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Dustin McLarty
e-mail: dfm@apep.uci.edu
Jack Brouwer
e-mail: jb@apep.uci.edu
Scott Samuelsen
e-mail: gss@apep.uci.edu
National Fuel Cell Research Center,
Engineering Laboratory Facility,
Irvine, CA 92697-3550
Hybrid Fuel Cell Gas
Turbine System Design
and Optimization
Ultrahigh efficiency, ultralow emission fuel cell gas turbine (FC/GT) hybrid technology
represents a significant breakthrough in electric power generation. FC/GT hybrid
designs are potentially fuel flexible, dynamically responsive, scalable, low-emission gen-
erators. The current work develops a library of dynamic component models and system
design tools that are used to conceptualize and evaluate hybrid cycle configurations. The
physical models developed for the design analysis are capable of off-design simulation,
perturbation analysis, dispatch evaluation, and control development. A parametric varia-
tion of seven fundamental design parameters provides insights into design and develop-
ment requirements of FC/GT hybrids. As the primary generator in most configurations,
the FC design choices dominate the system performance, but the optimal design space
may be substantially different from a stand-alone FC system. FC operating voltage, fuel
utilization, and balance of plant component sizing has large impacts on cost, perform-
ance, and functionality. Analysis shows that hybridization of existing fuel cell and gas
turbine technology can approach 75% fuel-to-electricity conversion efficiency.
[DOI: 10.1115/1.4024569]
1 Introduction
The world faces a pending energy revolution. The current
means by which transportation, residential, and industrial energy
needs are met will not sustainably power the economy into the
future. The lack of a national energy policy has stalled many
promising technologies, due to uncertainty in fuel costs, environ-
mental liabilities, foreign oil security, and public policy. Three de-
sirable features for future energy solutions are diversity in
primary energy sources and generation technology, improved effi-
ciency in energy conversion and use, and optimally matching
energy technologies and resources to specific uses.
Energy technologies of the future require high efficiency, low
emissions, scalability, and dispatchability. Fuel cell gas turbine
(FC/GT) hybrid technology meets these requirements with dem-
onstrated fuel-to-electricity conversion efficiency as high as 56%
(lower heating value (LHV)) [1,2] and theoretical plant efficien-
cies exceeding 75% [3]. FC/GT hybrids designs are fuel flexible,
dynamically responsive, scalable, low-emission generators [4,5].
Fuel cell-gas turbine (FC/GT) hybrid technology has demon-
strated the ultrahigh efficiency, ultralow emissions, and fuel flexi-
bility necessary to achieve local, state, and federal targets for
future energy conversion [6–9]. Integration of fuel cell and gas
turbine technologies into a single symbiotic system represents a
breakthrough in electric power production technology. Gas tur-
bine performance limitations result from the Carnot limit govern-
ing all heat engines, but a fuel cell extracts work directly from the
chemical potential energy, bypassing the entropy-generating com-
bustion process entirely. However, a fuel cell cannot fully utilize
the fuel or all of its chemical energy, severely hindering overall
system efficiency. Hybrid FC/GT systems capture and oxidize the
anode off-gas to drive turbomachinery and produce additional
electricity and air compressor power. Molten carbonate and solid
oxide fuel cells are well-suited for hybridization with a gas turbine
generator [10,11]. Both operate at high temperature and can be
manufactured at scales congruent with existing turbomachinery.
Physical demonstrators are expensive to build and operate;
thus, physical models must be employed to conduct design and
performance studies that may justify a novel technology, such as
FC/GT hybrids. Accurate simulation of FC/GT behavior can only
be achieved with a methodology meeting the following
guidelines:
•Physical, chemical, and electrochemical processes that gov-
ern each component must be resolved from first principles,
with the exception of compressor and turbine components,
whose behavior is well characterized by empirical maps.
Detailed electrochemical and heat transfer models are neces-
sary to capture the effects of temperature, oxidant concentra-
tion, or fuel utilization changes [2].
•Dimensional models are superior to bulk models for their
ability to capture detailed spatial information, accurate tem-
perature and concentration profiles, and physical behavior
unrepresented by equivalent circuit models. Bulk physical
models are computationally efficient and useful for first
approximations in the design phase but not for dynamic
studies.
•Accuracy is paramount for the heat transfer in a nodal model.
Physical parameters, such as wall thickness, channel dimen-
sions, and material properties, are critical in determining the
convective and conductive surface areas between nodes. The
principle means of heat transfer throughout the stack is con-
duction through the solid materials and must be determined
as accurately as possible.
Simulating a specific FC/GT hybrid for a design study and sim-
ulating a generic FC/GT hybrid for dynamics and control studies
requires different parameter specifications. Designing a scalable
model based upon several dimensionless parameters leads to
robustness and versatility. Flexibility and scalability can be used
to simulate any existing or future system, employing one of four
design methods: (1) sizing the turbomachinery to meet the air
flow needs of a given fuel cell system, (2) sizing the FC system to
integrate smoothly with an existing turbine, (3) scaling both fuel
cell and turbine to meet a desired system output, or (4) modifying
operating conditions, simulating off-design performance, to inte-
grate a fully specified FC and gas turbine combination. To achieve
high efficiency and robust performance using the final method
requires the two primary systems to be extremely well suited for
each other. Some flexibility in the operating conditions, heat
exchangers, recirculation, and bypass loops allows integration of
Contributed by the Advanced Energy Systems Division of ASME for publication
in the JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY. Manuscript received
February 25, 2013; final manuscript received April 16, 2013; published online June
17, 2013. Editor: Nigel M. Sammes.
Journal of Fuel Cell Science and Technology AUGUST 2013, Vol. 10 / 041005-1
Copyright V
C2013 by ASME
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some existing off-the-shelf technologies to function well in a
hybrid FC/GT, but achieving ultrahigh efficiency typically
requires specific design attention to both the FC and GT compo-
nents. The methodology developed for this study can apply to any
of the above design scenarios; results presented will focus upon a
completely flexible design of the components, because this pro-
vides a fair basis of comparison and requires only a specification
of power output. The process used in the current work is as
follows:
(1) Specify the FC type, physical dimensions, geometry, and
electrochemical properties. These parameters can be cali-
brated to an existing physical system or taken from the lit-
erature and are then held constant throughout the design
process.
(2) Simulate the fuel cell by specifying four of the following
eight conditions and solving for the remaining four under
steady operating conditions: air flow; fuel flow; cell power;
voltage; inlet temperature; average temperature; tempera-
ture gradient; and fuel utilization. The method chosen was
to specify power, average temperature, temperature gradi-
ent, and fuel utilization and then determine the remaining
operating and outlet conditions. These four were chosen for
the likelihood of being reported as a common comparison
basis by manufacturers as performance features or operat-
ing constraints.
(3) Simulate the balance of plant components using the outlet
conditions specified by the fuel cell simulation. Depending
upon the precise hybrid configuration, different design pa-
rameters will be available for modification. In the current
system configuration studied, five of the following ten pa-
rameters must be specified: net system power; FC stack
size; GT mass flow; FC air flow; FC inlet temp; recircula-
tion; pre/postcombustor fuel; fuel/air preheater size; and
turbine inlet temperature (TIT). The five design parameters
specified were net system power, FC air flow and inlet tem-
perature (from FC simulation), and the amount of addi-
tional fuel supplied to a pre- and post-FC combustor (zero).
(4) Combine the dynamic fuel cell and dynamic balance of
plant components into a single model with the sizing and
operating conditions specified by their respective individual
models, and confirm that the steady-state performance
arrives at the desired operating temperature and power out-
put conditions.
(5) Apply a control strategy to physical inputs, such as valves,
fuel flow, and blowers, to test the dynamic response to per-
turbations, including ambient temperature, fuel chemical
content, and electric load changes.
Steps 2–4 have been repeated for a parametric design study that
yields valuable insights regarding design parameters for consider-
ation when developing hybrid systems. Figure 1specifies the opti-
mization process for specific design parameters. Three distinct
computational models were used to converge to an optimal config-
uration. The parameters shown in Table 1specify the design
point, average operating temperature, operating power density,
voltage, and temperature rise across a single cell. The flexible tur-
bomachinery model can utilize ten different compressor and tur-
bine maps relevant to a variety of turbine designs: radial or axial
and single or multispool. Generic performance maps of mass flow
rate, pressure, shaft speed, and efficiency are employed, but cali-
bration to manufacturer data is possible. Figure 2shows an exam-
ple single spool, axial, compressor, and turbine map operating
near its design point.
2 Background
The primary synergy of an FC/GT hybrid is that the FC waste
heat drives the gas turbine, which in turn supplies the air flow nec-
essary for stack cooling plus additional electricity. The effective-
ness of hybridizing an electrochemical device with a heat engine
relies on a precise balance between heat generation and exchange
with electric power production. The primary components must be
sized appropriately for the specific cycle configuration and operat-
ing conditions. The tradeoffs in system efficiency, cost, complex-
ity, and robustness must be carefully balanced in the design phase.
Fig. 1 Hybrid design methodology
Fig. 2 Empirical compressor and turbine maps
041005-2 / Vol. 10, AUGUST 2013 Transactions of the ASME
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Varying the cell dimensions, stack size, operating pressure, fuel
utilization, and a host of other parameters can potentially improve
integration [12]. A key difference in hybrid technology compared
to stand-alone FC systems is that the optimal fuel utilization may
be substantially lower, due to the ability to convert a portion of
the generated heat into electricity through the turbomachinery. In
addition, the desired system operating temperatures may differ
due to the potential of using an established temperature difference
to drive the heat engine [4]. In a hybrid FC/GT, additional fuel
can reduce fuel cell losses while providing thermal input to the
turbine [13].
Investigations of integrated FC/GT hybrid system dynamics
have been ongoing at the National Fuel Cell Research Center
(NFCRC) for over 10 years. Early collaborative work with the
National Energy Technology Laboratory determined that creative
control strategies would be required to protect sensitive equipment
during perturbations. This initial work included carbonate fuel
cell models previously validated on the ability to simulate internal
reformation of methane [14]. Each laboratory independently
developed individual models and control strategies.
Recent work extended previous capabilities with simulation of
a variable speed compressor. This allowed for an additional con-
trol input for maintaining cathode inlet temperature that both lab
models showed decreasing in the previous work [15,16]. The
results presented in this study showed improvements in the con-
trollability of the stack temperature. It was noted that the load
shed resulted in a lower fuel cell power, lower GT power, and
slightly higher efficiency.
Despite excellent efficiency and emissions specifications, the
market success of FC/GT systems is limited by high capital costs.
Niche applications, such as natural gas pipeline pressure reduction
stations, present possible market entry points for high-temperature
fuel cell systems [17]. Most solid oxide fuel cell-gas turbine
(SOFC-GT) hybrid systems demonstrated to-date have operated in
a very narrow range suited to maintain steady fuel cell tempera-
ture and operation while minimizing dynamics and degradation
[1,3,10,18]. Burbank et al. [19] introduce two additional degrees
of control by utilizing a variable-geometry nozzle turbine and an
auxiliary combustor that can provide additional heat to the turbine
inlet stream. This new system configuration allows for a system-
wide turndown ratio of 5:1, meaning the system can safely operate
at 20% of its rated power production capacity [19]. No bypass or
bleed flow paths were needed to accomplish this turndown. The
system performs best, 63% efficient, at 30% power and operates
at 53% efficiency at full power.
Higher level analyses have also sought to characterize off-
design performance of hybrid systems. System level analysis is
capable of determining a suite of operating conditions that can be
plotted into performance maps, characterizing the system under
off-design conditions [20].
The world’s first pressurized SOFC-GT hybrid prototype was
tested at the University of California, Irvine. A Siemens–
Westinghouse tubular fuel cell system producing 180 kWe was
paired with a 75-kW Ingersoll–Rand gas turbine. The resulting
hybrid system was capable of producing up to 220 kW during its
2900 h of testing at the NFCRC. The data gathered validated mod-
eling approaches developed at the NFCRC [18]. The system
achieved fuel-to-electricity conversion efficiencies of 53%.
The use of FC-GT hybrids is not limited solely to terrestrial
power generation applications. Interest has arisen from the aero-
space industry for an efficient power generation device to meet
the increasing electrical demands of commercial aircraft and
unmanned aerial vehicles. NASA and the NFCRC collaborated to
model different configurations of the SOFC-GT system that would
be suitable for aerospace applications [21].
The SOFC-GT cycles investigated in this detailed design analy-
sis work are only a few of the many configurations that have been
proposed. A similar design with an intercooled gas turbine was
previously studied at the NFCRC [12]. The simulation was con-
ducted for a steady-state optimization by varying the pressure,
moisture content, excess cathode air, and ratio of low-pressure to
high-pressure compressors. The study determined optimal condi-
tions that produced 75% electrical efficiency based on LHV of
natural gas with 55% excess air. The authors were able to con-
clude that higher operating pressures increase efficiency at the
expense of additional development cost [12].
The current study differs significantly from previous hybrid FC/
GT design studies, in that it fully considers the impacts of seven
major design parameters on performance and optimizes the bal-
ance of plant integration with each specified fuel cell operating
condition. Internal fuel cell temperature, current, and species dis-
tributions allow for consideration of additional heat transfer path-
ways between the fuel cell and cathode air stream. A fully
dynamic turbomachinery model capable of resolving off-design
performance and mass flow determines the turbomachinery
response to different inlet temperatures and flow rates. A detailed
physical heat exchanger model is scaled to achieve optimal ther-
mal integration of the fuel cell and turbine in the specified hybrid
configuration. The detailed physical description of each compo-
nent justifies the predicted direct and indirect impact each opera-
tional specification has on net system performance.
3 Model Development
Many FC/GT hybrid configurations have been proposed. This
work focuses on one of the most promising designs for high effi-
ciency, controllability, and fuel flexibility. The use of ceramic
SOFC technology permits the design of a pressurized topping
cycle, as shown in Fig. 3, due to the high temperature, solid state,
and oxygen ion conduction nature of the technology. This cycle
configuration was chosen based upon its simplicity, performance,
and controllability. The current analysis, which focuses on the
design aspects of the FC/GT hybrid system, utilizes a set of fully
dynamic, spatially discretized, physical models. These models
have been developed for simulation of experimental test data, con-
trol studies, and off-design analysis and comprise a set of ten indi-
vidual component models for the following: compressor; turbine;
shaft; fuel cell; heat exchangers; blower; oxidizer; plenum and
mixing volumes; external reformer; and control valves. This sec-
tion presents the assumptions and high-level derivation; precise
programming details are proprietary. The components can repre-
sent a variety of different FC/GT cycles by integrating in a variety
of configurations. A methodology for determining the size of each
device for a given set of operating conditions was developed and
used to parametrically compare the rated performance of the
specified cycle under eight changing parameters. It was deter-
mined that nine system parameters could be used to completely
specify the outputs and state points of the SOFC-GT topping con-
figuration. A fixed system power output provided a basis for sensi-
tivity analysis of design and operating conditions. The 100-MW
scale was selected for the application of ultrahigh efficiency
power generation from coal in an advanced integrated gasification
Table 1 Fuel cell operating requirements
Fuel cell type SOFC
Operating power density 100–700 (mW/cm
2
)
Average operating temperature 700–850 C
Limiting stack temperature rise 50–100 C
Table 2 Fuel heating values
Lower heating value (LHV) Higher heating value
Fuel (kJ/kmol) (kJ/kmol)
CH
4
802,952 890,835
H
2
240,424 284,469
CO 305,200 305,200
Journal of Fuel Cell Science and Technology AUGUST 2013, Vol. 10 / 041005-3
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fuel cell–gas turbine plant, producing a hydrogen-rich syngas for
utilization in a 100-MW FC/GT power block. A brief discussion
of each system component is now presented.
A spatially and temporally resolved fuel cell model has been
developed using the MATLAB-SIMULINK
V
R
interface. The model is
derived from first principles and incorporates the necessary
physics, chemistry, and electrochemistry for both molten carbon-
ate fuel cell (MCFC) and SOFC simulations. The model also
includes a novel approach to simplified simulation and analysis of
3D geometries, while capturing the thermal coupling between
stack and air and fuel-flow manifolding. Internal, indirect internal,
and external reforming are all considered with Fuel Cell Energy’s
Direct Fuel Cell
V
R
(DFC), providing the basis for indirect internal
reforming with a specialized reformer cell between each ten active
cells. A generic planar cross- and counterflow geometry permits
scalability and applicability to cell and stack designs present in
industry practice. Further details of this novel high temperature
FC model are presented in previous publications [22].
A dynamic compressor and turbine model developed solely for
this work utilizes dynamic conservation equations and industry
standard performance maps. The approach solves a dynamic tor-
que balance equation for the shaft and includes back-pressure cal-
culations and internal mass storage. Compressor and turbine
performance characteristics from steady-state performance and ef-
ficiency maps describe design and off-design behavior. Shaft
speed, pressure ratio, and flow rate are normalized using the fol-
lowing equations:
NRPM ¼RPM ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
T0=Tdes
pRPMdes (1)
NFlow ¼Flow
Flowdes
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
T0=Tdes
p
Pin=Pdes
(2)
PR ¼Pout Pdes
Pin PRdes
(3)
Despite physical similarities, the compressor and turbine mod-
els require different solution strategies. The compressor model
inputs include ambient conditions, shaft speed, and an outlet pres-
sure calculated from the downstream exhaust. Conservation of
energy applies to solid and gaseous control volumes of both turbo-
machinery devices. Equations (8) and (9) present the control vol-
ume approach, with the subscripts s,f, and arepresenting the
solid, fluid, and ambient conditions, and h
c
is an approximate con-
vective heat transfer coefficient. All sensible enthalpies, h, are cal-
culated using five-parameter temperature curve fits, and isentropic
efficiency is determined by a look-up table, specifying the pres-
sure ratio, normalized shaft speed, and normalized flow rate,
dTf
dt ¼
_
Wþh_
nðÞ
inout þhcAT
sTf
Cp
Pout8
RUTflow
(4)
dTs
dt ¼hcAT
fTs
þerAT
4
aT4
s
cpm(5)
_
W¼_
nout
hisen hin
gisen
(6)
The simulated turbine inputs are temperature, concentration,
and flow rate as well as ambient exhaust pressure. A numerical
solver uses empirical performance maps to calculate turbine inlet
pressure, outlet temperature, and power produced. Due to the format
of the normalized flow tables, the system model requires an iterative
approach to find the inlet pressure. The inlet pressure determines
pressure ratio, and separate look-up tables use that value to specify
a nondimensionalized mass flow rate. If the calculated mass flow
rate from the turbine exceeds that of the compressor, the pressure
decreases until equilibrium (steady operation) is reached; similarly,
an excess of mass exiting the compressor will build pressure until
the turbine can match the flow rate or a surge event occurs.
The plenum volume method treats the gaseous volume of each
component as a pressure vessel, increasing in pressure when
excess mass enters and decreasing when excess mass leaves, and
uses the pressure difference between components to determine
mass flow rates. The dynamic continuity expression can be
applied with laminar flow using friction factors, empirical correla-
tions, or maps.
dP
dt ¼_
nin _
nout
ðÞRuTflow out
8turb
(7)
The slightly different equations for shaft power and temperature
apply to the turbine, with g
T
representing the turbine efficiency. The
subscripts s,f,andaspecify the solid, fluid, and ambient conditions.
_
WT¼h_
n
ðÞ
in_
nout hin hin hises
ðÞ
gT
½
(8)
dTf
dt ¼
_
WTþh_
nðÞ
inoutþhcAT
sTf
cPout8turb
RuTout
(9)
dTs
dt ¼hcAT
fTs
þerAT
4
aþT4
s
cpm(10)
Axial and radial turbomachinery operate on single or multiple
concentric shafts to eliminate gearing, mechanical losses, and
failure. This constrains single-shaft devices to the same real
shaft speed, which is either synchronous, operating at multiples
of 60 Hz (50 Hz in Europe), or asynchronous. Both require
Fig. 3 SOFC hybrid cycle diagram
041005-4 / Vol. 10, AUGUST 2013 Transactions of the ASME
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significant electrical hardware to convert mechanical energy to
electricity and prepare for interconnection with a utility grid net-
work. This study employs a simple torque balance shaft model
with appropriate rotational inertia; however, this analysis limits
its scope to fixed shaft speed performance, and thus complete
explanations of the dynamics are omitted.
Hybrid FC/GT system configurations often require high-
temperature heat exchangers manufactured from stainless steel
and/or ceramics. A quasi-2D heat exchanger model is constructed
that discretizes the heat exchanger length into ten control vol-
umes, each comprising a hot gas, solid, and cold gas volume. This
method develops a spatial temperature profile and avoids effec-
tiveness limitations of bulk models. Total surface area, adjusted
by varying the number of plates, determines the heat transfer rate
and net effectiveness. This method approximates the required heat
exchanger surface area and neglects complex geometric considera-
tions of some heat exchanger designs in favor of computational effi-
ciency to enable dynamic simulation. Conservation of energy
analysis for the heat exchanger model is detailed in Eqs. (11)–(13).
dThot
dt ¼
h_nðÞ
inouthcATin þTout
2Ts
cv8
HXnode C(11)
dTcold
dt ¼
h_
nðÞ
inouthcATin þTout
2Ts
cv8
HXnode C(12)
dTsolid
dt ¼
hcATin þTout
ðÞ
cold
2Ts
hcATin þTout
ðÞ
hot
2Ts
kcAT
nþ1þTn12Ts
ðÞ=Lnode
2
6
6
6
6
4
3
7
7
7
7
5
cv8
HXsolid q
(13)
An oxidizer or combustor combines the anode and cathode off-
gas to react the remaining fuel. A successful hybrid FC/GT design
maximizes the use of heat generated by the FC stack and by the
combustion of anode off-gas to drive the turbine, power the com-
pressor, and produce additional electricity. A combustor can also
be fired with additional fuel, and some designs use a combustor to
increase turbine inlet temperature, control the system, and/or
dynamically increase system output. This typically reduces system
efficiency and should be limited to start-up and shut-down proce-
dures, if high efficiency is important. The mixing of anode and
cathode off-gas in the oxidizer is expressed in Eqs. (14) and (15).
_
nout ¼Xþ_
nXi
ðÞ
fuelþ_
nXi
ðÞ
off
(14)
xout;i¼_
nXi
ðÞ
airþ_
nXi
ðÞ
fuelþ_
nXi
ðÞ
off
_
nout
(15)
The combustion modeled in this work accounts for the same
seven species as the remainder of the model and considers four
reactions in Eqs. (16)–(19).
methane :CH4þ2O2!2H2OþCO2(16)
carbon monoxide :CO þ1
2O2!CO2(17)
hydrogen :H2þ1
2O2¼H2O(18)
water gas shift :CO þH2O!CO2þH2(19)
Once again, a control volume conservation of energy approach is
employed to balance the energy flowing into the combustor, the
energy flowing out of the combustor, the heat lost to the environment,
and the heat generated by the combustion process. The heat release of
each of the four chemical reactions occurring within the fuel cell and
combustion chamber are calculated from the standard heating rates
presentedinTable2.
dTc
dt ¼
hcATcTamb
ðÞþh_nðÞ
air
þh_
nðÞ
off þh_
nðÞ
fuel
h_nðÞ
outQion transfer
2
43
5
Cp
Pcomb8comb
RUTcomb
(20)
Both MCFC and SOFC hybrid systems may utilize recirculation
and/or bypass flows. The mixing of the primary and recirculated
streams is modeled with a perfectly stirred and nonreacting plenum
volume. Continuity and conservation of mass account for species flow
rate and determine the exiting composition. Conservation of energy
determines the exit temperature of the mixed gas and accounts for am-
bient losses with a separate energy balance for the mixing chamber.
_
nmix ¼X_
nXi
ðÞ
1þ_
nXi
ðÞ
2
(21)
Xmix;i¼_
nXi
ðÞ
1þ_
nXi
ðÞ
2
_
nmix
(22)
dTmix
dt ¼
hcATmix Tpipe
þh_
nðÞ
1þh_
nðÞ
2h_
nðÞ
mix
cp
Pmixer8mixer
RUTmix
(23)
A blower operates similar to a compressor, often with signifi-
cantly lower pressure rise. The current analysis treats the blower
as a compressor with fixed isentropic efficiency and calculates the
parasitic power consumed by the blower for any particular operat-
ing condition. Cathode exhaust recirculation is simulated, with an
analysis accounting for energy lost to inefficiencies and cooling.
Here, the subscript re defines the recirculated gas stream, and
once again, sand arepresent the solid and ambient conditions.
The blower power is calculated using the following energy bal-
ance, wherein the sensible enthalpy under isentropic conditions,
h
isen
, is found as a function of the isentropic temperature:
dTre
dt ¼
_
WBþh_
nðÞ
inout þhcAT
sTre
ðÞ
Cp
Pout8
RUTre
(24)
dTs
dt ¼hcAT
re Ts
ðÞþerAT
4
aT4
s
cpm(25)
_
WB¼_
nout
hisen hin
gisen
(26)
Tisen ¼Pout
Pin
c1=c
(27)
Electrical power is generated in the FC, the turbine generator, and
a steam bottoming cycle generator, if a bottoming cycle is
employed. Similarly, fuel may be provided to the system at different
points: an air preheater, reformer, FC, or post-FC combustor. All
sources must be accounted for when calculating the net power and
efficiency of the system. The system efficiency is found using
known heating values for the fuel, multiplying by the fuel flow rates,
and dividing the net power produced by this quantity as follows:
_
WNet ¼_
WTurbGen þ_
WFC þ_
WSteamGen (28)
gcyc ¼
_
WNet
_
nfuelHVfuel
(29)
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4 Steady-State Design Performance Results
A parametric study is conducted for seven design parameters
that span the range of the available technology for SOFC and tur-
bine technology. These parameters can often be found on manu-
facturer specifications sheets (power density, utilization,
compression ratio, or operating temperature) or derived from the
specified state points (temperature gradient or compressor/turbine
efficiency). The seven design parameters are:
(1) temperature differences across the fuel cell stack
(2) fuel cell operating power density
(3) fuel cell fuel utilization
(4) fuel cell stack air preheating
(5) peak compressor/turbine efficiency
(6) system operating pressure
(7) fuel cell trilayer average operating temperature
An important design feature of the SOFC topping cycle studied
is the size of the air preheater. A larger heater reduces the amount
of cathode recirculation, which increases efficiency, but lowers
the turbine inlet temperature (TIT), which reduces system effi-
ciency. The combined effects of these design parameter choices
depend upon the part-load efficiency of both the blower and tur-
bine. Use of a heat exchanger with a bypass loop at this point of
the cycle allows for substantial controllability. The heater bypass
generates increased air flow at constant temperature by cooling
the heater exhaust and relying upon additional recirculation heat-
ing of the cathode inlet stream. Table 3presents a comparison of
design operation with different heater sizes for 80% fuel utiliza-
tion, 200 C temperature rise across the stack, and a power den-
sity of 500 mW/cm
2
. The 200 C heater represents the baseline
design, to which subsequent figures have been normalized.
4.1 Stack Temperature Rise. Stack temperature gradient
and overall temperature rise plays a determining role in system ef-
ficiency and fuel cell durability. Manufacturers often specify a
maximum thermal stress sustainable by the system to be met at
design and during off-design performance. Intuitively, a greater
temperature rise across the stack requires less air flow and thus
smaller turbomachinery, resulting in higher system efficiency.
The model supports this but to a lesser extent than expected.
Figure 4presents the results of this sensitivity analysis. Thirteen
important design variables are evaluated as either better or worse
than the baseline system design. For some features, higher values
indicate a better design, efficiency, voltage, compressor size, tur-
bine % power, stack power, generator power, and TIT; for others,
a lower value is an improvement, recirculation, blower power,
stack and heat exchanger sizes, and trilayer (sometimes called
PEN for positive electrode, electrolyte, negative electrode) tem-
perature gradient. Each variable has been scaled to its maximum
deviation from the mean value in the sensitivity analysis, thus
allowing sensitivity comparisons among all of the design
parameters.
Reducing the temperature gradient across the cell 50 C reduces
efficiency 1.2%, but may substantially improve system durability
and lifespan. The lower than anticipated reduction in efficiency is
due to the additional cathode preheat effectiveness, which cap-
tures more exhaust heat from a lower temperature turbine exhaust
to reach the same pre-recirculation temperature. This additional
heat capture offsets the negative impact of a larger turbine and
additional recirculation necessary to achieve a 30% increase in
airflow. A 25% increase in recirculation reduces the additional air-
flow requirement on the turbomachinery to less than 10%. One
could not capture this design impact without the detailed mani-
folding heat transfer model that is able to accurately correlate in-
ternal temperature distributions, air flow rates, and inlet and
exhaust states of the cathode stream. The additional recirculation
reduces the oxygen concentration and increases the blower para-
sitic, both contributing to the slight reduction in system efficiency.
The efficiency loss is doubled an additional 2.4% for a further 50
C reduction in cell-temperature gradient.
4.2 Fuel Cell Operational Power Density. The second oper-
ating condition studied was fuel cell power density. Variations in
operating power density present a clear trade-off between cost and
efficiency. Fuel cells operate closest to their ideal efficiency at low
power densities, but cost per kW of capacity is inversely propor-
tional to power density. Stand-alone fuel cell systems exhibit
efficiency behavior closely mirroring the polarization curve and are
typically designed to operate at power densities that balance effi-
ciency with power production or cost. A hybrid system, however,
has the luxury of capturing a portion of the fuel cell-generated heat,
thereby reducing the negative impact of operating at higher power
densities. The balance of efficiency and power production (cost) in
a hybrid system should thus tilt towards higher power density oper-
ation than that one would chose for the same fuel cell operated in a
stand-alone system. Additionally, operating at high pressure per-
mits even higher power densities with the same electrochemical
loss and heat generation. The impact of increasing or decreasing
the fuel cell power density is shown in Fig. 5.
Figure 5affirms that lower operating power densities result in
higher efficiencies; however, the change is less for a hybrid sys-
tem than for the FC itself. The operating voltage is directly pro-
portional to FC efficiency and exhibits a greater differential drop
with increasing power density than the hybrid system efficiency.
Reducing power density from 600 mW/cm
2
to 200 mW/cm
2
increased efficiency from 63% to 70% LHV, yet required a three-
fold increase in stack size to achieve the same system power. An
interesting attribute of FC technology is the capability to achieve
higher efficiencies at reduced power. This holds true for the
hybrid system as well, and dynamic studies indicate a greater
Table 3 Initial design results
Air preheat 0 C 100 C 200 C
Voltage Volts 0.855 0.863 0.866
DT trilayer K 101.7 100.4 96.8
Stack size Cells 306,400 303,700 302,200
Stack power MW 84.1 83.5 83.4
Gen power MW 16.6 17.1 17.0
Blower power MW 0.70 0.55 0.40
Efficiency % 65.0 66.1 66.4
Comp size kg/s 74.4 87.7 107.2
Turbine % % 16.5 17.0 17.0
Air heater Plates 0 891 2762
Fuel heater Plates 1042 1898 2270
Turbine inlet K 1332 1220 1095
Recirculation % 64.09 55.54 42.28
Peak temp K 1072 1072 1071
Cath outlet K 1061 1061 1061
Fig. 4 Design impact of stack temperature profile
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capability to load follow compared to a stand-alone fuel cell sys-
tem. This off-design behavior is superior to most electrical-
generating technologies that often exhibit steep performance
drops when operating at reduced output.
Figure 5shows an inverse relationship between voltage and
compressor size and a positive relationship between voltage and
trilayer temperature gradient. This indicates that the higher FC ef-
ficiency (i.e., higher voltage) reduces air flow requirements and
necessitates a smaller turbine. Similarly, the higher voltage gener-
ates less heat, causing lower temperature rise across the cell. Inter-
estingly, the TIT rises at lower power density. The same amount
of anode off-gas oxidizes with less air flow, producing higher tem-
peratures (and lower mass flow) entering the turbine.
4.3 Fuel Cell Operational Fuel Utilization. The next operat-
ing condition investigated was fuel utilization. Other authors have
hypothesized that operating at reduced fuel utilization in the fuel
cell would increase the turbine inlet temperature and produce more
energy from the turbomachinery. Despite the fact that the fuel is
underutilized in the more efficient of the two devices, the fuel cell,
these authors argue that the benefits to the stack voltage and TIT
outweigh the efficiency penalty of reduced fuel utilization [23,24].
The results presented in Fig. 6show a steep decline in system
performance, from 67% to 52% LHV, with decreasing fuel utiliza-
tion. This system efficiency decline occurs despite the rise in fuel
cell operating voltage and TIT, as others have predicted. Operat-
ing this hybrid cycle at reduced fuel utilizations does provide
some interesting side benefits. The stack size is reduced due to the
greater amount of power derived from the turbine generator, the
compressor size and trilayer temperature gradient are reduced due
to the higher operating voltage, the parasitic blower power is
reduced due to the reduction in cathode air flow, and the fuel
heater size is reduced due to the higher TIT at which heat is
exchanged. It is expected that, for a particular configuration of FC
and GT, where the turbine was slightly oversized, reduced fuel
utilization could be beneficial to supply sufficient thermal energy
to the turbine; however, in an optimized design, the higher effi-
ciency component, the FC, should be designed to generate the
maximum amount of power possible from the supplied fuel, as
shown in Fig. 6.
4.4 FC Air Preheat. The performance of a thermodynamic
cycle can often be improved with heat recuperation. Advanced
Brayton cycles employ intercooling and staged compression,
with large and efficient heat exchangers recovering the heat for
use elsewhere in the cycle. Applying a recuperative heat
exchanger to the SOFC-GT hybrid allows use of post-combustor
or post-turbine exhaust gases to preheat cathode inlet air. This
reduces the cathode recirculation required, raising oxygen con-
centrations and improving system efficiency. The design analysis
demonstrated little benefit from heat recuperation of the combus-
tor exhaust, which is unexpected but indicative of the design,
which already captures combustor exhaust heat in the turbine.
Analysis identifies an improvement from 65% to 66% LHV with
200 C of preheating rather than none. Reduced recirculation
increases required turbomachinery size, while lower turbine inlet
temperature reduces efficiency. Thus, despite the obvious
improvements in parasitic load and oxygen concentration, the
net system output remains quite similar for the case of adding
recuperation to the design.
Figure 7would seem to indicate the inclusion of an air pre-
heater provides little benefit to the system performance and should
not be part of the design. However, the inclusion of an air
preheater allows for an additional bypass loop. Bypassing the air
preheater serves to cool the cathode inlet air stream, requiring
additional recirculation to preheat the air. This boosts the air flow
rate, providing more cooling to the fuel cell stack when necessary.
Even a well-designed system will require additional cooling under
instances of increased ambient temperature, decreased ambient
pressure, and some fuel perturbations. In addition, including a
heat exchanger and bypass valve allows independent control of
inlet temperature and flow rate, which is often required for control
purposes. Finally, such a design may also provide required flexi-
bility for coping with long-term cell degradation.
4.5 System Pressure. Table 3and the Fig. 7show air preheat
positively affects system efficiency, if only minimally. Air preheat
can be achieved through heat exchange with fuel cell off-gas or
by additional compression. This provides motivation for operating
a hybrid system at higher pressures. Raising system pressure from
5 atm to 10 atm yields significant improvement in fuel-to-electric-
ity conversion performance from 65% to 69% LHV. Operating at
8 atm rather than 5 atm raises efficiency to 68% and may be more
Fig. 6 Design impact of stack fuel utilization Fig. 7 Design impact of air preheating
Fig. 5 Design impact of stack power density
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feasible in the near term than 10 atm. The voltage gains and
reduced blower power requirements shown in Fig. 8are largely
responsible for these improvements.
4.6 Turbine Efficiency. Proper sizing of the two major com-
ponents is a key factor in integrating a fuel cell and gas turbine.
The previous analyses showed fuel cell operating voltage and
efficiency produced large variations in optimal compressor size.
Efficiency of the turbomachinery also impacts performance and
the relative sizing of the two primary components. The peak effi-
ciency for the characteristic map is investigated between 70% and
100%, with most real turbines operating between 85% and 95%
efficiency.
The turbomachinery only produces 15% of the net power of a
hybrid, but Fig. 9demonstrates the large impact of turbine effi-
ciency on overall system performance. A significant portion of
turbine power drives the compressor, operating at a fixed load.
Thus, a 10% reduction in turbine power reduces net gas turbine
power by 25% and overall hybrid system power by 4%. Net tur-
bine power diminishes quickly as the turbine operating point shifts
away from the high-efficiency island of the performance map.
This sensitivity highlights the importance of matching the turbine
to the fuel cell, since an oversized turbine will operate well below
peak efficiency.
Compressor efficiency is also highly dependent upon the oper-
ating position of the turbomachinery and thus can compound the
impact of an improperly sized system. The effect of diminishing
compressor efficiency does not impact system performance as
greatly as turbine efficiency (see Fig. 10). Since the air flow
passes through at a lower temperature in the compressor, ineffi-
ciencies of compression do not produce the same amount of
energy loss as in the turbine. However, by looking at the generic
axial compressor map, one might suppose efficiency drops off
quicker when operation moves away from the compressor design
point, resulting in similar system losses during off-design
operation.
4.7 Fuel Cell Operational Temperature. Average fuel cell
operating temperature was the final design consideration investi-
gated in this parametric sensitivity study (Fig. 11). The overpoten-
tial parameters used in this study, particularly Ohmic losses, are
sensitive to operating temperature. The resulting higher voltage at
higher temperatures improves system performance by lowering
cooling demands, shrinking the necessary turbomachinery, and
thereby increasing the portion of power produced in the fuel cell.
Heater size requirements are reduced, since heat transfer is more
effective at the higher cathode exhaust temperatures. The hotter
exhaust and smaller heat exchangers result in an increased TIT,
thereby improving the turbomachinery efficiency as well.
Increased fuel cell operational temperature primarily reduces the
area-specific resistance and increases cell degradation. The cur-
rent results suggest that, if two fuel cell systems are capable of
similar performance and lifespan, the higher temperature system
is more amenable to hybridization. This is one of several reasons
why high temperature SOFC technology should be pursued for
this application over the slightly lower temperature molten car-
bonate technology.
5 Observed Trends
Choosing a design point for a FC/GT hybrid represents a
complex trade-off between cost and performance. Additionally,
individual components may have different performance character-
istics when integrated into any particular hybrid configuration.
Figure 12 presents the performance impact each independently
studied parameter has on total system performance. Each colored
Fig. 8 Design impact of system pressure
Fig. 9 Design impact of turbine efficiency
Fig. 10 Design impact of compressor efficiency
Fig. 11 Design impact of average cell temperature
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arrow represents the variation of a single parameter within
the range of values outlined previously. This chart seeks to illus-
trate the relative impact of each design parameter on complete
system performance. Figure 12 illustrates that power density and
average trilayer temperature affect both voltage and efficiency,
where compressor and turbine efficiencies affect only system effi-
ciency. What is interesting about this chart is that the typically
direct relationship between voltage and system efficiency in a FC
device is skewed by the impact on the integrated system, particu-
larly for fuel utilization and system pressure. Combining the
effects of changing several system parameters may be used to
achieve optimum configurations for cost, efficiency, or durability.
The curvature of each arrow implies nonlinearity in the applica-
tion of each design choice; however, the trends toward increasing
efficiency, voltage, recirculation, or turbine power fraction (as
will be seen in the next figures) will remain fixed. The combined
manipulation of multiple design parameters may exhibit interact-
ing benefits that may compound or contradict the trends, as shown
in Figs. 12–14.
Turbomachinery efficiencies of the compressor and turbine
have little to no effect on voltage but a small effect on system effi-
ciency. Figure 12 also shows the larger impact that turbine effi-
ciency has on performance. This impact is due to the fact that the
power production in the turbine is much greater than consumption
in the compressor, and thus, 10% of additional losses in the tur-
bine accounts for a greater total system energy loss than 10%
losses in the compressor. This may be important when selecting
turbomachinery that will operate at off-design conditions, noting
that it will be more important to maintain the expander near its
highest rated efficiency.
Figure 13 illustrates the relative impact each design considera-
tion has on the necessary amount of cathode recirculation, assum-
ing a recuperating heat exchanger is not used, and the portion of
total power provided by the gas turbine. This relationship is im-
portant at the design stage for appropriately sizing the turbine and
blower or designing an ejector. The amount of cathode recircula-
tion will also largely determine the margin of controllability of
the inlet temperature when using a variable air flow-rate turbine.
Interestingly, Fig. 13 illustrates a decoupled behavior, meaning
that some design choices affect primarily the amount of recircula-
tion, while others affect the portion of power derived from the tur-
bine. Increasing power density and decreasing fuel utilization
both raise the turbine inlet temperature, having a similar effect as
increasing turbine efficiency. Increasing the temperature rise
across the FC reduces air flow and preheating needs that were
accomplished through cathode recirculation. The excess energy
given off by the FC remains nearly constant; therefore, the turbine
output is unaffected. Operating temperature provides an interest-
ing exception, which impacts both recirculation and turbine output
by requiring additional preheating through recirculation and pro-
viding less energy to the turbine, due to reduced Ohmic losses.
Recirculation controls the air flow rate and temperature of the
cathode. A change in stack temperature gradient requires a change
in recirculation only and minimally affects turbine size and power.
A system change that reduces FC efficiency typically increases
turbine output through additional heat generation that becomes
available to the turbine. Examples of this include increases in
power density and fuel utilization and decreases in average oper-
ating temperature. Optimally sizing the turbomachinery for the
hybrid application is extremely important, but the relationship
between turbine size and fuel cell size is complicated. A slightly
oversized turbine can be throttled back to achieve a near optimal
design, but a subscale turbine cannot provide the air flow neces-
sary to meet the stack requirements.
It is therefore clear from Fig. 14 that the turbine should be
expected to output nearly 20% of the rated power of the FC stack.
A compatible turbine must match the flow rate, inlet temperature,
and power output specified by the hybrid configuration and the
nominal fuel cell output. Precisely matching all three conditions is
unlikely. Thus, the turbine will typically operate off-design, either
by derating pressure, turbine inlet temperature, or both. The tur-
bine selected for hybridization should be sized to provide at least
120% of the air flow required by the FC, less any recirculation.
This will often correspond to a low-pressure turbine nominally
producing 20% of the rated fuel cell output. Reaching the speci-
fied turbine inlet temperature can be achieved with additional
post-FC oxidation, but the turbine should nominally be rated for
200 C greater than the operating temperature of the fuel cell.
Figure 14 illustrates two seemingly contradictory trends toward
improving system efficiency. Those design features that would
improve the turbine efficiency will improve system efficiency as
well as the portion of power contributed by the turbine. Those sys-
tem parameters that increase the FC efficiency will decrease the
energy available to the expander and thus decrease the turbine
Fig. 12 Voltage and efficiency as dependent variables
Fig. 13 Recirculation and turbine % power as dependent
variables
Fig. 14 System efficiency and turbine % power as dependent
variables
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contribution while increasing system efficiency. To achieve opti-
mal efficiency, the higher efficiency device, the FC, should con-
tribute the greatest to the system output. This does not imply that
using a smaller compressor will make a hybrid system perform
better; often this would cause the hybrid to fail completely. What
this trend implies is that designing a system that requires less air
flow, and therefore a smaller compressor, implies an increase in
FC efficiency. From a capital cost perspective, the turbomachinery
will be cheaper, per kW, than the FC stack and related compo-
nents, and therefore, designs maximizing the power from the tur-
bine will likely reduce the initial system cost.
6 Conclusions
The primary considerations when designing a hybrid FC/GT
system are stack-power density, operating temperature, stack tem-
perature rise, system pressure, fuel utilization, and the relative
size of the turbomachinery. These design selections and the FC
structure and material set, determine the operating voltage and
therefore the operating efficiency of the FC. These decisions, in
turn, determine the air-flow requirements and heat available to
drive the turbomachinery, with the difference in preheating and
air flow provided by the cathode recirculation. High voltage, typi-
cally achieved by operating at low power density, resulted in the
highest achievable system efficiency but the largest necessary FC
stack size. Higher system pressure improves voltage and effi-
ciency but requires sturdier components and applies mainly to
large systems utilizing axial flow turbomachinery. Typical axial
turbines are designed for high-pressure ratios, but utilization of
the low pressure spool only could produce system pressures ame-
nable to SOFC integration. System pressures between 4 and 8
atmospheres would bring the design within the operating regime
of existing hardware. Higher fuel utilization actually has a nega-
tive impact on fuel cell voltage for the configurations considered
here but improves system performance by employing more fuel in
the electrochemical reactions. It is important to note that the effi-
ciency penalty associated with reduced fuel utilization is less in a
hybrid system than in a stand-alone FC system. It is extremely
likely that the optimal operating condition for a specific FC stack
will be at lower fuel utilization when hybridized with a gas tur-
bine. The side benefits of lower fuel utilization include reduced
degradation effects, less chance of fuel starvation, more even spa-
tial current and temperature distributions in the stack, and greater
dynamic operating flexibility. Higher operating temperatures
reduce ionic resistance, increase the turbine inlet temperature
closer to nominal conditions, and raise overall hybrid system effi-
ciency. The drawbacks of high temperature operation include
accelerated voltage degradation and the requirement of potentially
exotic interconnect and sealant materials. An optimal system may
be able to achieve ultrahigh fuel-to-electricity conversion effi-
ciency but fall short of economic viability. The fuel cell stack rep-
resents the single largest capital cost, so that minimizing the stack
size requirement reduces cost significantly. Achieving size reduc-
tions primarily occurs by raising power density. In the current
study, increasing power density from 400 to 500 mW/cm
2
reduces
the stack size by 25%, with only a 2.6% efficiency penalty. Elimi-
nating the air preheating heat exchanger reduces the cost signifi-
cantly but may diminish the ability to sufficiently control stack
operating temperature. Replacing air preheating with additional
compression heating raises efficiency if the fuel cell can safely
handle the pressure without cracking. Increased pressure improves
power density, allowing for additional trade-offs between efficiency
and reducing stack size even further. Optimizing the system with
cost-minded design choices can produce a highly efficient (65%
LHV or better) system with a substantially higher specific power
output than a stand-alone FC system.
Acknowledgment
The authors thank the U.S. Department of Defense Fuel Cell
Program and Mr. Frank Holcomb of the Construction Engineering
Research Laboratory of the Engineer Research and Development
Center for partial support of the current work under contract num-
ber W9132T-08-C-0003.
Nomenclature
A¼area
C¼thermal capacitance
C
p,v
¼specific heat (constant pressure, constant volume)
Flow ¼turbomachinery flow rate
h¼enthalpy
h
c
¼convection coefficient
k
c
¼conduction coefficient
m¼mass
M¼Mach number
N¼normalized turbomachinery parameter
P¼pressure
PR ¼pressure ratio
Q¼sensible enthalpy of ions
RPM ¼shaft speed
R
u
¼universal gas constant
T¼temperature
V¼velocity
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