IEEE Power & Energy Magazine - July/August 2020 - 74

Cascading is an event where a first outage causes
one or more outages in a second stage and so on,
eventually causing a system to collapse.
WI were in this area, with more than half (339) of the highly
critical WI branches having a DegreeC $ 2.
Three abutting areas in another region had the highest
percentage of vulnerable branches within the WI. None was
in the group discussed above. Two of these areas also had
the highest percentages of critical branches in the WI. Two
other areas in the same region also had high percentages
of critical branches. In other words, this region was doubly
stressed by being both highly vulnerable and highly critical.
Clearly, the stress problems are different for different parts
of the system. The study raised the following issues that are
beyond the purview of normal analyses done by transmission service operators:
✔ How should the problems identified by the metrics affect system planning or operations?
✔ Why are some areas very critical?
✔ Why does the system have 74% more critical branches
than vulnerable ones?
✔ Why are some areas critical but not particularly vulnerable, while other areas are more vulnerable?
✔ Which areas are most vulnerable to other particularly
critical areas, and why?
✔ How can one make areas inherently less critical or less
vulnerable?
There were more than 600 million DFAXes in the
aforementioned study-a daunting number. But, the stress
metrics provide a remarkable tool to use when assessing
the risk of blackouts. On an ordinary laptop, the computation of the metrics took on the order of minutes once the
DFAXes were computed and stored. New ways of thinking
will be needed to answer questions like the ones raised in
this section.

Adequacy and Implications
of Stress Metrics
Adequacy of Stress Metric
Two fundamental issues may seem to have been overlooked
in our work. First, nonlinear effects like voltage collapse
and instability are often involved in cascading. The branch
and path flows are expressed in terms of their limits in
megawatts, but the megawatt limit of a branch or path is
determined by the most restrictive issue, whether thermal,
voltage, instability, and so on. The nonlinear problems
generally occur as a result of high-megawatt loading, so
measuring stress in terms of megawatts does not ignore
the nonlinearities.
74

ieee power & energy magazine

Finally, full ac-contingency analysis models voltages. It
may be used instead of DFAX analysis and is only slightly
more time-consuming. We emphasize the DFAX approach
in part to highlight the fact that the cascading failure network differs from the traditional Ybus network. Also, a
single set of DFAXes is valid for studies of changes in generation and demand, whether these are drivers of changes in
stress or possible mitigation actions.
Second, the metrics are the results of first-contingency
analyses. Cascading is an event where a first outage causes
one or more outages in a second stage and so on, eventually causing a system to collapse. How can the metrics work
without simulating secondary contingencies? The answer is
that it is not only impractical to simulate all possible double contingencies, for instance, but only a tiny fraction of
them lead to cascading. We found the multiple-contingency
study by Bhatt et al. to be very useful, but we do not think
that they want to do this in real time or for planning studies. It is too much work for too little information and is not
needed to measure stress, a necessary condition for cascading to occur.

Which Metric Is Best?
Each metric evaluates stress in a different way. None has
been shown to be best. Correlation analysis reveals mostly
low correlations among the metrics. It is reasonable for the
stress of a complex system to be multifaceted. Furthermore,
four metrics are not too many to track, and combining them
into a single metric would reduce information unnecessarily.
As an analogy, consider that medicine also uses a vector of
four or five stress metrics, called vital signs. It is more useful
to know that "the pulse is quite high, but everything else is
normal," rather than "the weighted sum of all the vital signs
is a bit above normal."

Some Practical Issues
As demand and generation grow, transmission systems expand to increase transfer capability. Previous work has
shown that this growth may increase stress. The increase
from year to year of the large DFAXes mentioned previously
seems to support this observation. As the system is reinforced to allow for more power to be transmitted, the ability
of failures to spread may also increase.
An important topic is how operators and planners may
reduce stress, but it is beyond our present scope. We have
shown only how to quantify stress, a necessary condition
for cascading to occur. The metrics provide a new tool to
july/august 2020



IEEE Power & Energy Magazine - July/August 2020

Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - July/August 2020

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