IEEE Power & Energy Magazine - July/August 2020 - 45

Probabilistic Risk-Averse
Framework to Identify Resilient
Network-Enhancement Options
Based on the aforementioned premises, we introduce a
resilience-oriented planning methodology based on a
stochastic, risk-averse, mathematical program for supporting
the decision-making process of identifying resilient network
enhancements. In the first stage, the proposed two-stage model
(Figure 3) intelligently selects specific network investments
from a set of candidate options, which are, in the second stage,
tested through the quantification of their resilience benefits in
probabilistic outage scenarios originated by stochastic simulation of natural hazards. As a result, the optimal portfolio of network investment decisions as evaluated through a given resilience metric (measured across various scenarios) is identified.
The stochastic generation and assessment of hazard and
outage scenarios are carried out through the following simulation-based steps:
1) Hazard characterization: In the first step, we generate various hazards with random magnitudes and
locations (this can be done by respecting historical
patterns). Additionally, spatiotemporal profiles may
be necessary to model hazards that change position and intensity dynamically (e.g., storms), spread
(bushfires), or attenuate their magnitude with distance
(earthquakes).
2) Vulnerability assessment of system components: By
using fragility curves (illustrated in Figure 4) that are
assumed to be known for various natural hazards and
system components, either through historical data or
on the basis of engineering modeling, we determine
july/august 2020

both 1) the hazard-dependent failure probabilities of
every network component (e.g., towers and lines as
well as substation and generation equipment) and 2)
the outage scenarios across the system, which are generated from these probabilities.
3) System response: This is the step where we simulate,
for each outage scenario identified above, the potential system cascading from automatic power flow rerouting, load/generation disconnection, and postcontingency redispatch (once cascading has ended). We
then assess the spatially resolved volumes of energy
not supplied. Importantly, prior to the outage, we assume a normal operation of the system by running an
economic dispatch problem in which the system infrastructure is intact.
4) System restoration: We simulate both a) the reconnection of failed/damaged network components once
these have been repaired (whose reconnection times
are determined probabilistically assuming that the reconnection events are exponentially distributed) and
b) the reconnection of load/generation, which is obtained using a postcontingency dispatch model.
Figure 5 illustrates the aforementioned process, and
Figure 6 shows a typical curve for the supplied demand,
which results from the simulation of the postfault events

First Stage
Propositions of
New SystemEnhancement
Options Through
the Optimization
of Resilience
Metrics

Enhancement
Option
Resilience
Metric

Second Stage
Simulations of
System Impact
and Response/
Restoration
After Random
Natural Hazards
Occur

figure 3. The quantitative approach used to identify optimal resilient system-enhancement options. (Source: Lagos
et al.)

1
Probability of Failure

namely, the predisturbance resilient state, disturbance
progress, postdisturbance degraded state, restorative state,
and postrestoration state. It also plainly highlights the type
of actions that can be applied for mitigating the impacts of
extreme events during these phases, such as preventive, corrective, emergency coordination, restorative, and adaptive.
However, this critical temporal evolution aspect is usually
missing in current reliability assessments for planning purposes, which mainly focus on the system response before
and right after the disturbance occurs (without including
system restoration).
In contrast, because the impact on the system due to an
HILP event is substantial, the explicit modeling of the system response and restoration is key in assessing different
options for enhancing resilience at the planning stage, especially those based on flexible and operational non-network
solutions. This time-varying characterization also enables
the modeling-targeted optimization of metrics specifically
designed for resilience-analysis purposes, thus providing
decision makers with the opportunity to select specific attributes of resilience that can be enhanced by implementing
different operational and investment decisions, which also
correspond to different enhancement propositions.

Hazard Intensity

figure 4. An example of a generic fragility curve for a
piece of network equipment.
ieee power & energy magazine

45



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
IEEE Power & Energy Magazine - July/August 2020 - Cover4
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