DOKUZ EYLÜL UNIVERSITY

GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

PERFORMANCE ANALYSIS AND OPTIMIZATION

OF INTEGRATED FUEL CELL-BATTERY SYSTEMS
FOR MARINE APPLICATIONS

by
Süleyman Aykut KORKMAZ

May, 2023
İZMİR
 PERFORMANCE ANALYSIS AND OPTIMIZATION
OF INTEGRATED FUEL CELL-BATTERY SYSTEMS
FOR MARINE APPLICATIONS

A Thesis Submitted to the

Graduate School of Natural and Applied Sciences of Dokuz Eylül University
In Partial Fulfillment of the Requirements for the Degree of Doctor of
Philosophy in Marine Engineering, Marine Transportation Systems Engineering
Program

by
Süleyman Aykut KORKMAZ

May, 2023
İZMİR
 Ph.D. THESIS EXAMINATION RESULT FORM

We have read the thesis entitled “PERFORMANCE ANALYSIS AND

OPTIMIZATION OF INTEGRATED FUEL CELL-BATTERY SYSTEMS
FOR MARINE APPLICATIONS” completed by SÜLEYMAN AYKUT
KORKMAZ under supervision of ASST. PROF. DR. K. EMRAH ERGİNER and
we certify that in our opinion it is fully adequate, in scope and in quality, as a thesis
for the degree of Doctor of Philosophy.

……………………………………….
Asst. Prof. Dr. K. Emrah ERGİNER

Supervisor

…………………………………….. ……………………………………...
Asst. Prof. Dr. Mustafa NURAN Prof. Dr. Can Özgür ÇOLPAN

Thesis Committee Member Thesis Committee Member

…………………………………….. ……………………………………...
Prof. Dr. Önder KIZILKAN Assoc. Prof. Dr. Ceyhun YILMAZ

Examining Committee Member Examining Committee Member

Prof. Dr. Okan FISTIKOĞLU

Director
Graduate School of Natural and Applied Sciences

ii
 ACKNOWLEDGMENT

The author would like to express deep gratitude to the thesis advisor Asst. Prof. Dr.
K. Emrah ERGİNER for his invaluable supervision, advice, encouragement, support,
and insight through the research process.

Also, the author would like to express the deepest appreciation to Prof. Dr. Can
Özgür ÇOLPAN, who has been a tremendous mentor to me during my graduate
studies. I have benefited from his boundless experience and guidance in my academic
life. In addition, I would like to acknowledge the valuable support and help of Asst.
Prof. Dr. Mustafa NURAN.

The author thanks his special research fellows Olgun KONUR, Onur YÜKSEL, Sera
Ayten ÇETİNKAYA, and Anıl ERDOĞAN for their valuable contributions to the
published articles, conference papers, and to this study, as well.

Last, but definitely not least, the author gratefully thanks his wife Jamal
ESENKANOVA for her understanding and supportive talks. Without her support and
motivation, I would not have completed this thesis.

And finally, the author thanks his self-sacrificing mother Elif KORKMAZ, and
lovely sisters F. Binnur KAYA and L. Zinnur YAPRAK for always supporting and
believing in me. The author would like to remember his deceased father Necati
KORKMAZ, who passed away on 8th June 2020. The author very much wishes he
could see him now he has completed his Ph.D.!

The author would like to thank Dokuz Eylul University’s Scientific Research
Projects for providing funding to his research with the project number
[2020.KB.MLT.012].

Süleyman Aykut KORKMAZ

iii
 PERFORMANCE ANALYSIS AND OPTIMIZATION OF INTEGRATED
FUEL CELL-BATTERY SYSTEMS FOR MARINE APPLICATIONS

ABSTRACT

The shipping industry has been under pressure to reduce its environmental footprint
due to increasingly stringent regulations. The “Green Ship" concept, which focuses on
zero or low exhaust gas emission propulsion systems, has gained attention in the
maritime community. To achieve the objectives, two case-studies are presented in this
thesis. In the first case-study, the environmental and economic impacts of using fuel-
cell and battery-based hybrid configurations are investigated. Phosphoric acid and
molten carbonate fuel cell systems can take the place of the diesel generators on a large
tanker to supply the vessel’s total electricity demand. Environmental and economic
analyses of the utilization of the specified fuel-cell systems with batteries on a large
commercial tanker vessel are provided. The results show that the carbon dioxide
emissions could be reduced by up to forty-nine-point seventy-five percent, and the
lowest electricity production cost is found at zero point one eight one USD per kilowatt
hour for current fuel prices with utilization of molten carbonate fuel cells and lithium
nickel manganese cobalt oxide battery cells. In the second case-study, the operating
parameters of a semi-empirical mathematical model of a proton-exchange membrane
fuel-cell (PEMFC) are extracted and compared using various metaheuristic algorithms
(MHAs). In this regard, sum-squared error (SSE) is employed as the objective function
to find values of seven unknown modeling parameters. As a case study, parameter
extraction is carried out utilizing the MHAs for a commercial PEMFC. Three different
multi-attribute decision-making methods are used to rank the MHAs. The results
showed that MFA had the lowest SSE and shortest run-time, while Grey Wolf
Optimizer achieved the highest objective function efficiency.

Keywords: Battery, fuel cell, marine, mathematical modeling, metaheuristic

algorithms, multi-attribute decision making, optimization.

iv
DENİZCİLİK UYGULAMALARI İÇİN ENTEGRE YAKIT PİLİ-BATARYA
SİSTEMLERİNİN PERFORMANS ANALİZİ VE OPTİMİZASYONU

ÖZ

Deniz taşımacılığı sektörü, giderek daha sıkı düzenlemelere tabi olduğundan,

çevresel ayak izini azaltma baskısı altındadır. "Yeşil gemi" konsepti, sıfır veya düşük
egzoz gazı emisyonlu tahrik sistemlerine odaklanarak denizcilik camiasında dikkat
çekmektedir. İstenilen amaca ulaşabilmek amacıyla bu tez yakıt pili sistemleri içeren
iki vaka çalışmasını incelemektedir. İlk vaka çalışmasında, yakıt hücresi ve batarya
tabanlı hibrit konfigürasyonların çevresel ve ekonomik etkileri incelenmektedir.
Fosforik asit ve erimiş karbonatlı yakıt hücresi sistemleri, bir kimyasal tanker üzerinde
dizel jeneratörlerin yerini alcak şekilde geminin toplam elektrik talebini
karşılamaktadır. Belirtilen yakıt hücresi sistemlerinin bataryalarla birlikte ticari bir
tanker gemisinde kullanımının çevresel ve ekonomik analizleri gerçekleştirilmektedir.
Sonuçlar, karbon dioksit emisyonlarının yüzde kırk dokuz virgül yetmiş beşe kadar
azaltılabileceğini ve erişimiş karbonatlı yakıt hücreleri ve lityum nikel manganez
kobalt oksit batarya hücrelerinin kullanımıyla güncel yakıt fiyatları için en düşük
elektrik üretim maliyetinin kilovat saat başına binde yüz seksen bir Amerikan doları
olduğunu göstermektedir. İkinci vaka çalışmasında, bir proton-değişim membranlı
yakıt hücresinin (PEMFC) yarı-ampirik matematiksel modelinin operasyon
parametreleri çeşitli meta-sezgisel algoritmalar (MSA) kullanılarak çıkarılıp
karşılaştırılmıştır. Bu bağlamda, yedi bilinmeyen modelleme parametresinin
değerlerini bulmak için toplam kare hatası (TKH) amaç fonksiyonu olarak
kullanılmaktadır. Vaka çalışması olarak, bir ticari PEMFC için MSA’lar kullanılarak
parametre çıkarımı gerçekleştirilmiştir. MSA'ları sıralamak için üç farklı çok kriterli
karar verme yöntemi kullanılmıştır. Sonuçlar, Moth Flame Algoritması'nın en düşük
TKH ve en kısa çalışma süresine sahip olduğunu, Grey Wolf Optimizer'ın ise en yüksek
amaç fonksiyonu verimliliğini elde ettiğini göstermiştir.

Anahtar Kelimeler: Batarya, yakıt pili, denizcilik, matematiksel modelleme, meta-

sezgisel algoritmalar, çok kriterli karar verme yöntemleri, optimizasyon.

v
CONTENTS
Page
Ph. D. THESIS EXAMINATION RESULT FORM…………..…………......………ii
ACKNOWLEDGEMENTS………………..……………..…………….……........…iii
ABSTRACT…………………………..……………..………………….……........…iv
ÖZ…………………………..……………..………………….……...……….....…....v
LIST OF FIGURES………..……………..………………….……...………….....….ix
LIST OF TABLES………..……………..………………….……...….………..........xi

CHAPTER 1 - INTRODUCTION..........................................................................1

1.1 Motivation of the Thesis ................................................................................4

1.2 Objective of the Thesis...................................................................................5
1.3 Thesis Outline ................................................................................................5

CHAPTER 2 - BACKGROUND AND LITERATURE REVIEW .......................7

2.1 Renewable Energy Sources and Technologies ................................................8

2.2 Hydrogen Energy and Fuel Cells ....................................................................9
2.2.1 Hydrogen Energy................................................................................9
2.2.1.1 Hydrogen Production ............................................................10
2.2.1.2 Hydrogen Storage Methods ..................................................14
2.2.2 Fuel Cell Technology .......................................................................17

CHAPTER 3 - EXTRACTING SEMI-EMPIRICAL MODEL PARAMETERS

FOR A COMMERCIAL PEMFC FOR MARINE VESSELS USING MHAS
AND MULTI-ATTRIBUTE DECISION-MAKING METHODS ......................20

3.1 Literature Review .........................................................................................20

3.1.1 Literature Review on Marine Vessels Utilizing Fuel Cell..................20
3.1.2 Literature Review on Modeling of PEMFCs .....................................23

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 3.1.3 Literature Review on Metaheuristic Algorithm for Parameter Extraction
of PEMFCs ......................................................................................26
3.2 Mathematical Modeling ................................................................................33
3.2.1 0D Semi-empirical Electrochemistry Model of PEMFC Stack ..........33
3.2.2 Metaheuristic Optimization Algorithms for PEMFC Stack Parameter
Extraction.........................................................................................36
3.2.2.1 Fitness Function Definition and Parameter Settings for MHAs
.........................................................................................................36
3.2.2.2 Genetic Algorithm (GA) .......................................................38
3.2.2.3 Differential Evolution (DE) ..................................................38
3.2.2.4 Salp Swarm Algorithm .........................................................39
3.2.2.5 Moth-Flame Algorithm (MFA) .............................................40
3.2.2.6 Whale Optimization Algorithm (WOA) ................................41
3.2.2.7 Sine Cosine Algorithm (SCA)...............................................43
3.2.2.8 Cuckoo Search Algorithm (CS) ............................................44
3.2.2.9 JAYA ...................................................................................45
3.2.2.10 Grey Wolf Optimizer (GWO) .............................................45
3.2.3 Multi-attribute Decision-Making Methods (MADM) ........................47
3.2.3.1 Technique for Order of Preference by Similarity to Ideal
Solution............................................................................................47
3.2.3.2 Multi-Objective Optimization on the Basis of Raito Analysis
.........................................................................................................49
3.2.3.3 Preference Ranking Organization Method for Enrichment of
Evaluations ...........................................................................50
3.3 Results and Discussion .................................................................................51
3.3.1 PEMFC Model Validation Results ...................................................51
3.3.2 Metaheuristic Algorithms and MADM Methods Results ..................54

CHAPTER 4 - ENVIRONMENTAL AND ECONOMIC ANALYSES OF FUEL

CELL AND BATTERY-BASED HYBRID SYSTEMS UTILIZED AS
AUXILIARY POWER UNITS ON A CHEMICAL TANKER VESSEL ........... 62

vii
 4.1 Literature Survey on Marine Transport Applications.....................................62
4.2 System Description.......................................................................................66
4.3 Modeling of Fuel Cell and Battery Configuration .........................................72
4.3.1 Mathematical Modeling of the Hybrid Power Plants .........................72
4.3.2 Environmental Analysis of Hybrid System .......................................76
4.3.3 Economic Analysis of Hybrid System...............................................77
4.4 Results and Discussion .................................................................................79
4.4.1 Mathematical Modeling Results of the Fuel Cell/Battery Hybrid System
on Chemical Tanker Vessel ..............................................................79
4.4.2 Environmental Analysis of the Hybrid System ..................................81
4.4.3 Economic Analysis of Hybrid System...............................................84

CHAPTER 5 - CONCLUSIONS ..........................................................................88

REFERENCES .....................................................................................................94

viii
LIST OF FIGURES
Page
Figure 2.1 Classification of energy resources and technologies .................................8
Figure 2.2 Classification of hydrogen production ....................................................10
Figure 2.3 The schematic of the compressed hydrogen storage and its subsystems .. 15
Figure 2.4 The pressure–capacity diagram according to the absorption and desorption
processes ..............................................................................................16
Figure 2.5 Schematic diagram of a fuel cell with its main components ....................18
Figure 3.1 Schematic of the operation of a PEMFC .................................................24
Figure 3.2 Classification of Fuel Cell Modeling ......................................................25
Figure 3.3 The number of related papers on the Web of Science for MHAs used in
PEMFC parameter extraction ................................................................28
Figure 3.4 The comparison of the polarization curves of the 250 W PEMFC using the
E-CGA as in this study and HGA as in the study of Mo et al. (2006): (a)
and (b) for identification and (c) and (d) for validation ..........................53
Figure 3.5 Polarization curve of H-1000XP.............................................................54
Figure 3.6 Polarization curves when estimated parameters of (a) MFA, (b) DE, (c)
JAYA, (d) CS, (e) IWOA, (f) GWO were used .....................................57
Figure 3.7 Convergence curves of each algorithm’s best solutions ..........................58
Figure 3.8 Distribution of the lowest error obtained by the algorithms in each run .. 58
Figure 3.9 Convergence curve of MFA ...................................................................59
Figure 3.10 Convergence curve of GWO ................................................................59
Figure 3.11 Convergence curve of CS .....................................................................60
Figure 3.12 Convergence curve of JAYA ................................................................60
Figure 4.1 Utilization hours of the plant according to operation modes ...................67
Figure 4.2 FC/battery hybrid electricity distribution system scheme ........................70
Figure 4.3 Ship power distribution system model algorithm scheme .......................73
Figure 4.4 State-based EMS algorithm scheme .......................................................74
Figure 4.5 Fuel consumptions on different operation modes and total fuel consumption
of the proposed combined systems and D/G plant .................................80

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Figure 4.6 CO2 production on different operation modes and total fuel consumption
from the fuel cell/battery hybrid systems and D/G plant according to
operation modes....................................................................................82
Figure 4.7 The production of (a) NOx, (b) N₂O, (c) VOC, (d) CO, (e) SOx, (f) PM
emissions from plants for different operation modes .............................84
Figure 4.8 SoH curves of batteries were (a) utilized (b) not utilized during the
navigation .............................................................................................85
Figure 4.9 LEC values obtained for each configuration mode...............................86
Figure 4.10 Electricity production costs of utilizing fuel cell/battery hybrid
configurations and D/Gs onboard .......................................................87

x
LIST OF TABLES
Page
Table 2.1 Fuel cell types and main specifications ....................................................19
Table 3.1 Parameter setting of the algorithms ..........................................................37
Table 3.2 The main parameters of the PEMFCs ......................................................52
Table 3.3 Ranges taken for the parameters’ estimation ............................................52
Table 3.4 Results of parameters for 250 W FC in Range 2 ......................................53
Table 3.5 Results of the statistical comparison ........................................................55
Table 3.6 The rank of each algorithm determined by selected MADM methods ...... 55
Table 3.7 The estimated parameters by the algorithms ............................................56
Table 4.1 Specifications of the marine diesel generators and electrical load ............67
Table 4.2 Technical specifications of the commercial PAFC ...................................68
Table 4.3 Technical specifications of the commercial MCFC ..................................69
Table 4.4 Proposed system configurations...............................................................70
Table 4.5 Selected battery cells for system configurations .......................................71
Table 4.6 EF of diesel fuels (g emission/ g fuel) ......................................................77
Table 4.7 Bunker prices for diesel fuels and LNG ...................................................79
Table 4.8 Optimum batteries and charge-discharge hours ........................................79
Table 4.9 The emission reduction potential of the proposed system configurations
compared to conventional diesel generators ..........................................82
Table 4.10 Weights, volumes, costs, and battery lifespans of the system configurations
...............................................................................................................................86

xi
 CHAPTER 1
INTRODUCTION

The driving force behind the increase in maritime transport is the growth in world
trade volume. According to the data gathered by the World Trade Organization
(WTO), the volume and value of world trade have increased by 400 times and 274
times in 2020 compared to 1950, respectively (World Trade Organization [WTO],
2022). A significant percentage of the increasing world's trade by volume is realized
by seaborne trade. In 2020, approximately 89% of the cargo in the world was
transported by maritime transportation (Ministry of Transport and Infrastructure
[MTI], 2021). During the transportation of the goods, the propulsion unit of the
maritime fleet is still mainly provided by internal combustion engines (ICEs) are the
main contributor to global warming and greenhouse gas emissions by using fossil-
based fuels such as Heavy Fuel Oil (HFO) and Marine Diesel Oil (MDO). The need to
close the door of fossil fuel usage in energy demand is not only due to the possibility
of depletion of these fuels soon, but also because the environmental effects can cause
irreversible damage.

The reduction in emission production by increasing energy efficiency has been

among the most important subjects for shipowners (Kaya & Erginer, 2021) in the last
two decades. International Maritime Organization (IMO) has also supported the
reduction in greenhouse gas (GHG) emission production based on maritime
transportation with new regulations and mandatory measures for ships, which were
first initiated with the adoption of MARPOL Annex VI - Prevention of Air Pollution
from Ships in 1997. SEEMP (Ship Energy Efficiency Management Plan) and EEDI
(Energy Efficiency Design Index) amendments were entered into force on 1 January
2013 that gave progressive CO2 emission reduction goals to ships by using energy
efficiency-increasing techniques and emission reduction technologies. Technological
advances have accelerated the achievement of these goals in the maritime industry.
However, it was reported that the effect of seaborne GHG emissions on global
anthropogenic CO2 emissions increased from 2.76% (962 million t) in 2012 to 2.89%
(1,056 million t) in 2018 (International Maritime Organization [IMO], 2020). IMO

1
took after the United Nation’s (UN) sustainable development goal 13 (climate action)
by adopting the initial strategy on the reduction of GHG emissions from ships. The
strategy aims at reducing the total annual ship based GHG emissions by at least 50%
by 2050 compared to 2008 (IMO, 2018).

The IMO has conducted four GHG studies on emitted emissions from ships in the
year 2000 (IMO, 2000), 2009 (IMO, 2009), 2014 (IMO, 2014), and 2020 (IMO, 2020).
Initially, IMO focused on reducing NOx and SOx emissions due to international
shipping activities, as demonstrated in Annex VI of the MARPOL Convention, which
is the first and main regulation that emphasized air pollution prevention requirements
from ships adopted in 1997. The Energy Efficiency Design Index (EEDI) and the Ship
Energy Efficiency Management Plan (SEEMP) were the first regulations to minimize
carbon dioxide-based airborne emissions from ships, and these were established in
Annex VI in 2011 and went into force in 2013. For different ship types and size
segments, EEDI is a technical measure that specifies a minimum energy efficiency
level expressed in grams of CO2 per ship's capacity mile for new ships to promote the
adoption of more energy-efficient equipment and engines, while the Ship Energy
Efficiency Management Plan (SEEMP) is a low-cost operational approach by applying
energy efficiency measures that creates a framework for enhancing the energy
efficiency of new or existing marine vessels over 400 GT (IMO, 2022). The IMO
introduced the Energy Efficiency Existing Indicator (EEXI) and Carbon Intensity
Indicator (CII) to minimize ship GHG emissions by making additional amendments to
Annex VI on the MEPC76 (Marine Environment Protection Committee 76) session in
June 2021. EEXI is a metric connected to a ship's technological design. Ships must
acquire EEXI approval just once throughout their lifespan, by the first periodical
survey taking place no later than in 2023 (Det Norske Veritas [DNV], n.d.). CII is a
marine vessel grading system based on in-service/operational efficiency (Lloyd
Register [LR], n.d.). EEXI and CII will come into effect in January 2023, so the carbon
taxation market is expected to be active in recent years based on airborne pollution
caused by shipping activities. Market taxation prices for bunker fuels are expected to
exceed $100 per ton (Gerretsen, 2022).

2
 One of the suggested solutions for decreasing emissions from ships is the
implementation of hybrid fuel cell systems, which has compelled shipping companies
to create innovative technologies and adopt alternative fuels to mitigate the
environmental consequences of their vessels. Shipping companies began by
implementing emission reduction measures recommended in SEEMP
recommendations, which are simple to implement and need low initial investment.
However, the acceptance of EEXI has resulted in the implementation of energy-
efficient equipment on all ships to fulfill the emission reduction objective of a 40%
reduction from 2008 levels by 2030.

Hybrid fuel cell systems are one of the recommended technologies in the guidelines
for reducing emissions from seaborne trade by generating energy from a range of fuels
such as hydrogen, ammonia, methanol, liquefied natural gas (LNG), and others, which
have also many advantages according to the other power systems such as high
modularity, high efficiency, low air emissions, and reduced noise emissions, no
moving parts, and fewer maintenance needs (Markowski & Pielecha, 2019).
Commercially available fuel cell technologies are proton-exchange membrane fuel
cells (PEMFC), alkaline fuel cells (AFC), direct methanol fuel cells (DMFC),
phosphoric acid fuel cells (PAFC), molten carbonate fuel cells (MCFC), and solid
oxide fuel cell (SOFC). Today, PEMFC has become the preferred fuel cell type among
fuel cells due to its technological maturity and high electrical efficiency (Sohani et al.,
2020). The fact that it has a shorter start-up time compared to fuel cells operating at
high temperatures, especially SOFC and MCFC, made it possible to use it in the field
of transportation (Department of Energy [DoE], n.d.-a). These features have enabled
research and development studies and projects to be considerably higher than other
fuel cells (van Biert, Godjevac, Visser, & Aravind, 2016) on the usage of PEMFC to
power small ferries, yachts, and boats that usually navigate in coastal areas (Coppola,
Micoli, & Turco, 2020).

3
1.1 Motivation of the Thesis

The shipping industry is a significant contributor to global greenhouse gas

emissions, and there is a growing need to reduce its environmental impact. Fuel cell
technology is a promising alternative to traditional combustion engines in the maritime
sector, offering high efficiency and low emissions. However, there are several
challenges to the implementation of fuel cell systems in different types of vessels,
including the development of accurate mathematical models, the selection of
appropriate fuel cell types, and the consideration of both environmental and economic
factors.

This thesis aims to address some of these challenges by presenting two case studies
focused on the application of fuel cell technology in small and large marine vessels.
The first case study focuses on the development of a semi-empirical model of a
PEMFC to be used in a small boat. Metaheuristic algorithms are used to extract the
model's parameters, and multi-criteria decision methods are applied to determine the
most suitable algorithm for the given application. The second case study considers the
environmental and economic implications of using fuel cells in a large tanker vessel.
Specifically, phosphoric acid fuel cells and molten carbonate fuel cells are evaluated
in a hybrid configuration with batteries, and the results are analyzed in terms of both
environmental impact and economic viability.

By conducting these case studies, this thesis contributes to the development of more
efficient and environmentally friendly marine propulsion systems. The results of this
research will provide valuable insights for engineers, designers, and policymakers
interested in promoting sustainable shipping practices.

4
1.2 Objective of the Thesis

The objectives of the thesis were:

• To develop a semi-empirical model of a PEMFC that can accurately predict its

performance.

• To evaluate the performance of several metaheuristic algorithms in extracting

the parameters of the PEMFC model using multi-criteria decision methods.

• To integrate a battery model with a state of health sub-system to consider the

aging effect of the batteries and predict the future fuel cell and emissions using
the outputs of the mathematical model.

• To analyze the addition of a battery pack to the system using various charging
strategies, and select the optimum energy storage configuration, charge-
discharge rates, and the number of parallel sets by considering battery price,
weight, and fuel-saving ratios.

• To assess the emission reduction (ER) of the proposed strategies for the current
and future time range and evaluate the economic performance of the proposed
configurations.

1.3 Thesis Outline

The following chapter provides a background and literature review of hydrogen and
fuel cell technologies. It covers renewable energy sources and technologies, hydrogen
energy, hydrogen production and storage methods, and fuel cell technology.

The third chapter presents a case study of utilizing PEMFC for a small fishing boat.
This chapter includes a literature review of marine vessels utilizing fuel cells,
modeling of PEMFCs, and metaheuristic algorithm for parameter extraction of

5
PEMFCs. It also presents the mathematical modeling of the PEMFC stack,
metaheuristic optimization algorithms, and multi-attribute decision-making methods.
The chapter concludes with the results and discussions of the PEMFC model validation
and metaheuristic algorithms with Multi Attribute Decision Making (MADM methods
ranking the metaheuristic optimization algorithms according to SSE, run-time, and
best objective function efficiency performance metrics.

The fourth chapter presents an environmental and economic analysis of fuel cell
and battery-based hybrid systems utilized as auxiliary power units on a chemical tanker
vessel. This chapter includes a literature survey on marine transport applications,
system description, and modeling of the fuel cell and battery hybrid configuration. It
also includes mathematical modeling of the hybrid power plants, environmental
analysis of the hybrid system, and economic analysis of the hybrid system. The chapter
concludes with the results and discussion of the environmental and economic analysis
of the hybrid system.

The last chapter provides a summary of the research findings, conclusions, and
recommendations for future research. The chapter also includes a discussion of the
contributions of the research to the field of fuel cell technology and maritime
applications.

6
 CHAPTER 2
BACKGROUND AND LITERATURE REVIEW

Internal combustion engines have dominated the world’s power demand since they
were invented in the 19th century. Although electric motor and battery technologies
emerged almost half a century earlier than internal combustion engines, the technical
maturity of internal combustion engines has reached earlier. The breakthrough for
technological advances in the field of renewable energy technologies came with
increased incentives following the 1973 oil crisis. These incentives resulted in the
invention of solar cell technologies (National Renewable Energy Laboratory [NREL],
n.d.) and the implementation of large wind farm projects in subsequent years (Nixon,
2008).

Global climate changes have been acting as another series of breakthrough events
in the field of green energy production. It has been shown that the share of fossil fuels
in the world’s energy mix reduces every passing year (Ritchie, Roser, & Rosado,
2022). Renewable energy sources have proven themselves to replace the position of
fossil fuels in the energy mix in the near future. However, renewable energy sources
have been struggling to solve some challenges, e.g., energy transportation, area
requirement, technical maturity, lack of incentives, and cost. Hydrogen can take part
in effectively transporting renewable energy by utilizing its high gravimetric energy
density. Although the production process of hydrogen can be carried out with fossil
fuel sources, the reducing cost trend of green hydrogen production with renewable
energy sources has increased the interest of the world, starting from the developed
countries, in hydrogen technologies. In addition, the future cost of hydrogen fuel
supply is projected to be below the current electricity costs supplied from grids in
European countries (Zhou & Searle, 2022).

This chapter introduces a brief introduction to renewable energy sources and

technologies that can be utilized for hydrogen production. Then, the production,
storage, and utilization methods of hydrogen are discussed. A comprehensive literature

7
survey is also conducted that presents the fuel cell utilization in marine transportation
and modeling studies of PEM fuel cells.

2.1 Renewable Energy Sources and Technologies

Energy sources could be classified into two main categories: non-renewable sources
and renewable sources (Artkın, 2018; Raza et al., 2016). Energy obtained from natural
sources that are renewed more quickly than is used up is referred to as renewable
energy. Every renewable energy source requires its technology to transform the source
of energy into a form of energy that can be used by humans or machines so, these can
provide electricity or fuels, such as hydrogen, that are similar to the ones currently
produced from fossil fuels.

Today, many countries use a mixture of renewable and non-renewable energy

sources in their energy supply due to energy security and reliability concerns. New
technologies that use renewable energy sources can produce electricity at a lower
environmental impact than can be produced from fossil fuels and nuclear energy.
Examples of renewable energy sources include wind energy, solar energy,
hydropower, biomass, geothermal energy, and marine/ocean (wave, current, and tide)
energy. A more detailed classification of energy sources is depicted in Figure 2.1.

Figure 2.1 Classification of energy resources and technologies (Adapted by the author from (Artkın,
2018; Ghosal, 2022; Raza et al., 2016))

8
 Systems that generate electrical power and/or heat using renewable energy sources
are called "renewable energy technologies." Photovoltaic solar panels, thermal solar
panels, photovoltaic-thermal (PVT) panels, wind turbines, geothermal power plants,
hydroelectric power plants, biomass-based power systems, and ocean/marine energy-
based power systems are accepted in this area (Kaltschmitt, Streicher, & Wiese, 2007).
Integration of these technologies into the existing energy infrastructure will be
essential in the process of moving toward sustainable development in terms of
environmentally sustainable, climate-friendly, and cost-competitive shortly.

2.2 Hydrogen Energy and Fuel Cells

Green hydrogen, an energy carrier based on green and renewable sources, offers
possibilities for sustainable transportation in the future. A diversified, growing number
of countries are looking at the potential of employing renewable energies, including
green hydrogen, for power generation and mobility. The use of green hydrogen as an
energy carrier in fuel cell systems is a promising alternative due to its ability to convert
chemical energy to electrical energy efficiently among competitors and provide
emission-free applications.

2.2.1 Hydrogen Energy

The hydrogen atom is the lightest and most abundant type of atom in nature. Thus,
provides a high gravimetric energy density of 120 Mj/kg which is 3 times that of
hydrocarbon fuels, such as gasoline has energy density of 44 Mj/kg (Ramirez-Vidal,
Sdanghi, Celzard, & Fierro, 2022). Hydrogen thus has the highest potential to replace
liquid fuels in terms of energy content and gravimetric energy density. In addition,
hydrogen is an extremely clean and renewable energy carrier for two reasons: First,
and most importantly, it can be utilized to store energy generated by wind and solar
power; second because it is a clean source of energy being non-polluting in terms of
particulate matter emissions.

9
 2.2.1.1 Hydrogen Production

Hydrogen can be produced from a variety of feedstocks. Hydrogen production

processes could be classified by source as fossil fuels and renewable sources. The
process of obtaining hydrogen from fossil fuels is divided into 2 main categories as
hydrocarbon reforming and hydrocarbon pyrolysis. Hydrogen production obtained
from renewable resources is divided into two; biomass processes and water splitting
(Nikolaidis & Poullikkas, 2017). A more detailed classification is shown in Figure 2.2.

Hydrogen Production Processes

1. Fossil Fuels
Hydrocarbon Reforming
• Steam reforming
• Partial oxidation
• Autothermal reforming

Hydrocarbon Pyrolysis
2. Renewable Sources
Biomass Process
• Biological
• Thermochemical

Water Splitting
• Electrolysis
• Thermolysis
• Photolysis

Figure 2.2 Classification of hydrogen production (Adapted by the author from (Nikoliadis & Poullikkas,
2017))

The method called "steam reforming" which is used to obtain hydrogen from
hydrocarbon fuels, is carried out endothermically by sending steam onto the
hydrocarbon fuel, and the main equations through the process are shown in Equations
2.1 – 2.3: (Nikolaidis & Poullikkas, 2017)

10
 1
Reformer: Cn Hm + nH2 O → nCO + �n+ 2 m� H2 (2.1)

WGS reactor: CO + H2 O → CO2 + H2 (2.2)

Methanation reaction: CO + 3H2 → CH4 + H2 O (2.3)

The other basic method is the partial oxidation method, in which oxygen is sent to
the hydrocarbon fuel as a reactant and the reaction takes place exothermically the main
equation of the process is shown in Equations 2.4 – 2.7: (Nikolaidis & Poullikkas,
2017)

1 1
Reformer: Cn Hm + 2 nO2 → nCO + 2 mH2 (catalytic)
(2.4)

1
Cn Hm +nH2 O → nCO + �n+ 2 m� H2 (non–catalytic)
(2.5)

WGS reactor: CO + H2 O → CO2 + H2

(2.6)

Methanation reaction: CO + 3H2 → CH4 + H2 O (2.7)

The method by which these two methods are combined is called the "autothermal
method”. This process aims to increase the amount of hydrogen production by using
the heat released in partial oxidation in the steam reforming process. The reaction
equation is shown in Equation 2.8: (Nikolaidis & Poullikkas, 2017)

1 1 1 1
Cn Hm + 2 nH2 O+ 4 nO2 → nCO+ �2 n+ 2 m� H2 (2.8)

Another method used to obtain hydrogen from hydrocarbon fuels is the pyrolysis
method, which is based on the thermal decomposition of the fuel itself. The general
reaction is given: (Nikolaidis & Poullikkas, 2017)

1
Cn Hm → nC+ 2 mH2 (2.9)

11
 The utilization of fossil fuel-based hydrogen production methods, despite their
convenience and cost-effectiveness, is deemed unsustainable in the long-term due to
their reliance on finite energy sources. To address this concern, there has been an
increasing focus on exploring alternative and renewable sources of hydrogen
production, including water splitting and biomass, to ensure sustainable energy
production.

Biomass is made from wood, aquatic plants, crops, and various waste resources
(municipal solid waste, animal waste, wood waste, food processing waste, industrial
waste, and biological waste) (Demirbaş, 2001). There are two basic methods for
producing hydrogen from biomass and one of them is the thermochemical process. It
is known that this method can provide hydrogen production at higher stoichiometric
ratios, much faster than biological methods, by pyrolysis and gasification methods
(Fremaux, Beheshti, Ghassemi, & Shahsavan-Markadeh, 2015). The hydrogen
production equations by the pyrolysis method and gasification method are shown in
Equations 2.9-2.11 and 2.13-2.14, respectively: (Nikolaidis & Poullikkas, 2017)

Pyrolysis of biomass → H2 +CO+CO2 +hydrocarbon gases + tar + char (2.10)

Cn Hm +nH2 O → nCO+(n+ 1⁄2 m)H2 (2.11)

CO+H2 O → CO2 +H2 (2.12)

Biomass + Air → H2 +CO+N2 +CH4 +other CHs + tar + H2 O + char (2.13)

Biomass + Steam → H2 +CO+CO2 +CH4 +other CHs + tar + char (2.14)

The other method of producing hydrogen from biomass is called a biological

process. The main approaches to producing hydrogen from biological wastes are
photo- and dark fermentations, direct and indirect bio-photolysis, and multi-stage or
sequential dark photo-fermentation. These methods are environmentally friendly and

12
contribute to the sustainable development of hydrogen production by requiring less
energy (Nikolaidis & Poullikkas, 2017).

In addition to biomass-based methods, several water-splitting technologies can

produce hydrogen from renewable sources such as solar and wind energy. One of the
most commonly used methods is electrolysis, which involves using an electric current
to split water into hydrogen and oxygen. The reaction can be represented by the
following Equation 2.15 (Liu, Xu, Yang, & Jiang, 2020).

2H2 O + electrical energy → 2H2 +O2 (2.15)

Electrolysis can be powered by renewable sources such as solar, wind, or

hydropower, making it a promising method for sustainable hydrogen production.

Another method is photolysis, which uses solar energy to split water molecules into
hydrogen and oxygen. In this process, a semiconductor material is used to absorb
sunlight and generate an electric current, which is used to split water. The reaction can
be represented by the following equation 2.16 (Walter et al., 2010).

2H2 O + photons → 2H2 +O2 (2.16)

Photolysis has the advantage of being powered directly by sunlight and can
potentially have high conversion efficiencies, making it an attractive option for
renewable hydrogen production (Walter et al., 2010).

Thermolysis is another water-splitting method that involves using heat to split water
into hydrogen and oxygen. This process can be powered by concentrated solar energy
or nuclear energy. The reaction can be represented by the following equation 2.17
(Boretti, 2022).

2H2 O + heat energy → 2H2 +O2 (2.17)

13
 Thermolysis has the potential for high efficiency and low environmental impact,
but it requires high temperatures and may involve the use of corrosive chemicals
(Boretti, 2022).

All of these methods for producing hydrogen from renewable sources, whether it
be through electrolysis, photolysis, or thermolysis, offer environmentally friendly and
sustainable approaches to hydrogen production. These methods require less energy and
produce fewer emissions, which contributes to the sustainable development of
hydrogen production (Hota, Das, & Maiti, 2023).

2.2.1.2 Hydrogen Storage Methods

Hydrogen storage is an important technology driving the advancement of hydrogen

and fuel cell technologies including stationary power, portable power, and
transportation applications. There are several methods found in the literature including
compressed hydrogen storage, metal hydrides, liquid hydrogen storage, cryo-
compressed hydrogen storage, and chemical hydride storage.

Compressed hydrogen storage is a widely-used technology that involves the

physical storage of hydrogen gas in high-pressure tanks. One of the primary benefits
of using a compressed hydrogen storage system is the ability to rapidly refuel vehicles
in as little as 3-5 minutes (Stetson, McWhorter, & Ahn, 2015). However, this
technology also has some limitations, particularly when used in portable applications
where the volumetric capacity of commercial tanks is low, even at high pressures
(Langmi, Engelbrecht, Modisha, & Bessarabov, 2022). A major disadvantage of
compressed hydrogen storage is the low volumetric density of the tanks, even at
pressures greater than 70 MPa. This limits the amount of hydrogen that can be stored
in the tanks, particularly for portable applications. Additionally, safety concerns are
associated with storing hydrogen at such high pressures. These issues must be taken
into consideration when designing and implementing compressed hydrogen storage
systems. Figure 2.3 presents a schematic of the compressed hydrogen storage system.
Further research is needed to address the limitations of compressed hydrogen storage,

14
particularly with regard to increasing the volumetric capacity of the tanks and
improving safety measures.

Figure 2.3. The schematic of the compressed hydrogen storage and its subsystems (DoE, n.d.-b)

Metal hydrides, referred to as MHx, have been identified as a promising class of

materials for hydrogen storage due to their versatile range of potential applications.
These applications include but are not limited to hydrogen fuel cell technology,
hydrogen production via electrolysis, hydrogen purification and separation, and
thermal energy storage systems. Research in this field has primarily focused on
complex hydrides composed of ionic alkali or alkaline earth metals and complex
anions containing centric atoms such as transition or main group metals or metalloids,
such as Fe, Ni, B, Al, or N, that are covalently bonded to hydrogen. These complex
metal hydrides have demonstrated potential as a practical hydrogen storage option,
with minimal energy requirements for hydrogen uptake and release.DoE, n.d.-c). The
performance of a metal hydride tank mainly includes the parameters. These are
capacity, releasing time, recharging time, and cycle life. The process of metal hydride
formation is exothermic and involves the release of heat. Upon the formation of metal
hydride, hydrogen can be liberated through the application of sufficient heat. Figure

15
2.4 illustrates the storage capacity of hydrogen in relation to pressure, with metal
hydride and adsorbent storage being the only methods of storage that do not rely on
chemical absorption in a liquid state. It should be noted that hydrogen is stored through
chemical absorption in a liquid state in all other storage methods. Aromatic molecules
with carbon–carbon double bonds are the most useful substances for liquid chemical
hydrogen storage. As an example, methylcyclohexane (C7H14) releases three H2
molecules when heated and occurs toluene (C7H8) (Berry, Martinez-Frias, Espinosa-
Loza, & Aceves, 2004).

Figure 2.4. The pressure–capacity diagram according to the absorption and desorption processes
(Aouaini, Bouazizi, Almoneef, Al-Ghamdi, & Lamine, 2021)

Cryo-compressed hydrogen and liquid hydrogen (LH2) storages are alternative

methods where hydrogen cools down and is liquidized at −253°C (ca. 20 K) and also
compressed into tanks that can be pressurized to approximately 250–350 atm (El-
Eskandarany, 2020). Therefore, the liquid hydrogen size requires larger tanks reaching
about 3 times larger than the currently used gasoline tank. Production of liquid
hydrogen requires the liquefiers use that employ different principles of cooling. There
are several techniques that liquid-state hydrogen production. These are the Linde-
Hampson liquefiers, the Linde dual-pressure liquefiers, the Claude liquefiers, the
Kapitza liquefiers, and the Hey-landt liquefiers (Veziroglu, Sherif, & Barbir, 2005).

16
2.2.2 Fuel Cell Technology

A fuel cell is a system that converts some of the chemical energy stored in a suitable
fuel directly into (direct current) electrical energy and heat through an oxidizer as a
result of a series of electrochemical reactions with high efficiency and low
environmental impact (Grove, 1839).

In 1838, Christian Friedrich Schönbein laid out the theoretical foundations of fuel
cell technology (Andújar & Segura, 2009). At the same time, William Robert Grove,
who worked independently of Christian F. Schönbein, produced the first fuel cell,
which he called a "gas voltaic battery", using materials similar to today's phosphoric
acid fuel cell (PAFC). As a result of a series of experiments, he was able to produce
hydrogen and oxygen on a platinum catalyst layer using a dilute sulfuric acid solution
and explained that an electric current was produced by passing the released electrons
through an external circuit (Grove, 1839). In addition, he observed that there was a
continuous current between the electrodes in the containers that he was sealing and
that the water level in the container increased as long as this current continued (Grove,
1843).

A single cell consists of two catalyst layers, an anode, and a cathode, separated by
an electrolyte and two current collectors (end plates) involving fuel and airflow
channels are located in the anode and cathode catalyst layer sides, respectively, and
the main components of the fuel cell as shown in Figure 2.5.

Fuel cells generate a continuous supply of power by utilizing the feed of fuel and
air through electrochemical reactions that occur at the catalyst layer. This concept was
first introduced by (Grove, 1843). Within the fuel cell, ions are transported from one
electrode to another through the electrolyte, while electrons travel through an external
circuit to produce electricity. Although a single cell is capable of generating power,
the output is typically insufficient. To produce a substantial amount of power, multiple
single cells are connected in series through a process known as "stacking." This

17
stacking process is generally accomplished through the use of bipolar plates, which
provide channels for the flow of oxidant and fuel throughout the stack.

Figure 2.5 Schematic diagram of a fuel cell with its main components

Fuel cells are classified by considering many different features. In particular, the
type of fuel used in the classifications, the type of electrolyte used in the fuel cell,
operating temperatures, and use in stationary or mobile applications were considered.
The fuel cell terminology that is widely used and most accepted is determined by the
type of electrolyte used and shown in Table 2.1. In addition, the most commonly used
fuel cell types today are (Mench, 2008) polymer electrolyte membrane fuel cells
(PEMFC), direct methanol fuel cells (DMFC), solid oxide fuel cells (SOFC), molten
carbonate fuel cells (MCFC), alkaline fuel cell (AFC), and phosphoric acid fuel cells
(PAFC). Each kind has its pros and cons. PEMFCs are popular for mobile applications
because of their lower operating temperatures, quick start-up times, and high
efficiency compared to other types of fuel cells. DMFCs are also popular for mobile
applications due to their high-power density and efficient conversion of methanol fuel.
These two are also classified as "low-temperature fuel cells" due to their low operating
temperatures. On the other hand, SOFCs and MCFCs are categorized as "high-

18
temperature fuel cells" because of their higher operating temperatures and are mainly
used in stationary applications. SOFCs and MCFCs are both considered to be more
energy efficient than PEMFCs and DMFCs because of their high-temperature
operation that could be utilized; however, their increased temperatures require more
expensive construction materials. PAFCs are also categorized as high-temperature fuel
cells; however, their operating temperatures are slightly lower than those of SOFCs
and MCFCs, and PAFCs use hydrocarbon fuels, such as natural gas and propane.

Table 2.1. Fuel cell types and main specifications (Mench, 2008)
Operating
Type of FC Electrolyte Material Mobile Ion
Temperature
Flexible solid per-
PEMFC OH- 30 – 100 ºC
fluorosulfonic acid polymer
DMFC Polymer electrolyte membrane H+ <100 ºC
AFC Potassium hydroxide solution H+ 50 – 200 ºC
A phosphoric acid solution in
PAFC H+ ~220 ºC
a porous silicon carbide matrix
Lithium/ Potassium carbonates
MCFC (CO3)2- ~650 ºC
in a porous matrix
Yttria (Y2O2 stabilized zirconia
SOFC O2- 500 ºC – 1000 ºC
(ZrO2)

19
 CHAPTER 3
EXTRACTING SEMI-EMPIRICAL MODEL PARAMETERS FOR A
COMMERCIAL PEMFC FOR MARINE VESSELS USING MHAS AND
MULTI-ATTRIBUTE DECISION-MAKING METHODS

Fuel cell vehicles’ low environmental impacts, current technological

advancements, and commercial manufacturing have opened the path to their
employment in a variety of areas. The usage of fuel cell technology in marine transport
has increased as the IMO’s environmental regulations have been tightened.

In this chapter, operating parameters of a semi-empirical mathematical model of a

proton-exchange membrane fuel cell (PEMFC) are extracted and compared using
various metaheuristic algorithms to analyze its behaviour in a fast and economical
manner before setting up for an application, which will then be utilized on a marine
vessel in this case. Sum-squared error is employed as the objective function to find the
values of seven unknown modeling parameters. The parameter extraction is carried
out by using the polarization curve data of a 1000 W commercial PEMFC. Three
different multi-attribute decision-making methods are used to rank the metaheuristic
algorithms in terms of performance.

3.1 Literature Review

3.1.1 Literature Review on Marine Vessels Utilizing Fuel Cell

There are several demonstration projects and a few commercial marine vessels
utilizing fuel cells as a main propulsion unit or auxiliary power unit.

World's first fuel cell boat HYDRA used an Alkaline Fuel Cell (AFC) system with
a 5.5 kW net power output. The passenger capacity of The Hydra is 22 passengers. A
propulsion system is powered by an electric motor that gets electricity from Alkaline
Fuel Cell. The debut was in June 2000 on the Rhine near Bonn, Germany. The vessel,
which operated as a ferryboat in Ghent, Belgium during an electric boat conference in
2000, transported roughly 2,000 passengers from 1999 to 2000. The vessel is certified

20
by the Germanischer Lloyd for passenger transport, and its fuel cell system is capable
of initiating operation even under sub-freezing temperature conditions, with an
operating voltage between 64 - 88 V and an operating temperature of 70 °C (Etaing,
n.d.).

Bristol City Council initiated a project named Green Capital in 2010. A local
consortium is constituted which consists of directors of Bristol Packet Boat Trips,
Number Seven Boat Trips, and Auriga Energy. A steel hull ferry is 11 meters long and
a 3.6-meter breadth, two permanent magnets DC motors powered by a 12-kW fuel cell
and named "Hydrogenesis" is constructed by Bristol Hydrogen Boats with CE marked.
Hydrogenesis is the first hydrogen-powered ferry to operate in the United Kingdom
which carries 12 passengers and 2 crew members. This is also the first commercially
available fuel cell boat in the UK and the cost of hiring for private purposes costs 130
pounds per hour in 2016 (Bristol Hydrogen Boats, n.d.).

The purpose of the "Protium" project is to apply modem technologies to a

traditional mode of transportation for use in a hybrid canal boat on the UK canal
network. The boat is converted from British Waterways maintenance craft to a canal
boat. The boat has a solid-state hydrogen store (TiMn2- based metal hydride store),
Proton Exchange Membrane (PEM) fuel cell (ReliOn Independence l000TM model),
lead-acid battery pack and high efficiency, permanent magnet (NdFeB) electric motor.
The speed limit for the majority of inland waterways in the UK is 6.4 kph. Thus,
providing an excellent opportunity for testing a low-power PEM fuel cell in a marine
environment. This boat is named "Ross Barlow" which is officially launched in
September 2007 (Bevan, Züttel, Book, & Harris, 2011). The system has a large
cylinder, each containing 30 kg of metal hydride power. The operating pressure of the
system is lower than 10 bars. Approximately 4 kg of hydrogen is obtained from the
solid-state hydrogen storage system. The forced air-cooled PEM fuel cell is rated at 1
kW and operates at 65 °C. The average fuel cell flow rate is measured at 15 L min-1.
There is a huge loss due to the purge of hydrogen to eliminate water management
problems (Bevan et al., 2011). The system is most suitable for low-power demand
applications. Therefore, speed limitation makes the system suitable for canals. A high-

21
power demand situation is provided by batteries. The converted boat and the designed
hybrid system are more efficient than the traditional engine and also more silent and
environmentally friendly.

The Zemships project was a groundbreaking initiative that marked the first instance
of fuel cell technology being implemented onboard a passenger vessel. This project
served as a tangible demonstration of the viability of fuel cell technology for use in
inland passenger ships during daily operations. The project was spearheaded by
Hamburg's Department for Urban Development and the Environment, and involved
the collaborative efforts of several key partners, including but not limited to ATG
Alster Touristik, Germanischer Lloyd, Hamburger University of Applied Sciences,
Hochbahn, hySolutions, Linde Group, Proton Motor Fuel Cell GmbH, and UJV
Nuclear Research Institute. Following the project's official conclusion in August of
2008, the FCS Alsterwasser has remained in normal line operation, overseen by ATG.
The vessel is utilized for a variety of purposes, including Alster roundtrips, Hamburg
channels, and charter trips (Dirk, 2013). Overall transported passengers are more than
43000 till the end of 2012 although no operation is possible in 2010 because of the fire
accident. And also fuel cell system is operated for 2500 hours till the end of 2012
(Dirk, 2013).

The Nemo H2 is the first boat powered by a fuel cell for 86 passengers and 2 crew
in Amsterdam which is owned by Boat Company Lovers. The dimensions of the boat
are 21.95-meter in length and 4.25-meter width. A propulsion system consists of 1
electrically powered, 75 kW stem thruster and 1 electrically powered, 11 kW bow
thruster. It has two 30 kW PEMFCs and a 70-kWh battery, and the maximum speed of
the boat is 8.6 knots per hour. Without refueling, the voyage time is 9 hours when the
speed is approximately 7 knots. Hydrogen is stored in 6 cylinders at 350 bar for 24 kg
of hydrogen. The canal boat meets all European regulations for barges. The boat is in
operation on the canals in Amsterdam since December 2009 (Oldsailor, n.d.). The new
boat cost more than double the cost to build than a canal boat running on a diesel
engine. Needs to visit a hydrogen dispensing station for a refill once a day. Normal
boats only need a fuel top-up once a week (The Green Light District, 2009).

22
 Choi et al. (2016) developed and installed a hybrid proton exchange membrane fuel
cell (PEMFC)/battery system for a 20-meter tourist boat with an output power of
approximately 85 kW and a speed of 6.6-7.8 knots. Rivarolo, Rattazzi, Lamberti, &
Magistri (2020) compared the energy efficiency, CO2 emissions, and other fuels for
the fuel cell system to be used in a ferry. The software was created at the University
of Genoa to study the design and cost of a 200-passenger capacity ferry operating on
the artificial lake of Itaipu. Rafiei, Boudjadar, & Khooban (2020) suggested a zero-
emission hybrid fuel cell/battery/cold-ironing system and used real data from a ferry
to examine hull design and energy resources. Balestra & Schjølberg (2021) created a
simulation tool that evaluates a user-selected configuration in a battery and fuel cell
power plant for marine applications that can produce the electricity required by the
energy management system realistically. Dall’Armi, Micheli, & Taccani (2021)
carried out simulations using different types of compressed hydrogen storage tanks
(Type 1,3,4) to analyze the peak shaving point of the low temperature (LT)-
PEMFC/battery system used for propulsion of a small-sized RoRo vehicle and
passenger ferry.

3.1.2 Literature Review on Modeling of PEMFCs

The schematic of a hydrogen-fed PEMFC and redox reactions are given in Figure
3.1 and Equations 3.1-3.3, respectively. Hydrogen fed from the anode side is separated
into positive and negative ions on the anode side of the FC. Positive ions move from
the anode to the cathode, whereas negative ions move through the external circuit, thus
electrical power is produced. Negative and positive ions reaching the cathode react
with oxygen, which is found in the air fed to the cathode, to form water (Colpan,
Nalbant, & Ercelik, 2018; Mench, 2008).

Anode: H2 →2H+ +2e- (3.1)

Cathode: 0.5O2 +2H+ +2e- →H2 O (3.2)

Overall: H2 +0.5O2 →H2 O (3.3)

23
 Figure 3.1. Schematic of the operation of a PEMFC

The performance assessment of fuel cells could be done through mathematical

modeling or experimental methods. Installation of an experimental FC setup could
have considerable disadvantages including the following: being time-consuming,
dealing with challenging issues such as effective hydrogen supply and storage, and the
high initial investment cost. However, developing a mathematical model is relatively
cheap compared to an experimental setup, and it is also quite useful to develop an
accurate mathematical model to study the feasibility of an FC-based system before its
installation (Kirubakaran, Jain, & Nema, 2009). Various FC models exist in the
literature and could be categorized as shown in Figure 3.2.

24
Figure 3.2 Classification of Fuel Cell Modeling (Adapted from (Ashraf, Abdellatif, Elkholy & El-
Fergany, 2022a))

1D and 2D models are frequently used in literature to determine the performance

analysis of the fuel cell. A non-isothermal, 1D, and 2-phase fuel cell model was created
by (Jiang, Yang, Jiao & Du, 2018). Sensitivity analysis was used to choose the model's
unknown parameters in a way that wouldn't compromise the model's dependability and
validity. It was determined as a consequence that the parameters influence both model
stability and cell performance and that the impacts of varying operating circumstances
should be included in the validation study. A 1D and dynamic PEMFC model that is
more suited for real-time applications was developed by (Lazar, Konradt &
Rottengruber, 2019). To make the created model acceptable for usage in complex
systems like real-time analysis, quick parameter studies, and comprehensive car
models, authors lowered the computing load with simpler equations obtained. (Shan,
Choe & Choi, 2007) created a 2D stack model and detailed the dynamic behavior of a
stack with two neighboring cells and end plate assemblies. To examine the
initialization behaviors and stack performance, simulations were conducted. The
authors were able to determine the parameters impacting the source terms of the
current density and the dynamic oxygen concentration distribution, as well as the
dynamic temperature distribution of the fuel cell stack both in the plane direction and

25
along the channel. To analyze the heterogeneities, present on a cell's surface and to
study the impact of operating conditions, (Robin et al., 2015) created a PEM fuel cell
2D and 1D model together. The fuel cell's activity is observed using the model
developed by seeing how it interacts with the environment. Analyses of a GDL
construct's effect on regional circumstances were also conducted. The PEM fuel cell's
3D and multiphase CFD model is frequently used to improve the cell's thermal and
water management (Zhang & Jiao, 2018). To examine the impact of the PEMFC
assembly stage on the mechanical condition of the active layer (MEA), (Carral & Mele,
2014) built a 3D model. By utilizing the developed 3D model, (Carral & Mele, 2014)
conducted experimental investigations to examine the impact of several
characteristics, including the number of cells and their placement within the stack, on
the mechanical state of the active layer (MEA) during the PEMFC assembly stage.
Consequently, the study revealed that optimal uniformity of MEA compression could
be achieved by utilizing a higher number of cells and positioning them at the center of
the stack. (Chen et al., 2021) have created a 3D polyphase PEMFC model with a wave
flow channel to create the best flow field structure to improve the output performance
of the fuel cell. Consequently, upon comparison of the wave flow channel with the
straight channel, the superiority of the former in terms of reactant gas transport and
removal of accumulated water in the microporous layer was established.

Among these models, semi-empirical 0-D models are generally advantageous to

assess the performance of a specific FC under different operating conditions in a
simple and fast manner. These 0-D models could be then integrated into system-level
models easily and effectively.

3.1.3 Literature Review on Metaheuristic Algorithm for Parameter Extraction of

PEMFCs

Optimization techniques are mostly classified as exact, heuristic, and metaheuristic

methods (Talbi, 2009). Exact methods offer the advantage of guaranteeing a correct
and exhaustive solution to the problem at hand. Nevertheless, the high computational
load that these methods typically impose renders them impractical for real-life cases

26
in general. On the other hand, heuristics and metaheuristics do not guarantee the best
solution but provide an acceptable and relatively fast solution. Therefore, heuristics
and metaheuristics are the most common approaches to solving complex real-world
optimization issues. Heuristic methods are specific to a particular problem. Thus, it
yields satisfactory results in a reasonable runtime. However, on the other hand, the
heuristic methods are problem-specific and cannot guarantee the optimal solution.
Therefore, solutions are needed that can be applied to a specific range of problem
groups, and metaheuristic methods have gained importance at this point. The “meta”
as a prefix describes the MHAs as higher-level heuristics (Dokeroglu, Sevinc,
Kucukyilmaz & Cosar, 2019) which are not problem-dependent solutions.

Figure 3.3 shows the number of papers published on several MHAs used for
PEMFC parameter extraction. The selection criteria for these papers are as follows:
articles in English published on or after 2018 and published in a journal listed in the
Science Citation Index Expanded (SCI-Expanded) as of June 2022. Considering these
results as well as algorithms with less run-time and parameter adjustment are chosen.
Hence, DE, SSA, MFA, WOA, SCA, CS, GA, GWO, and JAYA optimization
algorithms were run according to a predetermined objective function in the scope of
this thesis.

Semi-empirical models give the coefficients used in the model by converging their
output data to the FC’s experimentally acquired polarization curve, thus providing
more reliable findings in determining the FC characteristic. There are various studies
on this kind of model for PEMFCs. For example, Amphlett et al. (1995) created a semi-
empirical mathematical model of a Ballard Mark IV solid PEMFC using Stefan
Maxwell, Nernst, Tafel, Nernst-Planck, and Ohm's Law equations. The unknown
parameters in the model were calculated using linear regression and experimental
results. This study has pioneered many other studies in the same field.

27
 JAYA 2018 2019 2020 2021 2022
Salp Swarm Algorithm
Teaching Learning Based Optimization
Gravitational Search Algorithm
Variable Neighborhood Search
Bat Algorithm
Whale Optimization Algorithm
Cuckoo Search
Tabu search
Firefly Algorithm
Grey Wolf Algorithm
Artificial Bee Colony
Ant Colony Optimization
Simulated Annealing
Differential Evolution
Genetic Programming
Particle Swarm Optimization
Genetic Algorithm
0 5000 10000 15000 20000 25000 30000 35000 40000
Number of Papers

Figure 3.3 The number of related papers on the Web of Science for MHAs used in PEMFC parameter
extraction

Mann et al. (2000) tested the performance of Ballard Mark IV and Mark V FCs at
various membrane thicknesses, water contents, and different flow rates of oxygen
using Amphlett et al. (1995)'s model with empirical formulas to find the unknown
parameters of the model. In some studies, to optimize these parameters, metaheuristic
algorithms (MHAs) were used to solve these non-linear equations.

Mo, Zhu, Wei & Cao (2006a) optimized the parameters required for the model by
utilizing four data sets (two for identification and two for validation) with a niche
Hybrid Genetic Algorithm (HGA). The authors utilized the difference between the
measured and the calculated voltage values with the Sum of Squared Error (SSE) as
the objective function. The work of Mo et al. (2006a) led various studies in the
literature to implement new MHAs to validate the PEMFC model (e.g. (Ali, El-
Hameed & Farahat, 2017; Turgut & Coban, 2016; Yang, Chellali, Lu, Li & Bo, 2016;
Priya, Babu, Balasubramanian, Kumar & Rajasekar, 2015; Sun, Wang, Bi &
Srinivasan, 2015)).

28
 MHAs could be classified into four main categories: swarm-based, nature-based,
physics-based, and evolutionary-based. All these categories have been studied in the
literature to identify the best values for the FC model's unknown parameters, and
researchers compared their findings with those of other studies in the literature.

Among these categories, swarm-based MHAs are the most diverse and extensively
covered in the literature to extract the optimized PEMFC values. There are numerous
studies to extract PEMFC parameters in the literature. Recent studies are discussed in
detail. Xu, Wang & Wang (2019) proposed a simple two-stage eagle technique based
on the JAYA algorithm and the Nelder-Mead simplex algorithm to effectively estimate
the parameters required in the FC model, and the results obtained from this algorithm
were compared with Gray Wolf Optimizer (GWO), Grasshopper Optimization
Algorithm (GOA), Salp Swarm Algorithm (SSA), and Multi-Verse Optimizer (MVO).
Chen & Wang (2019) adopted the adaptive strategy of step size to improve the search
capability and proposed the Cuckoo Search with the Explosion Operator (CS-EO)
Algorithm using the explosion operator to avoid stagnation in the local optimum. The
authors compared the CS-EO with CS, Particle Swarm Optimization (PSO),
Gravitational Search Algorithm (GSA), and Adaptive Cuckoo Search (A-CS). Cao, Li,
Zhang, Jermsittiparsert & Razmjooy (2019) proposed a new Seagull Optimization
Algorithm (SOA) that integrated the Lévy flight mechanism to give faster convergence
rates and compared it with the different algorithms in the literature. Danoune, Djafour,
Wang & Gougui (2021) created the Whale Optimization Algorithm (WOA) to improve
the semi-empirical model and define the optimal parameter for different PEMFCs. The
WOA was compared with various algorithms including the Genetic Algorithm (GA),
PSO, and Artificial Bee Colony (ABC) Optimization. To experimentally validate the
model, Heliocentris FC 50 was used together with the data of BCS 500 W and Ballard
V. The accuracy of performance under different operating conditions was investigated.
Ren & Eslami (2022) presented a new metaheuristic-based technique to extract the
optimum unknown PEMFC parameters. To provide a more accurate and fast result,
WOA was developed using the Fractional Order-Based (FO) design. The proposed
algorithm utilizes SSE as the fitness function. FO-WOA was compared using six
benchmark functions with the original WOA, World Cup Optimization (WCO)

29
algorithm, Elephant Herding Optimization (EHO), and Lion Optimization Algorithm
(LOA). Validation of the proposed model was carried out using two well-known
commercial FCs, which are Nexa PEMFC and 250 W PEM. Authors claimed that the
best SSE values are obtained with a reasonable trade-off from convergence time by
FO-WOA. Ashraf, Abdellatif, Elkholy & El-Fergany (2022b) utilized a newly
developed swarm-based MHA called Hone Badger Optimizer (HBO). Three well-
known PEMFCs (Mark V FC, SR-12, and 250 W) were selected to evaluate the
performance of the HBO algorithm at diverse temperatures and supply pressures in
steady-state circumstances. The Sum of Quadratic Errors (SQEs) was utilized as the
fitness function to compare other well-known optimization algorithms. Tona-Swarm
Optimizer (TSO) and Equilibrium Slime Mould Optimizer (ESMO), along with HBO,
were also run by the authors and compared. The results of other algorithms used for
comparison were obtained from literature. Various statistical comparisons and
sensitivity analyses were done, and it was found that HBO is capable of handling the
parameter extraction tasks effectively compared to others. Singh, Nijhawan, Singla,
Gupta & Singh (2022) proposed a new hybrid algorithm to estimate the optimal
PEMFC parameters. PSO and Dingo Optimizer (DOX) were combined to provide a
robust algorithm. The proposed hybrid algorithm was tested with selected 10
benchmark test functions which are both uni-modal and multi-modal. Concerning
convergence, stability, and efficiency, PSO, DOX, GWO, GWO-CS, and PSO-GWO
hybrid algorithms were compared. The specifications of Ballard Mark V PEMFC were
selected to extract the parameters. Friedman ranking test was also conducted, and
hybrid PSO-DOX was found to perform better in terms of efficiency, accuracy,
precision, computational time, and stability. Rezk, Wilberforce, Taha, Alahmadi &
Olabi (2022) conducted a two-staged study that consists of modeling and optimization
parts. An Adaptive Network-Based Fuzzy Inference System (ANFIS) was used to
develop the PEMFC model with experimental datasets. The study aimed to find the
optimum output power point which is tightly dependent on the fuel pressure, oxidant
pressure, fuel flow rate, and oxidant flow rate. GWO was utilized to find the optimum
power point by twenty-two datasets gathered from the experimental setup. Fifteen of
these datasets were used for training and others for testing phases. Root Mean Square
Error (RMSE) was used for evaluating the modeling accuracy. Integration of the

30
ANFIS model and GWO algorithm provided increased power output of up to %56.
Bald Eagle Search (BES) is another robust newly developed MHA. Another study by
Rezk, Olabi, Ferahtia, & Sayed (2022) applied this algorithm to estimate the unknown
model parameters of two commercial PEMFCs (NedStack PS6 and BCS 500 W). The
algorithm was compared with other algorithms using statistical validation methods,
namely Analysis of Variance (ANOVA) and Tukey Honestly Significant Difference
(HSD), in terms of accuracy, convergence rate, and robustness. SSE was used as the
fitness function and the best, worst, mean, median, and standard deviation metrics were
utilized to carry out statistical results. The authors revealed that the BES algorithm
gives the best performance values among the compared algorithms.

Another algorithm category that stands out among various MHA-based

optimization techniques is the evolutionary-based algorithms, which have been used
for many years. There are several studies on these algorithms in the literature. Zhang
& Wang (2013) used an adaptive RNA-GA algorithm inspired by the biological RNA
mechanism and proposed an adaptive genetic strategy based on the coefficient of
variation to preserve population diversity and avoid premature convergence. A multi-
strategy Adaptive Differential Evolution (DE) developed for parameter optimization
problems was presented by Gong & Cai (2014), briefly named rank-MADE. This
algorithm was compared with the variants of the DE algorithm, Self-Adaptive DE
(SaDE), JADE, Called Composite DE (CoDE), and DE with Differential Evolution
with Global and Local Neighbourhoods (DEGL) algorithms. To improve the adaptive
and dynamic performance of the DE algorithm, Sun et al. (2015) developed the Hybrid
Adaptive DE (HADE) algorithm by utilizing the biological genetic strategy and
compared the HADE algorithm with standard GA, PSO, DE, and adaptive DE. As a
result, the authors showed that the HADE algorithm gives better results. Priya et al.
(2015) created a new objective function with a zero derivative of power according to
the current at the highest power point, which solved with a simple GA to determine
the necessary parameters in the FC model. Kandidayeni, Macias, Khalatbarisoltani,
Boulon & Kelouwani (2019) made parameter optimization for three different
commercial FCs. The authors used the Shuffled Frog-Leaping Algorithm (SFLA),
Firefly Optimization Algorithm (FOA), and Imperialist Competitive Algorithm (ICA)

31
for parameter optimization and compared their results with algorithms used in other
studies in the literature.

Other types of MHA categories, physic-based and nature-based algorithms, are less
commonly used compared to swarm-based and evolutionary-based algorithms. As an
example of physic-based algorithms, Fathy, Elaziz & Alharbi (2020) presented a tried-
and-tested new hybrid optimization approach, which includes a Vortex Search
Algorithm (VSA) and DE. The authors used a new algorithm created for the
optimization of 3 commercial FCs and compared the results with simple VSA and DE.
Rezk et al. (2022) proposed a new methodology for Gradient-Based Optimizer (GBO)
to find the optimal parameters for the semi-empirical FC model. The authors compared
different algorithms from the literature for three different commercial FCs as 250 W
FC stack, NedStack PS6, and SR-12 500 W. As an example of nature-based
algorithms, Priya & Rajasekar (2019) applied a newly developed nature-based flower
pollination algorithm that has the ability of high convergence speed, easy
implementation, exceptional capacity to find the global optimum point, and less
reliance on the initial solution. In the study, the authors made a comprehensive
comparison in terms of SSE, individual absolute error, relative error values, and model
parameter values and claimed Flower Pollination Algorithm (FPA) outperforms the
GWO algorithm and all other methods in error analysis with the fewest number of
iterations and curve fitting. Kandidayeni et al. (2019) used three different MHAs as
mentioned above and one of them is the firefly optimization algorithm. Two different
PEMFCs (NedStack PS6 and BCS 500 W) were used to compare the evaluated
algorithms with the literature. Subsequently, 500-W Horizon PEMFC was utilized to
verify the models. The study showed that FOA yields reasonable results with an
insignificant difference compared to SFLA. Messaoud, Midouni & Hajji (2021)
evaluated the Modified Moth-Flame Algorithm (M-MFA) with three frequently used
PEMFCs - 250 W, NedStack PS6, and BCS 500W – in the literature. The authors
applied the two SSE and RMSE as objective functions and integrated the uncertainty
to analyze the performance of the algorithm. In the investigation, the effect of the
number of unknown parameters on the results was also investigated. Comparison with
other algorithms was conducted by gathering data from literature. It was claimed that

32
the estimated results by the proposed algorithm for the 250 W PEMFC with eleven
unknowns exactly match the measured data.

The literature review indicates that researchers have substantially coded one or two
novice algorithms as hybrid or non-hybrid in their studies. Then, the results have been
compared with other studies found in literature. In addition, the parameter
determination of certain commercial FCs (e.g., Ballard Mark V, BCS 500 W,
NedStack PS6, SR-12, and Temasek) has been studied frequently. However, according
to the authors’ knowledge, there has been no parameter extraction study on the H-
1000XP commercial FC, which has been commonly used in the Shell Eco-Marathon
and Efficiency Challenge Hydromobil competitions.

3.2 Mathematical Modeling

3.2.1 0D Semi-empirical Electrochemistry Model of PEMFC Stack

The output voltage of the FC stack can be obtained in Equation 3.4:

Vfc =(VNernst -Vact -Vohmic -Vcon ) ∙ Ncell (3.4)

where 𝑉𝑉𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 is the reversible cell voltage known as Nernst voltage, 𝑉𝑉𝑎𝑎𝑎𝑎𝑎𝑎 represents
the activation polarization that is caused by the slowness of the reactions at the
electrode surface, 𝑉𝑉𝑜𝑜ℎ𝑚𝑚𝑚𝑚𝑚𝑚 represents the ohmic polarization that is the resistance which
implies all electrical and ionic conduction losses through the electrolyte, catalyst
layers, cell interconnects, and contacts, 𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐 represents the concentration polarization
that is associated with the concentration difference between the fuel/air channel and
the chemical species on the electrode surface, and 𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑙𝑙 is the number of cells
(Alpaslan et al., 2021). The Nernst voltage can be calculated with Equation 3.5 (Mo et
al., 2006a; Amphlett et al., 1995).

33
VNernst =1.229-0.8 ∙ 10-3 (Tstack -298.15)+4.3085 ∙ 10-5 Tstack ∙ �𝑙𝑙𝑙𝑙�𝑝𝑝𝐻𝐻2 � + 0.5 ∙
(3.5)
𝑙𝑙𝑙𝑙�𝑝𝑝𝑂𝑂2 ��

where 𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is the stack temperature (K), 𝑝𝑝𝐻𝐻2 is the partial pressure of the hydrogen
(bar), and 𝑝𝑝𝑂𝑂2 is the partial pressure of the oxygen (bar). The partial pressure of the
hydrogen can be obtained with Equation 3.6.

-1
⎡ Ifc ⎤
1.635 �A � RH ·Psat
sat ⎢
� -1⎥⎥
a H2 O
pH =0.5 ∙ RHa ∙ PH2 O ⎢�exp � 1.334
cell
�∙ (3.6)
2
⎢ Tstack P a ⎥
⎣ ⎦

If the pure oxygen is fed to the cathode side of the FC, the partial pressure of oxygen
at the cathode can be calculated using Equation 3.7.

-1
⎡ Ifc ⎤
4.192 �A � �RH ·Psat �
⎢ � -1⎥⎥
c H2 O
pO =Pc -�RHc ∙ PH2O �· ⎢�exp �
sat
1.334
cell
�∙ (3.7)
2
⎢ Tstack Pc ⎥
⎣ ⎦

If the air is used instead of pure oxygen, the partial pressure of oxygen at the cathode
can be calculated using Equation 3.8.

Ifc
0.79 0.291 �A �
pO =Pc -�RHc ∙ PH
sat
2O
�- ∙ pO ∙ exp � 0.832
cell
� (3.8)
2 0.21 2 Tstack

where 𝑅𝑅𝐻𝐻𝑎𝑎 and 𝑅𝑅𝐻𝐻𝑐𝑐 are relative humidity of vapors in the anode and cathode,
respectively. 𝐼𝐼𝑓𝑓𝑓𝑓 is the FC operating current (A), 𝐴𝐴𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 is the active cell area (cm2), 𝑃𝑃𝑎𝑎
is the anode pressure (bar), and 𝑃𝑃𝑐𝑐 is the cathode pressure (bar). 𝑃𝑃𝐻𝐻𝑠𝑠𝑠𝑠𝑠𝑠
2 𝑂𝑂
is the saturation
pressure of the water vapor (bar) and can be calculated as a function of the stack
temperature using Equation 3.9 (Mo et al. 2006; Amphlett et al. 1995).

34
 H2 O )=2.95 ∙ 10 ∙ (Tstack -273.15)-9.18 ∙ 10 (Tstack -273.15)
-2 -5
log10 ( Psat 2
(3.9)
+1.44 ∙ 10-7 ∙ (Tstack-273.15)3 -2.18

The activation polarization can be calculated depending on the stack temperature

and oxygen concentration with Equation 3.10,

Vact=-[ξ1 +ξ2 ∙ Tstack +ξ3 ∙ Tstack ln�CO2 �+ξ4 ∙ Tstack ∙ ln (IFC )] (3.10)

where 𝜉𝜉𝑘𝑘 (𝑘𝑘 = 1,2,3,4) are the semi-empirical coefficients based on theoretical
equations with kinetic, thermodynamic, and electrochemical foundations (Mo et al.
2006), and 𝐶𝐶𝑂𝑂2 is the oxygen concentration (mol∙cm-3) that can be calculated using
Equation 3.11 (Mann et al., 2000).

pO 498
CO2 = � 2
� ∙ 106 exp �- � (3.11)
5.08 Tstack

The ohmic polarization depends on the membrane resistance (Ω), 𝑅𝑅𝑚𝑚 , and contact
resistance (Ω), 𝑅𝑅𝐶𝐶 , as shown in Equation 3.12.

Vohmic =IFC ∙ (Rm +RC ) (3.12)

The membrane resistance depends on the resistivity of the membrane (Ω.cm), 𝜌𝜌𝑚𝑚 ,
membrane thickness (cm), 𝑙𝑙, and effective membrane area (cm2), which is shown in
Equation 3.13.

ρm ∙ l
Rm = (3.13)
Acell

The membrane resistivity (𝜌𝜌𝑚𝑚 ) can be calculated with Equation 3.14 for Nafion
membranes.

35
 Ifc Tstack 2
181.6 �1+0.03 ∙ � � ∙ � ( )2.5 �
303 � ∙ J
+0.062
Acell
ρm = (3.14)
Ifc T -303
�λ-0.643-3 �A �� ∙ exp �4.18 ∙ � stack ��
cell Tstack

where 𝜆𝜆 is an adjustable parameter related to the membrane and its preparation

process (Mo et al., 2006). The concentration polarization can be calculated using
Equation 3.15.

J
Vcon =-β ∙ ln �1- � (3.15)
Jmax

where 𝛽𝛽 is the parametric coefficient (V) that depends on the cell and its operation
state (Mo et al. 2006), 𝐽𝐽 is the actual current density (A∙cm-2), and 𝐽𝐽𝑚𝑚𝑚𝑚𝑚𝑚 is the maximum
current density (A∙cm-2).

3.2.2 Metaheuristic Optimization Algorithms for PEMFC Stack Parameter

Extraction

3.2.2.1 Fitness Function Definition and Parameter Settings for MHAs

In this thesis, the model parameters were optimized using different MHAs to
converge the results of the PEMFC model to the results obtained from the literature or
manufacturer data to enhance the model. The output voltage was calculated at the
points corresponding to each current value using the mathematical equations explained
in Section 2.1. As a result, the suggested fitness function serves as a metric for the
estimated parameters’ quality. The SSE, given in Equation 3.16 was selected as the
fitness function.

SSE=Min ��[Vmeas (i) - Vcalc(i)]2 � (3.16)

i=1

36
 where 𝑁𝑁 is the amount of measured data points, 𝑖𝑖 stands for the iteration counter,
𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 is the measured voltage of the FC, and 𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 denotes the calculated voltage of
the FC. Several MADM methods with different principles were also described in
Section 2.4. These methods were used to decide the best-performed MHAs for the H-
1000XP case study. The MAE and the objective function efficiency were calculated
with Equation 3.17 and Equation 3.18, respectively. The coefficient of determination
(R2), which is a well-known performance measurement metric, was used to evaluate
the strength of the relation in regression using Equation 3.19.

∑Ni=1|Vmeas (i)-Vcalc (i)|

MAE= (3.17)
N

OFmin
η= ���� ×100 (3.18)
𝑂𝑂𝑂𝑂

�(i))2
∑ni=1(Vcalc (i)-V
2
R = 2 (3.19)
∑ni=1�Vmeas (i)-Vcalc (i)�

where 𝑂𝑂𝐹𝐹𝑚𝑚𝑚𝑚𝑚𝑚 is the lowest cost of the objective function, ����

𝑂𝑂𝑂𝑂 is the average value
���� = ∑100
of 100 computed objective functions that can be calculated as 𝑂𝑂𝑂𝑂 𝑖𝑖=1 𝑂𝑂𝐹𝐹𝑖𝑖 ⁄100.

𝑉𝑉� is the mean of the data. The parameter setting of the algorithms is given in Table
3.1. Maximum iterations were set to one thousand for each algorithm.

Table 3.1 Parameter setting of the algorithms

Algorithm Parameters
Number of Genes Mutation Rate Crossover Rate
DE
30 0.85 0.2
Population size α β
CS
30 0.01 1.5
Population size Linear Component
SCA
30 2
Population size p
IWOA, WOA
30 0.5
Population size b
MFA
30 1

GWO, IGWO, Population size

Jaya, SSA 30

37
 3.2.2.2 Genetic Algorithm (GA)

The genetic algorithm (GA) is one of the first and most well-regarded evolutionary
algorithms in literature. GA is based on one of the most fundamental theories in the
field of biology called the theory of evolution and was invented by Holland (1992) in
the nineteen seventies. The main objective of all organisms is to be a survivor and
Charles Darwin’s theory claims that natural selection provides the survival of the fittest
offspring in a competitive environment, and this is the basis of the GA. Natural
selection refers to changes in an organism's genotype (crossover or mutation) that
improve its chances of surviving in future generations. Those genetic variants that
boost an organism's chances of survival are retained and passed down from generation
to generation. Therefore, the genes of better-fitting organisms are passed down to
future generations. Therefore, the future generation can also benefit from positive
changes in the genotype (selection concept of GA by crossover, mutation, and elitism
concepts). The interaction of organisms with one another in the form of cooperation
or competition provides the foundation for the fulfillment of these changes. Because
of its unique features, each creature has its concept of what constitutes a beneficial
transformation, fit, or good, as the challenges encountered in daily life have their
constraints and solution sets (fitness or objective function concept and constraints
concept of GA). However, it is generally agreed that modifications that create a
competitive edge on resources are beneficial (minimization or maximization concept
GA). GA seeks the best solution by replicating all these principles within the
framework of the restrictions and objective function established to solve our
difficulties in practically every field.

3.2.2.3 Differential Evolution (DE)

Differential evolution (DE) presented by Storn & Price (1997), is a type of

evolutionary algorithm that is used in searching for continuous optimization problems.
In terms of robustness, ease of application, and quickness, it has remarkable
advantages over other evolutionary methods and swarm-based techniques. The steps
of the DE are mutation, crossover, and selection. While executing these stages, each

38
possible solution is evaluated by comparison with a target set. To reach the target, the
mutation is utilized, and between the potential solution and gathered target a crossover
is ensured. For instance, in Equation 3.20, 𝑆𝑆𝑎𝑎 is a possible solution and, 𝑆𝑆𝑎𝑎𝑎𝑎 is the
target vector for 𝑆𝑆𝑎𝑎 from 𝑆𝑆𝑏𝑏 , 𝑆𝑆𝑐𝑐 , 𝑆𝑆𝑑𝑑 (Karci, 2017; Storn & Price, 1997).

SaT = Sb +f(Sc-Sd ), f ∈ [0,2] (3.20)

Here, f is the scaling vector that supervises the amplification of alterations. The
crossover is provided by the operator depicted in Equation 3.21, 𝑆𝑆𝑎𝑎𝑎𝑎 , and 𝑆𝑆𝑎𝑎 are used
in the operator.

SaT,i if rand≤Cr
SaU,i = � Cr ∈ [0,1] (3.21)
Sa,i else

where the rate of crossover is denoted as Cr. The selection process is executed using
the operator in Equation 3.22.

S if f(SaU )≤f(Sa )
Sa,next = � aU (3.22)
Sa else

3.2.2.4 Salp Swarm Algorithm (SSA)

The salp swarm algorithm (SSA) is one of the novice methods among swarm-based
algorithms that mimic the behaviors of salps living in the ocean. SSA, demonstrated
by (Mirjalili et al., 2017), has provided enhancements for some applications. SSA is a
fast, comprehensive, and easy algorithm that can be applied to both single-objective
and multi-objective optimization problems (Faris, Mirjalili, Aljarah, Mafarja &
Heidari, 2020). The population of salps is split into two categories as followers and
leaders. The leader is located at the beginning of the remaining salps, which are the
followers. The salp position is stored in a matrix (x) with a dimension of the number
of variables (n). The target of the swarm is the food source denoted as F. Equation
3.23 is executed to update the leader’s location (Mirjalili et al., 2017).

39
 Fj +c1 ∙ �c2 ∙ �ubj -lbj �+lbj � c3 ≥0 4I 2
-� �
x j= �
1
c1 =2e L (3.23)
Fj -c1 ∙ �c2 ∙ �ubj -lbj �+lbj � c3 <0

Here 𝑥𝑥 1𝑗𝑗 is the location of the leader, 𝐹𝐹𝑗𝑗 is the food source’s location, 𝑙𝑙𝑙𝑙𝑗𝑗 and 𝑢𝑢𝑢𝑢𝑗𝑗
are the lower and upper bounds in the jth extent, respectively. The c numbers are
defined randomly. The leader chooses the position regarding the food and 𝑐𝑐1 is a
crucial parameter for this operation. L is the maximum iteration number, and I is the
present iteration. The followers’ positions (𝑥𝑥 𝑖𝑖𝑗𝑗 ) are renovated rearranging Newton’s
law of motion presented in Equation 3.24 (Mirjalili et al., 2017).

1
xi j = �xi j +xi-1 j � (3.24)
2

3.2.2.5 Moth-Flame Algorithm (MFA)

Moth-flame optimizer (MFA) mimics the pathfinding methods of moths named

transverse orientation. Moths can travel among large areas using a straight path by
retaining the fixed angle regarding the moon that provides effective navigation at
night. In addition, artificial light sources such as flame allure the moths immensely.
The algorithm is a recent method among the swarm optimization algorithms and was
presented by Mirjalili (2015a). Initially, moths disperse indiscriminately, and a matrix
denotes M stores their locations. The columns of N indicate the number of variables
(d) the rows depict the number of moths (n). The fitness values of M are assessed and
saved in an array (OM) for all moths ,(Nadimi-Shahraki, Fatahi, Zamani, Mirjalili &
Abualigah 2021). Equation 3.25 illustrates the matrix M and the array OM.

m1,1 m1,2 … m1,d OM1

m2,1 m2,2 … m2,d OM2
M= � ︙ ︙ ︙ ︙ � OM= � ︙ � (3.25)
mn,1 mn,2 … mn,d OMn

A similar procedure is executed for flames tracked by moths. The positions of

flames are saved in a similar matrix F and their fitness values are stored in an array

40
OF. At the beginning of the algorithm, the OF array is commenced by depending
ascending order of the OM array. In the following iterations, the algorithm will update
the F according to the best agent. Equation 3.26 indicates a logarithmic spiral
determined for the algorithm. The positions of each moth (𝑀𝑀𝑖𝑖 ) and flames (𝐹𝐹𝑗𝑗 ) are
updated using the spiral formula (S (𝑀𝑀𝑖𝑖 , 𝐹𝐹𝑗𝑗 )).

S�Mi ,Fj �=Di ∙ ebt ∙ cos(2πt)+Fj (3.26)

where the distance between ith moth and jth flame is denoted as 𝐷𝐷𝑖𝑖 , t defines the
required closeness between moth and flame (t=1 is the farthest and t=-1 is the closest),
and b is a random constant that varies between -1 and 1, which determines the shape
of the spiral. 𝐷𝐷𝑖𝑖 is found using Equation 3.27 (Nadimi-Shahraki et al. 2021; Mirjalili
2015).

Di = �Fj -Mi � (3.27)

3.2.2.6 Whale Optimization Algorithm (WOA)

Whale optimization algorithm (WOA) is also a novice swarm-inspired MHA

presented by Mirjalili & Lewis (2016). WOA is inspired by hunting strategies named
bubble-net feeding behavior of humpback whales. The whales usually hunt small
fishes close to the surface of the water by forming bubbles to approach their prey. This
provides to keep the small fishes together and to come near their prey without being
noticed. The main parts of the algorithm are encircling prey, bubble-net attacking, and
searching for prey (Celik & Karadeniz, 2020; Mirjalili & Lewis, 2016). Initially, the
whales identify their prey and surround them. The position of the best agent is assumed
to be the best candidate and other agents update their position according to the best.
This strategy is modeled using Equations 3.28-3.29) (Lee & Zhuo, 2021; Mirjalili &
Lewis, 2016):

*
�D �⃗ ∙ �X⃗ -X
�⃗ = �C �⃗(t)� (3.28)

41
 *
�X⃗(t+1)= �X �⃗ ∙ �D
�⃗ (t)-A �⃗� (3.29)

where t is the iteration number, 𝑋𝑋⃗ is the position vector, 𝑋𝑋⃗ ∗ represents the position
vector of the ideal solution achieved so far, calculation of coefficient vectors denoted
as 𝐴𝐴⃗ and 𝐶𝐶⃗ is depicted in Equations 3.30-3.31:

�A⃗= 2 ∙ a�⃗ ∙ r⃗-a�⃗ (3.30)

�⃗= 2 ∙ r⃗
C (3.31)

where 𝑟𝑟⃗ is a vector formed randomly between 0 and 1, 𝑎𝑎⃗ is lowered linearly from
2 to 0. After the location of the prey is designated, using shrinking encircling or spiral
updating position methods the bubble-net strategy can be simulated. The first method
can be modeled utilizing the decrease of 𝑎𝑎⃗ value. This decrease provides the variation
limits of 𝐴𝐴⃗ vector. The latter behavior is presented in Equations 3.32-3.33:

' *
�X⃗(t+1)= �D
�⃗ ∙ ebl ∙ cos(2πl)+X
�⃗ (t) (3.32)

' *
�D
�⃗ = �X
�⃗ (t)-X
�⃗(t)� (3.33)

�⃗′ is the margin of the whale to the prey, b is the shape constant of the
where 𝐷𝐷
logarithmic spiral, and l is a random number that varies between -1 and 1. In the WOA,
the whales come to their prey with a linear (shrinking encircling) or spiral movement.
The possibility of each movement is 50% and the movement is determined in Equation
3.34:

*
X �⃗ ∙ D
�⃗ (t)-A ��⃗
if p<0.5
�X⃗(t+1)= � (3.34)
�⃗ (t) if p≥0.5
' *
��⃗ ∙ ebl ∙ cos(2πl)+X
D

where p is a random scalar between 0 and 1. The whales explore their prey randomly
regarding the location of each other. 𝐴𝐴⃗ can be used to model this behavior, if 𝐴𝐴⃗ is

42
greater than 1 or less than -1, the agent is compelled to move away from the reference
agent. This strategy is modeled with Equations 3.35-3.36:

�D �⃗ ∙ �X⃗rand -X
�⃗= �C �⃗� (3.35)

�⃗(t+1)= �X
X �⃗ ∙ D
�⃗rand -A ��⃗� (3.36)

3.2.2.7 Sine Cosine Algorithm (SCA)

Sine cosine algorithm (SCA) is based on behaviors of mathematical sine and cosine
functions. It is a population-based algorithm and was introduced by Mirjalili (2016).
SCA initializes different initial solution sets randomly and makes them glide through
to the best solution by utilizing sine and cosine functions. It is a responsive and simple
algorithm that can be easily implemented to tackle several optimization issues
including feature selection, parameter estimation, and scheduling (Abualigah &
Diabat, 2021). The algorithm starts with the optimization phase of random solution
sets iteratively. Then the solution sets are updated for exploration and exploitation
stages using Equations 3.37-3.38. In the former stage, random solutions are formed to
find the possible best regions of the search space. The latter phase decreases the
randomness and variations, which are less compared to the first stage (Abualigah &
Diabat, 2021; Mirjalili, 2016).

i =Xi +r1 ∙ sin(r2 ) ∙ |r3 Pi -Xi |

Xt+1 t t t
(3.37)

i =Xi +r1 ∙ cos(r2 ) ∙ |r3 Pi -Xi |

Xt+1 t t t
(3.38)

where 𝑋𝑋𝑖𝑖𝑡𝑡 represents the location of the current solution and 𝑃𝑃𝑖𝑖𝑡𝑡 is the target position
in the iteration t, dimension i, and 𝑟𝑟1 , 𝑟𝑟2 , 𝑟𝑟3 typifies random numbers. The usage
condition of these equations is specified with the random number 𝑟𝑟4 . If the 𝑟𝑟4 is smaller
than 0.5, Equation 3.37, else Equation 3.38 is used to update the position.

43
 3.2.2.8 Cuckoo Search Algorithm (CS)

Based on the combination of cuckoo breading strategies and Levy Flight

mechanism of the birds, the Cuckoo Search (CS) Algorithm is a swarm-inspired global
optimization algorithm that mimics the searching nest and reproduction strategies. The
algorithm is introduced by Yang & Deb (2009) and to define the algorithm, three
idealized rules were determined (Bindu & Reddy, 2013):

• One egg is spawned by each cuckoo, and the egg is dropped into a random nest.
• The highest quality nests will be inherited by the following generations.
• Available nests are considered constant and the probability of discovery by a
cuckoo 𝑃𝑃𝑎𝑎 is between 0 and 1.

The algorithm is initialized by generating possible solutions, and it continues with

determining the optimal decision. Candidate solutions were formed using Equation
3.39 based on the given three rules (Zhang, Yu, Luo & Zhang, 2020).

i = Xi +a⊕L(β)
Xt+1 t
(3.39)

where X is the position vector, t is the iteration number, and I is the number of bird
nests. The step-size factor 𝑎𝑎 controls the random search limits and it is greater than 0.
The point-to-point multiplication is referred to as ⊕, and 𝐿𝐿(𝛽𝛽 ) is the optimization
route determined randomly. The required distance that the cuckoo searches are defined
by the Levy flight step size (𝑎𝑎 ⊕ 𝐿𝐿(𝛽𝛽 )). The relation of Levy flight route and t is
named as Levy probably distribution indicated in Equations 3.40-3.41 (Zhang et al.
2020).

i = Xi +a⊕L(β)
Xt+1 t
(3.40)

L(β)~u= tβ , (1<β≤3) (3.41)

44
 3.2.2.9 JAYA

Rao (2019) created the algorithm "JAYA", which means "victory", in 2016 in
Sanskrit. It is a modern population-based MHA that combines the advantages of
evolutionary and Swarm Intelligence algorithms. While evolutionary algorithms
provide an advantage in finding the best result around a local search space, Swarm
Intelligence algorithms are better at locating the global optima for the entire search
space. JAYA algorithm combines these two specifications and has several benefits
over other population-based algorithms, including being simple to use, adaptable, with
the least tuning requirement, and flexible. The JAYA algorithm can handle constrained
or unconstrained problems within the scope of single or multi-objective (Zitar, Al-
Betar, Awadallah, Doush & Assaleh, 2022). The algorithm depends on the difference
between the candidate solution with the best and the worst candidates multiply with
random numbers between zero and one for every iteration. The formula of the JAYA
algorithm is given in Equation 3.42.

X' j,k,i =Xj,k,i+r1,j,i ∙ �Xj,best,i -�Xj,k,i ��-r2,j,i ∙ �Xj,worst,i-�Xj,k,i �� (3.42)

where 𝑋𝑋𝑗𝑗,𝑘𝑘,𝑖𝑖 is the current solution, 𝑋𝑋 ′𝑗𝑗,𝑘𝑘,𝑖𝑖 is the newly updated solution, and 𝑟𝑟1,𝑗𝑗,𝑖𝑖
and 𝑟𝑟2,𝑗𝑗,𝑖𝑖 are two random numbers generated uniformly for each iteration to balance
the exploitation and exploration processes. 𝑋𝑋𝑗𝑗,𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏,𝑖𝑖 and 𝑋𝑋𝑗𝑗,𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤,𝑖𝑖 are the best and the
worst solution for the variable j at ith iteration. The distances between the current-best
and current-worst candidates indicate higher exploitation for closer ranges and higher
exploration for higher ranges. If 𝑋𝑋 ′𝑗𝑗,𝑘𝑘,𝑖𝑖 provides a superior solution, 𝑋𝑋𝑗𝑗,𝑘𝑘,𝑖𝑖 is dropped
in favor of 𝑋𝑋 ′𝑗𝑗,𝑘𝑘,𝑖𝑖 . Every accepted solution serves as the input for the following
iteration.

3.2.2.10 Grey Wolf Optimizer (GWO)

The grey wolf optimizer (GWO) was presented in 2014 by (Mirjalili, Mirjalili &
Lewis 2014). The algorithm is inspired by the leadership structure and social hunting
system of grey wolves. The GWO utilizes the alpha, beta, delta, and omega wolves to

45
find the optimal solution to the issue. The three steps of the hunting technique include
tracking, encircling, and attacking prey. The hunting (optimization) is guided by 𝛼𝛼, 𝛽𝛽,
and 𝛿𝛿 wolves in the GWO algorithm, and in each step of the hunt, have always those
three best solutions and update it whenever a better solution is discovered. The
mathematical model of the algorithm for encircling prey and attacking modeled
between Equation 3.43 to Equation 3.44 as follows:

�D �⃗ ∙ �X⃗p (t)-X
�⃗= �C �⃗p (t)� (3.43)

�⃗(t+1)=X
X �⃗ ∙ D
�⃗p (t)-A ��⃗ (3.44)

where 𝐴𝐴⃗ and 𝐶𝐶⃗ are coefficient vectors, 𝐷𝐷

�⃗ is the distance vector, t indicates the

current iteration, 𝑋𝑋⃗𝑝𝑝 is the position vector of the prey, and 𝑋𝑋⃗ is the position vector of a

grey wolf. 𝐴𝐴⃗ and 𝐶𝐶⃗ are computed in Equations 3.45-3.46:

�A⃗=2a�⃗ ∙ r⃗1 -a�⃗ (3.45)

�C⃗=2 ∙ r⃗2 (3.46)

where 𝑟𝑟⃗1 and 𝑟𝑟⃗2 are random vectors between zero to one and components of 𝑎𝑎⃗ are
linearly decreasing from two to zero to reduce the randomness and the magnitude of
the movement proportional to the iteration number. At the beginning of the
mathematical model, the best three solutions are assumed as 𝛼𝛼, 𝛽𝛽, and 𝛿𝛿 grey wolves.
Other wolves update their location favorably to these wolves, as calculated in
Equations 3.47-3.49 are derived in this regard (Mirjalili et al., 2014):

D ��⃗1 ∙ X
��⃗α = �C �⃗α -X
�⃗�, D ��⃗2 ∙ X
��⃗β = �C �⃗β -X
�⃗�, D �⃗3 ∙ X
��⃗δ = �C �⃗δ -X
�⃗� (3.47)

�X⃗1 =X �⃗1 ∙ (D
�⃗α -A ��⃗ ), �X⃗2 =X �⃗1 ∙ (D
�⃗β -A ��⃗ ), �X⃗3 =X �⃗3 ∙ (D
�⃗δ -A ��⃗ ) (3.48)
α β δ

46
 �⃗1 +X
X �⃗2 +X
�⃗3
�X⃗(t+1)= (3.49)
3

where the subscripts as 𝛼𝛼, 𝛽𝛽, and 𝛿𝛿 indicate the wolves. Equation 45 analysis
reveals that 𝐴𝐴⃗ lies between -2𝑎𝑎⃗ and 2𝑎𝑎⃗. Attacking the prey is provided by decreasing
the 𝑎𝑎⃗ value from two to zero. Thus, the exploitation part of the algorithm is achieved
successfully. To carry out the exploration (search) part of the algorithm random �𝐴𝐴⃗ �
values are selected higher than one to allow the divergence of wolves to search for
prey.

3.2.3 Multi-attribute Decision-Making Methods (MADM)

MADMs are used to order the algorithms and the most optimal single-objective
metaheuristic optimization techniques are determined for the FC parameter extraction
problem. Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS),
Multi-Objective Optimization on the Basis of Ratio Analysis (MOORA), and
Preference Ranking Organization Method for Enrichment of Evaluations
(PROMETHEE) are the decided methods for the ranking process due to their wide
usage and reliability. In addition, the ranking alterations of three methods that use
different principles are aimed to be demonstrated and discussed. The SSE and runtime
are considered non-beneficial, and objective function efficiency is taken as the
beneficial criteria. The equal-weighting method, which is one of the objective
weighing techniques, is utilized to appoint the weights of criteria. Since it is an initial
benchmarking study conducted to determine the optimal algorithms for further
applications of the stated PEMFC parameter optimization process, this weighting
method is decided.

3.2.3.1 Technique for Order of Preference by Similarity to Ideal Solution

TOPSIS is a frequently utilized MADM that can be applied to problems consisting

of many criteria and alternatives and is easy to use. TOPSIS was developed by Hwang

47
and Yoon in 1980 (Yuksel & Koseoglu, 2022; Tzeng & Huang, 2011). The first step
of the TOPSIS method is to normalize the decision matrix (𝑛𝑛𝑖𝑖𝑖𝑖 ) with vector
normalization in Equation 3.50.

xij
nij = , i=1,…,m ;=1,…,n
(3.50)
�∑m 2
i=1 xij

The weighted normalized decision matrix (𝑟𝑟𝑖𝑖𝑖𝑖 ) is then calculated and the positive
ideal (PIS) and negative ideal solutions (NIS) are determined using Equations 3.51-
3.53.
rij =wj ∙ nij , i=1,…,m ;j=1,…,n (3.51)

max�rij |i=1, …,m� if j∈B

PIS=�r+1 , …, r+j , …, r+n � where v+j = �
max�rij |i=1, …,m� if j∈C (3.52)

𝑚𝑚𝑚𝑚𝑚𝑚�𝑟𝑟𝑖𝑖𝑖𝑖 |𝑖𝑖 = 1, … , 𝑚𝑚� 𝑖𝑖𝑖𝑖 𝑗𝑗 ∈ 𝐵𝐵

𝑁𝑁𝑁𝑁𝑁𝑁 = �𝑟𝑟1− , … , 𝑟𝑟𝑗𝑗− , … , 𝑟𝑟𝑛𝑛− � 𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑣𝑣𝑗𝑗− = �
𝑚𝑚𝑚𝑚𝑚𝑚�𝑟𝑟𝑖𝑖𝑖𝑖 |𝑖𝑖 = 1, … , 𝑚𝑚� 𝑖𝑖𝑖𝑖 𝑗𝑗 ∈ 𝐶𝐶 (3.53)

Finally, the distance of each alternative (𝑆𝑆𝑖𝑖+ and 𝑆𝑆𝑖𝑖− ) is determined with Equations
3.54-3.55 and the closeness coefficients (𝐶𝐶𝐶𝐶𝑖𝑖 ) of each alternative are calculated with
Equtaion 3.56. The highest 𝐶𝐶𝐶𝐶𝑖𝑖 value gives the best result (Çelikbilek & Tüysüz, 2020;
de Farais Aires & Ferreira 2019).

m 2
S+i =�� �rij -r+j � ,i=1,…,m (3.54)
i=1

m 2
S-i =�� �rij -r-j � ,i=1,…,m (3.55)
j=1

S-i
CCi = + -
Si +Si (3.56)

48
 3.2.3.2 Multi-Objective Optimization on the Basis of Ratio Analysis

MOORA is a weighted normalization method that is frequently used and proposed

by Brauers & Zavadskas (2006). This method considers all possible alternatives and
criteria. It offers straightforward implementation, quick computation, less
mathematical burden, and excellent reliability. The ratio, reference point, full
multiplicative, and important factors are four different types of MOORA (Yuksel &
Koseoglu, 2022; Kundakci, 2016).

Ratio and reference point formats were used in this study. Each criterion is assumed
to have an equal weight by the MOORA-Ratio (Yuksel & Koseoglu, 2022; Kundakci,
2016; Brauers & Zavadskas, 2006). Creating a decision matrix is the first stage in the
MOORA-Ratio process. After that, the decision matrix is normalized in Equation 3.57.

xij
x*ij =
(3.57)
�∑nj=1 x2ij

Weighted normalized decision matrix (𝑣𝑣𝑖𝑖𝑖𝑖 ) with the multiplication of weights (𝑤𝑤𝑗𝑗 )
is used to find the normalized matrix with Equation 3.58.

vij =x*ij ∙ wj (3.58)

The performance of decision choices is calculated with Equation 3.59 and

preference values (𝑦𝑦𝑖𝑖∗ ) are obtained. Finally, the 𝑦𝑦𝑖𝑖∗ values are sorted in descending
order.

g n

y*i = � vij - � vij (3.59)

j=1 j=g+1

49
 3.2.3.3 Preference Ranking Organization Method for Enrichment of Evaluations

The PROMETHEE I (partial ranking) and PROMETHEE II (full ranking) were

invented by J.P. Brans and first presented in 1982 by Nadeau and Landry at a
conference held in Québec, Canada (Brans & De Smet, 2016). To ensure detailed
analysis, PROMETHEE allows obtaining both partial and certain priorities. Firstly, to
create the dataset, the decision points, evaluation factors, and weights should be
determined by the decision-maker. After that, the decision-maker should choose a
selection function to indicate the evaluation factors and illustrate the internal
interactions. The preference function must be the standard evaluation criterion
employed in the study if the decision-maker lacks an evaluation criterion (Yuksel &
Koseoglu, 2022; Brans & De Smet, 2016; Şenkayas & Hekimoğlu, 2013). It is
necessary to ensure pairwise comparisons between each evaluation factor and each
decision point. Equation 3.60 may be used to display the common preference function
when A and B exhibit two distinct decision points.

0 f(A)≤ f(B)
P(A,B) = � (3.60)
p[f(A)-f(B)] f(A)>f(B)

Equation 3.60 can be used to calculate the preference indices using typical
preference functions in Equation 3.61.

π(A,B)= � (wi ∙ Pi ∙ (A,B)) (3.61)

i=1

In the next, positive (𝜑𝜑 + ) and negative (𝜑𝜑 − ) superlative degrees are obtained using
Equation 3.62 and Equation 3.63.

1 (3.62)
φ+ = � π(A,x)
n-1

50
 1
φ- = � π(x,A) (3.63)
n-1

where 𝑥𝑥 shows the decision points except for A. PROMETHEE I is used to

determine a partial ranking. The method makes sure that positive and negative
superlative degrees are compared pairwise to get the best choice point. Finally,
PROMETHEE II can be used to precisely rank the choice points. Priority degrees can
be calculated with Equation 3.64 and sorted in descending order. Consistent with this,
if (𝐴𝐴) > 𝜑𝜑(𝐵𝐵), alternative A is superior (Yuksel & Koseoglu, 2022; Brans & De
Smet, 2016; Şenkayas & Hekimoğlu, 2013; Behzadian, Kazemzadeh, Albadvi &
Aghdasi, 2010).

-
φ(A)= φ+ (A)+φ (A) (3.64)

3.3 Results and Discussion

In this section, results are presented and discussed through the sub-sections. In sub-
section 3.3.1, validation of the semi-empirical mathematical model and the results of
the various algorithms used were examined comparatively. Sub-section 3.3.2 provides
the performance evaluation and comparison of various metaheuristic optimization
algorithms on the described fitness function.

3.3.1 PEMFC Model Validation Results

The basic parameters of the 250 W FC (Mo et al., 2006) are used for the validation
of the E-CGA, and those of the H-1000XP is used for the comparison of the different
algorithms. The main parameters of these fuel cells are shown in Table 3.2.

51
Table 3.2 The main parameters of the PEMFCs
Parameters 250 W H-1000XP
Number of cells, 𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 24 50
Active cell area, 𝐴𝐴𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (𝑐𝑐𝑐𝑐2) 27 77
Maximum current density, 𝐽𝐽𝑚𝑚𝑚𝑚𝑚𝑚 , (A∙cm-2) 0.86 0.56
Membrane thickness, 𝑙𝑙 (𝜇𝜇𝜇𝜇) 127 125
Rated power (𝑊𝑊) 250 1000
Inlet anode pressure, 𝑃𝑃𝑎𝑎 (𝑎𝑎𝑎𝑎𝑎𝑎) 1–3 0.56
Inlet cathode pressure, 𝑃𝑃𝑐𝑐 (𝑎𝑎𝑎𝑎𝑎𝑎) 1–5 1
Stack temperature, 𝑇𝑇 (𝐾𝐾) 343.15 – 353.15 328
Relative humidity in the anode, 𝑅𝑅𝐻𝐻𝑎𝑎(-) 1 1
Relative humidity in the cathode, 𝑅𝑅𝐻𝐻𝑐𝑐 (-) 1 1

The study of Mo et al. (2006) was used as the reference for the validation of the
semi-empirical mathematical model. In their study, a niche genetic algorithm was used
to calculate the unknown modeling parameters. In this thesis, E-CGA was used to
compare the results of this algorithm-based model with the study of Mo et al. (2006).
Four data sets (two for validation and two for identification) were used. In the reference
study (Mo et al., 2006), Range 2 was used for parameter estimation, as shown in Table
3.3. Range 1 was used in this study to better understand algorithm convergence since
it has a greater range than range 2 (Xu et al., 2019). In the reference study (Mo et al.,
2006), the SSE value for four data sets was calculated as 16.6081. In this thesis, the
SSE value was calculated as 13.467.

Table 3.3 Ranges taken for the parameters’ estimation (Xu et al. 2019)
𝜉𝜉1 𝜉𝜉2 𝜉𝜉3 𝜉𝜉4 𝛽𝛽 𝑅𝑅𝑐𝑐 (𝑉𝑉) 𝜆𝜆
Range 1 Min -1.19969 1e-3 3.6e-5 -2.6e-4 0.0136 1e-4 10
Max -0.8532 5e-3 9.8e-5 -9.54e-5 0.5 8e-4 24
Range 2 Min -0.952 1e-3 7.4e-5 -1.98e-4 0.016 1e-4 14
Max -0.944 5e-3 7.8e-5 -1.88e-5 0.5 8e-4 23

The comparison of the parameters is given in Table 3.4 and the comparison of the
polarization curves between the reference study and this study is given in Figure 3.4.
It can be seen from this figure that the results of the reference study and this study are
well matched.

52
Table 3.4 Results of parameters for 250 W FC in Range 2
Algorithm 𝜉𝜉1 𝜉𝜉2 𝜉𝜉3 𝜉𝜉4 𝛽𝛽 𝑅𝑅𝑐𝑐 (𝑉𝑉) 𝜆𝜆 SSE
HGA -0.944 3.01e-3 7.4e-5 -1.8e-4 0.02914 1e-4 23 16.6081
E-CGA -0.949 3.07e-3 7.696e-5 -1.88e-4 0.0315 1.04e-4 22.99 13.4670

Figure 3.4 The comparison of the polarization curves of the 250 W PEMFC using the E-CGA as in this
study and HGA as in the study of Mo et al. (2006): (a) and (b) for identification and (c) and (d) for
validation

The polarization curve of the H-1000XP was obtained using the unknown model
parameters given in Table 3.4 found by E-CGA. The polarization curve obtained using
the E-CGA is compared with the manufacturer's datasheet, as shown in Figure 3.5
(Horizon Educational [HE], 2021). In conclusion, comparing the polarization curve
obtained with the E-CGA with that from the manufacturer's datasheet, it is clear that
these are very close, and the SSE value is low, as shown in Table 3.4 The high accuracy
of the model proves the accuracy of the equation set used. In the rest of the study, this
equation set was used to calculate the unknown model parameters by applying various
MHAs to find the best suitable MHA.

53
 Figure 3.5 Polarization curve of H-1000XP (Experimental data were taken from (HE, 2021))

3.3.2 Metaheuristic Algorithms and MADM Methods Results

The selected 10 algorithms were run using Python 3.10, all on the same computer.
The specifications of the computer are Intel(R) Core(TM) i5-9400 CPU @ 2.90GHz,
8GB Ram, and the operating system is Windows 10 (64 bits). The algorithms were
assessed regarding different error measurement methods for ensuring a precise
comparison of the performance and were ranked by TOPSIS, MOORA, and
PROMETHEE according to SSE, run time, and objective function efficiency. This
efficiency was considered beneficial, and the run-time and SSE were taken as non-
beneficial criteria. Runtimes were selected as the overall duration of 100 runs for each
algorithm. The weights of the criteria were calculated using one of the objective-
weighing methods called equal weighting. The method relies on assigning equal
weights to each criterion so that sum equals one. The rankings and performance of
algorithms were compared and discussed. Table 3.5 specifies the performance metrics
of each algorithm.

54
Table 3.5 Results of the statistical comparison
Algorithm Runtime (S) Best SSE Worst SSE Mean SSE η R2 MAE
WOA 1316.7 0.4449 0.7681 0.5030 88.4558 0.9987 0.1097
IWOA 2946.3 0.4449 0.5140 0.4595 96.8143 0.9987 0.1097
GWO 1485.4 0.4456 0.5779 0.4749 93.8367 0.9987 0.1096
IGWO 2787.7 0.4450 0.4781 0.4513 98.6034 0.9987 0.1097
JAYA 1298.5 0.5599 118.1836 10.8045 5.1817 0.9983 0.1276
MFA 1054 0.4389 0.6368 0.4523 97.0298 0.9987 0.1141
SCA 1238.9 0.4916 1.6004 0.7358 66.8123 0.9985 0.1133
SSA 1298.8 0.4486 0.6448 0.5080 88.3112 0.9987 0.1098
DE 1067.7 0.4457 0.5035 0.4698 94.8669 0.9987 0.1101
CS 2354.1 0.7864 11.4660 3.5792 21.9723 0.9976 0.1538

Table 3.6 indicates the rank of each algorithm according to the specified MADMs
(TOPSIS, MOORA, and PROMETHEE) methods considering decided weighting
factors.

Table 3.6 The rank of each algorithm determined by selected MADM methods
ALGORİTHM TOPSIS RANK MOORA RANK PROMETHEE RANK
WOA 5 4 3
IWOA 10 10 8
GWO 6 5 5
IGWO 9 7 7
JAYA 7 9 9
MFA 1 1 1
SCA 4 6 6
SSA 3 3 4
DE 2 2 2
CS 8 8 10

The results of MADM methods ranking with equal weights showed that MFA is
ranked as the first, and DE is the second optimal algorithm for this problem regarding
all three methods. MFA has the lowest runtime and SSE and the second-highest
objective function efficiency among all. TOPSIS ranked GWO and IWOA as the last
two algorithms due to their remarkably higher run times. The last two choices of
MOORA were IWOA and JAYA. On the other hand, PROMETHEE pointed out
JAYA and CS for the last two spots. Among the algorithms, GWO has the highest

55
objective function efficiency. Considering the MAE and R2 values of the algorithms,
GWO and IGWO offered the lowest error rates. In other words, MFA provided the
lowest error on a total error basis, while GWO on a mean error basis ensured the lowest
error for this problem. CS has the poorest SSE among the others and its run time is the
third, and its objective function efficiency is the second worst. Because of these, it was
ranked last by PROMETHEE and eighth by the other MADM methods. Although
JAYA ensured a relatively fast solution, its objective function efficiency and
consistency were inadequate for this problem. Table 3.7 depicts the parameters found
by the best solution for each algorithm.

Table 3.7 The estimated parameters by the algorithms

Algorithm 𝝃𝝃𝟏𝟏 𝝃𝝃𝟐𝟐 𝝃𝝃𝟑𝟑 𝝃𝝃𝟒𝟒 𝝀𝝀 𝑹𝑹𝒄𝒄 (𝑽𝑽) 𝜷𝜷
MFA -1.2516 0.0042 0.0001 0.0001 11.0198 -0.0014 0.0967
DE -0.9689 0.0029 0.00004 -0.0001 24 0.0001 0.0979
SSA -0.9638 0.0034 0.0001 -0.0001 21.4509 0.0001 0.0955
SCA -0.8532 0.0025 0.0000 -0.0001 24 0.0004 0.0951
WOA -0.8532 0.0031 0.0001 -0.0001 23.9949 0.0001 0.0982
IGWO -1.0637 0.0031 0.0000 -0.0001 23.9330 0.0001 0.0983
JAYA -1.1997 0.0034 0.0000 -0.0001 17.4219 0.0003 0.0888
CS -1.1997 0.0038 0.0001 -0.0001 17.1406 0.0001 0.0870
GWO -0.8734 0.0025 0.00004 -0.0001 23.9792 0.0001 0.0981
IWOA -1.0731 0.0031 0.00004 0.0001 24 0.0001 0.0983

For comparison purposes, the top two positions by all three MADM methods
(MFA, DE) and four algorithms ranked in the last two places by at least one of the
methods (IWOA, GWO, JAYA, CS) are illustrated and discussed. Figure 3.6 illustrates
the convergence of the polarization curves to the experimental data when employing
the parameters obtained through the designated algorithms.

TOPSIS method with equally weighted criteria ranked the GWO and IWOA as the
worst-performed algorithms since the run time of these algorithms was remarkably
higher. However, for applications that do not require fast solutions, these algorithms
can be preferable options. Especially, GWO was the most consistent algorithm in 100
runs, and its performance was the best according to MAE and R2 metrics. GWO
provided the same performance regarding MAE and R2 metrics with a more acceptable

56
run time, however, its objective function efficiency was slightly lower than JAYA,
while CS ensured the poorest error rates and objective function efficiency among the
algorithms. Although JAYA provided an acceptable run time, the consistency and
objective function efficiency of the algorithm was not admissible for this problem. The
run time of the CS was the third worst, and it did not perform well regarding the
objective function efficiency and error rates. PROMETHEE method ranked these
algorithms as the poorest for this problem set.

(a) (b)

(c) (d)

(e) (f)

Figure 3.6 Polarization curves when estimated parameters of (a) MFA, (b) DE, (c) JAYA, (d) CS, (e)
IWOA, (f) GWO were used (Experimental data were taken from (HE, 2021))

The consistency of the algorithms was determined numerically using the objective
function efficiency metric. Figure 3.7. illustrates the convergence curves of each
algorithm’s best solutions. Figure 3.8. shows the distribution of the lowest error rates
found by the algorithms in each run. Enlarged versions are also given in the figure to
highlight where the values are close to zero.

57
 Fig.7 shows that JAYA is the algorithm that reached the best SSE value with the
lowest iteration number. However, the best SSE value of JAYA is higher than other
algorithms. IWOA and MFA followed the JAYA by converging the global optimum
solution time. Especially, IWOA found the ideal solution before the 100th iteration
which indicates that its runtime can be lowered significantly with the adjustment of
the number of iterations. In Fig. 3.8., the illustration of the objective function
efficiency metric was ensured. GWO, MFA, and IWOA are the most consistent
algorithms as can be seen in the figure.

Figure 3.7 Convergence curves of each algorithm’s best solutions

Figure 3.8 Distribution of the lowest error obtained by the algorithms in each run

58
 The convergence performances of the algorithms were evaluated with the objective
function efficiency metric. 1000 iterations and 100 runs were selected to benchmark
the algorithms. However, it should be noted that algorithms with high efficiencies
obtained the best results significantly earlier than 1000 iterations. Particularly, MFA
and GWO ensured consistent and fast convergence which can be seen in Figure 3.9.
and Figure 3.10. The number of iterations can be optimized, and lower run times can
be achieved for these algorithms. This adjustment can make GWO preferable for this
problem and boost the performance of MFA to even higher regarding the run time.

Figure 3.9 Convergence curve of MFA

Figure 3.10 Convergence curve of GWO

59
 Figure 3.9 indicates that MFA reached the optimum solution before the 200th
iteration in the majority of runs. In Figure 3.10, the convergence is sharper for GWO
which means, the optimum solution was approached at the beginning of the iterations.
Before the 400th iteration, the algorithm commonly found the optimum result for the
specific run. The algorithms having low efficiencies could not achieve low error rates
even in the 1000th iteration in most of the runs. Figure 3.11 and Figure 3.12
demonstrate the convergence curves of CS and JAYA, respectively.

Figure 3.11 – Convergence curve of CS

Figure 3.12 – Convergence curve of JAYA

60
 CS detected the optimum solution slightly more efficiently than JAYA. However,
at the end of the 100 runs, its error rate remained the highest. The algorithm becomes
insufficient for the fields that require a low error rate. The convergence of JAYA
seemed stacked in the local optima depicted in Figure 3.12. Even though the lowest
SSE was found as 0.56, the mean SSE was absurdly high can be seen in Table 3.5. For
applications where stability is a top priority, instability makes the algorithm unusable.

61
 CHAPTER 4
ENVIRONMENTAL AND ECONOMIC ANALYSES OF FUEL CELL AND
BATTERY-BASED HYBRID SYSTEMS UTILIZED AS AUXILIARY
POWER UNITS ON A CHEMICAL TANKER VESSEL

This chapter investigates the environmental and economic impacts of implementing

fuel cell and battery-based hybrid configurations. Phosphoric acid and molten
carbonate fuel cell systems in the place of diesel generators of a large tanker to supply
the vessel’s total electricity demand. Environmental and economic analyses of the
utilization of the specified fuel cell systems with LiNiCoALO2 and LiNiMnCoO2
chemical types of battery cells on a large marine vessel are provided in this thesis. In
addition, the assessment of the most suitable battery cell and charge-discharge hours
for fuel cell systems is carried out with a grid-search algorithm. Six different fuel cell
and battery configurations are investigated to obtain the optimum system layout.

4.1 Literature Survey on Marine Transport Applications

The studies on fuel cell-based marine systems have increased nowadays. There are
some EU projects and theoretical studies found in the literature that are discussed in
detail through this sub-section both commercial vessels and demonstration projects.

The "Fuel Cell Technology for SHIPs" (FCSHIP) project, which ran from 2002 to
2004, had the main goals of evaluating safety concerns, assessing not only the
economic but also the environmental aspects of FC usage, and assessing the potential
of FC use for both main propulsion and auxiliary power units. During the project,
various types of fuels and FCs (PEMFC, MCFC, and SOFC) were studied. As a
consequence of the project, PEMs are chosen for small-medium power systems, while
MCFC and SOFC systems are appropriate for high-power applications requiring high
volumetric power density hydrocarbon-based fuels. The only method to minimize
GHG emissions among these fuels is to utilize natural gas or green hydrogen (Coppola
et al., 2020). Another project that utilizes LNG as fuel is the FELICITAS subproject
II, which was completed between 2005 and 2008. 250 kW SOFC developed by Rolls-

62
Royce for stationary systems evaluated on sea conditions. Furthermore, the utilization
of alternative hydrocarbon-based fuels that could be used instead of hydrogen and the
waste heat recovery potential of SOFC were also investigated and proven tests held on
board a mega yacht (Klingner, 2009). MultiSchiBZ project is the successor of the
SchiBZ projects funded by the German Federal Ministry of Transport and Digital
Infrastructure on the large cargo vessel MS Forester that has two phases development
phase between 2018-2020, and a demonstration phase between 2020-2022. The main
goal of the project is to develop a SOFC system that has more than 50% efficiency and
is operated with low-sulfur diesel fuel or LNG as an energy source. Other goals of the
project are to design a more realistic heat exchanger that includes the effects of
temperature variance and heat transfer to optimize the reforming process of LNG
(e4Ships, n.d.-a). Worthy to note that the “RiverCell2” (e4ships, n.d.-b) and “Pa-X-ell
2” (e4ships, n.d.-c) projects carried out between 2017-2021 facilitate HT-PEMFC with
methanol as a primary energy source and LNG as optional.

The MC-WAP project (Centro Per Gli Studi Di Tecnica Navale [CETENA] 2011),
which received funding from the EU, was conducted between 2005 and 2010 to design
and develop onboard MCFCs with an output ranging from 100 kW to 500 kW as
auxiliary power units (APUs) for RoPax, RoRo, and cruise vessels. The project
encompassed several main objectives, including the development of an integrated
MCFC system capable of meeting auxiliary loads of up to 500 kWe fueled by diesel
oil, enhancing the safety, performance, and reliability of the balance of plant
components, and reformer technology in the maritime environment. In selected
typologies of vessels, the conventional diesel generators were partially or entirely
replaced with the MCFCs. The project's principal outcomes included the identification
of new rules for reforming procedures and marine applications of FCs, as well as the
determination of the operating conditions of MCFC-APUs under vibrations, motions,
and marine environment. As a case study, Micoli, Coppola & Turco (2021) selected a
SOFC powered by LNG as an auxiliary power unit for a cruise ship. The authors
investigated the assumption that a 20 MW SOFC system was installed on the ship and
conducted a comparison using three generations of dual-fuel engines. The study
revealed that significant reductions in SOx, CO, NOx, and PM pollutants could be

63
achieved while decreasing CO2 emissions by 11%. Additionally, the authors calculated
the placement of the SOFC system in terms of weight and volume according to the
most recent international norms and proposed a system. Based on the calculations, it
was determined that the SOFC system is both heavier and takes up more room.
However, it was discovered that this circumstance had no significant impact on the
ship's stability and buoyancy. The EU-funded project “NAUTILUS” began on July 1,
2020, intending to develop LNG-fueled SOFC-battery hybrid gensets that would
gradually replace internal combustion engine-based generators for long-haul
passenger ships. The generated energy is used to meet the ship's entire heating and
power requirements (German Aerospace Center [DLR], n.d.). In the FellowSHIP
project carried out between 2003 and 2011, a 320 kW MCFC, fed with LNG, was
installed as an auxiliary power unit on an offshore-supply vessel named “Viking Lady”
(Tronstad, Høgmoen, Haugom & Langfeldt, 2017). The main findings from the
FellowSHIP project are slow response time of fuel cells could be compensated with
batteries to provide improved safety, fuel savings, and a significant amount of
emissions reduction. Other benefits are related to reductions in machinery maintenance
costs, and noise and vibration reduction. The project also helped remove impediments
to the commercialization of fuel cell and battery hybrid technology and alleviate safety
concerns (Alnes, 2018).

Inal & Deniz (2020) assessed the fuel cell types for ships in their study based on
multi-criteria decision analysis including PEMFC, MCFC, PAFC, and SOFC. The cost
analysis of the fuel cell types showed that the PEMFC has the lowest installation cost,
followed by PAFC and MCFC, respectively. However, the operational cost of PEMFC
was found to be the highest due to the costs of pure hydrogen and storage equipment.
The average cost ranking between PAFC and LNG-fueled MCFC was reported slightly
in favor of PAFC due to its lower initial cost. Another study conducted by the same
authors (Inal & Deniz, 2021) also revealed the usage of a 2.8 MW MCFC operating
with LNG instead of a conventional diesel engine for a chemical tanker, utilizing 27
trip data of a chemical tanker for 10 months in 2018. Fuel transitions in ECAs are also
considered in the computations to get more precise results. As a consequence, it is
claimed that the emission values are calculated correctly and obtained a 99% decrease

64
in SOx, PM, and NOx emissions, and a 33% reduction in CO2 emissions. Seyam, Dincer
& Agelin-Chaab (2022) proposed a propulsion system design for ships utilizing a
hybridized 4 MW SOFC system with organic Rankine cycle and gas Brayton cycle
systems. The results showed that the utilization of sustainable fuels of LNG and
hydrogen in the system would reduce carbon emissions by 80% and improve the
energy efficiency of the propulsion system by 14%. Roh, Kim, Jeon & Yoon (2019)
set up a test bench consisting of LNG-fueled MCFC, lead-acid battery, and D/G to
consider fuel consumption and emission reduction compared to the standalone
operation of a commercial diesel generator for selected five different types of vessels
with various operation modes. A simple rule-based EMS is proposed according to the
load and SoC of lead-acid batteries. As a result, the average CO2 reduction potential is
reported between 70% to 74%.

Tronstad et al. (2017) reviewed the use of fuel cells in marine applications. It has
been seen that all mentioned fuel cell projects and applications have used PEM, SOFC,
or MCFC, and none of them used PAFC (Tronstad et al., 2017). However, the only
study that mentioned the usage of PAFC in a maritime application was carried out by
(Winkler, 2009). The project was funded by United States Maritime Administration
(MARAD) to meet auxiliary loads of a power barge with PAFCs. No other information
about the project could be found in the literature. Bassam (2017) conducted a more in-
depth analysis of the literature on fuel cell maritime applications, looking at 62
research published since 2000. PAFC was not utilized in these theoretical research and
initiatives, according to the study. For researchers who want to examine the maritime
applications of the fuel cell in more detail, some of the notable studies could be
summarized (Sürer & Arat 2022; Dall’Armi et al., 2021; Xing, Stuart, Spence & Chen,
2021; Coppola et al., 2020; Markowski & Pielecha, 2019; Leites, 2016; Van Biert et
al., 2016). However, when studies in the other fields are examined, current studies are
encountered in which the use of PAFC as a stationary power unit is investigated as a
thermo-economic (Wilailak et al., 2021), potential replacement with utilizing NG as
fuel (Nam, Nam & Lee, 2021), and combined heat, power, and hydrogen generation
systems (Park et al., 2021). Besides, a commercial PAFC-type fuel cell named

65
PureCell Model 400, produced by Doosan company, and sold commercially, can use
hydrogen or LNG as fuel, used in commercial applications.

The studies in the literature show that the continued use of conventional internal
combustion diesel engines as the main engine or auxiliary power unit is the biggest
obstacle to reducing the emissions by seaborne trade to the targeted levels in 2050.
There is only one study found in the literature related to environmental and economic
analyses of fuel cell-battery hybrid system design that can fully meet the electricity
demand of ocean-going tanker ships by considering different operation modes
(Korkmaz et. al, 2023). Despite the commercial availability of PAFC products, their
suitability for marine applications remains largely unexplored. The marine application
of MCFC systems, on the other hand, has been limited to their use as main propulsion
units on small vessels, and they have not yet been utilized to fulfill the entirety of the
auxiliary power demand of large vessels. The literature survey shows that there have
been no studies by the author that evaluate the most suitable battery brand and charge-
discharge hours for PAFC and MCFC systems with a grid-search algorithm. One part
of this thesis aimed to analyze and discuss the potential environmental and economic
impacts of implementing various fuel cell/battery hybrid configurations instead of
marine D/Gs to compensate for the auxiliary power demand of the vessel.

4.2 System Description

The ship electricity generation plant of an oceangoing tanker vessel was modeled
using Python language. The plant consists of three equivalent marine diesel generators
and can produce electricity up to 3.15 MW. The data gathered from ship trial tests of
marine diesel generators were used to construct the mathematical model of the plant.
Six different operation modes of the system and their electrical loads were obtained
from electrical load tests also carried out during ship trail tests. Specifications of one
generator in the simulated system and electrical loads of the operation modes are
demonstrated in Table 4.1. The utilization hours of these modes were obtained from
port calls and position history data collected from (Marine Traffic, 2021). Figure 4.1
illustrates the utilization hours of the operation modes between 06 December 2019/06

66
December 2021. The route of the ship involved oceangoing navigations mainly on the
Europe-North America route. 67% of the utilization hours were spent during
navigational operations, and the remaining were coastal operations. Yuksel &
Koseoglu (2022) provided the mathematical background, validation, and operating
principle for the conventional ship power distribution system model. The emissions of
diesel fuels were calculated using emission factors published by Kuzu, Bilgili & Kiliç
(2021).

Table 4.1 Specifications of the marine diesel generators and electrical load
Prime Mover Alternator
Engine/Generator MCR 960/900 kW Output Capacity 1,312.5 kVA
Rpm 900 Voltage 450 V
Cylinder Bore/ Piston Stroke (mm) 210/320 Frequency 60 Hz
3
Swept Volume per Cylinder (dm ) 11.1 Poles 8
Piston Mean Speed (m/s) 9.6 Voltage Variation 2.50%
Compression Ratio 17:1 Voltage Adjust 5%
Mean Effective Pressure (bar) 24.1 Power Factor 0.8 Lagging
Electrical Load
Operational Mode Load (kW) Current (A)
On navigation 850.6 1,364.152
On navigation with tank heating 1,195.7 1,917.607
At berth 1,122 1,799.410
During cargo handling 1,781.5 2,857.085
During anchorage 571.3 916.224
During anchorage with tank heating 863 1,384.038

Figure 4.1 Utilization hours of the plant according to operation modes

67
 The proposed system configurations involve the usage of commercial fuel cells
supported by battery packs instead of marine diesel generators in the plant. The first
fuel cell type used in the study is the PAFC which uses phosphoric acid electrolytes.
The mean electrical efficiency of PAFCs varies between 40-50%, but the
implementation of heat recovery systems could rise the efficiency up to 80% (Tronstad
et al., 2017), and the operating temperature is 150-200 °C. Equation 4.1, Equation 4.2,
and Equation 4.3 demonstrate the electrochemical reactions of PAFC (Lindorfer,
Rosenfeld & Böhm, 2020). Catalog data of Doosan PureCell Model 400 (Doosan Fuel
Cell America INC [DFCA], 2018), which is a PAFC, is used in the mathematical
model. Table 4.2 indicates the technical specifications of the commercial PAFC.

Anode: H2 →2H+ +2e- (4.1)

1
Cathode: 𝑂𝑂 + 2H+ +2e- → H2 O (4.2)
2 2

Total: O2 + 2H2 → 2H2 O (4.3)

Table 4.2 Technical specifications of the commercial PAFC (DFCA, 2018)

Fuel Cell Type PAFC
Electric Power Output 440 kW
Electrical Efficiency 45%
Peak Overall Efficiency 90%
LNG Consumption 98.4 (m³/h)
NOₓ 0.009 (kg/MWh)
CO₂ 454 (kg/MWh) without heat recovery
VOC 0.005 (kg/MWh)
CO 0.005 (kg/MWh)

The second type of fuel cell used in the proposed system layouts is the MCFC. The
molten carbonate salts are used as electrolytes and these are heated up to 700 °C
(Marefati & Mehrpooya, 2019). The high operating temperatures provide fuel-type
flexibility to MCFCs. The electrical efficiency of an MCFC changes between 50-60%,
but the total efficiency could be up to 85% with heat recovery systems. This type of
fuel cell is considered suitable for higher energy applications. Equation 4.4, Equation

68
4.5, and Equation 4.6 depict the electrochemical reactions of MCFC (Tronstad et al.,
2017). SureSource 1500 model of Fuelcell Energy company is selected as the MCFC
type (Fuelcell Energy [FE], n.d.). Table 4.3 demonstrates the main specifications of
the MCFC.

3 →O2 + H2 O+2e
Anode: H2 + CO-2 -
(4.4)
3 →2CO2 + 2e
CO + CO-2 -

1
Cathode: 𝑂𝑂 + CO2 +2e- → CO-2 (4.5)
2 2 3

Total: 2H2 + O2 → 2H2 O (4.6)

Table 4.3 Technical specifications of the commercial MCFC (Inal & Deniz, 2021; FE, n.d.)
Fuel Cell Type MCFC
Electric Power Output 1400 kW
Electrical Efficiency 47% +- 2%
LNG Consumption 615.12 (m³/h)
NOₓ 0.0045 (kg/MWh)
CO₂ 444.5 (kg/MWh) without heat recovery

PM 9.07∙106 (kg/MWh)
SOx 0.000045 (kg/MWh)

Figure 4.2 illustrates the proposed electricity distribution system layout of the
vessel. The conventional system consists of three equivalent marine diesel generators
with 1.05 MW power output and one emergency generator. The CO2 value given in
Table 4.3 involves the required CO2 loop for the startup process of the MCFC. In the
study, marine diesel generators are replaced with fuel cells and battery packs to meet
the electrical load of the ship. The emergency generator (E/G) is kept for safety
concerns. As seen in Figure 4.2, the air is supplied with a blower to the cathode side
of the fuel cell. The produced water in the system is pumped to the water tank and it is
also used in the system for mixing with LNG. With the help of the mixer and heat
exchanger, a water gas shift reaction is occurred to produce hydrogen for utilization in
the fuel cell plant (Inal & Deniz, 2021).

69
Figure 4.2. FC/battery hybrid electricity distribution system scheme (Adapted from (Cahyagi &
Koenhardono, 2018; İnal & Deniz, 2021; Oways, 2019))

The system configurations are depicted in Table 4.4. The installed auxiliary power
generation capacity of the vessel has remained at 3.15 MW which is the cumulative
capacity of the existing three generator sets onboard.

The first and second configurations were designed to meet the electrical load with
fuel cells, and battery packs are placed to compensate for operational loads when the
vessel requires fast response time during quick load changes. In the other four
configurations, batteries and fuel cells meet the load together. C3 and C4 cases utilize
batteries during navigation to compare the environmental and economic results with
C5 and C6 cases. While the batteries meet the majority of the electrical load in the
discharge state, the fuel cells meet both the system load and the charge load in the
charging state. The case of battery usage during navigation is examined to observe the
impacts of battery life on the economic performance of the systems.

Table 4.4 Proposed system configurations

Fuel Cell Battery usage
Configuration Code Fuel Cell Power Battery Capacity
Type during navigation
C1 2 x 1.4 MW MCFC 0.35 MWh No
C2 6 x 0.44 MW PAFC 0.51 MWh No
C3 2 x 1.4 MW MCFC 0.95 MWh Yes
C4 5 x 0.44 MW PAFC 0.95 MWh Yes
C5 2 x 1.4 MW MCFC 0.95 MWh No
C6 5 x 0.44 MW PAFC 0.95 MWh No

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 The suitable battery for the different system configurations and the optimum
charging-discharging times were obtained from a grid-search iterative selection
algorithm that calculates the LNG consumption with possible charging-discharging
hours. Battery usage during navigation operations was evaluated to increase battery
life. The ship's electricity grid requires 450 V AC and the inverter demands 800 V DC
input to give this output (Yuksel & Koseoglu, 2022). This is achieved by connecting
320 serial cells. Table 4.5 illustrates the specifications of the selected battery cells on
the system.

Table 4.5 Selected battery cells for system configurations ((Panasonic, 2021; PowerXtra, 2021; Molicel,
2018; LGChem, 2014))
Nominal Voltage
Battery Code Capacity (mAh) Price ($) Weight (kg)
(V)
B1 3,350 3.6 11.82 0.048
B2 3,500 3.7 10 0.048
B3 3,500 3.7 8,82 0.049
B4 3,200 3.7 5.45 0.049

In this regard, initially, the conventional ship power distribution plant of 50,000
deadweight tons (DWT) oceangoing oil/chemical tanker vessel involving three
equivalent D/Gs was modeled according to six different operation modes. The realistic
fuel consumption calculation of D/Gs was ensured according to varying load sharing
regarding the power demand in each operation with a numerical model. Then,
commercially available PAFC, MCFC, and battery sets were selected. Six different
fuel cell/battery configurations were investigated to obtain the optimum system layout.
A state-based EMS was designed to control the charge/discharge processes of the
batteries. Hybrid configurations were proposed in the first two configurations (C1 and
C2) as the batteries are only utilized to meet the rapid load changes required from the
vessel. C3 and C4 configurations were modeled to continuously utilize the batteries on
all operations of the vessel. C5 and C6 used batteries only in coastal operations having
frequent load changes to increase the battery life, thus the navigation operations were
not included. The performance of the proposed fuel cell/hybrid system configurations
was evaluated using environmental and economic analyses, and the results of utilizing

71
fuel cell/hybrid system configurations as auxiliary power units in the vessel were
compared with the utilization of the existing D/G plant onboard.

4.3 Modeling of Fuel Cell and Battery Configuration

There have conducted two case studies in the scope of the thesis. The first case
study involves a large oil/chemical tanker working with PAFC and battery hybrid
configuration. The environmental and economic analyses of this case study are carried
out using catalog data of a commercial PAFC unit; thus, no fuel cell modeling
equations are utilized.

4.3.1 Mathematical Modeling of the Hybrid Power Plants

The mathematical model of the plant with fuel cell and battery configurations is
created using Python programing language. A state-based energy management strategy
(EMS) is proposed to control the battery charging and discharging processes. Figure
4.3 illustrates the mathematical model's algorithm scheme whereas Figure 4.4 depicts
the EMS's working logic.

EMS function takes the battery state and previous state of charge (SoC) as inputs,
and it starts with calculating the available maximum battery capacity from the function
obtained from battery aging curves. The curves are gathered from the technical data
sheet of the selected battery cells (Panasonic, 2021; PowerXtra, 2021; Molicel, 2018;
LGChem, 2014). Then, the function computes the state of health (SoH) and checks
through the battery state. According to the SoC and battery state, the decision of
keeping or updating the state is taken. Finally, available battery capacity and updated
SoC are calculated.

72
Figure 4.3 Ship power distribution system model algorithm scheme

73
 Figure 4.4 State-based EMS algorithm scheme

The algorithm of numerical simulation of fuel cell-battery powered ship electricity

distribution plant is initiated with reading data and importing necessary libraries and
functions. The model computes the operation hour and reads the operation mode from
the data. Then, the fuel cell-battery configuration and battery charge-discharge hours
are determined. Empty lists to save calculations of iterations are also created in this
step. In the next step, an iteration over operation dates is initiated and for cases 1 and
2 LNG consumption and emissions are computed. If the case is 3 or 4, battery usage
is to be considered, so a nested iteration is started over total operation seconds. To
control the loop, cycle and operation hour counters are constructed and updated
through the loop. Inside the loop, using pre-written functions by authors, battery
charge-discharge currents were calculated. SoC, SoH, and battery state are determined
and updated using the EMS function explained above. Battery voltage is computed
using SoC-voltage curves provided by the technical datasheets of the battery cells.
Finally, the gas consumption and emissions from the plant are calculated and saved to
the initiated empty lists. The LNG consumption resulting in emissions of PAFC and
MCFC based on the power output (in kW) has been obtained from the technical

74
datasheets of the fuel cells. Assuming that the fuel cells operate at constant efficiency
values shown in Tables 4.2 and 4.3 where their characteristics are given, fuel
consumption values are calculated depending on the required power generation
determined according to the specified configuration and operating modes. The grid-
search iterative selection algorithm tried the combinations of battery charging-
discharging hours within the limits permitted by the manufacturer to obtain the
optimum system performance for each configuration. While the minimum LNG
consumption for each system design is the target of the algorithm, the ideal
charging/discharging times have shaped the optimum EMS logic and schematic.

𝑆𝑆𝑆𝑆𝑆𝑆 is computed using the Coulomb counting method (Saxena, Hendricks & Pecht,
2016; Sepasi, Ghorbani & Liaw, 2015). Equation 4.7 shows the mathematical
expression of the 𝑆𝑆𝑆𝑆𝑆𝑆 calculation over time.

t
SoC(t)=SoC(0)- �� η ∙ I(t)�Cav � (4.7)
0

where 𝑆𝑆𝑆𝑆𝑆𝑆 (𝑡𝑡) is the 𝑆𝑆𝑆𝑆𝑆𝑆 at time 𝑡𝑡, 𝑆𝑆𝑆𝑆𝑆𝑆 (0) is the 𝑆𝑆𝑆𝑆𝑆𝑆 at the beginning of the
operation, 𝐶𝐶𝑎𝑎𝑎𝑎 is the available capacity of the battery, 𝐼𝐼(𝑡𝑡) discharging or charging
current at the time 𝑡𝑡, 𝜂𝜂 is the coulombic efficiency which is taken as 1 in this study.
The charging procedure is constant current with constant voltage, and the discharging
protocol is constant current with a constant C rate. To avoid increased inner resistance
and improve battery life, the SoC range of the batteries in the model is kept between
20% and 80% (Saxena et al., 2016). Voltage is calculated from the function obtained
from SoC-voltage curves (Panasonic, 2021). Equation 4.8 indicates the charge voltage
(𝑉𝑉𝑐𝑐 ) and Equation 4.9 depicts the discharge voltage (𝑉𝑉𝑑𝑑 ) calculations from the SoC for
the selected battery cell.

Vc,2,3,4 =-�0.93 ∙ SoC2 �+(2.02 ∙ SoC)+3.13

(4.8)
Vc,1 =�-29.91 ∙ SoC5 �+�65.73 ∙ SoC4 �-�51.8 ∙ SoC3 �+�17.84 ∙ SoC2 �
-(3.55 ∙ SoC)+4.19

75
 Vd,2,3,4 =�2.45 ∙ SoC3 �-�4.95 ∙ SoC2 �+(04.15 ∙ SoC)+2.48
Vd,1 = �4.042 ∙ SoC5 � - �9.2056 ∙ SoC4 � + �7.87 ∙ SoC3 � (4.9)

− �3.144 ∙ SoC2 � + (0.6 ∙ SoC) + 2.63

The state of health (𝑆𝑆𝑆𝑆𝑆𝑆) is calculated using Equation 4.10 (Omar et al., 2014).

SoH(t)= Cact (t)⁄Cinit (4.10)

where 𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎 is actual and 𝐶𝐶𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 is the initial battery capacity. Equation 4.11 depicts
the calculation of 𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎 obtained from the battery aging curves of specified battery cells
(Panasonic, 2021; PowerXtra, 2021; Molicel, 2018; LGChem, 2014).

Cact =-0.3607 ∙ cb +3412.86 for battery 1

Cact =-0.2374 ∙ cb +3479.6 for batteries 2 and 3 (4.11)
Cact =-0.2171 ∙ cb +3181.4 for battery 4

where 𝑐𝑐𝑏𝑏 is the number of battery cycles. Equation 4.12 depicts the battery-inverter
power conversion calculation.

Pcon =ηcon ∙ Pbat , discharging

� (4.12)
Pbat=ηcon ∙ Pcon, charging

The efficiency factor (𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐 ) of the AC/DC converters in the system are assumed as
0.99 (Ovrum & Bergh, 2015). Battery power is denoted as 𝑃𝑃𝑏𝑏𝑏𝑏𝑏𝑏 and 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐 represents the
converted power.

4.3.2 Environmental Analysis of Hybrid System

The mathematical model computes the emission amounts sourced by diesel fuels
by using emission factors taken over from Kuzu et al. (2021). Equation 4.13 is the
emission calculation and Table 4.6 indicates the emission factors for the MDO and
HFO.

76
 Ei = � θk ∙ EFi (4.13)
k

where E is the total emission, 𝜃𝜃 is the fuel consumption of the vessel, EF is the
emission factor, k is the operation mode and i represents the pollutant type.

Table 4.6 EF of diesel fuels (g emission/ g fuel) (Kuzu et al., 2021)

Pollutant CO2 N2O NOx VOC CO PM SOx
EF MDO 3.206 0.00015 0.0961 0.00308 0.00277 0.00097 0.01
EF HFO 3.114 0.00015 0.0903 0.00308 0.00277 0.00278 0.025

LNG consumption and emissions of the fuel cell-battery configurations are

calculated using Equation 4.14.

mi = � Pk ∙ tk ∙ ∂i (4.14)
k

where 𝑚𝑚 is the pollutant or LNG mass in kg, P is the required total power of the
operation, t is the operation time in hours, and 𝜕𝜕 is the emission or gas consumption
coefficient given in Tables 4.2 and 4.3.

4.3.3 Economic Analysis of Hybrid System

Economic analyses of the specified configurations have been carried out to detect
the feasibility of systems. Investment costs are calculated considering the inflation
between the year of gathered price information and 2022 by using the Chemical
Engineering Plant Cost Index (CEPCI). The prices are obtained as $1,125,000/unit for
the PAFC project in 2006 and $4,992,000/unit for the MCFC project in 2010. The
current prices are estimated as shown in Equation 4.15 and Equation 4.16:

Cost2022,PAFC = Cost2006,PAFC ∙ ( CEPCI2022⁄CEPCI2006 ) (4.15)

Cost2022,MCFC = Cost2010,MCFC ∙ ( CEPCI2022⁄CEPCI2010 ) (4.16)

77
 where 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶2006 = 499.6, 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶2010 = 550.8 (Turton, Shaeiwitz, Bhattacharyya
& Whiting, 2018), 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶2022 = 806.3 (Jenkins, 2022).

Following the cost determination, the capital recovery factor (CRF) is shown in
Equation 4.17, which converts the entire current value to a flow of even yearly
payments at the annual interest rate (i = 5%) over the system life (LT) of 10 years for
fuel cells (Kanuri, 2012), and the life span of batteries computed using the ordinary
least squares regression (Tian, Zeng, Gu, Zhang & Yuan, 2021; Yang & Yeh, 2018).

CRF= i ∙ (1+i)LT�[(1+i)LT -1] (4.17)

The levelized energy cost (LEC) is the ratio of the entire cost, including
maintenance and operating costs (𝐶𝐶𝑜𝑜𝑜𝑜 ), to the annual energy produced by the plant, as
established in Equation 4.18 by (Tian et al., 2021):

LEC=(CRF ∙ Cost2022 + Costom )/(Ẇ net ∙ t) (4.18)

where 𝐶𝐶𝑜𝑜𝑜𝑜 is taken as 1.5% of the total cost (𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶2022 ), 𝑊𝑊𝑛𝑛𝑛𝑛𝑛𝑛 is the net power
output from the plant, and t is the working hours. The working hours are computed
using the reference tanker ship's real-time operational data acquired from port calls
and position histories. 𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒 is the cost of electricity, which is computed from fuel prices
and total energy production of plants as given in Equation 4.19 (Yang & Yeh, 2018):

cele = � θk ·Costfuel,j /(Ẇ net ·t)k (4.19)

k

where k is the operation mode, 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 is the fuel price, and j is the fuel type used
in the specified operation modes. The conventional plant utilizes very low sulfur fuel
oil (VLSFO) during navigation and marine gas oil (MGO) near coastal areas. The
average prices for the specified date range and current prices that have risen due to
global political agenda were taken for both diesel fuels (for twenty ports average) and

78
LNG (for Rotterdam port) from (Ship and Bunker, 2022). Current prices were obtained
on May 30th, 2022, and given in Table 4.7.

Table 4.7 Bunker prices for diesel fuels and LNG (Ship and Bunker 2022)
Fuel Price Reference Bunker Price ($/t)
Two-years average 461.5
VLSFO
Current 988
Two-years average 530
MGO
Current 1,275
Two-years average 810.5
LNG
Current 1,509

4.4 Results and Discussion

4.4.1 Mathematical Modeling Results of the Fuel Cell/Battery Hybrid System on

Chemical Tanker Vessel

The grid-search iterative selection algorithm iterated over specified batteries and
charging-discharging hour combinations that targeted to find the configurations having
minimum fuel consumptions. Charge and discharge times were tried between 3 and 8
hours. Table 4.8 indicates the optimum batteries and charging-discharging
combinations retrieved from grid-search iterative selection algorithm results. Results
provided that the lowest LNG consumption is achieved when B2 batteries are used
during navigation, and B4 batteries give the best results when these are not used during
navigation phases. The fastest charging and the slowest discharging combination gave
the best results for all battery-utilized combinations. The long-term support of the
batteries to the system has had a positive effect on reducing the LNG consumption of
the FCs.

Table 4.8 Optimum batteries and charge-discharge hours

Configuration Battery Charge Discharge Battery Usage During
Code Code Hour Hour Navigation
C3 B2 3 8 Yes
C4 B2 3 8 Yes
C5 B4 3 8 No
C6 B4 3 8 No

79
 The environmental and economic analyses were carried out using the calculated
fuel consumption of D/Gs and fuel cell/battery hybrid systems for six different
configurations. The fuel consumption of each operation mode and their environmental
effects were taken into consideration in the analyses. It is important because the
calculations are based on the utilization of VLSFO during navigational phases and
MGO during non-navigational phases. Figure 4.5 indicates the total fuel consumption
of the combinations and fuel consumption distribution according to operation modes
for 2 years of operation of the reference vessel.

Figure 4.5 Fuel consumptions on different operation modes and total fuel consumption of the proposed
combined systems and D/G plant

The conventional D/G plant consumes 2,349.36 t of VLSFO during navigation

operations and 1,186.15 t of MGO for port and anchorage operations. Without using
the batteries, fuel cell configurations of C1 and C2 consume 2,731.56 t and 2,789.93 t
of LNG, respectively. 211.37 t of LNG saving was attained for the MCFC/battery
hybrid configuration (C5) when the batteries support port and anchorage operations in
comparison with the C1 configuration. The PAFC/battery system with battery usage
during coastal operations (C6) provided an LNG saving of 215.89 t when compared
with the PAFC/battery hybrid system of C2.

80
 The most remarkable fuel consumption reductions were achieved in C3 and C4
cases where the batteries support all operations. Especially, LNG consumption of C3
and C4 configurations during navigation was reduced to 1,343.01 t and 1,371.71,
respectively. It indicates that an LNG saving of %26.7 during navigation operations
and a total of 25.6% fuel savings could be achieved by utilizing batteries with fuel
cells at all operations. For the port and anchorage operations, C5 and C6 ensured
slightly lower LNG consumption due to the increased SoH of batteries compared to
C3 and C4. The total LNG consumptions are higher for PAFC systems because of the
higher specific LNG fuel consumption compared to MCFC systems. Since the power
output of the PAFC system is less, the system design was made to run more than one
PAFC in parallel. In the MCFC system, on the other hand, the number of operating
MCFCs mostly remained constant due to the higher power output. The impact of
battery usage in reducing LNG consumption was greater in PAFC systems because
battery usage reduces the number of PAFCs utilized for the operation. In general, the
battery-pack utilization during the navigation decreases the LNG consumption
remarkably for each FC type.

4.4.2 Environmental Analysis of the Hybrid System

This section highlights the environmental impacts of the selected combinations and
their potential to reduce air pollutant emissions. Table 4.9 depicts the potential
emission reduction percentages of each combination compared to a conventional D/G
plant. The emission coefficients provided by the commercial PAFC and MCFC
catalogs were used to calculate the air pollutant amount. N/A values represent that the
emission coefficient is neglected in the fuel cell catalog.

Potential N₂O emissions were completely prevented and the production of NOx,
PM, SOₓ, VOC, and CO emissions can be largely avoided by utilizing proposed system
configurations. Especially for increasing the air quality near coastal areas, fuel cell
plants can be promising alternatives. Although LNG usage still caused CO2
production, a remarkable amount of CO2 emissions can be prevented by fuel cell
plants. The battery support to fuel cells reduced LNG consumption, which also impacts

81
CO2 reduction positively. Figure 4.6 shows the total CO2 production and distribution
of CO2 emissions according to operation modes for each fuel cell/battery hybrid
configuration and D/G plant.

Table 4.9 The emission reduction potential of the proposed system configurations compared to
conventional diesel generators
Pollutant
C1 (%) C2 (%) C3 (%) C4 (%) C5 (%) C6 (%)
Type
CO₂ 32.44% 31.00% 49.75% 48.67% 37.67% 36.34%
N₂O 100% 100% 100% 100% 100% 100%
NOₓ 99.98% 99.95% 99.98% 99.97% 99.98% 99.96%
VOC N/A 98.60% N/A 98.96% N/A 98.71%
CO N/A 99.14% N/A 99.36% N/A 99.20%
PM 99.998% N/A 99.999% N/A 99.998% N/A
SOₓ 99.9989% N/A 99.9992% N/A 99.999% N/A

Figure 4.6. CO2 production on different operation modes and total fuel consumption from the fuel
cell/battery hybrid systems and D/G plant according to operation modes
The fuel-cell battery hybrid system configurations produced fewer CO2 emissions
compared to the conventional D/G plant. Particularly, the C3 and C4 reduced the total
CO2 emission in two years by 5,531.06 t and 5,411.64 t respectively. Lowering the
LNG consumption with battery support provided CO2 emission reductions of 1,006.35
t and 977.65 t during navigation for the respective system designs. Battery support on
fuel cells also made a difference to lower CO2 for the other operations. The

82
environmental effect of C3 and C4 are considerably lower than other combinations
regarding CO2 reductions. Especially, to achieve the decarbonization goals set by IMO
and European Union, the utilization of FC plants as the auxiliary power units on large
commercial marine vessels is a feasible option according to the analysis. If the
infrastructure of fuel-related resources is prepared, installing commercially available
FC units in newly constructed ships, and retrofitting older ships can be a solution for
reducing CO2 emissions. Figure 4.7 illustrates the remaining emissions from the D/G
plant and fuel cell/battery hybrid systems according to each operation mode. In the
subplots of Figure 4.7, the left vertical axes represent the D/G emissions, and the right
vertical axes show the fuel cell/battery hybrid system-based emission productions.

Figure 4.7 highlights that the fuel cell/battery hybrid configurations can prevent
approximately 326 t of NOx and 70 t of SOₓ emissions in two years. These values are
crucial considering that the emission reduction calculation involves only the auxiliary
engines of one vessel. Among fuel cell-battery systems, the configurations that utilize
the battery support provided a greater reduction potential for these emissions. In terms
of the prevention of emissions from marine vessels, fuel cell plants showed satisfactory
performance. The investment related to capturing SOx and NOx on board can be shifted
towards the FC technology to achieve sustainable transportation.

83
Figure 4.7. The production of (a) NOx, (b) PM, (c) VOC, (d) CO, (e) SOx, (f) N₂O emissions from plants
for different operation modes

4.4.3 Economic Analysis of Hybrid System

The environmental analysis results showed that all fuel cell/battery hybrid
configurations could reduce fuel consumption and CO2 emissions by 31 - 49.75%
when compared with D/G utilization. The utilization of batteries during navigation,
given as C3 and C4 configurations, increased the energy efficiency of the vessel. The
utilization of batteries for longer service periods will increase the completed
charge/discharge cycles, cause a reduction in the battery life and increase the systems’
investment costs throughout their lifetime. In this section, the economic performance
of the six-fuel cell/battery hybrid configurations was investigated considering LEC
and 𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒 .

84
 The estimation of the battery lifespans was ensured from SoH variation curves. SoH
curves of the cases that examine battery usage during the navigation are shown in
Figure 4.8. Ordinary least square regression was fitted to these curves to predict the
life of the battery.

Figure 4.8 SoH curves of batteries were (a) utilized (b) not utilized during the navigation

When the batteries were utilized during navigation, battery life was calculated as
3.75 years. The battery life can be expanded up to 11.62 years without using the
batteries when the ship is on the course. Even though battery utilization during
navigation provides remarkable emission reduction, the battery lifespan is affected
negatively by this type of usage frequency. Table 4.10 highlights the battery lifespans,
weight, volume, and costs of the fuel cell-battery configurations. PAFC systems have
slightly lower weights and volumes compared to MCFC units. C4 has the lowest
weight and volume compared to other combinations due to the lower number of fuel
cells. The investment cost of the PAFC units was also lower than MCFC units. C5
and C6 require one set of battery packs during the system’s lifetime. On the other hand,
battery sets should be replaced three times for C3 and C4, which vastly increases the
costs of the combinations.

LEC is defined as the investment costs including operation and maintenance costs
per unit of energy production of the hybrid configurations. The normalized values
indicate comparable data to assess the economic performance of the proposed
configurations regarding the investment costs. LEC values for each configuration were
calculated by using Eq. 18 and the results were depicted in Figure 4.9. It can be seen
that the LECs of PAFC configurations (C2-C4-C6) were found lower than MCFC
configurations (C1-C3-C5). The lowest LEC was obtained from the C6 configuration.

85
This result is expected because the battery sets of C3 and C4 configurations need to be
changed two times in the given system lifetime of 10 years due to high utilization time
in total voyages, which causes rapid degradation of batteries and an increased number
of charge/discharge cycles. It is also lower than the C2 configuration because of one
more fuel cell utilized in C2, and non-utilized batteries added to the C2 configuration
for safety concerns.

Table 4.10 Weights, volumes, costs, and battery lifespans of the system configurations
Configuratio
C1 C2 C3 C4 C5 C6
ns
𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 [$] 14,847,237 11,232,101 17,869,685 12,332,537 15,262,309 9,725,161

𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝒐𝒐𝒐𝒐 [$] 222,708 168,481 268,045 184,988 228,934 145,877

Battery Code B4 B4 B2 B2 B4 B4
Number of
133 194 339 339 371 371
parallel cells
System
564.98 533.86 569.68 448.94 570.33 449.59
Volume (m3)
Weight (t) 200.31 175.02 203.43 148.52 204.04 149.13
Battery Life
- - 3.75 3.75 11.62 11.62
[years]

However, the LEC values should be evaluated by considering the environmental

and remaining economic analysis results because LEC values do not involve the fuel
consumption of specified systems and can be considered as a base for comparing the
investment costs.

0.054
C5 0.085
0.069
C3 0.100
0.063
C1 0.083
0.000 0.020 0.040 0.060 0.080 0.100 0.120
LEC ($/kWh)

Figure 4.9. LEC values obtained for each configuration mode

86
 𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒 of all configuration modes were obtained by using the fuel prices of LNG in
Eq. 20 and given in Figure 4.10 VLSFO utilization during navigation and MGO
utilization near coastal areas were taken into consideration for the calculation of 𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒
values of D/G usage onboard to compare the existing electricity production cost of the
vessel with the results of proposed configuration modes. The economic analyses for
𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒 values were carried out using two parameters as current fuel prices and average
fuel prices of 2 years when the operational data of the vessel were taken. The analysis
results showed that 𝑐𝑐𝑒𝑒𝑙𝑙𝑒𝑒 of C3 configuration is the lowest. High price hikes in the MGO
market decreased the economic feasibility of electricity generation with D/Gs.
Although LNG fuel prices are higher than MGO and VLSFO prices for both scenarios,
it can be seen that 𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒 of C3-C4 configurations are very competitive when compared
to onboard electricity production with D/Gs, considering the decrease in the fuel
consumption of the vessel with the proposed fuel cell/battery hybrid configurations.
𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒 of the proposed systems increased by almost 2 times compared to average fuel
prices of 2 years.

0.30
0.243 0.248
0.25 0.224 0.229 0.226
0.181 0.185
0.20
cele ($/kWh)

0.131 0.133 0.123

0.15 0.120
0.097 0.099 0.101
0.10

0.05

0.00
C1 C2 C3 C4 C5 C6 D/G
Average Fuel Prices (2 years) ($) Current Fuel Prices ($)

Figure 4.10 Electricity production costs of utilizing fuel cell/battery hybrid configurations and D/Gs
onboard

87
 CHAPTER 5
CONCLUSIONS

In this thesis, the parameter optimization problem for H-1000XP PEMFC was
handled using nine relatively novel algorithms. Initially, to validate this solution
methodology, the results found by E-CGA were compared with experimental test
values of a 250 W PEMFC gathered from (Mo et al. 2006). The manufacturer data for
the H-1000XP PEMFC was used for the comparison of the different algorithms. The
algorithms were evaluated regarding error rate with various metrics, run time, and
objective function efficiency. Three MADM methods were utilized to rank the
algorithms according to the mentioned criteria. The main conclusions derived from the
thesis are listed below:

• MFA algorithm was ranked as the best by all MADM methods and ensured the
optimum solution set with low SSE, runtime, and high objective function
efficiency. One of the evolution-based algorithms, DE, also offered reliable
performance and was placed second. These two methods were found suitable for
the given issue, and their performances could be further improved with targeted
hyper-parameter tuning.

• In terms of objective function efficiency, R2 and MAE, IGWO, and GWO provided
the best results. However, the runtime was remarkably higher for this algorithm
yielded be ranked 9th by TOPSIS. Due to the same reason, MOORA and
PROMETHEE selected GWO for the 7th rank which is not a satisfactory ranking
either. However, in the consistency requiring applications, it could be considered a
valid option. Its runtime could be optimized, and SSE could be lowered with a
hyper-parameter tuning either.

• Convergence speeds of the MFA and IGWO were also found as the best which
means the 1000 iterations could be lowered to decrease the running times of these
algorithms.

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• Among the convergence speeds of the best solution sets, IWOA was the fastest
algorithm for finding the ideal solution before the 100th iteration. Its running time
could be decreased remarkably by ensuring parameter tuning.

• JAYA and CS algorithms were found to be not suitable for this problem. JAYA
solved the problem with a competitive runtime, but its objective function efficiency
and convergence speed was the worst among others. The runtime of the CS was
lower than GWO and IWOA however, compared to other algorithms it remained
slow. The objective function efficiency of the CS was slightly better than JAYA,
but its error metrics were the worst which made it unsuitable for the application.
MADM methods ranked these two algorithms in low spots either.

In conclusion, this study provides valuable insights into the parameter optimization
of H-1000XP PEMFC and suggests several areas for future research. The parameter
optimization of PEMFC has been a frequently studied topic and numerous algorithms
were tried on various FCs. This thesis presented an optimization algorithm
benchmarking to detect the parameters of H-1000XP PEMFC. The results of this thesis
could be useful for scientists that aim to build a mathematical model or investigate the
algorithms to solve a similar problem for the specified FC. Some recommended areas
for future studies include expanding the benchmarking with the addition of different
algorithms, a more specialized hyperparameter tuning of mentioned algorithms with
various prominent features, and a verification process of the determined parameters
using the experimental data which will be obtained by laboratory trials of H-1000XP
PEMFC.

In this thesis, the conventional ship power distribution plant of a 50,000 DWT
oceangoing tanker vessel involving three equivalent D/Gs was simulated using a
Python environment. The realistic fuel consumptions of D/Gs are calculated by
regarding the power demand of the vessel at varying loads in each operation with a
numerical model. The ship trial test data of onboard D/Gs were used to model the plant
according to six different operation modes. The utilization hours of these modes were
obtained from port calls and position history data between 06 December 2019/06

89
December 2021. The route of the ship involved oceangoing navigations mainly on the
Europe-North America route.

This thesis aimed to analyze and discuss the potential environmental and economic
impacts of implementing fuel cell/battery hybrid configurations instead of marine
D/Gs to compensate for the electricity demand of the vessel. The novelty of the theis
is as follows:

• There have found no studies in the literature related to environmental and economic
analyses of fuel cell-battery hybrid system designs that can fully meet the electricity
demand of ocean-going tanker ships.

• Although there are commercially available PAFC products, they have not yet been
evaluated for marine applications.

• Marine applications of MCFC systems are found to be limited with MCFC

utilization on main propulsion units of small vessels. They have not been used to
supply all of the auxiliary power demand of large vessels.

• The literature survey shows that there have been no studies that evaluate the most
suitable battery brand and charge-discharge hours for PAFC and MCFC systems
with a grid-search algorithm.

In this regard, commercially available PAFC, MCFC, and battery sets were
selected. Six different configurations of fuel cell-battery combinations were
investigated to obtain the optimum system layout. A state-based EMS was designed to
control the charge/discharge processes of the batteries. Hybrid configurations were
proposed in the first two configurations (C1 and C2) as the batteries are only utilized
to meet the rapid load changes required from the vessel. C3 and C4 configurations
were modeled to continuously utilize the batteries on all operations of the vessel. C5
and C6 used batteries only in coastal operations having frequent load changes to

90
increase the battery life, thus the navigation operations were not included. The main
conclusions derived from the thesis were given as follows:

• Results show that the lowest LNG consumption is achieved when B2 batteries are
used during navigation, and B4 batteries give the best results when they are not used
during navigation phases.

• The fastest charging and the slowest discharging combination gave the best results
for all battery-utilized combinations.

• LNG consumption of C3 and C4 configurations during navigation was reduced to

1,343.01 t and 1,371.71, respectively. It indicates that an LNG saving of %26.7
during navigation operations and a total of 25.6% fuel savings could be achieved
by utilizing batteries with fuel cells at all operations.

• Potential N₂O emissions were completely prevented and the production of NOx,
PM, SOₓ, VOC, and CO emissions can be largely avoided by utilizing proposed
system configurations.

• Although LNG usage still caused CO2 production, a remarkable amount of CO2
emissions can be prevented by fuel cell plants. The battery support to fuel cells
reduced LNG consumption, which also impacts CO2 reduction positively. The
utilization of fuel cell/battery hybrid configurations could reduce fuel consumption
and CO2 emissions by 31 - 49.75% when compared with D/Gs.

• When the batteries were utilized during navigation, battery life was calculated as
3.75 years. The battery life can be expanded up to 11.62 years without using the
batteries when the ship is on the course.

• The LECs of PAFC configurations (C2-C4-C6) were found to be lower than MCFC
configurations (C1-C3-C5). The lowest LEC was obtained from the C6
configuration as 0.054 $/kWh. This result is expected because the battery sets of C3

91
 and C4 configurations need to be changed two times in the given system lifetime of
10 years due to high utilization time in total voyages, which causes rapid
degradation of batteries and an increased number of charge/discharge cycles.

• The lowest 𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒 was found to be a C3 configuration with the values of 0.181 and
0.097 $/kWh for the current fuel prices and average fuel prices of 2 years when the
operational data of the vessel were taken, respectively.

• C3-C4 configurations are very competitive when compared to onboard electricity

production with D/Gs, considering the decrease in the fuel consumption of the
vessel with the proposed fuel cell/battery hybrid configurations. 𝑐𝑐𝑒𝑒𝑒𝑒𝑒𝑒 of the
proposed systems increased by almost 2 times compared to average fuel prices of 2
years.

The limitations of the thesis are as follows:

• The LNG consumption of fuel cells was calculated from technical datasheets at the
given efficiency values.

• In the utilization times of the operation modes, maneuvering durations were added
to the port operations’ utilization due to the close electric demand, and lack of exact
maneuvering times.

• The small changes in the operational load during operations were neglected and
assumed constant loads.

In future studies, the analyses can be extended with different fuel cell technologies,
e.g., PEMFC and SOFC. A detailed mathematical model of the specified fuel cell types
can be implemented to deepen the analyses. The operational load and utilization time
data of the marine diesel generators can be improved by collecting from a commercial
ship in more detail with more frequent timestamps to improve the accuracy of the

92
electric load model. Different types of EMS algorithms can be utilized in the model to
evaluate the system performance by comparing the outputs of the algorithms.

93
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