IEEE Power & Energy Magazine - July/August 2020 - 71

LODFs
Most of the analyses discussed in this section considered
only monitored and outaged branches in the SW WI, but
the DFAXes incorporated the branches and flows in the
entire WI. Figure 3 shows the distribution of the values of
DFAXes for outaged and monitored branches in the SW
WI, which is typical of such distributions for other systems. For example, the 2016 summer high-demand case
(the upper curve) had roughly 5.79 million DFAXes. Figure 3 shows that most of them are very small, with only
approximately 43,500 having absolute values greater than
0.1. The absolute values of just 4,305 DFAXes were greater
than or equal to a large, but arbitrary, 0.7. (The 0.7 in this
figure has no special significance and is unrelated to any
other 0.7 in this article.)
Figure 3 has two very significant properties. First, 4,305,
a large number, if that many outaged/monitored branch
pairs are at risk of cascading, is just a tiny fraction (roughly
0.07%) of the 5.79 million DFAXes for this case, most of
which are essentially zero. The DFAXes with higher values are for outaged branches that are more tightly coupled
to monitored branches. The fewer tightly coupled outaged/
monitored branch pairs, the less failures will propagate, all
else being equal. This "good news" presented in Figure 3
means that the EHV system, by its nature and due to how
it is planned, is highly immune to cascading. The outage
of one branch threatens only, at most, a few others. This is
one reason why we have so few cascading blackouts. Indeed,
july/august 2020

the study by Bhat et al., which went beyond the DFAXes
to compute the postoutage flows, as do our metrics as well,
also showed that most of the exhaustively selected single and
double contingencies will not cause overloads.
Second, the three distributions in Figure 3 are for the
2012 and 2016 summer high-demand cases and the 8 September 2011 preblackout case, respectively, as listed in
Table 5. Although they are close together, to the naked eye,
the middle curve (2012 case) clearly has more higher-value
DFAXes than does the lower curve (2011). The upper curve
(2016 case) also has more higher-value DFAXes than does
the middle curve. In fact, the 2016 distribution has 30%
more large DFAXes ($ 0.7) than does the 2011 distribution,
which is a significant difference. This "bad news" shown in
Figure 3 seems to suggest that the natural growth of the system leads to tighter coupling and a greater risk of cascading,
all else being equal.
Why would this happen? Generally, network upgrades are
made to accommodate an increased flow of power through
the grid. It seems that increasing the grid's ability to transmit power also makes it more able to transmit failures. This
is true even for the SW WI, with its relatively low demand

table 5. The WI cases studied (the data in this table
are for the SW region only).
Case

Demand/Generation (MW)

2016 summer high

62,691/57,578

2016 spring high

44,229/40,472

2016 winter high

38,931/36,085

2016 winter low

27,530/30,500

2016 summer low

34,577/32,010

2011 preblackout

51,619/46,752

2012 summer high

61,933/57,841

10,000,000

Number of DFAXes

consistent because they were prepared by the same engineers for the same purposes using consistent assumptions.
Of course, the dispatch of generation reported in Table 5 for
the high-demand cases was different from dispatch reported
for low-demand cases. As the high demands in winter,
spring, and summer also differed from each other, so too
did their dispatches, and the same was true for low-demand
winter and summer cases. There was one theme: the SW
WI was almost always a net importer from remote power
plants, and the demand in every case was greater than the
local generation. Being able to compare consistent, though
different, load and generation patterns was very useful.
It is rare for such data to be available, and it is unheard
of to give researchers access to a preblackout reconstruction, such as the 2011 preblackout information listed in
Table 5. The WI study was unique in that it used realistic
data on a full-scale system, and the enhancing contribution
of the WECC to the study of cascading blackout prevention
is gratefully acknowledged. The 2012 and 2016 cases were
not intended to be N−1 compliant; they were meant to be
used in operating studies to identify and resolve problems.
Unfortunately, the 2011 preblackout case was not N−1 compliant due to failures in practices and procedures. All of this
data was provided by the WECC and handled, purged, and
reported on under a strict Critical Energy/Electric Infrastructure Information discipline.

2016 Summer High
2012 Summer High
8 September 2011 Preblackout

1,000,000

100,000
4,533 DFAXes ≥ 0.7
(2016 Summer High)

10,000

1,000

3,493 DFAXes ≥ 0.7
(8 September 2011)
0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Absolute Value of DFAXes

figure 3. DFAX distributions for the SW WI.
ieee power & energy magazine

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IEEE Power & Energy Magazine - July/August 2020

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