# The Value of Ancillary Services for Electrolyzers

Andrea Gloppen Johnsen1, Lesia Mitidatri1, Donato Zarrilli2, and Jalal
Kazempour1  1 Department of Wind and Energy Systems, Technical University of
Denmark, Kgs. Lyngby, Denamrk  2 Siemens Gamesa Renewable Energy, Hamburg,
Germany
{anglopj, lemitri<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

While renewable hydrogen production is envisioned as the main business for
electrolyzers, the provision of frequency-supporting ancillary services to the
power grid can be seen as their potential by-products. This can generate
additional revenue streams for electrolyzers, accelerating their integration
by making them more financially attractive. This paper conducts a value
analysis for an electrolyzer in Denmark. We develop a mixed-integer linear
optimization model, wherein the physical characteristics of the electrolyzer
are accurately captured. This model enables the electrolyzer to make informed
bidding decisions in the day-ahead electricity as well as the frequency
containment reserve (FCR) and the manual frequency restoration reserve (mFRR)
markets. By carrying out an ex-post analysis based on historical activation,
we provide lower and upper bounds for the profit of the electrolyzer, such
that the true profit could lie in between depending how activation has been
modeled in the bidding stage. We find that an electrolyzer in the Danish
bidding zone DK1 could have earned 57% more in 2021 by proving ancillary
services, while this profit increase in both bidding zones DK1 and DK2 for
2022 could have been drastic.

###### Index Terms:

Electrolyzer, hydrogen, ancillary services, value analysis, mixed-integer
linear programming.

##  I Introduction

Electrolyzers and in general power-to-X facilities are envisioned as key
elements for green transition, as a solution to electrify hard-to-abate
sectors including heavy transport and energy-intensive industry [1].
Converting power to hydrogen and then to green fuels also facilitates
technically and financially the realization of ambitious projects such as two
energy islands in the Baltic and North Seas, each with $3$-GW offshore wind
capacity in the first stage, and more in the longer run [2]. Besides, in
future renewable-based power systems with flexibility scarcity, electrolyzers
as flexible power loads can considerably contribute to flexibility provision.
Among others, one main barrier against the rapid integration of electrolyzers
is uncertainty regarding their long-term profitability [3].

Aiming to accelerate the integration of electrolyzers, this paper provides a
value analysis on how much more an electrolyzer in Denmark could have earned
in $2021$ and $2022$ by the provision of ancillary services. Among others, we
consider frequency containment reserve (FCR) and manual frequency restoration
reserve (mFRR) services, since there are mature markets for these services in
Denmark with relatively high prices. The ability of electrolyzers to provide
FCR as a fast service is investigated in [4], concluding that electrolyzers
might have even faster response times than conventional generators for both
upwards and downward regulation. The value analysis requires the accurate
modeling of the physics of the electrolyzer as well as developing a bidding
strategy model, enabling the profit-maximizing electrolyzer to optimally
participate in day-ahead electricity, FCR, and mFRR markets, besides its
business in the hydrogen sector. For this purpose, we develop a mixed-integer
linear optimization model with a set of activation-aware constraints, which is
critical in the case of an energy-intensive service such as mFRR.

The current literature on the value analysis of ancillary services for
electrolyzers is limited. In the discussion paper [5] by the Danish
transmission system operator (TSO), Energinet, such a value is analyzed with a
simple power-to-hydrogen conversion factor, discarding physical
characteristics of electrolyzers and the effect of service activation on
hydrogen production. A value estimation of the FCR services for an
electrolyzer in the Nordic synchronous region ($\rm{DK}2$) is conducted in
[6], where a detailed model of the electrolyzer physics is adopted, showing
that FCR participation could account for $72$% of the total electrolyzer
revenues. However, the activation of reserves is not accounted for as no
energy-intensive reserve products are considered. Similarly, [7] and [8]
investigate the economic feasibility of ancillary service provision for an
electrolyzer located in France and Germany, respectively, again without
accounting for activation. Finally, [9] conducts an economic evaluation of an
electrolyzer which enforces through chance constraints that the activated
reserve will not exceed the capacity with a high probability. However, it
allows the electrolyzer to overbid reserves, relying on the assumption of
having an accurate probabilistic forecasting of the reserve activation. This
paper proposes a pragmatic activation-aware approach for the participation of
electrolyzers in ancillary service markets.

The rest of the paper is structured as follows: Section II describes the
physics of electrolyzers and explains the target markets. Section III provides
the bidding strategy model. Section IV presents the numerical results.
Finally, Section V concludes the paper.

##  II Preliminaries

Here, we describe the electrolyzer physics and target markets that forms the
basis of the model stated in Section III.

###  II-A Electrolyzers

Electrolyzers are electrochemical assets that consume power and water,
splitting the water molecules into oxygen and hydrogen. We limit our focus on
conventional electrolysis technologies such as alkaline and polymer
electrolyte membrane In reality, the electrolyzer efficiency is a non-linear
function of the consumed power, with a peak efficiency at around $30$% nominal
loading. To avoid a non-linear model while accurately representing the physics
of the electrolyzer, we apply an electrolyzer model as proposed by [10], where
the hydrogen production curve is approximated by a piece-wise linear function,
at the cost of adding a set of binary variables.

Furthermore, electrolyzers are subject to three separate operational states,
namely online, standby, and off. In the online state, the electrolyzer
produces hydrogen and consumes electricity. Due to safety concerns, this state
has a minimum loading of around $10$%. In the standby state, the electrolyzer
is not producing hydrogen, but consuming a small amount of electrical energy
to maintain the ability to resume hydrogen production and transition into the
online state within seconds or minutes. Finally, in the off state, the system
is shut off completely, no longer consuming electricity nor producing
hydrogen. Once the electrolyzer enters this state, it requires up to a couple
of hours to transition to the online state.

###  II-B Bilateral Contracts and Target Markets

The produced hydrogen is assumed to be sold through bilateral hydrogen
purchase agreements (HPAs) at a fixed hydrogen price, as no market for
hydrogen currently exists. In our formulation, the hydrogen demand is
represented through a set of tube-trailers that arrive on-site and depart at a
given daily schedule. When a tube-trailer has arrived on-site, it functions as
a gas storage, with a storage capacity that must be respected. Further, if no
tube-trailer is present on-site, or any present tube-trailer is full, the
system cannot produce hydrogen as there is no off-take possibility. Another
important aspect of the HPA is the possibility of a minimum demand requirement
over a given time period, for example daily. This requirement provides
certainty for the off-taker but may add operational challenges to the
producer, obliging them to produce under unprofitable price conditions.

As reported in the Energinet report [5], electrolyzers are expected to operate
in multiple frequency-supporting ancillary service markets, bringing an
opportunity for additional revenue streams111The automatic FRR (aFRR) market
is disregarded as its procurement in Denmark follows a pay-as-bid scheme with
monthly auctions [11].. In addition, electrolyzers must participate in the
day-ahead electricity market to procure electricity, if not being
(sufficiently) supplied by co-located wind or solar units. Note that the
recent renewable fuels of non-biological origin (RFNBO) delegated act by the
European Commission [12] defines certain operational conditions under which
electrolyzers producing green hydrogen are allowed to directly buy power from
the grid. This paper considers a single electrolyzer only, without being
combined with wind turbines or other renewable assets. Therefore, the
electrolyzer buys all power it requires from the grid, discarding RFNBO
conditions. Now, we briefly describe target markets for electrolyzers in
chronological order of market closure time in Denmark.

FCR market: In the Continental Europe synchronous area including the Danish
bidding zone $\rm{DK}1$, FCR, also known as primary reserve, is the fastest
frequency service — note that it is not the case in the Nordic synchronous
area, including the other Danish bidding zone, i.e., $\rm{DK}2$. The FCR
capacity market is a mechanism used to stabilize the electricity grid by
providing a reserve of power that can be automatically activated within
seconds in response to changes in frequency. The product is symmetric, meaning
that a placed bid is identical both for upward and downward regulation. In
$\rm{DK}1$, the FCR market closes at $8$ $\rm{AM}$ the day before delivery,
and bids can be placed for every $4$-hour blocks. The market is operated with
uniform pricing. In all target markets, it is assumed that the electrolyzer is
price-taker. Therefore, the electrolyzer forecasts the FCR price and decides
to bid a reserve quantity accordingly. By this, the decision variable is the
quantity bid. The forecasted price together with the quantity bid form the
final bid of the electrolyzer to be placed.

mFRR market: The product being traded in this market is the reserved capacity
for manual frequency services, also known as tertiary reserve. The mFRR market
is a mechanism used to ensure sufficient capacities to balance electricity
supply and demand in real time. It is a reserve that can be activated within
$15$ minutes in response to imbalances in the system. The market is split into
two separate auctions for the procurement of the reserve capacity and the
energy activation of the reserve. First, the mFRR market is closed at $9$:$30$
$\rm{AM}$ the day before delivery. Bids placed consist of quantity in terms of
reserved capacity for every $1$-hour interval, and a price per MW per hour.
The market is settled with uniform pricing. Once a reserve bid is accepted,
the electrolyzer is obliged to submit a corresponding regulation bid (a price)
for the energy activation of the reserve into the balancing market. Whenever
needed, bids are activated following the merit order curve, and activation is
remunerated with the uniform balancing price.

Day-ahead electricity market: The electrolyzer places bids for quantity and
price to procure electricity for the following day. A separate bid consisting
of the forecasted day-ahead price and a quantity can be placed for each hour.
In Denmark, the day-ahead market gate closure is at noon the day before
delivery, and is settled with uniform pricing. The day-ahead bid should
respect the reserve bids placed in the FCR and mFRR markets. We assume that
there is no information gain between the different gate closure times, and
therefore that all bids can be placed simultaneously.

##  III Model Formulation

Notational remark: Hereafter, lower-case symbols are variables, whereas upper-
case and Greek symbols are parameters. In addition, symbol $z$ is used for
various binary variables.

###  III-A Electrolyzer Profit

This section presents a deterministic mixed-integer linear programming (MILP)
problem, maximizing the total profit of an electrolyzer operating in the day-
ahead, FCR, and mFRR markets, while selling hydrogen at a fixed price with a
minimum production requirement. The profit-maximizing objective function reads
as

$\displaystyle\underset{\mathcal{X}}{\operatorname{max}}\hskip 5.69046pt$
$\displaystyle\sum_{t\in\mathcal{T}}\Big{(}h^{\rm{e}}_{t}\lambda^{\rm{h}}+p^{\rm{m\uparrow}}_{t}\lambda^{\rm{m\uparrow}}_{t}+p^{\rm{m\downarrow}}_{t}\lambda^{\rm{m\downarrow}}_{t}-p^{\rm{DA}}_{t}\lambda^{\rm{DA}}_{t}\Big{)}$
$\displaystyle+$
$\displaystyle\sum_{i\in\mathcal{I}}p^{\rm{F}}_{i}\lambda^{\rm{F}}_{i}\Delta
T^{\rm{F}},$ (1)

where $\mathcal{X}$ is the set of variables, and will be defined later at the
end of this section. While index $t\in\mathcal{T}$ represents $1$-hour time
intervals, $i\in\mathcal{I}$ denotes $4$-hour periods. Both these indexes are
needed to model the FCR market. The first term in (1) is the revenue of
selling hydrogen, which is the product of hydrogen production $h^{\rm{e}}_{t}$
and the fixed hydrogen price $\lambda^{\rm{h}}$. The mFRR capacity bids
(second and third terms) are split into that of the upward
$p^{\rm{m\uparrow}}_{t}$ and downward $p^{\rm{m\downarrow}}_{t}$ reserves to
be sold at forecasted prices $\lambda^{\rm{m\uparrow}}_{t}$ and
$\lambda^{\rm{m\downarrow}}_{t}$, respectively. The fourth term represents the
cost of procuring power from the day-ahead market, including the quantity bid
$p^{\rm{DA}}_{t}$ and forecasted price $\lambda^{\rm{DA}}_{t}$. Finally, the
last term corresponds to the profit of selling FCR capacity, where the
quantity $p^{\rm{F}}_{i}$ is placed for a $4$-hour interval $i$ at forecasted
price $\lambda^{\rm{F}}_{i}$, where $\Delta T^{\rm{F}}=4$. At the time of the
bidding decisions, it is complicated to provide accurate forecasts for hourly
balancing prices of the day of delivery. Therefore, we neglect the potential
revenues/costs from activation in real time, and maximize the total profit to
be earned in the day-ahead stage only.

We can categorize constraints in the three strands of electrolyzer, bidding,
and activation constraints, which will be given in the next three subsections.

###  III-B Electrolyzer Constraints

The electrolyzer is modeled with a varying efficiency level, depending on the
operational point, via a piece-wise formulation of the hydrogen production
curve. We also model its three operational states, as already explained in
Section II-A.

Piece-wise hydrogen production curve: Each segment $s$ on the production curve
is defined within a range of electrolyzer consumption power, i.e.,
$\underline{P}_{s}$ and $\overline{P}_{s}$. These segments are activated based
on the scheduled electrolyzer power consumption $p^{\rm{e}}_{t,s}$, if no
reserves are activated:

$\displaystyle\underline{P}_{s}z^{\rm{e}}_{t,s}\leq
p^{\rm{e}}_{t,s}\leq\overline{P}_{s}z^{\rm{e}}_{t,s}$ $\displaystyle\forall
t\in\mathcal{T},s\in\mathcal{S},\ $ (2a) where $z^{\rm{e}}_{t,s}$ is a binary
variable for the segment selection. The rationale of using these binary
variables is that the concave relaxation is no longer tight due to the
presence of reserve revenues in the objective function. Further, we should
ensure that at most one segment can be active at any time, i.e.,
$\displaystyle\sum_{s\in\mathcal{S}}z^{\rm{e}}_{t,s}\leq 1$
$\displaystyle\forall t\in\mathcal{T}.$ (2b)

The hydrogen production $h^{\rm{e}}_{t}$ is defined as a linear function of
the electrolyzer power consumption $p^{\rm{e}}_{t,s}$, with a slope $A_{s}$
and intercept $B_{s}$ depending on the active segment, i.e.,

$\displaystyle
h^{\rm{e}}_{t}=\sum_{s\in\mathcal{S}}\big{(}A_{s}p^{\rm{e}}_{t,s}+B_{s}z^{\rm{e}}_{t,s}\big{)}\Delta_{\rm{T}}$
$\displaystyle\forall t\in\mathcal{T},$ (2c)

where $\Delta_{\rm{T}}\\!=\\!1$. For a coherent formulation, an auxiliary
variable $p^{\rm{tot}}_{t}$ is defined, representing the total power
consumption across segments at any time period $t$:

$\displaystyle p^{\rm{tot}}_{t}=\sum_{s\in\mathcal{S}}p^{\rm{e}}_{t,s}$
$\displaystyle\forall t\in\mathcal{T}.$ (2d)

Operating states: The three operating states of the electrolyzer are defined
by one binary variable each, i.e., $z^{\rm{on}}_{t}$, $z^{\rm{sb}}_{t}$, and
$z^{\rm{off}}_{t}$. The online state $z^{\rm{on}}_{t}$ is defined so that
hydrogen production occurs in the online state only:

$\displaystyle z^{\rm{on}}_{t}=\sum_{s\in\mathcal{S}}z^{\rm{e}}_{t,s}$
$\displaystyle\forall t\in\mathcal{T}.$ (2e)

It is also possible to define the online state as the sum of all segment
selection variables without defining a new binary variable, but it is here
defined for clarity. The standby state $z^{\rm{sb}}_{t}$ is defined as

$\displaystyle p^{\rm{sb}}_{t}=z^{\rm{sb}}_{t}P^{\rm{sb}}$
$\displaystyle\forall t\in\mathcal{T},$ (2f)

stating that there is no hydrogen production, but the electrolyzer is still
consuming power $p^{\rm{sb}}_{t}$ to keep the system pressurized and heated
for quick start-up of the production. The power consumption is assumed
constant at $P^{\rm{sb}}$. In case of a complete shut down of the electrolyzer
and surrounding system $z^{\rm{off}}_{t}$, there is a minimum down-time
required due to the time it takes to re-heat and pressurize the system. The
down time is defined by the $t$-dependent set $\mathcal{N}_{t}$ as

$\displaystyle z^{\rm{off}}_{t}-z^{\rm{off}}_{t-1}\leq z^{\rm{off}}_{n}$
$\displaystyle\forall t\in\mathcal{T}\setminus\\{1\\},n\in\mathcal{N}_{t},$
(2g)

where $\mathcal{N}_{t}$ is defined as the $N^{\rm{down}}$ next periods from
$t$. Finally, the electrolyzer must only be in one state at any time, i.e.,

$\displaystyle z^{\rm{on}}_{t}+z^{\rm{sb}}_{t}+z^{\rm{off}}_{t}=1$
$\displaystyle\forall t\in\mathcal{T}.$ (2h)

###  III-C Bidding Constraints

The bids into the day-ahead, FCR, and mFRR capacity markets are all limited by
the scheduled electrolyzer consumption and power capacity.

Day-ahead quantity bids: It is defined as the total scheduled consumption of
the electrolyzer, including the stand-by consumption:

$\displaystyle p^{\rm{DA}}_{t}=p^{\rm{tot}}_{t}+p^{\rm{sb}}_{t}$
$\displaystyle\forall t\in\mathcal{T}.$ (3a)

Note that the power consumption of the compressor is assumed to be embodied
within the production curve of the electrolyzer, therefore it is not
explicitly indicated in (3a).

Reserve quantity bids: As the FCR market is symmetric, i.e., the identical
capacity $p^{\rm{F}}_{i}$ is reserved for activation in both directions, it
must be limited both by the ability to up regulate and down regulate the power
consumption of the electrolyzer. The mFRR reserve is, however, split between
the upwards and downwards reserve, hence each reserve bid
$p^{\rm{m\downarrow}}_{t}$ and $p^{\rm{m\uparrow}}_{t}$ is limited in its
respective direction only. As the electrolyzer can participate in both markets
simultaneously, it is the sum of reserves in each direction that is
constrained. For the downward reserve, this is simply limited by the
difference between the electrolyzer capacity $C^{\rm{e}}$ and the scheduled
power consumption $p^{\rm{tot}}_{t}$. Further, as the electrolyzer has a cold
start time of up to $2$ hours, the reserve cannot be provided if the
electrolyzer is shut off. For the downward reserve we enforce

$\displaystyle p^{\rm{F}}_{i}+p^{\rm{m\downarrow}}_{t}\leq
C^{\rm{e}}\big{(}1-z^{\rm{off}}_{t}\big{)}-p^{\rm{tot}}_{t}$
$\displaystyle\forall t\in\mathcal{T}_{i},i\in\mathcal{I},$ (3b)

where $\mathcal{T}_{i}$ is the set of hours $t$ within the $4$-hour interval
$i$. For the upward reserve, the total bids are limited by the difference in
the scheduled power consumption and the minimum allowed electrolyzer power
$\underline{E}$, i.e.,

$\displaystyle p^{\rm{F}}_{i}+p^{\rm{m\uparrow}}_{t}\leq
p^{\rm{tot}}_{t}-\underline{E}\big{(}1-z^{\rm{off}}_{t}\big{)}$
$\displaystyle\forall t\in\mathcal{T}_{i},i\in\mathcal{I},$ (3c)

where the off-state binary variable is included to avoid infeasibility in the
case of no consumption.

Minimum and maximum bid sizes: Both FCR and mFRR capacity markets operate with
minimum and maximum allowed bid sizes. These limits are enforced by the
following constraints, with the binary variable $z^{\rm{F}}_{i}$ enabling a
FCR bid in the range of $\underline{P}^{\rm{F}}$ and $\overline{P}^{\rm{F}}$.
The binary variables $z^{\rm{m\uparrow}}_{t}$ and $z^{\rm{m\downarrow}}_{t}$
serve similarly for the mFRR bids:

$\displaystyle\underline{P}^{\rm{F}}z^{\rm{F}}_{i}\leq
p^{\rm{F}}_{i}\leq\overline{P}^{\rm{F}}z^{\rm{F}}_{i}$ $\displaystyle\forall
i\in\mathcal{I}$ (3d)
$\displaystyle\underline{P}^{\rm{m}}z^{\rm{m\downarrow}}_{t}\leq
p^{\rm{m\downarrow}}_{t}\leq\overline{P}^{\rm{m}}z^{\rm{m\downarrow}}_{t}$
$\displaystyle\forall t\in\mathcal{T}$ (3e)
$\displaystyle\underline{P}^{\rm{m}}z^{\rm{m\uparrow}}_{t}\leq
p^{\rm{m\uparrow}}_{t}\leq\overline{P}^{\rm{m}}z^{\rm{m\uparrow}}_{t}$
$\displaystyle\forall t\in\mathcal{T}.$ (3f)

###  III-D Activation Constraints

The capacity reserved in ancillary service markets can be activated upon
deviations of the grid frequency. This causes deviations in the hydrogen
production, which might be infeasible in a system where there are upper and
lower limits to the possible hydrogen off-take. For the FCR bids, it is
assumed that the activation is symmetric in both directions, so that the total
difference from the scheduled hydrogen production due to activation is
negligible. For the mFRR bids, however, the activation could be energy-
intensive, and a large deviation in the scheduled production could yield full
tube-trailers or unmet minimum demand requirements. Assuming an expected
upward mFRR activation $\alpha^{\rm{act\uparrow}}_{t}$ or a downward mFRR
activation $\alpha^{\rm{act\downarrow}}_{t}$ at time period $t$, a set of
constraints is defined to ensure that the capacity bids are feasible in terms
of deviations in hydrogen production. Note that
$\alpha^{\rm{act(.)}}_{t}\\!=\\!1$ refers to the full capacity activation for
one hour.

Upward mFRR activation: In this case, the actual power consumption
$\sum_{s}p^{\rm{act\uparrow}}_{t,s}$ of the electrolyzer is defined as

$\displaystyle\sum_{s\in\mathcal{S}}p^{\rm{act\uparrow}}_{t,s}=p^{\rm{tot}}_{t}-p^{\rm{m\uparrow}}_{t}\alpha^{\rm{act\uparrow}}_{t}$
$\displaystyle\forall t\in\mathcal{T}.$ (4a)

Let the binary variable $z^{\rm{act\uparrow}}_{t,s}$ define the range for
where a segment on the production curve is active based on the activated power
consumption. By this, we restrict $p^{\rm{act\uparrow}}_{t,s}$ by

$\displaystyle\underline{P}_{s}z^{\rm{act\uparrow}}_{t,s}\leq
p^{\rm{act\uparrow}}_{t,s}\leq\overline{P}_{s}z^{\rm{act\uparrow}}_{t,s}$
$\displaystyle\forall t\in\mathcal{T},s\in\mathcal{S},$ (4b)

while only one segment is allowed to be active:

$\displaystyle\sum_{s\in\mathcal{S}}z^{\rm{act\uparrow}}_{t,s}\leq 1$
$\displaystyle\forall t\in\mathcal{T}.$ (4c)

The actual hydrogen production following an upward activation can then be
calculated based on the power consumption and corresponding segment on the
production curve, i.e.,

$\displaystyle
h^{\rm{act\uparrow}}_{t}=\sum_{s\in\mathcal{S}}\big{(}A_{s}p^{\rm{act\uparrow}}_{t,s}+B_{s}z^{\rm{act\uparrow}}_{t,s}\big{)}\Delta_{\rm{T}}$
$\displaystyle\forall t\in\mathcal{T}.$ (4d)

Even if the full activation of mFRR occurs, the hydrogen production is still
constrained by the minimum hydrogen demand $\underline{H}$ over time period
$\mathcal{T}$, i.e.,

$\displaystyle\sum_{t\in\mathcal{T}}h^{\rm{act\uparrow}}_{t}\geq\underline{H}.$
. (4e)

Downward mFRR activation: In this case, the actual power consumption
$\sum_{s}p^{\rm{act\downarrow}}_{t,s}$ of the electrolyzer is defied as

$\displaystyle\sum_{s\in\mathcal{S}}p^{\rm{act\downarrow}}_{t,s}=p^{\rm{tot}}_{t}+p^{\rm{m\downarrow}}_{t}\alpha^{\rm{act\downarrow}}_{t}$
$\displaystyle\forall t\in\mathcal{T}.$ (4f)

We define the binary variable $z^{\rm{act\downarrow}}_{t,s}$ to indicate the
corresponding production curve segment. Similar to the upward activation
constraints, we enforce

$\displaystyle\underline{P}_{s}z^{\rm{act\downarrow}}_{t,s}\leq
p^{\rm{act\downarrow}}_{t,s}\leq\overline{P}_{s}z^{\rm{act\downarrow}}_{t,s}$
$\displaystyle\forall t\in\mathcal{T},s\in\mathcal{S}$ (4g)
$\displaystyle\sum_{s\in\mathcal{S}}z^{\rm{act\downarrow}}_{t,s}\leq 1$
$\displaystyle\forall t\in\mathcal{T}.$ (4h)

The actual hydrogen production following a downward activation can then be
calculated as

$\displaystyle
h^{\rm{act\downarrow}}_{t}=\sum_{s\in\mathcal{S}}(A_{s}p^{\rm{act\downarrow}}_{t,s}+B_{s}z^{\rm{act\downarrow}}_{t,s})\Delta_{\rm{T}}$
$\displaystyle\forall t\in\mathcal{T}.$ (4i)

In this case, the additional hydrogen production should respect the upper
limit of available capacity of tube-trailers on site. Let $d\in\mathcal{D}$ a
set of tube-trailers. A set of auxiliary variables is defined tracking the
dispensed hydrogen $h^{\rm{d}}_{t,d}$ and state of tube-trailers for the
activated hydrogen flow $s^{\rm{d}}_{t,d}$. These flows are then constrained
by the dispenser capacity $C^{\rm{d}}$, the tube-trailer availability
indicated by the binary parameter $Z_{t,d}$, and their capacity $S^{\rm{d}}$:

$\displaystyle
h^{\rm{act\downarrow}}_{t}=\sum_{d\in\mathcal{D}}h^{\rm{d}}_{t,d}$
$\displaystyle\forall t\in\mathcal{T}$ (4j) $\displaystyle
h^{\rm{d}}_{t,d}\leq C^{\rm{d}}Z_{t,d}$ $\displaystyle\forall
t\in\mathcal{T},d\in\mathcal{D}$ (4k) $\displaystyle
s^{\rm{d}}_{t,d}=h^{\rm{d}}_{t,d}$ $\displaystyle\forall t=1,d\in\mathcal{D}$
(4l) $\displaystyle s^{\rm{d}}_{t,d}=s^{\rm{d}}_{t-1,d}+h^{\rm{d}}_{t,d}$
$\displaystyle\forall t\in\mathcal{T}\setminus\\{1\\},d\in\mathcal{D}$ (4m)
$\displaystyle s^{\rm{d}}_{t,d}\leq S^{\rm{d}}$ $\displaystyle\forall
t\in\mathcal{T},d\in\mathcal{D}.$ (4n)

With separate sets of constraints for upward and downward activated hydrogen
flows, it is ensured that all market bids are feasible for any assumed
expected activation. This is intrinsically a conservative approach, as
activation in one direction can be fully or partially cancelled out by
activation in the other, which is not accounted for in this formulation.
However, accounting for this effect requires information regarding the timing
and frequency of activation, as the number of consecutive hours of activation
in one direction is of significance when constrained by tube trailer capacity
and minimum demand requirements. An alternative approach is to only apply the
activation constraints on the net activation. In the proposed formulation, the
risk can be adjusted through the selection of expected activation,
$\alpha^{\rm{act\uparrow}}_{t}$ and $\alpha^{\rm{act\downarrow}}_{t}$. If set
to zero, the model does not take activation into account at all. If set to
one, the bids are robust in terms of activation in any direction.

Now, we list variables as $\mathcal{X}$ = $\\{h^{\rm{act\uparrow}}_{t}$,
$h^{\rm{act\downarrow}}_{t}$, $h^{\rm{d}}_{t,d}$, $h^{\rm{e}}_{t}$,
$p^{\rm{act\uparrow}}_{t,s}$, $p^{\rm{act\downarrow}}_{t,s}$,
$p^{\rm{DA}}_{t}$, $p^{\rm{e}}_{t,s}$, $p^{\rm{F}}_{i}$,
$p^{\rm{m\uparrow}}_{t}$, $p^{\rm{m\downarrow}}_{t}$, $p^{\rm{sb}}_{t}$,
$p^{\rm{tot}}_{t}$, $s^{\rm{d}}_{t,d}$, $z^{\rm{act\uparrow}}_{t,s}$,
$z^{\rm{act\downarrow}}_{t,s}$, $z^{\rm{e}}_{t,s}$, $z^{\rm{F}}_{i}$,
$z^{\rm{m\uparrow}}_{t}$, $z^{\rm{m\downarrow}}_{t}$, $z^{\rm{off}}_{t}$,
$z^{\rm{on}}_{t}$, $z^{\rm{sb}}_{t}\\}$, where $\boldsymbol{z}$ is the set of
binary variables, and the rest are non-negative continuous variables.

##  IV Numerical Study

We first explain our case studies and then provide numerical results. All
input data and source codes are shared in [13].

TABLE I: Price inputs for three case studies |  $\boldsymbol{\lambda^{\rm{h}}}$ [EUR/kg] |  Other prices  $\boldsymbol{\lambda}$ [14, 15]
---|---|---
$\rm{DK}1\ 2021$ | $10$ | Historical prices from $\rm{DK}1$ in $2021$
$\rm{DK}1\ 2022$ | $10$ | Historical prices from $\rm{DK}1$ in $2022$
$\rm{DK}2\ 2022$ | $10$ | Historical prices from $\rm{DK}2$ in $2022$

###  IV-A Description of Case Studies and Ex-post Analysis

We consider an electrolyzer of $10$ MW, as this is the maximum bid size for
the FCR and mFRR services in the Danish bidding zone $\rm{DK}1$. For the
purpose of the value analysis, it is assumed that all tube-trailers are
exchanged at midnight, and are available all day. Further, we assume a daily
demand of $2000$ kg H2, corresponding to approximately $50\%$ of the daily
production capacity of the electrolyzer.

Case studies: The MILP model (1)-(4) is applied to three different case
studies, built upon historical prices in $\rm{DK}1$ and $\rm{DK}2$ in $2021$
and $2022$, summarized in Table I. The first two case studies, namely
$\rm{DK}1\ 2021$ and $\rm{DK}1\ 2022$, explore how offering ancillary services
to the TSO changes the total profit of an electrolyzer operating in the
$\rm{DK}1$ zone. The reason for including the third case study, i.e.,
$\rm{DK}2\ 2022$, is that the upward mFRR prices were relatively low in
$\rm{DK}1$ in the years $2021$ and $2022$, so we are interested in exploring
$\rm{DK}2$ with comparatively higher mFRR prices. Note that the Danish TSO,
Energinet, has recently implemented a joint reserve market for $\rm{DK}1$ and
$\rm{DK}2$. As further integration between the Nordic ancillary service
markets is planned as part of the Nordic Balancing Model [11], it is deemed a
reasonable assumption that mFRR prices will increase in $\rm{DK}1$. Fig. 1
depicts the distribution of day-ahead, FCR222For the $\rm{DK}2$ case study,
FCR-N prices are applied. , and upward mFRR prices333The Danish TSO is
currently not procuring downward mFRR capacities. in $\rm{DK}1$ and
$\rm{DK}2$, corresponding to our three case studies. Four different model
variations are applied to three case studies:

  1. 1.

No AS: It stands for no ancillary services. This variation serves as a
benchmark, wherein the electrolyzer only participates in the day-ahead market
as a power consumer and sells hydrogen.

  2. 2.

Oracle: This model serves as an ideal benchmark, where the electrolyzer
participates in ancillary service markets with perfect foresight on the
reserve activation. Hence, at the time of solving the MILP model (1)-(4), the
electrolyzer perfectly knows the values of $\alpha^{\rm{act\uparrow}}_{t}$ in
(4a) and $\alpha^{\rm{act\downarrow}}_{t}$ in (4f) for every hour $t$. This
variation provides insight into the maximum potential profit (upper-bound)
that the electrolyzer could have earned.

  3. 3.

$\boldsymbol{\alpha=0}$: In this variation we enforce
$\alpha^{\rm{act\uparrow}}_{t}$ in (4a) and $\alpha^{\rm{act\downarrow}}_{t}$
in (4f) to be zero in the day-ahead stage. Here, the electrolyzer will still
always respect the total capacity limits of the reserve, but assumes that
there will be no change in the scheduled hydrogen production due to placed
reserves. Therefore, any activation may challenge the hydrogen production plan
and lead to infeasibility in the downstream processes. This could be a severe
case if upward mFRR is significantly activated, requiring the electrolyzer to
remarkably reduce the power consumption, thereby the risk of not fulfilling
the minimum daily hydrogen production requirement. One may see this model
variation pragmatic (not assuming any future knowledge of activation) but
optimistic (assuming that the hydrogen schedule will not be compromised).

  4. 4.

$\boldsymbol{\alpha=1}$: On the contrary, the electrolyzer here assumes the
full mFRR activation will happen at every hour $t$. This variation is again
pragmatic, but conservative.

Figure 1: Distribution of day-ahead, FCR, and upward mFRR prices in $\rm{DK}1$
and $\rm{DK}2$ in $2021$ and $2022$.

Ex-post analysis: Three case studies and four model variations are compared
ex-post, where the true realization of the reserve activation and balancing
prices are revealed. See Fig. 2 for an overview of the ex-post analysis. Once
the MILP model (1)-(4) is solved, we fix the mFRR and FCR capacity
reservations and day-ahead schedules. The final profit of the electrolyzer in
every day is calculated based on the true activation and the balancing prices
realized. Recall that the true hydrogen production in model variations
$\boldsymbol{\alpha=0}$ and $\boldsymbol{\alpha=1}$ might vary from their day-
ahead schedule when we account for the true activation. We do not assume a
penalty for any unmet hydrogen demand.

As explained in Section II-B, after the mFRR capacity bids are accepted, the
mFRR capacity providers are obliged to submit an activation price, the so-
called regulation bid. The TSO activates mFRR reserves in the balancing stage
according to the merit order principles, i.e., starting from cheapest
regulation bids. Hence, for our ex-pots analysis, it can be assumed that if
the electrolyzer places a regulation bid that is lower than the realized
balancing price $\lambda^{\rm{B}}_{t}$, the reserved capacity would have been
activated. Further, it is assumed that the electrolyzer is price-taker and
would place a regulation bid that is equal to the opportunity cost in the case
of upward activation, i.e., the lost revenue from selling hydrogen. Assuming a
constant efficiency $\bar{\eta}$ for the electrolyzer, this opportunity cost,
and thereby the regulation bid, can be computed as
$\bar{\eta}\lambda^{\rm{h}}$. We consider the same regulation bid for upward
and downward activation. Finally, the activation would only occur if the power
system experiences an imbalance. While the real activation of mFRR reserves
occurs per $15$-minute interval, the relevant historical data found is only
given in hourly resolution[14]. It is therefore assumed that a capacity
reserve is fully activated for a whole hour if the described conditions are
fulfilled. The Danish TSO is currently procuring upwards mFRR reserves only,
i.e. reserves for the case of a supply deficit in the system. Let
$I_{t}\\!<\\!0$ note a negative system imbalance. The assumed realized upwards
activation for every time period $t$ is then

$\alpha^{\rm{real\uparrow}}_{t}=\begin{cases}1,&\text{if }\
\bar{\eta}\lambda^{\rm{h}}\leq\lambda^{\rm{B}}_{t}\text{ and }I_{t}<0\\\
0,&\text{otherwise.}\end{cases}$

MILP
(1)-(4)$\lambda_{t}^{\rm{\\{DA,F,m\uparrow,m\downarrow}\\}},\alpha_{t}^{\rm{act(\cdot)}}$$p_{t}^{{\rm{DA}}^{*}}$$p_{t}^{{\rm{F}}^{*}}$$p_{t}^{{\rm{m\uparrow}}^{*}}$$p_{t}^{{\rm{m\downarrow}}^{*}}$Ex-
post profit$\alpha_{t}^{\rm{real(\cdot)}},\lambda_{t}^{\rm{B}}$

Figure 2: Overview of the ex-post analysis. Superscript ∗

denotes the optimal day-ahead schedules.

###  IV-B Results and Discussion

For the case studies $\rm{DK}1\ 2021$ and $\rm{DK}2\ 2022$, Fig. 3 shows the
ex-post annual profit of the electrolyzer, whereas Fig. 4 depicts the
cumulative FCR and upward mFRR capacities that the electrolyzer offers over a
year. In both cases, particularly in $\rm{DK}2\ 2022$, the participation of
the electrolyzer in ancillary service markets could yield a manyfold in
profits, largely due to very high FCR prices, peaking at around $3,000$ EUR/MW
in $2022$ (see Fig. 1).

Figure 3: Ex-post annual profit in $\rm{DK}1\ 2021$ and $\rm{DK}1\ 2022$.
Figure 4: Cumulative reserve capacities the electrolyzer provided over a year
for cases $\rm{DK}1\ 2021$ and $\rm{DK}1\ 2022$.

For $\rm{DK}1\ 2021$, the profit in the oracle (upper bound) is around $57\%$
higher than that in the case with no ancillary services. The interesting
observation is that the profit in the pragmatic variations, i.e.,
$\boldsymbol{\alpha=1}$ and $\boldsymbol{\alpha=0}$, is not significantly
lower than that in the oracle, as the main increase in profit arises form the
FCR market. Further, it is seen that for the oracle and
$\boldsymbol{\alpha=0}$ variations, the electrolyzer offers services in both
FCR and mFRR markets, whereas it only provides FCR in $\boldsymbol{\alpha=1}$.
This implies that the mFRR market is not attractive for the electrolyzer when
considering activation. Fig. 4 shows that the $\boldsymbol{\alpha=0}$
variation places more bids in the mFRR up reserve over the year 2021 than the
FCR market. This is, however, largely driven by the electrolyzer “leftover”
capacity when, e.g., operating at full load due to low day-ahead prices,
rather than the profitability of the reserve itself.

For $\rm{DK}1\ 2022$, we observe an extreme case. When not providing ancillary
services, the profit is almost zero due to very high day-ahead prices, making
the hydrogen generation financially unattractive. However, owed to very high
FCR prices, the estimated profit is around EUR $30$ million in the oracle,
while it is around EUR $19$ million in two pragmatic variations. The
electrolyzer mostly offers FCR, although mFRR services have also been offered
to some extent. This raises the question of why the model is still placing
bids in the mFRR market when FCR prices are several times higher.

There are two aspects of the FCR market design that makes it in some cases
less advantageous for the electrolyzer than the upward mFRR market, even with
the higher prices. The first reason is the symmetric nature of the FCR
service. While it is obvious that this limits the electrolyzer to offering at
maximum half of its available capacity, it is also important to note that it
limits the electrolyzer from operating at full load when providing FCR. This
is disadvantageous due to the fact that the electrolyzer is exposed to the
day-ahead prices. In low-price hours, it might therefore be beneficial to
rather utilize those hours for hydrogen production than for FCR services,
especially considering the minimum daily hydrogen production requirement.
Second, the FCR service must be provided in time blocks of four hours. Thus,
the electrolyzer is either not able to utilize low day-ahead prices fully, or
forced to produce during high prices while providing FCR.

We now explore the effect of activation on profits. As historical $\rm{DK}1$
prices for mFRR are relatively low, we consider the $\rm{DK}2\ 2022$ case to
investigate the effect of upward mFRR activation. Fig. 5 shows the cumulative
ex-post profit development when the electrolyzer, in addition to hydrogen
production, participates in: (i) the mFRR market only, (ii) both mFRR and FCR
markets, and (iii) the FCR market only. In all cases, we also plot the profit
evolution in the oracle and when no ancillary services are offered, indicating
upper and lower bounds, respectively. It is clear from all three plots in this
figure that the participation in ancillary service markets significantly
increases the total profit. While $\boldsymbol{\alpha=0}$ yields a higher
profit compared to $\boldsymbol{\alpha=1}$, it may also lead to unmet hydrogen
demand. In total, $82$ tonnes of hydrogen demand was not met for the
electrolyzer participating in the mFRR market only, not meeting the daily
minimum hydrogen production requirement in $192$ days throughout the year
$2022$. This may cause issues for the electrolyzer as per existing bilateral
contracts. However, with a robust (pessimistic) approach to activation, i.e.,
$\boldsymbol{\alpha=1}$, the profit has still increased from $0.9$ to $2.5$
million euro when the electrolyzer participates in both ancillary service
markets. Note that the mFRR activation approach is not relevant to the case
with the FCR market participation only (right plot).

Figure 5: Cumulative ex-post profit in the $\rm{DK}2\ 2022$ case.

##  V Conclusion

This paper analyzed to what extent the profit of an electrolyzer could have
been increased in Denmark in $2021$ and $2022$ by providing FCR and upward
mFRR services, in addition to their main hydrogen business. Specifically, we
address the question of how the activation of the energy intensive mFRR
reserve effect downstream processes of hydrogen and if this should be
accounted for in the value estimation of the service. We considered a case
when the electrolyzer only produces hydrogen (lower bound for the profit), and
another case when it participates in FCR and mFRR markets too while having a
perfect insight into future activation (upper bound for the profit). We also
considered two cases with simple but pragmatic approaches to activation. We
find that the profit could have been increased by around $57$% in $\rm{DK}1$
in $2021$. This profit increase could have been drastic in $2022$, increasing
from almost zero to millions euro, depending on the size of the electrolyzer.
In both $\rm{DK}1$ cases, the increase in profit is driven by the FCR
provision, as FCR reserve prices were several times higher than mFRR prices.
We carried out a similar analysis for an electrolyzer in $\rm{DK}2$ for
$2022$, and observed a profit increase by a factor of $2.7$ with a robust
activation approach, and by a factor of $5.4$ for the oracle case. It is here
observed that not accounting for the potential mFRR activation may lead to
large quantities of unmet demand, and thus an overestimation of the value of
the reserve.

This analysis should be extended in several directions, therefore we do not
advise investing in electrolyzers just based on the current analysis. First,
we have assumed that the electrolyzer has perfect insight into day-ahead, FCR,
and mFRR market prices, which is very unlikely to be the case in practice. The
future work should model the price uncertainty and potential price
correlations among markets. In addition, the tube-trailer availability may
cause an extra source of uncertainty. Second, we have assumed that the
electrolyzer is able to provide FCR services without the need for any
auxiliary asset like a battery, and discarded the degradation cost. However,
such a cost could be significant. Third, ancillary service prices in
$\rm{DK}1$ and $\rm{DK}2$, especially in $2022$, were unusually high and
different from their trend in previous years. A distinct analysis, which is
not straightforward, is required to explore whether we should still expect
such high prices in the coming years. It is also critical to investigate from
the perspective of the TSO how the demand will evolve for ancillary services
in future and whether it is a reasonable assumption that the electrolyzer can
still sell its services entirely. This is important since a high investment in
electrolyzers is expected in Denmark ($4$-$6$ GW by $2030$, doubling the
current peak demand), irrespective of their business potential in ancillary
service markets. However, such a demand analysis should also consider the
upcoming integration of national reserve markets in Europe. Finally, this
analysis should be extended by considering hybrid plants with combined co-
located electrolyzer, renewable, and storage assets, and enforce RFNBO
conditions [12] for power procurement from the grid.

## Acknowledgement

We thank the Danish Energy Technology Development and Demonstration Programme
for supporting this research through HOMEY project (Grant number: 64021-7010).

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