Integrated Evaluation of Ship Performance and Emission Reduction in Solid Oxide Fuel Cell–Based Hybrid Marine Systems

Abstract

This study presents a first-of-its-kind investigation into retrofitting domestic vessels with a novel hybrid system integrating a Solid Oxide Fuel Cell (SOFC) and an Internal Combustion Engine (ICE). Using a Lake Ferry and an Island Ferry as case studies, three power-sharing scenarios (10–20% SOFC contribution) were examined for cruise and port operations. The results show that increasing the SOFC power share enhances overall system efficiency, reducing daily fuel energy consumption by up to 9% while achieving SOFC efficiencies of 58–60% in port. The design analysis confirms the physical retrofit feasibility for both vessels, with all scenarios occupying 72–92% of available machinery space. However, increasing the SOFC share from 10% to 15–20% raised total system weight by 10–20% and volume by 12–27%. Economically, the system demonstrates strong viability for high-utilization vessels, with Levelized Cost of Energy (LCOE) values of 236–248 EUR/MWh, while the sensitivity analysis highlights the SOFC capital cost as the dominant economic driver. Environmentally, the hybrid system achieves annual CO₂ reductions of 46–51% and NOx reductions of 51–62% compared to conventional diesel systems, with zero NOx emissions in port. The SOFC-ICE hybrid system proves to be a robust transitional pathway for maritime decarbonization, particularly for vessels with significant port-side operating hours.

1. Introduction

Marine transportation has long been a cornerstone of global connectivity, facilitating trade and travel between nations. Maritime transportation is responsible for transporting over 80% of freight [1,2]. In the European Union (EU), maritime transportation is a cornerstone of trade, accounting for 77% of the region’s external trade and 35% of intra-EU trade [3]. According to deadweight tonnage, a metric used to evaluate cargo-carrying capacity, ships flying the flag of an EU member state accounted for over one-fifth of the global fleet in 2019. Individuals and companies registered in the EU own more than one-third of the ships involved in international trade [3]. Maritime transportation is critical for connecting the EU to global and local trade markets.

Ships operating solely on domestic routes accounted for roughly half of the EU’s maritime traffic in 2023, as measured by ships calling at ports [4]. The frequent journeys of ferries and roll-on, roll-off (Ro-Ro) passenger ships were a major factor in this count. Nearly 3.4 billion tons of products were handled by EU ports in that same year. Italian ports handled 472 million tons of freight, ranking second highest among European countries in maritime freight transport [5].

However, the maritime sector has an environmental impact globally and within the EU. Studies reveal that marine transportation contributes approximately 3−4% of the EU’s total carbon dioxide (CO₂) emissions [6]. Among all transportation modes reported in the EU greenhouse gases (GHG) inventory of 2022, maritime transport contributed 14.33% of total transport GHG emissions, the second-highest mode after road transportation [7]. It should be noted that this percentage includes the contribution of international shipping and national navigation (domestic maritime transport). The European Environment Agency, which was in charge of creating this inventory, considered no limitation on the gross tonnage of ships, but it considered the amount of fuel sold for navigation purposes inside the EU countries.

The emissions from maritime transportation inside the EU are divided into emissions from national navigation and international maritime transport. The maritime sector has shown little progress in reducing emissions in recent decades. The national navigation emissions have shown a weak reduction trend since 2005, except for the significant reduction in 2020 because of the COVID-19 pandemic.

CO₂ from fuel combustion was by far the most significant form of GHG emissions produced by the maritime transportation industry. In 2022, 135.5 million tons of CO₂ emissions were produced overall by 12,744 ships (ships above 5000 gross tonnage) reporting their emissions in EU-MRV (monitoring, reporting, and verification). For this purpose, the recorded CO₂ emissions in the MRV portal from its start in 2018 until the recent one in 2022 have been analyzed [8]. About 32.6% of all CO₂ emissions resulted from domestic vessels berthing in ports (at berth) and operating between ports in EU countries as intra-EEA voyages. The remaining 67.4% resulted from extra ships operated internationally, either their voyage started or ended in the European Economic Area (EEA).

Ship emissions are a special problem for coastal areas, as almost 40% of the EU’s population resides within 50 km of the coastline. Particulate matter (PM), nitrogen oxides (NOx), sulfur oxides (SOx), and carbon monoxide (CO) are among the chemicals released by ships that can have an impact on human health. These emissions may be substantial in regions with a high volume of maritime travel. Regarding the emissions data contained in the EU inventory report for 2022 [9], the national navigation produced 74.5% (21.6 kt), 31.2% (221.2 kt), 33% (14.5 kt), and 6.6% (100.3 kt) of all SO₂, NOx, PM2.5, and CO emissions resulting from the non-road transport sector in the EU. SOx emissions resulting from the utilization of fossil fuels onboard ships are mainly sulfur dioxide (SO₂).

It is anticipated that international shipping will increase throughout the ensuing decades. It is anticipated that global trade will expand by 9% between 2030 and 2050 and that the amount of transportation for all ship types will increase by 24% by that time. Furthermore, the International Marine Organization (IMO) has projected that, under the business-as-usual scenario, the marine sector’s GHG emissions will rise to roughly 90–130% of 2008 emissions by 2050 [10].

The waterborne transport sector is looking into the transition to zero-emission technologies to reduce environmental impacts. Therefore, retrofitting the ships’ power systems with advanced systems based on fuel cell technology represents a valuable step towards the target of zero-emission waterborne transport. Domestic vessels, such as Short-Sea Ferries, Lake Ferries, and Island Ro-Pax Ferries, provide a unique potential for such developments due to their operational characteristics and closeness to urban areas where emission reductions are essential. Furthermore, hybrid systems that combine Solid Oxide Fuel Cell (SOFC) and Internal Combustion Engine (ICE) demonstrate tremendous potential for optimizing performance while resolving the cost and risk constraints associated with early technology adoption. However, the viability and integration of such systems on domestic vessels have received little attention in the literature.

For this purpose, the current paper aims to investigate the feasibility of retrofitting exisiting domestic vessels with advanced power systems, with a focus on fuel cell technologies, to aid in the transition to sustainable navigation. The study aims to investigate the feasibility and performance of a unique hybrid system that combines SOFC and ICE for use on domestic vessels.

2. Literature Review of SOFC-Based Systems

SOFC systems have attracted a lot of attention in recent years because of their high efficiency, extremely low emissions, and noiseless operation. Their limited development state, low gravimetric and volumetric density, and high costs have prevented widespread implementation of this promising technology [11]. An SOFC may take minutes to respond to a load [12,13]. The start-up period of SOFCs can be longer than 10 min to prevent large temperature gradients and thermal stresses. In addition, the effective commercialization of SOFCs is challenged by the fact that they can be significantly heavier and larger than a conventional ICE with a comparable power output. For maritime applications, the main drawbacks of an SOFC system as a standalone propulsion system for small vessels (domestic vessels) are the high capital expenses, low energy density, and slow transients, as reported in [14]. Additionally, they need to operate at a constant load, and they require a long time for the start-up procedure. Thus, they operate mostly as an Auxiliary Power Unit (APU) to satisfy hotel load demands [15] rather than for propulsion.

To overcome these limitations, integrating SOFCs with thermal energy recovery systems in a hybrid configuration presents a promising pathway. The high-temperature exhaust from an SOFC can be utilized in a bottoming cycle to enhance overall system efficiency. Extensive research exists on SOFC integration with Gas Turbines (GT) [16,17] and Steam Turbines (ST) [18], where the turbine expands the anode-off gas (AOG) to generate additional power. While such systems can achieve high efficiencies (e.g., ~68% for a 1.5 MW SOFC-GT [19]), they suffer from critical drawbacks for marine use: (i) poor part-load efficiency (e.g., dropping to ~37% at 57% rated power [20]), (ii) complex control and slow transients due to intricate coupling [20,21], and (iii) high capital costs, exacerbated by the expense of small-scale turbines [20].

A more responsive alternative is the hybridization of SOFC with Internal Combustion Engines (ICE). ICEs offer superior transient response, higher part-load efficiency, and lower sensitivity to ambient conditions compared to GTs [22,23]. Research on SOFC-ICE systems has explored integrations with Homogeneous Charge Compression Ignition (HCCI) [24,25,26] and Spark Ignition (SI) engines [27,28]. In these studies, the SOFC typically acts as the primary power generator (>70% share), with the ICE serving as a bottoming cycle fueled by the SOFC’s AOG. This configuration prioritizes maximum electrical efficiency, with reported system efficiencies reaching 59–73% for stationary applications [29,30].

However, a critical gap exists in translating these systems to maritime propulsion. Shipboard power systems must balance efficiency with stringent constraints on weight, volume, and economic viability over a vessel’s lifetime. Previous maritime-focused SOFC-ICE studies [31,32] have made valuable contributions but exhibit notable limitations. Sapra et al. [31] modeled a 750 kW atmospheric SOFC-ICE but did not consider optimal design points or key maritime metrics, such as retrofit weight/volume, and detailed economic feasibility. The reported hybrid efficiency (42–45.2%) was comparable to, but did not surpass, modern marine gas engines (e.g., Rolls-Royce Bergen C26-33 (η = 44.4%) [33], Wärtsilä 6L20DF (η = 43.5%) [34], and Caterpillar 3512E (η = 41.5%) [35]).

Ma et al. [36] investigated an ammonia-fueled SOFC-ICE for a tanker, achieving 46.6% efficiency with a 70% SOFC share. However, this study has several gaps; there is no explanation of the economic performance of such a configuration in terms of capital and operational costs, nor the design feasibility of such a configuration in terms of weight and volume. Also, the hybrid system efficiency using 70% SOFC could not compete with advanced marine gas engines of the same power rating.

The literature reveals a common theme: prior research, whether for stationary or maritime use, overwhelmingly prioritizes fuel-to-power efficiency, with the SOFC as the primary power source. This approach does not align optimally with the operational profile of many vessels, especially domestic ferries, which require robust power for propulsion transients and spend significant time at berth. Furthermore, comprehensive assessments that simultaneously evaluate the design feasibility (weight/volume), economic lifecycle cost (LCOE), and environmental impact of such hybrids are conspicuously absent.

To fill this gap in the literature, the current paper presents a multi-aspect assessment methodology to investigate the feasibility of an innovative hybrid system between SOFC and ICE, where the ICE contributes a significant share of the load (80–90% of the hybrid system’s total power). This hybrid system is based on a more flexible ICE, which can be operated using a blend of AOG and natural gas to cover the power demand of ships, rather than being dependent on AOG only as a bottoming cycle, like that proposed in the literature studies [29,30,37]. The analysis is grounded in the off-design performance maps of the hybrid system [38], ensuring that the investigated scenarios represent feasible and near-optimal operating points for the actual duty cycles of the case study vessels.

Crucially, this work incorporates SOFC performance degradation modeling over the system’s operational lifetime and conducts a probabilistic uncertainty and sensitivity analysis to assess the robustness of economic and performance outcomes under realistic parameter variations.

3. Domestic Vessels as Case Studies

This study focuses on small domestic vessels whose operational characteristics, including a lower requirement for propulsion power, predictable schedules, and operations in urban areas, make these ideal candidates for innovative power systems and alternative fuels. For this study, two case studies of domestic vessels have been selected. These include a lake RoPax ferry that operates on Lake Garda in Italy as an inland waterway transport mode to connect various towns [39]. Also, an island RoPax ferry connects two islands in Italy for short-sea navigation [40].

Table 1. Characteristics of the RoPax ferries.

Parameter	Unit	Lake Ferry	Island Ferry
Navigation Route	(-)	Lake Garda	San Pietro–Sardinia Island
Length–Breadth–Depth	(m)	54–10.8–2.34	77–17.2–4.53
Carrying capacity	(-)	1000 passengers + 48 cars	771 passengers + 142 cars
Displacement	(ton)	558	1994
Maximum service speed	(knots)	9.7	11.5
Annual operational hours	(hours)	2188	8640
Available Machinery space	(m3)	45	57

shows the main characteristics of the two ships.

The ship’s characteristics and the power empirical formulas are employed to create the ship’s power profile, expressed by correlating the required power at different ship speeds. The daily power demand profile for the case studies was evaluated and is presented in Figure 1.

Moreover, the data has been analyzed to extract the operational time of each mode (cruise and port), the required power, and energy consumption per day (Figure 2).

4. Methodology and Modeling Framework

The integration of innovative energy systems onboard ships has emerged as a crucial strategy for addressing the dual challenges of environmental sustainability and operational efficiency in the maritime industry. This section focuses on the comprehensive feasibility of deploying a hybrid system combining SOFC and ICE onboard domestic vessels. This study develops a systematic methodology, as shown in Figure 3. The methodology begins by identifying and analyzing reference vessels from domestic vessels (Section 3).

Also, the first phase intends to develop the operational profile of the reference vessel, considering its navigational route, operational data, and varying power demands under different operating modes (such as cruise operations and hoteling mode while docked in port). This operational profile serves as a key input for designing the hybrid system.

In the second phase, the integrated SOFC-ICE system is designed, with a specific focus on the required Balance of Plant (BoP) and Power Conditioning Equipment (PCE). This phase incorporates the development of different hybrid system scenarios by varying the power split between the SOFC and ICE.

The third phase builds on the findings of the previous phases to model the energy profile of the hybrid system, considering the system efficiency. This phase includes calculations of fuel energy consumption, which are critical for assessing the performance. The fourth phase addresses the design analysis of the hybrid system, considering key parameters such as the weight and volume requirements of the SOFC, ICE, BoP, PCE, and fuel storage system (FSS). These design factors directly impact the feasibility of retrofitting the hybrid system onboard domestic vessels.

The fifth phase focuses on the economic analysis of the hybrid system scenarios, employing models for capital expenses (CapEx), operational expenses (OpEx), and voyage expenses (VoyEx). The levelized cost of energy (LCOE) is calculated to provide a comprehensive assessment of the economic viability of the proposed hybrid configurations. Also, an uncertainty and sensitivity analysis is be conducted for LCOE by changing the main economic parameters. Finally, an environmental analysis is proposed to be conducted in the sixth phase by calculating the CO₂ and NOx emissions to rank the environmental impacts of using the SOFC-ICE hybrid system instead of conventional power system configurations.

4.1. General Modeling Assumptions and Boundary Conditions

This study adopts a quasi-steady-state, time-weighted system modeling framework to evaluate the feasibility of integrating SOFC with ICE onboard domestic vessels. The analysis is conducted at the system level, with a focus on operationally representative duty cycles rather than fast transient dynamics. The following general assumptions apply to all analysis modules:

I.

Vessel operation is decomposed into discrete operating modes, cruise and port, each characterized by a constant duration and energy demand per day.

II.

The SOFC is operated under controlled load conditions and is assumed to remain within its safe thermal operating envelope, avoiding rapid load transients.

III.

The ICE is responsible for accommodating load fluctuations and transient power demands during cruise mode.

IV.

All calculations are performed, assuming steady ambient conditions representative of temperate maritime environments.

V.

The analysis focuses on tank-to-propeller emissions and costs; upstream fuel production emissions are excluded.

These assumptions are consistent with the operational characteristics of domestic ferries with repetitive daily routes and predictable power demand profiles.

4.2. Hybrid System Scenarios

The current paper proposes the integration of SOFC and ICE as a novel marine propulsion system for domestic vessels fueled by liquefied natural gas (LNG). To increase the hybrid system’s efficiency, the AOG is recirculated and blended with LNG to be used in the ICE to deliver additional electrical power. As shown in Figure 4, the hybrid system is proposed to have dual operation modes; the first one is for propulsion during cruise mode, generating power with ICE and SOFC. In this way, the ICE guarantees the necessary responsiveness during high load demand, load transients, and fast maneuvering. The SOFC satisfies the hotel load, delivers part of its generated electric power for propulsion, and increases the hybrid system’s electrical efficiency by feeding the ICE with AOG. The second operation mode is based on using SOFC to generate the electrical power required for hotel operations during their existence in port areas. The full configuration of the integration concept between SOFC and ICE, including BoP, is described in [38].

The case studies under investigation (Section 3) will be used to examine the feasibility of this innovative hybrid system. The innovative power system will be designed to deliver 1000 kW and 1200 kW as target power for Lake and Island Ferries, respectively. The amount of effective energy will be designed to accommodate an endurance of around 10.5 h and 24 h for Lake and Island Ferries, respectively. The current study investigates three scenarios for SOFC-ICE integration during cruise operations, as shown in

Table 2. Hybrid system scenarios in cruise operations for Lake and Island Ferries.

Scenario Number	SOFC Modules	Load % (SOFC-ICE)	Lake Ferry	Island Ferry
			Power (kW)	Power (kW)
1	2	10–90%	100–900	120–1080
2	3	15–85%	150–850	180–1020
3	4	20–80%	200–800	240–960

. The hybrid system scenarios investigated in this study are defined by varying the installed SOFC capacity through the number of identical SOFC modules integrated into the hybrid power system. Each SOFC module has a maximum power output of 60 kW.

For cruise operation, the minimum required SOFC power in Scenario 1 has been defined based on the hoteling demand of the vessels, ensuring that the installed SOFC capacity can fully cover port operations while also contributing to propulsion during sailing. The second and third scenarios are proposed by increasing the SOFC share in cruise operations to investigate its effect from a design, economic, and environmental perspective.

4.3. Energy Demand Analysis Approach

The fuel energy consumption for each system configuration is calculated based on the power demand for each operational mode, its corresponding duration, and the energy efficiency of the power generation system. The daily fuel energy required $E{C}_F$ (GJ/day) to cover the defined endurance time (End) and is computed using Equation (1).

$${EC}_F=\sum _{End}\sum _{j=1}^j{\displaystyle \frac{{PD}_j\times {OT}_j}{{\eta }_j}}\times 3.6\times {10}^{-3}$$

(1)

where ${PD}_j$ is the power demand for each operating mode (j), ${OT}_j$ is its corresponding operational time, and ${\eta }_j$ is the system efficiency in the j-operating mode (cruise and port) calculated as shown in Equation (2).

$${\eta }_{ cruise}={\displaystyle \frac{P_{SOFC}+P_{ICE}}{\left({\dot{m}}_{fuel,SOFC}+{\dot{m}}_{fuel,ICE}\right)· LH{V}_{fuel}}}, {\eta }_{port}={\displaystyle \frac{P_{SOFC}}{{\dot{m}}_{fuel,SOFC}· LH{V}_{fuel}}},$$

(2)

where $P_{\mathit{SOFC}}$ and $P_{\mathit{ICE}}$ are the power outputs of the SOFC and ICE, respectively, ${\dot{m}}_{\mathit{fuel}}$ is the fuel mass flow rate, and $LH{V}_{fuel}$ is the lower heating value of the LNG (48 MJ/kg). The efficiency of the SOFC–ICE hybrid system during cruise operation is represented as a function of the SOFC design load factor. The SOFC load factor is defined as the ratio between the electrical power required from the SOFC system during operation and the installed nominal electrical capacity of the SOFC system for each hybrid scenario.

For each scenario, the SOFC design point during cruise is set by the minimum required SOFC contribution and the number of installed 60 kW modules. For Lake Ferry, Scenario 1 requires 100 kW, achieved with two modules (120 kW) operating at an 83.3% load factor. For Island Ferry, SOFC operates at its nominal capacity (100% load factor) in all scenarios. These points form the basis for system sizing and performance evaluation.

Figure 5a presents the efficiency curves of the SOFC–ICE hybrid system in cruise as a function of the SOFC load factor for the three investigated scenarios. These curves were developed based on the detailed off-design modeling of the hybrid system reported in [38]. The off-design analysis accounts for the electrochemical performance of the SOFC system and the interaction between the SOFC anode-off gas and the ICE. For all cruise operating points, the SOFC fuel utilization factor is fixed at 60%, which was identified in the off-design analysis as the optimal operating condition ensuring high electrical efficiency while maintaining safe electrochemical and thermal margins [38].

During port operations, the hybrid system operates in a different configuration in which the ICE is switched off, and the SOFC system supplies the entire onboard electrical demand. In this operating mode, the SOFC functions as a standalone power generation unit, and its electrical efficiency depends solely on its load factor, as shown in Figure 5b. This efficiency curve was evaluated at a fuel utilization factor of 80%, which was identified as an optimal operating condition for port hoteling applications [38].

To account for the long-term performance decay of the SOFC system, a linear degradation model is applied relative to the stack’s total useful lifetime. The model assumes a total efficiency loss $\Delta {\eta }_{\mathit{SOFC}}^{\mathit{total}}$ (in percentage points) occurring linearly over the stack’s rated lifetime of 40,000 h. The instantaneous SOFC electrical efficiency at cumulative operating hours $h$ is evaluated as shown in Equation (3).

$${\eta }_{ SOFC}\left(h\right)={\eta }_{ SOFC, BoL}-({\Delta \eta }_{SOFC}^{total}\times {\displaystyle \frac{h}{ Z_q}})$$

(3)

where $Z_q=\mathrm{40,000}$ h is the stack lifetime and ${\eta }_{\mathrm{SOFC}, \mathrm{BoL}}$ is the beginning-of-life efficiency taken from Figure 5. The cumulative operating hours $\mathrm{h}$ for each year are derived from the vessel’s annual operational profile (8640 h/year for Island Ferry and 2188 h/year for Lake Ferry).

An average degradation rate of 0.25% per 1000 h is assumed and aligned with long-term targets for stable stationary SOFC systems operating on natural gas [41]. Therefore, a baseline total efficiency loss ($\Delta {\eta }_{SOFC}^{total}$) of 10% over the stack lifetime is expected if the lifetime is 40,000. For sensitivity analysis, the loss per 1000 h is varied between 0.125% (high-stability cells) and 0.5% (accelerated degradation under harsh maritime conditions), as detailed in Section Uncertainty and Sensitivity Analysis.

In the annual energy calculation, the SOFC efficiency for the year $n$ is taken as the average efficiency over that year’s operating interval. This time-varying efficiency directly affects the annual fuel consumption $E{C}_{F,n}$ and, consequently, the voyage expenditures ($VoyE{x}_n$) in the economic analysis. Future research should integrate more advanced, real-time degradation models, such as polarization-loss-decomposition methods and online health-state estimation [42,43], to enable dynamic lifetime prediction and optimized maintenance scheduling for maritime SOFC systems.

4.4. Design Analysis Approach

The design analysis approach aims to assess the feasibility of implementing clean power systems, considering the physical limitations of the case study in terms of available weight and volume onboard. The design analysis offers insights into the feasibility of each scenario for the operational profile of the ship by measuring and examining weight and volume factors. This method makes sure that the systems chosen are feasible with the vessel’s propulsion needs and physical limitations.

Each power system is composed of the SOFC, ICE, BoP, and other components. The latter includes PCE, such as DC/DC converters, variable frequency drives (VFDs), DC/AC inverters, and DC cabinets, as well as PTO/PTI motors, which are essential components of the propulsion system. The design analysis approach also assessess the weight and volume requirements of fuel storage systems to support the identified endurance time.

The weight and volume of the hybrid system scenario (HSS) are evaluated as shown in Equations (4) and (5) [44], considering the inclusion of the weight and volume of the FSS based on the developed energy profile.

$$W_{HSS}=W_{FSS}+\sum _{PG}{\displaystyle \frac{P_{PG}}{{GD}_{PG}}}+\sum _{BoP}{W}_{BoP}+\sum _{PCE}{\displaystyle \frac{P_{PG}}{{GD}_{PCE}}}$$

(4)

$$V_{HSS}=V_{FSS}+\sum _{PG}{\displaystyle \frac{P_{PG}}{{VD}_{PG}}}+\sum _{BoP}{V}_{BoP}+\sum _{BoP}{\displaystyle \frac{P_{PG}}{{VD}_{PCE}}}$$

(5)

where W and V are the weight in (tons) and volume in (m³), respectively. The resulting weight and volume of power system components can be calculated by dividing the delivered power by the gravimetric power density (GD) and volumetric power density (VD), respectively. The PG refers to power generation, including the SOFC and ICE. For this study, actual design data have been collected, as shown in

Table 3. Design information for different power system components.

Component	Product Reference	Gravimetric Density (kW/ton)	Volumetric Density (kW/m3)	Ref.
ICE	Bergen C26:33L6PG	91.43	70.10	[33]
SOFC	Bloom Energy	21.96	11.1	[45]
Converter-Inverter	Foripower	5128	9936	[46]
DC cabinet	ABB ACS880	1041.67	549.72	[47]
PTO/PTI motor	ABB M3BP 500LA 4	1864.4	389.6	[48]

.

4.5. Economic Analysis Approach

The economic assessment of installing a hybrid system is crucial in maritime applications to help the decision-makers in their selection. Therefore, the current paper will economically assess the different scenarios using LCOE as a cost assessment indicator. The LCOE can be calculated as shown in Equation (6) by adjusting all future costs, including OpEx and VoyEx, up to current values while taking a discount rate into account.

$${LCOE}_{HSS}={\displaystyle \frac{({CapEx}_{HSS}^d+{CapEx}_{HSS}^{ind})+\sum _{n=1}^{LT}\frac{\sum _x{OpEx}_{x,n}}{{(1+d)}^n}+\sum _{n=1}^{LT}\frac{{VoyEx}_n}{{(1+d)}^n}}{\sum _{n=1}^{LT}\frac{{EE}_{HSS,n}}{{(1+d)}^n}}}$$

(6)

where d and n represent the discount rate and the n-th year of the lifetime, respectively. The current study considers 5% and 25 years as the discount rate (d) and the number of lifetime (LT) years, respectively. ${EE}_{HSS,n}$ is the annual energy generated by the hybrid system scenario in MWh. Costs associated with the investment required to purchase the power system components are referred to as the direct capital expenses (${CapEx}_{cps}^d$) as shown in Equation (7). While the indirect capital expenses, including commissioning, installation, engineering, and design costs, are referred to (${CapEx}_{cps}^{ind}$).

$${CapEx}_{HSS}^d={CF}_{FSS}\times {EC}_{F,PG}+\sum _{PG}{P}_{PG}\times {CF}_{PG}+\sum _{BoP}{P}_{HSS}\times {CF}_{BoP}+\sum _{PCE}{P_{HSS}\times CF}_{PCE}$$

(7)

where ${CF}_{PG}$, ${CF}_{BoP}$ and ${CF}_{PCE}$ are cost factors in EUR/kW for power systems, BoP, and PCE (DC/DC converter, VFD, PTI/PTO motor, and DC/AC inverter), respectively. The FSS cost factor (${CF}_{FSS}$) in EUR/GJ can be calculated by using the financial maps available in [49] and multiplying by the required fuel energy (${EC}_{F,PG}$) to be stored per endurance time. The cost factors of different components in the hybrid system are reported in

Table 4. Cost parameters of power system components.

Component	CapEx Factor (EUR/kW)	OpEx Factor (% of CapEx/year)	Ref.
ICE	600	2%	[50]
SOFC	5000	2%	[41]
PTI/PTO motor	250	1%	[51]
VFD	120	1%	[52]
Converter/inverter	120	1%	[52]
LNG reformer	370	-	[53]

. All costs are expressed in EUR.

The ${\mathrm{O}\mathrm{p}\mathrm{E}\mathrm{x}}_{x,\mathrm{n}}$ is the annual operating and maintenance expenses of the x-th component in the power system. It must be noted that the replacement cost of SOFC stacks is considered in their OpEx category. The anticipated expansion of the market leads to lower replacement costs being 50% of the initial investment [44]. In the current study, the lifetime of SOFC stacks is assumed to be 40,000 h [54]. Also, the stacks of fuel cells are assumed to account for 75% of the system’s CapEx, respectively [55]. The number of replacements of the FC can be calculated as shown in Equation (8).

$$N_{RE}={\displaystyle \frac{{{LT}_{ship}\times J}_{trip,ann}\times {OT}_{trip}}{Z_q}}-1$$

(8)

where ${LT}_{ship}$ is the lifetime of the ship in years, $J_{trip,ann}$ is the number of trips per year, ${OT}_{trip}$ is the duration of the trip in (h), and $Z_q$ is the lifetime of SOFC in hours. In the formula, a subtraction of (1) indicates the initial installation of SOFC in the investment phase.

The OpEx of fuel processing and PCE is assumed to be 1% of their CapEx [52]. The VoyEx evaluation is based on the annual fuel consumption; therefore, its value can be calculated as shown in Equation (9).

$${VoyEx}_n=\sum _{year}{EC}_{F,PG}\times {(CF}_{fuel}+{CF}_{pf})$$

(9)

where ${CF}_{fuel}$ is the fuel cost factor in EUR/GJ, and ${CF}_{pf}$ is the port charge for bunkering [56]. The cost factor of LNG (24.1EUR/GJ) is based on the fuel cost calculator tool of the Mærsk Mc-Kinney Møller Center [57].

Uncertainty and Sensitivity Analysis

The economic feasibility of the proposed SOFC-ICE hybrid system is subject to uncertainties in key economic parameters. To robustly quantify the impact of these uncertainties and identify the most influential variables, a probabilistic analysis combining Monte Carlo simulation and global sensitivity analysis is conducted. The LCOE is the primary output metric.

Four parameters with high uncertainty and significant influence on total system cost were selected for analysis: SOFC capital cost, SOFC stack lifetime, LNG fuel price, and SOFC degradation rate. Each parameter is assigned a uniform probability distribution across its plausible range, reflecting a lack of prior knowledge about where within the range the true value may lie. The distributions are summarized in

Table 5. Parameters for sensitivity analysis: baseline values and probability distributions.

Parameter	Symbol	Baseline Value	Probabilistic Range
SOFC CapEx	${\mathrm{C}\mathrm{F}}_{SOFC}$	5000 EUR/kW	3000–7000 EUR/kW
SOFC Stack Lifetime	${\mathrm{Z}}_q$	40,000 h	30,000–50,000 h
LNG Fuel Price	${\mathrm{C}\mathrm{F}}_{fuel}$	24.1 EUR/GJ	18.1–30.1 EUR/GJ
Degradation rate	dSOFC	0.25%/kh	0.125–0.5%/kh

.

A Monte Carlo simulation with 10,000 iterations is performed for each case. In each iteration, a random value for each of the four parameters is sampled independently from its uniform distribution. The LCOE is recalculated using the integrated energy-economic model. This process yields a probability distribution of possible LCOE outcomes for each case, from which key statistics (mean, median, standard deviation, 5–95th percentile range) are extracted.

To complement the uncertainty quantification and identify which parameters drive the output variance, a global sensitivity analysis is conducted using the results of the Monte Carlo simulation. For each case, the Pearson correlation coefficient ($r$) between each input parameter $p$ and the output LCOE is calculated as shown in Equation (10).

$$r_p={\displaystyle \frac{\sum _{i=1}^N(p_i-\bar{p}\left)\right(LCO{E}_i-\overline{LCOE})}{\sqrt{\sum _{i=1}^N(p_i-\bar{p}{)}^2\sum _{i=1}^N({LCOE}_i-\overline{LCOE}{)}^2}}}$$

(10)

where $N=\mathrm{10,000}$, $p_i$ and $LCO{E}_i$ are the sampled values in iteration $i$, and $\bar{p}$ and $\overline{LCOE}$ are their respective means. The absolute value of $r_p$ ($\mid r_p\mid$) indicates the strength of the linear relationship, serving as a robust measure of parameter importance. A value close to 1 denotes a strong, dominant influence on LCOE variability, while a value close to 0 indicates negligible influence.

4.6. Environmental Analysis Approach

The current section shows the environmental approach to analyzing the innovative hybrid system between SOFC and ICE. The current study focuses on calculating CO₂ and NOx emissions. The NOx emissions are produced only from the ICE, while the CO₂ emissions are expected from the SOFC and ICE. Because innovative integration has a particular approach to integration based on the utilization of AOG as a fuel in the ICE, the author developed an approach to calculate the specific emissions of NOx and CO₂.

First, it is essential to determine the stoichiometric air-fuel ratio (AFR), which is the ideal mass ratio of air to fuel needed for complete combustion. This ratio varies depending on the composition of the fuel. Since the AOG-NG fuel has a unique composition at each design point, the stoichiometric AFR must be recalculated every time using the following steps. The first step involves calculating the stoichiometric air requirement based on the combustion reaction for each component of the fuel, as outlined in Equation (11).

$$C_x{H}_x+\left(x+{\displaystyle \frac{y}{4}}\right)O_2\to x{CO}_2+{\displaystyle \frac{y}{2}}{H}_{2}O$$

(11)

For each fuel component, the number of oxygen moles required is ($x+{\displaystyle \frac{y}{4}}$). Figure 6 shows the combustion reaction of each fuel component that exists in the AOG-NG fuel.

Then the mass of oxygen required to complete the combustion of each fuel component has to be calculated based on the molar mass of the fuel component ($M_{comp}$) and oxygen ($M_O$) and the mass fraction of each component in the fuel ($z_{comp}^{fuel}$). Then the stoichiometric AFR can be calculated by dividing the total oxygen requirement by the mass fraction of oxygen in the air ($z_{O2}^{air}$) as presented in Equation (12).

$${AFR}_{stoich}={\displaystyle \frac{\sum _{comp}{z}_{comp}^{fuel}\times \left(x+\frac{y}{4}\right)\times \frac{M_O}{M_{comp}}}{z_{O2}^{air}}}$$

(12)

Also, it is important to evaluate the air excess ratio (λ) by dividing the air’s actual mass flow rate by the stoichiometric mass flow rate of air as presented in Equation (13).

$$\lambda ={\displaystyle \frac{{\dot{m}}_{air}^{actual}}{{AFR}_{stoich}\times {\dot{m}}_{fuel}}}$$

(13)

In the developed model, the NOx emission can be calculated for each scenario based on the fuel composition and the exhaust. For this purpose, the reference pollution emission mass concentration (${pemc}_{NOx, ref}$) of NOx is assumed to be 500 mg/Nm³ at 5% reference oxygen in the exhaust ($M_{O2}^{exh-ref}$) to calculate the parts per million in volume (ppmv) of NOx. However, this value can be corrected to the actual value in the simulated scenario following the formula in Equation (14).

$${ppmv}_{NOx}={\displaystyle \frac{{pemc}_{NOx, ref}}{{\rho }_{NO2}}}\times {\displaystyle \frac{M_{O2}^{air-in}-M_{O2}^{exh-out}}{M_{O2}^{air-in}-M_{O2}^{exh-ref}}}$$

(14)

where $M_{O2}^{air-in}$, and $M_{O2}^{exh-out}$ are the molar fraction of O₂ in the air at the inlet and the actual molar fraction of O₂ in the exhaust at the outlet, respectively. For this purpose, the NO₂ density (${\rho }_{NO2}$) equals 2.05 kg/m³. The actual oxygen percentage in the exhaust can be calculated as shown in Equation (15).

$$M_{O2}^{exh-out}={\displaystyle \frac{M_{O2}^{air-in}\times (1-\lambda )}{0.25\times \frac{z_H^{fuel}}{M_H}\times \frac{M_{air}}{{AFR}_{stoich}}-\lambda }}$$

(15)

where $z_H^{fuel}$ is the mass fraction of hydrogen in the fuel. $M_H$ and $M_{air}$ are the molecular weights of hydrogen and air, respectively. Equation (16) can be used to calculate the specific emission of NOx in g/kWh.

$$\begin{array}{c}{spe}_{NOx}={\displaystyle \frac{{ppmv}_{NOx}}{{10}^6}}\times z{\displaystyle \frac{{\rho }_{NO2}}{{\rho }_{gas}}}\times \left(\lambda \times {AFR}_{stoich}+1-0.5\times {\displaystyle \frac{M_{H2O}}{M_H}}\times z_H^{fuel}\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\times {SFC}_{ICE}\hfill \end{array}$$

(16)

where ${\rho }_{gas}$ is the density of exhaust gas (1.362 kg/m³). ${SFC}_{ICE}$ is the specific fuel consumption of the ICE in g/kWh.

Furthermore, the CO₂ emissions are evaluated to figure out the environmental impact of the hybrid system. Using the carbon balance method, the CO₂ emissions per kg of fuel combusted in an ICE can be calculated. For each component in the fuel, the CO₂ produced per kilogram of fuel component can be calculated using its combustion reaction (specifically, the number of carbon atoms (x)), following the formula in Equation (17).

$${{CO}_2}_{comp}={\displaystyle \frac{x\times M_{CO2}}{M_{comp}}}$$

(17)

Then, the weighted average CO₂ emission per kilogram of fuel can be calculated using the mass fraction of each component in the fuel, as shown in Equation (18).

$${{CO}_2}_{fuel}=\sum _{comp}{z}_{comp}^{fuel}\times {{CO}_2}_{comp}$$

(18)

Using the efficiency of ICE (%) and the energy content of the fuel (MJ/kg), the specific CO₂ emission for ICE can be calculated, as shown in Equation (19).

$${spe}_{{CO}_2, ICE}={\displaystyle \frac{{{CO}_2}_{fuel}\times {10}^3}{{LHV}_{fuel}\times 0.2778\times {\eta }_{ICE}}}$$

(19)

where ${LHV}_{fuel}$ is the lower heating value of fuel in MJ/kg, while the factor 0.2778 is to convert MJ to kWh. The resulting specific emission of CO₂ (${spe}_{{CO}_2, ICE}$) is measured in g/kWh related to the output energy from the ICE.

Regarding the CO₂ emission generated from the SOFC system in the hybrid system, it is more related to the exhaust produced after the turbocharger. It can be calculated based on the amount of exhaust and the mass percentage of CO₂ in its composition, as shown in Equation (20).

$${spe}_{{CO}_2, SOFC}={\displaystyle \frac{z_{{CO}_2}^{exh}\times {\dot{m}}_{exh}}{P_{SOFC,net}}}\times 3.6\times {10}^6$$

(20)

where $z_{{CO}_2}^{exh}$ is the mass fraction of CO₂ in the SOFC exhaust (exh), ${\dot{m}}_{exh}$ is the mass flow rate in kg/s of exhaust, $P_{SOFC,net}$ is the net generated power from the SOFC system, and ${spe}_{{CO}_2, SOFC}$ is the specific emission of CO₂ from the SOFC system in g/kWh.

5. Results and Discussions

This section investigates the feasibility analysis results of different integration scenarios of SOFC and ICE onboard a Lake Ferry and an Island Ferry. This section is divided into four subsections; the first one is related to the energy analysis results, while the second, third, and fourth subsections represent the feasibility assessment results from the design and economic, and environmental points of view, respectively.

5.1. Energy Demand Analysis Results

Daily fuel energy consumption is significantly affected by the system’s efficiency across different operating modes. The previous work of the authors [38] proved that the efficiency of the SOFC system increases during part-load operation. This finding also aligns with real-world performance curves from Convion [58].

In the context of port operations, the SOFC system should operate under part-load conditions to meet the required hoteling power, especially when the installed SOFC power capacity is increased, as outlined in Scenarios 2 and 3. As a result, the SOFC efficiency in port operations for Island Ferry rises from 55% in Scenario 1 to 60.1% in Scenario 2 and 59.3% in Scenario 3, confirming that part-load conditions enhance efficiency. Therefore, the port’s daily fuel consumption is reduced in Scenarios 2 and 3 compared to Scenario 1, as illustrated in Figure 7b.

Additionally, the hybrid system efficiency during cruise operating modes improves in Scenarios 2 and 3 as a highly efficient SOFC contributes by a high load share, and a high fraction of the AOG is available to be combusted in the integrated engine. This is aligned with the findings of operating the SOFC-ICE system during the cruise at the optimum point (60% UF and 100% SOFC load share) that concluded in [38].

The results also reveal a reduction in cruise energy consumption for the Lake Ferry, decreasing from 43.36 GJ/day in Scenario 1 to 39.27 GJ/day in Scenario 3. Also, the cruise energy consumption for the Island Ferry has been reduced from 71 GJ/day in Scenario 1 to 64.5 GJ/day in Scenario 3. Therefore, the increment in SOFC power share in the total output power from the hybrid system is beneficial in terms of energy efficiency.

Impact of SOFC Degradation on Fuel Consumption

The integration of the SOFC degradation model reveals the significant long-term impact of stack performance decay on fuel consumption. While beginning-of-life (BoL) efficiencies drive the results in Figure 7, the effective annual fuel requirement increases progressively over the system’s operational life.

Table 6. Impact of SOFC degradation on annual fuel energy consumption (GJ/year) at selected lifecycle stages.

Vessel	Scenario	Year 1 (BoL)	Year 8	Year 16	Year 25 (EoL)	Cumulative Increase
Lake Ferry	S1	2601	2714	2855	2680	4.76%
	S2	2479	2581	2709	2551	4.52%
	S3	2363	2456	2573	2429	4.31%
Island Ferry	S1	8055	8468	8055 *	8928	5.28%
	S2	7646	8015	7646 *	8423	4.95%
	S3	7337	7680	7337 *	8058	4.79%

Note: Values marked with (*) correspond to a year in which an SOFC stack replacement occurs, resetting efficiency to BoL values.

presents the annual fuel energy consumption at strategic intervals over the 25-year lifespan, incorporating the baseline degradation rate of 0.25% per 1000 h. The final column quantifies the cumulative percentage increase in total fuel consumption compared to a hypothetical non-degrading system operating at constant BoL efficiency.

The data reveals two distinct degradation profiles shaped fundamentally by operational intensity. The Island Ferry, with its high annual runtime, exhibits a pronounced cyclic pattern where consumption rises substantially by Year 8, approximately 11% above BoL values due to accumulated degradation, then resets to BoL levels in Year 16 following a stack replacement. This sawtooth pattern repeats, resulting in a final Year 25 consumption similar to Year 8 and a cumulative fuel penalty of 4.8–5.3%.

In contrast, the Lake Ferry, with significantly lower annual operating hours, shows a more gradual, near-linear increase until its single stack replacement near Year 18. Consumption peaks at Year 16 at roughly 9.8% above BoL before the replacement causes a reduction in Year 25, yielding a lower cumulative penalty of 4.3–4.76%. This stark difference underscores that degradation is not a fixed technological cost but an operationally dependent variable, where vessels with high fuel cell usage face substantially amplified lifecycle fuel penalties.

A further critical observation is that the degradation penalty, expressed as a percentage, is inversely related to the SOFC power share. For a given vessel, scenarios with higher SOFC contribution (S3) consistently show a lower cumulative percentage increase. For instance, the Island Ferry’s penalty decreases from 5.28% in S1 to 4.79% in S3. This occurs because higher-SOFC-share scenarios benefit from greater BoL system efficiency. Consequently, the same absolute amount of SOFC stack efficiency loss translates into a smaller relative increase in overall system fuel consumption.

5.2. Design Analysis Results

In this subsection, the design analysis results of retrofitting ships with the innovative integration between SOFC and ICE are presented. For the retrofitting process, the weight and volume of hybrid system components have been evaluated, including SOFC, natural gas ICE, natural gas fuel/fuel storage system (FSS), BoP components, and PCE.

The weight and volume of the fuel storage system are based on the daily fuel energy consumption. The findings of fuel consumption in the previous subsection are supported by the weight and volume results of hybrid system scenarios, shown in Figure 8. The weight and volume of fuel and fuel storage systems for ships are reduced by increasing the SOFC power share, as represented in Scenarios 2 and 3.

As shown in Figure 8, the reduction in weight of the fuel storage system in scenarios 2 and 3 cannot compensate for the increment in SOFC weight, as the total weight increases by 10% and 20% compared to the baseline scenario (Scenario 1) for the Lake Ferry, respectively, while it increases by 4.4% and 13.5% for the Island Ferry. Similarly, the total volume in the case of the Lake Ferry increases by 9.5% and 19.1%, respectively, while volume rises by 12.3% and 25% in the case of Island Ferry.

In addition to mass and total volume, the feasibility of retrofitting the SOFC–ICE hybrid system onboard the investigated vessels is evaluated through a quantitative space-claim analysis. For the Lake Ferry, the evaluated SOFC system installation volumes for Scenarios 1, 2, and 3, respectively, correspond to space occupancy ratios of 72%, 82%, and 92% of the available machinery space (45 m³). Even in Scenario 3, which represents the highest installed SOFC capacity, sufficient residual space remains to accommodate auxiliary systems. The results indicate that all three scenarios are physically feasible from a space-claim perspective for the Lake Ferry, with Scenario 1 offering the largest integration margin.

For the Island Ferry, the required SOFC installation volumes are 41.6 m³, 46.7 m³, and 51.9 m³ for Scenarios 1, 2, and 3, respectively. When comparing the required hybrid system volume to the available machinery space of 57 m³ of the Island Ferry, these values correspond to occupancy ratios of approximately 73%, 82%, and 91%. Similarly to the Lake Ferry, all scenarios remain within acceptable spatial limits, with Scenario 3 approaching but not exceeding the practical upper bound for retrofit installation.

The space-claim analysis confirms that the selected SOFC operating conditions do not impose additional spatial penalties. Overall, the results demonstrate that the proposed SOFC–ICE hybrid configurations are physically realizable from a space-claim and layout standpoint for both vessels and all investigated scenarios.

5.3. Economic Analysis Results

This subsection presents the economic analysis results based on the approach discussed in Section 4. The results of direct CapEx for the different hybrid system scenarios along with cost breakdown for the system components, are shown in Figure 9.

Figure 9 illustrates the breakdown of direct CapEx for both vessels. In Figure 9a, the baseline configuration for the Lake Ferry shows a total direct CapEx of about EUR 1.51 million. In this case, the ICE system represents the largest share at 36%, followed closely by the SOFC system at 33%. Increasing the SOFC load share in Scenario 2 raises the total direct CapEx by 18% to roughly EUR 1.79 million, mainly due to the higher SOFC investment, which grows to 42% of total CapEx. Although ICE costs decrease in this scenario, the reduction is too small to balance the rise in SOFC costs. Scenario 3 amplifies this effect: total direct CapEx increases by 36% compared to the baseline, reaching about EUR 2.06 million, with the SOFC share increasing to 48%.

Figure 9b presents the results for the Island Ferry. The baseline scenario requires about EUR 1.82 million in direct CapEx. When the SOFC load share is increased in Scenario 2, total direct CapEx rises by 17% to around EUR 2.14 million, driven by SOFC costs increasing to 42% of the total. In Scenario 3, total direct CapEx reaches approximately EUR 2.46 million, a 35% rise from the baseline, with the SOFC share expanding to 49%.

The variations between scenarios highlight the cost implications of increasing the SOFC load share. While the ICE costs decrease in Scenarios 2 and 3, the overall Direct CapEx rises significantly due to the high costs of the SOFC system.

In Scenario 1 for the Lake Ferry, the total OpEx is EUR 25.8 thousand, with the ICE system contributing the largest share at 41.8%, followed by the SOFC system at 38.7%. When the SOFC power share is increased in Scenarios 2 and 3, ICE-related OpEx decreases by about 6% and 11% relative to the baseline. This reduction, however, is outweighed by the rise in SOFC OpEx, which grows to 58.1% of annual OpEx in Scenario 2 and 77.5% in Scenario 3. The same behavior occurs for the Island Ferry as the annual OpEx (excluding the replacement cost of stacks) increased from EUR 30.9 thousand in Scenario 1 to EUR 43 thousand in Scenario 3.

Voyage expenditure (VoyEx) depends directly on annual fuel consumption, which in turn reflects the efficiency of the system described in Section 5.1. As expected, the improved efficiency in Scenarios 2 and 3 leads to lower VoyEx values than in the baseline. Figure 10a shows this reduction for the Lake Ferry: VoyEx decreases by 4.9% in Scenario 2 and by 9.5% in Scenario 3. However, these savings are not large enough to counter the increases in CapEx and OpEx. As illustrated in Figure 10a, the total costs rise to EUR 6.07 million in Scenario 2 and EUR 6.44 million in Scenario 3, representing increases of 6.3% and 12.6% over the total cost of Scenario 1. Across the three scenarios, CapEx becomes a progressively larger share of total cost, reflecting the higher investment required for greater SOFC contribution. VoyEx, by contrast, decreases due to improved fuel efficiency, while OpEx remains comparatively stable, indicating limited sensitivity to the level of SOFC integration.

For the Island Ferry, the same efficiency trend appears. Figure 10b shows that VoyEx falls by 5.3% in Scenario 2 and by 9.3% in Scenario 3 compared to Scenario 1, directly linked to reduced fuel consumption. In Scenario 2, this reduction is sufficient to offset the increases in CapEx and OpEx, leading to a total cost of EUR 13.45 million, only 2% higher than the baseline value of EUR 13.18 million. In Scenario 3, total costs reach EUR 13.87 M, an increase of 5.3% over the baseline. This outcome indicates that although higher SOFC power shares increase CapEx and OpEx, the corresponding reduction in VoyEx helps moderate the overall cost impact. The results highlight the value of selecting an optimal SOFC–ICE power split to balance investment and operating costs.

The results underline the need to balance capital expenditures and voyage-related savings when selecting an integration strategy. Increasing the SOFC power share can improve system efficiency but also raises investment requirements. To better assess these trade-offs, the LCOE was calculated for all scenarios, as shown in Figure 11.

For the Lake Ferry, Figure 11a shows that the baseline LCOE is 331 EUR/MWh. When the SOFC power share increases, the LCOE rises to 352 EUR/MWh in Scenario 2 (an increase of 6.3%) and to 373 EUR/MWh in Scenario 3 (an increase of 12.6%). This trend mirrors the growth in CapEx reported in Figure 9a, indicating that a higher SOFC contribution, while potentially improving performance, results in higher long-term energy costs, especially given the Lake Ferry’s limited operating hours in port.

Although the total costs of implementing a hybrid system are higher for the Island Ferry than for the Lake Ferry, the longer operating hours in port (15 h versus 2 h) mean that the Island Ferry generates more annual energy. This leads to significantly lower LCOE values. As shown in Figure 11b, the baseline LCOE for the Island Ferry is 236 EUR/MWh, much lower than the Lake Ferry’s 331 EUR/MWh.

When the SOFC share increases in Scenarios 2 and 3, the LCOE for the Island Ferry rises only slightly to 241 EUR/MWh (+2.1%) and 248 EUR/MWh (+5.3%), respectively. These modest increases align with the total cost behavior shown in Figure 10b. The results suggest that, for the Island Ferry, higher SOFC integration improves efficiency while maintaining strong economic viability, demonstrating that enhanced SOFC power sharing can be achieved without major cost penalties.

When comparing the LCOE results of the SOFC-ICE system between the Lake Ferry and the Island Ferry, it is evident that applying the system in the Island Ferry results in a significant reduction in LCOE compared to the Lake Ferry. LCOE for the Island Ferry is 110 EUR/MWh lower in Scenario 2 and 124 EUR/MWh lower in Scenario 3 compared to the Lake Ferry. This difference is primarily due to the Island Ferry’s higher operating hours for the hybrid system, longer port hours, and greater generated power, which collectively enhance the system’s efficiency and reduce energy costs.

Uncertainty and Sensitivity Analysis of LCOE

The simulation results provide a probability distribution of possible LCOE outcomes for each case, moving beyond a single deterministic value. Figure 12 presents the probability density functions (PDFs) for the Lake Ferry and the Island Ferry across all three scenarios.

The probability density functions in Figure 12 quantitatively demonstrate the robustness of the Island Ferry’s economic advantage. While the mean LCOE for the Lake Ferry shows a clear upward trend across scenarios (mean LCOE: 333, 354, and 375 EUR/MWh), the Island Ferry maintains substantially lower and more stable values (mean LCOE: 239, 244, and 252 EUR/MWh). More importantly, the Island Ferry exhibits narrower distributions, with standard deviations of approximately 24–25 EUR/MWh across all scenarios compared to the Lake Ferry’s wider spread of 28–34 EUR/MWh.

This is further evidenced by the range metrics: the Island Ferry’s LCOE varies by 116–128 EUR/MWh between minimum and maximum values, whereas the Lake Ferry’s uncertainty range spans 136–169 EUR/MWh. These results confirm that not only is the Island Ferry’s LCOE lower, but its economic outcome is also more predictable and less sensitive to parameter uncertainties, making it a more bankable investment case. The widening distribution for the Lake Ferry, particularly in Scenario 3, reflects the compounding effect of increasing SOFC integration on economic uncertainty when annual utilization is low.

Figure 13 presents the absolute Pearson correlation coefficients for each parameter across scenarios. The analysis reveals a fundamental and strategically important shift in economic sensitivities as SOFC integration increases. In Scenario 1, where the SOFC contributes only to hoteling, not for propulsion, fuel price emerges as the overwhelmingly dominant cost driver, with correlation coefficients of 0.88 for the Lake Ferry and 0.95 for the Island Ferry. This reflects traditional marine propulsion economics, where voyage expenditure constitutes 60–70% of total lifecycle costs.

However, as SOFC contribution increases to 20% in Scenario 3, a marked transition occurs: SOFC CapEx gains substantial prominence, with correlations rising to 0.75 for the Lake Ferry and 0.52 for the Island Ferry. For the Lake Ferry in particular, SOFC CapEx becomes the primary cost driver in Scenario 3, surpassing fuel price in influence. This evolution marks a critical shift from operational to capital-intensive economics, characteristic of emerging fuel cell technologies. The degradation rate exhibits only moderate correlation (0.09–0.14) across all cases, while stack lifetime shows negligible influence (<0.05). This indicates that uncertainties in long-term performance and replacement schedules have a limited impact on overall economic variability compared to upfront costs and fuel prices.

The Island Ferry demonstrates stronger sensitivity to fuel price but reduced sensitivity to SOFC CAPEX compared to the Lake Ferry. This occurs because the Island Ferry’s higher annual energy output spreads capital costs over more megawatt-hours, making each unit of energy less sensitive to changes in equipment costs. Consequently, the Island Ferry is more affected by fuel price fluctuations but more resilient to uncertainties in SOFC technology costs.

5.4. Environmental Analysis Results

Using the calculation methods for CO₂ and NOx emissions (Section 4.6) and considering the energy required for both port and cruise operations, the annual emissions of CO₂ and NOx were estimated for both ships. These emissions were compared to those produced by the MDO-ICE system (installed engine onboard) and LNG-ICE system (specifically the Bergen C26:33 model [33]) to figure out the environmental benefits of this innovative system. It is noted that the emission factor of CO₂ and NOx in the case of LNG-ICE is 2.75 gCO₂/g-fuel, and 1.4 g/kWh, respectively. While it is 3.21 gCO₂/g-fuel and 2.41 g/kWh in the case of MDO-ICE (assuming it fulfills the IMO Tier 3 requirement), respectively. For both ships, the annual CO₂ emissions are presented in Figure 14 for each scenario.

Figure 14 demonstrates that the SOFC-ICE system significantly lowers CO₂ emissions compared to the MDO-ICE system, particularly in port areas. For both ships, emissions in the port are reduced by approximately 71.3% when using Scenario 1 of the SOFC-ICE system and further increase to a 78.5% reduction in Scenario 3. Over a year, the total CO₂ emissions reduction (both in port and cruising) for the Lake Ferry is about 46.3% (468 tons of CO₂) with Scenario 1, increasing to 49.7% (502 tons of CO₂) with Scenario 3. For the Island Ferry, the total CO₂ emissions reduction is about 43.7% (equivalent to 1569 tons of CO₂) with Scenario 1, rising to 50.9% (1678 tons of CO₂) with Scenario 3.

Additionally, the SOFC-ICE system substantially reduces CO₂ emissions compared to the LNG-ICE system, particularly in port areas. The reduction in the port increases from 55.4% in Scenario 1 to 67% in Scenario 3. Annually, the total CO₂ emissions in the case of the Lake Ferry are reduced by 4.5% (25 tons of CO₂) in Scenario 1, increasing to 10.5% (60 tons) in Scenario 3, as illustrated in Figure 14a. For the Island Ferry, the total annual CO₂ emissions are reduced by 8.3% (155 tons of CO₂) in Scenario 1, rising to 14% (264 tons of CO₂) in Scenario 3, as illustrated in Figure 14b. For both ships, the projected annual NOx emissions are presented in Figure 15 for each scenario.

As shown in Figure 15, integrating SOFC with the ICE system leads to a substantial reduction in NOx emissions, especially during port operations, since the SOFC produces no NOx in this mode. For the Lake Ferry, NOx emissions during cruise mode decrease by 52% in Scenario 1 compared to the conventional MDO-ICE system (Figure 15a), with the reduction increasing to 60.5% in Scenario 3. On an annual basis, the Lake Ferry achieves a 53.7% reduction in NOx emissions in Scenario 1, rising to 61.8% in Scenario 3. For the Island Ferry (Figure 15b), cruise-mode NOx emissions decrease by 43%, 48.3%, and 56.4% for Scenarios 1, 2, and 3, respectively. The overall annual NOx reduction relative to the MDO-ICE system is 50.6% (4.8 tons) in Scenario 1, increasing to 62.2% (5.94 tons) in Scenario 3.

The innovative integration of SOFC and ICE also offers significant environmental advantages over the LNG-ICE system in terms of NOx emissions. In port areas, the SOFC-ICE system in both ships eliminates NOx emissions, whereas the LNG-ICE system produces 1.7 tons and 5.54 tons of NOx annually for the Lake Ferry and the Island Ferry, respectively. For the Lake Ferry, the annual NOx emissions compared with the LNG-ICE system are reduced by 20.1% in Scenario 1, increasing to 34.2% in Scenario 3. For the Island Ferry, the SOFC-ICE system reduces NOx emissions annually by 14.8% in Scenario 1 (0.8 tons of NOx) compared to the LNG-ICE system, with this reduction increasing to about 35% in Scenario 3 (1.93 tons of NOx).

These findings prove that this innovative SOFC-ICE hybrid system has significant environmental benefits over the traditional MDO-ICE system and LNG-ICE system. This integration is considered a transitional solution toward decarbonization in maritime applications, with the potential to smoothly achieve the IMO milestone of 2030, which targets the reduction in GHG emissions by 20−30% compared to 2008 levels [59]. Also, it is noted that this innovative integration has the potential to reduce more emissions than presented here. This can be achieved by increasing the SOFC power share, which can be feasible in the future with the technological development of SOFC for maritime applications.

6. Conclusions

This paper has undertaken a pioneering exploration into the feasibility of retrofitting existing domestic vessels, marking a first-of-its-kind study in the maritime sector. The research specifically examines the potential of converting diesel-powered systems to an innovative integration between turbocharged SOFC and ICE.

The performance assessment of this innovative integration between SOFC and ICE has been implemented using the Lake Ferry and the Island Ferry as case studies. The performance has been evaluated over three different scenarios: Scenario 1 (10% SOFC power share), Scenario 2 (15% SOFC power share), and Scenario 3 (20% SOFC power share). The main conclusions are shown as follows:

• The energy analysis demonstrates that increasing the SOFC power share enhances overall system efficiency. The SOFC efficiency in port operations improved to approximately 60% under part-load conditions, while the hybrid system efficiency in cruise mode reached 53.2%. This yielded daily fuel energy reductions of up to 9.1% for the Lake Ferry and 8.9% for the Island Ferry. The integrated degradation model revealed that higher SOFC shares also reduce the relative lifecycle fuel penalty, with cumulative consumption increasing by only 4.3% for the Lake Ferry and 4.8% for the Island Ferry over 25 years compared to a non-degrading baseline.
• The design analysis confirms the physical retrofit feasibility of the SOFC-ICE hybrid system, despite increased mass and volume with higher SOFC shares. For the highest integration (Scenario 3, 20% SOFC share), total system weight for the Lake Ferry increases by 20% (19% for the Island Ferry) and volume by 27% (25% for the Island Ferry) compared to Scenario 1 (10% SOFC share), due to the SOFC’s lower power density. Crucially, a quantitative space-claim analysis demonstrated that all scenarios remain within the vessels’ available machinery space, with occupancy ratios of 72–92% for the Lake Ferry and 73–91% for the Island Ferry, confirming that the systems are installable without exceeding spatial constraints.
• Economically, the hybrid system presents a trade-off between high capital investment and operational savings. For the Island Ferry with high utilization, the Levelized Cost of Energy (LCOE) remained competitive (236–248 EUR/MWh) across all scenarios, as fuel savings (VoyEx) partially offset the increased SOFC capital and operational costs. In contrast, the Lake Ferry’s lower operating hours resulted in a higher LCOE (331–373 EUR/MWh), making the economic case more sensitive to the SOFC share.
• The uncertainty analysis revealed a fundamental shift in economic drivers: while fuel price dominates in low-SOFC scenarios, SOFC capital cost becomes the primary sensitivity factor in high-integration cases (20% SOFC share). This highlights that the economic viability of future, deeper decarbonization hinges critically on reducing SOFC costs.
• The SOFC-ICE hybrid system delivers substantial emission reductions, positioning it as a viable transitional decarbonization technology. Compared to conventional MDO-ICE, the system achieves annual CO₂ reductions of 46–51% and NOx reductions of 51–62%, with port-area NOx eliminated entirely. It also outperforms modern LNG-ICE, providing CO₂ reductions of 4.5–14% and NOx reductions of 15–35%. These reductions already meet and exceed the IMO’s 2030 GHG reduction targets, with potential for further improvement as SOFC technology matures and higher power shares become feasible.

In conclusion, the SOFC-ICE hybrid system gains competitiveness at economic and energy efficiency levels not only for vessels having a large yearly number of operating hours but particularly for vessels having a daily operating profile (like Island Ferry ones) where the harbor/hoteling operation is relevant (e.g., 62.5% of the overall daily operating hours for the Island Ferry) as in this phase the SOFC system is significantly more efficient than the ICE, while during the sailing period the increase in the efficiency is less relevant.

Building on these findings, future research should prioritize dynamic control strategies for SOFC-ICE power transitions. Investigations into alternative low-carbon fuels (e.g., ammonia, methanol) and advanced health monitoring for SOFC degradation are critical for maritime reliability. Expanding the integrated assessment framework to larger ship types and conducting comparative analyses with other decarbonization pathways will further clarify the role of SOFC-ICE hybrids in the broader maritime energy transition.

Building on the sensitivity analysis results, future work could explicitly model technology learning curves and perform parametric optimization to determine the SOFC cost and durability thresholds at which higher power shares (e.g., >30%) become the economically optimal configuration, providing a clear roadmap for technology development and investment.