Modelling and Validation of a Fuel Cell Electric Bus

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Modelling and Validation of a Fuel Cell Electric Bus

Jørgen Kristoffer Tuset

Thesis submitted for the degree of Master in Renewable Energy Systems

30 credits

Department of Technology Systems

The Faculty of Mathematics and Natural Sciences

UNIVERSITY OF OSLO

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Modelling and Validation of a Fuel Cell Electric Bus

Jørgen Kristoffer Tuset

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Modelling and Validation of a Fuel Cell Electric Bus http://www.duo.uio.no/

Printed: Reprosentralen, University of Oslo

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Abstract

Alternative powertrains for city transit buses have rapidly increased in popularity as a way to reduce emissions from the transport sector.

Modelling can be used as a valuable tool to understand what parameters are affecting the efficiency of the powertrain. This thesis presents a fuel cell electric bus model based on the Van Hool A330 FC bus equipped with a Ballard FCvelocity®HD6 150 kW PEM fuel cell. This specific bus was chosen to create a point of reference as it was in service from 2013 to 2016 in the Oslo Metropolitan area, operated by Ruter as part of the European CHIC project. The main objective is to simulate the hydrogen consumption for the fuel cell electric bus given a specific driving cycle.

To realize the objective, a proton exchange membrane fuel cell model is presented. The fuel cell model responds to operating and physical parameters and outputs cell voltage, stack voltage, hydrogen consumption, current density, efficiency and power. The fuel cell model provided a good fit with experimental data available for the Ballard FCvelocity®HD6 150 kW allowing it to be integrated into the fuel cell electric bus model with confidence. The fuel cell electric bus model responds to changes in physical parameters and outputs the hydrogen consumption, system power demand, battery state of charge and fuel cell performance metrics.

Under an extended 7,73 hour Braunschweig driving cycle with 5 kW of auxiliary load the hydrogen consumption was 10,34 kgH₂/100km.

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Acknowledgement

I would like to thank my main supervisor Øystein Ulleberg for giving me good ideas and guidance and and my co-supervisors Ragnhild Hancke and Sabrina Sartori for providing valuable feedback. I would also like to thank my family and friends who helped keeping me motivated during these bizarre times.

Jørgen Kristoffer Tuset

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List of Figures

2.1 Overview of the model structure and calculation order (Lazar et al., 2019) . . . 6 2.2 Voltage losses in the fuel cell with the resulting polarization

curve (Ariza et al., 2018) . . . 8 2.3 Estimated water flux thorugh the membrane at various

thicknesses at 70 ^◦C. For VVP: the relative humidity were 96% cathode and 38% anode. LVP: cathode were flooded (100% liquid volume fraction) and 38% RH anode. LLP: both anode and cathode were flooded. For all the tests, pressure

= 1 bar (Lazar et al., 2019). . . 16 2.4 Simplified model flow. . . 19 2.5 Braunschweig driving cycle, time-speed (Barlow et al., 2009). 20 2.6 Remy HVH410-150 DOM efficiency map (Remy, 2012). . . . 22 3.1 Overview of the workflow and thought process to answer

the problem statement. . . 24 4.1 Overview of the model structure and calculation order . . . 26 4.2 Testing the model against experimental data by SINTEF, 2019. 29 4.3 Voltage losses at 100 kPa. . . 30 4.4 Testing the model against experimental data by Wang et al.,

2003 withT=_{50, 70}^◦CandP=₃atm. . . 31 4.5 Voltage losses at 70^◦C. . . 32 4.6 Performance of the Ballard FCvelocity®HD6 150 kW simu-

lation, comparison against experimental data by Q. Li et al., 2014. . . 33 4.7 Efficiency and H₂ consumption of the Ballard FCvelocity®-

HD6 150 kW simulation. . . 35 4.9 Cell voltage losses of the Ballard FCvelocity®HD6 150 kW. . 35 4.8 Polarization curve of the Ballard FCvelocity®HD6 150 kW. . 36 4.10 Power flow logic. . . 40 4.11 Charging logic determined by battery SOC. . . 41 4.12 System power demand duringBW short 5 kW cycle. Trian-

gles indicates where the total system power demand exceeds 265 kW. . . 42 4.13 Battery SOC % for the first two hours of theBW long 5 kW

cycle. . . 43

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4.14 Step current limitation during the BW short 5 kW cycle.

Positive indicates that the fuel cell could not step up to fully cover the power demand and the missing power is covered by the battery. Negative indicates the fuel cell operating at a higher power than what is demanded by the system. . . 43 5.1 Polarization curve comparison using a liquid water ratio of

0,47 versus 0,4. . . 45 5.2 Comparing the effect of platinum loading on electrodes. . . 45 5.3 Historical temperature in Oslo, sourced from www.yr.no . . 47 A.1 FCEB Simulink model . . . 60

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List of Tables

2.1 Ethalpies and entropies for fuel cell reactant and products at

25^◦Cand 1 bar (EngineeringToolbox, 2017) . . . 7

2.2 Braunschweig driving cycle key parameters (Barlow et al., 2009). . . 20

4.1 Model inputs for the fuel cell model. . . 27

4.2 Model parameters and constants for the fuel cell model. . . . 28

4.3 Main model parameters for SINTEF, 2019. . . 29

4.4 Main model parameters for Wang et al., 2003. . . 31

4.5 Operating parameters for the Ballard FCvelocity®HD6 150 kW. . . 33

4.6 Nominal and maximum operating point for the Ballard FCvelocity®HD6 150 kW. . . 34

4.7 Bus sizing parameters and coefficients. . . 37

4.8 Partial and full braking regeneration conditions. . . 40

4.9 FCEB results for 6 different profiles. . . 41

4.10 Selected data points, reported consumption by Ruter’s FCEB. 41 4.11 Key points, reported consumption by Ruter’s FCEB. . . 42

A.1 Base parameters and constants for the fuel cell model. . . 59

A.2 Base inputs for the fuel cell model. . . 59

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List of Abbreviations and Nomenclature

Abbreviations

FCEB Fuel Cell Electric Bus

ICE Internal Combustion Engine MEA Membrane Electrode Assembly PEMFC Proton Exchange Membrane Fuel Cell SOC State of Charge

CHIC Clean Hydrogen in European Cities

Nomenclature

A Active fuel cell area,cm² A_f Vehicle cross section,m² a_f Acceleration vector,m/s² a Water activity

a_i Catalyst-specific areacm²/mg C Molar concentration,mol/cm³

C_w Membrane water concentration,mol/cm³ c_d Drag coefficient

D_i Diffusion coefficient,cm²/s

D_λ Diffusion coefficient of water through membrane,cm²/s E_i Voltage, V

EW Membrane equivalent weight, g/mol f Membrane liquid volume water fraction F Faraday constant, 96845 C/mol

∆G Gibbs free energy J/mol

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∆Gi Activation energy, J/mol i Current density,A/cm²

i₀ Exchange current density, A/cm²

i_{0,re f} Reference exchange current density,A/cm² i_L Limiting current density,A/cm²

j_i Water flow, mol/s

K_λ Hydraulic permebility of the membrane,cm² L_i Catalyst loading,mg/cm²

m_f Total mass of vehicle, kg N_i Molar flux,mol/cm²s P Power, W

P_i Pressure at inlet, bar p_i Partial pressure, bar P_{re f} Reference pressure, bar Q Heat flow, W

R Universal gas constant, 8, 3144Jmol⁻1K⁻1 s_i Liquid water volume fraction

T_i Temperature, K

T_{re f} Reference temperature, K v_f Speed vector,m/s

X_i Molar fraction

α_i Charge transfer coefficient δ Thickness, cm

ρ Density

η Efficiency

τ Electrode Tortuosity

γ Pressure dependency coefficient λ Membrane water content e Electrode porosity σ Conductivity, S/cm

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Chapter 1

Introduction

The European Union adpoted the 2030 Agenda for Sustainable Develop- ment in 2015 in which the EU has the objective of cutting 40% in greenhouse gas emissions, gain 32% renewable energy share and a 32,5% improvement in energy efficiency compared to 1990 levels. The transportation sector in the EU currently accounts for 30,8% of the total energy used with a renewable energy share of 7,6% in 2017 (eurostat, 2019), where heavy duty trucks and buses are responsible for 6% of total EU CO₂ emissions (Eu- ropean Commission, n.d.). Private sectors and governments are working hard to develop and implement alternative sources for energy generation to reduce the reliance on fossil fuels and subsequently limiting greenhouse gas emissions. In the transportation sector this has lead to exploring alternative powertrains, such as battery electric vehicles, hybrid electric vehicles and fuel cell electric vehicles. In this work the focus is on fuel cell electric vehicles, specifically fuel cell electric buses (FCEB) which utilizes hydrogen fueled fuel cells and batteries in order to power the electric motor. Provid- ing a zero-emission alternative to traditional internal combustion engines (ICE).

In Europe this has led to pilot projects testing out the viability of fuel cell electric buses in cities. Three of these projects include Clean Hydrogen in European Cities (CHIC), Joint Initiative for Hydrogen Vehicles across Europe (JIVE) and JIVE 2. The CHIC project was active from 2010 to 2016, while JIVE and JIVE 2 started in 2017 and 2018 respectively and is active today (2021).

The CHIC project was one of the first large scale projects in Europe to deploy and test FCEB and hydrogen refueling stations in European cities.

The project spanned to 9 cities across Europe and one city in Canada. CHIC operated a total of 54 FCEB buses with a consumption ranging from 8 kg H₂/100 km to 16 kgH₂/100 km, with the average being 12,1 kgH₂/100 km.

The average availability was recorded as 69% where the objective was 85%.

Comparing this to the availability of a diesel bus at 95% shows that FCEB at the time of the CHIC project were not reliable enough to fully replace a fleet of diesel buses (Ruter, 2017, Müller et al., 2017).

Combined the two JIVE projects has planned deployment of nearly 300 fuel cell buses in 22 cities, in addition to providing the necessary

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infrastructure, making it the largest deployment in Europe to date. The end goal is to show bus operators the commercial viability of fuel cell buses without subsidies. The main objectives of the JIVE projects are to achieve a maximum price of€650.000/€625.000 (JIVE/JIVE 2) for a standard 12 m bus, reach an availability of 90% and demonstrate how low cost renewable hydrogen can be obtained. The project has received funding from the Fuel Cells and Hydrogen Joint Undertaking (FCH JU) under the European Union Horizon 2020 framework (Stolzenburg et al., 2020).

The core of a FCEB is the fuel cell. In automotive applications the most commonly used fuel cell technology is the proton exchange membrane fuel cell (PEMFC) usually operating at temperatures between 60^◦Cand 80^◦C. A PEMFC has a fuel energy efficiency (chemical to electrical) of around 45- 60% compared to an ICE with a fuel energy efficiency of 30% (X. Li, 2006), making a FCEB more energy effective.

Vehicle modelling is a valuable tool to create more efficient powertrains, but also to compare different powertrain technologies. A few recent publications related to FCEB modelling are presented. Kivekäs et al., 2018, compared the energy consumption of 5 different bus powertrain configurations using driving cycle variation and variation in passenger load by creating 3000 synthetic cycles on line 11 in Espoo, Finland. Yulianto et al., 2017, modelled a FCEB and a battery electric bus using Matlab Simulink, comparing the battery state of charge, energy consumption and difference in mass. Jinquan et al., 2021, investigated a real time energy management strategy using dynamic programming and model predictive control for a FCEB which considers intersection speed planning for better fuel economy and to reduce the overall strain on the fuel cell.

Proton Exchange Membrane Fuel Cell

Performance of a PEMFC is visualized by comparing the total voltage losses to its real cell voltage at a given current. The goal of efficient fuel cell design is keeping these voltage losses to a minimum. PEMFC models become an important tool in exploring PEMFC performance given various parameters. The recent trend in 3D modelling of PEMFC seems to focus on one specific part related to the PEMFC performance. Zhang et al., 2017, Developed a 3D multiphase PEMFC model investigating the gas and liquid flow in channels and porous electrodes. They found that adding baffles in the cathode channels reduced the concentration polarization by increasing the oxygen concentration and aiding in water removal from channels. Mohammedi et al., 2020, investigated the effect of different cross- section shape design in a PEMFC with a single straight channel and its impact on performance and mass transfer. Cai et al., 2021, did a similar study as Mohammedi et al., 2020, investigating how adding various shaped blockades to the channel impacted the mass transfer and flow. S. Li et al., 2020, developed a 2D numerical model exploring the effect of membrane thickness on overall cell performance. They found that a thinner membrane decreased the ohmic resistance increasing the cell voltage at a given current density.

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Multi-dimensional PEMFC models are useful to create understanding and explore individual behavior in parts of the fuel cell. However these models are usually very computationally intensive and takes a lot of time to simulate. Shekhar, 2013, Did a master thesis comparing the accuracy between 1D and 3D PEMFC models, concluding that 1D models are useful for testing various operational and physical parameters for practical applications, though the results are different from the 3D models. Some recent 1D models include:

• Abdin et al., 2016, developed a 1D PEMFC model using Matlab Simulink and based the model largely on physical parameters.

• Vetter and Schumacher, 2019, published a free open reference 1D two- phase PEMFC model written in Matlab.

• Lazar et al., 2019, presented an open-source dynamic 1D PEMFC model with a low computational load making it suitable for real time applications.

1.1 Problem Statement

The open tools existing today to model buses either have no option for fuel cell operation or the fuel cell model is lacking. At the same time the available data for the large fuel cells typically used in heavy duty vehicles do not provide enough information to integrate them into a FCEB model.

This thesis will provide the equations needed to fully simulate the Ballard FCvelocity®HD6 150 kW PEMFC intended for heavy duty vehicles while disclosing all parameters and simulated performance parameters. With the end result of creating a FCEB model which can calculate the hydrogen consumption and give insight to other performance results. This creates three questions which must be answered in order:

• How accurate is this fuel cell model compared to other models and experimental results?

• What is the performance of the simulated Ballard FCvelocity®HD6 150 kW (efficiency, power output, polarization curve), and how accurate is the simulation compared to experimental results?.

• What is the consumption of the simulated fuel cell electric bus (kg H₂/100km) in contrast to real reported consumption?

Scope of Work

The following main limitations and simplifications have been made:

• Infrastructure required by the FCEB such as hydrogen refueling stations have not been considered.

• The FCEB is modeled without a hydrogen supply system and a detailed compressor.

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• Custom driving cycles have not been made.

Other assumptions related to specific modelling of the PEMFC and FCEB are presented in their respective chapters.

1.2 Structure of the Thesis

The governing equations required to model the PEMFC and FCEB are presented in chapter 2 where each sub-chapter covers a specific part. The approach used to tackle the problem and split it into smaller parts is presented in Chapter 3. Chapter 4 contains the validation and results of both the PEMFC and FCEB model. The results from chapter 4 and theory from chapter 2 are combined in chapter 5, where model results and the background theory are evaluated. At the end, the conclusion and ideas for future work are presented in chapter 6 .

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Chapter 2

Theory and Literature

2.1 Proton Exchange Membrane Fuel Cell Basic Chem- istry

A proton exchange membrane fuel cell (PEMFC) is an electrochemical device which converts chemical energy into DC electricity. The three main active components of a PEMFC are an oxidant electrode (cathode), a fuel electrode (anode) and a membrane between them. This composition is called the membrane electrode assembly (MEA). The PEMFC utilizes a polymer membrane which is impermeable to gases, but allows proton transport. Reactant gases are delivered to the electrodes causing the electrochemical reaction to occur at the surface of the catalyst between the electrolyte and membrane. At the anode, hydrogen splits into protons and electrons, where the electron travel through current collectors on to the outside circuit where useful work is performed on an external load before returning to the catalyst side of the membrane. The hydrogen proton goes through the polymer membrane. On the cathode side the hydrogen proton and electron react with the supplied oxygen producing water (Babir, 2013).

The half cell reactions are as follows (X. Li, 2006):

Anode:H2−→2H⁺+2e⁻ Cathode: 1

2O₂+2H⁺+2e⁻−→H₂O (Eq. 2.1) Combining the two half cell reactions yields an expression for the overall cell reaction, where W is the electric energy output:

H₂+¹

2O₂ −→ H₂O +W+Waste Heat (Eq. 2.2) This only covers the MEA, while a full fuel cell system needs additional support components to function optimally which include (Babir, 2013):

• Continuous supply of reactant gases given at a set temperature and humidity.

• Cooling system to maintain operating temperature.

• DC/DC converter for a steady output voltage supplied to the system.

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2.2 PEMFC Model

The PEMFC model used in this project is an open-source one dimensional model developed by Lazar et al., 2019 with additions related to partial pressure and concentration. The model is written in MATLAB and runs inside Simulink. It is built upon simplified equations in order to reduce the computational demand, meaning the PEMFC model can be integrated into a vehicle model. Based on the variable inputs and the set physical parameters the model outputs cell voltage, stack voltage, power, efficiency and hydrogen consumption. Figure 2.1 shows the basic model structure.

Figure 2.1: Overview of the model structure and calculation order (Lazar et al., 2019)

The next chapter will explain the mathematical equations forming the model.

2.2.1 Theoretical Fuel Cell Potential

The theoretical maximum amount of electrical energy is given by Gibbs free energy, ∆G. Gibbs free energy is given by the change in enthalpy of the system while subtracting the product of temperature and change in entropy. For a system at constant temperature and pressure this can be written as (Doan et al., 2020):

∆G=_∆H−_T∆S (Eq. 2.3)

As mentioned, for an electrochemical cell the maximum amount of work done or received is correlated to Gibbs free energy:

W_el =_∆G (Eq. 2.4)

The relationship between and electrochemical cell and gibbs energy can further be written as:

W_el =_∆G=−nFE_cell (Eq. 2.5)

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Where:

n = is the number of electrons per molecule (for H₂ = 2 electrons per molecule .

F = the faraday constant of 96,485 C/mol.

Re-arranging Eq. 2.5 gives the theoretical fuel cell potential (Norby, 2020):

E_cell = −_∆G

nF (Eq. 2.6)

To calculate ∆G for fuel cell reaction Eq. 2.3 is used together with an enthalpy and entropy table:

∆Hf @ 25^◦C(kJ/mol) _∆s_f@ 25^◦C(kJ/mol)

HydrogenH2 0 0,1307

Oxygen,O₂ 0 0,2052

H₂O(l) _-285,8 _0,070

Table 2.1: Ethalpies and entropies for fuel cell reactant and products at 25^◦C and 1 bar (EngineeringToolbox, 2017)

Applying the fuel cell reactants and products gives the following equation (Khotseng, 2019):

∆G(l) = (H_f)H₂O(l)−T−(s_f)H₂O(l)−(s_f)H₂−1/2(s_f)O₂=−237.1kJ/mol (Eq. 2.7) Inputting ∆G, n and F into Eq. 2.6 calculates the theoretical fuel cell potential:

E_cell = −_∆G

nF = ²³⁷¹⁰⁰^{J mol}

−1

2∗96485C mol⁻¹ =1, 23V (Eq. 2.8) The theoretical fuel cell potential at 25^◦Cand 1 bar is 1,23V.

2.2.2 Real cell voltage

The estimated real cell voltage E_cell is based on subtracting the various voltage losses happening inside the cell from the ideal cell voltage E_T,p. These losses are summarized as activation polarization lossesE_act,i, ohmic lossesE_ohmand concentration polarization lossesEcon(Babir, 2013). As seen in the equation below.

E_cell = E_T,p−E_act,i−E_ohm−E_con (Eq. 2.9) Figure 2.2 shows how the losses inside the fuel cell affects the resulting polarization curve. A polarization curve shows the voltage output for a given current density (current per unit area of the surface). The calculations behind the losses are explained in the next sub chapters.

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Figure 2.2: Voltage losses in the fuel cell with the resulting polarization curve (Ariza et al., 2018)

2.2.3 Ideal Cell Voltage

The theoretical fuel cell voltage changes with both temperature and partial pressure. Substituting Eq. 2.3 into Eq. 2.6 yields an expression on the effect of temperature (Babir, 2013):

E_T =− ∆H

nF − ^T∆S n f

(Eq. 2.10) Where∆His the change in enthalpy while∆Sis the change in entropy.

The effect of partial pressure can be expressed using the Nernst equation. The Nernst equation relates how the electrochemical potential changes with the partial pressure and is derived from Gibbs free energy. It is written as (Lower, 2021):

E=E^◦− ^RT

nFlnQ (Eq. 2.11)

Where Q is the reaction quotient. The partial pressure of the reactants are given as a function of the saturation pressure of water, reactant pressure and temperature. Where the saturation pressure of water (atm) is calculated by (Springer et al., 1991):

log P_H₂_O =−2, 1794+0, 02953∗Tc−9, 1837∗10⁻⁵∗T_c²+1, 4454∗10⁻⁷∗T_c³ Tc =Temperature in Celsius.

(Eq. 2.12)

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The partial pressure of hydrogen and oxygen are given by Spiegel, 2008:

p_H₂ =0, 5∗ ^P^H²

exp(1, 653∗i/T_an^1,334)−P_H₂_O p_O₂ = ^P^O²

exp(4, 192∗i/T_cat^1,334)−P_H₂_O

(Eq. 2.13)

When considering a fuel cell reaction using hydrogen and oxygen, the Nernst equation becomes (Babir, 2013):

E_P = E₀+ ^RT nF ln

p_H₂p^0,5_O

2

p_H₂_O

(Eq. 2.14) Combining Eq. 2.10 and Eq. 2.14 yields an expression for the ideal cell voltageE_T,P:

E_T,P =− ∆H

nF − ^T∆S n f

+ ^RT

nF ln

p_H₂p^0,5_O

2

p_H₂_O

(Eq. 2.15) The changes brought by enthalpy∆Hand entropy∆Swith temperature can be neglected as the error is very small below 100 ^◦C (Babir, 2013), Eq.

2.15 can then be written as :

E_T,P =1, 482−0, 000845T+0, 0000431T ln

p_H₂p^0,5_O

2

(Eq. 2.16) 2.2.4 Activation Polarization Losses

Activation polarization is the activation overpotential required for the cell to overcome the activation energy needed to get the reaction started.

This is the voltage difference from the equilibrium potential of the cell (Menictas et al., 2014). Activation overpotentials result from the resistance to electrochemical reaction kinetics in the anode and cathode, meaning the speed in which the reaction can occur. In the case of fuel cells the oxygen reaction need higher overpotentials, giving that oxygen reaction is a lot slower compared to the hydrogen oxidation (Babir, 2013).

The activation overpotentialE_act,i can be estimated based on the Butler- Volmer equation. The Butler-Volmer equation describes the relationship between electrode potential and current density (Dickinson and Wain, 2020).

i=i₀

exp

−α_RdF(E−Er) RT

−exp

α_OxF(E−Er) RT

(Eq. 2.17) Butler-Volmer equation (Babir, 2013)

Where:

• i= electrode current density, A/m²

• i₀= exchange current density, A/m²

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• E= Electrode potential, V

• E_r= Equilibrium potential, V

• T= Temperature, K

• α_Rd = Charge transfer coefficient, reduction

• α_Ox= Charge transfer coefficient, oxidation

• F= Faraday constant

• R= Universal gas constant

Assuming that α_Rd = α_Ox, Eq. 2.17 can be inverted yielding the activation potential: (Marangio et al., 2009):

E_act,i = ^RTⁱ

α_iFarcsinh i

2i_0,i

(Eq. 2.18) This equation can be applied to both the anode and cathode:

E_act,an = ^RT^an

α_annFarcsinh i

2i0,an

(Eq. 2.19)

E_act,cat = ^RT^cat

α_catnFarcsinh i

2i_0,cat

(Eq. 2.20) In order to use the equations above the exchange current density i0

is needed. The exchange current density in electrochemical reactions is similar to the reaction rate constant found in chemical reactions which quantifies the speed of the reaction. By utilising a reference exchange current density (value at 25^◦Cand 1.0125 bar) the exchange current density for any temperature and pressure can be calculated by (Babir, 2013):

i₀ =i^{re f,i}₀ a_iL_i P_r

P_{re f} γ

exp

− ^∆^Gⁱ RT_i

1− ^Tⁱ

T_{re f}

(Eq. 2.21) Where:

• i^{re f,i}₀ = reference exchange current density per unit catalyst area.

Anode = 1∗10⁻³Acm⁻², cathode = 1∗10⁻⁹Acm⁻²

• a_i= catalyst specific area,cm²mg⁻¹

• L_i= catalyst loading,mg cm⁻²

• P_r= reactant partial pressure, bar

• p_{re f} = reference pressure, 1,025 bar

• γ= pressure dependency coefficient, 0,5

• ∆Gi = activation energy,kJ mol⁻¹

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• R= universal gas constant, 8,314J mol⁻¹K⁻¹

• T= temperature, K

• T_{re f} = reference temperature, 298, 15K(25^◦C)

A high exchange current density means the surface of the electrode is more active, this results in lowering the energy barrier needed by the charge in moving from electrolyte to catalyst surface, and vice versa (Babir, 2013).

Song et al., 2007 showed that the activation energy∆G_i varies under real operating conditions, but for simplicity reasons constant values are chosen.

2.2.5 Membrane Water Content

The water content λ inside a Nafion-membrane is estimated by using a function of water activity a. This polynomial equation was fitted by Springer et al., 1991 based on their experimental results.

λ=0, 043+17, 81a−39, 85a²+35, 0a³ f or0<a≤1 (Eq. 2.22) λ=14+1, 4(a−1) f or1<a ≤3 (Eq. 2.23) Distribution of water in the membrane is assumed to be uniform (Lazar et al., 2019). The water activityais given by (Jiao and Li, 2011):

a=RH+2s (Eq. 2.24)

WhereRHis the relative humidity andsthe liquid water volume fraction in the pore regions of the membrane. In this model it is assumed that liquid water only exists in the catalyst layer of the fuel cell. In order to account for nonhomogenenous water distribution inside the channels a logarithmic average is used forRHands(Lazar et al., 2019).

The equation for estimating the maximum amount of non-frozen water membrane water during a cold start at subzero temperatures is given by Jiao and Li, 2009 and is based on the experimental results by Thompson et al., 2006.

λ_sat =







=_{4, 837} i f T <223, 15K

= [−1, 304+0, 01479T−3, 594∗10⁻⁵T²]⁻¹ i f 223, 15K≤T <T_{f rost}

>λ_{n f} i f T ≥T_{f rost}

(Eq. 2.25) Saturated membrane water contentλsat, (Jiao and Li, 2009)

The non-frozen water concentration C_w in the membrane is estimated by using a proportional correlation between the membrane density ρmem, polymer equivalent weightEWand the water contentλ(Babir, 2013).

Cw= ^ρ^m

EWλ (Eq. 2.26)

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2.2.6 Ohmic Losses

The ohmic resistance inside the fuel cell occurs due to the resistance of electron flow through the various fuel cell components such as electrolyte, electrodes, current collectors and their physical contact points. Using Ohm’s law to describe the losses gives:

E_ohm =iR_i (Eq. 2.27)

wherei=current density andR_i= the total resistance of the cell. The total losses can be summarized as (Abdin et al., 2016):

R_i =R_el+R_pl+Rmem (Eq. 2.28) Where the contributing resistances are:

• R_el= electrodes.

• R_pl= bipolar plates.

• R_mem= membrane.

According to Babir, 2013, the electronic resistance contribution is so small it is negligible. Through experimental results Laurencelle et al., 2001, showed that the ohmic overpotential is mostly related to the membrane humidity and cell temperature. Thus in this model only the ionic loss caused by the membrane resistance is considered. The ohmic overpotential is then calculated based on Ohm’s law (Abdin et al., 2016):

E_ohm = ^δ^memⁱ

σmem (Eq. 2.29)

where σmem is the membrane conductivity and δmem is the membrane thickness (when wet). The membrane thickness is assumed to be constant.

(Lazar et al., 2019).

The membrane conductivityσmem is given by fitting experimental data by Weber and Newman, 2004:

σmem =1, 16max{0,f −0, 06}^1,5exp

15000 R

1 T_{re f} − ¹

T

, (Eq. 2.30) T_{re f} =353, 15K(80^◦C), f = ^λV^W

λV_W+V_m, (Eq. 2.31) Vm = ^EW

ρmem, VW = ^{18, 01528}

ρ_W(T) ^{(Eq. 2.32)} Where f represent the water volume fraction of the membrane. Calculated byVm, the membrane equivalent weightEWdivided by membrane density ρmem, and V_W the molar volume of liquid water divided by the water densityρ_W(T)(Vetter and Schumacher, 2019). The density of waterρ_W(T) at 1 bar can be estimated by (Lazar et al., 2019).:

ρ_W(T) =999.972−7∗10⁻³(T−4)²∗10⁻³ (Eq. 2.33) Calculated inkg m⁻³

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2.2.7 Concentration Polarization

Concentration polarization occurs when the fuel and oxidant is rapidly consumed at the electrodes and concentration gradients (when the concentration is higher in one area than the other) are formed. The Nernst equation relates how the electrochemical potential changes with the partial pressure or concentrations. This is also known as nonstandard conditions.

∆V= ^RT nF ln

CB

C_S

(Eq. 2.34) Nernst equation

Where:

C_B = bulk concentration of reactant, mol cm⁻³

C_S= concentration of reactant at the surface of the catalyst, mol cm⁻³ (Babir, 2013).

By utilzing Fick’s law of one dimensional diffusion and Faraday’s law of electrolysis this relationship is obtained (Babir, 2013):

i= ^{n f} ∗D_i∗(C_B−C_S)

δe (Eq. 2.35)

WhereDiis the diffusion coefficient.

The current density at the point where the reactant is consumed at the same pace as it is reaching the surface of the catalyst is known as limiting current density. At this current density the surface concentration of reactants equals 0 and the fuel cell is unable to produce a higher current. By using the previous equation Eq. 2.35 and C_S = 0, i = i_L, the limiting current density becomes:

i_L = ^nFDⁱ^C^B

δ_e (Eq. 2.36)

The bulk concentrationC_b is estimated by the ideal gas law and mole fractions of reactant in the gas mixture. Mole fractions are calculated by (X.

Li, 2006, Musio et al., 2011):.

X_H₂_O = ^P^H²^O P X_H2 =1−X_H₂_O

X_O₂ = ¹−X_H₂_O 1+ (79/21)

(Eq. 2.37)

The total concentration in the mixture is given by the ideal gas law:

C= ^P

RT (Eq. 2.38)

And the bulk concentration becomes:

C_B_i =X_i∗C (Eq. 2.39)

WhereidenotesH₂orO₂from Eq. 2.37.

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By combining the three equations Eq. 2.34, Eq. 2.35 and Eq. 2.36 the following equation is obtained which relates the voltage losses in the fuel cell due to concentration polarization (Babir, 2013):

Econ= ^RT nFln

iL

i_L−i

(Eq. 2.40) Eq. 2.40 can underestimate the real concentration polarization losses and a gain factor K is added to better approximate the behaviour of the polarization curve. The gain factor makes the curve more aggressive and decreases earlier than with just the equation alone (Musio et al., 2011).

To calculate the diffusion coefficient D found in Eq. 2.36, Vetter and Schumacher, 2019, utilized the Chapman-Enskog formula in addition to a saturation correction(1−s)(Rosén et al., 2012).

D_i = ^e

τ(1−s)³D_{i,re f} T

T_{re f}

1,5P_{re f} P_i , T_{re f} =353, 15K; P_{re f} =1, 01325bar

(Eq. 2.41) In the model it is required to add an external reference value for the diffusion coefficient D_{i,re f}. This reference value is then adjusted per Eq.

2.41 using electrode porositye, tortuosityτ, temperatureT, pressurePand the ratio of liquid water volumes. The liquid water volumes has a value between 0 and 1 where 1 serves as a fully flooded channel. (Lazar et al., 2019). For the reference diffusion coefficientD_{i,re f} the following values are used (Vetter and Schumacher, 2019):

• D_H_{2,re f} =1, 24cm²/s(hydrogen in water vapor)

• D_O_{2,re f} =0, 28cm²/s(oxygen in air)

• D_H₂_{O,re f} =1, 24cm²/s(Water vapor in hydrogen, anode side)

• D_H₂_{O,re f} =0, 36cm²/s(water vapor in air, cathode side) 2.2.8 Cell and Stack Performance

Fuel cell efficiency is the ratio between work produced (electricity) and fuel (hydrogen) consumed. The electrical efficiency in this model η_electric is based on the lower heating value of hydrogenE_LHV. Using Eq. 2.6 and

∆HLV H =242kJmol⁻¹, the theoretical voltage is calculated in Eq. 2.42. The heat flowQis calculated by using the power delivered by the fuel cell and the efficiency and is given in Eq. 2.44. It is assumed that the product water evaporates and leave the stack(Babir, 2013).

E_LHV = −_∆G

nF = ²⁴²^kJmol

−1

2∗96485 =1, 254V (Eq. 2.42) η_electric = ^E^cell

E_LHV (Eq. 2.43)

Q_stack =

P_stack η_electric

−P_stack (Eq. 2.44)

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Fuel cell stack heat flow.

2.2.9 Water Transport

The transport of water jw from anode to cathode is split into three parts:

osmotic j_osmo, diffusive flow j_{di f f} and hydraulic permeation j_hyd. The equation for the cathode has j_gen, which is the water produced on the cathode side as a result of the electrochemical reaction. Whenjwis positive the water concentration increases (Lazar et al., 2019).

j_w,anode = j_{di f f} +j_hyd−josmo (Eq. 2.45) j_w,cathode= j_gen+j_osmo+j_hyd−j_{di f f} (Eq. 2.46) The rate in which water is produced on the cathode side (mol⁻¹cm⁻²) is (Babir, 2013):

jgen = ⁱ

2F (Eq. 2.47)

Three assumptions are made to reduce the water transport complexity (Lazar et al., 2019).

• Only water transport through the membrane is considered. Other water transport mechanisms (both liquid and vapour) related to the porous catalyst layer and gas diffusion layers are ignored.

• Liquid water is only present when the gas mixture has been saturated.

• The two water phases, liquid and vapour, are not utilized directly.

Using experimental data from Adachi et al., 2010, Lazar et al., 2019 used a curve fitting tool in order to adjust the equations for the diffusive and hydraulic flow. The three cases show permeation of water flux through Nafion membranes at various thicknesses based on water phase and differential pressure at 70 ^◦C. The three cases are: vapor-vapor (VVP), liquid-vapor (LVP) and liquid-liquid permeation (LLP) and is displayed in figure 2.3.

The next part will show the different equations which make up the sub- parts of j_w. In addition, the experimental data is used later to adjust the equations used for calculating diffusive and hydraulic flow.

Osmosis

Osmosis is movement of water through the membrane. In the case of fuel cells, water is dragged from the anode to the cathode. This is also known as electroosmotic drag. The water transport due to this effect can be written as (Babir, 2013):

josmo =nosmoI

F (in mols⁻¹cm⁻²) (Eq. 2.48) Wheren_osmo is the electroosmotic drag coefficient which is defined as the number of water molecules per proton. According to Babir, 2013 this

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Figure 2.3: Estimated water flux thorugh the membrane at various thicknesses at 70 ^◦C. For VVP: the relative humidity were 96% cathode and 38% anode. LVP: cathode were flooded (100% liquid volume fraction) and 38% RH anode. LLP: both anode and cathode were flooded. For all the tests, pressure = 1 bar (Lazar et al., 2019).

coefficient has varied greatly in published papers over the years due to different methods of measurement and data fitting. In this model an equation from Dutta et al., 2001 is used for estimating the electroosmotic drag coefficient, which is reliant on the (average) water content in the membraneλ.

nosmo =0, 0029λ²+0, 05λ−3, 4∗10⁻¹⁹ (Eq. 2.49) Diffusion

The effect of water generation and electroosmotic drag on the cathode side often results in flooding on the cathode side and drying out the anode side.

However back diffusion creates a counter flow which helps against drying the membrane on the anode side (Ji and Wei, 2009). The flow of water from this process can be estimated by integrating Fick’s law through the membrane (Abdin et al., 2016):

j_{di f f} = ^AD^λ^∆^C^w

δmem (Eq. 2.50)

Where: A= the cell area, Dλ = the average diffusive coefficient of water,

∆Cw = the difference in water concentration between the anode and cathode, and δ_mem = membrane thickness. In this equation δ_mem is set as a constant with a value of 201µm. This equation is used as a reference in order to calculate the diffusion for the VVP and LVP scenarios.

The diffusion coefficientD_λ used in Eq. 2.50 is estimated by Vetter and Schumacher, 2019 who refitted the measurement data done by Mittelsteadt

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and Staser, 2011. The resulting equation is dependent on water contentλ and membrane temperatureT_mem.

D_λ = ^{3, 842λ}

3−32, 03λ²−67, 74λ λ³−2, 115λ²−33, 013λ³+103, 37

∗10⁻⁶exp

20∗²⁰⁰⁰⁰ R

1

T_{re f} − ¹ T_mem

, T_{re f} =353, 15K

(Eq. 2.51)

The next three equations use the correction for VVP and LVP as mentioned earlier and is based on the data points from figure 2.3. When there is a mixture of gaseous and liquid phases a linear scaling based on j_{di f f}_,vvpandj_{di f f}_,lvpis applied (Lazar et al., 2019).

j_{di f f}_,vvp =0, 9178∗j_{di f f}(σ|0, 0201)(−947, 5δ²_mem−6, 198δ_mem+1, 508) (Eq. 2.52) j_{di f f}_,lvp=3, 592∗j_{di f f}(σ|0, 0201)(−687δ²_mem−21, 73δ_mem+1, 714)

(Eq. 2.53) j_mix =j_{di f f}_,vvp+ (j_{di f f}_,lvp−j_{di f f}_,vvp)∗ |(s_anode−s_cathode)| (Eq. 2.54) Where VVP-correction is used in when there is no liquid water and LVP if one side is flooded with liquid water.sin Eq. 2.54 refers to the liquid water volume fraction.

Hydraulic Permeation

Hydraulic permeation occurs when there is a pressure difference between the anode and the cathode. With this pressure difference water can be pushed through the membrane (Babir, 2013). This effect is only considered when liquid water is present in both anode and cathode. The water flux related to hydraulic permeation is given by (Jiao and Li, 2011):

j_hyd= ^AC^w^K^λ

µ_wδ_mem ∆P∗ 10⁵ (Eq. 2.55) j_hyd is linearly correlated with the pressure gradient ∆P, which is the pressure difference between both sides of the membrane. ∆P is affected by the cell area A, water concentration in the membrane C_w, hydraulic permeability K_λ, dynamic viscosity of waterµ_w and membrane thickness δmem.

The dynamic viscocity of water µ_w is estimated by a function of temperature and constants (Likhachev, 2003):

µw=µ₀exp

aµp+ ^E^µ−bµp R(T−θ_µ−c_µp)

(Eq. 2.56) Likhachev, 2003 utilized tabulated values from experimental data contain- ing the viscosity of water at various temperatures and pressures. The constants found which fit the formula are:

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• µ₀=2, 4055∗10⁻⁵ Pa·s(Pascal-second and reference value)

• a_µ =4, 42∗10⁻⁴bar⁻¹

• Eµ =4, 753kJ mol⁻¹

• bµ=9, 565∗10⁻⁴kJ(mol bar)⁻¹

• θµ=139, 7K

• c_µ =1, 24∗10⁻²K bar⁻¹

The pressurePof Eq. 2.56 is ignored as the pressure levels a typical PEM fuel cell operate at is low enough that p only has a minor impact on the water visocityµ_w(Lazar et al., 2019).

Jiao and Li, 2011 suggests the following relationship between hydraulic permeability K_λ and membrane water content λ, using a constant value K_w =2, 86∗10⁻²⁰:

K_λ =K_wλ (Eq. 2.57)

From the experimental data by Adachi et al., 2010, the correlation between hydraulic flow of water and the membrane thickness appears to be nonlinear. Thus to better estimate the hydraulic flow an adjustment function is applied. This function takes the membrane thickness into account and is at a reference pressure difference of 0,025 bar (Lazar et al., 2019):

K_λ,LLP











=0, 1158K_λ

5, 749∗10⁻³ δ_memexp[−1, 326] forδ_mem≥0, 005cm

=0, 1158K_λ

2, 518∗10⁻⁴ δ_memexp[−1, 872] forδ_mem<_{0, 0056}cm

(Eq. 2.58)

At last the hydraulic flow is corrected for the pressure difference between anode and cathode, where j_{hyd,re f} is j_hyd from Eq. 2.55 after applying the correction from Eq. 2.58, Lazar et al., 2019:

j_hyd,LLP = j_{hyd,re f}(32, 41δ_p+0, 06016) (Eq. 2.59)

2.3 Bus Modelling - QSS Toolbox

The QSS Toolbox is a vehicle simulation library designed for Matlab Simulink. It is developed by ETH Zürich Insitute for Dynamic Systems and Control. The model built by the QSS Toolbox is simulated in a quasistatic approach, meaning the model is built "backwards". Instead of calculating the vehicle speed from forces, the model calculates acceleration from the velocity given by a driving cycle and determines the forces acting on the vehicle in each time step (1s) (Guzzella and Sciarretta, 2013).

The inputs for the system are speedvand accelerationa, supplied by a driving cycle. The forces acting on the wheels are calculated in each time

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step. For each time step the vehicle is assumed to run at a constant speed and acceleration. The forces acting on the wheels are used as input for the transmission gear which outputs the required torque and revolutions per minute (rpm) to the motor. The motor in turn calculates the energy required to move the vehicle at the current speed and acceleration and feeds the energy requirement to the control system which distributes the load to the fuel cell and battery. The control system is not a part of the QSS library. Figure 2.4 display a simplified model flow. The next sub-chapters will explain the relevant modelling blocks and their equations as described in the included QSS manual (Guzzella and Amstutz, 2005) or by examining the calculation flow within Simulink.

Figure 2.4: Simplified model flow.

2.3.1 Driving Cycle

The driving cycle provides input to the system and is sourced from a normalized test drive or test cycle. A driving cycle is defined by at least two vectors: A time vector and a vehicle speed vector. The acceleration vector is calculated from the supplied speed vector using:

a_f(k∗h) = ^v^f(k∗h+h)−v_f(k∗h

h ,k=1, . . .k_max−1, a_f(k_max) =0 (Eq. 2.60) Where k is the current time of the simulation, h is the size of time-step, and v_f the vehicle speed. The driving cycle used in this model is the Braunschweig cycle, measured in the Lower Saxony German town of Braunschweig. This driving cycle is frequently used to model city buses.

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The cycle is characterized by "stop and go" driving with a low amount of cruising at a steady speed. The key parameters are listed in table 2.2 and the time-speed graph in figure 2.5.

Figure 2.5: Braunschweig driving cycle, time-speed (Barlow et al., 2009).

Parameter Value

Duration 1740s

Max speed 58, 2km/h

Average total speed 22, 6km/h Average driving speed 27, 03km/h

Distance 10, 9km

Idle time 16, 55%

Stops per km 2, 39

Table 2.2: Braunschweig driving cycle key parameters (Barlow et al., 2009).

2.3.2 Vehicle Forces

The vehicle forces are calculated on the basis of the average speed from the current and previous time-step and acceleration. The forces acting on the vehicle are split into three parts and subsequently added together to get the torque acting on the wheels (Guzzella and Amstutz, 2005).

Rolling resistance:

F_roll =m_f ∗g∗mu (Eq. 2.61) Aerodynamic:

Faero = ¹

2∗ρ∗c_d∗A_f ∗v² (Eq. 2.62)

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Inertia (resistance to acceleration):

F_inertia=m_f ∗(1+mt2m_f)∗^a

h (Eq. 2.63)

Where:

• m_f = Total mass of vehicle (kg).

• mu= Rolling friction coefficient.

• ρ= Air density.

• c_d= Drag coefficient.

• mt2m_f = Rotating mass (%).

• A_f = Vehicle cross section or frontal area (m²)

The added resistance from climbing or gradients are not considered as this value is not included in the driving cycle. The speed and acceleration of the wheels are dependent on the wheel radius:

ω_wheel =v∗r_wheel⁻¹ (Eq. 2.64)

aω_wheel = a∗r_wheel⁻¹ (Eq. 2.65)

2.3.3 Simple Transmission

The simple transmission assumes that kinematic relationships are ideal and there are no inertia effects by backlashes, which is loss of motion caused by the gaps in gear teeth. The relationship between torque or rotational speed is fixed to the gear ratio and is given by:

ω_trans =ω_wheel∗gear_ratio (Eq. 2.66) aωtrans =aω_wheel∗gear_ratio (Eq. 2.67)

T_trans+=

P_GT0

ω_wheel +T_wheel

gear_ratio∗e_GT (Eq. 2.68) T_trans− =

P_GT0

ω_wheel ∗e_GT+T_wheel

gear_ratio∗e_GT⁻¹ (Eq. 2.69) Where:

• ω_trans= Speed of the fly wheel, rad/s.

• aω_trans= acceleration of the fly wheel, rad/s².

• Ttrans= torque on the fly wheel, Nm.

• P_GT0= Idling losses (friction), W.

• e_GT= efficiency of gearbox.

T_trans+andT_trans−denotes if the torque flow goes from engine to wheel (+) or wheel to engine (-).

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2.3.4 Electric Motor

The electric motor requires the torque and rotational values outputted by the transmission. The output of the electric motor is the required electric power demanded by the transmission in the time-step. The motor efficiency is given based on a lookup table which relates the required torque and rotational speed to a given efficiency. The lookup table consists of two quadrants, the first quadrant is active when the vehicle is accelerating:

T_EM >0 andω_EM > 0. The second quadrant is active during deceleration:

T_EM < 0 and ω_EM > 0. The power required by the electric motor is expressed as (Guzzella and Amstutz, 2005):

P_EM = ω_EM∗T_EM∗ ¹

η_EM(ω_EM, T_EM₎ (Eq. 2.70) T_EM = (aω_trans∗θ_EM) +T_gear, ω_EM =ω_trans (Eq. 2.71) Whereθ_EM = motor rotational inertia (kg∗m²). The efficiency map can be seen in figure 2.6 and is referenced to create the lookup table used in the model. It is assumed that the motor has the same effectiveness in both quadrants.

Figure 2.6: Remy HVH410-150 DOM efficiency map (Remy, 2012).

2.3.5 Battery

The input to the battery model block is electric power (W). Given a positive input the battery discharges and when the input is negative it charges. The output is the current state of charge (SOC). SOC is the current charge of the battery, relative to its maximum capacity. The power is integrated after calculating it from the known power and voltage of the battery, from which the actual battery charge is calculated. This leads to an implicit equation as the voltage is dependent on the battery charge and from the current either

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charging or discharging the battery. From the QSS Toolbox manual the equations for the charging mode are given as (Guzzella and Amstutz, 2005):

q(k∗h) = ^Q(k∗h)

Q₀ , Q(k∗h) =Q(0) +

∑

k

i(k∗h)∗h (Eq. 2.72) WhereQ0is the nominal capacity, andQ(0)the initial charge of the battery.

c(k∗h) = ⁱ(k∗h)

i₀ , i₀ = ^Q⁰

1h (Eq. 2.73)

Wherei₀is the current where the battery is fully charged in one hour. C rate is the rate in which the battery is charged or discharged in 1 hour based on its nominal capacity.

Two weightsu_1Landu_0Lare calculated and depend on the C rate:

u₁_L(c(k∗h)) =C_L₄∗c(k∗h) +C_L₃ (Eq. 2.74) u₀L(c(k∗h)) =CL2∗c(k∗h) +C_L₁ (Eq. 2.75) C_L₄ is the internal resistance, C_L₃ the varying battery voltage, C_L2 the internal resistance causing the initial voltage drop, and C_L1 the nominal battery voltage. These 4 variable descriptions are not explicitly stated in the QSS manual (Guzzella and Amstutz, 2005), but deducted based on similar equations in the Vehicle Propulsion Systems book (Guzzella and Sciarretta, 2013).

Using the two weightsU_1LandU_0Lthe battery load is calculated by:

uBL(k∗h) =u_L1(c(k∗h))∗q(k∗h) +u0L(c(k∗h)) (Eq. 2.76) When the battery is discharging the equations are similar, except for the negative C rate in Eq. 2.74 and Eq. 2.75.

By using the the equations for voltage Eq. 2.74 and Eq. 2.75, in addition to the power Eq. 2.76, makes it possible to calculate the voltage as a function of power only. During charging the following equation is obtained:

u_BE(k∗h) = ¹ 2

c_L3∗q(k∗h) +c_L1+

q

(cL3∗q(k∗h) +cL1)²+4∗(cL4∗q(k∗h) +CL2)∗

P_BL∗(k∗h)/i₀)

(Eq. 2.77) The battery power can then be written as:

P_BE(k∗h) =u_BE(k∗h)∗^u^BE(k∗h)−u_Ei(k∗h)

R_Ei(k∗h) ^{(Eq. 2.78)} In discharge mode the coefficients in Eq. 2.74 - Eq. 2.77 changes from c_Ln to c_En. The internal resistance constants, c_L₂,c_E₂ and c_L₄,c_E₄ may change from charge to discharge. While the voltage constants have to be c_L1 =c_E₁andc_L3 =c_E₃, as proven with physical considerations (Guzzella and Sciarretta, 2013).

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Chapter 3

Methodology

To answer the questions set out in the problem statement, a systematic approach has been used. The fuel cell model and the FCEB model are set up individually before being combined at the end to produce the final result.

An overview of the workflow is displayed in figure 3.1 and the steps are discussed below.

Figure 3.1: Overview of the workflow and thought process to answer the problem statement.

Modelling and Validation of a Fuel Cell Electric Bus

Modelling and Validation of a Fuel Cell Electric Bus

Jørgen Kristoffer Tuset

Thesis submitted for the degree of Master in Renewable Energy Systems

30 credits

Department of Technology Systems

The Faculty of Mathematics and Natural Sciences

UNIVERSITY OF OSLO

Modelling and Validation of a Fuel Cell Electric Bus

Jørgen Kristoffer Tuset

Abstract

Acknowledgement

Contents

List of Figures

List of Tables

List of Abbreviations and Nomenclature

Abbreviations

Nomenclature

Chapter 1

Introduction

1.1 Problem Statement

1.2 Structure of the Thesis

Chapter 2

Theory and Literature

2.1 Proton Exchange Membrane Fuel Cell Basic Chem- istry

2.2 PEMFC Model

2.3 Bus Modelling - QSS Toolbox

∑

Chapter 3

Methodology