The role of solid oxide fuel cells in future ship energy systems

Abstract

With rising concerns about emissions from shipping, fuel cells are expected to take an important role in ship propulsion. In particular, solid oxide fuel cells (SOFC) offer high efficiency with the possibility of combined heat and power production.
In this paper, we investigate energy, cost, and emission savings on ships resulting from the use of SOFCs using an optimization-based approach. A global sensitivity analysis was used to investigate the effects of the high uncertainty of problem parameters. This setup is applied to two case studies: a cruise ship and a tanker.
The results show that SOFCs could provide a reduction in ship greenhouse gas emissions by up to 34% and that when using natural gas as fuel, SOFCs are the most cost-optimal solution that allows a significant reduction in GHG emissions. A wider adoption of SOFCs would also lead to a decrease of other pollutant emissions. The sensitivity analysis shows that the lifetime of the stack is the most impacting uncertain parameter, followed by fuel prices and by the investment cost of the SOFC stack.
The study highlights that, in a future of stricter constraints on greenhouse gas emissions and where the SOFC technology will be fully industrialized, SOFCs will be able to play an important role in bridging shipping towards decarbonization.

Full text

Energy, Vol. 194, No. 1, 2020.
DOI: https://doi.org/10.1016/j.energy.2019.116811
The role of solid oxide fuel cells in future ship
energy systems
Francesco Baldia,b*, Stefano Moretb,c, Kari Tammid, Franc¸ois Mar´
echalb
Abstract
With rising concerns about emissions from shipping, fuel cells are expected to take an important role in ship
propulsion. In particular, solid oxide fuel cells (SOFC) offer high efficiency with the possibility of combined heat
and power production. In this paper, we investigate energy, cost, and emission savings on ships resulting from
the use of SOFCs using an optimization-based approach. A global sensitivity analysis was used to investigate
the effects of the high uncertainty of problem parameters. This setup is applied to two case studies: a cruise
ship and a tanker. The results show that SOFCs could provide a reduction in ship greenhouse gas emissions by
up to 34% and that when using LNG as fuel, SOFCs are the most cost-optimal solution that allows a significant
reduction in GHG emissions. A wider adoption of SOFCs would also lead to a decrease of other pollutant
emissions. The sensitivity analysis shows that the lifetime of the stack is the most impacting uncertain parameter,
followed by fuel prices and by the investment cost of the SOFC stack. The study highlights that, in a future of
stricter constraints on greenhouse gas emissions and where the SOFC technology will be fully industrialized,
SOFCs will be able to play an important role in bridging shipping towards decarbonization.
Keywords
solid oxide fuel cells — low carbon shipping — ship energy systems — ship propulsion — multi-objective
optimization — global sensitivity analysis
aIntegrated Energy Systems, Italian National Agency for New Technologies, Energy and Sustainable Development (ENEA), Via Martiri di
Monte Sole 7, 40129 Bologna, Italy
bIndustrial Process and Energy Systems Engineering (IPESE), ´
Ecole Polytechnique F´
ed´
erale de Lausanne (EPFL), Rue de l’Industrie 17,
1950 Sion, Switzerland
cBusiness School, Imperial College London, Ayrton Rd, Kensington, London SW7 2AZ, United Kingdom
dSchool of Engineering, Department of Mechanical Engineering, Aalto University, Espoo, Finland
*Corresponding author: francesco.baldi@enea.it
Contents
1 Introduction 1
1.1
A brief outlook on shipping and its impact on the
environment ..........................1
1.2 Shipping and global warming . . . . . . . . . . . . . . 2
1.3 The potential of fuel cells . . . . . . . . . . . . . . . . . 2
1.4
Research and development of SOFCs in shipping 3
1.5Gapandaim ..........................4
2 Method 4
2.1 Optimization of the ship energy system . . . . . . . 4
2.2 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . 7
3 Application 7
3.1Casestudies ..........................7
Cruise ship •Chemical tanker
3.2 Problem parameters . . . . . . . . . . . . . . . . . . . . . 9
Solid oxide fuel cell
•
Internal combustion engines
•
Gas boilers
•
Heat pumps
•
Batteries
•
Other cost-related parameters
•
Emission factors •Ship demand
4 Results 12
4.1 Multi-objective optimization . . . . . . . . . . . . . . . 12
4.2 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . 13
5 Discussion 16
5.1 Results discussion . . . . . . . . . . . . . . . . . . . . . 16
5.2Futurework..........................17
6 Conclusion 18
References 18
1. Introduction
The shipping industry has a strong impact on the maritime
and global environment and is expected to grow in the coming
years due to increasing trade and passenger volumes. The use
of fuel cells, given their high efficiency and low emissions,
can be a solution to this issue.
1.1 A brief outlook on shipping and its impact on
the environment
Shipping is one of the fastest growing industries in the world,
given its strong ties with international trade [
80
]. The amount

The role of solid oxide fuel cells in future ship energy systems — 2/22
of goods transported by sea has increased by more than 150%
since 1990, and is still expected to grow as a consequence
of global economic development. While aviation and rail
transport challenge shipping for some specific trades, it is
widely recognized that the economy relies heavily on ship-
ping, and that there is no other transportation mode that can
compete in terms of costs, operational flexibility, requirements
of infrastructure, and reliability [80].
Despite its beneficial effect on economic development,
shipping is an important source of harm for humans and for the
environment because of its pollutant emissions. It is estimated
that approximately 70% of the emissions from shipping are
emitted within 400 km of land, making shipping a relevant
environmental concern not only for coastal areas [18].
Most of the attention has historically focused on three ma-
jor pollutants: nitrogen oxides (NO
X
), sulphur oxides (SO
X
)
and particulate matter (PM). In more recent years, however,
as a consequence of the increased awareness at a global level,
CO
2
emissions from shipping have become more important
on the agenda of maritime stakeholders.
1.2 Shipping and global warming
Shipping is estimated to contribute to between 2-3% of global
CO
2
emissions [
71
]. If the shipping sector was a country,
it would be the seventh largest global contributor to anthro-
pogenic CO2emissions, between Japan and Germany [62].
As a consequence of international pressure, the Interna-
tional Maritime Organization (IMO, the body of the UN that
regulates international shipping) has addressed the issue of
reducing greenhouse gas (GHG) emissions from shipping.
In 2013 the Energy efficiency design index (EEDI) and the
Ship energy efficiency management plan (SEEMP) were in-
troduced with the aim of increasing the efficiency in ship
design and operation, respectively [
48
]. While these measures
represented a step forward for a reduction of CO
2
emissions
from shipping, their effectiveness was quickly criticized by
experts in the field, as they were deemed inaccurate and weak
[71, 41].
More recently, however, efforts further intensified. In
2018 the IMO officially adopted an initial strategy aiming at
reducing GHG emissions from shipping by 50%, compared
to 2008 levels, by 2050, and to work towards a complete
decarbonization by the end of the century [49].
Researchers have been working on making ships more
energy efficient since long before IMO regulations, often
in relationship with increases in oil prices. Traditionally,
research focused on hull and propeller lines [
47
,
44
], but
in recent years researchers started to investigate a wider set
of options for reducing fuel consumption and, hence, carbon
emissions [39].
Operational solutions are generally characterized by low
initial costs, but also by a relatively limited potential in fuel
savings. Operational solutions have a potential for reducing
GHG emissions lower than 10%, apart from case of lowering
the speed (which, however, has wider implications such as the
increase in fixed and inventory costs) [48].
Design solutions show a relatively higher potential, but
still not definite solution to the problem. Waste heat recovery,
despite the impressive volume of research produced in this
field [
53
], was estimated to have a potential for reducing
emissions of up to only 8% [
48
]. Even in the case of solutions
with higher maximum potential, such as air lubrication and
wind propulsion, it should be noted that the estimated benefits
are much dependent on the ship type and route, and only in
few cases the upper-boundary of the range is considered to be
achievable.
Among more impacting solutions, battery-powered ships
have become a reality in recent years; most applications are
seen in hybrid systems, for peak-shaving [
86
,
30
], with ex-
pected savings of up to 20% with, however, only few cases of
full battery-powered vessels [
51
]. Unfortunately, even assum-
ing a further increase in battery performance and a decrease
in price, batteries are still seen as a solution for short- to
medium-range shipping, but not for intercontinental trade.
1.3 The potential of fuel cells
In this context, there has recently been a rising interest in the
use of fuel cells for marine propulsion.
Fuel cells provide generally very favourable conditions
from an environmental perspective. They operate with virtu-
ally no direct pollutant emissions, even when carbon-based
fuels are used. They show a high conversion efficiency, par-
ticularly at medium-low load, which is where ships are most
often operated during their lifetime [
7
], and they are highly
modular, making them effective almost regardless of the in-
stalled size.
Fuel cells are generally classified as either low- or high-
temperature fuel cells. Among low-temperature fuel cells,
proton-exchange membrane fuel cells (PEMFC) are efficient
(up to 60% gross efficiency, [
82
]), relatively compact, and
behave well in dynamic conditions, making them a potentially
very promising candidate for transportation, where they have
been successfully tested for applications on cars, buses, and
on ships [
35
]. Their main limitation lies in the lack of fuel
flexibility: PEMFC can only be run on hydrogen, and if other
fuels are used they need to be first converted to hydrogen;
the PEMFC catalyst is very prone to poisoning, and hence
requires high-purity hydrogen. This requirement is particu-
larly challenging for long-distance operations, as storing large
quantities of pure hydrogen is a non-trivial challenge. In these
regards, [
81
] estimated that, for voyage times above approxi-
mately 100 h, the use of PEMFCs for ship propulsion becomes
difficult because of their need to run on pure hydrogen.
High-temperature fuel cells can use different catalysts as
a consequence of the higher operational temperature. In these
conditions, CO
2
and CO molecules are no longer poisoning,
and CO can even act as a potential fuel. Solid oxide fuel cells
(SOFC) in particular offer a high fuel flexibility for various
gases and liquids, e.g., methane, ethanol, methanol, propane,
LPG, diesel, DME, ammonia, and more. More importantly,

The role of solid oxide fuel cells in future ship energy systems — 3/22
SOFCs have demonstrated their high efficiency, high availabil-
ity and reliability, and good durability. State-of-the-art SOFC
systems provide an electrical efficiency of around 60% and a
CHP system efficiency up to 85-90% [
34
]. SOFC-GT hybrid
system can even achieve electrical efficiencies of as high as
70% [
13
]. Although lifetime is also considered an issue for
SOFCs, system duration of 40 000 hours are a reasonable
objective for SOFC technology [
78
], and a runtime record
of SOFC systems of 10-year continuous operation has been
recorded [73].
SOFCs can therefore be identified as the most potential
fuel cell technology for medium to long distance ship appli-
cations. However, due to the slow start-up and load shifting,
SOFCs are expected to handle base loads of thermal and elec-
tric energy demand, hence built within a hybrid system where
other components (engines, PEMFCs, batteries) take care of
the dynamic behavior of the demand.
1.4 Research and development of SOFCs in ship-
ping
Despite being more the exception than the rule, there are
documented cases of fuel cells being used in ship energy
systems.
Most of the working examples are related to the use of
PEMFCs, as a consequence of the higher maturity of the tech-
nology. PEMFCs have been successfully used on submarines
[
69
] and tested for long periods on a passenger ferry [
87
]. A
more thorough review of these systems on board ships can be
found in [81].
In general, the advantages in terms of low noise and vibra-
tions have historically made naval applications to be among
the first to be tested. In these regards, the US Navy succesfully
tested the use of SOFCs for the propulsion of torpedo boats
in slow-cruising mode [
33
], while a steam turbine is used
to power the propeller during the high-speed mode. While
this application has limited interest for the broader market
of merchant ships, it still provides a convincing validation
for the fact that SOFCs can withstand the challenges of the
maritime environment [
32
,
31
], and that they can be used suc-
cessfully also in applications with tight limitations in volume
and weight.
In addition to their use in naval applications, SOFCs have
been often suggested for use as auxiliary power units (APU)
[
22
]. Fuel cells, working at high efficiency over a wide range
of loads and directly generating electric energy, are particu-
larly suitable for this application, and the interest in SOFCs
is mostly related to the ability of these systems to use a wide
range of fuels.
Many of the cases cited in literature refer to the use of
SOFCs in combination with an external reformer fuelled with
Diesel, something which would make the system easy to adapt
to current ship energy systems. These systems can achieve
up to 55% [
75
,
24
] electrical efficiency, with the additional
potential for providing high-temperature heat, resulting in a
net fuel consumption reduction of close to 50%. These types
of systems were also tested in experimental conditions (as
opposed to modelling studies), with promising results [59].
In addition to Diesel-powered units, other arrangements
for SOFC-based APUs were proposed, such as the use of
methanol [
65
], considered a promising alternative to conven-
tional fuels, and in combination with solar panels and elec-
trolyzers, with the aim of only using the SOFC in port when
the main engines are not in operation [63].
Despite the beneficial effects on fuel consumption, the use
of SOFCs for auxiliary power generation can only achieve
limited results. In most ships propulsion constitutes the largest
part of the energy demand (see, for instance, [
3
], where propul-
sion is documented to represent 70% of the energy demand for
a chemical tanker, or [
76
] and [
10
], where this contribution is
estimated between 76% and 88% for fishing vessels). Engines
used for propulsion have high operational efficiency (large
two-stroke engines can reach 55% efficiency), and benefits
are expected to be lower when compared to the substitution
of auxiliary engines. Nevertheless, SOFCs have several ad-
vantages when compared to low-speed Diesel engines:
•They have no direct emissions of NOXand PM.
•
They maintain the high conversion efficiency over a
very wide range of operations.
•
The modular nature improves the redundancy of a hypo-
thetical SOFC-powered system: having a system pow-
ered by ten 1 MW cells instead of one 10 MW Diesel
engine makes it inherently safer.
•
The direct generation of DC electricity from the SOFC
allows high freedom in the regulation of rotating ma-
chines such as compressors, pumps, and propellers.
•
When operated on natural gas, they do not have prob-
lems of methane slip, which was shown to have the
potential of completely offsetting the benefits of using
a low-carbon fuel [12].
Several researchers have hence investigated the potential
benefits and challenges of a ship design where the SOFC pro-
vides most, if not all, of the on board power demand. The
system proposed by [
19
] relies on Diesel engines for the main
propulsion system, while recurring to SOFCs for low speed
(and, hence, low power) operations. While the majority of
the fuel savings achieved in the work of [
19
] are a conse-
quence of the reduction in the speed of the ship, the use of
SOFCs provides additional benefit to the system’s operations.
Similary, in the work proposed by [
2
], the largest share of
the energy demand is still provided by two-stroke dual-fuel
Diesel engines, but a GT-SOFC hybrid unit is connected to
the same switchboard in a full-electric system, and can hence
contribute to the ship’s energy demand for both hotel load and
propulsion. The high efficiency of the system makes it suit-
able for fulfilling EEDI regulations even for phase 4, related
to ships built after 2040. The hybrid GT-SOFC system was
also proposed by [
25
] and [
40
] for naval applications. These

The role of solid oxide fuel cells in future ship energy systems — 4/22
systems have a very high theoretical efficiency of up to 70%,
but are still not available commercially.
The low power density of SOFCs is often considered as
a major obstacle to a more widespread adoption of these sys-
tems in transportation. While PEMFCs have power densities
comparable to Diesel engines, most of the SOFCs available
today on the market have a relatively low power-to-weight
and power-to-volume ratio. Even though volume- and weight-
related constraints are not as strict for ships as they are for cars,
buses and planes, it is still true that any extra volume taken
the ship’s power plant cannot be used for transporting cargo.
In the work of [
19
] the design of the proposed power system
also included drawings of the system layout, thus showing the
feasibility of the system from this perspective. This limitation
is, however, rarely addressed in scientific literature.
1.5 Gap and aim
As shown in the review of existing literature and developments
in the application of SOFC systems to ships, the following
gaps in scientific literature were identified and addressed in
this paper:
•
Design of the full power plant of a ship where the SOFC
takes the largest share of the onboard energy conver-
sion. All the studies mentioned in available academic
literature focus on the use of SOFCs as APUs, or at
most as the minor element of a hybrid system mostly
based on Diesel engines.
•
Design of SOFC-driven ship power plants based on op-
timization principles. All papers identified in scientific
literature base the decision of the system topology, and
particularly of the size of the SOFC, on heuristics rather
than on an optimization of the system.
•
Design of SOFC-drive ship power plants based on pro-
cess integration principles. Of the studies available in
literature, only the work [
19
] includes the heat demand.
•
Optimization-based studies on ship energy systems
rarely include an analysis of the sensitivity of the results
on the problem assumptions.
As a consequence of the gaps in scientific literature iden-
tified above, the aim of this work is that of investigating the
challenges of designing a ship’s power plant based on SOFCs
for its largest part. Compared to the previous literature on the
subject, this paper aims at:
•
Performing an optimization of the system in terms of
the types of components installed, and their size, instead
of simply providing a feasible design with respect to its
economic and environmnental performance.
•
Including all energy demands (propulsion, auxiliary
electricity, heat).
•
Including the influence of known limitations on SOFC-
based designs, such as the limited dynamic abilities of
SOFCs and their low power-to-weight and power-to-
volume ratios.
•
Performing a global, two-stage sensitivity analysis of
the results of the optimization.
The research that is presented in this paper is part of a
broader project, ”Optimal Design and Control of Cruise Ship
Energy Systems” (ODes aCCSES). The project, funded within
the H2020 funding program, aimed at investigating methods
and technologies for reducing the environmental impact of
cruise ships focusing on the use of optimization techniques
for the design of the ship energy system. Among its main
results, the project (concluded in January 2019) identified high
temperature fuel cells as one of the most promising solutions
for future efficient and low-impact energy systems [4].
2. Method
This paper aims at investigating the potential for the integra-
tion of SOFCs in ship energy systems. The method proposed
to answer this question is divided in two parts:
1.
Multi-objective optimization of a generic ship energy
system, with the SOFC included among the possible
alternative energy conversion technologies that can be
selected by the optimizer (see Section 2.1).
2. Sensitivity analysis of the optimization problem (2.2).
2.1 Optimization of the ship energy system
In this paper, the optimization of the system is based on the
superstructure described in Figure 1.
The SOFC is the core of the system, and it can generate
both electrical and thermal energy. Electric power can also be
generated by medium-speed and high-speed gas and Diesel
engines (MS-GE, HS-GE, MS-DE, HS-DE). All of them can
be associated with a waste heat recovery (WHR) system for
providing heat (both high temperature (HT) and low tempera-
ture (LT) heat) to the onboard auxiliary demand. In addition,
Diesel and gas boilers and heat pumps are included as addi-
tional means for fulfilling the heat demand.
While the overall superstructure is pre-defined, the sizes
of its different units are not fixed and should be defined based
on the characteristics of the specific case the system is applied
to.
For this reason, in this paper the problem of the sizing
of the system is approached as a MILP problem and solved
using the OSMOSE framework, specifically developed for
the solution of MILP-based energy integration problems [
85
].
The size of each component of the power plant (fuel cell,
Diesel engines, boilers, etc.) are the decision variables of
interest for the problem. The energy and mass streams for each
component at each time step also appear in the optimization
as decision variables. The MILP approach was selected based
on the high reliability and speed of available solvers. The
proposed system and optimization are then applied to two
case studies, described more in detail in Section 3.1.

The role of solid oxide fuel cells in future ship energy systems — 5/22
Figure 1. Graphical representation of the proposed ship energy system.
Starting from the premise that shipping will need to further
reduce its impact on the environment in the future, in the
maritime business, as in many other industries, investment
decisions are always taken with the cost dimension in mind.
For this reason in this study the concept of multi-objective
optimization (MOO) was used, where the two, competing
objectives are defined in Equation 1.
fobj,1=mGHG fobj,2=Cop +Cinv,ann (1)
where the operational cost (
Cop
), the annualized investment
cost (
Cinv,ann
) and the yearly GHG emissions (
mGHG
) are de-
fined in equations 2, 3 and 4, respectively.
Cop =∑
uεU
∑
tεT
f0
u,t(cfuel +cCO2EFCO2)˙
Emax
fuel,u∆ttξt+
cLV ∑
uεU
fu˜pu˙
Emax
size,u+cLW ∑
uεU
fu¯pu˙
Emax
size,u(2)
Cinv,ann =∑
uεU
fucinv,var
u˙
Emax
size,u
Fann
u
(3)
mGHG =∑
uεU
∑
tεTEFCO2+GHGeq
CH4EFCH4·f0
u,t˙
Emax
el,u∆ttξt
(4)
where the problem parameters: the fuel cost (
cf uel
), the carbon
tax rate (
cCO2
), the maximum fuel consumption of each utility
u
(
˙
Emax
fuel,u
), the duration of each time step (
∆tt
),the number of
occurrences of each time step during the year of reference (
ξt
,
see later in the text for more details), the variable (i.e. size-
dependent) investment cost of each utility (
cinv,var
u
), the maxi-
mum energy/material flow used for sizing purposes of each
utility
u
(
˙
Emax
size,u
), the specific cost of lost volume (
cLV
) and
lost weight (
cLW
), and the power density of each conversion
unit (power-to-volume
˜pu
and power-to-weight
¯pu
). The GHG
emissions are calculated based on emission factors for CO
2
and CH
4
emissions, where the latter are converted to equiv-
alent CO
2
emissions using a conversion factor (
GHGeq
CH4
) of
28 [
58
] for a 100 years horizon. The annualization factor
(
Fann
) is defined in Eq. 5 and is a function of the lifetime of
each utility (
Ny
u
) and of the interest rate (
i
).
U
and
T
represent
the set of utilities and of time steps included in the problem,
respectively.
Fann
u=(i+1)Ny
u−1
i(1+i)Ny
u
(5)
It should be noted that, compared to common expressions
for the evaluation of operational costs, Equation 2 also in-
cludes a contribution coming from the cost of lost volume and
weight. This is due to the fact that, in transport applications,
the total volume and weight of the system are often limited
resources, that need to be used for other purposes. To take
this into account, the second and third terms of Equation 2
attribute a specific cost to the lost volume and weight, which
are multiplied to an estimation of the total volume/weight of
the power plant.
The problem variables to be optimized are: the load of

The role of solid oxide fuel cells in future ship energy systems — 6/22
each utility
u
at each time step
t
with respect to its maxi-
mum installed power (
f0(u,t)
, ranges between 0 and 1); the
sizing of each utility with respect to its maximum installed
power (
f(u)
, also ranges between 0 and 1); the on-off deci-
sion of each utility for each time step (
y0(u,t)
, binary); and
the installation decision for each utility (
y(u)
, also binary).
The aforementioned variables are related by the following
constraints:
f0
u,t≤fu∀t in T,u in U(6)
f0
u,t≤y0
u,t∀t in T,u in U(7)
y0
u,t≤yu∀t in T,u in U(8)
where Equation 6 represents the fact that a utility cannot
operate at a higher power than the maximum installed size,
Equation 7 that a utility can only have a non-zero load if it is
turned on, and Equation 8 that a utility can only be used if it
is installed.
To take into account the fact that some units cannot be
freely operated in the whole 0% to 100% range, an additional
constraint is added to take this aspect into account (see Eq.
9). The constraint on the lower boundary needs to depend
also on the time-wise activation variable, which makes it
nonlinear. The equation is linearized through the introduction
of a dummy variable.
y0
u,tfuλmin
u≤f0
u,t≤fuλmax
u∀t in T,∀u in U(9)
One special constraint has to be defined for the SOFC in
order to account for its poor dynamic properties, and more
particularly for its very long start-up time. This was accounted
in this work by assuming that the SOFC, if installed, has to
be constantly kept running above its minimum load. This is
implemented using equation 10:
ySOFC =y0
SOFC,t∀t in T(10)
The optimization problem is further constrained by the
fact that energy and material balances must be respected at all
times:
∑
uεU
f0
u,t˙
Emax
l,u+∑
pεP
˙
El,p,t=0∀t in T,l in L(11)
where
˙
Emax
l,u
represents the maximum value of the net en-
ergy/material flow
l
for unit
u
, and
˙
El,p,t
represents the en-
ergy/material flow
l
at time step
t
of the process
p
, typically
representing the energy demand of the system.
The case of heat is treated differently, in order to simulta-
neously account for the first and second law of thermodynam-
ics, by using the concept of heat cascade [45]:
∑
uεU
f0
u,t˙
Qmax
k,u+∑
pεP
˙
Qk,p,t+Rk+1−Rk=0∀t in T,k in K
(12)
with:
Rk≤0∀k in K(13)
R1=0,RNk+1=0 (14)
where the
Rk
represents the energy cascaded form the tem-
perature interval
k
to the lower temperature intervals, and
K
represents the set of temperature intervals of the heat cascade.
˙
Qmax
k,u,t
is defined as the sum of the maximum contributions of
all heat streams
s
of unit
u
in the temperature interval
k
and
˙
Qk,p,t
as the sum of the contributions of all heat streams
s
of
process pin temperature interval kat time step t:
˙
Qmax
k,u=∑
sεSu
˙
Qmax
k,s,u(15)
˙
Qk,p,t=∑
sεSp
˙
Qk,s,p,t(16)
It should be noted that the heat cascade as defined in
Equation 12 is valid only for all units that are allowed to
exchange heat with each other. Depending on the specific case,
some units might not be in conditions of directly exchanging
heat (e.g. because of logistic, economic, or safety constraints).
In this case, one heat cascade is defined for each group of
units that are allowed to exchange heat with each other.
To accurately represent variability of the demand while
avoiding excessive computational burden on the solver, the
concept of typical periods was used to model the energy de-
mand and the ambient conditions of the system [
26
]. The
notion of typical periods is based on the assumption that the
yearly demand of a generic energy system can be represented
by a limited set of periods, where the term period can refer
to a day, a week, or a voyage, defined by a sequence of time
steps. The problem is hence defined by
Nt
time steps, which
are sub-divided among
Ntp
typical periods. The total duration
of yearly operations is then reconstructed as:
∑
tεT
∆ttξt=8760 (17)
where every
∆tt
has an assigned value for
ξt
, which represents
how many times during a year the corresponding typical pe-
riod is expected to occur. In each problem there are only
Ntp
different values for
ξt
, and the value of
ξt
is the same for all
time steps
t
belonging to the same typical period. A more
detailed description of the theory behind the use of typical
days, and on how to calculate them, is provided in the work
of [26].

The role of solid oxide fuel cells in future ship energy systems — 7/22
In addition to the problem-level equations, each unit is
defined by additional constraints. The general form of the
different energy streams of a generic unit is given by Eq.
11. As energy conversion units are generally defined by the
efficiency of the conversion process, in this formulation this
is given by:
ηl,u=
˙
Emax
l,u
˙
Emax
fuel,u
(18)
It should be noted that Equation 18 implies that the conver-
sion efficiency of each component is constant, regardless of
the environmental or operational conditions. This relatively
strong assumption, made necessary by the linearization of the
problem, is common in the field of energy systems optimiza-
tion [
29
,
84
], and has limited influence on the final design.
While a piece-wise linearization could help improving the ac-
curacy of the model, it would also increase the computational
requirements because of the additional binary variables.
In order to take into account the important impact of the
temperature of environmental conditions on the performance
of the heat pump, the coefficient of performance was calcu-
lated as shown in Eq. 19 and 20 [
46
], thus using the second-
law efficiency of the heat pump as design parameter.
COP
HP,rev =THP,cond
THP,cond −THP,evap
(19)
COP
HP =εCOP
HP,rev (20)
The problem definition also includes batteries as means
of energy storage. These are modelled with a state variable
indicating the current state of charge of the storage, that is
calculated for each time step in accordance to the following
definition:
∆Eu,t=˙
Emax
uf0
u(cha),t−˙
Emax
uf0
u(dis),t∆tt(21)
where the subscripts
(dis)
and
(cha)
refer to the discharge
and charge processes. It should be noted that, to preserve
the overall energy balance, it is here assumed that the state
of charge of the energy storage must be the same at the start
and at the end of each typical period. Electric energy storage
in batteries also involves losses in the charging-discharging
cycles. These are accounted through an electrical energy flow,
representing charge/discharge losses in the battery:
˙
Eloss
u,t=˙
Emax
uf0
u(cha),t1
ηcha
u−1+˙
Emax
uf0
u(dis),t(1−ηdis
u)
(22)
2.2 Sensitivity analysis
Sensitivity analysis studies how the uncertainty in the output
of a model can be attributed to different sources of uncertainty
in the model input [
68
]. Given the uncertainty concerning
most of the parameters used in the optimization process, it
is important to understand what are the most impacting pa-
rameters with regards to the existing uncertainty, or range
of variation. The two-stage global sensitivity analysis (GSA)
methodology, as proposed by [
55
] for energy system optimiza-
tion, was used. It includes a first stage of parameter screening
and a second stage of parameter prioritization; the reader
is referred to the aforementioned publication for additional
details.
The rationale for the two-stage process lies in the computa-
tionally expensive nature of the determination of the parameter
prioritization using variance-based methods. As it would be
too time-consuming to apply these methods directly to the
full set of uncertain parameters, a first stage of parameter
screening is included, based on the Morris screening [
56
] as
improved by Campolongo et al. [
14
], that allows estimating a
proxy for the total sensitivity index (
ST
) in a computationally
efficient way. Only the parameters that are considered signifi-
cant based on the Morris screening are further analyzed using
a more accurate, and computationally expensive, approach.
In this study, this selection was made based on having a sen-
sitivity value higher than 5% of the maximum value for at
least one of the outputs of interest. Given the scope of this
study, the installed power of the SOFC (
Pinst
SOFC
) and the total
annualized cost (Ctot) were used for the selection.
Pinst
SOFC =fSOFC ˙
Emax
size,SOFC (23)
Ctot =Cinv,ann +Cop (24)
Once a limited set of the most influential parameters is thus
identified, variance-based methods for GSA can be applied.
In this paper, the method originally proposed by Sobol [
72
]
and later improved by Saltelli [
67
] was used. Both the Morris
method and of the Sobol GSA method were implemented
using the SAlib Python package [37].
3. Application
3.1 Case studies
The methodology described in Section 2 for exploring the
role of SOFCs in future ship energy systems was applied
on two case studies, described in this section: a cruise ship
(Section 3.1.1) and a chemical tanker (Section 3.1.2). The two
cases were selected based on the availability of operational
measurements of the energy demand, and on the preference to
apply the proposed methodology on two cases with substantial
differences in mission and operational profile.
3.1.1 Cruise ship
The case study for a cruise ship is based on the work presented
in [
6
], and refers to a small cruise ship (176.9 m long, beam
of 28.6 m) with a capacity of 1800 passengers operated in the
Baltic Sea. The ship is equipped with several amenities and
with a large system for heating, ventilation and air condition-
ing (HVAC), making its auxiliary energy demand larger and
more varied than that of a standard cargo vessel. The ship
currently in operations is equipped with a total of eight Diesel

The role of solid oxide fuel cells in future ship energy systems — 8/22
Figure 2. Propulsion
engines: four main engines with a power of 5760 kW each,
and four auxiliary engines with a power of 2780 kW each.
The heating demand is fulfilled by six heat recovery steam
generators (HRSG), located on the exhaust line of the four
auxiliary engines and of two of the four main propulsion en-
gines, by a recovery system for the engine cooling waste heat,
and by two oil-fired boilers. This work focuses on the case of
a newly built ship of similar size and operational profile.
The energy demand is based on [
6
]. The heat demand
is assumed to be subdivided in a low-temperature heating
system operated between 40 to 60
◦
C and used to fulfill the
demand for air conditioning, and a high-temperature system
using steam at 110
◦
C that fulfills the heating demand for other
on board uses, such as for the machine room or the galley.
The demand, originally based on a full year of operations,
was clustered into a total of five typical days, one of which
being an “extreme day” for the propulsive power demand,
each made of 13 variable-length time steps (see Figure 2 to
5):
•Winter (ξ1−13 =31)
•Mid-season (C) (ξ14−26 =172)
•Mid-season (H) (ξ27−39 =112)
•Summer (ξ40−52 =41)
•High propulsion demand (ξ53−65 =9)
This is justified by the fact that the ship operates on daily
cruises, and hence the operational and ambient fluctuations
take place with a cycle of the same duration. The four main
typical days represent normal ship operations in three differ-
ent seasons (hence the difference in heat demand), while the
Figure 3. Electric power
Figure 4. High temperature heating

The role of solid oxide fuel cells in future ship energy systems — 9/22
Figure 5. Low temperature heating
extreme day represents high-speed sailing conditions. The
demand hence resulting from the clustering of the original
dataset into typical days is 25.9 GWh for propulsion, 15.5
GWh for electricity, 6.6 GWh for high temperature heat de-
mand and 8.6 GWh for low temperature heat demand.
3.1.2 Chemical tanker
The case study for a chemical tanker is a Panamax vessel with
a cargo capacity of 47000 tons. The ship currently uses two
4-stroke Diesel engines rated 3,840 kW each for propulsion,
both connected to a common gearbox. The gearbox is, in
turn, connected to a controllable pitch propeller and to an
electric generator which provides 60 Hz current to the ship.
Additionally, two auxiliary engines rated 682 kW each can
also provide electric power. Auxiliary heat needs are fulfilled
by the HRSG or by auxiliary boilers. A more detailed analysis
of the ship and its energy demand can be found in [3].
A similar approach is used as for the case of the cruise
ship to reduce the number of time steps of the optimization,
hence defining some ”typical periods”. In this case, however,
the ship does not operate on a regular, daily basis, and the
assumption of ”typical days” would not be realistic. For
this reason, for this case study the ”typical day” approach
was substituted by a ”typical voyage” one. The summary of
the demand data is provided in Table 1, which is based on
the analysis of the dataset presented in [
3
]. The three days
represent respectively a short-sea voyage (total voyage time:
78 hours), a long-sea voyage (total voyage time: 222 hours)
and a high-speed, long-sea voyage (total voyage time: 222
hours, higher propulsion power demand at sea), where the
latter takes the role of ”design-voyage”.
3.2 Problem parameters
The complete list of uncertain parameters with the respec-
tive reference and boundary values are provided in Tables
2-6, while details about the specific assumptions for each
parameter are provided in subsections 3.2.1 to 3.2.8.
When not otherwise mentioned, the following assump-
tions were employed:
•
For efficiency-related parameters, the uncertainty was
assumed to be ±6% based on the findings of [55].
•
For investment cost-related parameters, the uncertainty
was assumed to be
±
21% based on the findings of [
55
].
•
For temperatures, the uncertainty was assumed arbitrar-
ily to be ±20% of the value in ◦C.
•
For lifetimes, the uncertainty was assumed arbitrarily
to be ±5 years.
In both cases, the GSA was applied to a total of 88 uncer-
tain parameters.
3.2.1 Solid oxide fuel cell
Cost factors related to the solid oxide fuel cells were derived
from [
11
]. The same reference was used to determine the
uncertainty, which was derived as a combination of the sensi-
tivity of the investment cost calculated as part of the sensitivity
analysis in [
11
], and of the variations related to the expected
production volume in the same study. Reference values refer
to a production volume of 1000 units per year. The assump-
tions related to the stack lifetime are derived from [70].
The efficiency and operating temperatures of the SOFC
were taken using the SOFC-based cogeneration unit by Con-
vion [
17
], that is being tested in selected projects for applica-
tion in the maritime industry [
38
]. The company reports rated
electric and thermal efficiency of 0.53 and 0.27 respectively
for their 58 kW unit. The lower bound (0.52) reflects the fact
that the actual efficiency might be marginally lower, while the
upper bound (0.60) was assumed based on the INNO-SOFC
targets [
8
,
27
]. The bounds for the thermal efficiency were
arbitrarily assumed to 0.20 and 0.35 based on the variation of
the electrical efficiency. Default values for the inlet and outlet
temperatures of the exhaust gas were taken from Convion
data.
Values for the maximum and minimum load were as-
sumed, and are mostly related to the concept of preserving the
conversion efficiency. SOFCs are known to preserve relatively
well the conversion efficiency over a wide range of operations.
Finally, the reference values assumed for power density
were taken from the results of the CH2P project [
15
]. The
lower bound was assumed extrapolating the performance of
the Convion module [
17
], while the upper bounds were as-
sumed based on the Delphi-APU prototype [65].
3.2.2 Internal combustion engines
Gas engines were modelled based on the two cases of ma-
rine gas engines: the Rolls Royce C25:33L9A as medium

The role of solid oxide fuel cells in future ship energy systems — 10/22
Typical Journey 1 (ξ1−7=40) Typical Journey 2 (ξ8−14 =20) Typical Journey 3 (ξ15−21 =5)
t [h] ˙
Wprop [MW] ˙
Wel [MW] ˙
Q[MW] t [h] ˙
Wprop [MW] ˙
Wel [MW] ˙
Q[MW] t [h] ˙
Wprop [MW] ˙
Wel [MW] ˙
Q[MW]
Port 18 0.0 0.3 0.2 48 0.0 0.3 0.2 48 0.0 0.5 1.2
Man. 3 3.0 0.7 0.2 3 3.0 0.7 0.2 3 3.0 0.9 1.2
Tank. Cl. 6 5.0 0.5 1.5 6 5.0 0.5 1.5 6 7.5 0.7 1.2
Sailing 30 5.0 0.4 0.2 114 5.0 0.4 0.2 114 7.5 0.6 1.2
Man. 3 3.0 0.7 0.2 3 3.0 0.7 0.2 3 3.0 0.9 1.2
Unload. 6 0.0 1 0.2 6 0.0 1.0 0.2 6 0.0 1.8 1.2
Port 12 0.0 0.3 0.2 42 0.0 0.3 0.2 42 0.0 0.5 1.2
Table 1. Typical journeys for the tanker case study
ECU Parameter Unit Ref. LB HB
SOFC (stack) cinv,var
uEU R
kWel 380 271 612
SOFC (system) cinv,var
uEU R
kWel 868 573 1296
SOFC (stack) Ny
uy 6 3 8
SOFC (system) Ny
uy 20 15 25
Gas Engine (MS) cinv,var
uEU R
kWel 675 529 821
Gas Engine (MS) Ny
uy 20 15 25
Gas Engine (HS) cinv,var
uEU R
kWel 575 451 699
Gas Engine (HS) Ny
uy 20 15 25
Diesel Engine (MS) cinv,var
uEU R
kWel 575 529 821
Diesel Engine (MS) Ny
uy 20 15 25
Diesel Engine (HS) cinv,var
uEU R
kWel 475 451 699
Diesel Engine (HS) Ny
uy 20 15 25
Gas Boiler cinv,var
uEU R
kWth 54 42 66
Gas Boiler Ny
uy 20 15 25
Battery cinv,var
uEU R
kWh 256 150 500
Battery Ny
uy 5 4 10
Heat Pump cinv,var
uEU R
kWth 550 431 669
Heat Pump Ny
uy 20 15 25
El. Generator cinv,var
uEU R
kWel 30 24 36
El. Generator Ny
uy 20 15 25
Table 2. Uncertain parameters, investment cost factors
ECU Parameter Unit Ref. LB HB
SOFC ηel - 0.530 0.520 0.650
SOFC ηth - 0.270 0.260 0.350
ICE (MS) ηel - 0.450 0.423 0.477
ICE (MS) ηHT - 0.156 0.147 0.165
ICE (MS) ηLT - 0.131 0.123 0.139
ICE (MS) ηeg - 0.263 0.247 0.279
ICE (HS) ηel - 0.400 0.376 0.424
ICE (HS) ηHT - 0.156 0.147 0.165
ICE (HS) ηLT - 0.131 0.123 0.139
ICE (HS) ηeg - 0.363 0.341 0.385
Gas Boiler ηth - 0.850 0.799 0.901
Battery ηch
el - 0.926 0.870 0.982
Battery ηdis
el - 0.975 0.920 0.990
Heat Pump ε- 0.450 0.500 0.550
Table 3. Uncertain parameters, efficiency
speed gas engine, and the Mitsubishi S16R-T2 high speed
ECU Parameter Unit Ref. LB HB
SOFC Tin
eg ◦C 220 176 264
SOFC Tout
eg ◦C 40 32 48
SOFC λmin - 0.1 0 0.2
SOFC λmax - 0.9 0.8 1
ICE (MS) Tin
eg ◦C 300 240 360
ICE (MS) Tout
eg ◦C 120 96 144
ICE (HS) Tin
eg ◦C 350 280 420
ICE (HS) Tout
eg ◦C 120 96 144
Gas Boiler Tin
eg ◦C 900 720 1080
Gas Boiler Tout
eg ◦C 120 96 144
Battery C - 2 1.5 6
Battery SOCmax - 0.7 0.5 0.8
Table 4. Uncertain parameters, other performance-related
parameters
ECU Parameter Unit Ref. LB HB
SOFC ¯pkW/kg 0.06 0.035 0.24
SOFC ˜pkW/m35 2 16
ICE (MS) ¯pkW/kg 0.07 0.063 0.077
ICE (MS) ˜pkW/m364 57.6 70.4
ICE (HS) ¯pkW/kg 0.25 0.225 0.275
ICE (HS) ˜pkW/m3195 176 215
Gas Boiler ¯qkW/kg 0.360 0.324 0.396
Gas Boiler ˜qkW/m3104 94 114
Battery ¯ekWh/kg 0.08 0.072 0.088
Battery ˜ekWh/m391 81.9 100.1
Heat Pump ¯qkW/kg 0.210 0.189 0.231
Heat Pump ˜qkW/m392 83 101
El. Generator ¯pkW/kg 0.212 0.191 0.254
El. Generator ˜pkW/m3126 120 151
Table 5. Uncertain parameters, specific power (weight- and
volume-based)
gas engine. The exhaust gas temperatures were assumed to
300
◦
C and 350
◦
C, respectively, based on general knowledge
related to the behaviour of these engine types. As for all other
traditional components, the lifetime was assumed to 20 years.
The investment cost of the MS engine was assumed based on
[
77
], while the investment cost of the HS engine, in absence
of more reliable information, was assumed to be 100 EUR/kW
lower compared to the MS engine, as HS marine engines are

The role of solid oxide fuel cells in future ship energy systems — 11/22
Parameter Unit Ref. LB HB
i- 0.08 0.06 0.13
cLV EUR/m3250 20 1000
cLW EUR/kg 0.105 0.084 0.127
cfuel EUR/kWh 0.0287 0.0261 0.0536
Table 6. Uncertain parameters, other cost-related parameters
ECU Source CO2CH4GHG NOX
SOFC [17] 374 0.0 374 0.0
Gas Engine (MS) [74] 440 4.1 555 0.9
Gas Engine (HS) [74] 495 4.9 633 0.9
Diesel Engine (MS) [52] 513 0.0 513 2.3
Diesel Engine (HS) [52] 577 0.0 577 2.0
Table 7. Emission factors for energy conversion units. All
values are given in [g/kWh]
known to be cheaper compared to MS ones.
The electrical efficiency was assumed to vary within 6%
of its reference value [
55
], while other efficiencies, related to
the energy share wasted to the exhaust gas and to the cooling
systems, were re-calculated based on energy conservation
principles. An uncertainty of 10% was assumed for the power
density parameters.
Engines also require the installation of an electrical gen-
erator to convert power from mechanical to electric. The
efficiency of this system was assumed to 0.95, while the in-
vestment cost was assumed equal to 30 EUR/kW [
79
]. Power
densities parameters were deduced from the generator in-
stalled on the Bergen C26:33L engine [66].
The default and uncertain parameters (apart from cost-
related ones) were assumed to be the same for gas engines
and Diesel engines (all shown under the category ”internal
combustion engines”, (ICE)).
3.2.3 Gas boilers
Gas boilers are modelled using a reference value for the first-
law efficiency of 0.85, based on [
16
] and [
57
]. For the sake
of modelling the heat cascade, the boiler is modelled as a hot
flow to be cooled from 900
◦
C to 120
◦
C. The specific cost was
assumed to 54 EUR/kW [
60
]. Power density parameters were
calculated based on the data from Aalborg OS boiler [43].
3.2.4 Heat pumps
In order to take into account the important impact of the
temperature of the low-temperature heat source, the efficiency
of the heat pumps was calculated as shown in Eq. 19 and
20, thus requiring a value for the exergy efficiency. This was
assumed to be equal to 0.45 based on [
36
], while the lower and
upper bounds were set to 0.4 and 0.55 arbitrarily. Reference
values for the power density were calculated based on the
Viessmann heat pump (model Vitocal HT 353.AHT147) [
83
].
For reference, for a heat pump operating with
Teva
= 303 K
and Teva = 363 K, the calculated COP is 2.72.
3.2.5 Batteries
Batteries are generally modelled using two efficiency values:
one for the charge, and one for the discharge process. The
reference values are taken from [
1
]. With relation to costs, the
reference investment cost is adapted based on [
61
], similarly
to the bounds (based on the expectations of future price devel-
opment, and on the type of information source). The reference
lifetime was assumed arbitrarily, similarly to its bounds, as
there is currently no well-detailed and trusted information
with relation to the expected lifetime of large scale lithium-
ion batteries, particularly for maritime applications. Power
density parameters were calculated based on the data from
Corvus Orca Energy maritime batteries [23].
3.2.6 Other cost-related parameters
The reference and bound values for the price of natural gas
(
Cf uel
) were estimated based on [
9
]. The values for the price
of MDO were based on the observation that MDO prices tend
to be correlated to LNG prices, with a 1.6 factor in between
[
20
]. This assumption was used for both reference, upper
bound and lower bound values. A value of 0.08 was assumed
for the interest rate (
i
), varying between 0.06 and 0.13 based
on [
42
]. The cost of lost volume and the cost of lost weight
were assumed based on an analysis of the cost of sea passage
(in the case of the cruise ship) and of the daily charter rates
(in the case of the tanker).
Discussions of implementing a market-based measure on
GHG emissions have been going on for some time now, also
in the maritime business. While today there is no direct cost
in shipping related to GHG emissions, the sensitivity analysis
should also include an evaluation of the potential impact of the
implementation of this type of measures. This was included,
as shown in section 2.1, in the form of a tax proportional to the
emissions of carbon dioxide. The reference value (and, thus,
the lower boundary) of the cost of one ton of CO
2
emitted
into the atmosphere is assumed to be equal to zero, based on
the current absence of a carbon tax in shipping. The upper
boundary was set to 0.2 EUR/kg, based on the scenario with
the largest carbon tax proposed in [64].
3.2.7 Emission factors
The analysis proposed in this paper includes three main pol-
lutant categories: PM, GHG (thereby including also the con-
tribution of methane slip), and nitrogen oxides (NO
X
). The
emission factors shown in Table 7 were used to estimate the
emissions resulting from the use of different energy conver-
sion units. Emission factors for CO
2
were calculated based
on the fuel used (LNG or MDO) and on the efficiency of the
energy conversion unit. Emission factors for CH
4
and NO
X
were retrieved from the references indicated in Table 8. A fac-
tor 28 was used to convert CH
4
emissions to CO
2,eq
emissions
[
58
]. Since the environmental objective is not included in the
GSA, the definition of uncertain bounds for emission factors
was not necessary in this study, apart from the influence of
the prime mover’s efficiency on CO2emission factors.

The role of solid oxide fuel cells in future ship energy systems — 12/22
3.2.8 Ship demand
While basing the analysis on available past operational data
is a reasonable choice, there is not certainty that the ship
will be operated in this same way in the future. The ship
might be sold to a different owner, employed on a different
route, operated at a different speed in a different climate.
For this reason, the ship demand is also considered to be
subject to uncertainty. In this work, it was assumed that the
uncertainty can be concentrated on two parameters for each of
the demands: the mean, and the standard deviation. Based on
this assumption, the demand used in each run of the sensitivity
analysis, at each time step, is calculated as described in Eq.
25.
˙
Es
l,p,t=˙
Eref
l,p,t(µs
l,p−µref
l,p)+(˙
Eref
l,p,t−µref
l,p)σs
l,p
σref
l,p
(25)
The
s
superscript refers to each optimization run of the
GSA, while the specific
ref
superscript refers to the reference
one.
µ
and
σ
represent the mean and standard deviation of
each type of demand. For each of these parameters a
±20%
uncertainty was arbitrarily assumed.
4. Results
4.1 Multi-objective optimization
The results of the MOO are shown in Figures 6 to 9. The
MOO problem is implemented using the
ε−
constraint method
[
50
], where the total GHG emissions of the system were
constrained to decreasing values, ranging from the single-
objective cost-optimal solution to the single-objective, GHG-
optimal solution.
The trade-off between total costs and the reduction in
GHG emissions appear clearly. In both case studies, focus-
ing on emissions can reduce them by up to more than 30%
compared to the cost optimal case, showing how a significant
reduction in ship emissions can be achieved already by acting
on the ship’s power plant.
This reduction, however, comes at a cost. In both case stud-
ies, reducing GHG emissions by approximately 30% comes
at a substantial increase in the total cost: +27% in the case
of the cruise ship and +43% in the case of the tanker, with
respect of the cost-optimal case. As expected, this increase
is due to the largest extent to the increase in the annualized
investment costs, that increase by up to 2.5 times in the cruise
ship case, and almost 3.5 times in the tanker case. On the
other hand, operational costs decrease, driven by the higher
system efficiency, and thereby lower fuel consumption, and
by the switch from MDO to LNG.
Finally, in the cruise ship case, there is a small, but still
significant contribution to the total cost related to the cost of
lost volume: in the Pareto-optimal scenario with the lowest
GHG emissions, this figure represents approximately 6% of
the total costs, and is estimated to generate a 14% increase
in operating costs. In the case of the tanker, where weight
is considered as the limiting factor, this element is instead
almost negligible: the difference in power density between
SOFCs and internal combustion engines is, as of today, larger
in terms of power-to-volume than in power-to-weight ratio.
65 70 75 80 85 90 95 100
0
2
4
6
8
Relative annual GHG emissions [%]
Yearly costs [MEUR]
Investment Cost
Operating cost
Total annualized cost
Cost of lost cargo
(a) Cruise ship
65 70 75 80 85 90 95 100
0
2
4
6
8
Relative annual GHG emissions [%]
Yearly costs [MEUR]
Investment Cost
Operating cost
Total annualized cost
Cost of lost cargo
(b) Tanker
Figure 6. Results of the multi-objective optimization:
Annualized costs
Figure 7 shows how the installed size of the different
components evolve when the constraint on the maximum
operating costs is modified. The installation of the SOFC
increases almost proportionally with the reduction of GHG
emissions, due to the higher efficiency and the absence of
methane slip phenomena. This is in line with the expectations:
SOFCs are the technology with the highest cost per installed
kW, but are also the most efficient, making them most suitable
when the focus is on operational costs and emissions. It should
be noted that the total installed size of the different prime
movers varies remarkably between the two cases. In both
ships the total installed power is dimensioned for ”limit cases”,
such as very high speed sailing. However, this is particularly
true for the cruise-ship case, where the ship normally sails at

The role of solid oxide fuel cells in future ship energy systems — 13/22
14 kn but is expected to allow sailing at 21 kn, thus explaining
the relatively large difference in total installed power.
In the case of the cruise ship, gas engines dominate in
the cost-optimal scenarios, as they are the cheapest to install.
With decreasing operating costs, they are first substituted by
the MS-GEs, until a switching point where the SOFC starts
to be installed instead of the MS-GE. The base concept is
that the most efficient energy conversion unit (the MS-GE or
the SOFC depending on the scenario) is used for base-load
and the HS-GE for peaks. This can be also seen in Figure
8: in spite of the installed power of more than 10 MW, the
HS-GE are only providing a minor contribution to the total
power share in most scenarios from medium to low total GHG
emissions.
In the case of the cruise ship, it is interesting to notice an
additional shift when GHG emissions are reduced by more
than 30% with respect to the unconstrained solution: in this
case, it can be seen that: i. much of the HS-GE installed power
is substituted by the MS-GE, to further reduce emissions at
the expense of a higher investment cost; ii. the SOFC installed
size further increases; iii. the optimal solution requires the
installation of a battery, which allows storing the excess elec-
tric energy converted by the SOFC when the electric power
demand is lower than the SOFC’s minimum load.
In the case of the tanker, instead, the HS-DE is chosen in-
stead of the HS-GE, and the Pareto front becomes a trade-off
between SOFC, MS-GE and MS-DE: the SOFC is the most
expensive to install, but also the one with the lowest GHG
emissions. The MS-GE is the best from an economic perspec-
tive because it uses LNG, that is assumed to be cheaper than
MDO, but the effects of methane slip makes it environmen-
tally worse than Diesel engines. Once again, the HS engine
is chosen mostly for peaks of power demand (in the case of
the tanker, for the high-speed voyage), and hence has little
contribution to the overall energy share (see Fig. 8)
Figure 9 shows the expected yearly emissions from the
different solutions on the Pareto front, showing the effect of
the higher share of SOFC use not only on GHGs, but also on
NO
x
and CO. It can be seen that the benefit of shifting towards
SOFCs goes beyond the gains in terms of GHG emissions:
All other emissions are also reduced, going practically to zero
for the lowest GHG emissions scenarios. By observing Figure
9 together with 8, it can also be seen the high importance of
the methane-slip phenomenon, and how much it influences
the type of solutions present on the Pareto-front: while CO
2
emissions are only reduced by a maximum of approximately
20% by shifting to an SOFC-based power plant, GHG emis-
sions are reduced by almost twice as much (approximately
35%). This is due to the high impact of methane slip on GHG
emissions from gas engines. It appears as a consequence that,
while a solution entirely based on gas engines would be opti-
mal from a cost perspective, this would not be necessarily the
case from an environmental one.
65 70 75 80 85 90 95 100
0
2
4
6
8
10
12
14
16
18
Relative annual GHG emissions [%]
Intalled Size[MW / MWh]
Gas Engines (HS)
Gas Engines (MS)
Diesel Engines (HS)
Diesel Engines (MS)
SOFC
Battery
Gas Boiler
(a) Cruise ship
65 70 75 80 85 90 95 100
0
1
2
3
4
5
6
7
8
9
10
Relative annual GHG emissions [%]
Intalled Size[MW / MWh]
Gas Engines (HS)
Gas Engines (MS)
Diesel Engines (HS)
Diesel Engines (MS)
SOFC
Battery
Gas Boiler
(b) Tanker
Figure 7. Results of the multi-objective optimization:
Installed sizes of the main components. All values are
expressed in terms of installed power [MW], save for the
battery, that is represented in terms of installed capacity
[MWh].
4.2 Sensitivity analysis
The two-step GSA as described in Section 2.2 was applied
to the two case studies. In both cases, the MOO problem
was modified into a single-objective optimization problem by
dropping the environmental objective, and only retaining the
cost-related one, with no constraint on the emissions. The
Morris screening was applied to the 65 uncertain parameters
with settings r = 50 trajectories and p = 4 levels. Two main
optimization variables were selected as outputs of interest:
the installed capacity of the SOFC unit (
Pinst
SOFC
), and the total
annualized cost (Ctot,ann).
The results of the analysis are shown in Fig. 10 for the

The role of solid oxide fuel cells in future ship energy systems — 14/22
65 70 75 80 85 90 95 100
0
20
40
60
80
100
Total GHG emissions [ton/year]
Power share [%]
Gas Engines (HS)
Gas Engines (MS)
Diesel Engines (HS)
Diesel Engines (MS)
SOFC
(a) Cruise ship
65 70 75 80 85 90 95 100
0
20
40
60
80
100
Total GHG emissions [ton/year]
Power share [%]
Gas Engines (HS)
Gas Engines (MS)
Diesel Engines (HS)
Diesel Engines (MS)
SOFC
(b) Tanker
Figure 8. Results of the multi-objective optimization:
Cumulative contribution to the total electric demand
(propulsion and auxiliary) from each technology.
most relevant parameters, selected based on having a sensitiv-
ity value higher than 5% of the maximum value for at least
one of the two variables of interest. Each of the two outputs is
represented as percentage of the maximum value with respect
to j-th output of interest.
The application of the screening allows reducing the space
to explore with a more detailed sensitivity analysis. 16 out of
the 65 uncertain parameters were selected for further analysis.
The results highlight the importance of cost-related parame-
ters on the installation decision, as expected: all cost-related
parameters (the lifetime of the stack, and the specific invest-
ment cost of the SOFC parts) are all included among the most
relevant parameters that are selected in the screening stage. It
is interesting to notice how the screening confirms the impor-
tance of including in the model the impact of the cost of lost
weight and volume: this is shown by the selection of related
parameters (cost of lost volume and weight, power density)
among the variables retained by the Morris screening in both
the cruise ship and tanker cases.
The comparison of the two case studies shows that the
Morris screening identifies as significant mostly the same
65 70 75 80 85 90 95 100
0
20
40
60
80
100
Relative annual GHG emissions [%]
Relative annual emissions [%]
CO
NOX
CO2
CH4
(a) Cruise ship
65 70 75 80 85 90 95 100
0
20
40
60
80
100
Relative annual GHG emissions [%]
Relative annual emissions [%]
CO
NOX
CO2
CH4
(b) Tanker
Figure 9. Results of the multi-objective optimization:
Pollutant emissions.
variables, with few exceptions. The screening performed
in the first phase of the GSA allowed applying the global
sensitivity analysis as described in Section 2.2 on a more
limited number of parameters.
The results of the application of the Sobol method for
GSA are presented in Figure 11a for the cruise ship and in
Figure 11b for the tanker. In each of the two figures, the
plot on the left refers the normalized sensitivity of the SOFC
installed power, while the one on the right to the normalized
sensitivity of the total annualized cost. For each parameter,
two sensitivity values are presented:
•The first-order sensitivity (S1)shows the ”main” sen-
sitivity of the selected output to the specific uncertain
parameter, that is defined as the ratio between the reduc-
tion of the expected value of the output variance when
fixing the i-th parameter to its nominal value (all other
parameters are varying), and the total variance of the
output.

The role of solid oxide fuel cells in future ship energy systems — 15/22
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
µ˙
QHT
Ny
GE(MS)
µ˙
QLT
i
”cinv,var
GE(MS)”
µPprop
µPel
Lmax
SOFC
σPprop
”cinv,var
SOFC,stack”
”ηel,GE(MS)”
cLNG
˜pSOFC
cvol
”ηel,SOFC”
”Ny
SOFC,stack”
cCO2
”cinv,var
SOFC,systems”
Normalized Morris sensitivity µ∗
µ∗
max 
Parameter
SOFC installed power
Total cost
(a) Cruise ship
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Ny
GE(MS)
µPprop
µPel
i
σPel
”cinv,var
GE(MS)”
Lmax
SOFC
σPprop
cLNG
”ηel,GE(MS)”
”cinv,var
SOFC,stack”
”cinv,var
SOFC,systems”
Lmin
SOFC
”ηel,SOFC”
cCO2
”Ny
SOFC,stack”
Normalized Morris sensitivity µ∗
µ∗
max 
Parameter
SOFC installed power
Total cost
(b) Tanker
Figure 10.
Results of parameter screening phase of the GSA
•
The
total-effect sensitivity (ST
is an index that attempts
to provide an estimate of the total effect of the spe-
cific uncertain parameter on the output of interest. S
T
thereby includes not only the effects of the i-th param-
−5·10−205·10−20.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
µ˙
QHT
µ˙
QLT
i
Ny
GE(MS)
”cinv,var
GE(MS)”
µPprop
σPprop
µPel
Lmax
SOFC
”cinv,var
SOFC,stack”
cvol
cLNG
”ηel,GE(MS)”
˜pSOFC
”ηel,SOFC”
cCO2
”cinv,var
SOFC,systems”
”Ny
SOFC,stack”
0
0
0.01
0
0.04
0.01
0.01
0
0
0
0
0.08
0.04
0.03
0.04
0.15
0.13
0.03
0
0
0
0.01
0.01
0.02
0.02
0.02
0.04
0.07
0.07
0.09
0.11
0.11
0.18
0.19
0.22
0.25
Cruise ship
Parameter
S1
ST
(a) Cruise ship
−5·10−205·10−20.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
µPprop
µPel
σPel
Ny
GE(MS)
i
σPprop
”cinv,var
GE(MS)”
”ηel,GE(MS)”
”cinv,var
SOFC,stack”
Lmax
SOFC
Lmin
SOFC
cLNG
”ηel,SOFC”
”cinv,var
SOFC,systems”
cCO2
”Ny
SOFC,stack”
0
0
0
0.02
0.01
0.02
0
0.02
0
0.05
0.08
0.04
0.09
0.1
0.08
0.17
0
0
0.01
0.01
0.02
0.04
0.05
0.07
0.09
0.12
0.14
0.15
0.26
0.3
0.34
0.43
Tanker
Parameter
S1
ST
(b) Tanker
Figure 11. Results of the parameter prioritization phase of
the GSA
eter alone, but also the combined effects of several
uncertain parameters.
Quite consistently, the application of variance-based meth-
ods substantially confirms the results of the Morris screening.

The role of solid oxide fuel cells in future ship energy systems — 16/22
As expected, the most relevant parameters for the installed
SOFC size are cost-related parameters. It should be noted,
however, that apparently the very first in the ranking is the
lifetime of the stacks. This is also related to the assumptions
for the bounds of the uncertainty range for this parameter
(between 3 and 8 years, with a reference value of 6), but it
clearly points out the relevance of this parameter. The rele-
vance of the fuel cost is also significant: higher fuel prices
will make it more significant to install efficient, but expen-
sive, technologies. The efficiency of the SOFC comes only in
fourth place, together with the efficiency of the MS-GE: the
two technologies are almost mutually exclusive, and as the
respective efficiency shift, the installed sizes are also expected
to follow. It should be noted, however, that the first-order
sensitivity to these parameters is much lower than the total
one. This can be explained by the fact that these parameters
actively influence the installed size of the SOFC mostly in
combination with other parameters, rather than directly.
As expected, also parameters influencing operational costs
have a relatively large impact on the optimal decision. This
can be seen by the presence of both the LNG fuel cost and of
the carbon tax rate high in the list, together with the efficiency
of the SOFC. The LNG cost and carbon tax rate act in the
exact same way: by proportionally increasing their respective
values, operational costs increase, thus making it more con-
venient to install the energy conversion units that feature the
highest conversion efficiency (in this case, the SOFC).
The results are very similar for the two case studies,
with the exception of the relevance of the cost of lost vol-
ume/weight, which appears to be more relevant in the cruise
ship case compared to the tanker case. This can be explained
by the fact that the power-to-volume ratio of SOFCs is worse
than their power-to-weight ratio, especially when compared
to internal combustion engines.
Based on the previous results, the uncertain parameters
that showed to have the highest impact on the installed size of
the SOFC were investigated with additional detail: the specific
investment cost and lifetime of the SOFC, and the price of
LNG. It should be noted that, while they are in reality different
parameters, the SOFC specific investment cost parameters and
the SOFC lifetime build together to one annualized specific
cost investment parameter, as shown in Eq. 3. Assuming to
only focus on the uncertainty on the lifetime of the SOFC
stack, and that the specific investment cost of the stack and
of the system behave according to a similar pattern (defined
by a common uncertain parameter ranging from 0 to 1, where
0 corresponds to the lower bound and 1 to the upper bound),
Figure 12a shows how the annualized specific cost investment
depends on these parameters. The sensitivity of the SOFC
installed size on the annualized specific cost investment and
on the LNG price is shown in Figure 12b. It appears clearly
that while the LNG price also has a role, the reduction of
the annualized specific cost investment is the main parameter
that makes a difference in the optimizer’s decision of whether
it is cost optimal to install a large SOFC on board, or not.
This reinforces the previous observation related to the high
difference between STand S1for the cLNG parameter.
5. Discussion
5.1 Results discussion
The results of this paper show that SOFCs could potentially
become an important technology for future ship power plants,
if there will be an additional drive towards reducing GHG
emissions. This paper showed that by means of changing the
main energy conversion unit on board from conventional ICEs
to SOFCs the gain in terms of GHG emissions could reach up
to 34%. This confirms the results of previous studies, where
the use of SOFCs was associated to significant energy savings
(e.g. 50% savings in [
24
]). The side-effect of dramatically
reducing emissions of other pollutants, such as NO
X
and CO,
also contributes to the environmental advantages of a wider
adoption of fuel cells in shipping.
However, the results also allowed to show that, as of to-
day, SOFCs would not be selected as part of a cost-optimal
solution, in spite of their higher conversion efficiency. This
comes as the consequence of their relatively high investment
cost, in conjunction with the expected low lifetime of the
fuel cell stacks. These results were also studied from the
perspective of the influence of the uncertainty on a number
of different parameters, and showed that high-uncertain cost-
related parameters, in particular the specific investment cost
of the SOFC, the lifetime of the stack, and the cost of fuel
have a high impact on the optimal installed size of the SOFC.
Given the positive expected impact on the environment from
a wider adoption of SOFCs as prime mover on board ships,
this suggests that policy makers should focus on decreasing
the investment cost gap by focusing on the up-scaling of the
production processes. On the other hand, while the higher
electrical efficiency of SOFCs suggests that they would bene-
fit from higher fuel prices or from policies with similar effects
(such as a carbon tax), this effect is relatively smaller. It
should also be noted that, as pointed out in earlier studies,
low-investment energy-efficient technologies with low pay-
back times are generally favored over solutions with a higher
initial cost, regardless of the long-term benefits [21].
The results also highlight the importance of one of the
main limitations still existing today to the use of SOFCs in
transport applications: their limited dynamic abilities. This is
shown, in this study, by the relatively high importance that the
only load-related parameter that was included in the study: the
minimum load at which the fuel cell can be operated, which
resulted of high importance in the case of the merchant vessel.
It should be noted, however, that while the assumption of the
existence of a minimum operating load allowed to account
for this limitation, this is far from the most accurate way of
representing this characteristic. For instance, SOFCs can,
in principle, idle while burning a limited amount of fuel to
maintain the temperature for a faster start-up; also, recent
developments for mobile SOFCs applications have allowed
reducing the start-up time; finally, the present optimization

The role of solid oxide fuel cells in future ship energy systems — 17/22
(a) SOFC specific annualized cost [EUR/kW] as a function of the
stack lifetime and of the relative specific investment cost of SOFC
stack and system
(b) Cost-optimal installed SOFC power [kW] as a function of
the SOFC specific annualized cost and of the LNG price.
Figure 12.
Parametric analysis of SOFC investment decision
setup did not allow for considering the existence of several
SOFC units: while the linearity of the formulation of costs
and fuel consumption prevents this from having any influence
on the results, the same is not true for the load limitation. This
suggests that this specific aspect should be taken into account
with additional details in future studies.
This high uncertainty casts a different light on future
optimization-based studies for the analysis of the potential
of fuel cell technologies in shipping. The importance of per-
forming a sensitivity analysis for this type of results was also
highlighted in previous studies [
77
], but up to date most opti-
mization studies of ship energy systems, also when cost opti-
mization is involved, do not include a GSA. The uncertainty
on these parameters plays an important role in the optimiza-
tion results, going beyond that introduced by, for instance,
model linearization. Future optimization studies should focus
on using uncertainty-based optimization methods, such as the
one proposed by [54].
It should also be noted that the results here presented
in terms of emissions are largely influenced by the methane
slip measured in marine gas engines [
74
]. Based on these
emission factors, as of today, gas engines have a higher impact
on the climate than traditional Diesel engines. While this is
not the main focus of this paper, this is an observation that
should lead policy makers not to overlook this aspect (as of
today, the only regulation for GHG emissions in shipping is
the EEDI, that takes into account the lower CO
2
emissions
from gas engines due to the lower carbon content, but does not
account for the methane slip). Future policies should explicitly
include all GHG emissions, so as to either drive towards a
more effective reduction of CH
4
emissions from gas engines,
or to provide an additional driver towards switching to other,
more environmental friendly technologies, such as fuel cells.
The results of the sensitivity analysis highlighted the large
impact of the uncertainty of the value of a potential carbon
tax rate as one of the most significant for the decision of the
installation of a SOFC as energy conversion unit. While the
uncertainty on fuel prices is aleatory, and hence impossible to
reduce, that on the price of carbon is decided by the relevant
institutions, that have thus a clear possibility to drive the
shipping sector towards higher sustainability.
5.2 Future work
To reduce the computational time of each optimization, a nec-
essary step when applying a GSA, an MILP approach was
used. This choice, compared to the widespread use of non-
linear approaches (see, among others, [
77
,
28
,
5
]) generates
an inevitable loss in accuracy. In particular, the effect of off-
design performance of both ICEs and SOFCs was neglected,
with efficiencies, temperatures and flows assumed to be con-
stant over the entire operational range. It has been proven
that a nonlinear approach can lead to better results in terms of
load-allocation [
5
,
28
]. Similarly, the linearization of the costs
also include a loss in accuracy, due to missing to model the
effects of the scale. Both these aspects should be investigated

The role of solid oxide fuel cells in future ship energy systems — 18/22
further in future studies, comparing the findings of this paper
with the results of the application of a nonlinear approach. As
observed in the previous section, however, the uncertainty in
the results of this study, connected to the large uncertainty
on many problem parameters, is significantly larger than the
accuracy loss related to using an MILP approach instaed of
an MINLP one.
While SOFC technology is rapidly developing, it is still
the case that these units generally have poor dynamic behavior.
In this study, this was accounted for by forcing SOFC units
to be kept running at all times, thus addressing the limitation
of long startup times. Future studies should also take into
account the limitations in terms of load-following behavior:
in real applications, energy storage devices might be required
to compensate for too rapid power fluctuations, and this should
be accounted for in the optimization problem.
This study also worked on the assumption of using an AC
power grid on board of the ship. If SOFCs are to become the
main energy conversion unit, the fact that both SOFCs and
batteries generate in DC, together with the known advantages
in terms of regulating rotating machines (such as pumps and
compressors) by means of frequency converters [
86
], the re-
sult could be further improved by assuming a DC power grid
instead.
Finally, there is an unexplored potential in terms of a better
integration of the SOFC thermal systems with the rest of the
ship. In this study, aiming at keeping a pragmatic approach,
the SOFCs is assumed to be used as ”stand-alone” boxes with
given inputs and outputs of fuel, electric power, and heat. In
reality, however, the internal heat balance of a SOFC system
can be shifted based on the main focus of the system, on the
costs of the heat exchanger network, and on other design and
operational parameters. The SOFC technology used in this
study can work at a 53% electrical efficiency and 27% ther-
mal efficiency, well-suited for cogeneration purposes. Other
SOFC-based cogeneration units have shown to be able to op-
erate at higher electrical efficiency, but with lower thermal
output, and at lower temperature. Future studies should focus
on estimating how the detailed optimization of the balance-
of-plant of the SOFC can influence the overall efficiency of
the system, thus helping future naval architects and fuel cell
developers in making the right design choices.
6. Conclusion
This paper presents the results of the optimization of a ship
propulsion plant using solid oxide fuel cells as the main energy
conversion device for the generation of electric power and
heat on board.
The results of this study showed that the proposed system
can achieve substantially higher performance compared to the
baseline, with the potential of reducing GHG emissions by
up to 34%. The results also showed that, in order to achieve
significant reductions in GHG emission, SOFCs are the most
cost-optimal solution when using natural gas as fuel. The
increase in total cost coming from a larger SOFC installed
on board can go up to 33% higher in the case of the cruise
ship and 43% higher in the case of the tanker. The case of the
cruise ship, given its more regular operational profile, seems to
be more suitable for a profitable installation of such systems,
also given their additional advantages of reducing noise and
vibrations.
The optimization problem was also analyzed in terms of
its sensitivity to the uncertainty of various problem param-
eters. This operation highlighted that the high uncertainty
on cost-related parameters for the SOFC makes a dramatic
difference in terms of cost-optimality. This observation leads
to the conclusions that future similar studies will need to take
uncertainty into account, given its high impact on the optimal
solution. In addition, from a practical perspective, the iden-
tified high relevance of parameters related to the investment
cost of SOFCs suggests the importance on focusing on abating
production costs, if a wider adoption of this technology in
shipping is to be expected in the future.
Acknowledgments
The work of FB is financed by the European Commission
with a H2020-MSCA-IF-EF grant (grant number 708288).
We would like to thank Antti Pohjoranta from VTT for the
fruitful discussions about the practical implications of the use
of fuel cells on board of ships, and Mar Perez-Fortes, Ligang
Wang and Jan van Herle for the discussions related to SOFCs,
their potential, and their modelling.
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