IEEE Power & Energy Magazine - January/February 2022 - 86

originated from wildfires. The model optimizes the following
set of decisions:
✔ Preventive measures: Investments in DER equipment
such as storage plants, backup generation, and network
investments. The model also finds the optimal
volume of demand response contracted. These measures
are made up front, precontingency, and thus are
present in all scenarios.
✔ Corrective measures: These measures depend on the
specific contingency and are scenario-dependent. We
model two types of corrective measures, fast and slow:
* Fast: Refers to the distribution system operation itself,
including demand curtailments and a (smart)
operation of system assets (topology control and dispatchable
DER). These actions can occur right after
a contingency occurs.
* Slow: Installing and dispatching mobile DER. These
actions feature a lag associated with the arrival of
mobile equipment.
The proposed optimization model is probabilistic, minimizing
expected costs (including the cost of investment,
operation, and energy not supplied, and eventually, a risk
metric to capture risk aversion). It also considers the occurrence
of several scenarios (each with a probability) in the
form of a comprehensive set of system outages, including
those triggered by wildfires. Importantly, in the event of a
wildfire, the probability of simultaneous outages becomes
high since a single fire event can affect various pieces of
system equipment. Here, ignition probability maps as those
in Figure 6 (and other risk indices associated with wildfires
discussed earlier) can inform about the places with the highest
risks of wildfires.
Illustrative Case Study Example
The model above was applied to the textbook-like system design
example displayed in Figure 8. This example was used in the
" Review of Distribution Network Security Standards " in the
United Kingdom to illustrate, from a fundamental viewpoint,
the problems of the current network standards and the potential
solutions going forward. This example seeks to determine,
in a greenfield fashion, the optimal system design to supply
areas A and B. The figure shows all candidate assets (i.e.,
investment propositions) to supply the constant loads in the
two distribution networks (25 MW in Area A and 50 MW in
Area B). The set of candidate assets includes six power lines
and distributed PV and battery systems in Area A. In case
of network outages, the choices of renting mobile generation
units and exercising demand response (DR) contracts in Area
A and B as corrective actions could also be considered as part
of the system design. Importantly, the failure rates of lines 5
and 6 are affected by the risk of wildfires, which increases
the probabilities of failures in that network corridor and originates
dependencies of line failure probabilities between
lines 5 and 6.
Under normal conditions, the outage rate of lines is one
occurrence per year with a mean time to repair of one day.
Under catastrophic wildfire conditions in the neighboring
area of lines 5 and 6 (one occurrence in 10 years), we assume
these lines will fail (simultaneously) and that their mean
time to repair increases to 30 days. Other relevant input
data include an energy price of US$50/MWh (use to buy
energy from the main grid), a value of lost load (VoLL)
equal to US$10,000/MWh, and the investment costs of
lines, PV, and storage of US$75/MW/km/yr, US$500/kW,
and US$200/kWh, respectively.
Regarding the mobile generation
units in both areas, the
system operator can rent them
at an hourly cost of US$68.5/
MW and operate them with a
US$200/MWh fuel cost. For
simplicity, DR features the same
costs as those of mobile units.
We also assume that the system
operator takes an average of
2.4 h and three days, respectively,
to install the mobile units
under normal and wildfire conditions.
Mobile units and DR measures
can cope with up to half the
power demand in each area.
We consider 22 scenarios,
figure 7. A representation of wildfires in Chile on 26 January 2017.
86
ieee power & energy magazine
in cluding one intact system
(with no outages), six N-1 line
outages, and 15 N-2 line outages.
The probabilities of these scenarios
are calculated assuming
independence and dependence
january/february 2022
IEEE Power & Energy Magazine - January/February 2022

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