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Energy and Buildings 107 (2015) 213–225

Contents lists available at ScienceDirect

Energy and Buildings

j ourna l ho me page: www.elsev ier .com/ locate /enbui ld

simplified PEM fuel cell model for building cogenerationpplications

ang-Woo Ham, Su-Young Jo, Hye-Won Dong, Jae-Weon Jeong ∗

ivision of Architectural Engineering, College of Engineering, Hanyang University, 222 Wangsimni-Ro, Seungdong-Gu, Seoul 133-791, Republic of Korea

r t i c l e i n f o

rticle history:eceived 19 May 2015eceived in revised form 20 July 2015ccepted 10 August 2015vailable online 14 August 2015

eywords:EM fuel cell

a b s t r a c t

A simplified model of a polymer electrolyte membrane (PEM) fuel cell has been suggested for simulatingpackaged commercial fuel cell systems. PEM fuel cell systems are used in building cogeneration appli-cations because of their high efficiency, low transmission loss and pollution, flexible scalability, and lownoise. In conventional cogeneration applications, optimization techniques are utilized to size a systemand determine proper operational strategies using simulations. To evaluate the performance of a build-ing cogeneration system, a fuel cell model should be concise but accurate to allow its implementation ina whole-building simulation program. Some existing models are appropriate for building applications,

HPuilding cogeneration

but they have some limitations in modeling when a commercial packaged fuel cell system is used. Toovercome these problems, a simplified fuel cell model is suggested for commercial packaged fuel cells byadding some new variables and validating through experimental and published data. This model is rela-tively simple compared to other models but can be easily utilized in some limited cases with performancepredictions.

© 2015 Elsevier B.V. All rights reserved.

. Introduction

Combined heat and power (CHP), which simultaneously gener-tes heat and power, has been extensively used recently owing tots high efficiency [1]. In addition, when CHP systems are used at

micro-scale or in a distributed manner (i.e., decentralized energyeneration), their efficiency in terms of primary energy is max-mized owing to their low transmission and heat losses [2–4].ecently, among many applicants in micro CHP systems, fuel cellystems have proved to be attractive in many aspects, includinghe facts that they have high electrical efficiency because of directonversion from fuel to electricity, low pollutant emissions, flexiblecalability, and production of low noise during generation [4].

Numerous recent studies [5–14] have focused on the build-ng cogeneration applications of polymer electrolyte membranePEM) fuel cells (also known as proton exchange membrane fuelells) because they have high power density (small stack size), highogeneration efficiency (sum of heat and power), and fast startupime owing to their low operating temperature [4,15,16].

In general building cogeneration applications, PEM fuel cell sys-ems generate power for buildings, and the recovered heat is usedor domestic hot water or heating. However, in the summer, the

∗ Corresponding author.

ttp://dx.doi.org/10.1016/j.enbuild.2015.08.023378-7788/© 2015 Elsevier B.V. All rights reserved.

surplus heat that is recovered is useless. Therefore, researchershave studied ways to utilize the heat for cooling. This techniqueis usually termed trigeneration or combined cooling, heating, andpower (CCHP) [17]. When fuel cells are used for cooling appli-cations, the general approach is to use the recovered heat forgenerators of absorption chillers [18,19]. However, the operatingstack temperature of a PEM fuel cell is 60–80 ◦C, which is not suffi-cient for the generation process in absorption chillers. Thus, someresearchers [20] have focused on the applicability of PEM fuel cellsfor the regeneration process in liquid desiccant dehumidificationsystems.

Another area of research applies PEM fuel cells to buildingcogeneration centers based on the design and operating strategiesof the fuel cell system. The amount of electricity generated by thefuel cell system and the heat recovered by it are not always equalto the power and heat demand of the buildings it serves. For thisreason, a system will generally be connected to the grid or will havebatteries with thermal storage to handle load variations [21]. Even ifthe system is connected to the grid and includes auxiliary heaters,sizing and operating strategies of the system must be optimized.Many studies have been conducted on these issues, and they havetypically employed optimization techniques based on operational

strategies of the system and target variables, such as the primaryenergy or the life cycle cost [10,22–25].

In general, the primary energy savings or life cycle cost is esti-mated based on the annual operation, and in this case, the general

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214 S.-W. Ham et al. / Energy and Bui

Nomenclature

a0, a1, a2 model coefficientsb0, b1, b2 model coefficientsBX fixed (bias) uncertaintycp,w specific heat of water (kJ/kg K)LHVfuel lower heating value of fuel (kJ/kmol)n number of measured dataNfuel molar flow rate of fuel (kmol/s)p number of predictors in the modelPAC,anc parasitic AC power (kW)PAC,net net generated AC power (kW)PAC,net,nom rated maximum power from manufacturer (kW)PAC,net,rated rated power at part-load condition from manu-

facturer (kW)PAC,PCU generated AC power after PCU (kW)PAC,ref generated AC power at reference condition (kW)PDC,net net generated DC power (kW)P* dimensionless power (–)Pgen,start average power generation in startup mode (kW)Puse,start average power use in startup mode (kW)PCU power conditioning unitPLR part-load ratio (–)Q recovered heat (kW)Qfuel caloric value of fuel (kW)Qfuel,ref caloric value of fuel at reference condition (kW)Qref recovered heat at reference condition (kW)Q ∗ dimensionless recovered heat (–)Q ∗

fuel dimensionless caloric value of fuel (–)r0, r1 model coefficientsSX random (precision) uncertaintyTw,in, Tw,out inlet/outlet temperature of stack cooling water

(◦C)UX overall uncertaintyVfuel fuel volume flow rate (m3/s)¯V fuel,start average fuel volume flow rate in startup mode

(m3/s)Vm molar volume of fuel (m3/kmol)Vw water volume flow rate (m3/s)ymeasured measured valueymeasured average value of measure dataypredicted predicted value by the model

Greek symbols˛, model coefficientsε0, ε1, ε2 model coefficientsεDC,net electrical (DC) efficiency of fuel cell�PCU PCU efficiency

3

ms[od

tdsccpi

one component (fuel cell system) in a whole building. Moreover,

�w density of water (kg/m )

ethod used estimates the expected consumption using computerimulations based on the general power and heating load profiles10,22,23,26,27]. In this case, one can notice that the modelingf each component (e.g., fuel cell, thermal storage) is essential toetermine the accuracy of the analysis.

Many studies have dealt with the modeling of fuel cell sys-ems. Components of the fuel cell are simulated individually usingynamic simulation, because the goal of such models is to designtacks and fuel cells systems [28–30]. However, for building appli-ations, the design of fuel cells is not typically an issue because

ommercialized fuel cell systems are typically installed with pre-rogrammed control algorithms. In addition, the fuel cell system

s not the only building component that should be modeled. Thus,

ldings 107 (2015) 213–225

in practice, the fuel cell model must be accurate but simple andimplementable in a whole-building simulation.

A few researchers have developed simplified PEM fuel cell mod-els for building applications. However, these models have somelimitations in practice because they are based on simple linearassumptions [22,31] or a stack polarization curve without bal-ance of plant [10,16,32–37]. In response, a simple and empiricalfuel cell model for building cogeneration simulation was devel-oped in the Annex 42 project of the International Energy Agency[38]. The model was basically developed for a solid-oxide fuelcell system [39] but was extended to a PEM fuel cell system[40]. The Annex 42 model is concise but accurate; however, ithas been noticed that a more simplified model is necessary forpractical implementations. Specifically, in real applications, res-idential fuel cells are available off the shelf, and only limitedparameters can be modified in this case without disassembling thepackage.

In this present research, a simplified PEM fuel cell model issuggested based on the Annex 42 model. The model aims at a com-mercial PEM fuel cell system in which the Annex model is difficult toimplement. With seven measurable variables (e.g., design capacity,AC power), the model predicts power, heat, and fuel consumption ofa fuel cell system by mapping performance curves through regres-sions. Although this model is not as specific as that in Annex 42, itcan be applicable to commercial fuel cells because it is manufac-tured with preprogrammed capacity controls (i.e., less performancevariations and part-load mode operation). First, in this research, asimplified PEM fuel cell model based on other fuel cell models [40]is derived, and then the proposed model is validated by experimen-tal measurements. The model is also validated by measurementdata acquired from open literature.

2. Simplified PEM fuel cell model

A simplified fuel cell model based on a previous fuel cell modelis introduced [40]. The suggested model is based on steady-stateoperation and empirical data. Although there is a wide range ofdynamic PEM fuel cell models, we concluded that the dynamicmodels are not suitable for analyzing the annual performance andeconomic feasibility of fuel cells in building applications becausethey are intended for stack design [28,29] or require a significantamount of performance information and calibration for each com-ponent and their control algorithms in a fuel cell system [30,41–44].That level of modeling for a fuel cell system is excessively timeconsuming considering that it is a small part of a building, anda viable option is to use a simple empirical model because thesystem exhibits relatively steady performance. Moreover, the sys-tem often cannot be investigated at the component level for somecommercial fuel cell packages. In contrast, the simplified fuel cellmodel based on empirical data is suitable for building applicationsbecause it can be easily coded into existing building simulationprograms, such as EnergyPlus [45] and TRNSYS [46]. Dynamic per-formance characteristics of the plant within a simulation time step(15–60 min) are negligible in the context of annual energy sim-ulations. Some studies have introduced simplified PEM fuel cellmodels for building cogeneration applications, but we found thatthese models are unsuitable for a building cogeneration applicationbecause they are either too simple [22,31] or limited to a polar-ization curve [16,32–36]. Whereas polarization curve modeling isaccurate, it requires time domain-based simulation platforms andstack-level modeling [30,41], which requires too much effort for

it is difficult to model a stack’s transient operation without disas-sembling the factory-assembled commercial fuel cell, which canyield malfunctions [27]. Thus, in building applications, the general

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S.-W. Ham et al. / Energy an

pproach is to use performance-based modeling because commer-ial fuel cell systems are manufactured and preprogrammed in aactory [27,39,47].

.1. Motivations

Our proposed model is based on the quasi-dynamic PEM fuel cellodel developed as part of Annex 42 by the International Energygency [38,40]. This model is a simple but accurate empirical modelhose purpose is to serve as a general model to be integrated into

nd interoperable among various building energy simulation pro-rams, thereby enabling overall performance evaluation of buildingogeneration systems. Although this model is relatively concisend can be integrated into whole-building simulation programs,e found that some commercial fuel cell systems have limitationsith regard to this model.

In a commercial fuel cell system, all components of the systemre assembled into one package including balance of plant (e.g.,eformer), and it is impossible to disassemble the whole packagend model each component owing to safety and security concerns.oreover, the system has preprogrammed capacity control algo-

ithms because the use of dynamic capacity control on the fuel celln order to meet load changes is unnecessary in stationary appli-ations. This is because the overriding design criteria in stationaryuel cells are durability and stable operation [48–50]. Thus, regard-ess of the fuel cell’s operational strategy (e.g., electricity-led oreat-led operation), auxiliary heaters and thermal storage, as wells electricity storage such as capacitors and batteries, are utilizedor handling variations in electricity and heat demand [21,51,52].his is very common in any CHP design [15,32,53]. For this reason, aypical capacity control algorithm for a commercial fuel cell aims toegulate the current density [54] to meet the required constant ACower by using a DC-DC converter and a DC-AC inverter [51,55,56].hus, many commercial fuel cells have preprogrammed capac-ty control algorithms (i.e., preset turn-down or part-load ratios).inally, the power and heat generation of commercial fuel cell pack-ges sometimes differs from the design capacity (in laboratory)fter installation. Therefore, the simplified model aims at commer-ial fuel systems in which application of the Annex model is limitednd new parameters of part-load ratio and AC power output aresed.

.2. Model derivation

(a) AC power. In the Annex 42 PEM fuel cell model [38,40], theuthors controlled two variables: AC power and the temperaturef the stack cooling water. As shown in Eq. (1), the generated netC power (PAC,net) can be estimated by subtracting the parasitic ACower (PAC,anc) consumed by ancillary devices from the total ACower (PAC,PCU), which is the AC power inverted by the power con-itioning unit (PCU). The inverted total AC power can be expressedimply as the product of the net generated DC power (PDC,net) andCU efficiency (�PCU), as shown by the following equation:

AC,net = PAC,PCU − PAC,anc = PDC,net�PCU − PAC,anc →∝ PDC,net (1)

In the Annex 42 model, the measured PDC,net and fuel consump-ion Nfuel are used to estimate electrical efficiency (εDC,net, see Eq.2)). In addition, the model suggested that εDC,net can be correlatedith a second-order polynomial in terms of PDC,net. However, whene used a previously reported dataset [40], we found that ε1 and ε2

ave relatively small values compared to ε0, and the relationshipetween PDC,net and Nfuel was almost linear. According to this cor-elation, we can conclude that the fuel consumption is a first-orderunction with respect to PDC,net because the lower heating value of

dings 107 (2015) 213–225 215

the fuel (=) is almost constant:

Nfuel = PDC,net

εDC,netLHVfuel

= PDC,net

LHVfuel

1

ε0 + ε1PDC,net + ε2P2DC,net

∝ PDC,net

ε0(2)

In addition, the Annex 42 model suggested that PAC,anc is linearlyrelated to Nfuel; based on this relationship and the form of Eq. (2),we can conclude that PAC,anc and Nfuel are first-order functions ofPDC,net. Thus, from Eq. (1), we can conclude that PAC,net is also a first-order function with respect to PDC,net, assuming that �PCU is almostconstant (±1.5% variations were previously reported [40]).

(b) Part-load ratio and dimensionless power model. Com-mercial fuel cells are controlled by means of a part-load ratiopreprogrammed based on testing conducted by the manufacturer.According to the literature [54,56], a PEM fuel cell controller mod-ulates the current density to meet the desired AC load, even if thepolarization characteristics and stack performance vary in responseto changes in the operational characteristics (e.g., stack temper-ature or operating time) [56–58]. Therefore, the preprogrammedpart-load ratio (Eq. (3)) was chosen as a parameter of the simplifiedmodel because the AC output of a fuel cell is almost constant regard-less of the operating point of current density and the resulting fuelconsumption:

PLR = PAC,net,rated

PAC,net,nom(3)

In practice, after installation, it is possible that the AC outputwould differ from the rated AC output reported by the man-ufacturer. However, according to the literature [59,60] and ourexperiments, the AC output remains nearly constant with time,despite such a discrepancy. Thus, it is more accurate to use dimen-sionless AC power that is based on the reference AC power afterinstallation.

In this research, the dimensionless power used (Eq. (4)) is basedon the measured power considering the performance degradationafter installation. The reference condition will be addressed in Sec-tion 2.2(c). To reflect the use of a preprogrammed controller, PAC,netis written as a function of part-load ratio (PLR), as shown in Eq.(5). This equation uses a second-order polynomial because the ACoutput resulting from the preprogrammed part-load ratio is notalways linear owing to differences in the PCU efficiency and para-sitic power (Eq. (1)) under different part-load ratio conditions andperformance degradation:

P∗ = PAC,net

PAC,ref(4)

P∗ = a0 + a1PLR + a2PLR2 (5)

(c) Dimensionless heat recovery model. Unlike the case of aportable fuel cell application, in a building application, both powerand heat are important. Thus, predicting the recovered heat issomewhat important in the simplified model. In the same way asthat adopted for power, we used dimensionless heat in this model(Eq. (7)), and the recovered heat (Q ) can be estimated based onmeasured data using Eq. (6). The dimensionless heat (Q ∗) is theratio of the recovered heat in the present condition (Q ) to that inreference condition (Qref):

Q = cp,w�wVw

(Tw,out − Tw,in

)(6)

Q

Q ∗ =

Qref(7)

The original Annex 42 model [38] predicted the recovered heatas a function of stack temperature, but one’s ability to measure

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216 S.-W. Ham et al. / Energy and Bui

0 0.4 0.8 1.2 1.60

0.4

0.8

1.2

2

Cel

l vol

tage

(V

)

Ideal thermal cell voltage (V)

Heat

Power

Oper ating point

ttca[atifcp

(t[inrwaQ(cw

P

t

Current den sity(A /cm )

Fig. 1. General polarization curve of a single cell.

he stack temperature can be limited in practice [56]. Moreover,he model must include a detailed representation of each sub-omponent in the cooling system—that is, the heat exchanger, their-cooler, and the pump. Owing to these limitations, Johnson et al.40] proposed a simplified heat recovery model including DC powernd stack cooling water temperature, the latter of which representshe stack temperature. Although this model is accurate but concise,t requires measurements for various points, which could be limitedor some other PEM fuel cells where collecting diverse data is inac-essible [60]. Specifically, replacing the DC power term with theart-load ratio degrades the accuracy of the model.

Therefore, we modified the heat recovery model as shown in Eq.8). Heat generation depends on the operating current density, andhe operating point is modulated to meet the required AC demand54,56], causing heat generation to fluctuate (Fig. 1). However, thedeal thermal voltage (i.e., the theoretical chemical energy) doesot change much, regardless of the operating point. Thus, it is moreeliable to predict the power and heat performance simultaneouslyhen predicting the generated heat (Fig. 1). We also found, through

detailed inspection of previously reported data [40,59,60], that˙ ∗ varies slightly with Tw,in, so we added a linear term (˛) in Eq.8). This dependency might be attributed to the slight performancehanges in the polarization characteristic when the stack coolingater temperature (Tw,in) is changed [56]:

P + Q

∗Q ∗ = AC,net

PAC,ref + Qref= r0 + r1PLR(˛Tw,in + Tˇ

w,in) (8)

According to the literature [40] and our experiment, we noticedhat the amount of recovered heat varies with the stack cooling

Fig. 2. Schematic diagram of a co

ldings 107 (2015) 213–225

water temperature. However, within the range of 10–40 ◦C, onlysmall differences were observed. Additionally, in the cold-startmode, electricity generation began when the temperature of stackcooling water reached values in the range of 40–50 ◦C. For this rea-son, the reference condition was set to a part-load ratio of 100% anda stack cooling water temperature of 40 ◦C.

Previous experiments illustrated the impact of outdoor air andstack coolant flow rate on fuel cell performance [59,60]. The gen-erated power is affected by neither the ambient air conditions(temperature and humidity) nor the flow rate because the fuel cellsystem is internally controlled to provide stable electricity. Fromthe data in [59], the coolant flow and ambient temperature canindirectly affect heat generation in fuel cells when there are specialconditions such as cold ambient air temperature or low coolantflow. When the ambient air is cold, the recovered heat could belost while flowing through the pipe and into thermal storage. Inother words, the performance variation due to cold air is presum-ably attributed to poor insulation [59]. Moreover, when the coolantflow is small and not sufficient to cool the stack, an auxiliary inde-pendent cooler operates, resulting in a reduction of recovered heat[59].

However, we also noticed that these conditions rarely exist inreal operation because the internal temperature of the fuel cellengine remained somewhat constant for a year by generating heatin the reformer. Moreover, generally, commercial fuel cell coolantis designed to provide sufficient cooling with sufficient flow. There-fore, the general model [38] shows that the recovered heat can beexpressed as stack (or coolant) temperature. Thus, in this research,we decided not to include the ambient temperature and coolantflow in the model.

2.3. Model structure and fuel consumption

Fig. 2 shows a schematic diagram of our fuel cell system, whichwas purchased from a vendor. The balance of plant differs slightlyfrom vendor to vendor, but the general configuration is almostidentical. A commercial fuel cell comprises various subcomponents,including the fuel processing module (reformer), air supply mod-ule, PCU, and heat recovery module (water tank) [21]. The role ofthe reformer is to convert fuel (e.g., methane gas, natural gas, orliquefied petroleum gas) to hydrogen gas, because procurement ofpure hydrogen as a fuel is rare in practice. For conditioning, conver-sion, and purification of the fuel, resources such as water, air, or partof the fuel are used in the reformer. Heat and electricity are gen-

erated in the fuel cell stack through electrochemical reactions, andthe generated DC electricity is converted to AC power in the PCU.To ensure sufficient reactions, hydrogen stoichiometry is generallymaintained above than 1.1, resulting in unconsumed hydrogen fuel

mmercial fuel cell system.

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S.-W. Ham et al. / Energy and Buil

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the commercial fuel cell system internally controls stack incoming

Fig. 3. Structure of the simplified PEM fuel cell model.

n the stacks [52]. One approach to reduce this wasted unconsumeduel is to reuse it as a fuel for combustion in the reformer [52]. Thus,he afterburner and anode tail gas oxidizer are not included in this

odel. Finally, heat is recovered through the use of cooling waternd a water tank. For safety, the system includes an air cooler, whichs operated to cool the water tank when the recovered heat exceedshe heat demand (i.e., temperature of the water tank).

As mentioned above, it is impractical to model all heat, mass,nd the electrical transport phenomena of the stack and other sub-omponents when analyzing a fuel cell for building cogenerationpplications. In addition, when the fuel cell system installed, onlyimited data can be measured without disassembling the system.herefore, we simplified the complex system by collecting easilyccessible and necessary data for building applications. The blackox model comprises 10 parameters: seven inputs (part-load ratio,et generated AC power, fuel consumption, fuel heating value, inletnd outlet temperatures, and volume flow rate of stack coolingater), and three outputs (generated power, generated heat, and

uel consumption) (Fig. 3).In this model, the input parameters are PLR and Tw,in. PLR is a

alue preprogrammed by the manufacturer, such as full-load andalf-load (Eq. (3)). By changing PLR, a user can modulate the fuel cellower as needed. The variable Tw,in is the temperature of water that

s used to cool the stack and other components. In fact, it is moreonvenient to measure the water temperature of the demand sidehan that of the cooling water (Fig. 2). However, the storage tanknterposed between them prevents the temperature of the watern the demand side from immediately affecting the performancef the fuel cell. Thus, in the simplified model, the cooling wateremperature indicates the temperature of the stack cooling water“Cooling water in” in Fig. 2), which directly affects the stack tem-erature. With this modeling strategy, one can simply incorporatehe fuel cell model with the existing thermal storage model [37] forhole-building simulation.

The output parameters of this model are generated power,ecovered heat, and fuel consumption. In practice, only these threeariables are useful in analyzing the building cogeneration system,o we disregarded all other possible output parameters.

Based on Section 2.2(a), we consider the relationship of PAC,netnd Nfuel to be almost linear. Furthermore, in Eq. (5), the variable*, which is proportional to PAC,net, is expressed as a second-orderolynomial with respect to PLR. Thus, Nfuel can be correlated with aecond-order polynomial with respect to PLR (Eq. (10)). However,he lower heating value of fuel (LHVfuel) varies with the type ofuel and the operating temperature and pressure, so the use of theotal caloric value of consumed fuel (Qfuel), rather than Nfuel, is moreccurate in general applications. Like power and heat, we also use aimensionless fuel heating value, as shown in Eq. (9). This dimen-

ionless fuel heat is expressed in Eq. (10). As shown in Eq. (11),he fuel heating value can be estimated by multiplying LHVfuel byhe volume flow rate of the fuel (Vfuel) measured onsite, whereas

dings 107 (2015) 213–225 217

LHVfuel can be calculated, measured, or quoted as reported by thefuel’s local distributor:

Q ∗fuel = Qfuel

Qfuel,ref(9)

Q ∗fuel = b0 + b1PLR + b2PLR2 (10)

Qfuel = VfuelLHVfuel

Vm(11)

3. Model validation

The main application of this model is to test the performanceof installed commercial fuel cells; in this research, the suggestedmodel was tested and validated experimentally. As mentioned ear-lier, commercial fuel cells are tested in the laboratory, and the actualperformance of each fuel cell after installation can differ from itsperformance in the laboratory. Based on our experimental results,we demonstrate that the proposed model can be applicable in realsettings.

3.1. Fuel cell system

The PEM fuel cell system was installed in a small chamber on thetop of a four-story factory building located in Incheon, South Korea.The fuel cell was fueled with natural gas, and all its system compo-nents (reformer, PCU, stack, and hot water storage) were assembledin one cabinet (Figs. 2 and 4b). The purpose of the system was togenerate power and heat for a liquid desiccant and evaporativecooling-assisted 100% outdoor air system (LD-IDECOAS) [20,61,62].The LD-IDECOAS system required heat to regenerate the desiccantsolution, and electricity was used for other components such asfans and pumps. In addition, the system was connected to the grid,so the stack generated constant AC power according to the presetpart-load ratio. When more electricity was generated than was con-sumed by the LD-IDECOAS, the surplus electricity was sent to thegrid. Hence, there was no electrical storage. However, the systemwas designed based on electricity, so a thermal storage tank andan air cooler were installed to control the temperature of the stackcooling water (Fig. 2). Table 1 summarizes other details relevant tothe fuel cell system.

3.2. Experiments

In this study, only seven variables needed to be measured dur-ing the experiments: part-load ratio, net generated AC power, fuelconsumption, fuel heating value, inlet and outlet temperature, andvolume flow rate of stack cooling water. Table 2 lists these mea-sured variables and their corresponding sensors.

The experiments were divided into three parts in this study. Thefirst part is to obtain steady-state data to calibrate the model sug-gested in this paper. As with general fuel cell systems for stationaryapplications, the part-load ratio is the only controllable variable forour fuel cell system, and stack cooling water temperature can becontrolled using an external chiller and heater. Thus, the part-loadratio and stack cooling water temperature were controlled in theexperiments (Table 4). The other part is to monitor the performancevariations in the fuel cell with changes in outdoor air conditions.Outdoor conditions are impossible to control in practice, so theperformance of fuel cells was intermittently recorded from June toDecember. Then, the collected data were statistically analyzed withrespect to the outdoor air conditions. As mentioned in Section 2.2,

water and gas conditions, and no significant changes were observedin its performance. The final step is to monitor the transient char-acteristics of the fuel cell system when it is in startup, shutoff, and

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218 S.-W. Ham et al. / Energy and Buildings 107 (2015) 213–225

Fig. 4. Test facility.

Table 1Fuel cell system summary.

Location Incheon, South KoreaType Polymer electrolyte membrane (PEM) fuel cellRated AC power 10 kW (electrical efficiency: 34.4% (LHV))Rated heat 13.94 kW (thermal efficiency: 49.5% (LHV))Balance of plant Reformer, PCU, hot-water storageFuel Natural gas (LNG)Capacity control 100% and 60% AC power (PLR = 1, 0.6) (grid-connected)

Table 2Measured variables and corresponding sensors used.

Measured variable Sensor Specifications andaccuracy

Net generated AC power(PAC,net)

Digital electricitymeter(LD3410DR-040, LSIS)

±1% of measurevalue

Inlet stack cooling watertemperature (Tw,in)

T-type thermocouple(MV2000, Yokogawa)

−200 to 400 ◦C±(0.15% + 0.7 ◦C) ofmeasure value

Outlet stack cooling watertemperature (Tw,out)

T-type thermocouple(MV2000, Yokogawa)

−200 to 400 ◦C±(0.15% + 0.7 ◦C) ofmeasure value

Stack cooling water flow(Vw)

Ultrasonic flow meter(TFM 100, TaehungM&C)

±1% of measurevalue

Gas flow rate (VFuel) Gas meter(G2.5L, Daesung)

0.025–4 m3/h±1.5% of measurevalue

LHV of fuel (LHVFuel) Obtained fromsupplier(http://www.kogas.or.kr)

Monthly averageLHV (kJ/m3)±2% of measuredvalue

Table 3Overall uncertainty of variables.

PAC,net Q QFuel Tw,in Tw,out Vw VFuel

Min 0.06 kW 0.19 kW 0.33 kW 0.72 ◦C 0.73 ◦C 0.0025 l/s 0.0005 m3/min

pob

t(s

Table 4Investigated test sets.

Temperature of inlet stack cooling water (Tw,in)

PLR 15 ◦C 20 ◦C 25 ◦C 30 ◦C 35 ◦C 40 ◦C

to 45 ◦C by the manufacturer to protect the water filter. Temper-ature in excess of 45 ◦C caused the preprogrammed controller to

Max 0.15 kW 1.48 kW 2.00 kW 0.89 ◦C 1.04 ◦C 0.0028 l/s 0.0025 m3/min

art-load change modes. The impact of dynamic characteristics onverall performance is not significant, but some of discussions wille presented in Section 3.6.

The experimental uncertainties (Table 3) were analyzed usinghe root-sum-squares (RSS) method [63]. The overall uncertainties

UX) were estimated through Eq. (12), and sensor accuracy andtandard deviations of measurements with a 95% confidential

0.6 � © © © � © © � ©1 � © © © © � © © © � ©

interval were used for the fixed (bias) uncertainty (BX) and therandom (precision) uncertainty (SX ), respectively:

UX =√

B2X +

(tSX

)2(12)

SX = 1√n

√√√√ 1n − 1

n∑i=1

(Xi − X

)2(13)

3.3. Validation process

The validation process was divided into two steps. First, theperformance of fuel cells was measured in the cases where thecontrollable variables (i.e., PLR and Tw,in) were set to their maxi-mum, minimum, and median values, for estimation of the empiricalcoefficients of the model (training variables), as indicated in Eqs. (5),(8), and (10) (marked by � in Table 4). After that, additional testswere conducted using other randomly chosen conditions (markedby © in Table 4) (i.e., testing variables), and the results were com-pared to the values predicted by the model during the first step. Todetermine the steady-state performance, each test was conductedfor one hour, and average values over periods of 30 min were esti-mated in the validation process [40]. In the first step, six total testswere conducted (including three different water temperatures andtwo part-load ratios), followed by an additional 13 tests.

The fuel cell used in this research had two capacity controloptions (two specific part-load ratio values; namely, 1 and 0.6). Thecapacity was based on AC power, and the coincidental and nomi-nal powers were 10 kW and 6 kW, respectively. In practice, we hadlimited control over the water temperature, which ranged from 15to 40 ◦C. In theory, a PEM fuel cell can be operated with stack tem-peratures of 80–100 ◦C; however, for safety reasons, it is usuallyoperated in the range of 60–80 ◦C [56]. Nevertheless, in our fuelcell, the temperature of the inlet stack cooling water was limited

operate the air cooler (Fig. 2). According to the manufacturer, thefilter used for purifying the stack cooling water would be damaged

Page 7

S.-W. Ham et al. / Energy and Buildings 107 (2015) 213–225 219

F colour in this figure citation, the reader is referred to the web version of this article.)

btttfblt

tsTasud[ii

C

M

3

auwa

t

Table 5Model coefficients of tested fuel cell.

ReferenceconditionsEquations

Power:8.72 kW

Heat:7.59 kW

Fuel:40.6 kW

Power (Eq.(5))

P* = 0.2367 + 0.7575PLRR2 = 0.9817

Heat + power(Eq. (8))

P∗Q ∗ = −0.1572 +1.493PLR(0.0008274Tw,in

+ T−0.0809w,in

)

R2 = 0.9992Fuel (Eq.

(10))Q ∗

fuel=

−0.1938 + 1.1913PLRR2 = 0.9982

ig. 5. Performance map of tested fuel cell. (For interpretation of the references to

y water at temperatures higher than 45 ◦C. This was attributed tohe use of open-loop stack cooling water. In other words, becausehe water in the thermal storage tank was directly introduced intohe stack, the filter should provide high-quality purification per-ormance to remove ions and contaminants from the cooling waterecause these substances could cause short circuits, and ultimately

ead to stack damage [52]. For this reason, the controllable range ofhe stack cooling water temperature was limited to 15–40 ◦C.

In this research, the accuracy of the model was evaluatedhrough two metrics: the coefficient of variation for the root meanquare error (CV(RMSE)) and the normalized mean bias error (MBE).hese two metrics are typically used to evaluate the accuracy of

calibrated energy model and measured data in whole-buildingimulations. They are also used for the component models in sim-lations [64]. CV(RMSE) (Eq. (14)) is used to evaluate the degree ofata scatter. Values less than 5% are considered to be acceptable64]. MBE (Eq. (15)) quantifies the bias of the model. Correspond-ngly, positive values indicate underestimation, and negative valuesndicate overestimation:

V(RMSE) = 1ymeasured

√∑i=1n

(ymeasured,i − ypredicted,i

)2

n − p× 100 [%]

(14)

BE =∑i=1

n ymeasured,i − ypredicted,i

ymeasured(n − p)× 100 [%] (15)

.4. Model validation on experimental results

The test results and model coefficients are summarized in Fig. 5nd Table 5. The model coefficients were estimated by regressionsing six boundary points within the controllable range, marked

ith filled blue dots in the figure. The other 13 tests for validation

re marked with hollow blue dots.All test results were compared to the values predicted by

he model. Although the values were predicted using only the

Range ofmodel

PLR: 0.6, 1 Tw,in: 15.1–40.3 ◦C

part-load ratio, the predicted AC power and fuel consumption val-ues agreed well with the measured values (Figs. 6 and 7). The mainreason is that the algorithm for stack capacity control is based on ACpower, and the fuel consumption actually depends on the stack’sfuel demand. As a result, the model yielded CV(RMSE) values of2.6% and 1.89% for power and fuel, respectively, and an MBE valueof nearly zero for both of these parameters.

The predicted and measured values of recovered heat werecompared (Fig. 8). The heat recovery model agreed well with themeasured data, and all tested data fell within the 10% error bound.The error of the heat recovery model was noticeably larger thanthat of the other variables—namely, power and fuel. In fact, theheat recovery model predicted the sum of power and heat, not theheat itself, and thus the predicted heat included the error of thepower model. Furthermore, the uncertainties associated with themeasurements of heat were noticed to be relatively large. The mainreason for this is the poor sensor accuracy of the water tempera-

ture. Because the heat generation was estimated based on Eq. (6),the errors of each variable were propagated with changes in tem-perature, leading to large uncertainties. In spite of the cycling andlarge uncertainty, we observed that the 1 h average of produced

Page 8

220 S.-W. Ham et al. / Energy and Buildings 107 (2015) 213–225

0 2 4 6 8 100

2

4

6

8

10

PAC,net,predicted [kW]

PA

C,n

et,m

easu

red

[kW

]

CV(R MSE) = 2.6%

MBE = 0%

5% error bound

Fig. 6. Power model validation with experimental data.

0 10 20 30 40 500

10

20

30

40

50

Qfuel,predi cted [kW]

Qfu

el,m

easu

red

[kW

]

5% er ror bound

CV(RMSE) = 1.89%

MBE = 0.32%

Fig. 7. Fuel model validation with experimental data.

0 2 4 6 8 100

2

4

6

8

10

Qm

easu

red

[kW

]

10% error bound

CV(RMSE) = 5.12%

MBE = -0.2%

h5

3

l

Table 6Model coefficients.

ReferenceconditionsEquations

Power: 0.9745 kW Heat:0.1538 kW

Fuel:0.2941 kW

Power (Eq.(5))

P* = −0.082 + 1.2194PLR− 0.221PLR2

R2 = 0.9988Heat + power

(Eq. (8))P∗Q ∗ = −0.0125 +0.6907PLR(−0.01519Tw,in +T0.1953

w,in)

R2 = 0.9981Fuel (Eq.

(10))Q ∗

fuel= 0.1456 +

0.6162PLR + 0.2348PLR2

R2 = 0.9993Range of

modelPLR: 0.25–1 Tw,in: 16.1–59.1 ◦C

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

PAC,net,predicted [kW]

PA

C,n

et,m

easu

red

[kW

]

5% error bound

CV(RMSE) = 1.43%MBE = 0%

Fig. 9. Power model validation with experimental data from [40].

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

Qfu

el,m

easu

red

[kW

]

CV(RMSE) = 1.08%MBE = 0.01%

5% error boun d

Qpredicted [kW]

Fig. 8. Heat recovery model validation with experimental data.

eat was relatively constant. The CV(RMSE) value of this model was.12%, and this value was within the acceptable range [64].

.5. Model validation on literature data

The simplified model was also validated based on data from theiterature [40]. The coefficients of the simplified model (Eqs. (5), (8)

Qfuel,predicted [kW]

Fig. 10. Fuel model validation with experimental data from [40].

and (10)) were estimated using multivariate regression [65]. Table 6presents the regression results. The reference condition is the fuelcell’s performance at PLR = 1 (100%) and Tw,in = 40 ◦C, as mentionedin Section 2.2(c). Correspondingly, the measured part-load ratioswere 0.25, 0.5, 0.75, and 1 (i.e., 25%, 50%, 75%, and 100%).

Figs. 9 and 10 compare the measured and predicted results for

power and fuel consumption, respectively. Although the modelspredict the generated power and the consumed fuel based on afixed part-load ratio, predictions from both models differed slightlyfrom the measured data. This was attributed to the facts that the

Page 9

S.-W. Ham et al. / Energy and Buildings 107 (2015) 213–225 221

0 0.4 0.8 1.2 1.6 20

0.4

0.8

1.2

1.6

2Q

mea

sure

d [k

W]

CV(RMSE) = 3.2%MBE = 0.01%

5% error bound

CV(RMSE) = 3.2%MBE = 0.01%

AlCetTA

rhaq(

3

sptomtscf1

Table 7Summary of transient variables in the fuel cell model.

Mode Durationtime

Values Description

Start-up 3 h Puse,start : 2.4 kW Electricityconsumption

Start-up 0.5 h Pgen,start : 5.3 kW Electricity generationin the fuel cell

Start-up 3 h ¯V fuel,start : 0.00018055 m3/s Gas consumption instart-up mode

Qpredicted [kW]

Fig. 11. Heat recovery model validation with experimental data from [40].

C power is generated according to the preprogrammed part-oad ratio, and the fuel is consumed accordingly. As a result, theV(RMSE) values were 1.43% and 1.08% for power and fuel mod-ling, respectively, which were within the acceptable range of lesshan 5% [64]. In addition, the MBEs were almost 0% for both models.hese results also indicate that it is acceptable to directly predictC power rather than the DC power.

Fig. 11 compares the measured and predicted values of the heatecovery model. Unlike the power and fuel models, the recoveredeat was affected by the temperature of the stack cooling water,nd scattered data were observed. The heat recovery model wasuite accurate and yielded an acceptable CV(RMSE) value of 3.2%<5%) and an MBE of nearly 0%.

.6. Transient characteristics

Although stationary fuel cell systems are generally designed forteady operation, transient operational characteristics in startup,art-load change, and shutoff modes must be considered to analyzehe annual performance of the whole building. Fig. 12 shows theperational characteristics of our fuel cell systems during startupode. According to the manufacturer, the warm-up period to start

he system takes 3 h because the reformer requires more than 2 h to

ufficiently increase its temperature to make pure hydrogen whileonsuming fuel. The test results showed that 2.5–3 h were neededor startup mode. For 2.5 h, the system consumed approximately.1 m3 of fuel (natural gas) without electricity generation. After

0

2

4

6

8

10

0

0.02

0.04

0.06

10:5310:3210:119:509:299:088:478:26

Ele

ctri

city

(ge

nera

tion

) [k

W]

Fue

l (co

nsum

ptio

n) [

Nm

3 /min

]

Time

Warm up period

Electricity

Fuel

Ele

ctri

city

(ge

nera

tion

) [k

W]

startkW6(a)

Fig. 12. Transient charact

Shut-off 2 h – At least 2 h is requiredto start after shut-off

that, it generated approximately 2.65 kWh of electricity and con-sumed 0.85 m3 of fuel for 30 min. Not shown in Fig. 12, the systemalso consumed electricity because it did not generate electricityduring this period. In both modes, the system consumed 2.4 kW onaverage. These values are summarized in Table 7.

The operational characteristics of the system in part-loadchange mode are shown in Fig. 13. As shown in Fig. 13a, 6–10 kWchange mode takes 20 min, and 10–6 kW change mode takes 5 min.In addition, shutoff mode takes less than 10 min to stop consumingfuel and generating electricity. However, the manufacturer pre-vents the fuel cell from being turned on again for 2 hours fromshutoff mode for safety reasons (cool-down time). Both part-loadchange and shut-off modes are completed in 10–20 min. The exper-imental results of startup, part-load change, and shutoff modes aresimilar to the data in [60].

The default time steps for whole-building simulation programssuch as EnergyPlus [45] and TRNSYS [37] are 15 and 60 min, respec-tively. Thus, only generation/consumption of electricity and fuel instartup mode must be considered in annual simulation. However,the time required by shutoff mode must be considered even thoughthere is no fuel consumption.

4. Application and discussion

4.1. Implementation example

In this section, an example application of the proposed modelwill be presented for guidance. After presenting the process ofmodel implementation in a whole-building simulation domain,simple calculation results will be discussed.

Fig. 14 shows the overall process of model implementation. First,after calibrating the fuel cell model, the whole-building simulationprogram calculates the building’s energy use in the current timestep, the information related to electricity and heating demand, and

0

2

4

6

8

10

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

8:137:527:317:106:496:286:075:46

Time

Fue

l (co

nsum

ptio

n) [

Nm

3 /min

]

Warm-up period

Electricity

Fuel

startkW10(b)

eristic – start mode.

Page 10

222 S.-W. Ham et al. / Energy and Buildings 107 (2015) 213–225

6

7

8

9

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

13:2713:2113:1513:0913:03

Mode change (6 to 10 kW)

ElectricityFuel

Time

Ele

ctri

city

(ge

nera

tion

) [k

W]

Fue

l (co

nsum

ptio

n) [

Nm

3 /min

]

6

7

8

9

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

15:2415:1815:1215:0615:00

Elec tricity

Fuel

Mode change (10 to 6 kW)

Ele

ctri

city

(ge

nera

tion

) [k

W]

Fue

l (co

nsum

ptio

n) [

Nm

3 /min

]

Time

kW6tokW10(b)kW10tokW6(a)

Fig. 13. Transient characteristic – part-load change mode.

Whole building simulation domain

Buil dingsurfac emod el

Buildi ngsystemmodel

Buil dingairflowmodel

Fuel cel l mode l

Elec tricitymodel

Heatrecoverymode l

Fue lmode l

Ther mal or ele ctric storage mode l

ThermalStor ageenergybalance

Auxiliar y de vic e

Fuel cel lAuxiliar y

cooler

Auxiliar yboiler

Requ ired electricityRequ ired heating energyHot water temperature

Hot water fl ow r ateTime step informati on

Fuel celloperation al schedul e

orcontrol algo rithm

In fuel cell :Genera ted elec tricit y

Generated heatFuel consumpti on

Net elec tricityNet heating energy

Temperature change in storag eElectr ici ty changes in batter y

Elect ricit ybatteryenergybalance

Ther mal storage constraint s for safe

operation in fuel cell(e.g., min and ma x

temperat ure in thermal storage)

Net elect ricit yNet fuel con sumpt ionHot water temperatur e

entati

hcebIutttteptttiidt

Fig. 14. Model implem

ot water information (if heating is implemented by hot water cir-ulation with a fuel cell system). The fuel cell model then estimateslectricity and heating energy generation in the current time stepy using Eqs. (4)–(11) based on the fuel cell’s control algorithm.

n general, schedule-based fuel cell operation (grid-connected) issed in stationary applications for reliable operation. In most cases,here are mismatches in electricity and heating demand betweenhe building and the fuel cell system. Thus, models for the elec-ricity battery (if it exists) and thermal storage are necessary. Inhese models, the net required electricity from the grid and heatingnergy from the auxiliary boiler are estimated. Moreover, the tem-erature changes in the thermal storage must be calculated becausehe performance of the fuel cell is affected by this factor. Finally,here might be minimum or maximum constraints for hot wateremperature (stack coolant) in the fuel cell system. If a fuel cell aux-

liary cooler or heater is installed for these reasons, the energy usedn these devices is added to the net electricity and heating energyemand, and some information such as hot water temperature isransferred to the next time step.

on schematic diagram.

Fig. 15 shows an implementation of the model with hourly timesteps. The example is simply estimated based on the load profileof a residential house presented in [30]. It is assumed that one fuelcell system modeled in this study handles three residential housesin [30]. That kind of load profile can be estimated in a whole-building simulation domain as presented in Fig. 14. In Fig. 15a, thepositive y-axis shows the electricity demand, and the negative partrepresents the electricity generation in the fuel cell system. In thisexample, a simple schedule-based control algorithm is used for thefuel cell system (gray polygon in Fig. 15a). The time 0:00–3:00 isthe startup period, 3:00–15:00 is 6-kW mode, and the remainderis 10-kW mode. The blue polygon represents electricity demand inthe building, and the orange one represents the demand in the fuelcell system in startup mode. The yellow polygon represents thenet electricity demand in the building (i.e., positive: buy electricity

from the grid; negative: sell electricity to the grid).

Fig. 15b is a daily heating demand profile based on the controlalgorithm in the electricity example. The blue, yellow, and graypolygons are heating demand in the building, net required heating

Page 11

S.-W. Ham et al. / Energy and Buildings 107 (2015) 213–225 223

(a) Daily electricity demand

eating demand

32

33

34

35

36

37

38

39

40

41

-10

-8

-6

-4

-2

0

2

4

6

8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Stor

age

tem

pera

ture

[°C

]

Hea

ting

dem

and

[kW

]

Time [hr]

Heating demand [kW] Fuel cell heati ng en ergy [kW]

Boiler heating energy [kW] Storage tem perature [C]

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Ele

ctri

city

dem

and

[kW

]

Time [hr]

Electricity demand (building) [kW] Electricity generation (fuel cell) [kW]

Electricity fro m grid [k W] El ectricit y d emand (fuel cell) [kW]

Start-up mode 6 kW mod e 10 kW mod e

lour in this figure citation, the reader is referred to the web version of this article.)

etiv

4

pemtdatiacipefoaf

Table 8Comparison of different fuel cell models for building cogeneration.

Model Modeling method Applications Limitations

Dynamicmodels[30,41,44]

Physical modelbased onelectrochemistry

Stack design anddynamicsimulation

Modelingdifficulties andinteroperabilitywith buildingsimulationprogram

TRNSYS [37] Physical modelbased onelectrochemistry

Annual simulationand control

Model is limited tothe stack

Annex 42 [40] Empirical model Annual simulationand control forgeneral fuel cellsystem

Steady-statemodel, eachcomponent shouldbe modeled

Present study Empirical model Annual simulationand control for

Steady-state modeland limited to the

(b) Daily h

Fig. 15. Implementation example. (For interpretation of the references to co

nergy in the boiler, and fuel cell heating energy, respectively. Inhis example, fully mixed thermal storage is assumed, and the heat-ng energy generation in the fuel cell system varies, although it isery small because of the small temperature changes in the storage.

.2. Discussions

In this study, a simplified fuel cell model is suggested forackaged fuel cell systems, and the model is validated againstxperimental results and published data. Although diverse fuel cellodels exist for building applications, this study specifically aims at

he packed system. Table 8 summarizes the characteristics of theiverse model. Some dynamic models based on electrochemistryre useful for designing stack and fuel cell systems [30,41,44], buthey are complex and have some limitations with regard to model-ng in practice. Although some building simulation programs suchs TRNSYS [37] and EnergyPlus (Annex 42 model) [40] provide fuelell models for analyzing building cogeneration, the TRNSYS models limited to the stack only. The Annex 42 model (EnergyPlus) isowerful in terms of building applications and applicable in gen-ral. However, the model’s use might be limited in some packaged

uel cell systems where component modeling is not accessible with-ut disassembly. In other words, the suggested model specificallyims at this case, and the Annex model should be more appropriateor the general case.

commercial fuelcell package

commercialpackage

In addition, there are a few limitations in the application ofthis model to whole-building simulation. Although the model

coefficients in Eqs. (3)–(11) in Tables 5 and 6 can be used for asimulation as a default case, the coefficients must be calibratedthrough experiments if the performance of the other fuel cell sys-tem must be analyzed. Furthermore, the performance of the model

Page 12

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24 S.-W. Ham et al. / Energy an

s valid only within experimental data because it is an empiricalodel that does not guarantee extrapolation. Finally, the use of a

omplex control algorithm for a fuel cell system is limited in thisodel. Some advanced fuel cells used in automotive engineering

an change their electricity generation according to the electricityemand. In this case, the fuel cell should be modeled by using otherynamic models. However, in general, the fuel cell system used inuilding applications is controlled based on a preset schedule, andhis kind of control algorithm is applied to this model.

. Conclusion

In building cogeneration applications, the main issues for engi-eers are to determine the size of the fuel cell systems and establishperating sequences because the cogeneration system cannot meetoth heat and power demands in real time. A general method tovercome this limitation is to use an optimization technique devel-ped based on simulations.

In this research, a simplified PEM fuel cell model, which can beasily implemented in whole-building simulation programs, wasuggested for commercial fuel cell packages, and the model wasalidated by experimental data and established research outcomes.he model showed good agreement with measurements. In addi-ion, a simple application of this model is presented.

Unlike other fuel cell models, this empirical model attempts toredict the performance of the fuel system without solving complexlectrochemical reactions. Correspondingly, this allows the modelo be implemented in whole-building simulation programs.

Although some existing models can be used with building simu-ation programs, they have some limitations when the commercialuel cell system is packaged and hard or impossible to disassem-le. Disassembling packaged commercial units is often difficultr undesirable owing to safety and security concerns. This studyuggested a simpler fuel cell model for that case. For those cases,his study utilizes new terms for part-load ratio and AC power to

odel the performance, which are controlled variables in com-ercial fuel cell systems for capacity control. Consequently, theodel is composed of only seven variables, which can be mea-

ured without disassembly. In addition, dimensionless heat andower variables were introduced in order to consider performanceegradation after installation.

In practice, the success of a fuel cell cogeneration systemepends on how the system is sized and operated. With properizing and operation, a cogeneration system provides savings inrimary energy and cost. When detailed modeling is possible, thennex model [40] is the first choice, but when it is not applicable,

he model developed herein can be used in practical applicationso establish sizing and operation strategies of fuel cell cogenerationystems both before and after installation.

cknowledgements

This work was supported by a National Research Foundationf Korea (NRF) grant funded by the Korean government (No.015R1A2A1A05001726).

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