Flexible hydrogen production from the perspective of the electrolyzer and storage operator

M ASTER T HESIS S UPPLY C HAIN M ANAGEMENT

Flexible hydrogen production from the perspective of the electrolyzer and storage operator

Author:

R.H. VAN Z OELEN

S2955253

r.h.van.zoelen@student.rug.nl

Supervisors:

Dr. E. Ursavas Dr. X. Zhu

Abstract

Developing a green hydrogen economy is seen as a potential solution for decarbonizing the industry and transportation sector. Moreover, this can be combined by a creating a peak shaving effect for growing fluctuation in electricity supply, by the increasing penetration of renewable energy sources. However, production of green

hydrogen during the supply peaks of electricity only leads to low utilization rates which makes the needed large investments of electrolyzer capacity unprofitable.

Therefore, this study presents a capacity determination and scheduling model for electrolyzer and storage operators to research factors that have a positive effect on the

profitability and ability to shave supply peaks of renewable energy sources as well.

The analysis is done with data from the HEAVENN project which aims to create a hydrogen valley in the Northern Netherlands. It is found that trading in multiple markets could lead to a higher peak shaving effect, but the volumes are limited. Also,

decreased electrolyzer CAPEX and increased price fluctuations are beneficial for flexible electrolyzer and storage operation. Finally the amount of served hydrogen

demand is an important choice to consider to make a profitable business case.

June 22, 2020

Contents

1 INTRODUCTION . . . . 2

2 THEORETICAL BACKGROUND . . . . 3

2.1 Capacity and scheduling problems for hydrogen value chains . 4 2.2 Production and scheduling problems . . . . 5

2.3 Future developments . . . . 7

2.4 Research contributions . . . . 9

3 METHODOLOGY . . . 10

3.1 Research design . . . 10

3.2 Problem formulation and assumptions . . . 11

3.3 Data collection and parameters . . . 13

3.4 Model formulation . . . 18

3.5 Model validation . . . 24

3.6 Data analysis . . . 27

4 RESULTS . . . 29

4.1 Results scenarios 2019 . . . 30

4.2 Results scenarios 2030 . . . 32

4.3 Sensitivity analysis . . . 36

4.4 Results of hypotheses . . . 41

5 DISCUSSION . . . 43

5.1 Discussion and practical implications for business cases . . . . 43

5.2 Limitations and further research . . . 50

6 CONCLUSIONS . . . 51

References 53 Appendices 60 A Renewable electricity generation . . . 61

B Profit functions . . . 62

C Peak shaving calculations . . . 62

D Code of the model . . . 63

Acknowledgements

I would like to thank the University of Groningen and especially my supervisors dr. Evrim Ursavas and dr. Stuart Zhu for support and provision of feedback during

the process. Also, I would like to thank people from the University and partners within the HEAVENN project for being ready to provide me with new insights and

inspiration. Lastly, I would like to thank my father and Bonnie from Papertrue for

proofreading my thesis.

1 INTRODUCTION

As global warming is accelerated by carbon emissions[1], it is a challenge to keep global warming under 2 degrees Celsius, as agreed by the United Nations[2], [3]. A global energy transition is needed since 81 percent of world wide supplied energy is produced by fossil fuels, which contributes to almost 100 percent of worldwide CO

emissions[4]. Hydrogen is seen as an essential part to realize these transition for several reasons. First, it offers ways to decarbonize multiple sectors[5], includ- ing steel, chemical and transport sectors that are accountable for 40 percent of the worldwide carbon emissions[6]. Further, hydrogen provides opportunities for cost effective transportation of energy over long distances and the re-use the natural gas infrastructure[5]. Lastly, to integrate the increasing amount of variable renewable energy (VRE) production, power-to-gas (P2G) is seen as essential to provide system flexibility by demand side management (DSM) and cost efficient large scale storage of energy[5], [7].

This paper will focus on this last stated benefit: hydrogen production with flexi- ble electricity loads matched with VRE overproduction. This is also known as the ability to shave output peaks of VRE sources[8]. When the penetration of electricity produced by VRE sources rise in a system, in time these sources produce more elec- tricity than is consumed, or way less than is demanded [9]. Studies that minimize the costs of the optimal future energy mix with regards to CO

reduction targets and conclude that producing hydrogen with excess electricity is a sufficient way of en- ergy storage, to deal with fluctuations in supply of VRE and demand[10], [11]. For example, Komiyama et al.[10] optimizes the energy mix in Japan to reduce 90 per- cent of CO

emissions. The distribution of excess electricity to produce hydrogen leads to an utilization rate of the electrolyzer of 5-20 percent[10]. Contradicting this, studies that investigate the profitability of green hydrogen production by electrolysis conclude that a high utilization of the electrolyzer is essential to keep the levelised costs of hydrogen (LCOH) acceptable[12], [13], [14], [15], [8]. Therefore, Michael- ski et al.[16] conclude that there is a gap between the business (microeconomic) and system (macroeconomic) perspective of green hydrogen production.

The aim of this research is to gain insights into the factors that will align the eco- nomic driven decisions of the electrolyzer and storage operators with the increased flexibility that is needed to integrate the VRE sources in the electricity system. The following research question will be answered:

What are the essential factors for hydrogen production and storage operators to produce hydrogen in a economical and flexible manner with regard to large scale VRE integration?

The behaviour of electrolyzer and storage operators is researched with a linear model

that optimizes the annual profitability. The model determines the optimal capacities

of installations within the electrolysis and storage system and the optimal operation

schedule on an hourly basis. The operation schedule is the determination of the

amount of hydrogen that is produced, stored and sold for every time unit. The cur-

rent literature provides indications for factors that might reduce the influence of the

electrolyzer utilization on profitability. In this research, four hypotheses are tested

to answer the research question. Different scenarios are created to test the effects

of several internal decisions and external future developments. The profitability of

the electrolyzer and storage operator and the balancing value for the electricity sys- tem are evaluated in every scenario. The balancing value is the amount of electric- ity consumption of the electrolyzer storage system during hours of overproduction by VRE sources minus the amount of consumption when VRE sources produce less than what is consumed. The data and characteristics of the HEAVENN project in the North of the Netherlands are used to create a realistic business case. Because there is a lot of uncertainty in the developments that may influence green hydrogen pro- duction[17], an extensive sensitivity analysis is performed to address influences of those factors. Moreover, the sensitivity analysis generalizes the insights to multiple settings with other market and situational conditions.

This research will make several contributions to the literature. Firstly, the models of Beehrbühl et al.[18] and Loisel et al.[19] are extended to investigate the opportuni- ties for different electricity sourcing strategies of an electrolyzer and hydrogen stor- age operator. Different options are compared very extensively. This resulted in in- sights of the electricity sourcing and capacity determination strategy within the de- bate how electricity prices and electrolyzer capital expenditures (CAPEX) will affect cost competitive hydrogen production by electrolysis[12], [15], [16], [17]. Thereby, the analysis is done from the perspectives of the electrolyzer and storage operator.

However, results are evaluated on the system perspective as well, which are leading to the needed insights in the effects of decisions of electrolyzer and storage opera- tors on the level of the electricity system[16]. Moreover, uncertainty of the most im- portant factors is researched as well[17]. Lastly, this research will contribute to the literature knowledge about certain business models for exploitation of electrolyzers with benefits for the total electricity system, such as Larscheid et al.[20] and Kopp et al.[21].

In addition, this study is useful for investors in electrolyzer and storage capacity. The impact of electricity prices and electrolyzer size are crucial for economic and com- petitive deployment of electrolyzers[12], [15], [16], [17]. This research gives insights into the considerations for which strategy should be chosen and what the effects of future developments and uncertain factors on those strategies might be. Practical recommendations are drawn for dependent parties: electrolyzer and storage opera- tors, investors in wind and solar parks and regulatory parties. The evaluation of the balancing value of the electrolyzer and storage operators give important insights for governments and electricity grid operators. It can help them to determine the incen- tives to harmonize large scale VRE integration in the energy system with hydrogen as an important energy carrier.

This paper will start with a theoretical background. In this section, the most impor- tant factors are retrieved from the current literature and hypotheses are made from them. Thereafter, the research setting and the model are presented in the methodol- ogy. The fourth section describes and analyses the results of the different scenarios.

The results are discussed with current literature and experts from the field to draw practical implications for business cases. Finally, the conclusions of this study are presented.

2 THEORETICAL BACKGROUND

For economic deployment of the hydrogen value chain, the levelized costs of hyrod- gen (LCOH) in comparison with the willingness to pay of the market are key[22].

In literature, the calculated levelized costs of hydrogen (LCOH) differ a lot (from 2

to 20 euro per kg), as result of different assumptions and system characteristics[17].

F

1: Overview hydrogen value chain

LCOH are determined by the function of the Net Present Value (revenues minus the variable, fixed and investment costs) minus the total revenues divided by the total quantities sold[16]. Electricity price and investments in electrolyzer capacity are the main drivers of these costs (+-80 percent), and both are affected by the utilization rate of the electrolyzer capacity[17], [16], [12], [13], [14], [15]. The next paragraphs describes how optimal capacity and scheduling problems for electrolysis and stor- age has been dealt with until now, how the electricity markets and value of flexibility can affect scheduling and capacity determination and what effects of future develop- ments are expected. Finally, the main contributions of this research are summarized and a conceptual model is presented.

2.1 Capacity and scheduling problems for hydrogen value chains

Introduction to the hydrogen value chain

The value chain of hydrogen is described as production, storage distribution and end-use (figure 1), for which different sources, systems and services can be cho- sen[23]. Traditionally hydrogen is produced by using different kinds of feedstocks or recovered from industrial processes[17]. Also, Dincer[24] describes plenty of meth- ods to produce so called ’green hydrogen’, which is hydrogen produced from green energy sources. For power-to-gas (PtG) and power-to-fuel (PtF), hydrogen produced by water electrolysis from renewable energy is considered as the key technology to produce green hydrogen[25], [26], [27]. The installation costs of the two main types (PEM and Alkaline) of water electrolysis differ between 1000 and 2000 euro/KW[25], [16].

Also for storing hydrogen, there are multiple options available[28]. Availability of large scale storage applications is highly dependent from geological character- istics[28]. Tarowski[29] investigated the possibilities for hydrogen storage in salt caverns, depleted oil and natural gas fields for Poland. In comparable ways, hy- drogen storage potential of salt caverns for Germany[16], France[12], Spain[15] and the United Kingdom[30] were investigated. From these studies, it can be concluded that there is a lot of capacity available that is technically feasible to store hydrogen in large volumes with relatively low impact on the total hydrogen production costs[16], [12]. However, when no caverns are available or investments are too large for rel- atively small storage amounts, more expensive storage in containers or tanks stays an option[31].

For distribution of hydrogen, studies compare transportation via pipelines, trucks and in gas or liquid forms[31], [32]. Since this study focuses on the production and storage operations of hydrogen where this gas is distributed by a gas transmission operator, issues of distribution are not the main considerations here.

Crucial for developing a value chain for hydrogen is the development of the end-

use markets[23]. Mentioned as one of the first markets to approach is the feedstock

for the methanol refining and production[33], ammonia synthesis[34] and iron and steel industry[35], since these are existing markets with high volumes of demand and responsible for a lot of carbon emissions [36]. Secondly, hydrogen can be used for heating[37] and cooling[38] as well, which can be implemented in residential[39]

and industrial[40] applications. Hydrogen has the advantage that it can easily be im- plemented in the current heat and cooling infrastructure[41]. Lastly, in the transport sector, besides electric, hydrogen fuelled vehicles are an opportunity for greeniza- tion of all land, air and water transports[42]. Fuel cell vehicles have advantages over battery electric vehicles such as faster fueling and better applicability for long dis- tance and heavier vehicles[13]. Other than the hydrogen markets, hydrogen can be converted into electricity again by a fuel cell. However, due to the rather low round trip efficiency of 35-55 percent, a lot of electricity is lost when transforming it from electricity to hydrogen to electricity back again[43].

2.2 Production and scheduling problems

Electrolyzers can be used to produce hydrogen with excess power in the electric- ity system with high penetration of VRE, but this results in operation with 2000- 3500 yearly load hours which is far from profitable due to the high electrolyzer CAPEX[12], [13], [14], [15], [16], [17]. To optimize profitability of hydrogen and storage operation, Beerbühl et al.[18] developed a model to optimize a scheduling and capacity determination problem of a hydrogen-ammonia production system.

Scheduling and capacity optimization of electrolysis and hydrogen storage balance the average electricity purchasing costs, and on the other hand the increasing invest- ment costs of capacity that is needed to buy more electricity during the hours with lower prices[18]. To improve the flexible use of electrolyzers in an economic way, more load hours of low cost electricity must be available [12], [13], [14], [15], [16], [20]. In the literature, multiple strategies are found to increase the amount of these hours. The main two directions are coupling renewable electricity sources (RES) to hte hydrogen production system and combining trading and provision of grid ser- vices in multiple electricity markets. The following sections will describe research that is done to improve flexible electrolyzer and storage operation.

Coupled RES-hydrogen systems

Many studies suggest coupling electrolysis and storage to VRE sources, especially wind generation[19], [44], [45], [46]. In coupled systems electricity generation sources are directly connected to the electricity consumer without grid connection. This can be beneficial when the electricity can be obtained more cost effective from these sources than from the market. Moreover, smart choices can be made regarding when to sell electricity and when to produce and sell hydrogen. Loisel et al.[19] found that coupling wind farm and electrolyzer operation increases the combined profitability and avoided wind curtailment. This shows that coupled wind generation can align with increasing the profitability and peak shaving effect without facing a trade-off.

However, this is from the perspective of an electrolyzer and storage operator. For a

wind farm operator, the profits are higher when only electricity is sold and excess

electricity is curtailed, instead of a combination of serving electricity and hydrogen

markets. This is because the high capital costs of the electrolyzer and compressors

do not exceed the extra revenues of the produced hydrogen[19]. The synergy of com- bined solar and wind sources has been proved to increase the electrolyzer utilization rate from 40 to 80 percent[47]. Therefore, the high infrastructure costs of electrolyzer and storage equipment are utilized more. This was even leading to more reduced curtailment in South-American weather conditions[48]. However, it has not been researched if this synergy effect of coupling multiple RES with hydrogen produc- tion is strong enough from the perspective of RES operators to invest in hydrogen production and storage capital that is needed. Moreover, it has not been researched if this would lead to more hydrogen production during the overproduction hours of renewable energy sources, when profit maximization is pursued. Therefore, this will be tested in the first hypothesis that is drawn in this study.

H1: By coupling multiple renewable energy sources and electrolyzer operation, an increased peak shaving effect and profitability is reached by optimal RES, electrolyzer and storage

operation.

Electricity markets and grid services

In the power system supply and demand needs to be matched at each point of time.

The flexibility of the electric system is determined by its capability to cope with uncertainty and variability in both supply and demand of power[7]. There are mul- tiple ways to affect the end-use electricity patterns and magnitude, by reducing, increasing or rescheduling energy demand. This is called demand side manage- ment[7]. Hydrogen production by electrolysis has several opportunities in serving flexibility to the energy system[7]. Firstly, flexible electrolyzer operation can be used to provide demand side management to the system, for example consuming more electricity when there is overproduction of VRE and less when there is shortage of electricity supply in the system [13], [14], [12]. Secondly, it can also provide sea- sonal shifting and storage when hydrogen is produced during the supply peaks and stored until there is demand for hydrogen or shortage of electricity production at other moments[7]. The business value of these options is determined by the price incentives that different electricity markets provide.

In Europe, there are different markets to purchase electricity: The forward, day ahead, intraday, imbalance and congestion market. The forward market is the gen- eral electricity market, where electricity can be traded for base-load, peak-load and super peak-load hours per week, month, quarter or year. On the day ahead market, electricity can be traded 24 hours in advance, with tariffs fluctuating for each hour of the day. Most studies that researched the grid coupled flexible electrolyzer op- eration assumed that electricity is purchased in this market[9], [14], [18], [19], [49].

Until 90 minutes before consumption, electricity can be traded on the intraday mar-

ket, for example cross-border trades and spot market trades. Thereafter, Balance

Responsible Parties (BRP) are responsible for balancing generation and consump-

tion of their suppliers and customers. Otherwise they have to pay the imbalance

price to the Program Responsibility Party (PRP), which is the Transmission Grid

Operator (TSO). The TSO is responsible for transport of electricity on high voltage

level. Also, the TSO watches over the frequency in the electricity grid. Therefore,

they contract parties to deliver minutes reserve, secundary control and primary con-

trol services. Guinot et al.[50] found that providing primary balancing services by

an electrolyzer in France was not profitable. Kröninger and Madlener[51] found

that only purchasing minute reserve services are profitable for direct sale of hydro-

gen, but reconversion to electricity makes it unprofitable. Kopp et al.[21] compares

the profitability of all reserve services and found that providing secondary control services had the most volume and was the most profitable. Still, volumes of these services remain small. Lastly, a congestion market is used by grid operators to over- come when the transmission capacity of cables is overloaded. Larscheid et al.[20]

investigated that the utilization rate of electrolyzers can increase with more rela- tively cheap load hours by providing congestion services to grid operators.

For a combined electricity and heat system, D’Sousza et al.[52] investigated how to optimize the business model by providing different flexibility services. The potential for electrolyzer and storage operators to trade in a combination of electricity markets has not been researched yet. Moreover, Larscheid et al.[20] and Kopp et al.[21] did not research the relation between providing flexibility services and the peak shaving effect of the electrolyzer. However there is a clear indication for this since more and more congestion and imbalances are seen and expected by increased penetration of VRE sources[53]. Moreover, the low prices in these markets are expected to give an incentive to invest in more capacity to utilize these low priced volumes. Therefore, this will be the second hypothesis that is tested:

H2: Trading in multiple electricity markets will increase the peak shaving effect and profitability by optimally operating the electrolyzer and storage facility.

Optimizing the electricity portfolio

Investigations of Jiang et al.[46] and Hou et al.[45] in coupled wind-hydrogen sys- tems suggest in their conclusions that providing ancillary services with these sys- tems will increase the profitability of these systems. Kopp et al.[21] also evaluates, next to ancillary services, the excess electricity consumption of renewable sources as the lucrative power procurement option. Although, the excess electricity was re- trieved via the grid and the synergy of combining procurement of multiple sources is not investigated. Currently it is unknown which combination of sources are the best for different situations, why certain combinations would complement each other or not, and how significant the impact on profit and the peak shaving effect is. There- fore, this study will evaluate the following third hypothesis, which is the combined effect of H1 and H2:

H3: By trading in multiple electricity markets and coupling renewable energy sources to hydrogen production, an increased peak shaving effect and profitability will be reached by

optimal RES, electrolyzer and storage operation.

2.3 Future developments

Next to the production strategies, some expected future developments will reduce

the impact of the utilization rate on the annual profitability of electrolyzer and stor-

age operators and are important to consider[17]. Developments with the largest

expected influence include the decrease of electrolyzer CAPEX[16], increase of elec-

tricity price fluctuations (especially caused by higher penetration of RES)[14] and

increasing markets for green hydrogen by the development of the fuel market and

higher willingness-to-pay due to governmental stimulation[13]. Currently, it is un-

known how these future developments combined with optimized multiple sources

of electricity influence profitability and the peak shaving effect of electrolyzer oper-

ation. Therefore, it will be tested how strongly these developments will influence

the outcomes of the optimal sourcing and operation strategy of the electrolyzer and storage systems.

Decreasing electrolyzer CAPEX costs

Today’s estimations are that electrolyzer CAPEX costs will drop for PEM towards values of 397 and 955 euro/KW and for Alkaline between 787 and 906 euro/KW[54].

The costs reduction of PEM technology is more difficult to predict since it is a more recent technology than Alkaline[54]. However, the potential of cost decreases are estimated as greater for PEM[55], [54]. When the influence of electrolyzer CAPEX costs are decreasing on the hydrogen production costs, the price of electricity will become more dominant for the determination of production hours and capacity of the electrolyzer. Also, it will be less expensive to install these installations combined with RES production. Therefore, it is expected that this development will increase the strength of H1, H2 and H3.

H4a: The reduction of electrolysis CAPEX combined with optimization of electricity sources will reduce the influence of electrolyzer utilization reduction on the annual

profitability of the operator

Increasing price fluctuations

Because electricity costs have a large share in the total hydrogen production costs, fluctuation in electricity prices are an important factor in determining the economi- cal feasibility of flexible electrolyzer capacity[14], [15]. What the electricity price and fluctuations of the future will become like might be hard to predict, but it is crucial in creating energy system scenarios for the future[17], [56]. Researchers agree that the greater the share of solar and wind in the energy mix in the future, more the fluctuations in electricity prices[12], [57]and more balancing capacity is needed for increasing hours with electricity excess [9]. It is found that from 20 to 30 percent of wind penetration, there is a need for storage to overcome significant amounts of cur- tailment[8], [9], [12]. It is expected that increasing price fluctuations and the need for grid services will lead to lower utilization rates for optimal electrolyzer operation. It might especially strengthen the effect of H2.

H4b: Increasing electricity prize fluctuations combined with optimization of electricity sources will reduce the influence of electrolyzer utilization reduction on the annual

profitability of the operator

Development of green hydrogen markets

Until now green hydrogen production costs cannot compete with the lower mar-

ket prices of hydrogen produced by traditional methods for feedstock[16] and the

low natural gas price[13], [17]. For these, markets production costs have to de-

crease or consumption should be stimulated by policies before these technologies

can compete with the existing markets and production volumes and margins can

increase. Because of the high market price of fuels for mobility applications, hy-

drogen as fuel could be produced cost competitive compared to grey alternatives

F

2: Conceptual model

already[16]. However, large scale hydrogen car commercialisation and refuelling in- frastructure has to be developed first before substantial hydrogen demand as fuel is available[13]. Increasing the margins and volumes of green hydrogen markets are not expected to benefit more from coupled RES or trading in multiple electricity markets. However, they are expected benefit the profitability and peak shaving ef- fect of flexible electrolyzer operation. Therefore, the influence of this development will be tested in H4c.

H4c: Increase of hydrogen market volumes and prices combined with optimization of electricity sources will positively influence the annual profitability and peak shaving effect

of electrolyzer and storage operation

2.4 Research contributions

It is seen that a lot of research is done to develop a green hydrogen value chain. How- ever, until now the investment costs for electrolyzer and storage operators are that high that they need a lot of load hours to earn back these costs while keeping costs of green hydrogen low[12], [13], [14], [15], [16], [17]. Coupling renewable sources and electrolyzers is found to reduce curtailments[19], [48] and smooth the output[46] of renewable sources. Also, it could be a cost efficient electricity source for the elec- trolyzer[19] and the combination of solar and wind can increase the electrolyzer uti- lization[47]. Further, trading in multiple and more real time electricity markets will improve the business case of electrolyzers[19], [20], [21] and other PtG systems[52].

However, the influence of those production strategies on the peak shaving effect on

the full energy system are not evaluated. Moreover, a combined scheduling and ca-

pacity determination optimization approach[18] is not used in prior research about

both strategies. Mostly, in prior research the capacity was already determined or the

scheduling was dependent on renewable electricity generation. The combination of

both strategies to optimize the electricity portfolio of more cost efficient load hours

will be researched along with the match with overproduction hours in an energy

system with high penetration of VRE. H1, H2 and H3 are tested to draw these con- clusions. H4 will investigate the influence of the most important developments on the optimized electricity portfolio and peak shaving effect, since the environment of green hydrogen value chains is evolving rapidly. Figure 2 gives an overview of the hypotheses. In this way, this research will contribute to the knowledge about opti- mized electrolyzer and storage operation with considerations of the future energy systems needs.

3 METHODOLOGY

3.1 Research design

The main goal of this research is to gain insights into what the effects of using differ- ent electricity sources are for an electrolyzer and storage system, assuming that the hydrogen production and storage operator will strive to profit maximization. There- fore, this study is characterized as an analytical axiomatic descriptive research[58].

The model that is developed determines the optimal scheduling and capacity invest- ment for the production and storage operator of hydrogen. Therefore, it might have prescriptive insights as well[58]. However, the main purpose of this research is to in- vestigate the interrelations between multiple factors, as shown in figure 1. The linear model will give insights for electrolyzer and storage systems in general, whenever they are at renewable production locations, industrial sites or other energy hubs. It should answer the questions of hydrogen producers, wind and solar park operators and policy makers about what happens to the optimal electrolyzer and storage ca- pacity and the peak shaving effect of this system when certain decisions are made or developments take place. Scenario modelling will be applied. Hypothesises 1 to 3 are tested by analysing different system scenarios as shown in table 1. For each sce- nario, the profit of the renewable energy production operator, the electrolyzer and storage operator (or combined at the coupled scenarios) and the peak shaving effect to the national electricity grid are delivered and evaluated.

Uncoupled Uncoupled

and and

Day ahead market Multiple markets

Coupled Coupled

and and

Day ahead market Multiple markets T

1: Designed scenarios

The model will be optimized for a time frame of one year, the most recent year of which data is available. This was 2019. Due to the hourly changing electricity price [18], a yearly time frame will not result in too many variables. For example, if the model is analyzed for a period of two years, twice as much variables are needed.

However, one year is enough to consider seasonality. The electricity prices and the

availability of wind and solar power in 2019 are compared to other years to ensure

the validity of the results. Next to the scenarios in table 1, the influence of forecast-

ing errors Power Purchase Agreements (PPA’s) are tested on the outcomes of the

research. Forecasting errors could occur because in reality it is not known what the intraday and imbalance prices and volumes will be before the day ahead market closes. PPA’s are contracts between energy suppliers and consumers for multiple years. In this study PPA’s between renewable energy source operators and elec- trolyzer operators with fixed agreed prices are researched, since in practice a lot of renewable energy is purchased with these type of contracts. Both are not taken into account initially since the influence of PPA’s is related a lot to the price and for every forecasting method, the errors will be different. However, the general implications of those factors are researched and taken into account in the conclusions. Further, it is seen that some factors are developing rapidly, which are expected to have huge impact on the system value gained by electrolyzer deployment. Therefore, hypothe- sis four is evaluated by scenarios for 2030 with the predicted change in parameters.

This is chosen for 2030, since this is a milestone year considered by the Paris Climate agreement[3] and many studies made their predictions for this year[54], [12], [13].

This benefits the selection of parameters for these scenarios and makes it possible to compare the outcomes of this study with other conducted research.

3.2 Problem formulation and assumptions

The main issue that is analyzed is what electrolyzer and storage capacity will be determined and what production schedule will be followed, given the available sources of electricity and the likely developments in the future. The model should be able to optimize the economical trade-off between sourcing electricity at the cheap- est cost or utilizing the installed capacity as much as possible. Therefore, the model optimizes a scheduling and capacity determination problem[18]. In order to answer the research question, for every scenario is analyzed how much its capacity deter- mination and scheduling strategy would contribute to the balance of the national electricity grid will be evaluated. The capacity determination and scheduling model for ammonia production by electrolysis of Beehrbühl et al.[18] is used with a few additions:

• Multiple electricity sources of electricity, including different electricity mar- kets[52], [21], [20] and multiple coupled renewable electricity sources[47], [48], added in the same way as the coupled wind model of Loisel et al.[19]. Through these additions, hypotheses 1 to 3 can be tested.

• Multiple hydrogen storage options, including tank and cavern storage[31].

The cavern storage option is added since mass storage, which decreases the costs of storing large amount of hydrogen, might influence the capacity and scheduling strategy.

• Instead of ammonia production, the goal of this system is to pre-fabricate hy-

drogen to contracted parties with multiple applications for it. Hydrogen is

produced to inject into a hydrogen pipeline grid in order to serve demand for

feedstock applications. Secondly, it is injected to the same hydrogen pipeline

grid or blended in the natural gas grid for heating applications. Thirdly, it is

used to serve customers who use it for fueling purposes. Finally, it can be used

optionally to generate electricity again by a fuel cell and sell it to one of the

electricity markets[19]. The multiple applications are added to research their

impact on capacity determination and scheduling strategy, as it is part of hy-

pothesis 4. The fuel cell is added since it makes it possible to research under

what circumstances power-to-power could lead to an higher balancing value

F

3: Electrolyzer and storage operation process overview

of the hydrogen production and storage system for the electricity grid by shift- ing electricity loads.

Figure 3 shows the production and storage system that is created by these addi- tions and which is analysed by the mathematical model. The system has three main sources: water that is purchased, electricity from wind turbines and solar panels if they are installed and electricity that is bought from the grid. Electricity can be bought on the day ahead, intraday, imbalance and/or congestion market. The blue arrows describe the water flows, the light red arrows the electricity from the grid and the dark red arrows the electricity from sources within the system itself. The electrolyzer consumes water and electricity (electricity could be obtained from own wind turbines and solar panels or one of the electricity markets via the grid connec- tion) to split H

O molecules into oxygen (O

) and hydrogen (H

), and also water for cooling. The oxygen and residual heat can be captured and sold or used for other applications as well[59]. It can reduce waste and increase profitability but has no major impact on the capacity determination and scheduling strategy and is there- fore not included in this study. The flows of hydrogen with a pressure smaller or equal to 150 bars is represented by the light green arrows. The hydrogen that is pro- duced is compressed from 30 to 150 bars by the first compressor. Both compressors use water for cooling and electricity for operation. It is compressed to 150 bars, since this the largest pressure that can be stored in caverns and which can be used for the fuel cell[31]. Afterwards, the hydrogen can be stored in tanks or caverns, until it can be used for three purposes. The first one is that it is sold to the contracted gas transmission grid operator to feed it in the grid for feedstock and heating applica- tions. Secondly, it can be compressed further to 700 bars to sell it to customers for fuel applications, such as cars, busses and boats. The flows of hydrogen on a pres- sure of 700 bars are presented by dark green arrows. After compression to 700 bars hydrogen can be stored again, since otherwise large amount of compressor capacity should be installed. Finally, the hydrogen can be used to generate electricity by the fuel cell. In this order, there are two outputs of the system: electricity and hydrogen.

Electricity can be generated by the installed renewables and sold to the day ahead

market or generated by the fuel cell and sold in one of the markets. Hydrogen can

be sold to the transmission grid operator for heating and feedstock purposes and to

customers for fueling applications.

Assumptions

The following assumptions are made to create the model in this paper:

• Electricity can be bought in multiple electricity markets[52]. Electricity prices are assumed to be exogenous parameters where the electrolyzer and storage operator act as price-taker in a large market[60], [61].

• For the day ahead market, it is assumed that there is unlimited availability to purchase and sell electricity for a electrolyzer and storage operator. 40 percent of Dutch electricity consumption is traded in this market so the impact of a single electrolyzer’s demand or supply is limited. Electricity from this market will be bought with Guarantees of Origin certificates. Renewable energy pro- ducers can sell a Guarantee of Origin for every renewable MWh of electricity they produce. Consumers can buy them to give their bought electricity the

’green’ label. For the intraday, imbalance and congestion market, the available electricity to purchase and sell is limited. This is because for example there is not always congestion in the grid. Moreover, the volumes on the intraday and imbalance market are small so for large electrolyzers it might not always be possible to buy their full demand from this market.

• Electricity on the day ahead market should be bought before is known what the prices and available volumes on the other markets are during the same hour.

Therefore, there should be bought less electricity on the day ahead market to take the possibility of buying cheaper electricity on the other markets. How- ever, implications of these forecast errors are neglected. To deal with these un- certainties, multiple solutions are researched[51], [62], [63] and they will effect the performance of the researched systems in this study. However, since the purpose of this study is to research the potential of combining different sources and not the effects of different forecasting strategies, those are excluded from the scope of this research and it is assumed that near optimal predictions can be made. However, a scenario with imperfect forecasts will be performed to indicate the effect of uncertainty on the outcomes of the study.

• The price paid for green hydrogen are assumed to be stable and based on agreements with customers, since there currently is no Dutch market price for green hydrogen.

• Hydrogen can be stored in tanks or caverns. Options of liquefying hydrogen or using Liquid Organic Hydrogen Carriers are excluded to withhold the model of becoming too complex[31].

• The produced hydrogen of the electrolyzer and storage operator can be sold to the gas transmission operator to be used for feedstock and heat purposes. For fuel applications, once in the three days, a truck of a customers will come to take its share of hydrogen demand.

3.3 Data collection and parameters

To obtain realistic results from the model, real data is used for the parameters of the model. An overview of the parameters used in the model are shown in table 2.

A suitable location to test this model is the Northern region of the Netherlands,

where the project HEAVENN aims to create a hydrogen valley by coupling different

Chemical substances

H

Hydrogen O

Oxygen

Units

kg kilograms tons metric tons (1000 kg)

(k)Wh (10

) watt-hours energy m

squared meters (k)W (10

) watt electric capacity m

cubic meters

Abbreviations

DA Day ahead market FEED Feedstock for industry

ID Intraday market HEAT Heat market

IB Imbalance market FUEL Fuel market

CON Congestion services El Electricity

STC Cavern storage W Water

STT Tank storage ELY Electrolysis

STT700 Tank storage 700 bars FC Fuel cell

Comp150 Gas compressor 150 bars WIND Coupled wind

Comp700 Gas compressor 700 bars PV Coupled photo voltaic Parameters

t Time step |hours|

c

( t ) (Time dependent) unit costs of electricity, water and hydrogen from/to mar- ket v |euros per kWh (n, l), kg (m) and m

( w )|

o General operational fixed costs |euros p.a.|

ι

Capital recovery factor of unit k |percent|

Λ

Specific investment in for one unit k |euros p.a.|

ζ

Capacity per unit k installed in kW (WIND, PV, ELY, FC, Comp150, Comp700) and in kg H

(STT, STT700, STC)

m

Annual maintenance costs per installed unit k

p

( t ) Electricity production of r during t |kWh per kW installed capacity|

α

Space required for installing one unit of r generation |m

| β Space available for installing WIND and PV |m

|

θ Distance between grid and system |km|

s

( t ) Available electricity supply of market n during t |kWh|

δ

ELY design full-load electricity consumption |kWh per produced kg H

| δ

FC design full-load hydrogen consumption |kg of H

per produced kWh|

η

Operation efficiency of unit u as percentage over the input hydrogen in kg

|percent|

f

Spec. demand of input j for unit u per kg H

d

( t ) H

demand of market m during t |kg|

d

( t ) Available demand for electricity in market l |kWh|

T

2: Description of units, abbreviations and parameters

sectors in a systematic approach. Within this project, mainly the data for the location Zuidwending is used because of the following reasons:

• Currently the storage buffer of natural gas is located here and therefore, there

is a lot of pipeline capacity that can be (re-)used. Also, the ground has a salt

layer which would be applicable for cavern storage. Therefore it is a location

that is easy to connect to the hydrogen grid that will be deployed in 2023.

• Zuidwending is close to a high voltage station located in Meeden, which is a node with connections to the Dutch, German and Danish electricity markets.

Therefore, it is possible to investigate in trading in different markets at this location.

• A lot of off-shore wind production is planned in the North Sea area for the coming years[64], which will lead to a huge demand for peak shaving and storage in the province of Groningen. Also, congestion issues are foreseen in this region and a few extensions of the station in Meeden in the coming years are already planned [65].

The focus of this research is solely on this case due to time constraints though the purpose is to obtain insights that can be generalized for electrolyzer production and storage systems in general. Therefore, some characteristics of Zuidwending are changed for research purposes. First, within the HEAVENN project, Zuidwending will mainly act as a hydrogen buffer and will only produce small volumes with a 1 MW electrolyzer, as the daugther company of the gas transmission grid operator.

In this study, the location is treated as contracted production facility for 2800 tonnes per year (tpy) of industrial feedstock, 300 tpy of domestic and industrial heat and 250 tpy of mobility. It will also be difficult to install wind turbines in this area due to resistance of local inhabitants. But this option is included for research purposes.

Table 3 and table 4 give an overview of the data that is used to operate the param- eters of the model in the chosen context. The data of day ahead prices, congestion requests and weather data for solar and wind generation are on an hourly basis.

The prices on the intraday and imbalance markets are provided by the Dutch TSO

(TenneT) per quarter of an hour. However, decisions in the model will be made per

hour; otherwise four times as much decision variables are needed. Therefore, for the

prices of the intraday and imbalance markets, the average price of an hour is taken

and for the volumes of available electricity to sell and buy, the total volume of the

hour is taken. The data of 2019 will be used since it is the most actual year and there

are no big outliners or special circumstances during this year. The average Dutch

day ahead prices of the last years are between 40 and 50 euro per MWh[53]. So the

41.2 euro in 2019 is on the lower side of this spectrum. German intraday prices lay

between 30 and 40 MWh the last years. Therefore, the average German intraday

price of 36.5 euro in 2019 can be seen as comparable to other years. The volumes

of imported and exported electricity are increasing every year in the Netherlands

and Germany as well, due to the extensions of international electricity transmission

capacity in Europe[53]. The imbalance prices were, as the day ahead prices, lower

than 2018 but in the range of the previous years, which could have had to do with

high fuel prices in 2018[53]. The congestion data for GOPACS, a platform of the

Dutch electricity grid operators to overcome congestion, could not be received di-

rectly since 2019 was the first year that this platform was in operation. Therefore,

ETPA, the intraday platform that executes the buy and sell orders, is not willing to

publish this data for external parties yet. However, for every hour that congestion

occurred, market messages were published on the website of GOPACS with the date,

hours and areas where sell and buy requests were. The total volumes of redispatch

volumes per month are published by TenneT[53]. In this way, the average volume

for each sell and buy request was calculated per month and the available sell and

buy request volumes per hour in Groningen were used as available electricity sup-

ply and demand in the congestion market. The average prices for buyers and sellers

are obtained from ETPA, which are 10 and 115 euro per MWh respectively and those are assumed in the model. The average volumes in table 3 are per hour. For the volumes of available electricity supply in the intraday, imbalance and congestion market, it is assumed that 5 percent of the total available electricity in that hour can be purchased by the electrolyzer operator, since there are also other parties trading in those markets. Also for the demand of electricity in those markets, it is assumed that 5 percent of the total available electricity can be sold by the electrolyzer operator.

A limitation is the difficulty to estimate how big the competition within the markets is and it is unclear how this will develop in the future. Therefore, this is included in the sensitivity analysis to give insights into the influence of the available amount of electricity in the intraday, imbalance and congestion markets per contracted ton of hydrogen demand that should be served on the outcomes of the model.

The hourly solar and wind generation are calculated for the specific characteristics of solar panel model ’Jinko 310 Wp Full Black’, the wind turbine model ’Nordex N100 Delta 3.3MW’ and weather data from Eelde for 2019. Compared to the last five years, the wind speed (on 10 meters above the ground) of 3,6 m/s was usual and 1034 J/cm

of global radiation was above average, where the last five years were already quite sunny for the Dutch climate. The hourly electricity generation of wind turbines and solar panels is calculated with the weather data of 2019, which were 3081 full load hours for wind and 891 full load hours for solar generation. Those are comparable to the 3237 and 854 full load hours which are taken into consideration for the Dutch Climate Agreement[66]. In Appendix A, it is shown how the generation of the wind turbines and solar panels are exactly calculated. The hydrogen demand for the different markets is based on the agreed volumes in the HEAVENN project. The demand is distributed over the hours in the same way as Loisel et al.[19]. For fuel customers, tanks of hydrogen leave every three days between 9:00 and 10:00 o’clock for delivery by truck. Hydrogen demand for heat has seasonal characteristics which means that 16.2 percent of the total demand for heat is consumed in January and 1.2 percent of the total heat demand is consumed in July.

The data of the units that are shown in table 4 are retrieved from the literature and evaluated by the (contextual) experiences of a project manager of the gas storage company at Zuidwending. The capacity of the installations can be expanded linearly by installing multiple units, which leads to more CAPEX and maintenance costs.

Therefore, no economies of scale are included in this model. Further, the following

electricity and water consumption rates of the units are used. The electrolyzer con-

sumes 47.8 kWh of electricity and 0.01 m

water per kg of hydrogen that is produced

on 30 bars[31]. The compressors use each 1 kWh of electricity and 0.001 m

of wa-

ter per kg of compressed hydrogen is from 30 until 150 bars and from 150 until 700

bars[16]. The efficiency of compressing hydrogen from 30 until 150 bars is 90 percent

and from 150 till 700 bars is 85 percent[19]. The fuel cell generates 1 kWh of electric-

ity per 0.073 kg of hydrogen and consumes 0.001 m

of water per kg of hydrogen that

is processed[51]. Although currently there are pastures between the natural gas stor-

age caverns in Zuidwending and no licenses for the total area to place renewables,

potentially there is 250,000 m

of land surrounded at the caverns. Between wind

turbines there should be a space of five times the rotor diameter to maintain efficient

production. Therefore, one wind turbine requires ( 100 ∗ 5/2 )

= 62, 500 m

. For

solar fields, 3000 panels per hectare can be placed, which means 10, 000/3000 = 3.33

m

per solar panel.

Electricity hourly data µ/MWh σ Source

Day ahead prices (APX) 41.2 11.3 Transparency.entsou.eu Intraday prices Germany 36.5 41.2 Regelleistung.net

Imbalance prices 42.6 37.0 TenneT.org

Congestion prices GOPACS 10/115 - ETPA

Imported volumes Germany 124.8 219.7 TenneT.org Imbalance downregulating 23.7 41.8 TenneT.org

Congestion buy requests 58.7 320.4 GOPACS and TenneT Exported volumes Germany 114.1 41.0 TenneT.org

Imbalance upregulating 39.2 11.4 TenneT.org

Congestion sell requests 1.5 6.5 GOPACS and TenneT

Generation data Volume per Source

Wind generation per kW 3081 kWh p/a KNMI

Solar generation per kW 891 kWh p/a KNMI

Hydrogen demand feedstock 2800 tonnes p/a

HEAVENN, Loisel et al.[19]

Hydrogen demand heat 300 tonnes

p/a

HEAVENN, Loisel et al.[19]

Hydrogen demand fuel 250 tonnes

p/a

HEAVENN, Loisel et al.[19]

Price data Price per Source

Hydrogen price feedstock 2.00 per kg Michaelski et al.[16]

Hydrogen price heat 1.68 per kg Michaelski et al.[16]

Hydrogen price fuels 5.40 per kg Michaelski et al.[16]

Water price 4.00 per m

Reuss et al.[31]

T

3: Overview and statistics of hourly data collection

Unit Capacity CAPEX

(euro’s)

Maintenance (costs/a)

lifetime (years)

Main source Electrolyzer 100 (kW) 100,000 3,000 10 Reuss et al.[31]

Fuel cell 100 (kW) 100,000 6,000 5 Kroninger[51]

Compressor 257 (kW) 450,000 4,500 15 Kroninger[51]

Storage tank 80 (kg) 46,160 923,2 25 Reuss et al.[31]

Storage cavern 6 mln. (kg) 100 mln. 2 mln. 30 Reuss et al.[31]

Wind turbine 3,300 (kW) 3.63 mln. 72,600 25 Armijo et al.[48]

Solar panel 0.31 (kW) 210 3.57 25 Armijo et al. [48]

Grid connec- tion

500 (kW/km)

12500 625 20 Jiang et al. [46]

T

4: Overview unit data collection

3.4 Model formulation

This section introduces the mathematical model that is used to analyse the problem described in section 3.2. An overview of the parameters, decision variables and indices are presented and described in table 2 and 5. First, the decision variables are introduced, then the objective function and thereafter will be continued with the constraints.

Decision variables

The first sets of decision variables in the model determine the operation and schedul- ing optimization of the model. X

( t ) is the amount of electricity in kWh purchased from electricity market n during time t. Y

( t ) is the amount of electricity in kWh from coupled source r that is used for the operation of units U during t. U is a sub- set of K and consists of processing units that need to be fed with inputs j for every kg of hydrogen that is processed by u during t, which are electricity and water. The amount of electricity consumed by unit u during t is described by E

( t ) , the amount of water that is consumed by unit u during t is described by W

( t ) and the amount of hydrogen that is processed by unit u during t is described by H

( t ) . B

( t ) is the amount of hydrogen in kg that is stored in s during t. Further, Z

( t ) is the amount of electricity in kWh produced by the fuel cell that is sold to market l during t and G

( t ) is the generated electricity in kWh by source r that is directly sold to the day ahead market during t. Finally, ψ

( t ) are the kilowatt hours of generated electricity by source r during t that are curtailed. Those decision variables are real numbers and non-negative, which is represented in (1)

X

( t ) , Y

( t ) , Z

( t ) , G

( t ) , ψ

( t ) , E

( t ) , H

( t ) , W

( t ) , B

( t ) ≥ 0 (1) Next to these decision variables, there is a set of decision variables to optimize the amount of installed units per unit type k. Those are represented by C

, in kW or kg of hydrogen. C

can only take integer values, since it is not possible to install a half storage tank or a half wind turbine.

C

≥ 0 C

∈ _N (2)

Objective function

The purpose of this model is to maximize the annual profits A in euros that are earned by the electrolyzer and storage operator. It is chosen to optimize profits since this is more appropriate for short-term models with hourly decisions over a period of a year, while for long-term analysis such as optimizations over multiple years or decades, cost minimization is more usual[67]. The objective function (3) is based on the structure used in many energy optimization problems and extracts for each time unit t the costs of the systems input from the revenues of the systems output.[18]

Finally, the annual capital investment, maintenance and operational fixed costs are

extracted from the final sum of revenues and costs during all hours of time[18].

Indices

J Set of entities consumed by processing H

. J = (El |kWh|, W |m

|) ,|J|=2 V Set of markets for electricity, hydrogen and water. V = (N ∪ L ∪ M ∪ W), | V | =

10

N ⊆ V Subset of electricity buy markets. N = (1:DA-GO, 2:ID, 3:IB, 4:CON-buy),

| N | = 4

L ⊆ V Subset of electricity sell markets. N = (5:DA, 2:ID, 3:IB, 6:CON-sell), | N | = 4 M ⊆ V Subset of hydrogen markets. M = (7:FEED, 8:HEAT, 9:FUEL), | M | = 3 W ⊆ V Subset of the water market. W = (10:W), | W | = 1

K Set of units that can be installed. K = (R ∪ U ∪ S ∪ A), | K | = 10 R ⊆ K Subset of (coupled) RES. R = (1:WIND, 2:PV), | R | = 2

U ⊆ K Subset of processing units. U = (3:ELY, 4:Comp150, 5:Comp700, 6:FC), | U | = 4 S ⊆ K Subset of storage options. S = (7:STT, 8:STT700, 9:STC), | S | = 3

A ⊆ K Subset of grid connections. S = (10:Grid), | A | = 1 Decision variables

C

Amount of units k (WIND, PV, ELY, FC, Comp150, Comp700,STT, STT700, STC, Grid) that are installed.

X

( t ) Amount of purchased electricity from market n during t |kWh|

Z

( t ) Amount of electricity sold to market l during t |kWh|

Y

( t ) Electricity from coupled source r used to operate units in U during t |kWh|

G

( t ) Generated electricity of source r during t directly sold to DA |kWh|

ψ

( t ) Amount of curtailed electricity generated by source r during t |kWh|

E

( t ) Electricity consumed by unit u at time t |kWh|

H

( t ) Hydrogen processed by unit u at time t |kg|

W

( t ) Water consumed by unit u at time t |m

| B

( t ) Hydrogen stored in unit s at time t |kg|

T

5: Declaration of (decision) variables and indices

maxA =

∑

(

∑

( c

d

( t )) +

∑

( c

( t ) Z

( t )) +

∑

( c

( t ) G

( t ))

−

∑

( c

( t ) X

( t )) −

∑

( c

W

( t ))) − C

∑

( ι

Λ

+ m

) − o

(3)

The revenues of the proposed system contain sold hydrogen and sold electricity.

c

( t ) describes the costs for one unit in market v. Set V contains multiple subsets,

N are markets with costs for buying electricity in kWh during t, L are markets with

costs for selling electricity in kWh during t, M are markets for hydrogen with costs

per kg and W are costs of water in m

. For the intraday and imbalance market, costs

for buying and selling electricity are the same during t. Both costs in M and W are

fixed over the time periods. This means that the revenues for sold hydrogen are

the amount of total hydrogen demanded by contracted parties in market m during

t multiplied by the costs for each market m. The same is done for electricity, the

difference being that the prices of electricity change over time in the markets n and

l. G

( t ) is the amount of electricity that is generated by coupled source r and is not

used for operating units in U, and therefore sold in the day ahead market. Since it is not possible to ramp up the production of the coupled solar and wind installations, these installations do not have the requirements to adapt to their production plans within an hour when the demand offers in the intraday, imbalance and congestion market are communicated. Therefore, the electricity generated from coupled wind turbines and solar panels can only be sold in the day ahead market.

The costs of inputs of the system are calculated in the same way and they consist of purchased electricity and water. For every t, the costs of electricity in market n during that time are multiplied by the amount of electricity purchased. The amount of electricity purchased for the full system, equation (8), equals the amount of elec- tricity obtained from the sources and markets with the needed electricity to operate the electrolyzer and compressors. Also, the amount of water consumption is depen- dent on the amount of hydrogen that is processed per unit in U. The total consumed water times the price of water gives the water costs during t.

The annual fixed costs contain investment costs Λ

per installed unit k. ι

is the cap- ital recovery factor of unit k. m

are the annual maintenance costs of unit k, which are obtained by dividing the percentage of the total investment costs expected for the maintenance of unit k by the expected life time in years of unit k [31], [16]. Oper- ational fixed costs (o) include loans for daily operation of the installations[18].

(Coupled) RES constraints

The way coupled renewable energy sources (RES) are modelled is based on the cou- pled wind hydrogen system model of Loisel et al.[19]. p

( t ) determines the produc- tion of RES r in kWh during t per installed capacity in kW. This is the amount of units r (C

and C

) installed times the capacity of one unit r (ζ

). The amount of elec- tricity from coupled source r that is sold in the day ahead market (G

( t ) ), consumed by processing units U (Y

( t ) ) and curtailed (ψ

( t ) ) during t should be equal to the available electricity from RES r during t (p

( t ) C

ζ

) because more electricity than available cannot be used. The electricity will be curtailed if there is more electricity than can be used by the electrolyzer, compressors and grid connection capacity to sell it in the day ahead market. Moreover, the decision to curtail electricity can be made when negative prices occur in the day ahead market.

G

( t ) + Y

( t ) + ψ

( t ) ≤ p

( t ) C

ζ

1, 2 ∈ R ∪ K (4) It is not possible to couple and install an unlimited amount of wind turbines and so- lar panels without grid connection to the hydrogen production and storage facilities, due to the limited space available in the neighbourhood. Therefore, a space limiting constraint is added [44]. β represents the area available in m

and α

is the required space in m

per installed unit of RES r.

C

α

+ C

α

≤ β (5)

The grid connection should be invested in to connect the renewable electricity sources

and the electrolzyer and storage system to the grid. Furthermore, the amount of in-

vestment in cables depends on the distance between the system and the grid connec-

tion, which is described by θ. C

is the amount of cables that is needed. One cable

has the capacity of transporting 500 kW of electricity over one kilometer (see table

4) and includes an investment of 12500 euros (Λ

0). So for example, if the distance

between the electricity grid and the system is two kilometers (θ) and should be able

to transport 1000 kWh of electricity per hour, the amount of cable needed is four (two kilometers long and double amount of capacity needed). The amount of elec- tricity that is transported from and to the system during t is the sum of the electricity produced by the renewable sources that is sold to the day ahead market (G

( t ) ), the sum of the electricity purchased in the electricity markets (X

( t ) ) and the sum of electricity generated by the fuel cell that is sold to the electricity markets (Z

( t ) ).

This should be less or equal than the grid connection capacity that is installed. The grid connection capacity is the amount of cables (C

) times the transport capacity per cable (ζ

) divided by the distance between the grid and the ELY-ST system (θ).

Which was

= 1000 kW in the example.

∑

G

( t ) +

∑

X

( t ) +

∑

Z

( t ) ≤ ^C

10

ζ

θ (6)

Electricity sourcing constraints

For the day ahead market, it is assumed that an unlimited supply of electricity is available[60], [61]. However, in the intraday market, imbalance market and conges- tion market, limited volumes are available during t[21]. Therefore, the purchased amount of electricity from market n is constrained by s

( t ) which represents the available volume in kWh in market n for price c

( t ) during t.

X

( t ) ≤ s

( t ) for 2, 3, 4 ∈ N (7) The electricity demanded by the processing units U during t[18] should be equal to the electricity that is received from the markets and coupled resources[19]. E

( t ) represents the electricity consumption of unit u during t in kWh. The fuel cell is not consuming electricity, so E

( t ) is always zero.

∑

X

( t ) +

∑

Y

( t ) =

∑

E

( t ) (8)

E

( t ) = 0 (9)

The amount of electricity that processing unit u consumes during t can not exceed the total capacity that is installed for ELY, Comp150 and Comp700 in u[18], [19].

Also here, the fuel cell is not included in this equation, the capacity is constrained in equation (20), since this processing unit does not consume electricity but generates electricity.

E

( t ) ≤ C

ζ

for 3, 4, 5 ∈ U ∪ K (10)

Electrolysis constraints

The efficiency of the electrolyzer is determined by its load factor, since the electricity

consumption per produced kg of hydrogen corresponds to the higher heating value

of hydrogen (HHV

)[68]. Beerbühl et al.[18] showed the difference between nonlin-

ear load dependent electrolyzer scheduling and linear scheduling. When using non-

linear functions, the load of the electrolyzer will be scheduled more often between 0