IEEE Power & Energy Magazine - July/August 2020 - 72

growth (see Table 5) and hence its relatively few upgrades to
the EHV network from year to year.
DFAXes, although interesting, do not reflect the pre- and
postcontingency flows on the network. The stress metrics do,
however, and are much more informative, as we will show in
the next section.

System Stress Metrics and Operating States
The four main columns of Table 6 show four system metrics: sampling vulnerability (RankV and DegreeV under the
tan heading) and criticality (RankC and DegreeC under the
blue heading) for the various cases and for the entire SW WI,
instead of for individual branches. The network metrics are
summations of the branch metrics in each case. The three colored rows highlight the cases with the highest values of stress.
Most branches have a RankV 1 1 for the six cases presented. That is, for most contingencies, the postcontingency
flows are less than the ratings for most of the monitored
branches. Nonetheless, consider the vulnerability columns.
The 2016 summer high-demand case has 259 monitored
branches with a RankV  $ 1, that is, they are "overloaded"
with postcontingency flows equal to or greater than their ratings. Because this case has 4,849 branches, 5.3% of them are
vulnerable to such postcontingency overloading, the other
95% are not. Approximately 108 (2.2% of the 4,849) of these
branches are particularly vulnerable, with postcontingency
overloads for two or more contingencies.
Consider now the two criticality columns for the same
2016 summer high-demand case. For each of 309 critical outages (6.4% of the total 4,849 branches), at least one
monitored line becomes overloaded to or above its rating.
Roughly 89 branches (1.8% of the total 4,849 branches) are
particularly critical: the outage of any of them would cause
at least two monitored lines to overload.

These stress metrics are highest (worse) for the highlighted cases: high-demand summer (HS) 2016, high-demand
spring (HSP) 2016, and before the 8 September 2011 Arizona/Southern California blackout. Knowledgeable engineers assessed separately what they considered to be the
relative risk to cascading of the various cases based on
demand, internal generation, imports, and seasonal maintenance practices. Their informal risk judgment is listed in
the next-to-last column of Table 6. Note that their judgments
of relative risk and the four stress metrics concur, with two
minor exceptions.
The differences in the four stress metrics, compared case
to case, are mostly in the first significant figure. The values
of the four metrics for the most stressed case, 2016 summer
high demand, are roughly twice the values for the second
most stressed case, preblackout 2011. And the metric values for the preblackout 2011 case are much higher, approximately double for three of the four metrics than for the
values for the next case, the HSP 2016. Most of the metrics
are similarly distinct and consistent for the three low-stress
cases. There is nothing subtle about the results of the stress
analysis; the metrics clearly and consistently signal real differences in stress.
The threshold value for the computation of the metrics is a choice left to the analyst. As noted in the text
and on the tables, Tables 6 and 7 use 100% of branch
ratings as degree thresholds. Tables 3 and 4 used 75% of
the branch ratings. Cascading has occurred with postoutage flows below the branch ratings, as in the 1965
and 2003 U.S./Canada cascading blackouts discussed
previously. Cascading has also not occurred although the
ratings were exceeded. If the threshold is too low, false
positives will appear. If it is too high, problems may be
overlooked. Like focusing a microscope, a reasonable

table 6. The number of stressed branches and the percent of all the branches in the SW WI region.
Cases
Season/
Demand

Vulnerability

Criticality

RankV ≥ 1
(DegreeV ≥ 1)

DegreeV ≥ 2

RankC ≥ 1
(DegreeC ≥ 1)

DegreeC ≥ 2

Informal Risk
Judgment

Branches
SW WI

High

259 5.3%

108 2.2%

309 6.4%

89 1.8%

Highest

4,849

Low

38

0.8%

4

0.1%

41

0.9%

1

0%

Low

4,785

High

51

1.1%

6

0.1%

49

1.1%

5

0.1%

Medium

4,534

Low

26

0.6%

4

0.1%

24

0.5%

2

0%

Lowest

4,563

109 2.4%

34

0.7%

96

2.1%

14 0.3%

High

4,553

126 3.1%

63

1.5%

183 4.5%

27 0.7%

Preblackout

4,096

Summer 2016

Winter 2016

Spring 2016
High
8 Sept. 2011

Thresholds = 100% of ratings for degree metrics.
The highest-stress metrics (by number and %) are highlighted in green.
72

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july/august 2020



IEEE Power & Energy Magazine - July/August 2020

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