IEEE Power & Energy Magazine - July/August 2020 - 46

System
Response 2

Hazard N

Outage N
Vulnerability
Assessment N

Repair 1

Repair 2

System
Restoration 1

Scenario 1

System
Restoration 2

Scenario 2

System
Response N

System
Restoration N

Scenario N

...

Outage 2

System
Response 1

...

Vulnerability
Assessment 2

Outage 1

...

Hazard 2

Vulnerability
Assessment 1

...

System Infrastructure
(Common to All Scenarios)

Hazard 1

Repair N

figure 5. A simulation of hazard-outage-repair scenarios for the system infrastructure under study.

associated with a scenario that follows this sequence: the
random generation of a) hazards, b)  network outages, and
c)  equipment repairs. Note that the shape of the curve in
Figure 6 can vary and be hazard and system specific. This
power supply curve is generated several thousands of times
(e.g., 10,000) for different hazard-outage-repair sequences
by using a Monte Carlo simulation. We consider a large
number of simulations to adequately capture the potential
consequences of a comprehensive set of natural hazards on
the power network.
After the simulations have been performed under several outage scenarios caused by natural hazards, a suitable
resilience metric can be selected and calculated for every
scenario. The metric could, for example, be the ENS or,
based on our previous work, one taken from the FLEP
resilience metric system [the FLEP metric assesses how
fast resilience drops (F-metric), how low resilience drops
(L-metric), how extensive is the postdisturbance degraded
state (E-metric), and how promptly the system recovers
(P-metric)]. After quantifying the effect of each scenario using the selected metric, the optimization problem
minimizes risk exposure subject to a budget constraint
(representing the total amount available to be invested

Supplied Demand

Precontingency
State

Hazard and System
Response

System Restoration

Time

figure 6. An example of supplied demand curve resulting
from each scenario simulated.
46

ieee power & energy magazine

in resilient network enhancement), thus identifying the
optimal portfolio of investment decisions that provides
the best hedge against the HILP events simulated. The
risk measurement being minimized can be determined by
calculating the expected value of the selected resilience
metric (e.g., ENS) across an appropriately selected worst
set of scenarios resulting from the stochastic simulation.
To do so, the conditional value at risk (CVaR) measurement can be used to consider only those scenarios representing the worst cases. More specifically, CVaR (also
referred to as CVaR a , although in this article, we use CVaR
without the subscript to simplify the notation) represents the
expected value across a predetermined set of worst cases.
An illustrative example of a probability distribution function (PDF) and its relevant parameters, with the ENS used
as the resilience metric, is shown in Figure 7. It should be
noted that the value of the parameter a also provides an
explicit indication of risk attitude, because 1 - a indicates
the size of the considered set of worst cases. A reliability
assessment would use the measurement of the EENS by
sampling across all of the sets of outages. In this averaging,
the impact of noncredible worst-case outages would normally be outweighed by the much more frequent credible
outages. In some reliability assessments, the consideration
of noncredible worst-case outages may even be ignored.
In the context of our framework then, this means that,
in the first approximation, the mean value (i.e., the EENS)
and the CVaR of the PDF shown in Figure 7 could be used
as the reliability assessment and the resilience assessment
measures, respectively. Furthermore, although optimizing
for the EENS/CVaR is useful to clearly identify decisions
from a reliability/resilience perspective, in practical settings,
where planners need to consider both criteria to make tradeoff decisions, optimizing on a linear combination of the
EENS and CVaR may also be a suitable option.
The proposed mathematical framework can be used to
select a wide-ranging portfolio of resilient network-enhancement options depending on the specific decision variables
considered in the problem, such as hardening infrastructure,
the installation of new assets, a provision of better response
times for repairing damaged infrastructure, restoring power,
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

Contents
IEEE Power & Energy Magazine - July/August 2020 - Cover1
IEEE Power & Energy Magazine - July/August 2020 - Cover2
IEEE Power & Energy Magazine - July/August 2020 - Contents
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IEEE Power & Energy Magazine - July/August 2020 - Cover3
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