IEEE Power & Energy Magazine - July/August 2020 - 50

particularly important in practice in the presence of budget
constraints and under the need for undertaking both reliable
and resilient enhancements in power networks.

Realistic Application to
Earthquakes in Chile
To demonstrate the applicability of the proposed resilienceplanning framework to the real world, the following case
study is used to identify resilience-enhancement decisions
among an array of multiple candidate solutions to protect
against earthquakes in the Chilean transmission system.

Case Study Description
The Chilean transmission system, which covers more than
3,200 km from Arica to Chiloe, is modeled through an
equivalent network composed of 40 nodes/substations and
56 transmission corridors (shown in Figure 9), representing
its infrastructure in 2018. For that year, electricity demand
was approximately 76 TWh, and generation supply included
mainly hydro [23 TWh (30%)], coal [30 TWh (39%)], and
gas [11 TWh (15%)] units, with minor participation from
wind [4 TWh (5%)] and solar resources [5 TWh (7%)]. The
total installed generation capacity was 24 GW.
To model the potential failure of system infrastructure
during an earthquake, we used the fragility curves of towers, generation units, and substations adopted by the U.S.
Federal Emergency Management Agency (Hazus-MH2.1),
which relates the probability of failure of these system components with the peak ground acceleration (PGA) at their
particular locations.
To calculate the PGA in different locations following an
earthquake with a given epicenter, we used validated models

capable of characterizing the strong ground-motion attributes observed in the 2010 Chilean earthquake.
We then randomly generated a comprehensive set of scenarios (e.g., 10,000), which follows this sequence.
1) The random generation of earthquakes and the PGA
calculation: Using a random location and a fixed intensity equal to 8.5 Mw, equalizing the conditions of
the most recent 2010 earthquake (which was one of the
worst earthquakes experienced in Chile), the PGA is
determined at the location of each system equipment.
2) The random generation of network outage: Once the
probabilities of outages are obtained from the fragility
curves, outages are simulated through a Monte Carlo
simulation.
3) The random generation of equipment repairs: Once
pieces of equipment fail, they are recovered by following a random process.
The system dispatch before, during, and after the earthquake was obtained by simulating five days, where the earthquake occurs in the first hour to capture the system collapse
as well as the system recovery. The analysis captures key
features of a resilient power grid.

Results: Portfolio Solutions for
Resilience Enhancement
Figure 10 shows the Pareto frontier between the risk measurement and the budget used to improve resilience. Here,
the risk measurement is the conditional EENS (CEENS),
where the ENS is averaged across worst-case scenarios, e.g.,
all the scenarios originated by very large earthquakes with
a magnitude of 8.8 Mw (in practice, we can assume that the
CEENS . the CVaR by an appropriate selection of the value

table 2. The reliability data and probabilities of failure under fair and adverse weather, and the marginal
probabilities of failure for the four states considered.
Fair
Adverse
Weather Weather

Circuit 1

Circuit 2

State
Probability

Available
Power Not
Capacity (MW) Supplied (MW)

Failure rate (occ/y)

0.2

20

Available

Available

0.999817

0.5224

0.999763

Repair rate (occ/y)

2,190

52

Unavailable

Available

9.13E-05

0.200373

0.000114

Unavailability

9.1E-05

0.27723

Available

Unavailable

9.13E-05

0.200373

0.000114

Availability

0.99991 0.72277

Unavailable

Unavailable

8.34E-09

0.76855

8.78E-06

Duration (h)

8,759

1

occ/y: occurrence per year.

table 3. The average and risk indicators of the four considered network design options.

50

Metric

N−0 Base Case

N−1

N−0 Shorter Repair Time

N−0 Underground

VoLL × EENS (US$)

538,532

38,464

470,506

280,428

VoLL × CVaR (US$)

4,113,206,199

3,846,412,398

2,690,095,838

2,837,833,988

Probability of double outage
under adverse weather (%)

7.7

7.7

2

2.6

ieee power & energy magazine

july/august 2020



IEEE Power & Energy Magazine - July/August 2020

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