IEEE Power & Energy Magazine - July/August 2020 - 47

Probability

and so forth. This addresses the
so-called r e si l ie nc e trilemma,
f (x )
that is, the need for balancing the
portfolio solution among several
options to make the system stronger, bigger, and/or smarter in a
resilient and cost-efficient manner. In particular, among the set
Conditional Expected Value for x ≥ z
of investment decisions used to
(Where the Probability of x ≥ z Is
Equal to 1 - α)
enhance system resilience, the folExpected Value for All x
lowing could be considered:
✔ new lines and transformers
to create alternative routes
to transfer power and provide redundancy or additionx = ENS
al reactive power to operate
Mean
z
CVaR
D
the network under weaker
(EENS)
(VaR)
conditions when several network assets are outaged due
figure 7. A CVaR concept for risk-averse resilience assessment, where 1- a indito HILP events
cates the size of the considered set of worst cases. D indicates total demand.
✔ substation, tower, and other
equipment hardening to make
the system more robust and stronger against HILP Illustrative Two-Busbar Example
events (this is modeled by shifting fragility curves to
the right)
Textbook Illustrative Case Study
✔ shorten response times by increasing expenditures in This simple example illustrates and demonstrates our proposed
enhanced stocks of network assets and equipment, framework, which identifies resilient enhancement options
more repair crews, and more online monitoring and against HILP events in network planning and, crucially, how
control solutions
these differ from other decisions that are more reliability ori✔ the installation of new flexible network technologies ented. The two-busbar network in Figure 8 features one 500-MW
such as special protection schemes, energy storage generating unit in node 1, one load in node 2 with a constant
units, flexible alternating current transmission sys- demand of 500 MW, and a transmission link between the two
tems, high-voltage dc (HVdc), and so on to make the nodes. Depending on the configuration (i.e., the number of
system more flexible to adapt to different conditions' circuits and their capacities) and reliability characteristics of
postfault, helping to mitigate the consequences of this link and assuming perfect reliability for the generator, this
power network can be adequate, secure, and/or resilient. As
HILP events
✔ the installation of distributed energy resources (such adequacy and security have historically been a part of relias microgrids, distributed generation, and so on) to ability analysis, we will consider a network to be reliable if
provide localized energy solutions when the main sys- it is both adequate and secure. We also use the dc power flow
approximation for the sake of simplicity.
tem fails.
There are several ways to apply this framework, especially
to implement the two stages illustrated in Figure 3, by using Reliability 1: Adequacy
mathematical programming methodologies. For the analy- Considering that adequacy is the ability of a power system
sis in this article, we used optimization via simulation (OvS) (including generation and network capacities) to supply the
techniques. These techniques determine the (nearly) optimal
portfolio of network enhancements based on a series of simulations. More specifically, from the perspective of the optimizer,
Power Transfers
Node 1
Node 2
which is the first stage, the simulator, which is the second stage,
is assumed to be a black-box model without a known mathematical structure. One of the key advantages of the OvS approach
500
00 MW
Transmission Link With
is that it allows for the inclusion of a great deal of operational
Unknown Configuration
details in the simulation stage, e.g., minimum stable generation
500 MW
levels, ramp rate limits, minimum startup and shutdown times,
and so on, which require a nonconvex formulation and are complex and hard to manage in closed form.
figure 8. The illustrative two-busbar system.
july/august 2020

ieee power & energy magazine

47



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
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