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Research Papers

# Techno-Economic Analysis and Feasibility Study of a Solid Oxide Fuel Cell-Battery Hybrid System for Water Taxi ApplicationPUBLIC ACCESS

[+] Author and Article Information
Datong Song

Energy, Ming and Environment Research Centre,
4250 Wesbrook Mall,
e-mail: datong.song@nrc-cnrc.gc.ca

Xinge Zhang, Roberto Neagu, Wei Qu

Energy, Ming and Environment Research Centre,
4250 Wesbrook Mall,

1Corresponding author.

Manuscript received March 14, 2018; final manuscript received November 16, 2018; published online January 18, 2019. Assoc. Editor: Vittorio Verda.

J. Electrochem. En. Conv. Stor. 16(2), 021010 (Jan 18, 2019) (13 pages) Paper No: JEECS-18-1027; doi: 10.1115/1.4042092 History: Received March 14, 2018; Revised November 16, 2018

## Abstract

A hybrid power system consisting of an intermediate temperature solid oxide fuel cell (SOFC) and a lithium-ion battery is conceptually designed for water taxi applications. The sizing method of such a hybrid system is developed based on the resistance, acceleration performance, cruising cycle, and the speeds of a water taxi under the conditions of daily operation time and charge neutrality over a 24 h period. A techno-economic analysis (TEA) is performed for the proposed hybrid system and compared with other two power sources, a typical internal combustion engine (ICE), and a battery-only system. A feasibility study based on the weight and the volume of the hybrid system is conducted. The potential reduction of greenhouse gases (GHG) emissions is calculated and compared with the GHG emissions from water taxies powered by an ICE and a battery-only, respectively.

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## Introduction

The increasingly strict regulations on greenhouse gas (GHG) emission motivate transportation industries, mainly the automobile manufacturers and ship builders, to explore alternatives to the internal combustion engine (ICE). Among all the technologies investigated, one of the most promising candidates is the electric propulsion where the electrical motors are powered by electrochemical systems, such as a battery, a polymer electrolyte membrane fuel cell (PEMFC), a solid oxide fuel cell (SOFC), or a hybrid power system. During the past decades, the electric powertrain technology has been significantly advanced and widely adopted by automobile industry. The commercialization of purely battery and hybrid powered electric vehicles (EVs) is happening world widely. Meanwhile, as a result of substantial investment from government and automakers, outstanding progresses for PEMFCs have been achieved. The applications of PEMFC in automobile, marine and auxiliary power units were extensively demonstrated [13]. In addition to the high cost, the commercial applications of PEMFCs in marine sectors are limited by the requirements of using high purity hydrogen as fuel, as well as on board storage capacity, the complexity of on-site generation of hydrogen, and its safe operation on marine vessels.

A SOFC is a solid oxide or ceramic electrolyte based electrochemical conversion device that produces electricity directly from oxidizing fuels at high temperatures. Comparing to PEMFCs, SOFCs have the following potential benefits:

• High overall efficiency.

• Fuel flexibility—the high-temperature operation of SOFCs allows for internal reforming of hydrocarbon fuels like natural gas, gasoline, or diesel, which could be thus directly feed into SOFCs—similar to using hydrogen as fuel. Additionally, carbon monoxide produced in the reforming process is oxidized without poisoning catalyst which greatly simplifies the fuel processing step.

• Heat produced by SOFCs can be recovered and used to provide energy to the endothermic steam-reforming process or supply cabin heating.

• The material cost for SOFCs is potentially lower than that for PEMFCs.

The nature of SOFC high-temperature operation attributes its unique characteristics which are considered not favor for mobile application such as

• weak thermal shock properties, hence,

• not suited for repetitive start-up/shutdown cycles, and

• long start-up time (SOFCs typically have a start-up time of several hours).

Envision the future applications based on the technology merits of SOFC, the pioneer and risk-taking companies are exploring opportunities to demonstrate SOFC in various marine vessels. The limited power range and cycle life of current SOFC systems confine the use of SOFCs more appropriate to auxiliary power units [4,5] than main power source in automotive or marine sectors [3]. The ABSOLUTE (advanced battery solid oxide fuel cell linked unit to maximize efficiency) project [6] might be the first attempt to combine a sodium-nickel chloride (ZEBRA) battery and an intermediate temperature solid oxide fuel cell (IT-SOFC) to form a hybrid driving power source for automotive applications. The project team published several papers [79] regarding the operation and the concept system design of the proposed battery-SOFC hybrid system and conducted a techno-economic analysis (TEA) [10] for a delivery van application under EU drive cycle requirements. The SchiBZ (ship-integrated fuel cell) project [11,12] was started from year 2009 and aimed to install and evaluate a 0.5 MW diesel-reformer integrated SOFC system on the vessel MS Forester where the SOFC system as the main propulsion power source. It was claimed that land-based commissioning of a 50 kW SOFC system on vessel MS Forester was taken placed in 2015 and test operation at sea was planned in 2016. So far, most of the SOFC projects for marine applications have been either delayed or discontinued due to various types of difficulties, such as insufficient financial support from government/industry, safety concerns, difficulties to modify the current shipboard, etc. [13]. Because of lacking of real operation data, using computer simulation is virtually a cost-effective way to conduct performance evaluation and TEA of SOFC systems in marine applications.

The power output of current available SOFC systems is in the range of several to tens of kWs per module unit which is more suitable for small vessel operation. To further explore the potential of SOFCs in marine applications, a typical water taxi operating in Vancouver city area is selected as the representative marine vessel for this study owing to its low propulsion power requirement and increasing emission control in the bay harbor area. This paper presents a case study of using an SOFC-battery hybrid system as the main power source for water taxi operation. A concept design of such hybrid system is proposed, and TEA study and feasibility analysis are performed.

## Concept Design of an Solid Oxide Fuel Cell-Battery Hybrid System for Water Taxi Applications

As a way to reduce GHG emissions from the fleet of water taxies operating in the False Creek area of Vancouver, an SOFC-battery hybrid power system is proposed in this study to replace the ICE diesel engines currently in use. To maximize the advantage and fully utilize the nature of an SOFC system, a continuous operation mode is assigned for the SOFC system to avoid its performance loss due to slow start up. A planar IT-SOFC is selected for its state of art performance. A lithium-ion battery is chosen for the hybrid system due to its relatively high power density and low cost compared to other types of batteries. The technical performance and cost used for this study are based on the state-of-the-art SOFC and lithium-ion battery, and U.S. DOE cost targets are used for long-term prediction.

Assumptions for the hybrid system are:

• Battery provides the maximum power for propulsion and accommodates all load transients.

• Battery acts as an energy buffer to minimize the sizes of the SOFC and dc/dc converter.

• Battery recharge from outside is not considered.

• SOFC operates in always-on mode.

• The architecture is series designed and battery dominant, meaning the battery will supply the intermediate energy and power requirements for water taxi operation.

• The hybrid system should be charge neutral within a 24 h period, i.e., the battery should be fully charged at both the beginning and the end of each day.

As a case study, the battery of the hybrid system is sized to meet the peak power requirement and acts as an “energy buffer,” while the SOFC is designed to satisfy the overall energy demand of a water taxi in such a way that the voyage range is limited by the size of the fuel tank rather than the size of the battery.

A series architecture design of the proposed water taxi hybrid concept is depicted in Fig. 1. During the operation of the hybrid system, the fuel cell continually charges the battery through dc/dc converter in both operation and nonoperation time. Battery can provide propulsion power for the motor/drivetrain system. SOFC management interface (SOFCMI), dc/dc control, and battery management interface are the control units for the specific requirements of each subsystem. Overarching these control units and interfacing with the remaining hardware and the operator is a water taxi management unit (WTMU). All controls are performed using the standard controller area network interface protocol.

The major functions of each management interface are summarized as follows:

• The SOFC management interface (SOFCMI) monitors and controls the SOFC system operation and has the following functions:

• ○ Controls delivery of fuel to the fuel cell at a required fuel utilization factor.

• ○ Monitors the temperature of the stack and components of the SOFC system and adjusts the cooling air flow supply to maintain the temperature within the defined limits.

• ○ Performs error detection, safety functions, and handles start-up and shutdown.

• ○ Sends and receives control codes from the WTMU and responds to instructions.

• Performs diagnostic checks on the system and records all operating values.

• The battery is primarily in one of the three operating modes: off, charge, or discharge. The battery management interface monitors and controls all aspects of the battery's operation, including:

• ○ temperature control;

• ○ charge and discharge control to avoid overcharge and over discharge;

• ○ error detection;

• ○ failed cell detection and management;

• ○ external interfaces; and

• ○ state of charge monitoring.

• Water taxi management unit (WTMU) controls the flow of mechanical and electrical energy around the hybrid system and acts as an overarching control system. It is also the interface between the operator and the hybrid system. The WTMU performs the following functions:

• ○ Receives input from the operator (acceleration, mode of operation, recharge time setting, etc.).

• ○ Provides information to the operator on battery SOC, fuel tank level, current mode of operation, etc.

• ○ Coordination and communication between hardware in the hybrid system, such as safety checking, watchdog timing, etc.

• ○ Executes the instructions required for each of the operating modes.

## Sizing Methodology of the Solid Oxide Fuel Cell-Battery Hybrid Power System for Water Taxi Applications

To explore the suitability of the SOFC and battery hybrid system for water taxi applications, two important issues needs to be addressed: (1) whether or not the technical performance of the hybrid system meet the requirements of water taxi applications; (2) how the weight and volume of the hybrid system affect the water taxi operation. This section will focus on the technical requirements of the hybrid system and weight and volume issue will be discussed in Sec. 5.

The sizing criteria are (1) the hybrid system should supply the power required for satisfactory performance over the required operation cycles of the water taxi and (2) the hybrid system operates in a regime that is charge neutral such that the vessel's voyage is not limited by the energy of the battery, but the capacity of the fuel tank and the ability to refuel for the SOFC system.

The power output of the SOFC and the capacity of the battery in the hybrid system are estimated based on the total vessel resistance, acceleration performance, and the speed profile in operation.

###### Resistance Calculation.

In general, the total resistance of a ship is composed of frictional resistance, appendage resistance, wave resistance, additional pressure resistances of bulbous bow and immersed transom stern, model–ship correlation resistance, and wind resistance. For the water taxi considered in this study, due to its relative simple design the resistances of appendage, bulbous bow near water surface, and immersed transom stern are neglected. Therefore, the total resistance is given by Display Formula

(1)$RT=RF(1+k1)+RA+RWave+RWind$

where $RF(1+k1)$ is the frictional resistance considering the form factor of hull, $RA$ is the model–ship correlation resistance, $Rwave$ is the wave resistance, and $Rwind$ is the wind resistance.

The detailed information to calculate each resistance in Eq. (1) is given in the Appendix.

###### Water Taxi Parameters.

Water taxi parameters used in this study are listed in Table 1.

Water taxi auxiliary load without air conditioning is estimated at 800 W.

###### Estimations for the Required Solid Oxide Fuel Cell Power Output and Consumed Battery Energy.

The power cycle can be determined by the water taxi parameters and the operation speed profile. For simplicity, the speed profile of a typical driving cycle for a water taxi is assumed to have an evenly acceleration from 0 to the cruising speed $v$ within the first $t0,v$ seconds, deceleration from $v$ to 0 in the last $t0,v$ seconds, and to cruise at speed $v$ in the middle.

The effective power (EP) is defined as the power required to move the water taxi at a given speed, and it is the product of the ship's total resistance and its cruising speed [15,17] Display Formula

(2)$PEP=vRT$

where $PEP$ is the effective power, and $RT$ is the total resistance.

Once the effective power is obtained, the brake power (BP) for the water taxi is estimated by Display Formula

(3)$PBP=PEPηD$

where $PBP$ is the brake power of the water taxi, and $ηD$ is the propulsive efficiency including the reduction gear, shaft, propeller, and hull efficiencies.

The maximum brake power needed for the water taxi within one operation cycle is Display Formula

(4)$PBP,max=max0≤t≤tcyc(PBP)$

It is assumed that the battery supplies all of the propulsion power so the required power output from battery can be determined by the electric motor efficiency and the power converter efficiency from the brake power as Display Formula

(5)$Pbatt=PBPηMηC$

The cumulative energy consumed by the water taxi during one operation cycle is calculated by Display Formula

(6)$Ecyc=∫0tcycPbattdt=∫0tcycPBPηMηCdt$

Basically, the power requirement changes according to the speed profile and the cumulative energy consumption increases linearly with the increase of the averaged brake power within one operation cycle.

For the water taxi hybrid system, it is assumed that the system is charge neutral over a 24 h period and that the SOFC system is “always-on” in order to avoid any damage arising from frequent start-up and shut-down cycles.

For simplification, it is assumed that the auxiliary load is constant. So the net energy consumed by the hybrid system over one operation cycle is given by Display Formula

(7)$Econsum=Ecyc+Pauxtcyc−Psofctcyc$

where $Psofc$ is the constant power output from the SOFC, and $Econsum$ is the net energy consumed by the hybrid system over one operation cycle.

For a whole day operation period, the net energy consumed during operation time should be balanced by the energy recharged from the SOFC during nonoperation time Display Formula

(8)$∫0topPbattdt+Pauxtop−Psofctop=Psofctnop$

where $top$ and $tnop$ are the operation and nonoperation times over a whole-day, respectively, Display Formula

(9)$top+tnop=24$

The SOFC power output can be determined from Eq. (8) as Display Formula

(10)$Psofc=124(∫0topPbattdt+Pauxtop)$

In reality, not all of the rated battery's capacity can be used for water taxi propulsion due to various reasons, such as measuring error, degradation, self-discharge, etc. For safety and conservative consideration, assuming only 70% of the battery's capacity is available for the water taxi propulsion, i.e., the SOC threshold for recharge is 30% Display Formula

(11)$SOCthresh=30%$

The net energy consumed from the battery is Display Formula

(12)$Econsum=(∫0topPbattdt+Pauxtop−Psofctop)/(1−SOCthresh)$

where $Econsum$ can be considered as the minimum requirement for the nominal battery energy.

Substituting Eq. (5) into Eq. (10) leads to Display Formula

(13)$Psofc=124(1ηMηC∫0topPBPdt+Pauxtop)$

Substituting Eqs. (5) and (13) into Eq. (12) results in Display Formula

(14)$Econsum=(1ηMηC∫0topPBPdt+Pauxtop)(1−top24)1(1−SOCthresh)$

Using an averaged constant brake power ($P¯BP$) will simplify Eqs. (13) and (14) as Display Formula

(15)$Psofc=(1ηMηCP¯BP+Paux)top24$

(16)$Econsum=(1ηMηCP¯BP+Paux)top(1−top24)1(1−SOCthresh)$

As an illustration, Fig. 2 shows the SOFC power requirement and battery energy consumption for a range of averaged constant brake power requirement over a 24 h period with an 8 h operation time per day.

Taking $PBP,max$ as the averaged brake power required by the water taxi, Fig. 3 demonstrates how the required power output from the SOFC and energy capacity from the battery change with the operation time per day.

It is noted that both the required SOFC power and battery energy increase monotonically with the increase of the operation time per day up to 12 h; thereafter, further increasing the operation time per day leads to continue linearly increment of the required SOFC power while decreases the needed battery energy because when the hybrid system operates over 12 h, the SOFC produces more energy than required for water taxi daytime operation; therefore, less battery energy is needed in order to meet the condition of charge neutrality over a 24 h period.

For different operation times per day and different average brake power requirements, the SOFC power and battery energy of the corresponding hybrid system are different. These variations can be checked based on Eqs. (15) and (16), and are shown in Figs. 4(a) and 4(b) for charge neutrality over a 24 h period.

As illustrated in Fig. 4, in case that more average break power is needed under certain circumstances, such as speed up to pass or accident avoidance, or if a new design for larger tonnage water taxi is considered, both the SOFC power and battery energy need to increase accordingly.

The SOFC system is known for its multifuel capability, such as compressed hydrogen gas (CHG), butane, liquefied petroleum gas (LPG), alcohols, compressed natural gas (CNG), gasoline, etc. The selection of fuel type for the SOFC system of the hybrid powered water taxi depends highly on the fuel price, refueling infrastructure, on-board processing technology, fuel tank size and material, etc. Detailed comparison for these three fuels, CHG, LPG, and CNG, can be found in Ref. [7]. LPG was chosen in this study due to its low price, high fuel economy, and availability of the refueling infrastructure.

###### Sizing of the Solid Oxide Fuel Cell-Battery Hybrid System.

The nominal energy of the battery in the hybrid system is determined by Eq. (16) as Display Formula

(17)$Ebatt,nom=Econsumηbatt$

where $ηbatt$ is the electric efficiency of the battery.

The power required to accelerate the water taxi from 0 to $vmax$ in time $t0$ is estimated by Display Formula

(18)$Paccel=(Mwt+Mcap,max)vmaxt0,maxvmax$

where $Mwt$ and $Mcap,max$ are the weight and maximum capacity tonnage of the water taxi, respectively.

Considering the brake power required at a cruising speed of $v$ (Eqs. (2) and (3)), the peak power of the battery can be estimated by Display Formula

(19)$Pbatt, peak=1ηbattηMηC{1ηDvRT+Paccel}$

Acceleration performance of a water taxi highly affects the peak power requirement of the battery in the hybrid system. For example, specifying a typical acceleration performance of a water taxi from 0 to $vmax=6$ knots in $t0=10 and 30$ s, correspondingly, and for a cruising speed of $v$, the peak power requirement for the battery to operate and accelerate the water taxi is given in Table 2.

In general, the battery cells can be arranged in a range of parallel and series configurations to match the battery's OCV to the electric motor's rated voltage, maximum power, and overall energy. If necessary, battery modules can be used to meet the power and energy capacity requirements for marine applications.

The SOFC stack size can be determined based on the power requirement of the SOFC system, the operating point (voltage, current density and efficiency) and the parasitic load incurred by the system. Based on the current SOFC technology, the operating voltage is ∼0.75 V at a current density of ∼0.5 A/cm2 under a normal operation condition. The parasitic load of the SOFC system is all of the power consumed by the air blower, sensors and actuators, and control electronics. The power consumption by an air blower is roughly estimated as 10% of the gross stack power of an SOFC. A constant 100 W load is assigned to the total SOFC control system Display Formula

(20)$Pparasitic=10%Psofc+0.1 kW$

Therefore, the required power output of the SOFC in the hybrid system should be Display Formula

(21)$Psofc, output=110%Psofc+0.1 kW$

where $Psofc$ is given by Eq. (15).

The SOFC electric efficiency ($ηsofc$) and methane fuel consumption ($Umethane, consum$, g/s) vary with its power output and can be estimated from the power output based on modeling [6,8]. The energy densities of methane and LPG fuels are 53.6 MJ/kg and 46.4 MJ/kg, respectively. Therefore, the LPG fuel consumption rate ($ULPG, consum$, g/s) of the SOFC system can be roughly estimated from the methane fuel consumption in [7,9] Display Formula

(22)$ULPG, consum=53.646.4Umethane, consum=1.1552Umethane, consum$

The sizing results for the proposed SOFC-battery hybrid system with an 8 h operation time per day over a 24 h period of charge neutrality in the water taxi case study are summarized in Table 3.

## Techno-Economic Analysis

To evaluate the feasibility of an SOFC-battery hybrid system for water taxi application, a life-cycle cost analysis is conducted in this section. Two cases are used as reference: one is the current water taxi powered by an internal combustion engine, and the other is the water taxi powered by battery only. The pure SOFC-powered water taxi is technically not suitable at this moment due to reliability issues caused by frequent start up–shutdown cycles and is therefore excluded from this study. The analysis only considers the power sources and neglects, at this stage, the benefits potentially arising from the structure and layout of the system, the heat recovery from the SOFC, etc. Only the capital cost and fuel consumption cost are considered in the cost analysis. For comparison purposes, the operation and maintenance cost and all the other costs (auxiliaries, installation, etc.) are assumed to be same for all the three power systems (hybrid, ICE and battery-only) and, therefore, are omitted from the cost estimation.

Similar to the formulae given in Ref. [10], the cost estimations for the SOFC-battery hybrid, the battery-only, and the ICE systems are summarized in the following.

The total cost of the SOFC-battery hybrid system includes the capital costs for battery, SOFC, and electrical motor and power electronics, and LPG fuel cost (CO2 cost is already included in the fuel unit price). The accumulative cost from the beginning of operation up to day $nday$ for the hybrid system is Display Formula

(23)$Chybrid=CChybrid,batt+CCsofc+CChybrid,motor+electro+CLPG+Chybrid,CO2=Ebatt,nomUCbatt+Psofc,outputUCsofc+Pbatt,peakUCmotor+electro+24ndayPsofc,outputULPG,consumρLPGUCLPG$

In Eq. (54), $Chybrid$ denotes the accumulative cost of the hybrid system; $CChybrid,batt$, $CCsofc$, and $CChybrid,motor+electro$ are the capital costs of the battery, the SOFC, and the electric motor and electronics in the hybrid system, respectively; $CLPG$ and $Chybrid,CO2$ are the LPG fuel cost and the carbon tax; $UCbatt$, $UCsofc$, $UCmotor+electro$, and $UCLPG$ are the unit price of the battery system, SOFC system, electric motor and electronics, and LPG fuel, respectively; $nday$ is the total number of days of the water taxi in operation; $ULPG, consum$ is the LPG fuel consumption of the SOFC system; and $ρLPG$ is the LPG fuel density.

To estimate the total cost of the battery-only system for water taxi application, the net energy consumed per day is Display Formula

(24)$Ebattonly,dayconsum=(∫0topPbattdt+Pauxtop)=1ηbatt(vRTηMηCηD+Paux)top$

and the nominal energy required by the battery-only system is Display Formula

(25)$Ebattonly,nom=Ebattonly,daycomsum(1−SOCthresh)$

The accumulative cost for the battery-only system is estimated by Display Formula

(26)$Cbattonly=CCbattonly+CCbattonly,motor+electro+Celectricity=Ebattonly,nomUCbatt+Pbatt,peakUCmotor+electro+ndayEbattonly,dayconsumUCelectricity$

where $Cbattonly$ represents the accumulative cost of the battery-only system, $CCbattonly$ and $CCbattonly,motor+electro$ are the capital costs of the battery-only and the electric motor and electronics in the battery-only system, respectively, and $UCelectricity$ is the unit price of electricity.

The accumulative cost for an internal combustion engine is estimated by Display Formula

(27)$CICE=CCICE+Cdiesel=Pbatt,peakUCICE+ndaytopvUCdiesel/Udiesel,consum$

where $CICE$ and $Cdiesel$ denote the accumulative cost of ICE system and the diesel fuel cost, respectively, $CCICE$ is the capital cost of the ICE system, $UCICE$ and $UCdiesel$ are the unit price of ICE and diesel fuel, and $Udiesel,consum$ is the diesel fuel consumption of the ICE.

The payback time is defined as the day when the accumulative cost of a hybrid system or a battery-only system equals to the accumulative cost of the ICE system during the same operation period. Making Eq. (23) equals to Eq. (27) and solving the operation time leads to the payback time as a function of the operation time per day Display Formula

(28)$npayback,hybrid−ICE=Ebatt,nomUCbatt+PsofcUCsofc+Pbatt,peakUCmotor+electro−Pbatt,peakUCICEtopvUCdiesel/Udiesel,consum−24PsofcUCLPGULPG,consumρLPG$

where $npayback,hybrid−ICE$ is the payback time of the hybrid system comparing with the ICE system.

Similarly, the payback time of the battery-only system comparing with the ICE system can be calculated by Display Formula

(29)$npayback,battonly−ICE=Ebattonly,nomUCbatt+Pbatt,peakUCmotor+electro−Pbatt,peakUCICEtopvUCdiesel/Udiesel,consum−Ebattonly,nomUCelectricity$

All the parameters used for the techno-economic analysis are listed in Table 4, and their values are found or estimated from the available literatures or the market prices.

A future price is assigned for both the battery and SOFC technologies in order to mimic the variation of payback times due to mass production of each technology. Since no data are available for electrical motors and power electronics used on water taxies, the price estimates used for vehicles [19] are adopted here for water taxi application. These values are the ones targeted for year 2020, as reported in the Review of the Research Program of the FreedomCAR and Fuel Partnership [19].

Cost predictions of the hybrid, battery-only, and ICE systems for a water taxi over several years of operation are presented in Fig. 5. For this analysis, it is assumed that the operation time per day is 8 h, and the hybrid system is charge neutrality over a 24 h period. The three power sources, the current ICE, battery-only, and the proposed SOFC-battery hybrid systems, are considered in order to identify the advantages and disadvantages of both the battery-only and the hybrid systems over the traditional ICE system. Two cases are analyzed: the first one, Fig. 5(a), simulates the case where the current prices for battery and SOFC technologies are considered, while the second one, Fig. 5(b), represents the case corresponding to lower prices for both battery and SOFC systems due to future technology advance and mass production.

Figure 5 clearly shows that the total costs for the three power systems in both cases increase with their accumulated operation times for an 8 h operation time per day and over a 24 h period of charge neutrality. From Fig. 5(a), it can be seen that the capital costs (the values on the left axis) of both the hybrid and battery-only systems are higher than that of the traditional ICE system while the fuel cost per day (represented by the slope of each line) for the ICE system is much higher than that of the battery-only and hybrid systems. At the current prices of battery and SOFC systems, the payback time of the hybrid system is about 1816 days, which is much higher than the payback time (774 days) of the battery-only system because both the capital cost and the fuel cost of the SOFC system are much higher than the corresponding costs of the battery system. Figure 5(a) also shows that under the current prices, the battery-only system is a better option than the hybrid system, as a replacement of the conventional ICE for water taxi application. Moving from case (a), which uses the current the prices of $10,000/kWh and$350/kWh for SOFC and battery systems, respectively, to case (b) where future prices of both SOFC and battery are reduced to $200/kWh and$150/kWh, respectively, Fig. 5(b) demonstrates that the payback time for the hybrid system is only 308 days, which is 3 days less than the payback time of the battery–only system (311 days), indicating that the hybrid system becomes economically attractive than the battery-only system under the future prices scenario.

Variation of the payback time with the operation hours per day is plotted in Fig. 6. It can be seen from Fig. 6(a) that the payback time of the hybrid system drops substantially from 4271 days with 1 h operation time per day to 957 days with 24 h operation time per day (nonstop service), because the increment of the fuel cost of the hybrid system is less than the increment of the diesel cost of the ICE system. The payback time of the battery-only system in Fig. 6(a) increases slowly with a longer operation time per day because a higher battery capacity is required for a longer operation time, which leads to a higher capital cost. Figure 6(a) also shows that the payback time of the hybrid system is always longer than that of the battery-only system, indicating that, under the current SOFC and battery prices scenario, the hybrid system is not economically attractive compared to the battery-only system, as a replacement for the ICE system on water taxies. Figure 6(b) plots the payback times of the hybrid and battery-only systems when the battery price drops from $350/kWh to$150/kWh and the SOFC price drops from $10,000/kW to$200/kW. The payback time for the battery-only system increases with the increase of the operation time per day for the same reason as in Fig. 6(a). It is worth to note from Fig. 6(b) that the payback time of the hybrid system first increases, due to the increasing cost of a larger capacity battery, and then decreases to almost zero when the operation time per day nears 24 h, because under this condition the required battery capacity is close to zero (as shown in Fig. 3) and the majority of the power of the hybrid system comes from its SOFC, which, in this scenario, has almost the same price as the ICE system ($200/kW for an SOFC versus$180/kW for an ICE). Figure 6(b) also indicates that, even in the future prices scenario, the payback time of the hybrid system is less than that of the battery-only system only when the operation time per day is longer than about 8 h. Therefore, the cost of SOFC must be substantially reduced to be competiveness for the application.

## Feasibility Discussions

The techno-economic analysis given in Sec. 4 primarily demonstrates that an SOFC-battery hybrid system could be a potential power source option for water taxi application in the future. To further explore the feasibility of such an application, additional factors, such as weight, volume, fuel economy, CO2 emissions, etc., should be considered. These factors will be addressed in the following paragraphs.

###### Weight and Volume.

Besides the power source, the weight and volume of an SOFC-battery hybrid system are the most critical factors to determine the performance of a water taxi and can be estimated from the SOFC power and battery energy requirements given by Eqs. (17), (19), and (21)Display Formula

(30)$Mhybrid=Ebatt, nomSEbatt+Pbatt,peakSPmotor+SPelectro+Psofc,outputSPsofc$
Display Formula
(31)$Vhybrid=Ebatt, nomEDbatt+Pbatt,peakPDmotor+PDelectro+Psofc,outputPDsofc$

where $Mhybrid$ and $Vhybrid$ are the weight and volume of the hybrid power system, respectively; $SEbatt$ is the specific energy of the battery; $SPmotor$, $SPelectro$, and $SPsofc$ are the specific power of the electrical motor, power electronics, and SOFC, respectively; $EDbatt$ is the energy density of the battery; $PDmotor$, $PDelectro$, and $PDsofc$ are the power density of the electrical motor, power electronics, and SOFC, respectively.

Some representative specifications for commercially available SOFC and battery systems are listed in Tables 5 and 6, respectively.

Battery energy efficiency varies with discharging/charging mode and current, i.e., the discharge/charge time. This variation is usually within 5% for electric vehicle operation [25]. For simplicity, a fixed 90% of battery energy efficiency is used in this paper.

The ICE system on the representative water taxi considered in this study is a Yanmar Diesel Engine (1GM10 with KM2P-1 Marine gear), and its specification is listed in Table 7.

Figure 7 demonstrates how the volume and weight of the hybrid system change with both the operation time per day and the average brake power, for charge neutrality over a 24 h period.

The variations of the weight and volume of the hybrid and battery-only systems with the operation time per day are presented in Fig. 8, where the weight and volume of the ICE system are kept constants. It can been seen from Fig. 8 that, as the operation time per day increases from 0 to 24 h, both the weight and volume of the battery-only system increase linearly due to the linear increment of the battery capacity requirement. On the other hand, the weight and volume of the hybrid system first increase and then decrease mainly due to the capacity change pattern of the battery in the hybrid system (as shown in Table 5). It is noted that, when keeping the same weight and volume as the ICE system, the hybrid and battery-only systems can only run 2.5 h per day. Comparing to the ICE system, heavier weight and larger volume will be needed for both hybrid system and battery-only systems in order to run more than 2.5 h per day. Further examining Fig. 8 reveals that only after 5.5 h of operation per day both the weight and volume of the hybrid system are less than that of the battery-only system but are still higher than the current ICE system. Figure 8 reveals that both the power density of current SOFC system and the energy density of present lithium-ion batteries are not sufficient to be competitive with the current ICE engine, unless substantial technology improvements occur.

###### Greenhouse Gas Emissions.

One important benefit of using the hybrid or battery-only systems to replacing the current ICE system is their low GHG emission. Three major GHG components, CO2, CH4, and N2O, are considered in this section. The CO2 emission factor for the electricity from BC Hydro is calculated as an average of British Columbia Hydro's GHG intensities for 2012 through 2014 [26]. The emission factor values for the electricity, LPG, and diesel fuels are given in in Table 8.

The CO2 amounts produced by the three power sources are calculated by the following equations: Display Formula

(32)$Mbattonly,CO2=Ebattonly,dayconsumEFelectricity,CO2$
Display Formula
(33)$Mhybrid,CO2=24Psofc,outputULPG,consumEFLPG,CO2$
Display Formula
(34)$MICE,CO2=topv/Udiesel,consumEFdiesel,CO2$

where $Mbattonly,CO2$, $Mhybrid,CO2$, and $MICE,CO2$ are the amounts of CO2 production per day from the three power systems, respectively, and $EFelectricity,CO2$, $EFLPG,CO2$, and $EFdiesel,CO2$ are the emission factors of electricity, LPG, and diesel fuels, respectively.

Similarly, the CH4 and N2O emissions can be estimated by replacing the corresponding emission factors.

Under the conditions of 8 h operation time per day and charge neutrality over a 24 h period, the GHG emissions per day from the three power sources are listed in Table 9. Note that there are no data calculated for the CH4 and N2O emissions from the battery-only system because no emission factors are available to estimate the emissions associated with charging the battery from the metropolitan grid. As shown in Table 9, the battery-only system has the lowest CO2 emission per day, due to the electricity used to charge the battery has the lowest CO2 emission factor, as listed in Table 8 (the electricity in the province of British Columbia (BC) of Canada is mostly generated from hydropower [26]). The next lowest is the hybrid system which partially uses LPG fuel for the SOFC. However, its CO2 emission factor is much higher than the emission factor of electricity in BC. The ICE system produces the highest CO2 emission per day which is 2.4 times higher than that from the hybrid system. The CH4 and N2O emissions per day from the ICE system are, respectively, 3 and 136 times higher than the amounts produced from the hybrid system. Therefore, both hybrid SOFC-battery system and battery only system showed clear advantage in GHG reduction in comparison with the current ICE system.

## Conclusions

A conceptual system design of an SOFC-battery system for a water taxi application is proposed, and the methodologies for TEA and feasibility studies for such a hybrid system are developed.

Without considering the constraints of weight and volume, the TEA analysis shows that both the SOFC-battery hybrid and the battery-only systems are economically better than the current ICE system after a long run operation, although their capital investments are higher than that of the latter. Comparing to the ICE system, the payback time of the proposed hybrid system is always longer than that of the battery-only system, under the current SOFC and battery prices scenario, no matter how long the operation time per day is. Once the SOFC and battery prices drop to $200/kW and$150/kWh, respectively, and the operation time per day is longer than 8 h, the hybrid system becomes economically more attractive than the battery-only system.

For implementations having the same weight and volume as the ICE system, both the hybrid and battery-only systems can only run 2.5 h per day. On the other hand, the hybrid and battery-only systems have to sacrifice their weight and volume in order to run a longer time per day. A hybrid system becomes lighter and smaller than a battery-only system only when the operation time per day is longer than 5.5 h.

Regarding GHG emissions, based on the assumption that electricity is mostly generated from hydropower, the battery-only system is the best choice for a long run operation of water taxies, and its GHG emissions are far lower than the other two power sources. When compared to the current ICE system, the hybrid system produces much less GHGs, thus being a very good candidate for GHG emissions reduction in water taxi applications.

## Acknowledgements

This project is financially supported by Transport Canada and the Marine Vehicle Program of National Research Council of Canada.

## Appendices

###### Appendix

The frictional resistance in Eq. (1) can be estimated by Display Formula

(A1)$RF=12ρCFSv2$

where $ρ$ is the seawater density, $S$ and $v$ are the wetted surface area and the cruising speed of the water taxi, $CF$ is the frictional resistance coefficient and can be calculated based on the ITTC 1957 friction formula [28] Display Formula

(A2)$CF=0.075( log10(Re)−2)2$

and the Reynolds number is Display Formula

(A3)$Re=Lwlvυ$

where $Lwl$ is the waterline length of the water taxi and $υ$ is the kinematic viscosity of seawater.

The form factor $(1+k1)$ in Eq. (1) describes the viscous resistance of the hull form in relation to the fractional resistance and can be estimated by [15,29] Display Formula

(A4)$1+k1=0.93+0.487118c14(B/Lwl)1.06806(T/Lwl)0.46106(Lwl/LR)0.121563((Lwl)3/∇)0.36486(1−CP)−0.60247$
Display Formula
(A5)$c14=1+0.011cstern$
Display Formula
(A6)$cstern={−25, pram stern with gondola shape−10, V−shaped section stern 0, Normal shape section stern+10, U−shaped section stern$
Display Formula
(A7)$LR=Lwl[1−CP+0.06CPlcb/(4CP−1)]$

In the above-mentioned equations, $B$ is the molded breadth, $T$ is the average molded draft, $∇$ is the molded displacement volume, $CP$ is the prismatic coefficient based on the waterline length $Lwl$, and $lcb$ is the longitudinal position of the center of buoyancy forward of $0.5Lwl$ as a percentage of $Lwl$ taking positive (+) values for forward and negative (−) values for afterward.

When the wetted surface area of the hull of a water taxi is not available, it can be approximated by Display Formula

(A8)$S=Lwl(2T+B)CM(0.453+0.4425CB−0.2862CM−0.003467B/T+0.3696CWP)+2.38ABT/CB$

where $CM$ and $CWP$ are the midship section coefficient and the waterplane area coefficient, respectively, $CB$ is the block coefficient on the basis of the waterline length $Lwl$, and $ABT$ is the transverse sectional area of the bulb at the position where the still-water surface intersects the stem.

The model–ship correlation resistance in Eq. (1) is calculated by Display Formula

(A9)$RA=12ρCASv2$

where $CA$ is the model–ship correlation allowance coefficient and is estimated by [15,29] Display Formula

(A10)$CA=0.006(Lwl+100)−0.16−0.00205+0.003Lwl/7.5(CB)4c2(0.04−c4)$
Display Formula
(A11)$c2=exp(−1.89c3)$
Display Formula
(A12)$c3=0.56(ABT)1.5/[BT(0.31ABT+TF−hB)]$
Display Formula
(A13)$c4={TF/Lwl, when TF/Lwl<0.040.04, when TF/Lwl≥0.04$
Here, $TF$ is the forward draft of the water taxi, and $hB$ is the position of the center of the transverse area $ABT$ above the keel line.

The wave resistance in Eq. (1) is determined by [15,29] Display Formula

(A14)$Rwave=c1c2c5∇ρg exp {m1(Fn)d+m4 cos(λ(Fn)−2)}$
Here, $c1$, $c2$, and $c5$ are parameters account for the influences of the half angle of entrance, the action of a bulbous bow, and a transom stern on the wave resistance, respectively. $g$ is the acceleration of gravity, $Fn$ is the Froude number based on the waterline length $Lwl$, and $m1$, $m4$, $λ$, and $d$ are parameters.

The wave resistance depends highly on the speed of the water taxi. At low speeds ($Fn<0.4$), the resistance for breaking wave at the bow is dominant while at high speeds ($Fn≥0.55$) the resistance from breaking waves for a full hull is prevailing. At the middle of the speed range ($0.4≤Fn<0.55$), resistances for breaking the waves generated by both the bow and the full hull should be considered.

In the low speed range ($Fn<0.4$), the parameters in Eq. (A14) are estimated as follows: Display Formula

(A15)$c1=2223105(c7)3.78613(T/B)1.07961(90−iE)−1.37565$
Display Formula
(A16)$c7={0.229577(B/Lwl)0.33333, When B/Lwl<0.11B/Lwl, When 0.11≤B/Lwl<0.250.5−0.0625B/Lwl, When B/Lwl≥0.25$
Display Formula
(A17)$iE=1+89 exp {−(Lwl/B)0.80856(1−CWP)0.30484(1−Cp−0.0225lcb)0.6367(LR/B)0.34574(100∇/Lwl3)0.16302}$
Display Formula
(A18)$c5=1−0.8AT/(BTCM)$
In the above-mentioned expressions, $AT$ denotes the immersed part of the transverse area of the transom at zero speed and $iE$ is the half angle of entrance representing the angle of the waterline at the bow in degrees with reference to the center plane but neglecting the local shape at the stem Display Formula
(A19)$m1=0.0140407Lwl/T−1.75254∇1/3/Lwl−4.79323B/Lwl−c16$
Display Formula
(A20)$c16={8.07981Cp−13.8673(Cp)2+6.984388(Cp)3, when Cp<0.801.73014−0.7067Cp, when Cp≥0.80$
Display Formula
(A21)$Fn=vgLwl$
Display Formula
(A22)$d=−0.9$
Display Formula
(A23)$m4=0.4c15 exp {−0.034(Fn)−3.29}$

(A24)$c15={−1.69385,when (Lwl)3/∇<512−1.69385+(Lwl/∇1/3−8.0)/2.36,when 512≤(Lwl)3/∇≤1726.910.0,when (Lwl)3/∇>1726.91$
Display Formula
(A25)$λ={1.446Cp−0.03Lwl/B,when Lwl/B<121.446Cp−0.36,when Lwl/B≥12$

In the high speed range ($Fn≥0.55$), the formula for the wave resistance remains the same as in Eq. (A14) and only the expressions for parameters $c1$ and $m1$ are replaced by the following: Display Formula

(A26)$c1=6919.3(CM)−1.3346(∇/Lwl3)2.00977(Lwl/B−2)1.40692$

(A27)$m1=−7.2035(B/Lwl)0.326869(T/B)0.605375$

In the middle speed range ($0.4≤Fn<0.55$), the wave resistance is a combination of both from the waves generated by the bow and the full hull and is estimated as Display Formula

(A28)$Rwave=Rwave|Fn=0.4+(10Fn−4){Rwave|Fn=0.55−Rwave|Fn=0.4}/1.5$

The wind resistance in Eq. (1) is calculated by [30] Display Formula

(A29)$Rwind=12CDρairATA(vR)2$

where $CD$ is the air drag coefficient and can be determined by empirical formula or by model tests and varies with the relative wind direction, $ρair$ is the air density, $ATA$ is the transverse projected area above the waterline, and $vR$ is the relative wind speed. The wind resistance can be negative in the case of strong following winds. The purpose of this study is to size the SOFC-battery hybrid system for water taxi applications, so a rectangular transverse projected area above waterline and a head wind direction are used here Display Formula

(A30)$ATA=B(H−T)$
Display Formula
(A31)$vR=vwind0+v$
here $H$ is the total height of the water taxi, and $vwind0$ is the maximum wind speed allowed for the operation of the water taxi. The mean value of wind speed in Vancouver area is about 13–20 kmh−1 [16]; therefore, a value of 10 knots or approximately 18 kmh−1 is assigned to $vwind0$.

The value of the air drag coefficient for a bluff body with a square box frontal area for Reynolds number > 103 is [30]

$CD=0.9$

## References

ERA-LEARN 2020 Project, 2012, “ Auxiliary Power Generator Based on PEM Fuel Cell for Nautic Applications,” accessed Dec. 6, 2018,
Dai, Z. , Wang, L. , and Yang, S. , 2017, “ Fuel Cell Based Auxiliary Power Unit in More Electric Aircraft,” IEEE Transportation Electrification Conference and Expo, Asia-Pacific (ITEC Asia-Pacific), Harbin, China, Aug. 7–10, Paper No. 978-1-5386-2894-2/17.
Biret, L. V. , Godjevac, M. , Visser, K. , and Aravind, P. V. , 2016, “ A Review of Fuel Cell Systems for Maritime Applications,” J. Power Sources, 327, pp. 345–364.
Rechberger, J. , Kaupert, A. , Hagerskans, J. , and Blum, L. , 2016, “ Demonstration of the First European SOFC APU on a Heavy Duty Truck,” Transp. Res. Procedia, 14, pp. 3676–3685.
Nehter, P. , Kleinohl, N. , Bauschulte, A. , and Leites, K. , 2014, “ Diesel Based Sofc-APU for Marine Applications,” 11th European SOFC and SOE Forum, Lucerne, Switzerland, July 1–4, pp. 1–8.
Brett, D. J. L. , Aguiar, P. , Brandon, N. P. , Bull, R. N. , Hayes, G. W. , Lillie, K. , Mellors, C. , Millward, M. , Smith, C. , and Tilley, A. R. , 2006, “ Project ABSOLUTE: A ZEBRA Battery/Intermediate Temperature Solid Oxide Fuel Cell Hybrid for Automotive Applications,” ASME J. Fuel Cell Sci. Technol., 3(3), pp. 254–262.
Brett, D. J. L. , Aguiar, P. , Brandon, N. P. , Bull, R. N. , Galloway, R. C. , Hayes, G. W. , Lillie, K. , Mellors, C. , Smith, C. , and Tilley, A. R. , 2006, “ Concept and System Design for a ZEBRA Battery–Intermediate Temperature Solid Oxide Fuel Cell Hybrid Vehicle,” J. Power Sources, 157(2), pp. 782–798.
Brett, D. J. L. , Aguiar, P. , and Brandon, N. P. , 2006, “ System Modelling and Integration of an Intermediate Temperature Solid Oxide Fuel Cell and ZEBRA Battery for Automotive Applications,” J. Power Resour., 163(1), pp. 514–522.
Brandon, N. P. , Aguiar, P. , Brett, D. J. L. , Bull, R. N. , Coop, I. , Galloway, R. C. , Hayes, G. W. G. , Lillie, K. , Mellors, C. , Millward, M. , and Tilley, A. R. , 2006, “ Design and Characterization of a Fuel Cell-Battery Powered Hybrid System for Vehicle Applications,” IEEE Vehicle Power & Propulsion Conference, Windsor, UK, Sept. 6–8.
Aguiar, P. , Brett, D. J. L. , and Brandon, N. P. , 2007, “ Feasibility Study and Techno-Economic Analysis of an SOFC/Battery Hybrid System for Vehicle Applications,” J. Power Sources, 171(1), pp. 186–197.
ThyssenKrupp Marine Systems, 2015, “ Sunfire 50 kW SOFC for Ship-Integrated Fuel Cell Project in Germany,” Fuel Cells Bull., 2015(11), pp. 3–4.
Leites, K. , Bauschulte, A. , Dragon, M. , Krummrich, S. , and Nehter, D. P. , 2012, “ SchIBZ—Design of Different Diesel Based Fuel Cell Systems for Seagoing Vessels and Their Evaluation,” ECS Trans., 4(1), pp. 49–58.
San, B.-G. , Zhou, P.-L. , and Clealand, D. , 2010, “ Dynamic Modeling of Tubular SOFC for Marine Power System,” J. Mar. Sci. Appl., 9(3), pp. 231–240.
Transport Canada, 2017, “ Small Vessel Register C05458BC,” Transport Canada, Ottawa, ON, Canada, accessed Dec. 6, 2018,
Roh, M.-I. , and Lee, K.-Y. , 2018, Computational Ship Design, Springer, Berlin, Chap. 5.
Environment and Climate Change Canada, 2017, “ Vancouver Historical Wind Speed,” Environment and Climate Change Canada, Vancouver, BC, Canada, accessed Dec. 4, 2018,
Pedersen, B. P. , and Larsen, J. , 2009, “ Modeling of Ship Propulsion Performance,” World Maritime Technology Conference (WMTC2009), Mumbai, India, Jan. 21–24, Paper No. WMTC 2009.
Qnovo, 2017, “ The Cost Components of a Lithium Ion Battery,” Qnovo, Newark, CA, accessed Dec. 6, 2018,
National Research Council, 2010, “ Review of the Research Program of the FreedomCAR and Fuel Partnership,” The National Academies Press, Washington, DC, Third Report.
Natural Resources Canada, 2017, “ Propane Price,” Natural Resources Canada, Ottawa, ON, Canada, accesssed Dec. 6, 2018,
Yanmar, 2017, “ Sailboat and Small Craft Engines,” Yanmar, Osaka Prefecture, Japan, accessed Dec. 6, 2018,
BCHydro, 2017, “ General Service Rate for Business,” BCHydro, Vancouver, BC, Canada, accessed Dec. 6, 2018,
Saxman, D. , 2016, “ Solid Oxide Fuel Cells: Technologies and Global Markets,” Global Information, Kawasaki, Japan, accessed Dec. 10, 2018,
Tesla, 2017, “ Powerwall,” Tesla, Palo Alto, CA, accessed Dec. 6, 2018,
Lu, R. , Yang, A. , Xue, Y. , Xu, L. , and Zhu, C. , 2010, “ Analysis of the Key Factors Affecting the Energy Efficiency of Batteries in Electric Vehicle,” World Electric Veh. J., 4(1), pp. 9–13.
Ministry of Environment, Victoria B.C., 2016, “ 2016/17 B.C. Best Practices Methodology for Quantifying Greenhouse Gas Emissions,” Ministry of Environment, Victoria, BC, Canada, accessed Dec. 6, 2018,
U.S. EPA, 2015, “ Emission Factors for Greenhouse Gas Inventories,” United States Environmental Protection Agency, Washington, DC, accessed Dec. 6, 2018,
ITTC, 2002, “ ITTC-Recommended Procedures, Resistance Uncertainty Analysis, Example for Resistance Test,” International Towing Tank Conference (ITTC), Shanghai, China, accessed Dec. 6, 2018,
Holtrop, J. , and Mennen, G. G. J. , 1982, “ An Approximate Power Prediction Method,” Int. Shipbuild. Prog., 29(335), pp. 166–170.
Molland, A. F. , Turnock, S. R. , and Hudson, D. A. , 2011, Ship Resistance and Propulsion: Practical Estimation of Ship Propulsive Power, Cambridge University Press, Cambridge, UK.
View article in PDF format.

## References

ERA-LEARN 2020 Project, 2012, “ Auxiliary Power Generator Based on PEM Fuel Cell for Nautic Applications,” accessed Dec. 6, 2018,
Dai, Z. , Wang, L. , and Yang, S. , 2017, “ Fuel Cell Based Auxiliary Power Unit in More Electric Aircraft,” IEEE Transportation Electrification Conference and Expo, Asia-Pacific (ITEC Asia-Pacific), Harbin, China, Aug. 7–10, Paper No. 978-1-5386-2894-2/17.
Biret, L. V. , Godjevac, M. , Visser, K. , and Aravind, P. V. , 2016, “ A Review of Fuel Cell Systems for Maritime Applications,” J. Power Sources, 327, pp. 345–364.
Rechberger, J. , Kaupert, A. , Hagerskans, J. , and Blum, L. , 2016, “ Demonstration of the First European SOFC APU on a Heavy Duty Truck,” Transp. Res. Procedia, 14, pp. 3676–3685.
Nehter, P. , Kleinohl, N. , Bauschulte, A. , and Leites, K. , 2014, “ Diesel Based Sofc-APU for Marine Applications,” 11th European SOFC and SOE Forum, Lucerne, Switzerland, July 1–4, pp. 1–8.
Brett, D. J. L. , Aguiar, P. , Brandon, N. P. , Bull, R. N. , Hayes, G. W. , Lillie, K. , Mellors, C. , Millward, M. , Smith, C. , and Tilley, A. R. , 2006, “ Project ABSOLUTE: A ZEBRA Battery/Intermediate Temperature Solid Oxide Fuel Cell Hybrid for Automotive Applications,” ASME J. Fuel Cell Sci. Technol., 3(3), pp. 254–262.
Brett, D. J. L. , Aguiar, P. , Brandon, N. P. , Bull, R. N. , Galloway, R. C. , Hayes, G. W. , Lillie, K. , Mellors, C. , Smith, C. , and Tilley, A. R. , 2006, “ Concept and System Design for a ZEBRA Battery–Intermediate Temperature Solid Oxide Fuel Cell Hybrid Vehicle,” J. Power Sources, 157(2), pp. 782–798.
Brett, D. J. L. , Aguiar, P. , and Brandon, N. P. , 2006, “ System Modelling and Integration of an Intermediate Temperature Solid Oxide Fuel Cell and ZEBRA Battery for Automotive Applications,” J. Power Resour., 163(1), pp. 514–522.
Brandon, N. P. , Aguiar, P. , Brett, D. J. L. , Bull, R. N. , Coop, I. , Galloway, R. C. , Hayes, G. W. G. , Lillie, K. , Mellors, C. , Millward, M. , and Tilley, A. R. , 2006, “ Design and Characterization of a Fuel Cell-Battery Powered Hybrid System for Vehicle Applications,” IEEE Vehicle Power & Propulsion Conference, Windsor, UK, Sept. 6–8.
Aguiar, P. , Brett, D. J. L. , and Brandon, N. P. , 2007, “ Feasibility Study and Techno-Economic Analysis of an SOFC/Battery Hybrid System for Vehicle Applications,” J. Power Sources, 171(1), pp. 186–197.
ThyssenKrupp Marine Systems, 2015, “ Sunfire 50 kW SOFC for Ship-Integrated Fuel Cell Project in Germany,” Fuel Cells Bull., 2015(11), pp. 3–4.
Leites, K. , Bauschulte, A. , Dragon, M. , Krummrich, S. , and Nehter, D. P. , 2012, “ SchIBZ—Design of Different Diesel Based Fuel Cell Systems for Seagoing Vessels and Their Evaluation,” ECS Trans., 4(1), pp. 49–58.
San, B.-G. , Zhou, P.-L. , and Clealand, D. , 2010, “ Dynamic Modeling of Tubular SOFC for Marine Power System,” J. Mar. Sci. Appl., 9(3), pp. 231–240.
Transport Canada, 2017, “ Small Vessel Register C05458BC,” Transport Canada, Ottawa, ON, Canada, accessed Dec. 6, 2018,
Roh, M.-I. , and Lee, K.-Y. , 2018, Computational Ship Design, Springer, Berlin, Chap. 5.
Environment and Climate Change Canada, 2017, “ Vancouver Historical Wind Speed,” Environment and Climate Change Canada, Vancouver, BC, Canada, accessed Dec. 4, 2018,
Pedersen, B. P. , and Larsen, J. , 2009, “ Modeling of Ship Propulsion Performance,” World Maritime Technology Conference (WMTC2009), Mumbai, India, Jan. 21–24, Paper No. WMTC 2009.
Qnovo, 2017, “ The Cost Components of a Lithium Ion Battery,” Qnovo, Newark, CA, accessed Dec. 6, 2018,
National Research Council, 2010, “ Review of the Research Program of the FreedomCAR and Fuel Partnership,” The National Academies Press, Washington, DC, Third Report.
Natural Resources Canada, 2017, “ Propane Price,” Natural Resources Canada, Ottawa, ON, Canada, accesssed Dec. 6, 2018,
Yanmar, 2017, “ Sailboat and Small Craft Engines,” Yanmar, Osaka Prefecture, Japan, accessed Dec. 6, 2018,
BCHydro, 2017, “ General Service Rate for Business,” BCHydro, Vancouver, BC, Canada, accessed Dec. 6, 2018,
Saxman, D. , 2016, “ Solid Oxide Fuel Cells: Technologies and Global Markets,” Global Information, Kawasaki, Japan, accessed Dec. 10, 2018,
Tesla, 2017, “ Powerwall,” Tesla, Palo Alto, CA, accessed Dec. 6, 2018,
Lu, R. , Yang, A. , Xue, Y. , Xu, L. , and Zhu, C. , 2010, “ Analysis of the Key Factors Affecting the Energy Efficiency of Batteries in Electric Vehicle,” World Electric Veh. J., 4(1), pp. 9–13.
Ministry of Environment, Victoria B.C., 2016, “ 2016/17 B.C. Best Practices Methodology for Quantifying Greenhouse Gas Emissions,” Ministry of Environment, Victoria, BC, Canada, accessed Dec. 6, 2018,
U.S. EPA, 2015, “ Emission Factors for Greenhouse Gas Inventories,” United States Environmental Protection Agency, Washington, DC, accessed Dec. 6, 2018,
ITTC, 2002, “ ITTC-Recommended Procedures, Resistance Uncertainty Analysis, Example for Resistance Test,” International Towing Tank Conference (ITTC), Shanghai, China, accessed Dec. 6, 2018,
Holtrop, J. , and Mennen, G. G. J. , 1982, “ An Approximate Power Prediction Method,” Int. Shipbuild. Prog., 29(335), pp. 166–170.
Molland, A. F. , Turnock, S. R. , and Hudson, D. A. , 2011, Ship Resistance and Propulsion: Practical Estimation of Ship Propulsive Power, Cambridge University Press, Cambridge, UK.

## Figures

Fig. 1

Schematic of the proposed SOFC-battery hybrid system

Fig. 2

SOFC power and battery energy requirements versus the averaged brake power with an 8 h operation time per day and over a 24 h period of charge neutrality

Fig. 3

SOFC power and battery energy requirements versus operation time per day over a 24 h period of charge neutrality

Fig. 4

(a) SOFC power and (b) battery energy requirements change with operation time per day and average brake power for charge neutrality over 24 h period

Fig. 5

Comparison of the predicted costs of the hybrid, battery-only, and ICE systems for the water taxi application with an 8 h operation time per day. (a) Current prices: SOFC $10,000/kWh and battery$350/kWh. (b) Future prices: SOFC $200/kWh and battery$150/kWh.

Fig. 6

Payback time versus operation time per day: (a) under current SOFC and battery prices and (b) under future prices

Fig. 7

Hybrid system weight (a) and volume (b) change with operation time per day and average brake power for charge neutrality over a 24 h period

Fig. 8

weight and volume comparisons for the hybrid and the ICE systems, as functions of operation time per day (fuel tank is excluded) for charge neutrality over a 24 h period

## Tables

Table 1 Parameters related to water taxi
Table 2 Peak power requirements of the battery for different acceleration performances
Table 3 Sizing results for the proposed SOFC-battery hybrid system
Table 4 Parameters for the techno-economic analysis (US dollars)
aConverted from Canadian \$0.1139 [22] at an exchange rate of 0.8.
Table 5 Specifications for a 3 kW SOFC system
Table 6 Specifications of a lithium ion battery system
Table 7 Yanmar diesel engine
Table 8 Emission factors
Table 9 Greenhouse gases emissions from the three power sources (unit: kg/day)

## Errata

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