Performance of SOFC and PEMFC Auxiliary Power Systems Under Alternative Fuel Pathways for Bulk Carriers

Abstract

Fuel cell technologies are increasingly investigated as alternatives to conventional auxiliary diesel generators in order to enhance shipboard energy efficiency and reduce greenhouse gas emissions. This study presents a unified and uncertainty-driven system-level assessment of solid oxide fuel cell (SOFC) and proton exchange membrane fuel cell (PEMFC) systems operating as auxiliary power sources on a 200 m bulk carrier. Both technologies are evaluated under identical vessel characteristics, operating profiles, auxiliary load levels (360–600 kW), and cost assumptions, and are benchmarked directly against a conventional three–diesel-generator configuration. A modular numerical framework is developed to model propulsion–auxiliary interactions for ship speeds between 10 and 14 knots. SOFC systems are assessed using grey, bio-derived, and green natural gas pathways, while PEMFC systems are examined under grey, blue, and green hydrogen supply routes. Performance indicators include annual fuel consumption, carbon dioxide (CO₂) emission reduction, net present value (NPV), internal rate of return (IRR), payback period (PBP), and marginal abatement cost (MAC). Economic uncertainty is explicitly embedded in the framework through Monte Carlo simulation, where fuel prices (±20%) and capital costs are sampled across defined ranges, generating probabilistic distributions rather than single deterministic estimates. This uncertainty-centred approach enables assessment of robustness, downside risk, and probability of profitability. Results show that replacing a single operating 600 kW diesel generator with fuel cell systems reduces auxiliary fuel energy demand by 25–35% for SOFC and approximately 15–25% for PEMFC relative to the diesel benchmark. Annual CO₂ reductions range from 1.1 to 1.3 kt for SOFC systems and 1.8–2.8 kt for PEMFC configurations. Under grey fuel pathways, median NPVs reach approximately 2–4.5 M$ for SOFC and 9–17 M$ for PEMFC as load increases, with IRRs exceeding 15% and 30%, respectively. Transitional pathways exhibit narrower margins, while renewable pathways remain more sensitive to fuel price variability. The findings demonstrate that fuel pathway cost dominates lifecycle outcomes under uncertainty and that hydrogen-based PEMFC systems exhibit the strongest economic resilience within the examined market ranges. The framework provides structured, uncertainty-aware decision support and establishes a foundation for integration into model-based systems engineering (MBSE) environments for early stage ship energy system design.

1. Introduction

Maritime transport underpins global trade, carrying more than 80% of global merchandise by volume. Despite its critical economic role, the sector remains heavily dependent on fossil fuels and combustion-based power systems. Conventional ships are predominantly powered by internal combustion engines operating on heavy fuel oil, marine diesel oil, or liquefied natural gas (LNG) due to their robustness, high-power density, and long-established operational reliability [1,2]. However, intensifying regulatory pressure to reduce greenhouse gas emissions and local air pollutants has accelerated the diversification of ship propulsion and onboard power generation technologies. Ships are progressively evolving from engine-centric platforms into complex energy systems that integrate alternative fuels and electrified subsystems [3,4,5,6]. This transition has direct implications for ship design and shipbuilding practice. Shipyards must accommodate emerging power technologies within constrained hull geometries and machinery arrangements, while maintaining compliance with classification rules, safety standards, and economic performance targets [7].

Modern ships require energy not only for propulsion but also for auxiliary and hotel loads, including lighting, heating, ventilation, and air conditioning (HVAC), cargo handling, navigation systems, and increasingly electrified onboard services. As a result, propulsion and power generation systems must be assessed holistically, accounting for interactions between main engines (ME), auxiliary diesel generators (DG), energy storage devices, and emerging alternative power sources. This systemic perspective has motivated the exploration of a wide range of power technologies, including internal combustion engines, fuel cells, batteries, gas turbines, and hybrid combinations thereof, operating on an expanding portfolio of fuels [8,9,10,11], alongside advanced waste heat recovery integrations [12].

Within this evolving maritime energy landscape, fuel cell development has progressed along two distinct yet complementary technological trajectories. High-temperature solid oxide fuel cells (SOFCs) have been primarily investigated for their fuel flexibility, high steady-state electrical efficiency, and compatibility with thermally integrated ship energy architectures. Their ability to internally reform NG and operate at elevated temperatures enables efficient base-load operation and potential integration with waste heat recovery systems [13,14]. In contrast, proton exchange membrane fuel cells (PEMFCs) have attracted considerable attention due to their low operating temperature, rapid start-up, modular scalability, and strong compatibility with hydrogen-based energy systems. These characteristics make PEMFCs particularly suitable for auxiliary power applications requiring dynamic load response and low acoustic emissions [15,16].

Despite the technological maturity of both fuel cell types, the existing body of literature remains largely fragmented. Comparative analyses are often conducted under different vessel typologies, operational envelopes, modelling boundaries, and performance metrics. As a result, direct cross-technology interpretation becomes inherently challenging. The absence of harmonised evaluation conditions has limited the ability to systematically clarify how SOFC and PEMFC systems perform within the same ship energy architecture. Consequently, technological selection is frequently influenced by context-specific assumptions rather than structured, system-level comparison.

The present study is motivated by the need to overcome this fragmentation by developing a unified, internally consistent performance framework. Instead of assessing each technology independently, both SOFC and PEMFC auxiliary systems are evaluated under identical vessel characteristics, operating speed ranges, auxiliary load profiles, and uncertainty assumptions. By embedding both technologies within the same bulk carrier energy configuration, the analysis enables a transparent comparison of annual fuel consumption, carbon dioxide (CO₂) emission reduction potential, and techno-economic performance. This unified approach shifts the analytical focus from isolated component efficiency toward integrated system behaviour under realistic marine operating conditions.

The novelty of this study does not lie in proposing fuel cells for marine auxiliary power per se, since both SOFC and PEMFC applications have been discussed in the prior literature. Instead, the originality lies in the development of a unified ship-level modelling framework that compares both technologies under identical vessel, operational, and economic assumptions; in the explicit treatment of alternative upstream fuel pathways within the same comparative structure; and in the embedding of Monte Carlo-based uncertainty propagation into techno-economic indicators, including net present value (NPV), internal rate of return (IRR), payback period (PBP), and marginal abatement cost (MAC), thereby generating probabilistic rather than deterministic decision metrics. This enables a harmonised, uncertainty-aware cross-technology assessment, which is largely absent from existing marine fuel cell studies.

Through consistent modelling and probabilistic evaluation, the work advances beyond isolated technology appraisal toward structured decision support. It provides a methodological foundation suitable for integration into digital ship energy architectures and future model-based systems engineering environments, where auxiliary power selection can be evaluated within a holistic, uncertainty-aware, and scalable design framework [17].

2. Literature Review

2.1. Solid Oxide Fuel Cell (SOFC) for Maritime Applications

The application of fuel cells in maritime systems has been investigated for more than two decades, with intensified activity after 2010 [18]. Early studies focused on conceptual feasibility and life-cycle performance, identifying auxiliary power generation as the most realistic entry point for fuel cell adoption. A seminal contribution compared methanol-fuelled SOFC auxiliary power units with conventional marine generators, demonstrating notable reductions in CO₂ emissions and local pollutants under favourable fuel pathways [19]. Subsequent work explored hybrid SOFC–gas turbine configurations, highlighting the potential of high-temperature fuel cells to achieve superior system efficiencies when integrated with bottoming cycles [20]. During this phase, research remained largely conceptual, with limited consideration of ship-specific operational constraints.

System-level integration began to receive greater attention. Several studies proposed hybrid diesel–fuel cell power plants for offshore and marine vessels, emphasising redundancy, load sharing, and improved efficiency under partial-load conditions [9,21]. Parallel research addressed control strategies and thermodynamic integration of SOFC systems in ship applications [22,23].

As SOFC concepts matured, research increasingly addressed performance under realistic operating conditions. A notable study evaluated the performance and availability of a marine generator SOFC–gas turbine hybrid system for a very large ethane carrier, showing that hybrid architectures could achieve availability levels comparable to conventional marine power plants when appropriate redundancy was applied [24].

Around 2020, the literature expanded beyond efficiency metrics to include multi-criteria assessments of fuel cell technologies and waste heat utilisation strategies. Studies assessed different fuel cell types for ship applications using decision-analysis frameworks [25] and explored cascade utilisation of SOFC waste heat for marine systems [26]. These works reinforced the view that replacing auxiliary DG with SOFCs is not only an emissions-reduction strategy but also a system-level efficiency enhancement.

Research increasingly emphasised hybridisation between fuel cells and conventional prime movers. Several studies investigated integrated SOFC–internal combustion engine architectures, highlighting the complementary roles of fuel cells for base-load operation and engines for transient response and peak demand [27,28].

At the same time, power gradient limitations of SOFCs motivated the inclusion of hybrid storage and advanced energy management strategies [29]. Fuel diversification also accelerated, with ammonia-fuelled SOFC systems emerging as a prominent research theme [30,31]. SOFC marine research exhibited a clear shift toward validation, control, and experimental realism. Studies investigated hybrid ship power systems using hydrogen and clean fuel blends [32], alongside experimental evaluations of SOFC performance under ship motions [33].

Economic and environmental assessments became increasingly detailed, integrating exergoeconomic and exergoenvironmental analyses [34]. Parallel work addressed energy management, frequency regulation, and optimisation of shipboard microgrids [35]. Ammonia and hydrogen pathways were further analysed within integrated SOFC systems [36]. In 2024, the literature increasingly focused on integrated propulsion and auxiliary architecture, combining SOFCs with engines, batteries, Organic Rankine Cycle (ORC) systems, and electrolysers. Studies examined methanol-fuelled SOFC hybrid propulsion systems for all-electric ships [37] and SOEC–engine combinations for hydrogen production onboard ships [38].

Optimisation-based studies became prominent in 2025, addressing multi-fuel SOFC systems [39], ammonia-fed SOFC polygeneration [40], and hybrid SOFC–engine–waste heat recovery architectures [41,42]. Critically, safety and operational risk were addressed through structured methodologies, including HAZOP-based assessments of marine SOFC fuel supply systems [43]. The techno-economic feasibility of methanol-fuelled SOFC propulsion systems was also quantified [44].

The most recent work synthesises these developments into comprehensive frameworks combining energy, exergy, economics, environmental impact (4E), safety, and intelligent control. A representative study applies a 4E assessment with multi-objective optimisation and intelligent control to ammonia-fuelled SOFC maritime systems, illustrating the field’s transition toward operational decision-support tools rather than isolated component studies [45].

2.2. Proton Exchange Membrane Fuel Cells (PEMFC) for Maritime Applications

In parallel with the development of high-temperature fuel cell systems, PEMFCs have been widely investigated for maritime applications, particularly due to their low operating temperature, rapid start-up, and superior dynamic response. Early marine PEMFC research focused on fundamental performance and efficiency assessment. An early contribution, Leo Mena et al. [46] quantified the thermodynamic performance of PEMFCs under marine-relevant operating conditions and demonstrated that electrical efficiencies of 40–50% could be achieved, albeit with strong sensitivity to operating pressure, temperature, and membrane hydration.

As interest in hydrogen-based maritime systems increased, research expanded toward hydrogen supply pathways and fuel processing for PEMFCs. Studies explored onboard hydrogen generation via reforming, highlighting the trade-off between reduced hydrogen storage requirements and increased system complexity, efficiency penalties, and balance-of-plant (BoP) demands [47,48]. These works clearly distinguished PEMFC systems from SOFCs, emphasising that PEMFCs generally require high-purity hydrogen or dedicated fuel processing units, which significantly influence system robustness in shipboard environments.

PEMFC research increasingly shifted from component-level analysis toward system-level integration in ships. Hybrid architectures combining PEMFCs with diesel generators, batteries, or renewable sources were investigated for cruise ships, ferries, and research vessels. Ghenaï et al. [49] demonstrated that PEMFC-based hybrid systems could substantially reduce fuel consumption and emissions during port stays and low-speed operation, while retaining conventional generators for peak demand and redundancy.

Dynamic behaviour and load-following capability rapidly emerged as central research themes. Unlike SOFCs, which are typically operated at quasi-steady base load, PEMFCs are often exposed to rapid power variations in shipboard direct current (DC) microgrids. System-level modelling studies showed that PEMFC stacks are highly sensitive to large load steps [50,51]. Allowable current ramp rates were found to be limited to avoid voltage instability, thermal stress, and accelerated degradation, reinforcing the need for hybridisation with batteries or other fast-response energy storage devices.

Experimental and demonstrator-based research further clarified both the opportunities and limitations of PEMFC deployment at sea. The feasibility of PEMFC-powered vessels was demonstrated through several real ship applications, including a research vessel [52] and the ZEUS vessel [53]. These studies confirmed that PEMFCs can enable zero-emission operation at the ship scale but also highlighted the critical importance of advanced control strategies, hydrogen storage integration, and conservative operating envelopes to preserve fuel cell lifetime.

Durability and degradation became increasingly prominent topics as PEMFC systems approached higher technology readiness levels. Material- and stack-level investigations showed that exposure to saline environments, humidity cycling, and mechanical stress can lead to irreversible membrane degradation and performance losses [54,55]. These findings were reinforced by system-oriented analyses [56], which explicitly linked ship operating profiles, vibration, inclination, and load cycling to observed degradation mechanisms.

From 2020 onward, PEMFC research increasingly incorporated techno-economic, risk, and system-optimisation perspectives. Maleki Bagherabadi et al. [57], Ferahtia et al. [58] demonstrated that PEMFC-based shipboard microgrids are often constrained more by energy management and degradation considerations than by nominal efficiency. Parallel work assessed hydrogen logistics and storage options [59,60], showing that storage method, rather than fuel cell efficiency alone, dominates system mass, volume, safety, and cost.

Recent studies have further expanded PEMFC research toward integrated and risk-aware energy systems. Russo et al. [61] explored reforming-based pathways to reduce onboard hydrogen storage, while Radica et al. [62] synthesised operational performance data under realistic marine conditions. At the same time, renewable-powered hydrogen production systems, as presented in [63], provided upstream context for PEMFC deployment, highlighting both feasibility and efficiency limitations under real sea conditions.

Overall, the PEMFC maritime literature shows a clear evolution from feasibility and performance assessment toward operational realism, durability analysis, and system-level optimisation. However, it consistently emphasises that PEMFC systems rely heavily on hybridisation with batteries or auxiliary generators to manage transients and that their long-term performance is strongly conditioned by hydrogen purity, environmental protection, and BoP reliability.

2.3. Linking PEMFC and SOFC Research in Maritime Energy Systems

When considered collectively, the PEMFC and SOFC literature highlights complementary functional roles within maritime energy systems, rather than direct technological competition. High-temperature SOFC systems have increasingly been positioned as efficient, fuel-flexible base-load power sources capable of replacing conventional auxiliary diesel generators while enabling system-level efficiency gains through thermal integration. Numerous studies have demonstrated that SOFCs can achieve high electrical efficiency under steady operating conditions and integrate effectively with waste heat recovery units, internal combustion engines, and hybrid multi-fuel architectures, thereby enhancing overall ship energy performance [24,26,27,28].

In contrast, PEMFC research has consistently emphasised attributes that are particularly relevant to operational flexibility and onboard service quality. PEMFC systems are characterised by low operating temperatures, rapid start-up capability, low noise and vibration, and high-power density, making them attractive for auxiliary power supply during low-speed operation, port stays, and hotel-load-dominated operating modes. At the same time, the literature highlights critical limitations of PEMFC deployment in maritime environments, including sensitivity to load transients, accelerated degradation under dynamic operation, and the logistical, safety, and purity requirements of hydrogen fuel supply [50,56].

These differing characteristics have led to distinct system integration philosophies. PEMFC-based ship power systems are commonly implemented within battery-buffered DC microgrids, where fuel cells operate within constrained load envelopes to mitigate degradation and enhance lifetime performance. In contrast, SOFC-based systems are more frequently integrated alongside internal combustion engines, gas turbines, or waste heat recovery systems, supplying relatively stable electrical and thermal base loads with limited sensitivity to short-term power fluctuations.

Overall, the reviewed literature shows that SOFC and PEMFC have been extensively investigated for marine applications, but largely along parallel and non-integrated research paths. SOFC studies typically focus on high-efficiency systems, fuel flexibility, and hybrid configurations, while PEMFC research emphasises low-temperature operation, dynamic response, and hydrogen-based applications. However, these studies are often conducted under different system boundaries, vessel types, operating conditions, and economic assumptions, leading to fragmented and sometimes incomparable conclusions. As a result, there is a lack of unified frameworks that enable a consistent, cross-technology comparison of SOFC and PEMFC systems within the same maritime context. This gap limits the ability to support robust decision-making for shipowners and policymakers. Therefore, the present study addresses this limitation by developing a harmonised modelling framework that evaluates both technologies under identical operational, economic, and fuel pathway assumptions, combined with an uncertainty-based techno-economic assessment.

3. Methodology and Numerical Model

This study adopts an integrated techno-economic and environmental assessment framework to evaluate the feasibility of replacing conventional auxiliary diesel generator sets with fuel cell systems in a merchant vessel. The analysis compares a reference configuration, based on a conventional main engine and diesel generators, with alternative configurations in which auxiliary electrical power is supplied by SOFCs or PEMFCs.

The methodology combines steady-state performance modelling of propulsion and auxiliary systems with economic evaluation and emissions analysis. Uncertainty in future costs and operational conditions is explicitly addressed through Monte Carlo simulation [64,65,66], enabling a probabilistic interpretation of the results rather than a single deterministic outcome.

3.1. Steady-State Performance Modelling

The power demand of the main propulsion engine is estimated as a cubic function of vessel speed, a relationship commonly used for displacement ships operating near their design condition. The required main engine power in kW at a given speed is expressed using Equation (1) [67].

$${\mathrm{P}}_{\mathrm{ME}}{=\mathrm{P}}_{\mathrm{NCR}}{\left({\displaystyle \frac{\mathrm{V}}{{\mathrm{V}}_{\mathrm{NCR}}}}\right)}^3$$

(1)

where P_ME is the required main engine power, V is the vessel speed along the propeller curve, P_NCR denotes the engine power at the nominal continuous rating, and V_NCR represents the corresponding service speed. This formulation provides a simplified yet robust representation of the hydrodynamic resistance characteristics of the vessel for comparative system-level assessments.

Total daily fuel consumption is evaluated for both the reference and alternative configurations. In the reference case, auxiliary power demand is met entirely by diesel generators, whereas in the alternative configurations it is supplied by SOFC or PEMFC systems. The total daily fuel consumption (FuelC_Total), combining both main engine and auxiliary systems, expressed in t/day, is evaluated as shown in Equation (2) [68].

$${\mathrm{FuelC}}_{\mathrm{Total}}={\displaystyle \frac{24}{{10}^6}}{(\mathrm{P}}_{\mathrm{ME}}\times {\mathrm{SFC}}_{\mathrm{ME},\mathrm{j}}{+\mathrm{P}}_{\mathrm{Aux}}\times {\mathrm{SFC}}_{\mathrm{Aux},\mathrm{j}})$$

(2)

where P_Aux is the auxiliary power demand (kW), supplied either by DG or fuel cell systems, SFC_ME and SFC_Aux are the specific fuel consumptions (g/kWh) of the main engine and auxiliary system, respectively. The factor 24 converts power to daily energy, and ${10}^6$ converts grams to tonnes.

For fuel cells, SFC_Aux is derived from performance data provided in Section 4.2 and Section 4.3. These data are interpolated as a function of electrical load to estimate hydrogen or NG consumption across the considered operating range. This approach captures the non-linear efficiency characteristics of fuel cells without resorting to detailed electrochemical modelling.

Annual energy consumption, expressed in GJ/year, is calculated by converting daily fuel consumption to energy using each fuel’s lower heating value (LHV) and summing over the operational days. This integrated approach provides a comprehensive steady-state performance assessment of both the main and auxiliary power systems and serves as the foundation for subsequent economic and environmental analyses.

3.2. Emissions Assessment Method

The environmental assessment focuses on quantifying CO₂ emissions associated with fuel consumption in both the reference and alternative system configurations. Emissions are evaluated on an operational basis, consistent with common practice in comparative marine energy system assessments [69,70]. Upstream emissions related to fuel production and distribution are not explicitly modelled but are indirectly reflected through the differentiation of fuel types and production pathways.

CO₂ emissions are calculated using fuel-specific emission factors expressed as the mass of CO₂ emitted per unit mass of fuel consumed. The daily CO₂ emissions are computed as shown in Equation (3).

$${\mathrm{E}}_{{\mathrm{CO}}_2}^{\mathrm{day}}={\displaystyle \sum _{\mathrm{j}}{\mathrm{FuelC}}_{\mathrm{j}}\times {\mathrm{EF}}_{{\mathrm{CO}}_2,\mathrm{j}}}$$

(3)

where FuelC_j is the daily fuel consumption in t/day for each fuel type j and EF_CO2,j is the corresponding CO₂ emission factor in tCO₂/t-fuel. For configurations with multiple fuels (e.g., main engine and auxiliary power), total daily CO₂ emissions are calculated as the sum of emissions from each fuel stream. Annual CO₂ emissions are then calculated by scaling daily emissions by the number of operating days per year.

For the reference configuration, total emissions are composed of contributions from the main propulsion engine operating on heavy fuel oil (HFO) and the auxiliary diesel generators operating on marine diesel oil (MDO). The CO₂ emission factor for HFO and MDO is 3.114 and 3.206 gCO₂/g-fuel, respectively. For alternative configurations, auxiliary power generation emissions depend on the selected fuel cell technology and fuel type. For hydrogen-based PEMFC systems, operational CO₂ emissions are assumed to be zero when hydrogen is consumed electrochemically. For NG-based SOFC systems, CO₂ emissions range from 240 to 334 g/kWh, depending on the SOFC load factor.

The annual CO₂ emission reduction (ΔE) achieved by integrating fuel cell systems is quantified as the difference between emissions from the reference and alternative configurations under identical operating conditions, as shown in Equation (4).

$${\Delta \mathrm{E}}_{{\mathrm{CO}}_2}^{\mathrm{annual}}{=(\mathrm{E}}_{{\mathrm{CO}}_2}^{\mathrm{ME}+\mathrm{DG}} {- \mathrm{E}}_{{\mathrm{CO}}_2}^{\mathrm{ME}+\mathrm{FC}})\times {\mathrm{Days}}_{\mathrm{oper}}$$

(4)

where Days_oper is the number of operating days per year. Uncertainty in emissions estimates arises primarily from variability in fuel consumption, operational profiles, and emission factors. Within the Monte Carlo simulation framework, fuel consumption and operational load levels are treated as stochastic variables, leading to distributions of CO₂ emissions and emission reductions rather than single-point estimates.

3.3. Economic Assessment Method

The economic assessment evaluates the financial viability of replacing conventional auxiliary diesel generators with fuel cell systems. The analysis is conducted from the ship owner’s perspective and focuses on investment-related and operational cost components that are directly affected by the choice of auxiliary power technology. The total cost of each configuration consists of:

• Capital expenditure (CapEx): includes upfront investment for fuel cell stacks, balance-of-plant components (battery modules and DC-DC converters), and fuel storage systems.
• Replacement costs (RepEx): costs of periodic replacement of fuel cell stacks and battery modules. Replacement costs are applied at predefined intervals, reflecting finite stack lifetimes, and are discounted to present value.
• Operational expenditure (OpEx): dominated by fuel costs for both propulsion and auxiliary power generation, operational and maintenance (O&M) cost of power system components, and additional CO₂-related taxes, applied proportionally to the annual emissions of each configuration.

Costs related to crew and insurance are assumed to be comparable across configurations and are therefore excluded from the comparative analysis. This assumption allows economic performance to be attributed primarily to differences in fuel efficiency, fuel prices, stack replacement requirements, CO₂ taxes, and upfront investment.

Fuel costs (C) are calculated based on the daily fuel consumption for each configuration and its corresponding unit fuel price. To enable a consistent comparison with the conventional auxiliary diesel generator configuration, the annual fuel cost difference is defined as the difference between the annual fuel cost of the reference configuration (ME + DG) and that of the alternative fuel cell–based configuration (ME + FC), as shown in Equation (5).

$$\Delta {\mathrm{C}}_{\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l}}^{\mathrm{t}}=({\mathrm{C}}_{\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l}}^{\mathrm{M}\mathrm{E}+\mathrm{D}\mathrm{G}} - {\mathrm{C}}_{\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l}}^{\mathrm{M}\mathrm{E}+\mathrm{F}\mathrm{C}})\times \mathrm{D}\mathrm{a}\mathrm{y}{\mathrm{s}}_{\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}}$$

(5)

Positive values indicate a reduction in annual fuel expenditure (savings), while negative values reflect an increase despite efficiency gains (penalty). CO₂ tax savings are added to annual operating costs based on the emissions savings of each fuel cell configuration, as shown in Equation (6).

$${\Delta \mathrm{C}}_{{\mathrm{CO}}_2}^{\mathrm{t}}{=\mathrm{Tax}}_{{\mathrm{CO}}_2}{ \times \Delta \mathrm{E}}_{{\mathrm{CO}}_2}^{\mathrm{FC}}$$

(6)

where ${\mathrm{Tax}}_{{\mathrm{CO}}_2}$ is the assumed price per tonne of CO₂ emissions. O&M of the fuel cell system vs. the reference configuration is calculated on an annual basis as shown in Equation (7).

$${\Delta \mathrm{C}}_{\mathrm{O}\&\mathrm{M}}^{\mathrm{t}}{=(\mathrm{O}\&\mathrm{M}}_{\mathrm{Rate}}^{\mathrm{ME}+\mathrm{DG}}\hspace{0.17em}\times \hspace{0.17em}{\mathrm{C}}_{\mathrm{CapEx}}^{\mathrm{ME}+\mathrm{DG}}\hspace{0.17em}-\hspace{0.17em}{\mathrm{O}\&\mathrm{M}}_{\mathrm{Rate}}^{\mathrm{ME}+\mathrm{FC}}\hspace{0.17em}\times \hspace{0.17em}{\mathrm{C}}_{\mathrm{CapEx}}^{\mathrm{ME}+\mathrm{FC}})$$

(7)

where the O&M rate represents the fraction of CapEx spent annually on maintenance of fuel cell or DG and auxiliary components. The total annual operational cost difference ($\Delta C_{\mathrm{OpEx}}^t$) can be evaluated as shown in Equation (8).

$${\Delta \mathrm{C}}_{\mathrm{OpEx}}^{\mathrm{t}}{=\Delta \mathrm{C}}_{\mathrm{fuel}}^{\mathrm{t}} {- \Delta \mathrm{C}}_{{\mathrm{CO}}_2}^{\mathrm{t}} {- \Delta \mathrm{C}}_{\mathrm{O}\&\mathrm{M}}^{\mathrm{t}}$$

(8)

A consistent set of economic and fuel-related assumptions is adopted to ensure comparability across configurations and to reflect current market conditions for both conventional and low-carbon fuels. To improve clarity and transparency, all key assumptions, including fuel prices, CapEx, O&M, and RepEx, are summarised in

Table 1. Economic and fuel assumptions.

Cost Category	Component	Unit	Value	Ref
Fuel cost	HFO	$/t	522	[71]
	MDO	$/t	794	[71]
	Grey NG–Bio NG–Green NG	$/t	870–1130–2900	[72]
	Grey H2–Blue H2–Green H2	$/t	2000–3250–4500	[72]
CapEx	PEMFC	$/kW	2100	[73]
	SOFC	$/kW	5000	[73]
	Battery	$/kWh	210	[74,75]
	Converter	$/kW	120	[76]
O&M	PEMFC	% of CapEx	2% CapEx/year	[73]
	SOFC	% of CapEx	2% CapEx/year	[73]
	Battery	% of CapEx	1% CapEx/year	[73]
	Converter	% of CapEx	1% CapEx/year	[73]
RepEx	PEMFC	$/kW	788	[77]
	SOFC	$/kW	1875	[77]

.

For fuel cells configurations, batteries and DC–DC converters are included as part of the balance of plant, providing transient power support and load management. Battery modules are specifically sized to provide the energy required to heat the SOFC during the start-up period, as well as to supply the auxiliary load during this time. The battery energy capacity required during the start-up period can be estimated using Equation (9).

$${\mathrm{BAT}}_{\mathrm{FC}}=1.5\times {(\mathrm{P}}_{\mathrm{FC}}\times {\mathrm{HEF}}_{\mathrm{FC}}{ + \mathrm{P}}_{\mathrm{FC}}\times {\mathrm{ST}}_{\mathrm{FC}})$$

(9)

where BAT_FC is the required battery energy capacity (kWh), and P_FC is the installed fuel cell power (kW). HEF_FC represents the heating-up energy factor of the fuel cell system (kWh/kW), which depends on the fuel cell type, as reported in [78], with values of 0.015 kWh/kW for PEMFC and 0.1005 kWh/kW for SOFC systems. ST_FC denotes the start-up duration (h), assumed to be 5 min (0.083 h) for PEMFC and 20 min (0.333 h) for SOFC systems. A safety factor of 1.5 is applied to account for uncertainties in start-up energy demand, battery state-of-charge limitations, and system losses. This formulation provides a practical and consistent basis for estimating battery capacity requirements for both SOFC and PEMFC systems.

The expected growth of the market is projected to reduce replacement costs to approximately 50% of the initial investment. In this study, the operational lifetime of fuel cell stacks is assumed to be 40,000 h [79]. Additionally, fuel cell stacks are estimated to account for about 75% of the total system CapEx [77].

The economic performance of the alternative configurations is evaluated using NPV, PBP, IRR and MAC. The NPV is calculated by discounting annual fuel cost differences over the project lifetime and subtracting the upfront capital investment required for the fuel cell system, as shown in Equation (10).

$$\mathrm{NPV}={\displaystyle \sum _{\mathrm{t}=1}^{\mathrm{n}}\frac{{\Delta \mathrm{C}}_{\mathrm{OpEx}}^{\mathrm{t}}}{{(1+\mathrm{r})}^{\mathrm{t}}}} - \left({\mathrm{C}}_{\mathrm{CapEX}}+{\displaystyle \sum _{{\mathrm{t}}_{\mathrm{rep}}}\frac{{\mathrm{C}}_{\mathrm{RepEx}}}{{(1+\mathrm{r})}^{{\mathrm{t}}_{\mathrm{rep}}}}}\right)$$

(10)

where r is the discount rate (3%), n is the project lifetime (30), t is the year, C_CapEx is the total capital investment cost of the fuel cell system, and C_RepEx is the replacement cost of fuel cell stacks at year t_rep. A positive NPV indicates that the investment yields a net economic benefit over its lifetime, while a negative value suggests that operational costs are insufficient to offset the initial investment and replacement requirements.

The payback period is defined as the ratio of capital investment and replacement cost to the annual operational cost difference, providing a simple indicator of the time required to recover the initial expenditure. The IRR is the discount rate at which the net present value is zero, calculated as shown in Equation (11).

$$0={\displaystyle \sum _{\mathrm{t}=1}^{\mathrm{n}}\frac{{\Delta \mathrm{C}}_{\mathrm{OpEx}}^{\mathrm{t}}}{{(1+\mathrm{r})}^{\mathrm{t}}}} - \left({\mathrm{C}}_{\mathrm{CapEX}}+{\displaystyle \sum _{{\mathrm{t}}_{\mathrm{rep}}}\frac{{\mathrm{C}}_{\mathrm{RepEx}}}{{(1+\mathrm{r})}^{{\mathrm{t}}_{\mathrm{rep}}}}}\right)$$

(11)

This formulation captures the effect of stack/component replacements, CO₂ taxes, and annual O&M costs in the IRR calculation.

The MAC is used to quantify the economic cost associated with reducing one tonne of CO₂ emissions. In this study, MAC is defined in Equation (12) as the ratio between the net incremental cost of the alternative system and the cumulative CO₂ emissions (ΔE) avoided over the project lifetime (n).

$$\mathrm{MAC}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{CapEX}}+{\displaystyle \sum {\mathrm{C}}_{\mathrm{RepEx}}}-{\displaystyle \sum _{\mathrm{t}=1}^{\mathrm{n}}\frac{{\Delta \mathrm{C}}_{\mathrm{OpEx}}^{\mathrm{t}}}{{(1+\mathrm{r})}^{\mathrm{t}}}}}{{\Delta \mathrm{E}}_{{\mathrm{CO}}_2}^{\mathrm{annual}}\times \mathrm{n}}}$$

(12)

Negative MAC values indicate scenarios in which emission reductions are achieved alongside net economic benefits, whereas positive values represent the cost per tonne of CO₂ avoided.

To evaluate long-term investment viability under uncertainty, a probabilistic economic analysis is conducted using Monte Carlo simulation rather than relying solely on minimum–maximum sensitivity cases. Two primary sources of uncertainty are considered: fuel prices and fuel cell capital costs. Fuel prices are varied within ±20% of their baseline values, while capital costs are sampled within predefined intervals of 2500–7500 $/kW for SOFC systems and 1050–3150 $/kW for PEMFC systems. The ±20% variation range applied to fuel prices is based on typical volatility observed in marine fuel markets and reported uncertainties in energy price forecasts for both conventional and alternative fuels. This range is considered sufficiently representative to capture realistic short- to medium-term price fluctuations while enabling a robust assessment of the sensitivity of economic performance indicators to fuel cost uncertainty.

For each auxiliary load level and fuel pathway, 1000 independent scenarios are generated. In each scenario, fuel prices and capital costs are randomly sampled within their respective ranges, and the corresponding NPV, IRR, PBP, and MAC are calculated over the project lifetime. This results in 1000 probabilistic realisations per case, allowing the analysis to move beyond simple extreme (min/max) outcomes and instead characterise the full statistical distribution of economic performance.

The resulting distributions provide insight into median values, interquartile ranges, and downside risk exposure under realistic market variability. These outcomes are presented as boxplots to facilitate structured comparisons across fuel types and auxiliary load levels.

4. Case Study and Power Systems Description

4.1. Ship and Engines Characteristics

The case study considers a 200 m-long bulk carrier representative of conventional deep-sea cargo vessels. Propulsion is provided by a single fixed-pitch propeller directly driven by the main engine. At the vessel’s service condition, a cruising speed of 14 knots is attained when the main engine operates at approximately 85% of its maximum continuous rating (MCR).

The propulsion plant is based on a low-speed, two-stroke marine diesel engine with a rated power of 6.4 MW. The main engine primarily operates on HFO and its low-sulphur blends, balancing compliance with international emission regulations and overall fuel cost efficiency.

The conventional auxiliary power configuration consists of three identical DG sets, each rated at 600 kW and operating on marine diesel oil (MDO). Under normal sea-going conditions, one DG is assumed to supply the hotel and auxiliary load, a second unit remains in standby to ensure redundancy and rapid load response, and the third unit is reserved for maintenance rotation or peak-load support.

In the alternative configurations examined in this study, the primary auxiliary power supply is provided by fuel cell systems, which replace the diesel generator normally operating under sea-going conditions. The FC system is sized to supply the full auxiliary electrical demand within the considered operating range of 360–600 kW. One of the existing DG units is retained in standby mode to ensure redundancy and provide backup power in the event of FC unavailability, while the third DG unit is removed from the auxiliary power architecture because it is unnecessary under the FC-dominant configuration. The installed FC capacity is therefore set to 600 kW, corresponding to the maximum auxiliary demand.

For the SOFC case, the total capacity is obtained by aggregating multiple modular units to reach 600 kW. For the PEMFC case, three 200 kW marine-certified modules are assumed to operate in parallel, ensuring redundancy and operational flexibility comparable to the three-DG arrangement. The CapEx calculations are therefore based on the total installed 600 kW fuel cell capacity. A schematic diagram is presented in Figure 1, comparing the conventional DG and the FCs arrangement for the auxiliary power.

A summary of the vessel’s main particulars, propulsion system characteristics, and fuel consumption parameters is provided in

Table 2. Ship and engine characteristics.

	Characteristic	Unit	Value
Ship	Ship type	-	Bulk carrier
	Length Between Perpendiculars	m	215
	Breadth	m	32.25
	Draft	m	13.8
	Deadweight	tonne	66,000
	Design speed at 85% MCR	knots	13.5
Main Engine	Rated power	kW	6400
	Rated speed	rpm	85.2
	SFC	g/kWh	170
	Lower Calorific value (LCV)	kJ/kg	40,200
Diesel Generator	Number	-	3
	Rated power	kW	600
	Rated speed	rpm	900
	SFC (load-dependent)	g/kWh	200–220
	LCV	kJ/kg	42,700

.

4.2. SOFC Characteristics

SOFCs are a high-temperature fuel cell technology characterised by operating temperatures typically in the range of 650–1000 °C and the use of a solid ceramic electrolyte [18]. In contrast to low-temperature PEMFCs, SOFCs enable internal fuel reforming, high fuel flexibility, and the production of high-grade waste heat, making them particularly attractive for applications requiring high electrical efficiency and combined heat and power potential. These characteristics have motivated increasing interest in SOFCs as a long-term solution for low-emission marine power generation [80].

Despite these advantages, no SOFC system has yet been specifically designed or commercialised for marine auxiliary power applications, mainly due to challenges related to thermal management, start-up time, dynamic operation, and system integration under shipboard constraints [81]. Consequently, the present study adopts a SOFC reference system, relying on validated published performance data to represent high-temperature fuel cell behaviour in the comparative assessment [82].

The SOFC system considered in this study is replicated from the authors’ previously published work in [82] and has a rated electrical capacity of 60 kW. While this unit rating is smaller than the total auxiliary demand of the case-study bulk carrier, it is used as a modular reference building block rather than as a standalone ship-level installation. The target auxiliary capacity of the vessel is 600 kW; therefore, the required SOFC installation is obtained by scaling and aggregating multiple 60 kW modules operating in parallel to reach the total demanded capacity. This modular scaling approach is technically justified because SOFC systems are inherently stack-based and commercially developed in repeatable unit sizes. Performance characteristics such as electrical efficiency and SFC are primarily load-dependent at the module level. These characteristics can be replicated across parallel units, provided that balance-of-plant scaling effects are properly accounted for in the capital cost model. Consequently, the 60 kW unit serves as a validated performance reference, while the economic assessment is conducted based on the full 600 kW installed capacity required for the bulk carrier auxiliary system.

Using a modular reference unit, therefore, does not imply undersizing relative to the vessel. Instead, it reflects practical system architecture, where multiple standardised SOFC modules are combined to meet shipboard auxiliary power requirements while preserving scalability, redundancy, and operational flexibility.

Due to the high operating temperature of SOFC systems, auxiliary energy is required during start-up to heat the stack and supply essential auxiliary components. To enable autonomous start-up, battery modules are integrated within the balance-of-plant and sized to cover the required start-up energy and auxiliary loads following the methodology presented in Section 3.3 [78]. For the 600 kW installation considered, the required battery capacity is 391 kWh. In addition, the battery supports transient load demands and improves operational stability.

The SOFC system is designed to be powered by NG, which is internally reformed within the fuel cell stack to produce hydrogen for electrochemical reactions. This system size is representative of small-scale auxiliary power units and allows direct comparison with PEMFC operation under similar load-following conditions. The efficiency and SFC as functions of load factors are presented in Figure 2 and are directly implemented in the present techno-economic and environmental analysis. The discrete performance data points obtained from [82] are converted into continuous curves using linear interpolation, allowing estimation of efficiency and SFC at intermediate load levels without introducing additional fitting assumptions.

The efficiency and specific fuel consumption (SFC) curves used in this study are based on the validated dataset reported in [82], which has been benchmarked against SOFC operation under steady-state conditions. The resulting performance trends are consistent with values reported in the literature for marine and stationary SOFC systems [27,83], supporting the reliability of the adopted modelling approach.

In the present analysis, fuel cell degradation is not explicitly modelled as a time-dependent efficiency decay; instead, it is indirectly accounted for through the assumed stack lifetime and replacement intervals. In addition, thermal integration effects, such as waste heat recovery from the high-temperature SOFC system, are not explicitly included in the efficiency calculations. The SOFC system is assumed to operate with internal reforming of natural gas, and efficiency penalties associated with external fuel processing are not explicitly modelled. These assumptions are consistent with the system-level scope of the study and allow for a harmonised comparison with alternative technologies.

In addition to performance characteristics, the physical feasibility of SOFC integration is assessed based on gravimetric and volumetric considerations. As no marine-adapted SOFC platform is currently available, the commercial Bloom Energy Server 6.5 [84] developed by Bloom Energy (San Jose, CA, USA) is used as a representative benchmark to estimate system-level physical characteristics. The selected unit has a rated electrical output of 325 kW, a total system mass of 14.8 t, and overall dimensions of 9 m × 1.3 m × 2.5 m, corresponding to a total system volume of 29.25 m³. Based on these specifications, the gravimetric power density is calculated as: Gravimetric power density = 21.96 kW/t, and volumetric power density is 11.11 kW/m³. These values reflect the substantial mass and volume associated with high-temperature components, thermal insulation, and balance-of-plant equipment inherent to SOFC systems.

The relatively low gravimetric and volumetric power densities highlight a key limitation of SOFC technology for near-term marine deployment, particularly in applications where space and weight constraints are critical. Nevertheless, the superior electrical efficiency and fuel flexibility of SOFCs justify their inclusion in this study as a high-efficiency reference case, enabling a meaningful comparison with PEMFC-based auxiliary power systems.

4.3. PEMFC Characteristics

PEMFCs represent a mature low-temperature fuel cell technology that has gained increasing attention for marine auxiliary power applications due to their favourable operational characteristics and environmental performance [18]. PEMFCs operate at relatively low temperatures, typically in the range of 60–80 °C, and convert the chemical energy of hydrogen directly into electrical energy through electrochemical reactions, producing water as the primary by-product. This direct energy conversion pathway enables high electrical efficiency while eliminating local emissions of nitrogen oxides, sulphur oxides, and particulate matter.

The selection of low-temperature PEMFC technology for auxiliary power systems in ships is primarily driven by its fast start-up capability [85], high-power density, and dynamic load response, which are critical for meeting fluctuating onboard auxiliary power demands.

Accordingly, a commercially available PEMFC system, the PowerCell Marine System 200 [86] from PowerCell (Göteborg, Sweden), is selected in this study as the reference auxiliary power unit for the case study analysis. This system represents a State-of-the-Art low-temperature PEMFC solution specifically developed for maritime applications and complies with relevant marine design and safety requirements. The Marine System 200 is rated at a net electrical output of 200 kW, making it suitable for covering a significant share of typical ship auxiliary and hotel loads during both port and sailing operations.

The selected PEMFC system is based on a modular architecture, allowing multiple units to operate in parallel to increase total installed capacity or enhance redundancy and operational flexibility. Although PEMFC systems operate at lower temperatures, auxiliary energy is still required during start-up to supply essential auxiliary components such as control systems, air compressors, and fuel supply units. For the 600 kW installation considered, the required battery capacity is 89 kWh.

Electrical power is delivered as DC, facilitating integration with shipboard power electronics, energy storage systems, and hybrid power management architectures. The system is designed to operate efficiently over a wide load range, which is a key requirement for auxiliary power applications characterised by variable demand profiles.

The main physical and operational characteristics of the selected PEMFC system, as relevant for system integration and performance modelling, are summarised in

Table 3. Main physical and technical characteristics of the PowerCell Marine System 200 [86].

Parameter	Value/Range	Unit
Rated net electrical power	200	kW
Operating temperature	60–80	°C
DC output voltage	550–1000	V
DC output current	45–405	A
Fuel type	Hydrogen (ISO 14687 compliant)	-
Hydrogen inlet pressure	3–3.6	bar
Cooling system	Liquid cooling	-
Recoverable heat output	<330	kWth

.

From a performance standpoint, the Marine System 200 exhibits load-dependent electrical efficiency and hydrogen consumption, characteristics particularly relevant for marine auxiliary power applications operating under variable load conditions. In this study, the system efficiency and SFC at different load levels are derived from the PowerCell datasheet [86] and presented in Figure 3.

The PEMFC performance data are derived from the manufacturer’s specifications of the PowerCell Marine System 200 [86]. The corresponding efficiency range (46–57%) and hydrogen consumption trends are consistent with reported experimental and demonstrator-based marine PEMFC applications [62,87], thereby providing confidence in the validity of the adopted model representation. Similar modelling assumptions are applied to the PEMFC system. The PEMFC system is assumed to operate on high-purity hydrogen, and additional energy requirements for hydrogen conditioning, compression, or onboard reforming are not explicitly included.

These performance curves provide a realistic representation of PEMFC behaviour under partial- and nominal-load operation and are used directly as inputs for the subsequent techno-economic and environmental analysis. The discrete data points extracted from the manufacturer’s datasheet [86] are processed using linear interpolation to generate continuous efficiency and SFC curves across the operating load range. As shown in Figure 3, the PEMFC system achieves its highest electrical efficiency in the mid-to-high load range, while SFC increases at lower load fractions, reflecting the influence of auxiliary power consumption and the inherent electrochemical losses of PEMFC operation.

5. Results and Discussion

The numerical model is developed and implemented in the MATLAB R2025a environment and applied to a representative bulk carrier to investigate the techno-economic and environmental implications of replacing conventional auxiliary diesel generators with fuel cell-based power generation systems. Two alternative auxiliary power configurations are examined: a main engine coupled with a solid oxide fuel cell system (ME + SOFC) and a main engine coupled to a proton exchange membrane fuel cell system (ME + PEMFC).

These configurations are designed to mirror the conventional three–diesel-generator arrangement described earlier in terms of total installed auxiliary capacity and redundancy philosophy. In the reference case, three 600 kW diesel generators are installed, with one typically operating, one on standby, and one available for maintenance rotation or peak demand. In the fuel cell-based configurations, the total installed auxiliary capacity is set to 600 kW, corresponding to the maximum expected hotel load, and is achieved through modular aggregation of fuel cell units.

For the PEMFC configuration, three 200 kW marine-certified modules operate in parallel, closely reflecting the three-unit structure of the conventional DG system in terms of redundancy and operational flexibility. For the SOFC configuration, multiple 60 kW modules are combined to reach the same total capacity, enabling comparable load sharing and partial-load operation.

Thus, while the underlying technology differs, the overall auxiliary power philosophy—modular capacity, parallel operation capability, and redundancy—remains consistent with typical bulk carrier arrangements.

5.1. Steady-State Performance Results

The performance of each configuration is analysed over an operating envelope representative of typical bulk carrier service conditions. Ship speeds are not treated as simple minimum–maximum boundary cases, nor are they modelled using uniform 1-knot increments. Instead, nine discrete operating points are explicitly evaluated: 10, 11, 11.3, 12, 12.3, 13, 13.2, 13.5, and 14 knots.

This selection includes representative slow-steaming conditions (10–12 knots), intermediate service points, and speeds approaching the design speed (13.5 knots). Additional intermediate values (e.g., 11.3, 12.3, 13.2 knots) are included to better capture non-linear propulsion power scaling. Since the main engine power demand approximately follows a cubic relationship with vessel speed, small variations near service speed can lead to disproportionately large changes in propulsion power and fuel consumption.

Therefore, the chosen speed set provides a structured yet non-uniform resolution of the operating envelope, allowing a more accurate representation of propulsion–auxiliary interactions across realistic bulk carrier service conditions, rather than relying solely on extreme values or evenly spaced increments.

In the alternative configurations, the auxiliary electrical demand is assumed to be supplied entirely by the fuel cell systems, which are sized to match the maximum expected hotel load of the vessel. A total installed auxiliary capacity of 600 kW is therefore adopted, corresponding to the upper bound of the analysed load range (360–600 kW).

This capacity does not represent a single monolithic unit but rather the aggregated output of multiple modular fuel cell units operating in parallel. The installed 600 kW rating ensures that the fuel cell configuration can fully replace conventional auxiliary diesel generators during peak auxiliary demand, while also allowing part-load operation at lower demand levels.

By matching the maximum auxiliary load with equivalent installed fuel cell capacity, the comparison with the conventional diesel generator arrangement remains technically consistent in terms of power adequacy and operational coverage.

The auxiliary demand is not limited to simple minimum and maximum cases. Instead, it is examined at incremental load levels ranging from 60% to 100% of the installed 600 kW capacity, corresponding to electrical loads between 360 kW and 600 kW. Intermediate load points are evaluated across this interval to capture progressive changes in system behaviour rather than relying solely on boundary conditions.

This incremental examination allows a systematic assessment of part-load and near-rated performance characteristics of the fuel cell systems. Since fuel cell efficiency, specific fuel consumption, and economic indicators are load-dependent, evaluating multiple operating points provides a more accurate representation of realistic hotel load conditions and enables clearer identification of how auxiliary demand interacts with overall vessel energy consumption.

For each operating point, the model computes the annual fuel consumption associated specifically with auxiliary power generation. The results are compared against a conventional reference configuration in which auxiliary electrical loads are supplied by diesel generators (DG), while the main propulsion engine remains unchanged. This comparative framework isolates the impact of replacing auxiliary DG with fuel cell systems and enables quantification of the resulting fuel consumption differences as functions of fuel type, auxiliary electrical load, and ship operating condition. The resulting performance indicators provide the basis for evaluating the relative merits of SOFC- and PEMFC-based auxiliary power systems for bulk carrier applications.

Figure 4 presents the annual auxiliary fuel energy consumption for three auxiliary power configurations—conventional DG, NG-fuelled SOFC, and hydrogen-fuelled PEMFC—across auxiliary electrical loads ranging from 360 kW to 600 kW. The vertical axis reports total auxiliary fuel energy demand in GJ per year, while the horizontal axis represents the corresponding electrical load. All values are calculated assuming 300 operational days per year.

A clear and nearly linear increase in annual fuel energy consumption is observed for all three configurations as auxiliary load increases. This trend reflects the proportional relationship between delivered electrical power and required fuel input under steady operating conditions. However, the magnitude of annual energy demand differs markedly between technologies.

The DG configuration exhibits the highest annual fuel energy consumption across the entire load range. At 360 kW, diesel auxiliary demand is approximately 2.45 × 10⁴ GJ/year, increasing to nearly 3.7 × 10⁴ GJ/year at 600 kW. This elevated energy requirement reflects the comparatively lower electrical efficiency of conventional auxiliary diesel generators.

The NG-fuelled SOFC configuration demonstrates the lowest annual fuel energy consumption at all load levels. Annual demand increases from roughly 1.55 × 10⁴ GJ/year at 360 kW to about 2.8 × 10⁴ GJ/year at 600 kW. This corresponds to an energy reduction of approximately 25–35% relative to diesel across the examined load range, highlighting the superior steady-state conversion efficiency of SOFC systems.

The hydrogen-fuelled PEMFC configuration lies between the SOFC and diesel cases. Annual consumption rises from approximately 1.75 × 10⁴ GJ/year at 360 kW to around 3.35 × 10⁴ GJ/year at 600 kW. While PEMFC systems achieve meaningful reductions compared to diesel generators, their total fuel energy demand remains higher than that of the SOFC configuration under the modelled assumptions.

The nearly parallel slopes indicate stable part-load behaviour and consistent efficiency differences across the load range. Overall, the figure confirms that replacing a conventional diesel generator with a fuel cell-based auxiliary system substantially reduces annual fuel energy demand, with the NG–SOFC configuration delivering the largest reduction, followed by the hydrogen–PEMFC system.

5.2. Carbon Dioxide Emissions Results

In addition to reducing fuel consumption, replacing auxiliary diesel generators with fuel cell systems significantly reduces carbon dioxide emissions. For the 300 operational days, Figure 5 illustrates the resulting daily CO₂ emission savings, expressed in tonnes per year, as a function of auxiliary electrical load for both SOFC- and PEMFC-based configurations. As with the SFC results, the CO₂ savings are independent of ship speed, confirming that the observed emission reductions are primarily driven by the auxiliary power generation strategy rather than by changes in propulsion operating conditions. The vertical axis represents the total annual CO₂ reduction in tonnes per year (t/year) relative to the diesel generator reference case, while the horizontal axis shows the auxiliary electrical demand.

A clear and nearly linear relationship is observed between auxiliary load and annual CO₂ emissions reduction for both fuel cell technologies. As auxiliary electrical demand increases from 360 kW to 600 kW, the avoided diesel fuel consumption in the reference configuration rises proportionally. Consequently, replacing the diesel generator with a fuel cell system results in progressively larger annual CO₂ reductions. All values are calculated assuming 300 operating days per year.

The PEMFC configuration consistently delivers the highest CO₂ mitigation across the full load range. At 360 kW, the annual CO₂ reduction is approximately 1830 t/year, increasing to nearly 2780 t/year at 600 kW. The slope of the PEMFC curve is steep and almost perfectly linear, indicating that emission savings scale strongly with increasing auxiliary demand. This reflects both the higher efficiency of the PEMFC system relative to diesel and the higher carbon intensity of the displaced reference fuel.

The SOFC configuration also achieves substantial emission reductions, although at lower levels compared to PEMFC under the assumed fuel pathways. At 360 kW, the annual CO₂ reduction is approximately 1080 t/year, rising to about 1340 t/year at 600 kW. The increase remains nearly linear, indicating stable performance across part-load and full-load conditions.

Across all load levels, PEMFC systems achieve roughly 70–100% higher annual CO₂ reductions than SOFC systems, depending on the operating point. The nearly parallel and smooth trends suggest that emission mitigation is primarily governed by load magnitude and intrinsic system efficiency, rather than nonlinear operational behaviour.

Overall, the figure demonstrates that replacing an operating diesel generator with a fuel cell auxiliary system yields significant annual CO₂ reductions, with the hydrogen-fuelled PEMFC configuration providing the greatest mitigation potential across the examined load spectrum.

5.3. Economic Assessment Results

The economic assessment is based on a consistent set of fuel price assumptions that reflect current market conditions and reported cost ranges for conventional and low-carbon fuels, as described in Section 4. These assumptions span a wide range of carbon intensities and economic conditions, allowing the cost-difference analysis to isolate how both fuel cell technology and fuel production pathways influence operating costs and lifecycle investment performance.

Figure 6 presents the annual OpEx difference in fuel cell-based auxiliary power systems relative to conventional diesel generators across auxiliary loads of 360–600 kW. Positive values indicate cost reductions compared to the diesel baseline (savings), while negative values represent cases in which the fuel cell system results in slightly higher operating costs (penalty).

For the SOFC configurations, the economic outcome remains strongly dependent on the NG pathway. Grey NG provides consistent and increasing annual savings, rising from approximately 4.4 × 10⁵ $/year at 360 kW to about 5.4 × 10⁵ $/year at 600 kW. The trend is nearly linear, reflecting both improved fuel efficiency relative to diesel and increasing auxiliary demand. Bio NG also yields positive savings, though at a lower magnitude, increasing from roughly 3.6 × 10⁵ $/year to about 3.9–4.0 × 10⁵ $/year across the load range. The smaller slope indicates that the higher cost of bio-derived gas partially offsets efficiency gains. In contrast, green NG results in substantial annual cost penalties. The OpEx difference decreases from approximately −2.0 × 10⁵ $/year at 360 kW to nearly −6.0 × 10⁵ $/year at 600 kW, showing that the high assumed price of fully renewable gas outweighs the efficiency advantage of the SOFC system, particularly at higher loads.

For PEMFC systems operating on hydrogen, the magnitudes are generally higher. Grey hydrogen delivers the largest annual operating savings, increasing from approximately 7.0 × 10⁵ $/year at 360 kW to nearly 9.5 × 10⁵ $/year at 600 kW. Blue hydrogen also provides significant savings, rising from about 5.2 × 10⁵ $/year to approximately 6.1 × 10⁵ $/year. Green hydrogen remains economically favourable in this figure, with positive annual OpEx differences decreasing slightly from roughly 3.3 × 10⁵ $/year at 360 kW to about 2.6 × 10⁵ $/year at 600 kW, indicating narrower margins as load increases.

Across all configurations, OpEx differences scale approximately linearly with auxiliary load, confirming that absolute economic impact grows with energy demand. However, the dominant driver of economic performance remains the fuel pathway cost structure. Grey fuels provide the strongest annual operating savings, transitional fuels yield moderate benefits, and fully renewable fuels can either narrow margins or impose penalties depending on their price assumptions.

To better understand the drivers behind the NPV results, Figure 7 and Figure 8 present a deterministic breakdown of lifecycle cost components for SOFC and PEMFC auxiliary configurations, respectively. Each stacked bar illustrates the cumulative contribution of fuel costs, O&M expenses, CO₂ taxation, CapEx, and replacement costs (RepEx) over the project lifetime. The black markers indicate the resulting total NPV for each load level and fuel pathway.

For grey NG–SOFC, total NPV remains positive and increases steadily with auxiliary load. At 360 kW, the total NPV (black marker) is approximately +2.0 M$, rising to nearly +4.5 M$ at 600 kW. The positive balance is primarily driven by two components: reduced fuel expenditure and avoided CO₂ tax relative to the diesel reference case. The fuel-related savings grow proportionally with load, which explains the near-linear upward trend in total NPV.

However, the positive balance is partially offset by significant CapEx (−3 to −4 M$) and RepEx (−4 M$) contributions. These capital-related components remain largely constant across load levels because installed capacity is fixed at 600 kW. Thus, as auxiliary demand increases, the operational savings scale upward while the capital burden remains fixed—structurally improving profitability.

For bio-NG–SOFC, the lifecycle structure tightens considerably. At 360 kW, total NPV is close to breaking even (approximately 0 to +0.5 M$), and at 600 kW it rises only modestly to about +1 M$. The fuel cost component is noticeably larger than in the grey NG case, eroding the margin generated by efficiency gains. The CapEx and RepEx burdens remain unchanged, so the system operates within a narrow economic corridor. Small variations in fuel price would easily push these cases into negative territory, which is exactly what the Monte Carlo results later confirm.

The green NG–SOFC configuration exhibits a fundamentally different structure. Here, the fuel cost dominates the lifecycle balance. At 360 kW, total NPV is approximately −10 M$, declining further to nearly −20 M$ at 600 kW. Unlike the grey and bio pathways, increasing auxiliary load amplifies the deficit. The reason is structural: the very high unit price of renewable NG scales directly with energy demand, while CapEx and RepEx remain constant. In other words, higher load intensifies exposure to expensive fuel rather than improving capital recovery.

The SOFC figure shows that capital intensity is significant but not decisive. The fuel pathway cost is the dominant driver, while system efficiency helps, but it cannot compensate for the cost of fuel.

For grey hydrogen–PEMFC, total NPV increases from roughly +9–10 M$ at 360 kW to approximately +15–17 M$ at 600 kW. The magnitude is substantially higher than for SOFC. The fuel savings component is large and avoided CO₂ taxation contributes significantly to the positive balance. Although CapEx (≈−3 M$) and RepEx (≈−3–4 M$) are present, they are proportionally smaller relative to the operational savings. As load increases, the fuel and CO₂-related benefits scale upward while capital remains fixed, generating accelerating economic gains.

For blue hydrogen–PEMFC, the total NPV remains positive but more moderate, increasing from about +6 M$ at 360 kW to roughly +8–9 M$ at 600 kW. The additional cost of carbon capture increases the fuel component relative to grey hydrogen, reducing the net margin. Nevertheless, the structural balance remains favourable across all loads. The system retains sufficient operational savings to comfortably offset capital investment.

The green hydrogen–PEMFC pathway presents a more delicate structure. Total NPV decreases slightly with load, from around +2.5–3 M$ at 360 kW to roughly +1 M$ at 600 kW. Unlike grey hydrogen, here the fuel cost component grows more rapidly than the CO₂ tax benefit. As auxiliary demand increases, the system becomes more exposed to high renewable hydrogen prices. However, unlike green NG in the SOFC case, the total balance remains positive across all loads. The margin narrows, but it does not collapse.

While Figure 7 and Figure 8 provide a deterministic decomposition of lifecycle cost components, they represent single-point evaluations based on baseline fuel price and capital cost assumptions. In reality, both fuel markets and technology costs are inherently uncertain and subject to volatility over the project lifetime. The structural cost composition identified in the deterministic breakdown—particularly the dominant influence of fuel pathway cost—indicates that variations in these parameters could materially shift lifecycle outcomes. It is therefore insufficient to evaluate only the expected NPV under fixed assumptions; the dispersion of possible outcomes under realistic market variability must also be examined.

To address this, the Monte Carlo analysis extends the deterministic framework by repeatedly sampling fuel prices and capital costs within predefined uncertainty ranges. This probabilistic approach enables the assessment of economic robustness, downside risk, and the likelihood of profitability. It avoids reliance on single baseline estimates. The resulting NPV distributions provide a detailed evaluation of the long-term economic viability of SOFC- and PEMFC-based auxiliary power systems under uncertainty.

The boxplots in Figure 9 and Figure 10 summarise the statistical spread of NPV outcomes, expressed in million dollars over the project lifetime, for auxiliary electrical loads between 360 kW and 600 kW and across the different fuel supply pathways.

For the SOFC operating on grey NG, the median NPV is consistently positive and significantly higher than previously stated. At 360 kW, the median NPV is approximately 2.0–2.5 M$, increasing steadily to roughly 4.0–4.5 M$ at 600 kW. The upward shift in load reflects the cumulative effect of higher annual fuel-cost savings as auxiliary demand increases. The interquartile ranges remain moderately compact around the median, indicating controlled sensitivity to ±20% fuel price variation and to capital cost uncertainty. Importantly, even the lower quartile remains above zero in most cases, confirming structurally robust profitability.

For bio-NG–SOFC, the distributions cluster close to the break-even threshold. Median NPVs lie near 0–1.0 M$ across the load range, with a slight improvement at higher loads. However, the interquartile ranges frequently intersect the zero line, indicating that a significant portion of the Monte Carlo realisations fall below zero. This confirms that bio-NG operation is economically marginal and highly sensitive to cost assumptions. Profitability is achievable but not structurally guaranteed.

In contrast, green NG–SOFC results are strongly negative and deteriorate with load. Median NPVs decline from approximately −10 M$ at 360 kW to nearly −19 to −20 M$ at 600 kW. The downward slope indicates that higher auxiliary demand amplifies the economic deficit because the elevated fuel price scales directly with energy consumption. Although uncertainty introduces dispersion, the entire distribution remains deeply negative, demonstrating that under current price assumptions, green NG operation imposes a persistent structural penalty.

Turning to PEMFC hydrogen pathways, the scale of the NPV distributions shifts upward substantially. For grey hydrogen, median NPVs increase from approximately 9–10 M$ at 360 kW to around 15–17 M$ at 600 kW. The distributions are entirely above zero, and even the lower whiskers indicate strongly positive outcomes. This demonstrates both high profitability and limited downside risk under the assumed efficiency and fuel price structure.

Blue hydrogen–PEMFC configurations also exhibit consistently positive NPVs, with medians rising from roughly 6 M$ to about 8–9 M$ across the load range. Although lower than grey hydrogen due to the cost premium associated with carbon capture, the distributions remain comfortably positive and scale favourably with load.

For green hydrogen, the NPV remains positive but declines slightly as load increases. Median values range from approximately 2.5–3.0 M$ at 360 kW to about 1.0–1.5 M$ at 600 kW. The narrowing margin at higher loads reflects the higher unit cost of renewable hydrogen. While most realisations remain positive, the lower quartiles approach the break-even threshold at elevated loads, indicating greater sensitivity to adverse price realisations.

Overall, the figures reinforce two structural conclusions. First, fuel pathway cost overwhelmingly governs economic performance, often more strongly than load variation. Second, hydrogen-based PEMFC configurations—particularly grey and blue hydrogen—demonstrate substantially higher NPV potential than NG-based SOFC systems under the modelled assumptions, while fully renewable pathways remain economically constrained despite their environmental advantages.

The MAC distributions derived from the Monte Carlo simulation provide a quantitative measure of the cost-effectiveness of CO₂ emission reductions achieved through SOFC- and PEMFC-based auxiliary power systems, accounting for uncertainty in fuel prices and capital costs. The MAC is expressed in $ per tonne of CO₂ avoided and reflects the combined economic and environmental performance of each configuration across auxiliary electrical loads ranging from 360 kW to 600 kW, as shown in Figure 11 and Figure 12.

For the SOFC operating on grey NG, the MAC remains consistently negative across all auxiliary load levels, confirming that CO₂ reductions are achieved with a net economic benefit. Median values range approximately from −70 $/tCO₂ at 360 kW to nearly −100 $/tCO₂ at 600 kW. The interquartile ranges remain fully below zero, although the spread widens slightly at higher loads. The increasingly negative median with load indicates that the economic efficiency of abatement improves as annual fuel displacement grows.

When SOFC operates on bio-NG, the MAC distributions shift upward toward cost neutrality. Median values lie roughly between −10 and −40 $/tCO₂, depending on load level. The interquartile ranges frequently straddle the zero line, particularly at lower loads, indicating that abatement can be either marginally cost-saving or marginally cost-incurring depending on fuel price realisations. The modest downward trend in median MAC at higher loads suggests some improvement in abatement efficiency, but economic neutrality remains sensitive to uncertainty.

In contrast, green NG–SOFC results in strongly positive MAC values that increase with load. Median values rise from approximately 320 $/tCO₂ at 360 kW to nearly 460–480 $/tCO₂ at 600 kW. The entire distribution remains well above zero across all load levels. The upward slope reflects the compounding impact of high renewable fuel cost as auxiliary energy demand increases, making abatement progressively more expensive in absolute terms.

For PEMFC configurations, a similarly structured but numerically distinct pattern emerges. Grey hydrogen yields strongly negative MAC values, with medians approximately between −160 and −180 $/tCO₂ across the load range. Interquartile bands remain entirely below zero, indicating robust economic benefit per tonne of CO₂ avoided. The relative stability of the medians suggests that abatement efficiency is only weakly dependent on auxiliary load for this pathway.

Blue hydrogen–PEMFC configurations exhibit moderately negative MAC values, with medians roughly between −90 and −110 $/tCO₂. Although less favourable than grey hydrogen, the distributions remain clearly below zero across most realisations, confirming that carbon capture–based hydrogen still enables economically advantageous emissions reduction under the assumed conditions.

Green hydrogen presents a markedly different behaviour. Median MAC values remain positive across all loads but decrease significantly with increasing auxiliary demand—from approximately 50 $/tCO₂ at 360 kW to values approaching 0–20 $/tCO₂ at 600 kW. The interquartile ranges shift downward with load, and at higher auxiliary levels, the lower quartiles approach zero. This indicates that while green hydrogen currently entails a positive abatement cost, increasing operational intensity improves its economic competitiveness.

Overall, the MAC analysis reinforces the dominance of fuel pathway cost in determining abatement efficiency. Grey pathways (both NG–SOFC and H₂–PEMFC) deliver emissions reductions at clearly negative marginal cost. Blue hydrogen remains economically favourable, though less strongly so. Bio-NG approaches neutrality with substantial sensitivity to uncertainty. Fully renewable fuels diverge: green NG exhibits high and increasing abatement cost, whereas green hydrogen shows improving competitiveness at higher loads, approaching cost neutrality under intensified operation.

The payback period analysis provides insight into investment recovery time, as shown in Figure 13 and Figure 14. For SOFC systems operating on grey NG, median payback periods range from approximately 6 to 8 years across the 360–600 kW load range. A slight downward tendency is observed at higher loads, reflecting stronger annual fuel savings as auxiliary demand increases. The interquartile ranges remain moderate, generally spanning 5–9 years, indicating manageable sensitivity to fuel price and capital cost uncertainty. Overall, grey NG–SOFC configurations demonstrate stable and commercially reasonable recovery times.

When a SOFC operates on bio-NG, the payback period is extended. Median values cluster around 8–10 years, with dispersion widening to approximately 7–12 years depending on load. While investment recovery remains achievable within the project horizon, the longer timeframe reflects the narrower operating cost margin associated with higher biofuel prices. The greater spread confirms increased sensitivity to uncertainty compared to the grey NG case.

For green NG–SOFC configurations, payback periods lengthen further and increase with auxiliary load. Median values rise from roughly 7–8 years at 360 kW to approximately 11–12 years at 600 kW. Upper whiskers extend toward 15–17 years in some realisations, highlighting significant downside risk. The upward trend with load indicates that the higher renewable fuel cost scales proportionally with energy demand, delaying capital recovery despite efficiency advantages.

Turning to PEMFC systems (upper figure), the shortest recovery times are observed for grey hydrogen. Median payback periods lie between approximately 4–5 years at 360 kW and 3–4 years at 600 kW. The decreasing trend with load reflects accelerating cost savings at higher auxiliary demand. Even under uncertainty, most realisations remain within a relatively narrow 3–6 year band, indicating rapid and robust capital recovery.

Blue hydrogen–PEMFC systems exhibit intermediate performance. Median payback periods are typically around 5–6 years across the load range, with some dispersion extending toward 7–8 years. Although carbon capture increases fuel cost relative to grey hydrogen, investment recovery remains commercially attractive and relatively stable.

Green hydrogen–PEMFC configurations display the longest recovery times among the hydrogen pathways. Median values increase from approximately 8 years at 360 kW to about 11–12 years at 600 kW. The upper whiskers reach 14–16 years in some cases, reflecting heightened sensitivity to fuel price uncertainty. The upward trend with load suggests that, under current price assumptions, higher operational intensity does not accelerate recovery but instead amplifies cost exposure.

Overall, the PBP analysis aligns with the NPV and MAC findings. Grey fuel pathways deliver the most rapid and robust capital recovery, followed by transitional fuels (bio-NG and blue hydrogen). Fully renewable pathways remain technically viable but exhibit longer and more uncertainty-sensitive recovery horizons. Across both technologies, fuel-pathway cost exerts a stronger influence on payback time than auxiliary-load variation, underscoring its central role in determining investment viability.

The IRR results further confirm the strong influence of fuel pathway on profitability, as shown in Figure 15 and Figure 16. For SOFC systems operating on grey NG (upper figure, left block), median IRR values increase steadily with auxiliary load, rising from approximately 13% at 360 kW to about 16–17% at 600 kW. The interquartile ranges broaden moderately at higher loads, but the entire distributions remain comfortably above typical discount rate benchmarks. This indicates robust profitability and improving return performance as annual fuel savings scale with auxiliary demand.

When SOFC operates on bio-NG, returns remain positive but are consistently lower. Median IRRs range roughly from 10 to 11% at 360 kW to approximately 12–13% at 600 kW. The dispersion is somewhat wider than in the grey NG case, reflecting increased sensitivity to fuel price uncertainty. Nevertheless, the distributions remain clearly positive across all loads, confirming economic viability under the assumed uncertainty ranges.

In contrast to earlier assumptions, green NG–SOFC configurations in the results do not exhibit undefined IRRs. It should be noted that the green NG-SOFC configuration does not achieve a positive IRR under the considered assumptions. This is mainly due to the high capital cost of the SOFC system and the elevated price of green fuel, resulting in insufficient cash flow to recover the initial investment over the project lifetime. Although the system offers higher efficiency and reduced CO₂ emissions, these benefits are not sufficient to offset the high capital and fuel costs.

Turning to PEMFC systems (lower figure), significantly higher returns are observed for hydrogen pathways. Grey hydrogen yields the strongest performance, with median IRRs rising from approximately 25–27% at 360 kW to nearly 36–38% at 600 kW. The upward slope highlights strong load-scaling benefits, and even the lower quartiles remain well above 20%, indicating highly attractive and resilient investment performance.

Blue hydrogen–PEMFC configurations also demonstrate strong returns, with median IRRs increasing from roughly 19–20% to about 23–26% across the load range. Although lower than grey hydrogen due to the added cost of carbon capture, profitability remains robust and improves with higher auxiliary demand.

Green hydrogen presents the lowest IRR among the PEMFC pathways but remains clearly positive. Median values decline slightly with load, from approximately 12–13% at 360 kW to around 9–10% at 600 kW. The modest downward trend reflects the stronger influence of the renewable hydrogen price at higher energy demand levels. Despite narrower margins, the majority of realisations remain above conventional hurdle rates.

Overall, the IRR analysis reinforces the hierarchy observed in the NPV and PBP results. For SOFC systems, grey NG delivers the highest and most stable returns, followed by bio-NG and then green NG. For PEMFC systems, grey hydrogen offers exceptionally strong and load-enhanced profitability, blue hydrogen remains financially attractive, and green hydrogen provides moderate but positive returns. Across both technologies, fuel pathway cost structure exerts a stronger influence on long-term investment performance than auxiliary load variation, underscoring its central role under uncertainty.

6. Conclusions and Future Research

6.1. Conclusions

This study developed and applied a unified, uncertainty-aware framework to compare SOFC- and PEMFC-based auxiliary power systems against a conventional diesel generator benchmark within a 200 m bulk carrier energy architecture. By evaluating both technologies under identical vessel characteristics, load ranges (360–600 kW), speed envelopes (10–14 knots), and probabilistic cost assumptions, the analysis eliminates methodological distortion and enables a transparent cross-technology comparison.

From an operational perspective, replacing one operating 600 kW diesel generator with a fuel cell system yields substantial performance improvements. SOFC configurations reduce auxiliary fuel energy consumption by approximately 25–35% relative to diesel, corresponding to annual CO₂ reductions of 1.1–1.3 kt. PEMFC configurations achieve larger emission reductions of approximately 1.8–2.8 kt per year. Emission mitigation scales nearly linearly with auxiliary demand, confirming stable part-load behaviour.

Lifecycle economic performance is strongly governed by fuel pathway selection. Under grey fuel pathways, SOFC systems exhibit median NPVs increasing from approximately 2 M$ to over 4 M$ as load increases, with IRRs rising from roughly 13% to 17% and payback periods of 6–8 years. PEMFC systems operating on grey hydrogen demonstrate substantially higher returns, with median NPVs of 15–17 M$ at higher loads and IRRs of 35–38%, reflecting both higher efficiency and stronger fuel-cost differentials relative to diesel.

Transitional pathways (bio-NG and blue hydrogen) remain economically viable but operate within narrower margins and exhibit greater sensitivity to price variability. Renewable pathways display contrasting behaviour: green NG produces structurally negative NPVs under current cost assumptions, whereas green hydrogen remains positive but with declining margins at higher loads.

The Monte Carlo analysis reveals that uncertainty is not a peripheral factor but a defining structural element. Fuel price variability and capital cost dispersion can shift NPV by several million dollars, particularly for marginal pathways. Grey fuel pathways maintain robust positive distributions across uncertainty ranges, while renewable pathways show increased downside exposure. In all cases, fuel-pathway cost exerts a stronger influence on lifecycle outcomes than auxiliary-load variation.

Overall, the results indicate that fuel cell auxiliary systems can significantly enhance shipboard efficiency and emissions performance when benchmarked against conventional diesel generators. However, long-term economic resilience depends predominantly on upstream fuel production economics rather than on stack-level efficiency alone. Embedding uncertainty directly within the evaluation framework provides a more realistic basis for decision-making and strengthens the suitability of the model for future integration into MBSE-driven ship energy system design and optimisation environments.

6.2. Future Research

Future work should extend the current steady-state framework to improve both technical realism and strategic relevance. Incorporating dynamic operating behaviour is essential to capture transient load response, start-up and shutdown sequences, stack degradation, thermal cycling effects, and long-term performance drift. Such dynamic modelling would enable more accurate estimation of fuel consumption across realistic operating profiles, stack replacement intervals, maintenance schedules, and lifecycle cost evolution. Moving from steady-state snapshots to time-dependent system behaviour will strengthen the robustness of both technical and financial projections.

Expanding the fuel pathway modelling to include well-to-wake emissions, fuel production variability, onboard storage penalties, and logistics constraints is also critical under lifecycle-focused decarbonisation regulations. Explicit carbon pricing scenarios should be systematically integrated. While the present results indicate avoided carbon costs in the range of 285,000–430,000 $/year per vessel, higher carbon price trajectories (300–400 $/tCO₂) could increase avoided costs to approximately 855,000–1.14 million $/year. Under such regulatory conditions, renewable fuel pathways that are currently marginal could become economically competitive. Embedding dynamic carbon pricing scenarios within the model would therefore enable more realistic long-term investment forecasting.

A key strategic extension of this work involves integration within an MBSE environment, such as Capella [88], following the Arcadia methodology. In this context, the auxiliary power model can be formalised as a parametric subsystem linked to ship-level functional requirements (e.g., “Provide Auxiliary Electrical Power,” “Meet CO₂ Reduction Target,” “Satisfy Economic Viability Criteria”). SOFC and PEMFC configurations can be instantiated as alternative logical and physical architecture solutions, each associated with parametric properties, including efficiency curves, fuel-pathway attributes, capital-cost ranges, and degradation assumptions. The mathematical relationships developed in this study (fuel consumption equations, NPV, IRR, MAC, and Monte Carlo uncertainty distributions) can be connected to Capella through parametric diagrams or co-simulation interfaces with external computational tools.

Within such an MBSE framework, changes in design variables—auxiliary load range, fuel price assumptions, carbon tax levels, stack lifetime, or regulatory constraints—would automatically propagate through the architectural model and update system-level KPIs. This enables early stage, uncertainty-aware trade-off analysis across performance, emissions, cost, and risk metrics. Rather than treating economic evaluation as a post-design verification step, the fuel cell assessment becomes an integrated decision module within the digital ship architecture. Advancing toward dynamic, carbon-price-sensitive, and MBSE-integrated modelling will therefore be essential to support the structured, risk-informed deployment of fuel cell-based auxiliary systems in future commercial vessels.