IEEE Power & Energy Magazine - July/August 2020 - 48

In reality, however, consumers are typically risk averse and,
arguably, prefer a more stable and predictable outcome from the
electricity network, even if this may (slightly) increase costs.
aggregate electricity demand at all times, the power network
in Figure 8 is adequate if the total (thermal) capacity of the
link is at least 500 MW. This can be achieved by a number
of network configurations, including the option of one single
circuit of 500 MW transferring power from node 1 to node 2.
This particular option, however, is evidently not N−1 secure.
Reliability 2: Security

From our previous work, we distinguish between two types
of security: deterministic N−k security and probabilistic
security. To comply with a deterministic N−1 security standard for network design, we need two circuits, each of (at
least) 500 MW to link nodes 1 and 2. A probabilistic standard, instead, demands an appropriate balance between the
cost of improving reliability, here in the form of investment
costs, and the associated savings in reliability operational
costs, measured through the improvement in the EENS
(resulting from the new investment) × the VoLL. Let us now
assume that there are only two possible "secure" configurations (i.e., the number of circuits and their capacities) for the
transmission link in question, and let us evaluate the cost and
benefits of each of them to identify the appropriate optimal
solution. Table 1 provides the basic reliability information
and costs of the following two alternatives:
✔ N−0 option: where two circuits of 250 MW are installed
✔ N−1 option: where two circuits of 500 MW are installed.
In both cases, the network has fully available capacity
99.976% of the time (further reliability information associated with outage and repair rates is presented in Table 2). In
this case, the N−0 solution is determined to be more economically efficient and therefore should be the one selected under
a probabilistic security approach; however, this solution is
sensitive to an array of economic and reliability parameters.
For example, if the VoLL is increased from US$1,000/MWh
to US$30,000/MWh, then the secure option changes from
the N−0 to the N−1 design solution.
Resilience

One of the key characteristics of the probabilistic security
analysis carried out in the previous section is its focus on the
EENS, which, as discussed, is not suitable for resilience studies dealing with HILP events. For the purpose of assessing
resilience then, let us assume that the (marginal) probabilities
of the four states previously evaluated (a no-fault state, two
single-fault states, and a double-fault state) originate from the
conditional probabilities displayed in Table 2. More specifically, Table 2 shows the probability of the four states under
48

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two different weather conditions, namely, fair and adverse
weather, as well as the marginal probability of the four states
considering both weather conditions.
For illustrative purposes, we assume that the failure
rate is 100-times higher for adverse weather and that repair
times increase from 4 h under fair weather conditions i.e.,
a repair rate of 2,190 occurrence per year (occ/y), to seven
days under adverse weather conditions (i.e., a repair rate of
52 occ/y). Also, adverse weather, in this example, is limited to 1 h per year (thus conventionally representing an
HILP event), while fair weather conditions occur during
the remaining time (i.e., 8,759 h).
To provide a hedge against such an HILP event, we analyze the following three options within the concept of a resilience trilemma (assuming that the initial condition is the
same N−0 network configuration selected under the probabilistic security approach described in the previous section):
✔ N−1 design: where we re-evaluate the option to install two circuits of 500 MW, i.e., making the network
"bigger" by adding redundancy
✔ N−0 with shorter response times under extreme
events: where we evaluate a contract with other network companies to use their repair crews under extreme events, which reduces the repair times from seven to three days (i.e., making the network "smarter")
✔ N−0 with underground cables: where we evaluate the
option to bury the current double circuits, each with
250 MW of capacity, thus halving the failure rate under both weather conditions, and assuming at the same
time, for simplicity, that the repair rate stays the same.
This is equivalent to a "stronger" system option.
Table 3 shows the impact of these new options on various
average and risk indicators, including
✔ the EENS of the ENS across all scenarios (economically valued at the VoLL)
✔ the CVaR of the ENS, that is, the average ENS across the
0.001% worst cases (economically valued at the VoLL)
✔ the probability of a double outage under adverse weather
conditions, which occurs for 1 h per year only.
As can be expected, changing the network design from
N−0 to N−1 provides the best results in terms of the EENS
cost, reducing it by 93% from approximately US$539,000
per year to US$38,000 per year. However, this decision
provides a very limited hedge against HILP events, reducing the CVaR by only 6% from US$4,113,000 per year to
US$3,846,000 per year. (Note that, in this case and the following ones, the probability of a double outage and the CVaR
july/august 2020



IEEE Power & Energy Magazine - July/August 2020

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