IEEE Power & Energy Magazine - July/August 2021 - 48

the morning. The other half of the diesel savings is a result
of the NAC algorithm, which increases the effectiveness of
the batteries by actively supporting the network.
Diesel savings is not the only cost consideration we care
about. The NAC algorithm additionally factors in the cost
that participating customers incur by deviating their battery
operation to assist the network (before any support payments).
When we focus on the days with peaks and consider both costs
together, the NAC approach still achieved a 24% reduction in
operating costs. When this number is compared to the 33%
diesel savings, this tells us that, for a small increase in cost to
prosumers, we achieve proportionately greater diesel savings.
During the trials, customers were more than compensated for
this increase in their operating costs through support payments,
which are discussed in the next section.
To analyze the remaining impact of forecasting errors, we
conducted a series of counterfactual experiments to evaluate
what diesel savings NAC could achieve if it had a perfect prediction.
The results show us there is still an opportunity for up to
3.5% in extra savings with a further improvement to forecasting.
Customer Benefits
The NAC approach seeks a solution that is the social optimum,
for the benefit of the whole, as measured by the sum
of everyone's costs, including the diesel generator. Such an
approach typically results in modifying the behavior of an
individual if it benefits the whole, which often has a cost to
the individual. On Bruny Island, this corresponds to altering
the batteries' charging and discharging behaviors to save a
greater amount of money on diesel expenses.
This raises two issues. First, we want to use at least part of
the savings to make sure that individuals are compensated for
the operating opportunity costs they incurred by modifying
their behavior. Second, we want to provide more incentives to
customers for the network support that their batteries provide.
We explore how these incentives can be set to reflect the value
of a battery to the network, e.g., based on being at a particular
location on the network or having more capacity to provide
network support when it is needed. We also wish to examine
how the combined PV-battery and NAC system benefits the
customers in general, not only during network support events.
To calculate the opportunity costs incurred when NAC
modifies a battery's charging and discharging behaviors,
we conducted a counterfactual simulation of the peak load
event without drawing on the batteries for network support.
This provided us with the cost or benefits an individual
would have received if he or she had retained the
sole use of the battery. The difference between a customer's
private cost in the counterfactual simulation and his or her
private cost in the NAC-enabled network support action is
the opportunity cost of the customer for participation in the
NAC system. During the trial, customers' payments were
always as great as this amount, which ensured that they
were never worse off for the support that they provided to
the network.
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Building on this style of counterfactual reasoning, we
can estimate a value for each battery for its storage capacity,
power, and location on the network, using tools from
cooperative game theory. A cooperative game models those
problems where a coalition of players cooperates to earn a
joint reward, which must be apportioned among the players.
Under this model, the group, or coalition, of batteries was
paid to provide enough load relief to overcome the predicted
network constraint.
Using the NAC algorithm, the batteries perform a collective
optimal network support action, and the coalition of batteries
as a whole receives a reward in the form of diesel cost
savings (or some proportion of the savings if the network or
utility may wish to keep some of the savings for itself). Thus,
the players in the cooperative game are battery owners, and
the payment to the coalition must be divided among them.
For this, we investigated the use of a solution concept called
the Shapley value, which is an approach to sharing rewards
popular in the economics and computer science literature
due to its favorable theoretical properties; however, it has
had little use in power systems beyond attempts to use it as a
rule for allocating transmission system costs.
In the project context, the Shapley value is the average
contribution a customer makes to reducing diesel costs over
all combinations of battery subcoalitions, that is, its individual
marginal cost reduction averaged over all combinations
of battery-owing participants. Paying customers
in this way differs from the typical pricing in power
networks, where LMPs are often used or retail pricing is
enacted when fixed offers are the norm.
The reasons for using the Shapley value here are that,
first, we want to give the network company the flexibility
to socialize some of the benefits, which is not possible when
using LMPs alone; some additional transfer is used in addition
to LMPs, which raises the same question of how to reallocate
the remaining savings. Second, we still want to signal
the value of battery support to customers using some form of
price discrimination.
The Shapley value has several desirable properties that
mean it results in a fair allocation of the network support
reward. In addition to these properties, we want to explore
how well it provides customers with payments that reflect
the network value of their actions to help incentivize investment
in the right locations on the grid. However, computing
the exact Shapley value is difficult because the number of
combinations of batteries (number of subcoalitions) grows
exponentially with the number of customers, but it can be
approximated by sampling.
Figure 7 illustrates the relationships among the Shapley
value payment for a network support event on 10 June
2018 and the three system characteristics: customer phase
(dot color), voltage ratio [Figure 7(a)] and battery use in the
no-NAC hypothetical [Figure 7(b)]. The first, shown by colored
points on both axes, is the customer's phase connection,
which is one of blue-red, red-white, or white-blue. Both
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IEEE Power & Energy Magazine - July/August 2021

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