# Synergy Among Flexible Demands: Forming a Coalition to Earn More from
Reserve Market

Peter A.V. Gade*†, Trygve Skjøtskift†, Henrik W. Bindner*, Jalal Kazempour*
*Department of Wind and Energy Systems, Technical University of Denmark, Kgs. Lyngby, Denmark
†IBM Client Innovation Center, Copenhagen, Denmark  Email addresses:
<EMAIL_ADDRESS>(P.A.V. Gade<EMAIL_ADDRESS>(T. Skjøtskift),
<EMAIL_ADDRESS>(H.W. Bindner<EMAIL_ADDRESS>(J. Kazempour).

###### Abstract

We address potential synergy among flexible demands and how they may earn more
collectively than individually by forming a coalition and bidding to the
reserve market. We consider frequency-supporting ancillary service markets,
particularly the manual Frequency Restoration Reserve (mFRR) market. The
coalition of flexible demands provides more reliable mFRR services, where in
comparison to individual demands, is penalized less for their potential
failure and is paid more for their successful activation. This synergy effect
is quantified as a function of the number of homogeneous assets in the
coalition. A subsequent payment allocation mechanism using Shapley values is
proposed to distribute the total earnings of the coalition among demands,
while incentivizing them to remain in the coalition. For our numerical study,
we use real price data from the Danish mFRR market in 2022.

###### Index Terms:

Demand-side flexibility, synergy effect, manual frequency restoration reserve,
Shapley values, payment allocation

##  I Introduction

###  I-A Background

It has been extensively addressed in the literature how the aggregation of
flexible demands can provide frequency-supporting ancillary services to the
power system [1], [2]. By ancillary services, we refer to various forms of
reserves, booked by the Transmission System Operator (TSO) in advance, to
activate them in the operational stage, if necessary. The key for ancillary
service provision by the aggregation of flexible demands is the availability
of a baseline forecast of total consumption. The TSO should approve in advance
the process adopted by the aggregation of demands for their baseline forecast.
This has been prescribed in the official documentation of the Danish TSO,
Energinet, issued for the pre-qualification of demand-side resources for
ancillary service provision [3].

The aggregation of flexible demands is incentivized for at least two reasons:
(i) to meet the minimum bid size requirement, if it exists, for ancillary
service markets [4], and (ii) to unlock the potential synergy among flexible
demands. By synergy, we refer to operational circumstances under which the
aggregation of flexible demands, compared to individual demands, may provide
ancillary services with a higher level of reliability, i.e., a lower rate of
delivery failure in the activation stage. By this, the whole aggregation is
penalized less for their potential failure and paid more for their successful
activation. We do not consider a case that, by aggregation, flexible demands
may offer a larger volume of ancillary services. Hereafter, we refer to the
aggregation of flexible demands as a coalition, being operated by an
aggregator. Here, we consider that the aggregator represents the coalition,
and may charge flexible demands for its service, i.e., facilitating the
creation of the coalition, which is not part of this study.

Several private initiatives for the provision of demand-side flexibility via
forming coalitions are currently taking place in Denmark. For example, IBM is
developing their Flex Platform, aiming to aggregate and control heterogeneous
assets in commercial and industrial sectors. The aggregated flexibility is
then shaped as flexibility services to be sold in various ancillary service
markets running by the TSO, among which the market for manual Frequency
Restoration Reserve (mFRR), also known as tertiary reserve, has usually the
largest trading volume. The collected profit is supposed to be allocated among
flexible demands in a fair manner. In addition, flexible demands might be
further incentivized by being informed about their contribution to the CO2
savings.

###  I-B Research questions and our contributions

Aggregation platforms such as the Flex Platform of IBM face two fundamental
questions: (i) How many demand-side assets are needed to be aggregated in
order to unlock the potential synergy, resulting in sufficiently reliable
ancillary services as prescribed by the TSO? and (ii) How to allocate payments
ex-post to individual flexible demands within the coalition?

We answer the first question by quantifying the synergy effect in terms of
total earning of the coalition as a function of the number of assets within
the coalition. For simplicity, we assume identical flexible assets, and limit
our question to their number. The future work should extend the question by
also considering the heterogeneity of assets as a further degree of freedom.
We show how individual assets are inherently unpredictable on their own, but
comparatively more predictable within the coalition.

We then answer the second question by proposing Shapley values [5] as a
mechanism to reward flexible demands for their contribution to the coalition.
This provides desirable economic properties such as individual rationality and
budget balance that incentivize flexible demands to stay in the coalition, as
opposed to acting individually. We illustrate this payment mechanism using a
stylized example of five flexible demands, each with numerous assets, in a
coalition, for which the aggregator bids in the mFRR market only. We conduct
our simulations based on real price data of the Danish mFRR market from 2022.

###  I-C Status quo

Numerous studies in the literature explored important aspects of demand-side
flexibility such as feasibility and controllability [6], [7], [8], [9], [10],
[11]. However, an important aspect that has been largely overlooked is the
potential synergy among demand-side assets, such as freezers, heat pumps,
ventilation systems, etc. Reference [1] investigates the value of flexible
consumption but do not touch upon the synergy effect of a portfolio of assets,
although it is mentioned that market barriers exist such as the minimum
bidding size. It has been shown in [12] how a portfolio of supermarkets can
deliver a granular power response which is made possible by the number of
supermarkets and their assets. Although it has not been explicitly mentioned,
it refers to a form of synergy effect, because an aggregator requires a
certain number of controllable assets to deliver a granular power response.
However, the estimation and value of flexibility ex-ante is not tied together
with any synergy effect. Note that demand-side synergy is also known in other
domains, e.g., for strategic and organizational diversification [13], but here
we specifically address demand-side flexibility for ancillary services in
power systems.

For the coalition of flexible demands, the baseline estimation is key, from
which the aggregator estimates the flexible capacity, as prescribed by the
Danish TSO [3]. Note that the coalition of flexible demands does not
necessarily have an operational baseline schedule as a generation unit does
[14]. In this work, we show that the demand-side flexibility provision becomes
slightly less sensitive to the accuracy of the baseline estimation due to the
synergy effect among assets within the coalition. In addition, it is important
to estimate the baseline while being aware of potential counterfactual
consumption when a flexible demand is activated. This problem has been studied
extensively. For example, [15] explains why baselines are not necessarily
suited for harnessing flexibility in the distribution grid, whereas [16]
instead shows how a mechanism based on capacity limitation services may work
more successfully in practice. Nonetheless, for the TSO-level ancillary
services aiming to instantaneously balance total production and total demand
in the entire system, the baseline approach is generally adopted as a common
practice. Some studies have proposed more innovative mechanisms as
alternatives. For example, [17] proposes a mechanism by which the aggregator
relies on self-reported baselines from individual flexible demands, removing
the incentive to inflate baselines. In our setting, this is not
straightforward to be implemented, since flexible demands have generally no
expertise or even motivation to report their own baselines. Recall that
flexible demands have their other primary business purposes, which is not
flexibility provision, and prefer to not get involved in complicated
mechanisms.

###  I-D Paper organization

The rest of the paper is organized as follows. Section II introduces the
proposed simulation setup. This includes an introduction to the mFRR services,
the mathematical expression of the coalition profit and the synergy effect,
and finally the description of the Shapley values as the payment mechanism.
Section III provides simulation results, illustrating the synergy among a
number of assets and the corresponding payment allocation mechanism. Lastly,
Section IV concludes the paper and outlines potential directions for the
future work.

##  II Simulation setup

###  II-A mFRR services

Ancillary services including mFRR are exploited by the TSO to balance the
power system such that at any instant the total production meets the total
demand, maintaining the nominal power grid frequency (50 Hz in Europe). In
Denmark, mFRR (as the tertiary reserve) is deployed after the activation of
comparatively faster ancillary services when a frequency drop occurs — mFRR is
only used for up-regulation. The mFRR service providers are paid according to
their (i) capacity in terms of MW, and (ii) up-regulation in terms of MWh, if
activated. Often, the mFRR providers are not activated, so their upfront
earning from the mFRR capacity availability constitutes a passive income. In
our setup, we apply a penalty when the mFRR provider fails in the activation
stage, i.e., the capacity does not match the actual up-regulation. For the
coalition of flexible demands, this could happen due to erroneous flexible
capacity estimation or unexpected failures when activating individual assets
for up-regulation. An example reason for the activation failure is to avoid
the violation of the temperature thresholds of thermostatically controlled
loads. For further details about mFRR, see [3], [4], and [18].

###  II-B Simulation setup for the aggregator

We use historical mFRR market prices, balancing market prices, and spot (day-
ahead) market prices from DK1 bidding zone (western Denmark) in 2022 [19],
denoted by $\lambda_{h}^{\text{mFRR}}$, $\lambda_{h}^{\text{b}}$, and
$\lambda_{h}^{\text{s}}$, respectively, for every hour $h$. The constant
penalty price for the failure in the activation stage is denoted by
$\lambda^{\text{p}}$.

In the reservation stage, e.g., in day $D$-1, we assume that the aggregator
considers the current consumption pattern of the coalition as the power
baseline $P^{\text{Base}}_{h}$ for the next day and bids capacity
$p^{\text{mFRR}}_{h}$ to the mFRR market. This reserve will be activated by
the TSO the day after, if needed. In the activation stage, i.e., in day $D$,
the true consumption pattern might be different than the baseline, i.e., the
consumption pattern of the previous day. Therefore, if the mFRR capacity is
activated, indicated by a balancing price higher than the spot price, the
coalition may fail in successfully delivering the promised up-regulation
(i.e., load reduction). For example, assume in day $D$-1 the coalition has
promised a mFRR capacity of 20 kW for a specific hour of the next day.
However, in that hour of day $D$, their consummation might be below 20 kW,
therefore if activated, the coalition could not deliver the service. The
profit of the coalition can be calculated as

$\displaystyle-\underbrace{\sum_{h=1}^{24}\lambda^{\text{s}}_{h}P^{\text{Base}}_{h}}_{\textrm{Energy
cost}}+\underbrace{\sum_{h=1}^{24}\lambda_{h}^{\text{mFRR}}p^{\text{mFRR}}_{h}}_{\textrm{Reservation
payment}}$
$\displaystyle\quad\quad+\underbrace{\sum_{h=1}^{24}\lambda_{h}^{\text{b}}p^{\text{b},\uparrow}_{h}}_{\textrm{Activation
payment}}-\underbrace{\sum_{h=1}^{24}\lambda_{h}^{\text{b}}p^{\text{b},\downarrow}_{h}}_{\textrm{Rebound
cost}}-\underbrace{\sum_{h=1}^{24}\lambda^{\text{p}}s_{h}.}_{\textrm{Penalty
cost}}$ (1)

Accordingly, the profit of the coalition includes the energy cost for
purchasing baseline demands $P^{\text{Base}}_{h}$ at spot prices
$\lambda^{\text{s}}_{h}$, the reservation payment by selling mFRR services
$p^{\text{mFRR}}_{h}$ at mFRR market prices $\lambda_{h}^{\text{mFRR}}$, the
activation payment for up-regulations (i.e., load reduction)
$p^{\text{b},\uparrow}_{h}$ at balancing prices $\lambda_{h}^{\text{b}}$, the
rebound cost by extra consumption $p^{\text{b},\downarrow}_{h}$ at balancing
prices $\lambda_{h}^{\text{b}}$, and finally the penalty cost, incurred by the
up-regulation not delivered $s_{h}$, penalized at the constant price
$\lambda^{\text{p}}$. Note that the first two terms, i.e., the energy cost and
the reservation payment, realize in day $D$-1 according to the baseline.
However, the remaining three terms are calculated in day $D$ based on the true
consumption pattern and the TSO activation.

For the sake of simplicity, we ignore the potential rebound effect of flexible
demands by enforcing $p_{h}^{\text{b},\downarrow}=0,\ \forall{h}$. In
addition, the energy cost is constant irrespective of the flexibility
provision, and therefore it can be removed from (II-B). Thus, we rewrite the
profit as

$\displaystyle\underbrace{\sum_{h=1}^{24}\lambda_{h}^{\text{mFRR}}p^{\text{mFRR}}_{h}}_{\textrm{Reservation
payment}}+\underbrace{\sum_{h=1}^{24}\lambda_{h}^{\text{b}}p^{\text{b},\uparrow}_{h}}_{\textrm{Activation
payment}}-\underbrace{\sum_{h=1}^{24}\lambda^{\text{p}}s_{h}.}_{\textrm{Penalty
cost}}$ (2)

In reality, there is a bidding process for both capacity and up-regulation,
however, it is discarded for simplicity. Furthermore, we do not consider the
control aspect of the coalition, i.e., the challenge of effectively following
the required response within an hour of up-regulation.

In (2), $p^{\text{mFRR}}_{h}$, $p^{\text{b},\uparrow}_{h}$, and $s_{h}$
correspond to the whole coalition. Each asset $i$ in the coalition has its own
baseline for power consumption, $p_{h,i}$ $\forall{i}\in\mathcal{I}$, such
that

$\displaystyle p^{\text{mFRR}}_{h}$
$\displaystyle=\sum_{i}p^{\text{mFRR}}_{h,i}$ (3a) $\displaystyle
p^{\text{b},\uparrow}_{h}$ $\displaystyle=\sum_{i}p^{\text{b},\uparrow}_{h,i}$
(3b) $\displaystyle s_{h}$ $\displaystyle=\sum_{i}s_{h,i}.$ (3c)

###  II-C Modeling individual baselines and quantifying the synergy

For simplicity, we consider homogeneous assets that are supposed to consume 1
kW in one hour of the day, and do not consume any power during the rest of the
day. An example for such an asset is a ventilation unit with on/off control.
We uniformly distribute assets with 1-hour 1-kW consumption over the day, such
that the baseline forecast $p_{h,i}$ for asset $i$ in hour $h$ is defined as

$\displaystyle p_{h,i}\thinspace=\begin{cases}1&\text{if}\quad
h\sim\mathcal{U}(1,24)\\\ 0&\text{otherwise.}\end{cases}$ (4)

For an aggregator, it is therefore complex to estimate $p^{\text{mFRR}}_{h,i}$
individually, but as the number of assets increases, the consumption of the
coalition converges to a predictable uniform consumption for all
$h\in\\{1,\ldots,24\\}$, so $p^{\text{mFRR}}_{h}$ becomes more predictable.
Here, the predictability simply means the prediction of the power consumption
for the next day, for which more advanced methods can be used [15]. This is a
stylized example as most assets have some degree of predictability, but it is
sufficient to show a relevant problem for coalitions of small-scale uncertain
demand-side assets.

Given the profit definition as in (2), the synergy effect of the coalition can
be quantified as

$\displaystyle\text{Synergy effect}=\frac{\text{Coalition
profit}}{\sum_{i\in\mathbb{I}}\text{Asset {i}'s profit}}$ (5)

where the synergy effect is simply defined as the ratio between the coalition
profit and the sum of individual asset profits. The difference between the two
will be due to the activation payment and the penalty cost, as the reservation
payments are the same.

###  II-D Shapley values as the payment mechanism

The Shapley value is a well-known mechanism to allocate contributions in a
cooperative game [5]. This notion fits perfectly with the concept of synergy
effect in a coalition of flexible demands. By using Shapley values, we fairly
allocate ex-post the total profit, expressed as in (2), collected by the
aggregator, among flexible demands.

Let $\mathcal{D}=\\{1,\ldots,D\\}$ denote the set of flexible demands $d$,
where $|\mathcal{D}|$ is the number of flexible demands. Each demand may
contain multiple assets, such that $|\mathcal{D}|$ demands altogether have
assets $\mathcal{I}=\\{1,\ldots,I\\}$. Every asset is modeled using (4).
Inspired by [5], the Shapley value $\phi_{d}$ for the flexible demand $d$,
i.e., the payment allocated to that demand, is calculated by

$\displaystyle\phi_{d}$
$\displaystyle=\sum_{\mathcal{S}\subseteq\mathcal{D},d\in\mathcal{S}}\frac{(|\mathcal{S}|-1)!\
(|\mathcal{D}|-|\mathcal{S}|)!}{|\mathcal{D}|!}\Big{[}v(\mathcal{S})-v(\mathcal{S}\backslash\\{d\\})\Big{]},$
(6)

where $\mathcal{S}$ represents every possible non-empty subset of the
coalition, $|\mathcal{S}|$ is the number of possible subsets, and
$v(\mathcal{S})$ is the value of the coalition subset $\mathcal{S}$, which is
the corresponding profit formulated as in (2). Similarly,
$v(\mathcal{S}\backslash\\{d\\})$ represents the value of coalition subset
$\mathcal{S}$ excluding the flexible demand $d$ with its corresponding assets.
The grand coalition is the one including all demands, whose value (profit) is
given by $v(\mathcal{D})=\sum_{d\in\mathcal{D}}\phi_{d}$.

The Shapley value in (6) can be thought of as the average marginal
contribution of the flexible demand $d$ across all possible coalitions in
$\mathcal{D}$. It can only be computed exactly for a relatively small number
of flexible demands, as the number of possible non-empty coalitions is equal
to $2^{|\mathcal{D}|}-1$. In this paper, we consider 5 demands, ending up in
31 possible coalitions. The Shapley values can be approximated when
$|\mathcal{D}|$ grows [20]. Note that the Shapley mechanism has desirable
economic properties such as individual rationality and budget balance.

##  III Simulation Results

We consider a coalition of five flexible demands, i.e.,
$\mathcal{D}=\\{d_{1},d_{2},d_{3},d_{4},d_{5}\\}$, with 1000 identical assets
in total. Each asset consumes 1 kW in one hour of the day, and nothing in the
remaining hours. By an on/off control, the consumption reduces from 1 kW to
zero. Figure 1 shows the consumption portfolio for a sample day, where 1000
assets, according to (4), are uniformly distributed among 24 hours.

We run our simulation over 233 days with the same demands, assets, and
ownership, however the daily consumption pattern may differ. As mentioned in
Section III, the consumption in one day is considered as the baseline for the
next day, while the true consumption pattern in the next day might be
different. The is the reason that the coalition may fail in successfully
delivering the mFRR services, if activated. In particular, this happens if the
aggregator has over-promised in the reservation stage, while in the activation
stage the consumption level is comparatively lower. We will show in this
section that, owed to the synergy effect, it is less likely that the coalition
with a comparatively higher number of assets fails to deliver the service.

Figure 2 illustrates the mFRR market prices $\lambda^{\text{mFRR}}_{h}$ as
well as balancing market prices $\lambda^{\text{b}}_{h}$ and spot (day-ahead)
market prices $\lambda^{\text{s}}_{h}$ for the first 233 days of 2022 in DK1.
The mFRR service is activated by the TSO in every hour $h$ if
$\lambda^{\text{b}}_{h}>\lambda^{\text{s}}_{h}$. The penalty price
$\lambda^{\text{p}}$ is fixed to 0.1 DKK/kWh. All source codes and input data
are publicly shared in [21].

Figure 1: The consumption profile of a coalition with five flexible demands,
owning 1000 assets in a sample day. Each asset consumes 1 kW in one hour of
the day. Figure 2: Spot market prices ($\lambda^{\text{s}}_{h}$), balancing
market prices ($\lambda^{\text{b}}_{h}$), and mFRR market prices
($\lambda^{\text{mFRR}}_{h}$) over the first 233 days of 2022 in DK1.

Figure 3 shows the simulation results, where the synergy effect, as defined in
(5), is quantified for an increasing number of assets, up to 1000. Even with
such uncertain assets, it only takes around 400 assets to get the synergy
effect curve flattened around 1.9.

Figure 3: Simulation results: The synergy effect by increasing the number of
assets. The rolling mean shows the average of the past 40 point values.

Figure 4 shows the Shapley values (payments) in a simulation of an extreme
case, wherein the flexible demand $d_{1}$ always fails in the activation
stage. In other words, the assets of $d_{1}$ never up-regulate and only
contribute to the coalition with their reserve capacity (which can never be
utilized). We run the simulation for an increasing value of the penalty price
$\lambda^{\text{p}}$. This figure shows that $d_{1}$ by being within the
coalition gets a non-negative payment when $\lambda^{\text{p}}<1.5$. This is
explained by the price data and how often the TSO calls for an activation
(recall it happens when $\lambda^{\text{b}}>\lambda^{\text{s}}$). If the power
grid would need more up-regulation services, we could expect $d_{1}$ loses
money with penalty prices even lower than 1.5 DKK/kWh. The orange curve shows
the payment to $\mathcal{D}/\\{d_{1}\\}$, i.e., to the aggregation of four
demands $d_{2}$ to $d_{5}$, when the coalition includes $d_{1}$, whereas the
green curve shows the same payment when $d_{1}$ was not a member of the
coalition. The difference of these two curves shows that
$\mathcal{D}/\\{d_{1}\\}$ benefits from having $d_{1}$ in the coalition, even
though $d_{1}$ gets negative payments. Hence, $\mathcal{D}/\\{d_{1}\\}$ is
better off with $d_{1}$ in the coalition. Similarly, the comparison of blue
and red curves shows that $d_{1}$ also prefers to be part of the coalition by
getting paid more (or paying less back). This shows all demands prefer to stay
in the coalition.

Figure 4: Simulation results: The impact of the penalty price
$\lambda^{\text{p}}$ on Shapley values (payments $\phi$). The orange curve
shows the payment to $\mathcal{D}/\\{d_{1}\\}$, i.e., demands $d_{2}$ to
$d_{5}$ when $d_{1}$ is a coalition member. The green curve shows the same
payment if $d_{1}$ was not a member of the coalition. Likewise, the blue (red)
curve shows the payment $\phi_{d_{1}}$ to $d_{1}$ when it is (it is not) a
member of the coalition.

##  IV Conclusion

This paper illustrated the synergy effect of a coalition of flexible demands,
and quantified it in terms of the number of assets bidding to the mFRR market.
We also discussed how flexible demands can be fairly paid ex-post using
Shapley values. By this, our simulation results showed that all flexible
demands are incentivized to stay in the coalition, as opposed to acting on
their own. Hence, the synergy effect allows flexible demands to balance the
power grid while receiving a revenue for doing so.

As potential directions for the future work, it is of interest to consider
dissimilar assets, treating the heterogeneity as another degree of freedom for
further unlocking potential synergy. One could hypothesize that dissimilar
assets can further complement each other in terms of flexibility provision.
One relevant example could be photovoltaic parks equipped with batteries
and/or electrolyzers, providing various frequency services. Moreover, as the
number of flexible demands increases, approximate Shapley values must be used
due to computational reasons. It is interesting to explore how it impacts the
fairness and distribution of payments.

## References

  * [1] B. Biegel, L. H. Hansen, J. Stoustrup, P. Andersen, and S. Harbo, “Value of flexible consumption in the electricity markets,” _Energy_ , vol. 66, pp. 354–362, 2014.
  * [2] J. MacDonald, P. Cappers, D. Callaway, and S. Kiliccote, “Demand response providing ancillary services: A comparison of opportunities and challenges in the US wholesale markets,” 2012, Lawrence Berkeley National Laboratory Report. [Online]. Available: https://www.osti.gov/servlets/purl/1632141
  * [3] Energinet (Danish TSO), “Prequalification of units and aggregated portfolios,” 2021. [Online]. Available: https://en.energinet.dk/Electricity/Ancillary-Services/Prequalification-and-test
  * [4] ——, “Introduktion til systemydelser,” 2021. [Online]. Available: https://energinet.dk/-/media/8F2B403B3A724197A179FF6DFD9A926C.pdf
  * [5] L. S. Shapley, _A value for n-person games_. Princeton University Press, Princeton, NJ, 1997.
  * [6] D. E. Morales Bondy, J. MacDonald, E. C. Kara, O. Gehrke, K. Heussen, D. Chassin, S. Kiliccote, and H. W. Bindner, “Redefining requirements of ancillary services for technology agnostic sources,” in _Proceedings of the 51st Hawaii International Conference on System Sciences_ , 2018, pp. 1–10.
  * [7] D. E. Morales Bondy, A. Thavlov, J. B. M. Tougaard, and K. Heussen, “Performance requirements modeling and assessment for active power ancillary services,” in _IEEE Manchester PowerTech Conference_ , 2017, pp. 1–6.
  * [8] D. E. Morales Bondy, O. Gehrke, A. Thavlov, K. Heussen, A. M. Kosek, and H. W. Bindner, “Procedure for validation of aggregators providing demand response,” in _Power Systems Computation Conference (PSCC)_ , 2016, pp. 1–7.
  * [9] D. E. Morales Bondy, G. T. Costanzo, K. Heussen, and H. W. Bindner, “Performance assessment of aggregation control services for demand response,” in _IEEE PES Innovative Smart Grid Technologies (ISGT Europe)_ , 2014, pp. 1–6.
  * [10] B. Biegel, M. Westenholz, L. H. Hansen, J. Stoustrup, P. Andersen, and S. Harbo, “Integration of flexible consumers in the ancillary service markets,” _Energy_ , vol. 67, pp. 479–489, 2014.
  * [11] D. S. Callaway and I. A. Hiskens, “Achieving controllability of electric loads,” _Proceedings of the IEEE_ , vol. 99, no. 1, pp. 184–199, 2011.
  * [12] R. Pedersen, J. Schwensen, B. Biegel, J. Stoustrup, and T. Green, “Aggregation and control of supermarket refrigeration systems in a smart grid,” in _IFAC Proceedings Volumes_ , 2014, pp. 9942–9949.
  * [13] G. Ye, R. L. Priem, and A. A. Alshwer, “Achieving demand-side synergy from strategic diversification: How combining mundane assets can leverage consumer utilities,” _Organization Science_ , vol. 23, no. 1, pp. 207–224, 2012.
  * [14] P. A. Gade, T. Skjøtskift, H. W. Bindner, and J. Kazempour, “Ecosystem for demand-side flexibility revisited: The Danish solution,” _The Electricity Journal_ , vol. 35, no. 9, p. 107206, 2022.
  * [15] C. Ziras, C. Heinrich, and H. W. Bindner, “Why baselines are not suited for local flexibility markets?” _Renewable and Sustainable Energy Reviews_ , vol. 135, p. 110357, 2021.
  * [16] C. Heinrich, C. Ziras, T. V. Jensen, H. W. Bindner, and J. Kazempour, “A local flexibility market mechanism with capacity limitation services,” _Energy Policy_ , vol. 156, p. 112335, 2021.
  * [17] D. Muthirayan, D. Kalathil, K. Poolla, and P. Varaiya, “Mechanism design for demand response programs,” _IEEE Transactions on Smart Grid_ , vol. 11, no. 1, pp. 61–73, 2019.
  * [18] Energinet (Danish TSO), “Ancillary services to be delivered in Denmark – Tender conditions,” 2021. [Online]. Available: https://en.energinet.dk/Electricity/Ancillary-Services/Tender-conditions-for-ancillary-services
  * [19] ——, “Energi data service,” 2022. [Online]. Available: https://www.energidataservice.dk/
  * [20] J. Castro, D. Gómez, and J. Tejada, “Polynomial calculation of the Shapley value based on sampling,” _Computers & Operations Research_, vol. 36, no. 5, pp. 1726–1730, 2009.
  * [21] “Github repository,” 2023. [Online]. Available: https://github.com/PeterAVG/synergy_paper