# Grid Tariffs Based on Capacity Subscription: Multi Year Analysis on Metered
Consumer Data

Sigurd Bjarghova∗, Hossein Farahmanda, Gerard Doormanb
aDepartment of Electric Power Engineering, NTNU – Trondheim, Norway
bStatnett – Oslo, Norway
∗ Corresponding author - Email<EMAIL_ADDRESS>
###### Abstract

While volume-based grid tariffs have been the norm for residential consumers,
capacity-based tariffs will become more relevant with the increasing
electrification of society. A further development is capacity subscription,
where consumers are financially penalised for exceeding their subscribed
capacity, or alternatively their demand is limited to the subscribed level.
The penalty or limitation can either be static (always active) or dynamic,
meaning that it is only activated when there are active grid constraints. We
investigate the cost impact for static and dynamic capacity subscription
tariffs, for 84 consumers based on six years of historical load data. We use
several approaches for finding the optimal subscription level ex ante. The
results show that annual costs remain both stable and similar for most
consumers, with a few exceptions for those that have high peak demand. In the
case of a physical limitation, it is important to use a stochastic approach
for the optimal subscription level to avoid excessive demand limitations.
Facing increased peak loads due to electrification, regulators should consider
a move to capacity-based tariffs in order to reduce cross-subsidisation
between consumers and increase cost reflectivity without impacting the DSO
cost recovery.

##  1 Introduction

###  1.1 Background

As a measure to reach emission targets, Norway is considering a significant
increase in electricity consumption by electrifying transport, off-shore
installations and various industries [1, 2]. Meanwhile, household peak loads
are expected to increase due to charging of electric vehicles (EVs) and
electrification of heating. This might increase peaks loads in parts of the
grid, which could result in significant expected grid investments in coming
years.

Against the backdrop of these developments and with the intention to reduce
grid investments, the Norwegian regulator (RME) proposed several new grid
tariff structures to incentivise demand response during peak load hours. One
of the suggestions by the Norwegian regulator, is a capacity subscription (CS)
tariff, where customers subscribe to a capacity level. Similar to current grid
tariff structures, it contains an annual fixed cost reflecting the
distribution system operator’s (DSO) fixed costs. In addition, there is a
capacity cost (per kilowatt), with some resemblance to an internet
subscription with a specific bandwidth speed. Demand below the subscription
level has a small energy term, which reflects marginal grid losses, whereas
demand above has a high energy term, which penalises excess use. This CS
tariff thus incentivises customers to keep their demand below the subscribed
capacity level. The tariff is ”static” in the sense that it always penalises
excess consumption, regardless of whether the grid has any congestions. This
is sub-optimal in terms of cost-reflectiveness, as consumers are penalised for
their peak demand whether there is a system peak or not.

To address the issue of system versus consumer peak coincidence, we suggest a
“dynamic” CS as an alternative, where capacity limits are only activated when
there is scarcity of grid capacity. In the case of scarcity, consumers are
physically limited to their subscribed capacity using load limiting devices
(LLD), unlike the static version where only an excess energy term has to be
paid111It would also be possible to use a “financial” version, which would
include payment for excess demand like in the static tariff. The excess cost
coefficient would be higher because activation is done only sporadically..
This dynamic capacity subscription concept is more efficient because there is
no penalty for using capacity when there is no scarcity. This form for
capacity subscription was first presented in [3], but there it focused on the
power market instead of the grid. “Activations” of the LLDs would be done by
the DSOs, which issue warnings in advance. Customers then have a reasonable
amount of time to plan for reducing demand during the activations, by demand
response or distributed energy resources (DER). Smart meters make it possible
not only to analyse demand patterns to find a fitting subscription limit but
also to implement such a grid tariff structure.

In previous work by the authors, “static” and “dynamic” CS tariffs were
analysed for a single customer for one year [4], where the results showed
mainly two things: sub-optimal static subscribed capacity levels do not
critically influence annual costs, and the dynamic optimal subscribed capacity
level depends heavily on amount of activations, which is unknown ex ante.
Furthermore, the need for a more extensive study covering more customers and
uncertainty in demand was highlighted. Capacity subscription was also found to
be the market design that was closest to optimum and leads to highest surplus
on the consumer side rather than the supply side [5].

The issue of social fairness has been raised in response to the suggested
network tariff change. Although new price signals and incentives to shift
towards more grid-friendly demand profiles can result in reduced socioeconomic
costs, this may have undesirable distributional side effects. In essence,
customers with grid-friendly demand profiles should have reduced costs and
vice versa, given a properly designed, cost reflective grid tariff structure.
The EU commission has highlighted in the “Clean Energy For All Europeans”
package [6] that ”The package also contains a number of measures aimed at
protecting the most vulnerable consumers”. It is thus important to consider if
vulnerable consumers could be harmed by the proposed tariff change. Further,
economic efficiency is not the only criterion of a grid tariff design. For the
DSO, cost-recovery and stability of annual revenues are particularly
important. On the consumer side, fairness and acceptance are considered to be
of high importance. These qualitative criteria are challenging to define,
which makes grid tariff design a difficult task [7, 8]. Still, the change from
energy-based to capacity-based tariffs is also taking place in the Dutch
speaking part of Belgium, Flanders, which will introduce a capacity-based grid
tariff from mid 2022. For households and small companies, this is based in the
rolling-average monthly 15-minute peak, with a minimum value of 2.5 kW [9].

###  1.2 Literature overview

Fairness-related issues of grid tariffs have also been discussed in recent
literature. A redistribution of costs between residential consumers was shown
in [10], where up to 15% of the costs were shifted from consumers with low
peak loads to consumers with high peak loads. [11] finds that demand charges
do not disproportionately impact low-income customers relative to rest of
sample, the results show that a demand charge tariff will change the bill of
roughly 10 % of the customers by more than 20%. Further, [12] points out that
a two-part tariff mitigates the potential average increase in tariff costs for
low-income customers. Capacity tariffs are found to be more fair than flat,
peak and Ramsey pricing in [13]. Although working well, capacity-based tariffs
might lead to over-investments in demand response or other types of
flexibility which might lead to other competition-related issues where
flexibility owners push costs over on other customers [14].

An advantage of capacity-based tariff structures is the removal of cross-
subsidisation of distributed generation, which is an increasing issue with the
rapid increase in photovoltaic panels [15, 16, 17]. [18] also claimed that
tariffs were more efficient with a fixed, energy-based and capacity-based
share to reduce cross-subsidies.

Demand charges are relatively common for commercial and industrial customers.
With the use of smart metering, the peak load of a certain time period
(typically monthly) is measured and the consumer pays per kilowatt or megawatt
peak. The authors in [15], observe that demand charges (like in Flanders [9])
have the ”early peak” issue where an early peak in a monthly measured network
tariff structure removes incentives for reducing peak loads for the rest of
the tariff period. This does not occur with CS tariffs as the excess energy
term applies for all peaks above the subscription level. Further, [19] showed
that consumers were relatively positive to demand-based tariffs under the
assumption that it is easy to monitor your consumption.

Like the static version of the capacity subscription tariff, demand charges
are inefficient if the customer peak does not coincide with system peak [20].
There has also been claims that energy-based tariff costs correlate strongly
with peak-demand, suggesting that demand-based tariffs are unnecessary [21].
This is supported by [20] in which the authors also question whether demand
charges are cost-reflective as system and consumer peak do not necessarily
coincide. However, these claims were made before the increase in residential
peak loads seen in countries with a high share of EVs [22].

Developments towards lower marginal costs of energy and more capital intensive
technologies presently increase interest in solutions based on capacity
subscription, both for energy and grid tariffs. Lack of capacity in
distribution grids was highlighted as an important barrier for electric
vehicle (EV) integration in Norway. In addition to the authors’ previous work,
[23, 24, 25] pinpoint that the coincidence factor of consumer versus system
peaks can be dealt with by forming energy communities (under a neighbourhood
tariff). Similar results are achieved in [26], which showed an increased
capability of integrating EVs into the distribution grid under a CS tariff
scheme. Also under competitive, local electricity market schemes, the market
is able to flatten peak loads [27]. An example is shown in [28], where the
concept of EV integration was demonstrated in a real case study in Norway,
where a neighbourhood were able to adopt more EVs by coordinating flexible
resources under capacity-based tariffs. Consumers adapting to grid tariffs is
an apparent consequence of higher distributed energy resources shares in the
future.

###  1.3 Contributions & paper organisation

The purpose of this paper is to investigate the economic impact and efficiency
of CS tariffs on consumers and DSO. Therefore, we analyse the impact on
passive consumers (with no production nor flexibility) under static and
dynamic CS tariffs for 84 customers with six years of demand data. The main
contributions of this paper are the following:

  * •

We analyse the economic impact of static and dynamic capacity subscription
grid tariffs for larger sample of consumers over multiple years.

  * •

We propose a method to determine the optimal subscription level based on a
stochastic approach and demonstrate the advantages of this method compared
with the naive approach of using the previous year’s data.

  * •

We demonstrate how many consumers that experience significant cost deviations
from capacity subscription tariffs compared with existing tariffs, in relation
to their relative peak loads.

  * •

Under dynamic capacity subscription, where demand is limited only when there
is a grid scarcity, we investigate the difference in how much capacity
consumers procure to avoid excessive demand limitations compared to the static
variant, modelled by an assumed discomfort function.

The remainder of the paper is organised as follows: Section 2 discusses the CS
grid tariff design. The model is presented in Section 3, followed by the case
study description in Section 4. Results and discussions are then presented in
Section 5, followed by conclusions and further work suggestions in Section 6.

##  2 Capacity tariffs

###  2.1 Static capacity tariff

The capacity subscription tariff proposed by the regulator has four
components: a fixed annual cost (€), a capacity cost (€/kW), an energy cost
(€/kWh) and an excess demand charge (€/kWh). Note that, in addition to the
grid tariff, the consumer pays for electricity and taxes, but in this paper we
only focus on the grid tariff. The annual consumer grid cost is calculated as
shown in (1).

$C^{tot}=C^{fix}+C^{sub}\cdot x^{sub}+\sum_{t}(C^{l}\cdot x_{t}^{l}+C^{h}\cdot
x_{t}^{h})$ (1)

Where $C$s are the various cost coefficients explained above, $x^{sub}$ is the
subscribed capacity, $x^{l}$ the annual consumption below the subscribed
capacity level and $x_{h}$ the demand in excess of the subscribed capacity.
$C^{l}$ should cover the average losses in the grid and is typically around
0.5€ct/kWh. Because $C^{h}$ is significantly higher, the consumer has an
incentive to keep demand below the subscribed capacity, $x_{sub}$.

According to the regulation, the grid companies that apply CS tariffs will be
obliged to recommend the $x^{sub}$ minimising $C^{tot}$ to the consumer.
Because hourly demand data will be available, this is in principle an easy
task based on ex post data. An updated proposal required that the last 12
months are used for determining the subscription level; it is changed
dynamically each month. In our analyses, we will find the optimal $x^{sub}$
based on six years of data, but we will also look at other ways to find
$x^{sub}$.

In this study, customers can subscribe to any capacity, whereas, in reality,
it is reasonable to assume that customers have to choose between discrete
steps with e.g. 0.25, 0.5 or 1 kW intervals. A high resolution of choices
makes it more complicated for customers to choose, whereas a low resolution,
with e.g. 1 kW intervals would create sub-optimal conditions for customers
with a low consumption due to a high deviation between optimal subscribed
capacity (e.g. 1.5 kW, and the choices that would be 1 or 2 kW). This is less
relevant as annual demand (and thus average demand) increases. We abstract
from this issue and assume a continuous scale in our study to get a more
precise idea of which subscription levels are optimal.

One of the design parameters of subscription-based tariffs is the frequency of
subscription level updates. From the perspective of the DSO, annual
subscription might be preferable, especially when demand is strongly
influenced by seasonal variations. On the other hand, consumers need
flexibility with respect to changing circumstances. Examples of changing
circumstances that heavily influences the optimal subscription limit could be
moving or investments in demand increasing/decreasing assets such as EVs,
house insulation upgrades or heat pumps.

In this paper, we (among other approaches) investigate a subscription level
which is decided annually ex ante. However, in a real implementation it must
be possible to adjust the level during the year, without allowing consumers to
subscribe to a low level in a typical low load season (summer in a cold
climate) and then increase subscription during a high load season. If this
were allowed, capacity prices would need to be adjusted correspondingly. The
approach proposed by the Norwegian regulator, to base subscription on demand
during the last 12 months, updated on a monthly basis, solves the problem of
the frequency of update, but is sub-optimal as we will show in this paper.
Moreover, it only partly takes into account major changes in demand, which
will only slowly result in a corresponding change in subscribed capacity.
Another possibility is that capacity is paid for on an annual basis, but that
is a secondary market for shorter commitment periods. We do not elaborate on
this issue in this paper, but it is an open issue for further research.

###  2.2 Dynamic capacity tariff

Capacity subscription was proposed in [5] for the power market. In [29], the
authors also indicated the possibility to use the same model for the grid
tariff structure. An essential feature of the dynamic CS is that demand is
limited to the subscribed capacity when there is scarcity in the system (i.e.
not enough generation capacity in the “market case” or an active grid
constraint in the present context). In such cases, the DSO (or TSO) activates
a Load Limiting Device (LLD), effectively limiting demand. To make this
acceptable for the consumer, it is necessary to have intelligent load control
that keeps demand below the subscribed limit, by switching off non-essential
demand like floor heating or other appliances. Delaying the charging of EVs is
also very well suited to keeping demand right below the limit. Here we use the
term “dynamic” CS, to distinguish it from the tariff proposed by the Norwegian
regulator [30]. The consumer cost is very similar to equation (1), but there
is no excess consumption above the subscription level, because demand is
limited instead. On the other hand, the consumer experiences a partial loss of
load, which in effect is a welfare loss that needs to be considered in the
cost optimisation. The annual customer total cost under the dynamic CS tariff
scheme is presented in (2).

$C^{tot}=C^{fix}+C^{sub}\cdot x^{sub}+\sum_{t}(C^{l}\cdot
x_{t}^{l}+\sum_{j}C_{j}^{VCL}\cdot x_{tj}^{VCL})$ (2)

The costs are very similar to the static CS tariff, but instead of an excess
energy term, consumers experience a discomfort cost ($C_{j}^{VCL}$ which
increases the more load $x_{tj}^{VCL}$ is cut. Because the discomfort costs
increases exponentially as more load is cut, this is segmented (indexed by
$j$) in a piecewise linearised fashion. The discomfort costs are discussed in
detail in Section 2.2.1.

####  2.2.1 Discomfort costs

To determine the optimal subscription level for dynamic CS, the consumer cost
of having to reduce load must be taken into account. This cost cannot be
observed, like the excess demand cost $C^{h}$ under the static CS tariff. The
value of lost load typically depends on customer type and duration of
disconnection, and represents the discomfort costs of electricity not served.
However, under the dynamic CS scheme, the load is only limited and not
completely disconnected. As stated in Section 2.2, intelligent load control
can be utilised, disconnecting only non-essential demand, which further leads
to lower comfort loss. The value of cut load ($C^{VCL}$) is a function of how
much load is disconnected. We use the formulation in (3), which was also used
in [4].

$C^{VCL}=\frac{VoLL}{1-e^{-b\cdot L}}(1-e^{-b(L-x^{sub})})$ (3)

Value of cut load is represented as a value between 0 and VoLL as a non-linear
curve as demonstrated in (3). The curve steepness is given by $b$. The load
$L$ and subscribed capacity level $x^{sub}$ decides the discomfort cost in a
certain time period. If $L$ never exceeds $x^{sub}$ (which translates to
subscribing to the maximum demand), discomfort costs will be zero. The impact
of different values of $b$ is visualised in Figure 1. A steep VCL curve (high
$b$) translates to the consumer having high discomfort costs of curtailing a
relatively low share of the consumer’s load. A low steepness (low $b$) implies
that the consumer is quite flexible and can curtail more load without
experiencing high discomfort. In this paper, we assume a steepness $b$ of 8,
resulting in a relatively steep discomfort cost curve, as shown in Figure 1.
This level implies that the cost of flexibility (and thus discomfort costs) is
relatively high, and also only results in small reductions in load. In
reality, this level could be adapted to each individual customer based on
their real discomfort costs.

Figure 1: Value of cut load with different steepness levels. VoLL is 5 € /kWh.

If a consumer has a peak load of 5 kW, the curtailment of 1 kW (20%) should
have a similar discomfort cost as a consumer with a 10 kW peak load who is
curtailed 2 kW (also 20%). This is a necessary simplification made to be able
to compare curtailment of different customer types. In this approach,
$C_{j}^{VCL}$ is decided based on the maximum load of the consumer in the
specific year that is simulated. The consequence is that 1 kW of curtailment
is not given the same discomfort cost for all consumers. The value of lost
load depends on customer type, duration and time [31], but we simplify by
setting it to 5 € /kWh.

####  2.2.2 Activation of capacity subscription

An important advantage of the dynamics CS tariff is that it does not punish
load above the consumer’s subscription limit in non-scarce hours, and thus
avoids the welfare loss caused by excess payment for a non-scarce resource. It
also rewards flexible users who can reduce their consumption when the system
requires it the most, or customers who simply do not have a high consumption
when there is grid scarcity, as those consumers could subscribe to lower
capacities and thus reduce their annul grid tariff costs. The system peak load
varies from year to year because some winters are colder than others. The DSO
will therefore invest in grid capacity that covers the highest peak in not
only a year, but for several years. If there is a considerable penetration of
electrical heating, this means that a winter without very cold periods could
have no capacity scarcity, whereas years with cold periods would result in
many hours with capacity scarcity. This makes it challenging to find a correct
number of activations. If the DSO sets the threshold for activation relatively
low, there could be so many activations that customers are incentivised to
subscribe to a capacity close to their peak load to avoid high discomfort
costs. The mentioned scenario would not increase social welfare much as the
situation would remain quite similar as it is today where end-users indirectly
pay to use whatever peak they want. If the threshold is high, the entire basis
for choosing a subscription limit is based on very few hours per decade, which
incentivises speculation in subscribing to 0 kW as well as demand response
investments. This could make it difficult for the DSO to recover their
existing costs, although they are reduced somewhat due a reduced peak load. To
keep a good compromise between the two, there needs to be some activations
each year, even if there is no severe capacity scarcity in the system.

Although the CS tariff primarily aims to reduce costly future distribution
grid investments by incentivising customers to reduce peak loads, the DSO is
not the only stakeholder here. The TSO who owns the transmission grid also has
an interest in reducing future grid investments by avoiding growth in capacity
use in areas with an increase in load. TSO and DSO interests therefore align
because DSOs pay transmission grid rent in the hour where the total peak
demand is the highest in the region. It is therefore realistic that both
distribution and transmission grid-related congestions could lead to
activations. Note that in this study we only base activations on local
congestions.

Another important aspect of activations based on local congestions is if
activations should be across the whole DSO grid (to avoid discrimination) or
if they can be limited to overloaded radials only. Clearly, the latter would
be the efficient solution, but it may contradict with rules on equal
treatment. The present rules in Norway do not allow, e.g., different tariffs
within the same DSO area, but it is not evident that a different number of LLD
activations would fall under this requirement. However, this looks probable.
On the other hand, it is clearly inefficient to activate LLDs across the whole
DSO area because one or two radials are overloading, and this problem
increases as the DSOs merge and become larger. A possible solution could be to
reduce the fixed part of the tariff $C^{fix}$ for consumers on “weak” radials
that can expect more LLD activations.

##  3 Model

###  3.1 Stochastic optimal static subscribed capacity problem

In Norway, the demand is weather dependent due to high penetration of
electrical heating. Future demand is therefore unknown and varies from year to
year. Therefore, choosing the optimal subscription level is a stochastic
problem. We model this by using a number of historical weather years,
represented by the index $s$, each having a probability $p_{s}$. Ideally,
these years should present a statistically representative sample for the
expected weather conditions. The consumer’s objective function is given by
(4).

$\min{C^{fix}+x^{sub}C^{sub}+\sum_{s}\sum_{t}p_{s}(x_{ts}^{l}C^{l}+x_{ts}^{h}\cdot
C^{h}})$ (4)

Energy bought from the grid is split into energy below ($x_{ts}^{l}$) and
above ($x_{ts}^{h}$) the subscribed capacity $x^{sub}$ in (5) and (6).

$x_{ts}^{l}+x_{ts}^{h}=L_{ts}\quad\forall t,s$ (5)

$x_{ts}^{l}\leq x^{sub}\quad\forall t,s$ (6)

###  3.2 Stochastic optimal dynamic subscribed capacity problem

In this case, the consumer’s objective function is given by (7). The objective
is straightforward, with an annual fixed cost, a subscription cost and an
energy fee. In contrast to the static CS tariff, excess energy use is no
longer possible, and the discomfort cost $C_{j}^{VCL}$ replaces $C^{h}$.
Because consumers have different load profiles and annual demand,
$C_{j}^{VCL}$ must be tailored for each consumer. The values used in these
simulations are based on the curve presented in Figure 1.

$\min{C^{fix}+x^{sub}C^{sub}+\sum_{s}\sum_{t}p_{s}{[(x_{t}^{l}\cdot
C^{l}+x_{tsj}^{VCL}\cdot C_{j}^{VCL}]}}$ (7)

Energy from the grid is split into energy below ($x_{ts}^{l}$) the subscribed
capacity $x^{sub}$ and the partially curtailed load $x_{tsj}^{VCL}$ above this
capacity in (8) and (9).

$x_{ts}^{l}+\sum_{j}x_{tsj}^{VCL}=L_{ts}\quad\forall t,s$ (8)

$x_{ts}^{l}\leq x_{t}^{sub}\quad\forall t,s$ (9)

##  4 Case Study

Hourly load data from 84 customers in the NO1 price zone for the period
2013-2018 were used in the analysis. Because of privacy rules, the data could
not be coupled to heating source or other information that might explain the
load profiles. To analyse the impact of CS tariffs, the consumer costs under
historical load data has been simulated with the existing energy tariff
alongside the static and dynamic CS tariff schemes. An overview of all the
simulations performed is presented in Figure 2. They are further explained in
the subsequent sections.

Figure 2: Overview of the case studies.

###  4.1 Customer data

A box plot of the spread in full load hours of the consumers is shown in
Figure 3. Full load hours are defined as the total annual demand divided by
the peak load. A high number indicates that the peak load is significantly
higher than the average load and vice versa. Full load hours therefore
indicate whether or not the customer has a flat, stable demand profile or few,
large demand spikes.

Figure 3: Boxplot of 84 customers’ full load hours. The median is shown as the
orange middle line. The box contains the 25 and 75% quartiles, whereas the
whiskers are 1.5 standard deviations. Outliers can be found outside the
whiskers.

The median value is around 2300 hours for all years. It is lowest in 2014 and
highest in 2017, the warmest and next coldest year, respectively, cf. Section
5.1. This looks counter intuitive as one would expect the highest demand in
the coldest year. However, even warmer years have a few cold days resulting in
high demand. On the other hand, cold years have high energy consumption, which
reduces the full load hours, and consequently there is no direct relation
between the lowest temperature and the number of full load hours.

###  4.2 Grid tariff costs

The underlying principle when setting the prices for the CS tariffs is that
the income of the DSO remains the same after the transition from the present
energy tariff. The annual fixed cost is set to the same for both CS tariffs.
This is also the case for the energy term, which is set to the cost of
marginal losses, estimated at about 0.5 €ct/kWh. We then vary the capacity
cost until we find the level that results in approximately the same
(aggregated) consumer costs as with the present tariff. All cost levels for CS
and existing energy-based tariffs are shown in LABEL:SCcosts and
LABEL:ETcosts, respectively. Finally, it is assumed that consumers do not
adapt to the new tariff222This is, of course, a conservative assumption. By
adapting behaviour, especially consumers with high peak demand, will save
costs and become better off than shown in the subsequent analyses. The whole
point of introducing capacity-based tariffs is to change consumer behaviour.
Note that for dynamic capacity subscription, there is an imposed change in
behaviour, i.e. keeping demand below the subscription limit during LLD
activations..

The short-term consumer benefit does not change under the static CS tariff. It
does change for the dynamic variant, which is taken into account through the
calculation of the discomfort costs, cf. Section 2.2.1.

Correctly pricing the dynamic CS tariff is not straightforward, because the
underlying principle of DSO cost recovery must be reconsidered. When demand is
physically limited to the subscribed capacity, DSO revenues are reduced,
because there is no payment for excess demand. On the other hand, over time,
this has the potential of significantly reducing grid investments. We
therefore argue that it is acceptable that DSO revenues decrease with dynamic
capacity subscription, because costs will decrease over time. Instead, we
consider that the consumers on aggregate should not be worse off when also
taking into account the increase in consumer costs (or rather, reduction in
benefit) caused by the demand reduction during LLD activation. The increase in
consumer costs is calculated using the VCL model explained in Section 3.2. The
consumer cost is also an expected value, as the number of activations is
unknown in advance.

Table 1: CS tariff costs Cost element | Cost | Unit
---|---|---
Fixed cost | 135 | $€/year$
Capacity cost (static) | 67.5 | $€/year$
Capacity cost (dynamic) | 54 | $€/year$
Energy term | 0.5 | $€ct/kWh$
Excess energy term | 10 | $€ct/kWh$
Value of lost load | 5 | $€/kWh$
Table 2: Present energy tariff costs Cost element | Cost | Unit
---|---|---
Fixed cost | 204.6 | $\frac{€}{year}$
Energy term | 1.859 | $\frac{€ct}{kWh}$

###  4.3 Activations

As mentioned in Section 2, we base activations on local congestions. We assume
that the DSO activates the LLDs when the aggregated load of the 84 customers
exceeds 390 kWh/h (peak load is 458 kWh/h). This is based on the idea that
this would be the limit in the local grid, but the number is chosen to obtain
results that illustrate the impact of the various tariff choices well. This
means that we get a total of 291 hours of activation in 6 years, or 0.55% of
the time. We see from Table 3 that more than half of the activations occur in
2015, whereas 2013 and 2016 have very few activations with only 13 and 10,
respectively.

Table 3: Overview of activations for all years. Activations | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | Total
---|---|---|---|---|---|---|---
Hours | 13 h | 42 h | 148 h | 10 h | 19 h | 59 h | 291 h
% of hours | 4.5% | 14.4% | 50.9 % | 3.4 % | 6.5 % | 20.3 % | 100%

We used the same probability of occurring for each of the six years, because
it is difficult to map those years convincingly on longer historical records
of winter temperatures. Even if this could be accomplished, it it is not a
good measure of the number of activations, as argued above. How probabilities
should be allocated, to the number of activations is a key topic for further
research, as this is an important parameter for the optimal subscription
level.

##  5 Results & discussion

An important question for capacity subscription is: to what level of capacity
should a particular consumer subscribe? With perfect foresight on demand and
activations, this is a simple optimisation problem, but in reality, demand and
prices are, of course, unknown. Still, the perfect foresight solution can be
used as a benchmark. We compare this with two other, realistic options:

  * •

Stochastic optimal subscribed capacity (stochastic optimum)

  * •

Reactive subscribed capacity (reactive level).

The stochastic optimal subscribed capacity is the subscription level resulting
in the lowest expected annual cost under uncertainty. By considering
uncertainty in domestic load, both high or low consumption profiles are taken
into account when choosing a capacity level.

The reactive subscribed capacity is the subscribed capacity level based on the
optimal level from the previous year. Essentially, this approach uses the
exact same demand profile and activation pattern as from the previous year.

We find the stochastic optimum, based on the six scenarios with load profiles
for 2013-2018. Temperatures dominate the load profiles in Norway due to high
share of electric heating in households, making it important to have load data
from both warm and cold winters to analyse the impact of the resulting
consumption.

As stated before, we only consider grid tariff costs, and ignore taxes, fees
and electricity prices.

###  5.1 Static capacity subscription

####  5.1.1 Stochastic approach

Under static CS tariffs, the optimal subscribed capacity level results in the
best trade-off between capacity costs and the excess energy term costs.
Although there are some variations in the optimal subscribed capacity from
year to year, the spread is not very large as seen in Figure 4. The figure
compares the annual deterministic optimum to the stochastic optimum. The mean
values are in all cases within a 5 margin, whereas the second and third
quartile are in all cases within a 10% margin of the stochastic optimum. The
most extreme cases show deviations up to 50%, but the whiskers (1.5 STD)
mostly stay within a 2 % margin.

Figure 4: Boxplot of 84 customers’ annual optimal subscribed capacity relative
to the stochastic optimum.

Due to the perfect foresight, the deterministic optimum will result in lower
costs than compared to stochastic optimum. The annual grid tariff costs under
the deterministic optimum is therefore never higher than under the stochastic
optimum, as shown in Figure 5. However, the spread in costs is tiny. In almost
all the cases, the cost when subscribing to the deterministic optimum and not
the stochastic optimum is less than 3% higher. Outliers show that the costs
can deviate up to roughly 14%, but this is rare. The spread in costs is
surprisingly low compared to the spread in optimal subscribed capacity.
However, this is fairly logical, as a higher subscription level results in
high capacity costs and lower excess energy costs and vice versa, which is
coherent with the results from [4].

Figure 5: Box plot of 84 customers’ annual cost when subscribing to the
deterministic optimal level, relative to the stochastic optimal level.

The sorted curve in Figure 6 indicates how the new CS tariff compares to the
existing energy tariff. The graph shows that the consumer annual costs
increases the most in 2018. The 2016 costs reach similar maximum deviations,
but not for as many consumers. These results imply that in 2018, the
stochastic level is further away from the ex-post optimal deterministic level.
This is confirmed in Figure 4, which shows that a significant number of
consumers would preferably subscribe to both lower and higher capacities (the
spread is relatively large). However, the costs over the six years are the
same (which is how the tariff cost level was set), meaning that costs simply
deviate from year to year. This is further elaborated and discussed in Figure
9, which shows that costs differ from year to year, but not more than the
existing energy tariff scheme.

Figure 6: Sorted annual simulated stochastic customer cost relative to energy
tariff costs.

####  5.1.2 Reactive approach

The stochastic approach requires several years of data in addition to being
somewhat complicated. A more straightforward approach would be to use the data
from the most recent year. As previously stated, we therefore use the term
reactive subscribed capacity level, which refers to using the optimal
subscribed capacity of the previous year in the current year. For example, the
reactive level corresponds to finding the optimal subscribed capacity of 2013
ex post and subscribing to that level in 2014.

The reactive level costs compared to the more robust stochastic approach
mostly results in slightly higher costs on average. From Figure 7, it can be
deduced that subscribing to the wrong CS level mostly results in non-dramatic
consequences as only outliers exceed an increased cost of 16% compared to the
stochastic approach. This is good news for DSOs that are afraid of their
customers making sub-optimal choices instead of using the more robust
stochastic approach. Outliers give up to 60% increased costs.

Figure 7:

The same results as in Figure 7 is illustrated as a sorted curve in Figure 8,
where we see that acting reactively works relatively well for roughly 80-90%
of the consumers (who only experience up to +10% cost increase), but results
in high price increases for some consumers.

Figure 8: Sorted curve of reactive costs relative to annual simulated
stochastic costs.

Looking at the results from a distance, Figure 9 shows that costs increase by
1.2 - 2.0 % for the total customer group when always subscribing to the
reactive subscribed capacity level compared to the deterministic optimum. The
figure also shows that there is a significant variation in annual costs,
regardless of the tariff. This is good for the DSO, who is interested in
predictable cost-recovery, but also for customers who should not experience
increasing cost fluctuations with CS tariffs. Of the CS tariffs, the
deterministic optimum is obviously always lowest, whereas the stochastic
optimum mostly gives lower costs than the reactive, except for 2018 when the
reactive subscribed capacity level gives slightly better results. This
exception occurs if the demand profiles from two years match relatively well,
and both deviate somewhat from the stochastic level. In general, the spread
from year to year is relatively small and does not vary more than the existing
energy tariff.

Figure 9: Aggregated annual consumer costs under the different approaches
(static CS).

###  5.2 Dynamic capacity subscription

Under the dynamic CS tariff scheme, the load profile characteristics in terms
of seasonal variations, flatness and “spikiness” significantly influence the
results because activation of the LLD only causes discomfort costs to the
consumer if the system peak correlates with the consumer peak. The DSO
forecasts demand peaks and sends activations based on expected grid
congestions. As peak load hours occur when demand is high, it is natural to
assume that the correlation between consumer peak loads and neighbourhood peak
loads are high. However, this is not always the case for the individual
customer. Customers with flatter load profiles and/or customers with other
heating sources than electricity do not necessarily share peak loads with the
system. Customers with low correlation between individual peaks and
activations will therefore be able to subscribe to relatively low capacities
because the discomfort costs during activations are low. Flexible customers
who can reduce load during activations will also be rewarded with the dynamic
CS tariff. We do not model any flexibility assets in this study, but model
demand flexibility implicitly by curtailing some load under the dynamic CS
tariff scheme.

####  5.2.1 Stochastic approach

Results show that customers subscribe to significantly higher capacities under
the dynamic compared to the static CS tariff, with the median increase roughly
30% higher, as seen in Figure 10. This is mostly due to the difference in
excess energy cost, which is 0.1 € in the static case, but up to 5 € (VoLL) in
the dynamic case because the customers are physically limited, cf. Figure 1.
The capacity cost is also somewhat lower in the dynamic case (adjusted to
match the DSO cost recovery). The spread is relatively large, with some
customers preferring to subscribe to as little as 40% under the dynamic
compared to the static CS tariff, indicating that their peak loads are not
coinciding with activations, or that their load profiles are flat. This stands
in contrast to some exceptions on the other side of the scale, where two
customers subscribe to more than 60% more in the dynamic case, indicating a
high correlation between activations and peak loads. It is therefore natural
that they would subscribe to more (and thus pay more) because activations
result in more load shedding. Due to the heavy variation in deterministic
dynamic CS levels, the importance of using a stochastic approach is clear.

Figure 10: Stochastic dynamic CS level relative to stochastic static CS level.

Compared to the old energy tariff, Figure 11 shows a significant spread in
annual costs under the dynamic CS tariff. 2015 especially has higher costs due
to the high number of activations leading to higher VCL.

Figure 11: Annual simulated dynamic costs compared to energy tariff costs.

####  5.2.2 Reactive approach

In general, the deterministic optimal subscribed capacity level under the
dynamic CS level varies much more from year to year due to the difference in
number of activations. In a year with few activations, the optimal
subscription level can be as low as zero or close to zero because of the low
VCL cost. On the other hand, years with many activations results, in a high
optimal deterministic subscription level. This shows that the reactive
approach cannot be used for dynamic CS.

Figure 12: Aggregated annual consumer costs under the different approaches
(dynamic CS).

In Figure 12, the aggregated annual consumer costs are shown. The blue bars
(bottom) represent actual monetary costs (which corresponds to the DSO’s
income), whereas the red bars on top of the blue are discomfort costs related
to the value of cut load and are not monetary costs. The costs under the
existing energy tariff scheme are shown as black bars. Acting reactively
clearly results in the highest costs as consumers subscribe to sub-optimal
levels. This leads to either extremely high discomfort costs if they have
insufficient subscribed capacity (as shown in 2017), or close to zero
discomfort costs due to subscribing to a high capacity (as shown in 2016).
Both cases result from reacting to few or many load limitation activations
from the previous year. This also leads to unacceptable variations in the
DSO’s revenues. When using the stochastic approach, the costs are more stable
and relatively similar to the energy tariff costs. The average total cost
(monetary + discomfort) are the same (by calibration), but this results in
somewhat lower revenues to the DSO. In the long run, this seems acceptable, as
dynamic CS probably is very efficient in reducing peak demand, reducing the
need for grid investments. Under the stochastic approach, the DSO income is
also relatively stable and does not vary more than the energy-based tariff
scheme. This is good news for DSOs who rely on stable income. The theoretical
optimal costs are of course lower than the other approaches.

Figure 13 in particular clearly illustrates that reactive determination of the
subscription level is a strategy that cannot be used for dynamic capacity
subscription. More advanced strategy like the proposed stochastic strategy are
necessary and are no impediment to implementation of dynamic capacity
subscription given the present availability of data and support tools on smart
phones.

Figure 13: Dynamic CS reactive costs relative to annual simulated dynamic CS
costs.

###  5.3 Consequences for consumers and the DSO

The correlation between load factor and cost-redistribution under the static
and dynamic CS tariffs is shown in Figure 14(a) and Figure 14(b),
respectively. The load factor is similar to full load hour term used for power
production, and represents how steep the peak load is compared to the annual
consumption. A low and high load factor implies that the peak load is high or
low compared to the annual consumption, respectively. A high load factor is
associated with flat low profiles which should be rewarded by CS tariffs. This
trend is shown clearly in the results. However, there is a spread in the data,
which stems from the fact that peak load is not always the deciding factor. If
a consumer has a high peak load in just a few hours, but a flat profile
otherwise, this is not penalised as heavily by the CS tariffs. In the dynamic
CS case, the spread is even larger as it also consider system peaks. Consumers
with peak loads outside of the system peak loads are not penalised as heavily
as those who coincide with system peaks.

Some of the negative impacts of consumer versus system peak coincidence could
be improved by only activating load limitation in parts of the grid where
there is scarcity. However, this is not allowed in Norway due to fairness
principles. This challenging compromise between cost-reflectivity and fairness
could be solved by the regulators. To achieve this, the regulator and DSOs
could investigate methods to properly compensate consumers that are located in
areas with more frequent load limitations, for example in the form of reduces
fixed costs. This is of increasing importance in countries where there are
few, large DSOs, with many customers. In those countries, it would be very
inefficient to limit load on all of them.

(a) Static CS tariff.

(b) Dynamic CS tariff.

Figure 14: Scatter plots of static and dynamic CS costs compared to the
energy-based tariff, in relation to the load factor. Linear regression is
shown as blue lines.

Currently, consumers with high peak loads are being subsidised by consumers
with flatter load profiles that have lower contributions to system peaks. A
potential move from energy-based to capacity-based network tariffs has
significant cost-reflectiveness advantages, as consumers would have an
incentive to reduce their peak load. As shown in Figure 12, the DSO income is
somewhat reduced when moving to dynamic CS tariffs as the cost is shifted onto
the consumer in the shape of discomfort costs333The DSO income is the same
when discomfort costs are included, but because they are not monetary costs,
the income is somewhat reduced.. This could be difficult for DSOs in the
short-term who rely on steady income. In the case of a move towards a dynamic
CS tariff, we therefore recommend a somewhat slower transition in terms of
reducing the grid tariff prices until the DSOs starts to see lower grid
investment costs. This transition period also benefits from the fact that the
more data, the better advice to consumers can be given. In general, Figure 9
and Figure 12 shows that DSOs can not expect the variance in annual income to
increase(given that the stochastic approach is applied), and should thus not
be used as an argument against moving towards capacity-based tariffs.

##  6 Conclusions & policy implications

This paper demonstrates the change in annual grid tariff costs for a sample of
household customers when applying capacity-based tariff structures. Two types
of capacity subscription tariffs were analysed; static and dynamic subscribed
capacity. Under the static capacity subscription tariff, results show that
using a stochastic approach to determine the subscribed capacity level using
several years with historical consumption data results in annual costs close
to the perfect foresight theoretical optimum. Acting reactively (based on the
previous year’s conditions), works reasonably well for most consumers, but
leads to significantly increased costs for a few consumers. The DSO cost
recovery is equally stable as under the energy tariff, with tiny variations
from year to year. Under the dynamic CS tariff, consumers are only limited
during hours with grid scarcity. The stochastic approach is significantly
better than acting reactively as the number of activations from year to year
is very different. Subscribing reactively leads to huge variations in
subscribed capacity from year to year, resulting in unacceptable demand
limitations and wide variations in annual DSO revenues. This approach cannot
be allowed used in practice. This can e.g. to some extent be avoided by
requiring a minimum subscription level.

Overall, the static CS tariff results in low to moderate changes in annual
costs for consumers, is robust to sub-optimal subscription levels and does not
result in increased variance in costs compared to the existing energy tariff.
Regulators should consider moving to such tariffs in the future, as capacity
subscription tariffs benefit from being more cost-reflective while maintaining
a stable DSO income. Advising consumers on optimal subscription levels is also
fairly easy with the suggested method, implying that regulator/DSO should be
able to help consumers find a reasonable subscription level. The tariffs also
redistribute costs between consumers based on their peak loads, removing some
cross-subsidisation from consumers with low peak loads to consumers with high
peak loads.

The impact of the dynamic CS tariff are more difficult to assess, because in
addition to the actual payments from consumer to DSO, also the loss of
consumer welfare due to demand limitations need to be taken into account. We
use a simple, assumed cost function for this effect. On the other hand, the
dynamic CS tariff offers a much more precise limitation on load which is more
efficient, as no load limitations or excess energy fees exist during hours
with no grid scarcity. The monetary costs for the consumers are relatively
stable but somewhat lower. In the case of a transition to dynamic capacity-
subscription tariffs, the regulator should consider a transition period before
the grid tariff prices are reduced according to the reduced future grid
investments. In order to avoid load limitation on many consumers in large DSO
areas, the regulator should look into methods to compensate consumers who are
frequently limited, which would increase overall efficiency of the tariff.

Further work might look deeper in the effect on particular consumer segments,
based on customer type data and heating sources, which could have shed extra
light on what type of consumers experience different cost impacts. Future work
is recommended to look more extensively into the impact of activation
scenarios, adding consumer flexibility and addressing the consumer types
implications. A method to estimate optimal subscription for dynamic capacity
subscription if no previous data (or only short period) is available should
also be of interest for further work. Moreover, the dynamic CS tariff could be
extended to only limiting load in grid areas with congestions. However, this
may not be allowed under existing regulation.

## Acknowledgement

This work was funded by the “DigEco - Digital Economy” project funded by the
NTNU Digital Transformation Initiative (project number: 2495996). We would
like to thank Roman Hennig and Laurens de Vries at TU Delft, and Matthias
Hofmann at Statnett for their useful input and contributions.

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##  Appendix A Industry & Participant Details

Industries |  Brief Overview |  Recruitment For Roles
---|---|---
Advertising |  _Conduct promotional work which aims to sell a project or service_ |  Central: Art director, Creative director

Secondary: Copywriter, Graphic designer, Illustrator, Animator, Social media
or SEO strategist, Media planner, Account manager
Business
Communications |  _Manage internal and external messaging to audiences such as employees, customers, stakeholders, the media, or the general public_ |  Central: Internal communications director, Communications specialist, Administrative assistant

Secondary: HR expert, Content strategist, Corporate PR
Education |  _Teach students and contribute to their learning and development_ |  Central: Middle school & high school teachers, Course instructor or professor (post-secondary)

Secondary: School principal or assistant principal, Freelance tutor, Reading
specialist
Journalism |  _Produce and disseminate reports to inform society on events, people, ideas, and anything else that might be considered “newsworthy”_ |  Central: Newspaper reporter, Columnist, Editorial writer

Secondary: Copyeditor, Fact checker, Section/Content editor, Newsroom
editor/manager, Freelance reporter (print/online or broadcast)
Law |  _Support and enforce established legal standards; advocate for clients_ |  Central: Junior and senior associates

Secondary: Law firm partner, Freelance attorney, Paralegal, Law clerk, Public
defender
Mental Health |  _Support, stabilize, and improve individuals’ mental health_ |  Central: Psychologist, Therapist, Psychiatrist

Secondary: Social worker, Case manager/coordinator, Clinical counselor
Software
Development |  _Design, program, deploy, and maintain software_ |  Central: Junior and senior full-stack developers

Secondary: Database engineer, Data scientist, Product manager
Table 4. Overview of how we thought about each industry, including the roles we described as central and secondary shared with our recruitment partners. |  | Participants |
---|---|---|---
Industries | Location | $n$ | Age Range | Gender |  Time in Industry
Advertising | New York City | 8 | 26 – 38 | Women: 4 |  2-5 years: 2
|  |  |  | Men: 4 |  6-10 years: 1
|  |  |  |  |  10+ years: 5
Business | Columbus | 8 | 24 – 54 | Women: 4 |  2-5 years: 3
Communications |  |  |  | Men: 4 |  6-10 years: 1
|  |  |  |  |  10+ years: 4
Education | Oakland | 7 | 29 – 51 | Women: 6 |  2-5 years: 2
|  |  |  | Men: 1 |  6-10 years: 1
|  |  |  |  |  10+ years: 4
Journalism | New York City | 8 | 25 – 42 | Women: 5 |  2-5 years: 3
|  |  |  | Men: 3 |  6-10 years: 2
|  |  |  |  |  10+ years: 3
Law | Columbus | 8 | 30 – 64 | Women: 4 |  2-5 years: 3
|  |  |  | Men: 4 |  6-10 years: 2
|  |  |  |  |  10+ years: 3
Mental Health | Oakland | 8 | 32 – 50 | Women: 5 |  2-5 years: 2
|  |  |  | Men: 3 |  6-10 years: 1
|  |  |  |  |  10+ years: 5
Software | New York City | 7 | 25 – 36 | Women: 3 |  2-5 years: 3
Development |  |  |  | Men: 4 |  6-10 years: 1
|  |  |  |  |  10+ years: 3
Table 5. Details about the location and participant makeup of each industry
group. Gender was self-reported by participants from a range of options,
including the option to self-describe. Recruitment was limited to participants
who had been in their industry for two or more years.

##  Appendix B Introduction to Generative AI

A key component of our workshops was offering participants a foundation for
thinking about generative AI. To this end, early in each workshop we led an
education section about 40 minutes in length. We began with a 20-minute
presentation covering:

  * •

a shared definition of AI

  * •

a very condensed history of AI and generative AI, focusing on key concepts
like the early aims in developing AI

  * •

a brief, non-technical explanation of what has changed recently with
transformer models and LLMs

  * •

15 key concepts regarding characteristics, benefits, and risks of generative
AI systems, to refer to throughout the workshop

Participants were encouraged to ask questions at any point during the
presentation, and then we spent an additional 20 minutes on further questions
and discussion. In each workshop, the presentation and Q&A was led by one of
two authors, both of whom are researchers who work in AI. We lightly
customized materials to each group’s industry.

The definition we provided is: “Artificial Intelligence is the ability of a
computer or a machine to think or learn,” and we provided additional color on
how we think about the terms: “computer or machine,” “think,” and “learn.”

The 15 concepts we shared include the following:

Bias:

— Generative AI tools may reflect social biases that are present in their
training data

Bland:

— Generative AI often generates “flat” or generic text, unless explicitly
directed to do otherwise

Brainstorming:

— Generative AI tools can create outlines, lists, drafts, possible solutions,
and more

Emergent Properties:

— Generative AI models may seem to possess abilities they were not designed to
have

Falsehoods:

— Generative AI can fabricate information or sources, or get facts wrong, yet
seem confident and compelling

Grammatical:

— Content generated by text-based Generative AI tools can be well-written,
using good syntax and avoiding typos

Identifies Tacit Structure:

— Generative AI can uncover steps and processes which were not previously
articulated

Memorization/Privacy Breaches:

— Generative AI may generate content identical to its training data

Mimicry:

— Generative AI can be asked to mimic genre, tone, phrasing, visual style, or
more

Non-Deterministic:

— Generative AI models can give responses which are variable, not consistent.
This means that when users input the same or similar prompts, the system may
not respond in the same way

Provenance Is Unclear:

— Generative AI tools may not be able to reliably trace specific content back
to a direct source in training data

Remixes:

— Generative AI always generates content based on its training data. It can
recombine data in unique ways, but is limited to re-mixing training data

Safety Not Guaranteed:

— Generative AI tools may have built-in safety systems to attempt to prevent
certain types of content or topics, but these are not infallible

Scale / Speed:

— Generative AI, like other AI and ML systems, is able to consider large
amounts of data and handle many tasks, over and over again, extremely quickly

Tweakable:

— Through “prompt engineering,” Generative AI tools can often be influenced to
generate content in a certain way

##  Appendix C Artifacts

Figure 1. _E6_ ’s industry map for education. During check-in participants
were invited to draw a map of their industry or field. Figure 2. _M2_ ’s
industry map for mental health. Figure 3. One of _A4_ ’s change cards,
discussing their expectations regarding generative AI’s ability to generate
still images. We designed change cards to: (1) scaffold an envisioning process
for individual participants about industry futures, through both open- and
closed-ended questions about changes they expect; (2) elicit reflection on the
participant’s feelings about those changes, through an open-ended prompt; and
(3) capture data that participants could revisit and build on in collaborative
discourse and workshop activities. The open-ended prompts on the card enabled
each participant to flexibly specify anything they found meaningful to
include, while closed-ended questions enabled us to determine concretely who
participants thought would be impacted by change, and the drivers of that
change. Participants completed change cards individually and then shared them
in a facilitated discussion. Figure 4. One of _L1_ ’s change cards, discussing
their expectations regarding quickly shifting demand for legal services.
Figure 5. _J5_ ’s policy suggests constraints on the use of generative AI in
the newsroom. We lightly customized the policy handout to each group’s
industry. Participants completed their policy handouts individually and then
shared them in a facilitated discussion. Figure 6. _B6_ ’s policy suggests
generative AI might be used to make compliance review more efficient for high
volume corporate communications.