minutes

Density

median

mean

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.5 1.0 1.5 2.0

1950 1960 1970

100

150

200

250

Total storm hours in the given year

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Electric Power Distribution Handbook

lower storm activity, signiﬁcant variation is possible. Consider these varia-

tions if reliability “baselines” are going to be set for performance-based rates.

Wind, icing, and temperature extremes all have signiﬁcant year-to-year vari-

ations that directly impact reliability indices. Watch out for a few years of

consistent weather; if the data from 1950–1955 of Figure 9.7 were used for

performance-based rates, we would be in trouble in following years.

The ﬁrst step in quantifying the effect of weather on interruptions is to

track weather statistics along with interruption statistics. Lightning, wind,

temperature, and other important weather statistics are available from

national weather services as well as private groups, and many statistics

have long historical records. Correlations between weather statistics and

interruptions can help quantify the variations. Brown et al. (1997) show an

example for a feeder in Washington state where wind-dependent failures

were analyzed. For this case, they found 0.0065 failures/mi/year/mph of

wind speed.

After correlating interruptions with weather data, we can extrapolate how

much reliability indices could vary using historical weather data. One could

even use weather statistics to come up with a normalized interruption index

that tried to smooth out the weather variations.

9.3 Variables Affecting Reliability Indices

9.3.1 Circuit Exposure and Load Density

Longer circuits lead to more interruptions. This is difﬁcult to avoid on

normal radial circuits, even though we can somewhat compensate by add-

ing reclosers, fuses, extra switching points, or automation. Most of the

change is in SAIFI; the interruption duration (CAIDI) is less dependent on

load circuit lengths. Figure 9.8 shows the effect on SAIFI at one utility in

the southwest U.S.

It is easier to provide higher reliability in urban areas: circuit lengths are

shorter, and more reliable distribution systems (such as a grid network) are

more economical. The Indianapolis Power and Light survey results shown

in Figure 9.9 only included performance of utilities in large cities. As

expected, the urban results are better than other general utility surveys.

Another comparison is shown in Figure 9.10 — in all states, utilities with

higher load densities tend to have better SAIFIs.

Figure 9.11 and Figure 9.12 show reliability for different distribution ser-

vices in several Commonwealth countries. The delineations used for this

comparison for Victoria are

• Central business district: used map boundaries

• Urban: greater than 0.48 MVA/mi (0.3 MVA/km)

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Reliability

451

• Short rural: less than 124 mi (200 km)

• Long rural: greater than 124 mi (200 km)

9.3.2 Supply Conﬁguration

The distribution supply greatly impacts reliability. Long radial circuits pro-

vide the poorest service; grid networks provide exceptionally reliable service.

Table 9.2 gives estimates of the reliability of several common distribution

supply types developed by New York City’s Consolidated Edison. Massive

redundancy for grid and spot networks leads to fantastic reliability — 50

plus years between interruptions. Note that the interruption duration

FIGURE 9.8

Effect of circuit length on SAIFI for one utility in the southwest U.S.

FIGURE 9.9

Comparison of the Indianapolis Power & Light Large City Survey of SAIFI to the general EEI

survey results (with storms excluded). (Data from [Indianapolis Power & Light, 2000].)

020406080100 120

0.0 0.5 1.0 1.5

Total circuit exposure, miles

SAIFI

020406080100 120

0.0 0.5 1.0 1.5

EEI survey

Large city

survey

0.0 0.5 1.0 1.5 2.0 2.5 3.0

100

SAIFI, events/year

Percent of utility indices

exceeding the x-axis value

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(CAIDI) increases for the more urban conﬁgurations. Being underground

and dealing with trafﬁc increase the time for repairs.

9.3.3 Voltage

Higher primary voltages tend to be more unreliable, mainly because of

longer lines. Figure 9.13 shows an example for one utility that is typical of

many utilities: higher voltage circuits have more interruptions.

On higher-voltage primary circuits, we need to make more of an effort to

achieve the same reliability as for lower voltage circuits: more reclosers, more

sectionalizing switches, more tree trimming, and so forth. With the ability

to build much longer lines and serve more customers, it is difﬁcult to over-

come the increased exposure. Keeping reliability in mind when planning

higher-voltage systems helps. On higher-voltage circuits, wider is better than

longer. Burke’s analysis (1994) of the service length and width for a gener-

alized feeder shows that for the best reliability, higher-voltage circuits should

FIGURE 9.10

Effect of customer density on SAIFI.

Average customers per mile of distribution line

SAIFI

0.5

1.5

2.5

20 40 60 80 100

California (ten-year average)

0.5

1.5

2.5

Illinois (three-year average)

0.5

1.5

2.5

Texas (three-year average)

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453

be longer and wider, not just longer (see Table 9.3). Usually, higher-voltage

circuits are just made longer, which leads to poor reliability. Having a long

skinny main feeder with short taps off of the mainline results in poor reli-

ability performance.

9.3.4 Long-Term Reliability Trends

Utilities rarely have very long-term data covering decades. The Canadian

Electrical Association has tracked reliability data for many years. Figure

9.14 shows SAIDI over a 40-year period for Canada. Signiﬁcant variation

exists from year to year. Part of this is due to the changing nature of the

survey (the utility base was not consistent for the whole time period). Much

of the variation is due to weather, even though the survey covers a huge

geographic area (we expect more variations for smaller geographic areas).

The data includes storms. Extreme years stand out. The worst year was

1998, which was dominated by the ice storm that hit Ontario and Quebec.

Over 1.6 million customers lost power; Hydro Quebec’s SAIDI for the year

was almost 42 h when it is normally less than 4 h.

FIGURE 9.11

Comparison of SAIFI by load density for several former British Empire colonies. (Data from

[Coulter, 1999].)

0 1 2 3 4 5

Central Business District

Urban

Short Rural

Central Business District

Urban

Short Rural

Central Business District

Urban

Short Rural

Long Rural

Central Business District

Urban

Short Rural

Long Rural

United Kingdom

New Zealand

South Australia

Victoria, Australia

SAIFI, Average interruptions per year

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FIGURE 9.12

Comparison of SAIDI by load density for several former British Empire colonies. (Data from

[Coulter, 1999].)

TABLE 9.2

Comparison of the Reliability of Different Distribution Conﬁgurations

SAIFI

Interruptions/Year

CAIDI

min/Interruption

MAIFI

Momentary

Interruptions/Year

Simple radial 0.3 to 1.3 90 5 to 10

Primary auto-loop 0.4 to 0.7 65 10 to 15

Underground residential 0.4 to 0.7 60 4 to 8

Primary selective 0.1 to 0.5 180 4 to 8

Secondary selective 0.1 to 0.5 180 2 to 4

Spot network 0.02 to 0.1 180 0 to 1

Grid network 0.005 to 0.02 135 0

Source:

Settembrini, R. C., Fisher, J. R., and Hudak, N. E., “Reliability and Quality Compar-

isons of Electric Power Distribution Systems,” IEEE Power Engineering Society Transmission

0 100 200 300 400

Central Business District

Urban

Short Rural

Central Business District

Urban

Short Rural

Central Business District

Urban

Short Rural

Long Rural

Central Business District

Urban

Short Rural

Long Rural

United Kingdom

New Zealand

South Australia

Victoria, Australia

SAIDI, Average interruption duration per year, minutes

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455

Overall, the reliability trend is somewhat worsening. The main factor is

probably the gradual move to higher-voltage distribution circuits and sub-

urbanization. These trends lead to longer circuits and more exposure.

Although, better record keeping (outage management systems) may be mak-

ing SAIDI appear worse relative to earlier approaches because interruptions

are recorded more accurately.

9.4 Modeling Radial Distribution Circuits

On purely radial circuits, the customers at the ends of the circuits unavoid-

ably have the poorest reliability. On radial circuits, we can analyze the

FIGURE 9.13

Effect of circuit voltage on SAIFI for one utility in the southern U.S.

TABLE 9.3

Mainline Lengths and Lateral Lengths for Optimal

Reliability (Assuming a Constant Load Density)

Voltage,

Main Feeder

Length, mi

Lateral Length,

Ratio of Main

Feeder to Lateral

Tap Length

13.8 1.51 0.95 1.59

23 1.81 1.32 1.37

34.5 2.09 1.71 1.22

Source:

Burke, J. J.,

Power Distribution Engineering: Fundamentals

and Applications

, Marcel Dekker, New York, 1994.

15 kV

25 kV

5 kV

0.0 0.5 1.0 1.5 2.0 2.5 3.0

100

SAIFI, interruptions/year

Weighted percent of feeders

exceeding the x-axis value

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reliability using series combinations of individual elements. If any series

component between the station and the customer fails, the customer loses

power.

Series elements can be combined as

where

= failure rate, normally in interruptions per year

= unavailability (total interruption time), normally in per unit, %, or h

or min per year

= average repair time per failure normally in per unit/year, %/year, or

h or min

The subscript

is the total of the series combination, and the subscripts

1, 2, …

indicate the parameters of the individual elements.

The failure rate

is analogous to SAIFI,

is analogous to SAIDI, and

analogous to CAIDI.

We can use these basic reliability predictions to estimate reliability indices

for radial circuits. Calculations quickly become complex if we try to account

for sectionalizing or have circuits with parallel elements or backfeeds. Reli-

ability analysis programs are available to model circuits with inputs similar

to a load-ﬂow program, except that switch characteristics are included as

FIGURE 9.14

Yearly SAIDI for Canada. (Data from [Billinton, 1981, 2002; CEA, 2001].)

1960 1970 1980 1990 2000

SAIDI, hours

lll l

ll l

Sn nn

UUU U r r r

=+++

=+++=+++

12 1122

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