A Techno-Economic Feasibility Analysis of a Hydrogen Power Plant in a Market Environment

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A Techno-Economic Feasibility Analysis of a Hydrogen Power Plant in a a

Market Environment

Luís Manuel Dias Rodrigues

Master’s Degree in Electrical and Computer Engineering Supervisor: Doutor Tiago André Teixeira Soares

Co-Supervisor: Prof. Doutor Vladimiro Henrique Barrosa Pinto de Miranda

February 28, 2023

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This work was carried out with the support of INESC-TEC and supervised at this institution by Igor Roberto Rezende e Castro de Abreu.

The following person collaborated with the supervising team in carrying out this work: João Paulo Fontoura de Oliveira.

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Atualmente, as alterações climáticas são consideradas um desafio global que exige uma ação imediata e sustentada. Enfrentar este problema requer uma abordagem multifacetada que envolve a redução da emissão de gases com efeito de estufa, melhorias de eficiência energética, e a promoção da utilização de fontes de energia renováveis, tais como a energia eólica e solar. No entanto, estas fontes de energia têm problemas relacionados com a sua elevada volatilidade e intermitência, o que significa que nem sempre podem satisfazer o consumo de forma consistente.

Uma das opções disponíveis com potencial para ultrapassar este problema é o hidrogénio, um portador de energia que é também o elemento mais abundante em todo o Universo. Contudo, os seus principais métodos de produção, baseados em combustíveis fósseis, não estão alinhados com as metas energéticas e ambientais definidas a longo prazo. No entanto, no caso do hidrogénio verde, obtido a partir da eletrólise da água utilizando energia de fontes renováveis, a sua produção e utilização não liberta dióxido de carbono para a atmosfera, tornando-o uma opção para auxiliar à transição energética em curso. O hidrogénio pode ser utilizado para armazenar energia durante longos períodos, substituir combustíveis fósseis usados em transportes e no aquecimento, e ser empregue como matéria-prima em vários processos industriais.

Por conseguinte, a União Europeia e muitos dos seus estados-membros, incluindo Portugal, têm definido estratégias para promover a produção, comercialização e utilização do hidrogénio para múltiplos usos. Mas, a criação de um ecossistema de hidrogénio de sucesso acaba por recair sobre a sua viabilidade económica.

Neste contexto, este trabalho está centrado no estudo e simulação do funcionamento de uma central de produção de hidrogénio para a produção de energia e para o fornecimento de vários clientes. Dois modelos e análises principais são realizados separadamente.

Na primeira análise, a Central de Hidrogénio participa num mercado de eletricidade, onde compra e vende energia elétrica, enquanto produz e vende hidrogénio para vários clientes. A op- eração da central é modelada utilizando um problema de otimização cujo objetivo é maximizar os lucros. Aqui, são especificadas as características técnicas e económicas dos principais com- ponentes da central de hidrogénio. São realizadas múltiplas simulações sob estas condições. Os resultados, relacionados com os preços do hidrogénio e vários indicadores financeiros, são calcu- lados e apresentados. Uma conclusão desta análise é que, atualmente, a opção mais económica é o hidrogénio cinzento eletrolítico, com um custo entre 4.72 C/kg e 6.88 C/kg. Relativamente à produção de hidrogénio verde, são simulados dois cenários principais. O primeiro conduz a um custo entre 10.6 C/kg e 21.7 C/kg, e entre 7.57 C/kg e 7.59 C/kg, no segundo.

Na segunda análise, a Central de Hidrogénio é instalada numa rede de distribuição, onde inte- gra uma Central de Energia Virtual. Mais uma vez, é utilizada como um problema de otimização para modelar o funcionamento da rede e dos Recursos Energéticos Distribuídos, mas visando min- imizar o custo de operação da rede. São realizadas várias simulações mediante diferentes cenários, onde se assume uma elevada prevalência de Fontes de Energia Renováveis. Os resultados mostram

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que a utilização de hidrogénio como Solução de Armazenamento de Energia tem um efeito pos- itivo na operação da rede. Este efeito foi mais notável durante a primavera e o verão, mas ainda é considerável nas restantes estações do ano. Com a adição da Central de Hidrogénio, foi pos- sível reduzir os custos de operação da rede, receber uma receita adicional da comercialização de hidrogénio e diminuir a dependência de fontes de energia externas, incluindo fontes de energia não renováveis.

Uma importante contribuição deste trabalho para o estado da arte é o desenvolvimento e im- plementação de dois modelos matemáticos para o funcionamento de Centrais de Hidrogénio, operando isoladamente ou integradas com vários Recursos Energéticos Distribuídos numa rede de distribuição.

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Today, climate change is regarded as a global challenge that demands immediate and sustained action. Tackling this major issue requires a multipronged approach that involves reducing the emission of greenhouse gases, increasing energy efficiency, and promoting the use of Renewable Energy Sources, such as wind and solar power. Nonetheless, these energy sources entail problems linked to their high volatility and intermittency, meaning they cannot meet steady energy demand.

One of the available options with the potential to help to overcome this problem is hydrogen, an energy carrier that is also the most abundant element in the entire Universe. However, its main production methods, based on fossil fuels, are not yet aligned with the long-term energetic and environmental goals. But, in the particular case of green hydrogen, obtained from the electrolysis of water using power from Renewable Energy Sources, its production and usage do not release carbon dioxide into the atmosphere, making it an option to assist in the ongoing energy transition.

It can be used to store energy for long periods of time, replace fossil fuels in mobility and heating sectors, and serve as a clean raw material for many industrial processes.

Therefore, the European Union and many of its member states, including Portugal, have been setting strategies to promote the production, commercialization, and use of green hydrogen. But, the creation of a successful hydrogen ecosystem ultimately falls upon its economic viability.

In this context, this work is centred on studying and simulating the operation of a Hydrogen Power Plant producing hydrogen for power generation and for supplying several customers. Two main models and analyses are carried out separately.

In the first analysis, the Hydrogen Power Plant strategically participates in an energy market, where it buys and sells electricity while producing and selling hydrogen for multiple customers.

This is modelled using an optimization problem whose objective is to maximize profits. This study includes the specification of the technical and economical characteristics of the main components of this power plant. Multiple simulations considering its participation in the Iberian Electricity Market are performed under these conditions. The results, related to hydrogen prices and several financial indicators, are computed and presented. An important conclusion from this analysis is that electrolytic grey hydrogen is the most economical option today, with a Levelised Cost Of Hydrogen ranging from 4.72 C/kg to 6.88 C/kg. Regarding the production of greenH₂, two main scenarios are simulated. The first one leads to a Levelised Cost Of Hydrogen between 10.6 C/kg and 21.7 C/kg, and between 7.57 C/kg and 7.59 C/kg, on the second one.

In the second analysis, the Hydrogen Power Plant is installed in a distribution grid, where it integrates a Virtual Power Plant. It is used an optimization problem to model the operation of the grid and Distributed Energy Resources, but with the objective to minimize grid operating cost.

Multiple simulations are carried out under different operating scenarios, where it is assumed a high prevalence of Renewable Energy Sources. Results show that the usage of hydrogen as an Energy Storage Solution has a positive effect on grid operation. This effect was more notable during Spring and Summer, but it is still considerable in the remaining seasons. With the addition of the Hydrogen Power Plant, it was possible to reduce grid operation costs, receive additional revenue

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from hydrogen commercialization and decrease dependence on external resources, including non- renewable energy sources.

An important contribution of this work to the state of the art is the development and implemen- tation of two mathematical models for the operation of Hydrogen Power Plants, either operating alone or integrated with several Distributed Energy Resources in a distribution grid.

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First and foremost, I would like to thank my supervisor, Dr Tiago Soares, for his availability, guidance, and patience. His experience and enthusiasm were vital to the development of this work.

To my co-supervisor, Prof. Dr Vladimiro Miranda, I would like to express my gratitude for contributing to my academic journey at FEUP.

To Igor Rezende and João Fontoura, I cannot thank them enough for all the time and for the assistance they gave me over the last few months.

I want to thank my parents for everything they have done for me, for all the unconditional support and for all the opportunities they have allowed me to have. This achievement would not have been possible without them.

To my friends and colleagues who were by my side along this journey, thank you for all the good moments spent together.

Lastly, a special thanks to FEUP and INESC-TEC, where every day I had and have the chance to learn from the best.

Thank you, Luís

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Antoine de Saint-Exupéry

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1 Introduction 1

1.1 Context and Motivation . . . 1

1.2 Objectives . . . 3

1.3 Related projects and publications . . . 4

1.4 Structure of the dissertation . . . 5

2 State of the Art 7 2.1 Hydrogen . . . 7

2.2 The hydrogen colour spectrum . . . 8

2.3 Electrolysers and water electrolysis . . . 9

2.3.1 Available technologies . . . 11

2.3.2 Efficiency . . . 12

2.3.3 Water consumption . . . 13

2.3.4 Costs . . . 13

2.4 Hydrogen compression . . . 14

2.4.1 Hydrogen density at different temperatures and pressures . . . 14

2.4.2 Hydrogen compression thermodynamics . . . 17

2.4.3 Hydrogen compressor power calculation . . . 18

2.4.4 Hydrogen compressor cost . . . 20

2.5 Hydrogen storage and transportation . . . 20

2.5.1 Compressed hydrogen . . . 20

2.5.2 Cryogenic hydrogen . . . 22

2.5.3 Cryo-compressed hydrogen . . . 23

2.5.4 Chemical hydrogen storage . . . 23

2.5.5 Hydrogen adsorption . . . 24

2.6 Fuel Cells . . . 24

2.6.1 Efficiency . . . 24

2.6.2 Fuel cell based cogeneration . . . 24

2.7 Hydrogen-powered Material Handling Equipment . . . 25

2.8 Hydrogen Refuelling Stations . . . 28

2.8.1 Structure and operation of HRS . . . 29

2.8.2 Hydrogen Refuelling Stations for MHE . . . 30

2.9 Analysis of relevant projects and publications . . . 31

2.9.1 Projects review . . . 31

2.9.2 Scientific papers review . . . 42

2.9.3 Overview of the reviewed projects and publications . . . 43 xi

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3 Hydrogen Power Plant Model 45

3.1 Hydrogen Power Plant structure . . . 45

3.2 Hydrogen Power Plant operator model . . . 46

3.2.1 Problem description . . . 46

3.2.2 Mathematical formulation . . . 47

3.3 Virtual Power Plant model with a Hydrogen Power Plant . . . 51

3.3.1 Problem description . . . 51

3.3.2 Mathematical formulation . . . 52

4 Simulation of a H2PP in an Energy Market 59 4.1 Techno-economic characteristics of the H₂PP . . . 59

4.2 Customer portfolio . . . 63

4.2.1 CHP microturbine . . . 63

4.2.2 Forklift fleet . . . 65

4.2.3 Transportation tube trailer . . . 66

4.2.4 Comparison between customers and hydrogen price for each one . . . 66

4.3 Simulation scenarios for a standalone operation of the H₂PP . . . 67

4.3.1 Simulation results of base case scenarios . . . 69

4.4 Simulation sub-scenarios for a standalone operation . . . 73

4.4.1 Removing one service at a time . . . 74

4.4.2 Considering the existence of only one service at a time, without changes . 76 4.4.3 Considering the existence of only one service at a time, changing its details 78 4.4.4 Changing the price of only the fuel cell . . . 80

4.5 Comparing hydrogen prices for each customer with other fuels . . . 84

4.5.1 CHP microturbine . . . 84

4.5.2 Forklift fleet . . . 85

4.5.3 Tube trailer . . . 86

4.6 Summary . . . 87

5 Simulation of a H₂PP as part of a VPP 89 5.1 Case characterization . . . 89

5.2 Results . . . 92

5.2.1 BAU: Distribution grid operation without the H₂PP . . . 92

5.2.2 Case 1: Base case with the H2PP . . . 96

5.2.3 Case 2: H2PP single service (Fuel Cell) . . . 100

5.2.4 Case 3: H₂PP operates without the Fuel Cell . . . 101

5.2.5 Case 4: Increased Capacity Factor for wind power . . . 102

5.2.6 Case 5: Limited line capacity with H2PP disconnected from the grid . . . 103

5.2.7 Case 6: Limited line capacity with H₂PP connected to the grid . . . 105

5.3 Summary . . . 107

6 Conclusion 109 6.1 Conclusions . . . 109

6.2 Future work . . . 111

References 113

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1.1 Global net electricity generation by source . . . 2

1.2 Hydrogen value chain . . . 3

2.1 Hydrogen colour spectrum . . . 8

2.2 Generic structure of an electrolytic cell . . . 10

2.3 H₂density under certain temperature and pressure conditions . . . 15

2.4 CompressedH₂density assuming an ideal gas and a non-ideal gas . . . 16

2.5 Compressibility factor Z ofH₂gas for different values of p and T . . . 16

2.6 Adiabatic compression work for methane, helium and hydrogen . . . 18

2.7 Energy required for compressing hydrogen compared to its HHV . . . 18

2.8 (a) Toyota 700 barH₂car tank (b) Hydrogenics 65m³- 30 bar tank . . . 21

2.9 (a)H₂pipelines (b)H₂tube trailer . . . 22

2.10 (a) Cryogenic tanker truck (b) LiquidH₂tank at NASA’s KSC . . . 23

2.11 Structure of a Hydrogen fuel cell forklift . . . 26

2.12 Structure of a HRS . . . 28

2.13 Structure of a HRS for MHE . . . 30

2.14 (a) Monthly distribution of load coverage (b)H₂SOC over the year . . . 33

2.15 (a) Daily load in 4 different months (b) HPP production and load . . . 34

2.16 (a) Monthly PV production and load (b) Monthly energy surplus and deficit . . . 35

2.17 (a) Colruyt Group logistic centre (b) Don Quichote demonstration plant . . . 37

2.18 Don Quichote technical layout . . . 37

2.19 (a) HyBalance facility (b) Tube trailer to transportH₂to customers . . . 38

2.20 Current of stack A and B andH₂flow during: (a) ramp up (b) ramp down . . . . 39

2.21 (a) The Raggovidda Wind Park (b) The Raggovidda wind-Hydrogen facility . . . 40

2.22 Diagram Raggovidda wind-Hydrogen facility . . . 40

3.1 Schematic of the structure of theH₂PP and its customers . . . 46

3.2 Overview of theH₂PP’s dispatch and economic analysis . . . 47

3.3 Overview of the VPP cost minimization algorithm. . . 52

4.1 Daily load curve of the CHP microturbine . . . 65

4.2 MaximumH₂intake of the forklift fleet HRS . . . 65

4.3 Hydrogen tube trailer loading procedure . . . 66

4.4 Grey scenarios - Relation between payback andH₂price for each customer . . . 70

4.5 Green scenarios - Relation between payback andH₂price for each customer . . . 71

4.6 PPA scenarios - Relation between payback andH₂price for each customer . . . . 71

4.7 Relation between the payback and fuel cell’s energy selling price . . . 81

4.8 Relation between the energy produced by the fuel cell and its selling price . . . . 81

4.9 Relation between the payback and fuel cell’s energy selling price . . . 82 xiii

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4.11 Relation between the payback and fuel cell’s energy selling price . . . 83

5.1 Configuration of the 37-bus distribution grid . . . 90

5.2 Load and renewable generation profiles in a typical day of Winter and Spring . . 91

5.3 Load and renewable generation profiles in a typical day of Summer and Autumn . 91 5.4 Wind and solar PV generation profiles in a typical day of Winter and Spring . . . 92

5.5 Wind and solar PV generation profiles in a typical day of Summer and Autumn . 92 5.6 BAU - Generation and load diagram during a Winter day . . . 94

5.7 BAU - Generation and load diagram during a Spring day . . . 94

5.8 BAU - Generation and load diagram during a Summer day . . . 95

5.9 BAU - Generation and load diagram during an Autumn day . . . 95

5.10 Case 1 - Generation and load diagram during a Winter day . . . 98

5.11 Case 1 - Generation and load diagram during a Spring day . . . 98

5.12 Case 1 - Generation and load diagram during a Summer day . . . 99

5.13 Case 1 - Generation and load diagram during an Autumn day . . . 99

5.14 Case 5 - Voltage levels and line capacity at 21 h in Winter . . . 104

5.15 Case 6 - Voltage levels and line capacity at 21 h in Winter . . . 106

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2.1 Chemical properties ofH₂and other fuels at STP . . . 7

2.2 Cost of different electrolysers, according to type and rated power . . . 14

2.3 H₂compressors estimated energy consumption. . . 19

2.4 Parameters for the proposed correlation . . . 20

2.5 Characteristics of six stationaryH₂tanks available in the market . . . 21

2.6 Locations of six salt caverns used forH₂storage . . . 22

2.7 Efficiency of multiple fuel cells . . . 25

2.8 Main characteristics of five different HRS in Europe . . . 29

2.9 Demo 1: Technical details of the electrolyser and fuel cell. . . 32

2.10 Demo 1: Technical details of the battery bank . . . 32

2.11 Demo 1: Technical details of the hydrogen tank . . . 32

2.12 Demo 1: Annual RES usage . . . 32

2.13 Demo 2: Technical details of the electrolyser and fuel cell . . . 33

2.16 Demo 3: Technical details of the electrolyser and fuel cell . . . 35

2.19 Demo 3: Yearly load and RES supply data . . . 36

2.20 First phase investment expenses (without VAT) . . . 38

2.21 Technical data of the electrolyser . . . 41

2.22 Economic data of the electrolyser . . . 41

2.23 Technical data of the fuel cell . . . 41

2.24 Services identified in the literature review . . . 43

4.1 Technical characteristics of the electrolyser . . . 60

4.2 Technical characteristics of the hydrogen storage tank . . . 60

4.3 Technical characteristics of the fuel cell . . . 60

4.4 Technical characteristics of the forklift fleet compressor . . . 60

4.5 Technical characteristics of the tube trailer charging compressor . . . 61

4.6 Economic aspects of the electrolyser . . . 61

4.7 Economic aspects of the hydrogen storage tank . . . 62

4.8 Economic aspects of the fuel cell . . . 62

4.9 Economic aspects of the forklift fleet compressor . . . 62

4.10 Economic aspects of the tube trailer charging compressor . . . 62

4.11 Parameters used in the economic analysis . . . 63

4.12 Technical characteristics of the CHP microturbine . . . 64 4.13 CHP hourly electrical output and fuel intake for aH₂volumetric percentage of 10% 64

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4.14 Consumption of each gas for aH₂volumetric percentage of 10% . . . 64

4.15 List and description of the six main simulation scenarios . . . 68

4.16 Average price of electricity in Portugal and number of green hours . . . 69

4.17 H₂prices for each customer, to reach a 13 years payback. . . 69

4.18 H₂prices for each customer to reach a payback period of 11 years and 15 years. . 72

4.19 Economic metrics corresponding to a 13 years payback. . . 72

4.20 Average yearlyH₂production and consumption, for a 13 years payback. . . 72

4.21 Grey17-20 Removing one service at a time:H₂prices for a 13 years payback . . 74

4.22 H₂prices for each customer, to reach a 22 years payback, without fuel cell. . . . 75

4.23 Green21 Removing one service at a time:H₂prices for a 13 years payback . . . 75

4.25 PPA17-20 Removing one service at a time:H₂prices for a 13 years payback . . . 76

4.27 Grey17-20 Only one service with no changes:H₂prices for a 13 years payback . 77 4.28 Green21 Only one service with no changes:H₂prices for a 13 years payback . . 77

4.29 PPA17-20 Only one service with no changes:H₂prices for a 13 years payback . 78 4.30 Grey17-20 Only one service, changing its details:H₂prices for a 13 years payback 79 4.31 Green21 Only one service, changing its details:H₂prices for a 13 years payback 79 4.32 PPA17-20 Only one service, changing its details:H₂prices for a 13 years payback 80 4.33 H₂prices for each customer, to reach a 13 years payback. . . 80

4.34 Price evolution of natural gas in the Portuguese market, excluding VAT . . . 85

4.35 H₂prices for CHP customer, to reach a 13 years payback. . . 85

4.36 H₂prices for forklift fleet, to reach a 13 years payback. . . 86

4.37 Price evolution of diesel for a bus operating company . . . 86

4.38 H₂prices for the tube trailer, to reach a 13 years payback. . . 87

5.1 Energy resources availability . . . 89

5.2 BAU: Energy resources bids andH₂prices . . . 93

5.3 BAU - Simulation results for a day of each season . . . 93

5.4 Case 1: Energy resources bids andH₂prices . . . 96

5.5 Case 1 - Simulation results for a day of each season . . . 97

5.13 Case 5 - Simulation results for a Winter day . . . 105

5.14 Case 5 - Average bus voltage and power line utilization . . . 105

5.16 Case 6 - Simulation results for a Winter day . . . 107

5.17 Case 6 - Average bus voltage and power line utilization . . . 107

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AWE Alkaline Water Electrolysers BAU Business As Usual

BESS Battery Energy Storage System BHM Biological Hydrogen Methanation CAPEX Capital Expenditure

CCGT Combined Cycle Gas Turbine CCS Carbon Capture and Storage CF Capacity Factor

CGS Residential Cogeneration System CHP Combined Heat and Power CO₂ Carbon Dioxide

DER Distributed Energy Resources DG Distributed Generation EU European Union

FC Fuel Cell

FCEV Fuel Cell Electric Vehicles FIT Feed-In Tariff

G2P Gas-to-Power

GAMS General Algebraic Modeling Language GHG Greenhouse Gas

H₂ Hydrogen

H2O Water

H2PP Hydrogen Power Plant HHV Higher Heating Value

HICEV Hydrogen Internal Combustion Engine Vehicles HPP Hydropower Plants

HPV Hydrogen Powered Vehicles HRS Hydrogen Refuelling Station HSS Hydrogen Storage System IRR Internal Rate of Return LCOE Levelized Cost Of Electricity LCOH Levelized Cost Of Hydrogen LHV Lower Heating Value

LOHC Liquid Organic Hydrogen Carriers MHE Material-Handling Equipment MIBEL Mercado Ibérico de Eletricidade MIP Mixed Integer Programming

NG Natural Gas

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NPV Net Present Value OPEX Operational Expenditure P2G Power-to-Gas

P2P Power-to-Power

PEM Proton Exchange Membrane

PEME Proton Exchange Membrane Electrolysers PEMFC Proton Exchange Membrane Fuel Cell PHES Pumping Hydroelectric Storage PPA Power Purchase Agreement PV Photovoltaic

RES Renewable Energy Sources ROI Return On Investment SOC State Of Charge

SOE Solid Oxide Electrolysers SPU Small Production Unit

STP Standard Temperature and Pressure SU External Supplier

TCO Total Cost of Ownership TRL Technology Readiness Level VPP Virtual Power Plant

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Sets

N_bus Set of buses N_DG Set of DG units Nload Set of loads Nstorage Set of storage units T Set of time periods Indexes

g Index for DG units i, j Indexes for buses l Index for loads st Index for storage units

t Index for time periods (e.g., 30 min (0.5), 60 min (1.0)) Parameters

η Efficiency π Price (m.u./pu)

B Susceptance, imaginary part in Admittance matrix (S) G Conductance, real part in Admittance matrix (S) HHV Higher Heating Value (kWh/kg)

LHV Lower Heating Value (kWh/kg) Decision variables

θ Phase angle B Binary variable m Mass

P Active Power Q Reactive Power S Apparent Power V Voltage magnitude X Binary variable Y Binary variable

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Subscripts and Superscripts

B Buying

Ch Charge process

CHP Combined Heat and Power

CP Compressor

Cut Generation curtailment power Dch Discharge process

ELEC Electrolyser

Export Exported to the transmission network FC Fuel Cell

FL Forklift

H₂ Hydrogen

Import Imported from the transmission network Max Upper bound limit

Min Lower bound limit NG Natural Gas

S Selling

Shed Shed load TRSP Transport TT Tube Trailer

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Introduction

This chapter exposes the motivation and the objectives of the work developed in the scope of this dissertation. More precisely, at first, the context in which this work is done and the motivation to develop it are exposed. Subsequently, the primary goals of this project are detailed, followed by a mention of other related projects and publications. At last, the structure and organization of this document are detailed.

1.1 Context and Motivation

In an effort to reduce the environmental impact of human activities and fight against climate change, the European Union (EU) intends to be climate-neutral by 2050, running on an economy with net-zero Greenhouse Gases (GHG) emissions [1]. This is in line with the goals of the 2015 Paris Agreement to keep the global temperature increase well beneath 2 °C and make efforts to keep it to 1,5 °C [2].

This evolution to a more sustainable society is a pressing need and an opportunity to lay the foundations for a better future for all. However, as countries keep developing and the human population keeps growing, the demand for energy is expected to continue rising [3]. To address this situation, the investment in Renewable Energy Source (RES), such as wind and solar power, is on the rise, and, as seen in Figure 1.1, their contribution is expected to keep growing over the next few decades. In spite of their benefits, RES also has some drawbacks. An important downside of these sources of energy is their intermittency, which means their output has a fast and uncontrollable variability, and their uncertainty [4].

For a normal and reliable operation of power systems, the variation of the production results in the need for additional electricity on the grid to balance demand and supply. Therefore, Energy Storage Systems (ESS) can be used to compensate for the volatility of wind and solar power.

The storage solutions can be based, for instance, on Battery Energy Storage System (BESS) or Pumping Hydroelectric Storage (PHES), but there is also the potential to do it using solutions based on hydrogen (H2) [6].

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Figure 1.1: Global net electricity generation by source [5].

Hydrogen is regarded as a flexible energy carrier with multiple applications across several sectors. It can be used in construction, industrial processes, transports, heating, and power generation, as depicted in Figure1.2[7].H₂also has the potential to replace fossil fuels in a variety of carbon- intensive processes, such as steel and chemical industry [8]. BlendingH₂with Natural Gas (NG) is also being considered to reduce Carbon Dioxide (CO2) emissions when burning methane [9].

Hydrogen Powered Vehicles (HPV) already exist and are divided into two different categories:

Fuel Cell Electric Vehicles (FCEV), where a fuel cell powered withH₂supplies electricity to electric motors, and Hydrogen Internal Combustion Engine Vehicles (HICEV), which have a modified version of the gas-powered internal combustion engine [10].

Due to its versatility,H₂produced from RES through electrolysis, called greenH₂, can have a crucial role in the pathway towards decarbonization, as its production and usage does not release CO₂to the atmosphere [11].

However, so farH₂ represents only a very small fraction of the European energy mix and is mainly produced from fossil fuels, commercialized at prices between 1.5 C/kg and 2 C/kg [8]. By the end of 2021, around 47 % of the globalH₂ production was from NG, 27 % from coal, 22 % from oil, and only about 4 % was greenH₂ [11]. ForH₂to really contribute to the fight against climate change, it is necessary to expand its production without the release of GHG [8].

As previously mentioned, wind and solar power are on the rise, but they have high volatility and intermittency. In order to mitigate this problem, it is possible to convert the RES surplus into H₂ through the electrolysis of water in a process called Power-to-Gas (P2G), since electric power is being used to produceH₂in the gaseous state. TheH₂gas shall then be stored for future use, being used as a fuel to produce electricity using fuel cells when it is more convenient. This second process is called Gas-to-Power (G2P). Combining Power-to-Gas and Gas-to-Power results in Power-to-Power (P2P), withH₂acting as storage.

In the past, there was some interest in greenH₂, but it never materialized. Today, with the cost decline of RES, technological developments and the pressing need to decrease GHG emissions,

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Figure 1.2: Hydrogen value chain [7].

Europe has a stronger interest inH₂that brings many new possibilities [8]. The contribution ofH₂ in the EU’s energy mix is expected to increase from only 2 % today to 13-14 % by 2050 [8].

Portugal, as a member of the EU, presented its National Strategy for Hydrogen (EN-H₂) in 2020, which intends to promote the gradual introduction ofH₂in multiple sectors of the economy.

This is regarded as an opportunity for the country to diversify and increase its security of energy supply [12]. Among the goals set in EN-H₂ until 2030 is the creation of 50 to 100 Hydrogen Refueling Station (HRS) in the national territory, reaching 2 GW to 2.5 GW of installed capacity in electrolysers and achieving an admixture of 10% to 15% of H₂ to NG in the NG network, by volume [13]. The Portuguese roadmap is aligned with the pursued environmental goals and decarbonization strategy, which also anticipates the decommissioning of several thermal power plants (coal and Combined Cycle Gas Turbine (CCGT) power plants) in Portugal and Spain [14].

For this study, the most interesting application of H₂ is its utilization as an energy carrier, allowing for energy storage and electricity generation, as well as sellingH₂ to other end users in the industry and transportation sectors.

1.2 Objectives

The decarbonization of the energy system depends heavily on the ability to largely integrate RES and store their surplus to be used in periods of energy scarcity or imbalance. More precisely, H₂will play a significant role as a way to store energy surplus from RES, which can be used later

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on to supply industries, transportation, NG networks and power systems. So, a market for green H₂ will emerge to assist energy systems through the desired decarbonization, and therefore, H₂ Power Plants (H₂PP) will play a major role.

In the context of assessing the role of aH₂PP in a market and network operating perspective, the specific objectives defined for this dissertation were the following:

• Identifying the key aspects of H₂ production and storage, with a particular focus on green H₂, and its main end-uses;

• Research, design, and development of aH₂PP energy model to be integrated into a market and energy dispatch problems;

• Integration of theH₂PP energy model into a market framework to assess the strategic participation of theH₂PP in multi-energy services in the Portuguese context;

• Design and development of a distribution network management methodology for the integration of a megawatt-scaleH₂PP in the distribution network, considering a large penetra- tion of Distributed Energy Resources (DER);

• Assess the techno-economic viability of integratingH₂PP in the Portuguese context.

1.3 Related projects and publications

The work developed in the scope of this dissertation partially concerns the objectives and results of two research projects, namely:

• DECARBONIZE – Development of strategies and policies based on energy and non-energy applications towards CARBON-neutral cities via digitalization for citizens and society (NORTE-01-0145-FEDER-000065);

• DECMERGE – Decentralized decision-making for multi-energy distribution grid management

(2021.01353.CEECIND).

The developed work has resulted in the writing of two scientific papers for journal publication.

The following should be referred to:

• Luís Manuel Rodrigues, Tiago Soares, Igor Rezende, João Paulo Fontoura and Vladimiro Miranda, “Economic Analysis of a Hydrogen Power Plant in the Portuguese Electricity Market”, Energies, vol. 16, no. 3, 1463, 2023 DOI:10.3390/en16031506;

• Luís Manuel Rodrigues, Tiago Soares, Igor Rezende, João Paulo Fontoura and Vladimiro Miranda, “Distributed Energy Resources Dispatch Considering a Hydrogen Power Plant”, Electric Power Systems Research (EPSR), ongoing.

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1.4 Structure of the dissertation

This document is organized into six chapters, whose content is summarized next.

Chapter 1 provides an introduction and general summary of the topic, presenting the main motivation and its relevance. The main goals of the work and the structure of the document are also outlined.

Chapter 2aims to present and describe the most important aspects and processes related to H₂and its value chain, with a specific focus on greenH₂. It begins with an overview of the most important characteristics ofH₂ and electrolysis. This is followed by a description of the main electrolyser types, storage techniques andH₂end-uses, including some of their technical aspects.

A review of recent projects and publications centred around the production, storage and usage of H₂in multiple activities is also carried out.

In Chapter3, the mathematical formulation behind the operation of aH₂PP is provided and two different and separate optimization problems are formulated. In the first problem, theH₂PP model is used to model the strategic participation of theH₂PP in multi-energy services with the goal of maximizing the profit of theH₂PP operator. In the second problem, the H₂PP model is incorporated in a distribution network for grid management and the goal is the minimization of operating costs.

Chapter4presents a set of simulations and economic analyses related to the first mathematical model, where theH₂PP participates in an energy market to maximize the revenue profit for its operator. The main technical and economical characteristics of theH₂PP are presented, the profile of its clients is delineated, and the simulation scenarios are described. Subsequently, the main results are displayed and examined.

Chapter 5presents a different set of simulations related to the second mathematical model, where theH₂PP is incorporated in a Virtual Power Plant (VPP) to minimize costs for the grid operator. Several scenarios are described, and the results gathered from their simulation are presented and studied.

Chapter 6 describes the main outcomes and conclusion that can be drawn from this work, followed by the possibilities that can be addressed in related future work.

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State of the Art

The current chapter presents, in a methodical manner, the most pertinent aspects and ideas related to the topic of this dissertation.

Thus, this segment begins with a description of a few fundamental ideas and concepts related to H₂, its production, storage and end-uses. Subsequently, it is done a summary of the most relevant works and projects related to greenH₂.

2.1 Hydrogen

Hydrogen is the most abundant element in the Universe. On Planet Earth, at normal temperature and pressure, it forms diatomic molecules ofH₂ in the gaseous state being a colourless, odourless and flammable substance. In spite of its plentifulness, this gas is not very common in our planet’s atmosphere, as due to its low weight it can easily escape into outer space. It is also extremely reactive, being found on chemical compounds, such as water and hydrocarbons, rather than in its pure form [15,16].

Some chemical properties of hydrogen and other fuels at Standard Temperature and Pressure (STP) (T = 0 ºC, p = 1 bar) are presented in Table2.1. It is easily noticeable that, among those four,H₂has the smallest density. Because of its low molecular weight, it has the highest energy content (Higher Heating Value (HHV) or Lower Heating Value (LHV)) by a unit of mass (kg), but the lowest energy content by a unit of volume (m³).

Table 2.1: Chemical properties ofH₂and other fuels at STP [17].

Property Unit H₂ Natural gas Diesel Petrol

Density (STP) [kg/m³] 0.089 0.777 846 737

Higher Heating Value (HHV) [kW h/kg] 39.4 14.5 12.7 12.9

[kW h/m³] 3.55 11.3 10.7 9.49

Lower Heating Value (LHV) [kW h/kg] 33.3 13.1 11.8 12.1

[kW h/m³] 3.00 10.1 9.98 8.92

7

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The heating value of a substance is defined as the amount of heat released during its combustion. The difference between HHV and LHV is explained next.

Water (H2O) is one of the products of the combustion of fuel. The amount ofH₂Oproduced depends on the quantity ofH₂present in that same fuel. As expected, due to the high temperature, this water forms steam, which retains a small portion of the energy released during combustion as the latent heat of vaporization. In other words, heat energy is stored in the vaporized H₂O.

Therefore, the HHV is defined as the gross amount of heat released during the combustion of a unit of fuel and includes the latent heat stored in the water vapour, which can be condensed, allowing for the retrieval of part of its energy. Meanwhile, the LHV is the amount of heat available on fuel after the latent heat of vaporization is deducted from the HHV [18].

2.2 The hydrogen colour spectrum

By the end of 2021, 96 % of theH₂produced worldwide was obtained from fossil fuels, with large emissions of GHG [11]. Most of thisH₂was locally produced for refineries and for ammonia production [19]. To differentiate and describe multiple methods of obtainingH₂, a colour-based convention is being used by several authors [9,20], as in Figure2.1.

Figure 2.1: Hydrogen colour spectrum [20].

Green hydrogen - Produced via water electrolysis using electrolysers. The energy used to power the electrolyser comes from RES, usually, wind and solar power [20]. Its price depends mostly on the cost of electrolysers and on the RES price [21].

Grey hydrogen - Obtained from fossil fuels, either through coal gasification or NG reforming, releasingCO₂ to the atmosphere [9,20]. Some authors consider that, when produced from coal, H₂is brown or black [22], and grey when produced from NG [22].

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Blue hydrogen - Similar to the previous process, but Carbon Capture and Storage (CCS) techniques are used, resulting in lowerCO₂emissions [9]. As such, its price depends on the price of fossil fuels, the technology used and the cost of CCS [21].

Pink hydrogen - The electrolysers are powered with energy produced from nuclear power plants [20]. It is also known as red or purple hydrogen [9,22].

Turquoise hydrogen - In this case, theH₂is obtained using a process called methane pyrolysis which producesH₂and solid carbon [20].

White hydrogen - For some authors, this refers toH₂found in underground deposits [20,22], while for others it is the one obtained by gasification of biomass [9].

The existence of yellowH₂is also accepted, but there is no consensus about it. Some say it is when the energy used in the electrolysis process comes exclusively from solar power [23], while others consider it asH₂obtained using electricity of mixed origins (fossil and renewable) [24].

In conclusion, hydrogen is only as clean as the energy used to produce it and so the attention has been turning to greenH₂, obtained by electrolysis’s water with energy obtained from RES.

2.3 Electrolysers and water electrolysis

Water electrolysis is the chemical reaction that occurs in water when it is passed through by an electric current, resulting in its separation into molecules ofH₂ and oxygen (O2) according to Equation2.1.

2H₂O→2H₂+O₂ (2.1)

This is done using an electrolytic cell, whose generic structure is shown in Figure2.2. The electric current flows between two separated electrodes, called anode and cathode, which are immersed in an electrolyte to increase conductivity. The electrodes must have good electric conductivity, be resistant to corrosion and show appropriate structural integrity. Also, the electrolyte cannot undertake any changes during the process, so it must not react with the electrodes. A separator (diaphragm) is essential to avoid the recombination of the generated oxygen and hydrogen, and it should have high ionic conductivity and stability [25].

The term electrolysis was first used by Michael Faraday when formulating the basic physical laws behind this chemical process in 1834, also known as Faraday’s Laws of Electrolysis. This word results from the combination of the Greek words "elektron" (amber, a material associated with electrical phenomena for centuries) and "lysis" (breakdown/decomposition) [27].

It is a process known for over two centuries, but it is not very clear who discovered it first since different statements can be found in the literature. However, most sources agree that, in the year 1789, Adriaan Paets van Troostwijk and Johan Rudolph Deiman were the first to produce hydrogen using electricity, with an electrostatic generator being used to break water into "combustible air"

(H2) and "life-giving air" (O2). Their experiments were successfully repeated by George Pearson, who reported his results to the Royal Society of London in 1797, noting that "...hydrogen and

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Figure 2.2: Generic structure of an electrolytic cell [26].

oxygen gases were produced by passing electric discharges through water”. At a subsequent time, William Nicholson republished Pearson’s paper in his own journal, making a contribution with several comments [28].

With the introduction of the Volta pile in 1800 by Alessandro Volta, an easily reproducible electricity source became available. With the ability to provide an almost constant voltage and to deliver energy over a longer period of time, this apparatus allowed for wider use of electricity, marking the beginning of electrochemistry as a science. Using this new device and their knowledge of water electrolysis, Nicholson and Anthony Carlisle repeated the experiments of van Troostwijk and Deiman, being able to analyse the anodic and cathodic products separately. The accessibility of this new battery increased the interest of many other researchers to perform more studies, but, according to Faraday’s first law, it takes high currents to mass produce chemicals, something that Volta’s pile could not achieve [28].

In the years that followed, new and more sophisticated electrochemical cell models were studied, leading to the creation of several patents, the publication of numerous papers and books, and the development of new devices. Among these can be found the electrochemical reactor for hydrogen production, designed by Charles Renard around 1890 and used to generateH₂for French military airships [28].

Around 1900 over 400 industrial electrolysers were already operating. Hydrogen was needed to produce ammonia for fertilizers and explosives, and so the electrolyser industry felt significant growth during the 1920s and the 1930s. Manufacturers like Oerlikon, Norsk Hydro and Com- inco started to supply plants in the multi-megawatt range. Many of these were installed close to Hydropower plants (HPP), so as to make use of an inexpensive electricity source [29].

Today these devices are the basic units of hydrogen production from water, converting electricity into chemical energy in a P2G process [28].

Depending on the type of electrolyte used in the cells, it is possible to distinguish between several types of electrolysers, from which the most important ones are [28]:

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• Alkaline Water Electrolysers (AWE);

• Proton Exchange Membrane Electrolysers (PEME);

• Solid Oxide Electrolysers (SOE).

2.3.1 Available technologies

AWE are the most mature water electrolysis technology and, nowadays, they are still the standard systems for large-scale electrolysis applications [25].

Each alkaline cell is made of a pair of electrodes, which are immersed in an aqueous electrolyte with a microporous membrane (diaphragm) separating them. The cathode is usually made of nickel with a catalytic coating, such as platinum. The anode can be made of nickel or copper metals coated with metal oxides, such as manganese, ruthenium or tungsten. Due to its high conductivity, Potassium Hydroxide (KOH) is typically the chosen electrolyte, but Sodium Hydroxide (NaOH) is also an option. During the reaction, the electrolyte is not consumed but has to be re- plenished over time because of diverse losses. The diaphragm keeps the produced gases apart and has to be permeable both to water and hydroxide ions. In the past, asbestos was used as separator material, but due to high corrosion and adverse health effects, many alternatives were developed, with current membranes being based on sulfonated polymers, polyphenylene sulphides, polyben- zimides and composite materials [27] [25].

The main advantages of AWE are a high Technology Readiness Level (TRL), lower costs and higher lifetime when compared to other technologies, and a good tolerance to impurities.

Meanwhile, the main disadvantages are a lower flexibility and slower start-up, a lowerH₂ purity and a large stack size [30].

Regarding PEME, the usage of exchange polymers for electrochemical applications dates back to the middle of the 20th century. In 1966, General Electric created the first electrolyser based on the proton conducting concept using a polymer membrane as the electrolyte, which they started to commercialize in 1978 [25].

Nowadays, PEME are perceived as the second most important electrolysis technology. Owing to the growing interest in the production of greenH₂and the opportunity to overcome some issues related to AWE, PEME have been receiving more attention [27].

The materials used for the electrode catalysts are usually platinum black, iridium, ruthenium, or rhodium and the most commonly used membrane is Nafion, which separates the electrodes and acts as a gas separator [31]. As an alternative to the liquid electrolytes employed in alkaline cells, in a Proton Exchange Membrane (PEM) cell, thin proton conducting membranes are used as electrolytes [27].

The main advantages of PEME are higher efficiency, higher flexibility, lower minimum load, lower power-up and power-down times, higherH₂purity and a more compact design. The main disadvantage is the higher cost [30].

Finally, the SOE is the least mature technology among these three. Based on steam electrolysis at high temperatures, between 600 ºC and 900 ºC, the SOE provides an opportunity to significantly

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reduce the consumption of electrical energy for electrolysis processes when compared to both AWE and PEME [27]. This is achieved by replacing part of the required electrical energy with thermal energy [31].

This concept is not new, as it started to be developed in the USA by General Electric and the Brookhaven National Laboratory during the late 1960s. In Germany, Dornier followed with the HOT ELLY project, which lasted until the mid-1980s. Significant technical progress was made, but the commercialization of these devices was still far from being a reality [28].

In solid oxide cells, the electrolyte is made of a thin, dense, and solid oxide layer, that turns conductive for ions at high temperatures [31].

The main advantages of SOE are high efficiency and low minimum load. The main disadvantage is the low TRL, higher costs, high operating temperatures and a large size [30].

2.3.2 Efficiency

The efficiency of an electrolyser is an important aspect to compare the performance ofH₂PP and to calculate the cost of electrolytic hydrogen. In general, it is given by the ratio between the energy contained in the producedH₂ and the energy used by the electrolyser to produce it [25].

However, there are two slightly different definitions available for this indicator [32].

According to the first definition, the energy contained in the producedH₂is given by its HHV, and as such, the efficiency of an electrolyser is:

ηELEC(%) =HHVH₂

CE

·100 (2.2)

whereηELEC is the electrolyser’s efficiency,HHVH₂ is the HHV ofH₂ andCE is the energy consumed by the device.

The second definition considers that the energy contained in the H₂ is given by its LHV, resulting in:

ηELEC(%) =LHVH₂

C_E ·100 (2.3)

whereLHV_H₂ is the LHV ofH₂.

As there is no definitive agreement about which method should be used, instead of a percentage many electrolyser manufacturers and suppliers choose to provide the energy consumed by the device, in kWh, to produce a certain amount ofH₂[33].

In this dissertation, it is the HHV ofH₂ that will be used to calculate the efficiency of an electrolyser.

This decision is supported by the majority of the works consulted that also use the HHV.

Besides, according to [27], due to the fact that electrolysers often use liquid water as feedstock, the energy required for evaporation of H₂Ohas to be taken into account, meaning that it is the HHV ofH₂that should be used for this calculation.

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Additionally, the heat released by the electrolyser can be used for other purposes, such as district heating, effectively increasing the efficiency of the electrolytic process and potentially reducingH₂production costs [34].

2.3.3 Water consumption

As shown, electrolysis relies on two fundamental inputs: electricity as the energy source and water as the main feedstock. Based on the stoichiometry of this reaction, for every kg of H₂ produced, at least 9 L (≈9 kg) of water is needed but, in reality, and due to process inefficiencies and losses, up to 20 L of water are required to obtain 1 kg ofH₂[35,36].

Since one of the goals of the creation of a H₂ economy is to decarbonize energy systems and fight environmental change, it is not irrelevant to analyse possible negative side effects of H₂ production for the environment. One of those is the consumption of a significant amount of freshwater and, as such, some authors have already examined this [35].

The water demand of electrolysis is not necessarily larger than that of other hydrogen production methods. Generating H₂ from NG with CCS takes between 13 and 18 L ofH₂Oper kg of H₂, while coal gasification uses between 40 and 86 L of water per kg ofH₂. Under these circum- stances, water is not a bottleneck for scaling up electrolysis, even in territories with a higher level of water stress where seawater desalination is an option, since reverse osmosis for desalination takes 3-4 kWh of electrical energy perm³ of water and should only have a minor impact on the final cost of hydrogen [35].

That last premise might be particularly important for countries like Portugal and Spain, which are investing in and planning the conception of multiple hydrogen projects while facing a high risk of water stress caused or aggravated by rising temperatures [37], more frequent and intense heatwaves [38] and longer droughts periods [39].

Additionally, according to other authors, a future replacement of fossil fuels byH₂for energy- related applications has the potential to result in the conservation of hydric resources, because nowadays, the exploitation of these hydrocarbons consumes a great amount of water in mining, hydraulic fracturing, cooling and refining. Furthermore, the water consumed for producing elec- trolyticH₂is expected to be particularly marginal when compared to other sectors, such as irri- gated agriculture. Concerns about freshwater scarcity call for a reduction in water extractions at all possible angles, and, therefore, pursuing solutions which allow theH₂economy to make use of Earth’s saltwater resources can further reduce its water footprint [36].

2.3.4 Costs

Regarding the cost of these devices, as seen in Table2.2, for an AWE, the Capital Expendi- ture (CAPEX) was around 600 C/kW in 2020, but it is expected to fall to 480 C/kW by 2024.

Conversely, the capital cost of a PEME was around 900 C/kW in 2020 and is expected to drop to 700 C/kW by 2024 [40,41]. According to these data, an electrolyser with a lower rated power has a higher CAPEX, in terms ofe/kW, when compared to a more powerful device.

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Table 2.2: Cost of different electrolysers, according to type and rated power.

Source Year Type Rated Power CAPEX (e/kW)

Demo4Grid [42] 2017 AWE 2.5 MW 680

Haeolus [43] 2018 PEME 2.5 MW 1328

Demo4Grid [42] 2017 AWE 5.0 MW 550

Demo4Grid [42] 2017 AWE 10 MW 530

Refhyne [44] 2018 PEME 10 MW 1000

Demo4Grid [42] 2017 AWE 20 MW 515

FCH JU [40] 2020 AWE ——— 600

FCH JU [40] 2020 PEME ——— 900

(future prospects[41]) 2024 AWE ——— 480

(future prospects[41]) 2024 PEME ——— 700

2.4 Hydrogen compression

As a consequence of hydrogen’s low density, its storage and transportation are very demanding tasks. At atmospheric pressure, 1 kg ofH₂occupies a volume of roughly 11000L or 11m³, while, in contrast, 1 kg of petrol can be stored in 1.4 L. Compression is one of the available options to overcome this obstacle and is seen as the ubiquitous solution in the gaseousH₂ supply network, helping to achieve more acceptable energy densities [45].

In spite of being widely used, compression is often considered to be one of the most expensive process units in theH₂supply chain, meaning that the selected technology and its associated costs are particularly relevant. Also, factors like flow rates, pressure ratio and required purity dictate the choice of compressor, energy consumption and the overall cost of compression [45].

2.4.1 Hydrogen density at different temperatures and pressures

Just like it happens with other substances, hydrogen’s density (ρH₂) does not change linearly with pressure and temperature [46], as seen in Figure2.3.

To explain why the density of this gas does not have a linear relation with those two parameters, it is necessary to understand the Ideal Gas Law (Equation2.4) [47]:

pV =nRT¯ (2.4)

where p is the absolute pressure (Pa), V is the volume (m³), n is the amount of substance (mol), ¯R is the universal gas constant (8.314 Nm/mol K) and T is the absolute temperature (K).

A mole is a collection of 6.023×10²³ particles. ForH₂every mole of molecules has a total mass of 2.016×10⁻³kg. With this in mind, Equation2.4can be written in terms of mass instead of moles as [47]:

pV =mRT (2.5)

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Figure 2.3:H₂density under certain temperature and pressure conditions [46].

where m is the total mass of gas molecules in kg and R is hydrogen’s specific gas constant, which has a value of 4124.18 Nm/mol K.

Density is defined as mass per unit volume (kg/m³), so Equation2.5is rewritten as:

p=ρRT (2.6)

However, these equations were only considered to be accurate until the 20th century when they were found to be just good approximations. As the name suggests, the Ideal Gas Law can only describe the behaviour of an ideal gas, a theoretical substance made of molecules that occupy negligible space and do not exert an attractive force on each other. But, in a real gas, its particles occupy space, reducing the available volume to hold more gas, and they attract each other, further increasing the pressure. The Ideal Gas Law can only closely describe the behaviour of a real gas at pressures up to 100 bar and at ambient temperatures. Above that, as the pressure increases, the results become less and less precise [47], as evidenced in Figure2.4.

Further ahead, it will be shown howH₂storage is done at pressures up to 700 bar. If used to determine hydrogen’s density in those situations, these equations would result in significant errors, but it is possible to correct them. At high pressures, the Ideal Gas Law leads to an overestimation of the density ofH₂and so, if this relation is used to computeρH₂, the resulting density is higher than the actual value. In other words, this means that the gas actually fills more volume than anticipated by the Ideal Gas Law, or that, if the volume cannot be increased, the gas will suffer an increase in pressure. Thus, by ignoring the space occupied by the molecules, the subsequent deviation from the Ideal Gas Law is in the form of compression and the gas occupies more space than predicted. One way of compensating for it is by using a compressibility factor Z. This factor, which depends on temperature, pressure and the nature of the gas, is derived from data obtained

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Figure 2.4: CompressedH₂density assuming an ideal gas and a non-ideal gas [48].

through experimentation [48]. Then, the adjusted gas law is established as :

p=ZρRT (2.7)

Figure2.5describes the variation of the compressibility factor forH₂with the temperature at high pressures. At ambient temperature, a value of 1.2 is reached at 300 bar. This means that if the Ideal Gas Law is used to calculate the mass ofH₂inside a container, the result will be 20 % greater than the real value [49].

Figure 2.5: Compressibility factor Z ofH₂gas for different values of p and T [49].

A procedure to calculate theH₂compressibility factor is described in [50]. According to this method, the value of Z forH₂can be computed using Equation2.8.

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Z=

9

∑

i=1 5

∑

j=1

vi jpⁱ⁻¹ 100

T j−1

(2.8) where

vi j=







1.000 3.054·10⁻⁴ −1.458·10⁻³ 2.345·10⁻³ 5.204·10⁻⁴

−4.278·10⁻⁴ 2.475·10⁻² −8.763·10⁻³ −3.201·10⁻² 1.359·10⁻²

−5.033·10⁻⁶ 7.602·10⁻⁵ −6.130·10⁻⁴ 1.589·10⁻³ 2.781·10⁻⁴ 3.259·10⁻⁷ −3.771·10⁻⁶ 3.0545·10⁻⁵ 3.0545·10⁻⁵ −7.691·10⁻⁵

−3.247·10⁻⁹ −1.041·10⁻⁸ 5.529·10⁻⁷ −3.121·10⁻⁶ 3.716·10⁻⁶

−8.725·10⁻¹¹ 2.5607·10⁻⁹ −2.393·10⁻⁸ 8.810·10⁻⁸ −8.608·10⁻⁸ 2.304·10⁻¹² −4.8093·10⁻¹¹ 3.665·10⁻¹⁰ −1.167·10⁻⁹ 1.047·10⁻⁹

−1.936·10⁻¹⁴ 3.648·10⁻¹³ −2.550·10⁻¹² 7.534·10⁻¹² −6.450·10⁻¹² 5.684·10⁻¹⁷ −1.018·10⁻¹⁵ 6.781·10⁻¹⁵ −1.915·10⁻¹⁴ 1.590·10⁻¹⁴







To conclude, by using this methodology, it is possible to get accurate values forH₂density at high pressures, even when considering changeable temperature and pressure conditions.

2.4.2 Hydrogen compression thermodynamics

The required work for compressing gases depends on the thermodynamics behind the compression and on the nature of the substance. The calculation of the required energy for compressing the gas is usually simplified by assuming an adiabatic or an isothermal process. The adiabatic process happens without the transference of any heat or mass between the thermodynamic system and the environment and at a constant entropy (isentropic), meaning that the temperature of the gas changes without any heat being exchanged between the fluid and its surroundings [51].

The energy consumed by an adiabatic compression is calculated by applying the undermen- tioned expression [52]:

W = γ γ−1p₀V₀

"

p₁ p₀

^γ⁻¹

γ

−1

#

(2.9) where W is the specific compression work (J/kg),γ is the heat capacity ratio (1.41 forH₂),p₀and p₁are the initial and final pressures (Pa) andV₀is the initial specific volume (11.1m³/kgforH₂).

Mostly due to its very low density, H₂ requires a larger amount of energy than methane or helium to be compressed to the same pressure [51].

Contrarily, in an isothermal process, the temperature of the gas remains constant during the compression and the required energy can be obtained using the next equation [52]:

W =p₀V₀ln p₁

p₀

(2.10)

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Figure 2.6: Adiabatic compression work for methane, helium and hydrogen [52].

Under real conditions, theoretical isothermal and isentropic compression can act as boundaries for realistic compression work. In the case of H₂, the difference in energy consumption as a percentage of its HHV is exhibited in Figure2.7[51].

Figure 2.7: Energy required for compressing hydrogen compared to its HHV [52].

In general, the compressed gas must be cooled down after each stage of compression to make it a less adiabatic and more isothermal process and, therefore,H₂is normally compressed in different stages. Multistage compressors are fitted with intercoolers and can operate between those two limiting curves. Besides, hydrogen easily transfers heat resulting from the compression to cooler walls, nearing the isothermal process. As seen in Figure2.7 for a final pressure of 800 bar, the compression energy requirements would amount to about 13 % of the energy content ofH₂[52].

2.4.3 Hydrogen compressor power calculation

In [45], the power of an isentropic (reversible and adiabatic) single-stage process is given by:

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P_ss=

γ−1 γ

Z ηisen

T_sucq_MR¯

"

p_disc psuc

^γ−1_γ

−1

#

(2.11) where Z is the average compressibility factor,ηisenis the isentropic efficiency,T_sucis the suction temperature (K),qmis the molar flow rate (mole/s),pdiscis the discharge pressure (bar) andpsucis the suction pressure (bar). Meanwhile, the power of an isentropic multistage process [45] is given by:

Pms=N γ−1

γ Z

ηisen

TsucqMR¯

"

p_disc p_suc

^γ_γ⁻¹_N

−1

#

(2.12) where N is the number of stages and is calculated according to

N= log

P_disc P_suc

log(x) (2.13)

where x is the compression ratio for single-stage. As reported in the literature [45], the value of x is usually between 2.1 and 4. Finally, a compressor’s rated power is given by [45]:

P_CP= P_ms ηmotor

(2.14) whereηmotoris the efficiency of the motor driving the compressor. The isentropic efficiency,ηisen, of an older compressor is between 60% and 65%, but in a more recent device, its value can reach up to 80% or even 85% [53]. In the meantime, the motor efficiency,ηmotor, can have a value up to 95% [45].

In [54], it is calculated the energy consumed by a real compressor. It is assumed an adiabatic compression model with a global efficiency of 50 %. This efficiency value already considers the efficiency of electrical power transformation and other supplementary systems, such as cooling.

The obtained results are provided in Table2.3.

Table 2.3:H₂compressors estimated energy consumption [54].

Year p_suc[bar] p_disc [bar] Stages Energy [KWh/kg]

2017

1 200 4 5.0

500 5 6.3

30 200 2 1.7

500 3 2.7

2025

15 200 2 2.4

500 3 3.5

60 200 1 1.1

500 2 2.0