Cost minimization of a hybrid PV-to-methanol plant through participation in reserve markets: A Danish case study

.


Introduction
Denmark has set ambitious targets, aiming for a 70% reduction in greenhouse gas emissions by 2030 and striving for carbon neutrality by 2050 [1].The country plans to employ renewable energy sources exclusively for electricity generation to meet these emission reduction goals [2].In this pursuit, Power-to-X (PtX) technology, which generates hydrogen (H 2 ) or H 2 -based products from renewable power, is anticipated to play a crucial role in decarbonizing sectors with high emissions, e.g.transport and agriculture [3].Denmark is currently in the initial phases of PtX development, with aims to achieve an electrolysis capacity of 4-6 GW by 2030 [4].While green H 2 and its derived fuels presently incur higher costs than their conventional counterparts, the load flexibility of PtX plants holds promise for potential reductions in production expenses [5].This study explores the production costs of PtX plant fuels and investigates the potential cost efficiencies achievable through load flexibility.
The research focuses on a specific PtX project in Denmark, a hybrid renewable energy system (HRES), dedicated to producing methanol as a shipping fuel.This HRES integrates a 300 MW photovoltaic (PV) plant interconnected with a 52.5 MW electrolyser capacity PtX plant designated for methanol production.Assessing the full lifetime cost of each unit of methanol produced, the study measures the methanol production cost using the levelised cost of methanol (LCoM).It focuses on optimizing operational expenses by analyzing the interplay between the HRES, electricity markets, and the electrical grid.Mathematical modeling is employed to optimize system operations, factoring in dayahead (DA) markets and frequency reserve provisions.The analysis encompasses electricity costs for powering the electrolyser and revenue generated by selling electricity to the grid.Additionally, the study scrutinizes the HRES's electrical flexibility and explores potential opportunities for reserve capacity provisions.The mathematical model adopts simplified methanol synthesis and distillation processes.https://doi.org/10.1016/j.ijhydene.2024 Incorporating the market bids of the HRES and real-world market data spanning more than a year, the model integrates operating setpoints of the electrolyser and PV plant to address potential market biases.The simulation covers complete operational years to calculate the LCoM.Capital and fixed operational costs are established based on available estimations in pertinent literature, considered as fixed values without potential cost reductions.
The paper is structured as follows: Section 2 initiates by providing foundational knowledge crucial for this study.It introduces relevant research in the PtX and market participation field, presents vital details on current electrolyser technologies for comparison, and gives a brief overview of the e-methanol production process.Furthermore, it outlines the electricity market and its associated conditions concerning frequency reserves investigated in this study.Finally, it examines the key economic metric, the LCoM.
Moving on to Section 3, this segment introduces the HRES system under consideration and presents the mathematical model that represents the physical system.Subsequently, Section 4 explores both operational and economic results, accompanied by a sensitivity analysis of the most significant parameters.
Section 5 delves into a detailed discussion of the case, while Section 6 provides the study's conclusive remarks.

Background
In the existing literature, the complexity of PtX technology components has been considered with varying degree.[6] presents an energy management system (EMS) model for an industrial cluster incorporating renewable generation, electric battery, electrolysis plant, H 2 storage, industrial facilities, and H 2 -consuming units.This EMS optimizes flexible power-consuming units (like H 2 compression, electrolysis, and battery) and H 2 -consuming plants (pyrolysis, methanol, H 2 compression, and ammonia).The model aims to minimize operational costs and maximize green H 2 production share, assuming perfect forecasts for renewable generation and DA electricity prices, without considering uncertainty.
In another study, [7], researchers investigate the flexibility and optimal operation of an alkaline-electrolyser-based power-to-methanol plant participating in the DA electricity market under uncertainty.They employ an advanced data-driven robust optimization technique to handle market uncertainty for a real-life system in Denmark.Their approach yields improved results compared to other optimization techniques, although it does not explicitly model market uncertainty.[8] assesses the economic feasibility of a power-to-H 2 system providing frequency regulation reserves in Denmark, using real market data.They propose an operational framework and find that the system is financially viable and enhances the stability of Denmark's power grid.Additionally, the paper discusses the potential of such systems to contribute to decarbonizing the energy sector.
In [9], the focus shifts to using a grid-connected electrolyser in a H 2 refueling station to provide frequency services to the grid.This model optimizes system component operation and sub-component sizing while accounting for market uncertainty represented by scenarios.The study applies real-world historical data and assumes a location in Belgium, utilizing European market data.
Another model, [10], explores a grid-connected virtual power plant (VPP) with synchronous generators, a pumped-storage plant, a wind power plant, and electric vehicles with bidirectional chargers in a parking lot.The VPP participates in the DA electricity market and an unspecified regulating reserve market to maximize profit.Uncertain parameters, such as DA prices and reserve activation probabilities, are managed using a point estimate method.
The authors of [11] address the scheduling problem of an electric vehicle aggregator, leveraging vehicle-to-grid capabilities.The aggregator takes part in the DA and reserve markets with the goal of optimizing charging and providing ancillary services.
In [12] the authors investigate cost-effective strategies for Power-to-Methanol processes, focusing on flexible operations and storage.They explore methanol synthesis from captured CO 2 and green hydrogen, emphasizing the impact of variable electricity costs.Using models with batteries and hydrogen storage, they optimize design and scheduling, highlighting the benefits of storage, particularly hydrogen, during fluctuating electricity prices.The study underscores the importance of flexible operation throughout the Power-to-Methanol plant to reduce costs, with even moderate flexibility in methanol synthesis significantly lowering production costs.
The paper [13] examines PtX technology in energy hubs, with a Danish case study on renewable fuel production.It explores integrating renewable sources to create sustainable fuels like green hydrogen or synthetic fuels.Through analysis of the Danish energy system, the study assesses the feasibility and implications of using PtX technologies for fuel production.The findings highlight potential benefits such as improved energy sustainability, reduced carbon emissions, and enhanced energy independence by converting excess renewable electricity into storable fuels for diverse applications.
The paper [14] centers on optimizing power-to-H 2 engagement in the Nord Pool electricity market.It examines how different bidding strategies affect plant operation within PtX systems, emphasizing the need to manage the cost and sustainability of purchased electricity from spot markets to improve efficiency and economic viability.Through analysis of market participation strategies, the study seeks to optimize the operation of plants converting power to hydrogen.The findings offer insights into how strategic bidding can impact plant performance and overall system efficiency amidst renewable energy integration.
This research pioneers a two-stage framework for managing market uncertainties and renewable energy production, offering crucial insights drawn from detailed modeling of Danish systems.Notably, the study [7] stands out for its comprehensive conversion of model outcomes into tangible economic results across the system's lifespan, particularly in the context of methanol plant operation.While existing studies predominantly simulate short-term scenarios, this research extends its focus to a full year, shedding light on the dynamics of renewable energy integration and market management over an extended period.Furthermore, it addresses a notable research gap by exploring the potential of PtX plants to provide reserve capacity from specific locations, thus offering valuable contributions to both academia and industry.

Electrolysers
The literature covers four types of electrolyser technologies, namely alkaline electrolysers (AEL), proton exchange membrane electrolysers (PEM), solid oxide electrolysers (SOEC), and anion exchange membrane electrolysers (AEME).Among these, AEL is the most widely used and has a well-established industrial history [15].PEMs are also commercially available, whereas SOECs are in the demonstration phase [16].The largest SOEC facility in the world has a nominal capacity of 2.6 MW [17], while AEL and PEM facilities have capacities of 150 MW [18] and 20 MW [19], respectively.AEME technology is still in the early stages of development and limited to prototypes.This summary focuses on the established electrolyser technologies, including AEL, PEM, and SOEC, while excluding AEME due to a lack of sufficient data.Currently, there is no dominant technology for all applications, and each faces challenges related to material performance, durability, and maturity, leading to increased competition in the field [5].The key specifications of the three electrolyser technologies are detailed in [20].

E-methanol production
There are currently three methods for e-methanol production via electrolysis.One method involves water electrolysis to produce H 2 gas, followed by catalytic methanol synthesis using carbon dioxide (CO 2 ) and H 2 .Another method splits water and CO 2 to create syngas (CO and H 2 ), which is then converted to methanol by reacting it with CO 2 .The third approach directly converts CO 2 and water into methanol through electrocatalytic synthesis.The most scaleable production method is the first one, combining water electrolysis with CO 2 hydrogenation to methanol (CTM) [21,22].
In the CTM process, CO 2 and H 2 are introduced into a reactor, resulting in methanol and water production.The gas stream from the reactor is cooled and directed into the flash separator, where raw methanol is separated from unreacted H 2 , CO 2 , and CO.Unreacted gases are recycled, with a small portion purged to eliminate inert gases [23].
To achieve the necessary purity for chemical or fuel applications, raw methanol undergoes column distillation.In this process, water is separated from methanol as the raw methanol is pre-heated to around 80 • C and then enters the column.Water is removed from the top, while methanol is collected from the bottom [24].

Electricity markets and frequency reserves
Since the liberalization of the European electricity sector in 1998, electrical energy and related products have been traded in open markets [25].In Denmark, like in most liberalized power systems, the electricity market is divided into a wholesale market and a retail market.The wholesale market further consists of sub-markets based on the time between a trade and the delivery of electricity.In this work, only the DA market is considered.
Further, the Danish Transmission System Operator (TSO) procures a set of reserve capacities through ancillary service markets.These ancillary services are essential for ensuring a reliable electricity supply, ensuring the power grid's ability to handle frequency deviation caused by e.g.imbalances in production schedules.Unlike energy trading in the DA market, reserve providers offer their capacity to adjust power generation or demand to maintain grid stability.
Denmark is split into two bidding zones, DK1, synchronous with Continental Europe, and DK2, synchronous with Northern Europe.As the two zones are part of different synchronous regions, they differ in ancillary service market structure.Only zone DK1 is considered, as the HRES is located in Kassø, Southern Jutland, near the German border, within DK1.In this area, there are three types of frequency reserves: Frequency Containment Reserves (FCR), automatic Frequency Restoration Reserves (aFRR), and manual Frequency Restoration Reserves (mFRR) [26].

Day-ahead market
The DA market is the primary marketplace for electricity trade in the Nordic region, accounting for approximately 70% of total power consumption [27].In this market, power producers and consumers can trade their power production and consumption one day before delivery.The market closes at 12:00 for all hours of the following day, and is cleared with a uniform price scheme.Any deviance in real time from the DA bid must be settled in the intra-day or balancing markets.As this work considered a deterministic framework, said markets are not considered.

Frequency containment reserve
In DK1, FCR is the quickest-responding reserve.FCR includes powerproducing or power-consuming units and is designed to maintain the frequency within a specific range centered around the nominal frequency of 50 Hz in continental Europe and the Nordics.The reserve payment is settled with a uniform price scheme, and is procured in blocks of four hours.It is a symmetric product, meaning that any reserved capacity can be activated both the upward (i.e. to increase system frequency) and downward (i.e. to decrease system frequency) direction.The activation of a reserve happens automatically as a function of the frequency in the grid, with a required respond-time of 30 s.There is a minimum bid size requirement of 1 MW, but no maximum [26].

Automatic frequency restoration reserve
In certain situations, a significant event in the power system can cause a larger frequency deviation that requires frequency restoration.When such a major frequency event occurs, all available FCR are activated, but they may not be sufficient to restore the frequency.In such cases, the aFRR is triggered by a signal from the TSO.These reserves are typically provided by larger generation units operating below their capacity or units that can be rapidly brought online, with a full response time requirement of 15 min.The activation of aFRR is usually enough to stabilize the system.Unlike FCR, aFRR is not activated based on direct frequency measurements but by a regulating signal sent from the TSO.The DK1 aFRR market has recently changed drastically, and is now part of the Nordic aFRR capacity market.Therefore, this market form is assumed [28].The Nordic aFRR reserve is asymmetrical, with separate procurement of the upward and downward reserves.Further it has an hourly bid structure with minimum and maximum bid volumes of 1 MW and 50 MW, respectively.

Manual frequency restoration reserve
The third and final reserve type in DK1 is the mFRR.As implied by the name, it is activated ''manually'' upon a direct request from the TSO's control center.In cases where the full aFRR is activated during a system event, the mFRR can be utilized to reset the aFRR if a new imbalance occurs.Additionally, if imbalances are predictable, the mFRR may be activated proactively without needing to trigger the aFRR.This type of activation is known as reactive deployment of mFRR.As with the aFRR, mFRR requires a full response time of 15 min.The market follows the same structure as that of the aFRR, with procurement of hourly asymmetrical reserves.The Danish TSO only procures the upwards reserve of mFRR, hence only the upward product is considered in this work.The reserve has a minimum and maximum bid requirement of 5 and 50 MW respectively.

Levelised cost of methanol
The assessment of economic performance is conducted through the calculation of the LCoM.This metric represents the average production expense for a unit of methanol throughout the system's entire lifespan, encompassing both direct costs and the capital expenditure necessary for project implementation.The LCoM calculation relies on the levelised cost of energy (LCoE) calculation method from [29], which defines LCoE as described in Eq. (1).
CAPEX represents the initial investment, while OPEX    and OPEX   denote the annual fixed and variable operations and maintenance expenses, respectively.  signifies the fuel cost in year ,   stands for the energy production in year ,  represents the anticipated system or asset lifetime, and  denotes the utilized discount rate.This equation is adjusted slightly to encompass the LCoM, seen in Eq. ( 2).
The LCoM calculation involves dividing costs into four main categories: CAPEX, OPEX    , OPEX   , and   , which represents the total methanol production.It is worth noting that fuel costs are not considered since the HRES operates without traditional fuel consumption.
CAPEX and OPEX    are costs that remain constant, regardless of the optimization model, and are not influenced by market dynamics or power flow tariffs.These costs are determined based on data from similar systems, with relevant simplifications made within the project's scope.
The primary components under examination include the PV plant, grid connection, electrolyser system, methanol plant, and CO 2 supply.Whenever possible, the calculation incorporates comprehensive cost estimates, encompassing expenses for the entire system, including installation, piping, labor, and power supplies.
OPEX   covers both costs and potential revenue generated through market engagement and grid tariffs.In favorable market conditions, the model may yield a net profit through market participation, potentially resulting in negative OPEX   values within the LCoM calculation.The values for CAPEX and OPEX    are average values from found literature and can be found in Table 1.The given values are total costs calculated for the specific HRES in consideration with the system specifics listed in Table 2. Calculations and more specific arguments can be found in the Appendix.
The discount rate, determining the LCoM based on capital costs and future earnings, is crucial.Actual CAPEX repayment conditions vary between projects, leading to differing LCoM results.
In the case of European renewable energy projects, two weighted average cost of capital (WACC) estimates are available [45].For projects with support mechanisms, the WACC ranges from 2.4% to 4.0%, whereas market-based projects have WACC rates ranging from 5.9% to 8.8%.The HRES project's WACC is set to 5.0%, which falls within this range.
Real tax rates, without accounting for inflation, are applied, with pre-tax figures including corporate taxes.Estimating the HRES lifespan is complex due to varied component lifetimes.Solar PV lasts 25-30 years [46], electrolyser stacks about 11 years, and balance-of-plant components 20-25 years [34].Stack replacement is factored into fixed OPEX.The authors of [47] assume reformers and methanol reactors last 40 years, and electrolysers 30.A conservative 25-year economic lifespan is assumed for HRES, covering all components realistically.
The grid tariffs for both producers and consumers within the HRES are contingent upon energy import/export.In regions dominated by producers, importing energy results in a transmission fee encompassing both domestic and international network operation and maintenance, alongside a system tariff covering power supply security, system operation, and reserve capacity.When exporting, only the feed-in tariff applies as the consumer tariff.These values are all based on the year 2021, as per [44].

Hybrid renewable energy system
The HRES is designed to produce approximately 32,000 tonnes of e-methanol annually.The system consists of a 300 MW PV plant connected to a PtX plant behind the meter (BTM), allowing direct supply of the PV plant's electricity to the PtX plant.The PtX plant comprises a PEM electrolyser unit with three 17.5 MW Siemens Silyzer 300 [48], providing a total capacity of 52.5 MW.The electrolyser uses power and demineralized water as inputs, with tap water supplied by the local water utility company.The HRES is illustrated in Fig. 1.
The methanol plant includes a methanol synthesis unit and a column distillation unit.The methanol synthesis uses compressed H 2 and CO 2 from biogenic sources supplied by local farmers.The CO 2 is stored onsite at 12 bar and -35 • C in a storage unit.The output of the methanol synthesis is raw methanol, stored in an on-site tank, which is designed to accommodate three days' worth of raw methanol production under nominal load conditions.The specifications can be viewed in Table 2.
The distillation unit consists of a single distillation column operating at a constant rate, providing a continuous inflow of raw methanol and outflow of pure methanol.The on-site tank storage capacity for pure methanol needs to be sufficient to contain the quantity generated over a span of one week.Given the assumed consistent nature of raw methanol distillation, the production of pure methanol remains constant across different weeks.This production volume is determined by scaling down the annual demand of 32,000 tons to a weekly basis.To ensure smooth production operations and account for potential delays in pickup schedules, an additional margin is incorporated, assuming that the storage reaches 90% of its capacity when filled with one week's worth of production.
The compressor operation strategy responsible for providing H 2 and CO 2 to the reactor is a design that ensures the compressors operate at maximum flow, maintaining a consistent pressure ratio and a uniform power input throughout the operation.
To introduce variability in the feed to the reactor, a recycle stream is incorporated, equipped with an adjustable valve for precise control.The level of adaptability in the compressors is primarily governed by the limiting factor and is characterized by a ramp rate of 5% of the nominal flow per minute [49].

Electrolyser efficiency
The trade of power typically represent a large cost or revenue for the HRES, and as the electrolyser is a large source of power consumption in the system, it is important to accurately represent the efficiency of the electrolyser.Low temperature electrolysers, such as PEM, have a characteristic non-linear efficiency that varies with the load setpoint, with a peak efficiency around 20-30% load.
The non-linear efficiency also yields a non-linear production curve, i.e. the relationship between power and H 2 mass flow, which is the relationship represented in the model for a linear formulation.To incorporate this non-linearity into a linear program, piece-wise linear approximation is applied, following [50].Here, the pieces or segments are chosen to best represent the actual efficiency of the electrolyser, focusing on capturing the peak efficiency point.The resulting approximation of the production curve can be seen in Fig. 2.

Reserve provision capability
To identify potential reserve markets for the HRES, an evaluation of the system's technical attributes in relation to the pre-qualification criteria set by the TSO is necessary [51].
The electrolyser, with a capacity of 52.5 MW and a 5% minimum load, operates within a range of 49.88 MW (95% of its capacity) by adjusting the load setpoint between 2.625 MW and 52.5 MW.Its ramp rate of 10% per second corresponds to 315 MW/min, crucial for meeting ramp rate criteria.
Aligned with the electrolyser's setpoint range, the methanol plant has a limited ramp rate of 5% of nominal flow per minute (2.625 MW/min), affecting the electrolyser's ramping ability due to matching H 2 production with compression and injection rates.Consequently, in the rest of the paper a maximum ramp rate of 2.625 MW/min is assumed for the electrolyser.
For mFRR, the PtX plant's bid is capped at 50 MW within its 49.88 MW range, allowing a 39.38 MW supply in 15 min.Regulation mandates that the reserve activation must adhere to a ramp rate limited to 20% per minute of the unit's nominal capacity.Consequently, the setpoint should not fluctuate by more than 10.5 MW per minute, ensuring no disruption to the plant's operation.Additionally, the minimum permissible bid in the mFRR market stands at 5 MW.
In bidirectional aFRR, the PtX plant adjusts setpoints by the reserve size in both directions, resulting in a bid range of 24.94 MW, with the same ramp rate requirements as mFRR.
In Nordic aFRR markets, assuming DK1 regulations, the PtX plant's capacity aligns with mFRR at 39.38 MW.
For FCR, symmetrical bid range of 24.94 MW mandates stringent ramp rates, requiring delivery of half the activated reserve in 15 s and the full reserve in 30 s, qualifying only at 1.31 MW.
Due to bid resolution rules, FCR supply is capped at 1 MW, while aFRR and mFRR are adjusted to the nearest ''100 kW'' unit, resulting in 24.8 MW and 39.3 MW, respectively.Fig. 3 demonstrates the PtX plant's capacity and rate of change abilities, aligning them with the regulations specific to each reserve type.The intersection highlights the technical feasibility for engaging in the respective reserve markets.Notably, the limitation on ramp rates is evident, placing a ceiling on reserve provision for all types at 2.6 MW/min.Moreover, the bidirectional nature of aFRR imposes an additional constraint, narrowing its range to 24.9 MW.
In summary, the HRES's suitability for various reserve markets depends on its technical attributes, with considerations for capacity, ramp rate, and bidirectional constraints.

Mathematical model
Mathematical programming optimizes HRES operations, with the main goal of improving methanol production cost efficiency over its operational life.Using system specs (see Table 2) and market data, an optimization model is created to manage HRES states and market engagement.
A deterministic reserve market model minimizes cumulative variable operational expenses (OPEX   ) in the HRES.It considers participation in both the DA and reserve markets, trading capacities for FCR, aFRR, and mFRR, with hourly time resolution to align with market dynamics assuming perfect foresight.
The model does not explicitly incorporate DA market involvement through bid prices and volumes.Instead, the HRES setpoints determine the traded volume, manifesting as either realized energy import or export.Notably, the bid exhibits complete inelasticity, signifying that the bid volume remains constant irrespective of the clearing price.
The variables that govern decisions in solving this optimization problem are the power setpoints and mass flow rates within the system.These variables are optimized due to their connection with operational costs in the DA electricity market.The model solves this optimization problem across a time set  , encompassing simulation hours ranging from  = 1, 2, 3, … , | |.
The primary aim of the model is to minimize the total cost, calculated as the sum of hourly power flow expenditures between the HRES and the grid, as represented in Eq. (3a).Within this equation,  grid  denotes the power flow between the HRES and the grid for each hour .Since the temporal resolution is hourly, this value represents both the power and energy exchanged within that hour.The variable energy cost combines the DA market price,  DA  , and the grid tariff,    , both power prices and grid tariffs are measured in e/MWh.In cases where power is drawn from the grid,  grid  > 0, or the HRES generates net power,  grid  < 0, corresponding values are    > 0 and    < 0. Upon selling power to the grid, the grid tariff exhibits a negative value.
The objective function also integrates revenue from participation in reserve markets, treating it as a ''negative operational cost''.In this context,  The above objective is subject to the following constraints.The model establishes power equilibrium through Eq. (3b), ensuring that the sum of grid imports,  grid  , and PV generation,  PV  , equals the combined consumption of the electrolyser,  elec  , and the compressors of the methanol plant,  comp .
Eq. (3c) and (3d) ensure the correct tariff collection based on the polarity of  grid  , whether the HRES acts as a net producer or consumer during a specific time period.As a consumer, a consumer tariff  CT is applied, and for production as producer tariff, Eq. (3e) guarantees that the absolute value of power exchanged with the grid remains within the capacity limits of the HRES grid connection, Eq. (3f) sets the upper limit for PV plant power generation, constrained by solar irradiance,  irr  .
Eq. (3g) establishes boundaries for the electrolyser setpoint, constrained by the system capacity,  elec , and the minimum load,  elec .
Eq. ( 3h) and (3i) enforce limits on the levels of raw and pure methanol storage, represented by  raw and  pure , respectively.
The efficiency of the electrolyser determines the H 2 mass flow rate, ṁH 2  , produced through its power consumption,  elec  .The relationship between these variables, given by Eq. (3j), is nonlinear.To maintain a linear formulation, the nonlinear relationship is approximated using piece-wise linear approximation.A set of  segments on the production curve is defined, with a corresponding auxiliary variable for the electrolyser power consumption  seg , .For each segment a linear function of the power consumption is defined, with slope   and intercept   , that yields the H 2 mass flow rate ṁH 2  .This can be seen in Fig. 2.
The binary variable  , is defined tracking which segment is active at any time.Each segment is only valid between two power setpoints on the electrolyser consumption curve,   and   , shown in Eq. (3k).
At any point in time, at most one segment can be active, Eq. (3l).
Finally, the actual electrolyser power consumption  elec  is defined as the sum of the auxiliary electrolyser consumption  seg , across all segments, Eq. (3m).
The electrolyser efficiency has a piecewise representation.Eq. (3n) and (3o) enforce limits on the ramp rates for electrolyser power consumption and compressed H 2 mass flow, respectively.
Conversely proportional to the H 2 mass flow rate, ṁH 2 , from the electrolyser to the reactor, a CO 2 mass flow, ṁCO 2

𝑡
, is supplied to the reactor.A fixed ratio,  in , between the two mass flows is established by Eq. (3p).Since there is no material loss in the reactor, the mass inflow of raw methanol, ṁRi  , a mixture of CH 4 OH and H 2 O, is the summation of the two mass flows into the reactor, as described by Eq. (3q).
Eq. (3r) ensures the system begins and ends with a raw methanol storage level of 50%, while the pure methanol storage starts empty as stipulated in Eq. (3s), indicating a recent delivery before the simulation period starts.
The raw methanol storage level follows Eq. (3t), incorporating the inflow, ṁRi  , and constant outflow, ṁRo .Similarly, the pure methanol storage level is affected by inflow, ṁpure , and outflow, ṁd  , the system demand, as defined in Eq. (3u).
In addition to the DA market, the model incorporates advanced foresight into several reserve markets, including FCR, aFRR, and mFRR markets.
Similar to the approach in the DA market, the HRES is regarded as a price-taker within all reserve markets.With perfect market foresight, the HRES is expected to consistently submit bids that will be accepted without influencing the market's clearing price.Consequently, there is no distinction between the volume of a bid and the accepted reserve volume.Moreover, explicit bid prices are unnecessary, as they align with the clearing price.Conforming to the reserve product types and structures outlined in Section 3.2, the following principles apply to reserve provision: • For each time period, , and reserve type, , the HRES may offer a reserve volume,  ψ  .• All reserve markets operate using the marginal pricing scheme, ensuring that all participants receive the market clearing price,  ψ  .• Every reserve type has a minimum bid volume,  ψ .
• Every reserve type has a maximum bid volume,  ψ .
• Each reserve type adheres to a bid resolution, bψ .
• FCR bids are presented in 4-hour blocks, while other bids are presented in hourly blocks.
In Eq. (4a), the variable rψ  , denoting the reserve volume in ''bid resolution units'', is restricted by either the minimum and maximum bid sizes in these units or is set to zero, determined by the binary decision variable  ψ  , where Eq. (4b) scales the reserve in ''bid resolution units'' to MW 1 by multiplying rψ  with the bid resolution bψ .These two constraints ensure that the provided reserve is either zero or falls within the allowed bid range, while considering the bid resolution specific to each reserve.
Eq. (4c) accounts for the 4-hour block rule in the FCR market, requiring every four consecutive hours to share the same reserve size.
Constraints (4d)-(4g) are introduced to guarantee that a sold reserve can indeed be supplied by the electrolyser, when activated.Eq. (4d) ensures that the total up-regulation reserve remains within the bounds of the available increase in power exported to the grid.This increase is restricted by the grid capacity,  grid , and the actual import/export value,  grid  .Similarly, Eq. (4e) prevents the total downregulation reserve from exceeding the available augmentation in power drawn from the grid.This augmentation is constrained by the grid capacity and net import/export value.Eq. ( 4f) and (4g) serve analogous functions for limiting down-and up-regulation reserves to the feasible increase and decrease in the electrolyser's setpoint, respectively. 1The reserve is not an actual unit of power but rather a reserved capacity of a given power that is ''reserved'' in case of activation.
Eq. (4h) ensures that the reserve volume, power setpoint, mass flow, and storage level decision variables remain non-negative.

Results
This section showcases the outcomes derived from the HRES.Section 4.1 delineates the operational aspects of the HRES, illustrating the methanol production process and elucidating the system's energy consumption.In Section 4.2, a comprehensive breakdown of the economic outcomes concerning the system's provision of balancing services and the LCoM is presented.Lastly, Section 4.3 offers a sensitivity analysis illustrating the impact on the LCoM when varying the capital expenditures of the PV system and electrolyser, along with changes in methanol demand.

HRES operation
Fig. 4 illustrates the dynamics of methanol mass flow and storage within the system.The upper graph shows the storage level, mass inflow, and pure methanol demand.Pure methanol consistently enters the pure methanol storage unit from the distillation unit at a constant rate labeled as 'Pure in.'As a result, the storage level gradually rises until the weekly pickup, where it is emptied before the cycle begins anew.
Meanwhile, the lower graph in Fig. 4 exhibits the flow rate of raw methanol and the corresponding storage level.The inflow of raw methanol into storage relies on H 2 production by the electrolyser, making it variable.While the outflow from storage to the distillation unit remains steady, the storage level fluctuates based on the electrolyser's operation, ultimately improving the system's operational adaptability.
Fig. 5 displays the monthly average energy consumption of the system, categorized by its sources: the production from PV panels and energy imports sourced from the grid.Notably, during summer, the PV plant significantly contributes to the system's energy needs, while energy imports become dominant in the winter months.June witnesses the peak contribution from PV, covering nearly 60% of the total energy consumed by the PtX system.Conversely, PV generation hits its lowest point in December, accounting for less than 10% of the consumption.Over the course of the year, solar PV power accounts for 66% of the total energy utilized by the system.
The system's overall consumption, represented as dots, remains relatively steady throughout the year, except for February, which experiences lower total consumption.This stability arises from the consistent weekly demand for methanol that the system must meet.The capacity of the PV plant notably exceeds that of PtX, resulting in surplus PV production, primarily occurring in the summer months, which is subsequently exported to the grid.

Affect of reserve market participation on cost
Fig. 6 visually represents the HRES involvement in the reserve market.In the lower plot, the hourly distribution of reserve capacity and the electrolyser's setpoint are displayed, with each bar's total height representing the electrolyser's nominal capacity.The upper plot showcases the corresponding prices in the reserve market along with the DA market price.
During the nighttime hours of June 11th, aFRR prices drop to zero, resulting in no allocation of aFRR capacity within that timeframe.Meanwhile, the mFRR price maintains a slight value above zero.The system responds by allocating capacity to mFRR due to increased PV generation and positive mFRR prices, showing a similar pattern in subsequent hours.
At 15:00 on June 11th, the electrolyser operates at a higher setpoint due to the lower DA price, offering the opportunity to engage in the upward aFRR market below a rate of 75 e/MW.As the DA price escalates in subsequent hours, the system adjusts the electrolyser setpoint, participating in the downward aFRR market at approximately 60 e/MW.
On June 12th from 2:00 to 4:00, with a decline in the DA price, maximizing the electrolyser setpoint becomes more lucrative, providing aFRR up-regulation reserve capacity.However, when the aFRR price drops simultaneously, the capacity shifts back to mFRR.It is crucial to note that FCR bidding operates in 4-hour blocks, evident in the analysis  around 11:00 on June 12th.As the aFRR price rises again at 16:00, the model switches to provide aFRR up-regulation accordingly.
Engaging in reserve markets generates various revenue sources.Fig. 7 specifically outlines the income resulting from active involvement in these markets.The comparison involves two scenarios: participation solely in the day-ahead (DA) market and engaging in both the DA and reserve (RE) markets, for the years 2020 and 2021.
The producer and consumer tariffs, set prices for each unit of energy, remain consistent across both years, unaffected by fluctuations in energy prices due to similar system consumption in 2020 and 2021.
For both years, the aFRR market proves to be the primary source of additional revenue, while the mFRR and FCR participation contributes to a lesser extent.
In 2020, reserve market revenues total 4.82 million euros, with FCR accounting for 16%, aFRR 79%, and mFRR 5%.Notably, participating in the reserve market maintains DA revenue at a similar level compared to non-participation, with a minor 2% increase in DA costs, a modest trade-off for the additional revenue from reserve markets.
As a result of engaging in the reserve market, the net loss of 4.32 million euros in 2020 transforms into a net profit of 0.43 million euros.Contrastingly, in 2021, operating solely within the DA market results in a higher net loss of 11.14 million euros.However, participation in the reserve market leads to a variable OPEX of 2.26 million euros.By actively engaging in reserve markets, the overall increase in market prices allows for potential profits rather than incurring higher losses due to escalating energy prices.

Levelised cost of methanol
The LCoM can be calculated using Eq. ( 2), incorporating the variable OPEX outcomes from the model, as well as the CAPEX and fixed OPEX estimates outlined in Table 1.This computation assumes a technical lifespan of 25 years and a WACC of 5%.Notably, the variable OPEX stands as the singular variable in the LCoM equation, emphasizing the direct influence of the model outcomes on the final production cost.
LCoM values are presented for 2020 and 2021 under two scenarios: solely participating in the DA market and participating in both the DA and RE markets.In 2021, the LCoM values amount to 1508 e/t and 1059 e/t for participating solely in the DA market and engaging in both markets, respectively.This illustrates a 30% reduction in LCoM when participating in the RE market.For 2020, the results are 1276 e/t and 1117 e/t, with a reduction of only 12% when participating in the RE market.
Comparison of these outcomes with estimates from various organizations reveals differing perspectives.For instance, IRENA suggests production costs for e-methanol ranging from 735 e/t to 1467 e/t [21] given that the CO 2 is sourced from biogenic sources using carbon capture and storage.Additionally, futures contract prices for conventional methanol in the Rotterdam market vary from 405 e/t to 490 e/t for 2021 [52].According to Fournas Wei [53], LCoM ranges from 658 e/t to 951 e/t in a techno-economic assessment of e-methanol produced from biomass using a PEM electrolyser for H 2 generation.Moreover, Sollai [54] concludes a specific LCoM of 960 e/t for a PtX plant situated in Sardinia.Fig. 8 illustrates the comparison between the simulated plant's LCoM and these diverse estimates.Most results of LCoM are within the bounds of other estimates.

Sensitivity analysis
A sensitivity analysis was carried out to evaluate how different key factors affect the efficiency and cost of producing methanol within the given system.The examined parameters include the CAPEX for PV systems and electrolysers, as well as the demand for methanol.
The CAPEX is obtained from external sources but involves significant uncertainty when applied to specific projects.Therefore, examining how modifications in these parameters affect outcomes is considered important.Adjusting the yearly methanol demand requires proportionate adjustments to both the fixed methanol flow into the dedicated storage tank and the tank's capacity.
Variations in parameters are directly implemented, altering values by ±20% in increments of 5%.Fig. 9 illustrates the impact of alterations in CAPEX components on the LCoM.Given that these values represent fixed one-time investments and the demand remains constant, the LCoM adjusts proportionally in response to these parameters.The most sensitive parameter observed is the CAPEX related to the PV plant, followed by the electrolyser CAPEX.CAPEX variations associated with the grid connection, methanol plant, and CO 2 storage are omitted due to their minimal effect on the LCoM, while the focus remains on examining the PV and electrolyser CAPEX in this scenario.A 20% fluctuation in PV CAPEX leads to LCoM deviations of 181 e/t for both 2020 and 2021, regardless of the HRES's participation solely in the DA market or in both the DA and RE markets.Meanwhile, for the electrolyser, the variation results in a deviation of 63 e/t.
During 2020, the parameter most susceptible to changes is the methanol demand, causing notable fluctuations in LCoM when production either decreases or increases.For instance, when involved in the RE market, a 20% rise in production correlates with a 6.7% reduction in LCoM, whereas a 20% decrease in production leads to a 13.9% increase in LCoM.However, in 2021, while engaging in the RE market, the variations in LCoM show a reverse trend compared to those observed in 2020.

Discussion
The outcomes derived from the variable OPEX and their impact on the corresponding LCoM underscore the significant influence stemming from both increased market engagement and the selection of the market year in simulations on production expenses.
Despite achieving cost reductions by participating in frequency reserve capacity markets, the production cost of e-methanol remains beyond the competitive threshold of conventionally produced methanol in Europe when viewed within an open market context.Nonetheless, it is important to note that these results fall within the e-methanol production cost range outlined by IRENA, implying a reasonable accuracy in the overall cost estimations.
Addressing the research question relies on the model's dependence on various assumptions and simplifications, which, in turn, exerted influence on the outcomes.Several of these assumptions underwent scrutiny during the sensitivity analysis, revealing that key CAPEX components, notably PV CAPEX, exhibited considerable sensitivity concerning the LCoM.Despite the maturity of PV technology, it is prudent to keep tabs on potential future cost fluctuations.The PEM electrolyser CAPEX emerged as the second most sensitive fixed cost parameter, indicative of its ongoing evolution.Hence, it is crucial to delve deeper into the current cost projections for this evolving technology.
The persistence of an assumed constant methanol demand throughout the investigation might necessitate reassessment based on market dynamics.In 2020, heightened production resulted in reduced unit costs.However, in 2021, both escalated and decreased annual production led to higher LCoM.The additional net costs in the DA market outweighed the advantages of increased production, highlighting a need to contemplate shorter contracts with offtakers, particularly in markets characterized by heightened price volatility.
Integrating supplementary revenue streams, such as selling surplus heat or produced oxygen as byproducts from electrolysis, holds the potential to diminish production expenses.Heat derived from PtX plants can be seamlessly integrated into district heating networks, potentially driving down PtX production costs.Previous research has demonstrated the economic viability of selling oxygen byproducts.
The simplification of the physical system, energy, and reserve markets was crucial to establish a realistic scope for the investigation.However, certain modeling choices warrant reevaluation for future studies.For the system itself, a more detailed representation of components influencing ramping times or adopting diverse ramping times from existing literature could bolster accuracy.Concerning energy and reserve markets, assumptions such as utilizing non-Danish reserve market data might deviate from the actual performance of the PtX plant in Kassø.While DK1 mFRR market data was directly utilized, proxy markets were predominantly employed due to mFRR's minimal contribution to reserve market revenue.FCR market data relied on the FCR Cooperation German bidding zone due to extreme FCR prices in the Danish zone, potentially leading to an underestimation of FCR revenue.aFRR revenue, a primary source of added revenue from reserve market participation, was based on Swedish market data, serving as a proxy for DK1 prices, aligning with DK1's future integration into the Nordic aFRR capacity market.
The modeling of reserve markets omitted considerations of energy delivery obligations linked to providing reserves.For example, FCR involves continuous energy delivery for minor frequency deviations, potentially impacting the electrolyser's setpoint and other components.
Assuming perfect knowledge of PV production, devoid of weather forecast variability, simplified decision-making but may diverge from real-world scenarios where changing weather forecasts necessitate compensatory actions regulating power markets.
In this study's context, the selection among deterministic, stochastic, or robust optimization models requires thoughtful consideration based on practical factors.Deterministic models are typically favored due to their simplicity and computational efficiency in contrast to their stochastic counterparts.The intricate nature of stochastic models necessitates considerable computational resources and runtime, which becomes challenging for comprehensive optimization spanning an entire year.Despite employing numerous scenarios within a stochastic model for weekly assessments, the resultant improvements were not substantial enough to warrant the necessity of stochastic optimization for achieving the study's objectives.While recognizing the theoretical advantages of stochastic or robust optimization, practical limitations, including computational demands and marginal enhancements in outcomes, lead to prioritizing deterministic modeling for the current objectives.
Two prospective research directions emerge aimed at delving deeper into the techno-economic facets of the PtX project and refining the developed model.From a techno-economic perspective, enhancements encompass evaluating the supplementary value derived from selling process heat to district heating networks, integrating the sale of generated oxygen from electrolysis as a revenue stream, and examining the repercussions of diverse demand obligations, including flexible production volumes.Energinet, the Danish TSO, has released new grid tariffs for 2024, introducing a substantial 90% discount on the consumer system tariff for power consumption surpassing 100 GWh/year [44].These alterations are highly advantageous for grid-connected PtX plants or large flexible consumers, potentially leading to significant cost reductions.
Enhancements to the optimization model could involve introducing a third-stage variable to emulate the stochastic nature of reserve activation and accounting for weather uncertainties.Additionally, specifying the thermodynamic and chemical attributes of methanol synthesis could provide deeper insights into the impacts of electrolyser setpoint alterations.Another avenue for improvement could be the inclusion of a H 2 storage tank to uncouple electrolyser production from H 2 injection into the reactor.

Conclusion
The study introduces a HRES combining a 300 MW PV plant and a 52.5 MW electrolyser for methanol production, with grid connectivity for power import and export.While technically versatile, the HRES faces limitations in reserve market engagement due to CO 2 and H 2 compressor ramp times and electrolyser setpoint constraints.Operational optimization through a mathematical model reveals favorable electrolyser setpoints aligning with high PV generation and low DA prices.Seasonal analysis highlights PV dominance in summer with reduced influence in winter.The model efficiently allocates electrolyser capacity to maximize market returns, with resulting LCoM values closely matching IRENA estimates.This underscores the economic benefits of HRES participation in reserve markets, indicating potential for enhanced renewable energy system sustainability through market involvement.

A.2. Electrolyser CAPEX and fixed OPEX
Recent estimates of electrolyser CAPEX range from 1335-1574 e/kW, showing a relatively small interval despite differences in location and institution.[34] bases its calculation on a 100 MW system with electrolysers, compressors, and power electronics.[20] refers to ''Full System CAPEX'', while [16,35] respectively discuss ''CAPEX requirements'' and include ''electric equipment, gas treatment, plant balancing, and engineering, procurement, and construction''.The applied CAPEX reference is the average of these figures at 1349.7 e/kW.The project-specific figure is calculated as:    = 1349.7 e/kW ⋅ 52.5 MW ⋅ 1000 = 70.9Me In [34], the yearly OPEX for a 100 MW PEM electrolyser system totals 13 e/kW, covering fixed O&M costs and stack replacement.In [33], the fixed O&M cost is 3% of CAPEX, resulting in 40.5 e/kW yearly OPEX.[20] reports total OPEX as 2-4% of CAPEX, leading to 40 e/kW yearly OPEX.[47] estimates stack replacement at 60% of CAPEX every 11 years, equating to 46.6 e/kW yearly.The range underscores significant variation in stack replacement costs.Considering this uncertainty, a combined 'full OPEX' is preferred.Adopting a consensus approach, the reference fixed OPEX is calculated at 3% of CAPEX, resulting in 40.49e/kW/year or 2.1 Me/year for the specified plant.

A.3. Methanol plant CAPEX and fixed OPEX
To compare with the project-specific methanol plant, tonnes per day (TPD) capacity is used.[36] reports 28.86 Me for a plant rated at 100 TPD.Scaling the HRES methanol plant to annual production allows direct comparison.With an annual demand of 32 kt, the plant size is estimated at approximately 88 TPD.Considering economies of scale, the CAPEX of [36] is applied, scaled to match the size of the HRES methanol plant at 25.4 Me.
= 28.86Me ⋅ (88 TPD∕100 TPD) = 25.4Me The 100 TPD system in [36] is chosen for the project-specific methanol plant, closely matching its size of 88 TPD.Its annual OPEX of 4.5 Meincludes maintenance and labor costs.Scaling by TPD capacity, the project-specific plant's estimated OPEX is 3.9 Me/year.This cost covers catalyst expenses, expected to be replaced every 3 years, with an annual cost ranging from 0.11-0.45Me [37][38][39].

A.4. CO 2 storage CAPEX and fixed OPEX
Considering the volume of the HRES storage, CAPEX estimates vary between 4-28 Me.The CAPEX of the 19500 m 3 tank in [40], priced at 10.2 Me, is selected due to its close resemblance to the dimensions of the HRES storage.
The CO 2 OPEX is determined primarily by the expected purchase price, anticipated to be the main running expense for supplying CO 2 to the methanol reactor.These costs are based on either market prices [41] or carbon capture technology costs [42,43], averaged to a reference price of 48.1 e/tonne.An annual consumption of approximately 43,000 tonnes results in an annual purchasing cost of 2.1 Me.

A.5. Grid connection CAPEX and fixed OPEX
[55] introduces the newly devised tariffing approach for power producers by the Danish TSO Energinet.This method, implemented on January 1st, 2023, now governs the project-specific expenses associated with grid connection.These expenses, as outlined in [44], encompass various costs, notably the grid connection contribution, comprising both a station fee and a connection fee.
The station fee encompasses expenses related to establishing the physical connection and facilitating expansions of the transformer station busbars, among other things.This fee is standardized according to the voltage level of the grid connection, with a fixed amount of 12 million DKK allocated for connections at the 400 kV level.
Conversely, the connection fee stands at 0.328 million DKK per MW of grid connection capacity.Given a capacity of 238 MW, the project-specific connection fee totals 78.1 million DKK.
The total grid connection CAPEX combines both the station fee and the connection fee, amounting to 90.1 million DKK, which is equivalent to 12.1 Me.
The grid connection does not have any fixed OPEX as all tariffs associated with the import and export of electricity are energy dependent [44], hence these are included in the variable OPEX of the plant which is decision dependent and hence included in the optimization problem.

Fig. 3 .
Fig. 3. Reserve type requirements for provisions and plant specifications.

ψ
represents the reserve volume provided, and  ψ  denotes the clearing price for reserve market  at time .

Fig. 7 .
Fig. 7. Revenue and cost structure for years 2020 and 2021 comparing results when bidding in the reserve market (RE) and when only bidding on the day-ahead market (DA).

Table 1
CAPEX and fixed annual OPEX cost components.