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Simulations of a flexible 100 kWel PEM Fuel Cell power plant for
the provision of grid balancing services
Elena Crespi1 *, Giulio Guandalini1, and Stefano Campanari1
1Department of Energy, Politecnico di Milano, Via Lambruschini 4A, 20156 Milano, Italy
Abstract. The continuous growth of non-programmable renewable energy resources penetration leads to
unpredictable oscillations of the net load faced by dispatchable power plants, hindering the reliability and
stability of the electric grid and requiring additional flexible resources. The EU project GRASSHOPPER
focuses on MW-scale Fuel Cell Power Plant (FCPP) based on low temperature PEM technology. The project
aims to setup and demonstrate a 100 kWel PEM FCPP, flexible in power output and designed to provide grid
support. This work presents a dynamic simulation model of the FCPP, developed to simulate plant flexible
operation and identify the best management strategy, aiming at optimizing the efficiency while reducing the
degradation rate. Cold start up simulations, according to a warm-up procedure limiting stack degradation,
result in a time to operation equal to 26 minutes. A sensitivity analysis is performed to determine which
parameters mostly influence the warm-up duration, showing that it is possible to reduce start-up time
substantially (e.g. down to 3 minutes with component preheating). On the other hand, simulations at variable
load along the entire range of operation (20-100 kWel), according to grid balancing requirements, show that
the plant is able to ramp up and down between the minimum to the maximu m load in about 40 seconds.
1 Introduction
Power generation has experienced in the last years a
continuous growth of renewable energy sources (RES)
penetration, as required to meet the greenhouse gas
emissions reduction targets set by most industrialized
countries [1]. New installations have been mainly based
on non-programmable resources (wind and solar
photovoltaics) whose discontinuous and uncertain
generation profile leads to unpredictable oscillations of
the net load faced by the other dispatchable power
plants, hindering the reliability and stability of the
electric grid. Additional flexible resources are therefore
necessary in the power system, able to rapidly face the
unbalances.
In this framework, the EU project GRASSHOPPER
[1] investigates the use of MW-scale Fuel Cell (FC)
power plants based on low temperature Polymer
Electrolyte Membrane (PEM) technology for the
provision of balancing services to the electric grid.
Indeed, the fast ramp rate and the load following
capability characterising this kind of systems make them
a possible source of flexibility for the provision of grid
ancillary services. The technical feasibility of large
MW-size PEM FC power plants has already been well
demonstrated, for example in the DEMCOPEM-2MW
project (FCH-JU 2015) [3]. GRASSHOPPER project
* Corresponding author: elena.crespi@polimi.it
aims at demonstrating the dynamic operation capability,
realizing the next-generation modular FC Power Plant
(FCPP) unit targeting stationary application in the MW
scale grid stabilization. The project is setting up a 100
kWel PEM FC pilot unit, demonstrating flexibility in
power output to provide grid support. The FCPP design
will be cost-effective, targeting an estimated CAPEX
below 1500 €/kWel (at a yearly production rate of 25
MWel), as required to enter the markets as a competitive
player. Joint development of MEA, stack and system
design is thus a primary focus. The flexible demand-
driven operation will be demonstrated with a gross
power set point range between 20 kWel and 100 kWel
and a ramp-up rate delivering 50 kWel within 20 seconds
and 100 kWel within 60 seconds.
In this work, a dynamic simulation model of the
GRASSHOPPER pilot plant is presented. The model
allows to simulate plant warm-up and variable load
operation to identify the best management strategy,
optimizing the efficiency while reducing the expected
FC degradation rate.
2 FC power plant layout
The layout of GRASSHOPPER 100 kWel FC pilot
power plant is shown in Fig. 1.
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0
(http://creativecommons.org/licenses/by/4.0/).
E3S Web of Conferences 238, 04003 (2021) https://doi.org/10.1051/e3sconf/202123804003
100RES 2020
Fig. 1 - Grasshopper 100 kWel FC power plant layout.
The stack is supplied with humidified pure hydrogen
and air. Humidification is obtained through packed-bed
shower-type humidifiers, that act also as scrubbers
removing the impurities from the gas. The stack
operating temperature, relevant for degradation and
efficiency, is controlled by the flow rate of coolant, a
glycol-water mixture flowing through a dedicated loop.
The thermal power is partially recovered to heat up the
water used for hydrogen and air humidification and
partially dissipated by a dedicated cooler. A valve,
located at cathode outlet, allows to control air
backpressure. Air ratio to stoichiometry is controlled by
regulating the rotational speed of the compressor.
Excess hydrogen is recirculated through a liquid ring
compressor and hydrogen ratio to stoichiometry is
controlled with a bypass system. Fresh hydrogen is
supposed to be available at sufficiently high pressure
(above 4 bar), thus it can be simply injected into the
system through a controlled valve.
The simultaneous control of backpressure, stack
temperature, air and hydrogen ratio to stoichiometry and
relative humidity will allow to optimize the system
performance and limit FC stack degradation.
3 FC plant dynamic model
A dynamic model of the 100 kWel FC power plant is
developed with the software Simulink. For each plant
component, a model able to solve mass and energy
balances during variable load operation is built, as
described in the following paragraphs. Fluid properties
are calculated for gases with the hypothesis of ideal gas
and ideal gas mixture, for water and water-coolant
mixtures considering ideal liquids with constant specific
heat. Component models are then combined together to
build the entire system model and PI-type controllers are
implemented for the control of system operation.
3.1 FC stack model
The single cell model is developed with a lumped-
volume approach, based on performance data available
from detailed simulations. Since the FC model has a
modular structure, the stack lumped model considers
several identical cells, electrically connected in series to
form a fuel cell stack. This approach allows to reproduce
large scale effects, as required by system simulation,
without a detailed description of the internal phenomena
in a single cell.
The model receives as input reactants and coolant
flow rate, composition, temperature and pressure at FC
inlet, and the set-point current density. The model then
solves mass and energy balances to determine flow rate,
composition, temperature and pressure of reactants and
coolant fluid leaving the FC stack. Gas build-up effects
in cells channels are neglected, both by a fluid-dynamic
and mass inertia point of view, since the volume of the
channels is negligible with respect to the volume of
other system components (i.e. humidifiers), where mass
accumulation is allocated. Temperature dynamic is
taken into account through the heat capacity of the stack,
that is lumped in the bipolar plates. Constant heat
transfer coefficients and no heat losses to the
environment are assumed. Pressure drops in the cells
channels are linearly dependent on the reactants and
coolant fluid volumetric flow rate at stack inlet,
assuming laminar flow conditions.
FC voltage and gross electrical power are calculated
on the basis of semi-empirical current-voltage
polarization curves. These curves are obtained from a
simplification of the theoretical polarization curve
equations, where the V(i) equation coefficients are
regressed on detailed datasets as reported in [4]. The
resulting curves take into account voltage dependence
on backpressure, air ratio to stoichiometry, air relative
humidity and temperature. Voltage dynamic due to the
charge and discharge of the cell double layer are
included in the model. However, being typical values
found in literature for the double layer capacitance
between 0.01 and 0.05 F/cm2 [5], the settling time
associated to this phenomenon results lower than 1
second, much faster than other important dynamic
effects such as those associated to the thermal inertia.
3.2 Air compressor model
The air blower is modelled through the machine
performance maps, allowing to compute the volumetric
flow rate of processed air, its temperature gain and the
compressor electric consumption, given the required
pressure gain and the rotational speed. The model
neglects mass accumulation and temperature dynamics
of the working fluid and of the machine. Since this
would affect the start-up time, it is assumed that the
compressor is switch on in advance and it reaches
thermal equilibrium before the simulation starts.
Dynamic effects connected to the mechanical inertia of
the machine, that slow down the rotational speed
variation, are instead included with the same approach
proposed in [6]: compressor rotational speed is
determined by a balance between the torque generated
by the electric motor and the torque required by the
compressor.
3.3 Air supply manifold
The air supply manifold model gathers the volumes
of all the supply line components, allowing to simulate
air build-up in the supply line. The resulting lumped
volume is located between the air compressor and the air
humidifier.
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Assuming constant temperature in the manifold
itself and ideal gas behaviour, the manifold model
solves mass balances to compute how the pressure of the
air in the supply line varies over time. The air flow rate
entering the manifold volume is imposed by the air
compressor while the air flow rate leaving the manifold
volume is set by the pressure drops in the components
located downstream and, mainly, by the backpressure
valve located at cathode outlet.
Air flow through the valve is modelled as a
compressible-fluid one-dimensional isentropic flow
through an orifice, with the assumption of subcritical
pressure ratio. An empirical discharged coefficient takes
into account deviation from one-dimensional flow [7].
3.4 Humidifier model
In the packed-bed shower-type humidifier, the gas
(air or hydrogen) is introduced at the bottom of the
packed-bed column and flows upwards, increasing its
humidity thanks to the evaporation of the water that
flows downwards. Residual liquid water accumulates in
the tank at column bottom; it is then heated up and
pumped back to the humidifier column top.
The model considers two sections: the packed-bed
column and the water tank. For each part, a lumped
volume approach is considered.
The packed bed column model determines flow
rates, composition, temperature and pressure of gas and
water leaving the column by solving mass and energy
balances, given the inlet streams properties. According
to industrial experience, it is assumed that the gas
always leaves the column in thermal equilibrium with
the sprayed water and fully saturated (humidifier
effectiveness 100%). No water drops are entrained by
the gas stream leaving the humidifier thanks to a
demister installed at the top of the column. Temperature
dynamic in the humidifier column is not included in the
model, being negligible with respect to temperature
dynamic in the humidifier tank. The packed-bed has a
void fraction equal to 90% of its volume. However, the
air humidifier model does not consider gas build-up in
the packed-bed column, since the volume of all the
components of the air supply line are gathered in the air
manifold. On the contrary, the H2 humidifier model
includes gas build-up possibility in the packed-bed
column. In this case, the flow rate of moist hydrogen
leaving the humidifier is imposed by the liquid ring
compressor which recycles the stack anode exhaust and
the inlet flow rate of fresh hydrogen is regulated in order
to control the pressure in the humidifier, and
consequently the FC anode backpressure.
The bottom water tank model solves mass and
energy balances, considering water accumulation and
temperature dynamic. The thermal inertia is associated
to the heat capacity of the accumulated water, being the
heat capacity of the tank walls negligible (< 5%). Perfect
mixing in the water tank is assumed.
3.5 Liquid ring compressor model
A stationary model is set up for the liquid ring
compressor, since it works within a narrow range of
rotational speed. The compression process is divided
into two sequential steps: compression of the hydrogen
stream and mixing with the water stream. Constant
isentropic and mechanical efficiencies are assumed to
compute the electrical power consumption. Mixing of
compressed hydrogen and liquid water in the liquid ring
compressor is modelled as an adiabatic process.
3.6 Heat exchangers
All the heat exchangers in the plant are counter-current
plate-type heat exchangers. Since the plate heat
exchanger has a modular structure and the hot and cold
fluids are assumed to be equally distributed among the
channels, it is modelled as a sequence of identical sub-
units. This sub-unit includes a single plate and half of
the adjacent cold and hot channels. The heat transferred,
the temperature of the plate itself and the temperature of
the outlet streams are calculated, discretizing the unit
along the direction of the channels (1D-model). For each
control volume resulting from the discretization
procedure, mass and energy balances are solved
assuming a uniform temperature for the plate, neglecting
heat transfer by conduction along the flow direction (due
to the relatively small thermal gradients and the
necessity to avoid more complex iterations which would
impact the simulation speed) and heat losses to the
environment. Temperature dynamic is related to the heat
capacity of the heat exchanger materials, while fluid
mass accumulation in the channels is neglected.
Constant values for water and coolant heat capacities as
well as for the heat transfer coefficients are assumed.
The thermal resistance of the plate is neglected. Pressure
is assumed to vary linearly with the volumetric flow
rates.
3.7 Pumps
A steady state model is realised also for the pumps. The
model computes the electric consumption of the pump,
as well as pressure and temperature of the outlet fluid
assuming constant isentropic and mechanical efficiency.
3.8 Pipelines
The model of pipelines, connecting the plant
components, includes calculation of pressure drops and
transport delay. Pressure drops in the pipes are
computed as a function of the volumetric flow rate.
Transport delay, representing the time that the fluid
takes to go from one component to the next one, is
simulated through a time delay that depends on pipe
length, diameter and volumetric flow rate. The
assumption of incompressible fluids is introduced (air
accumulation, as already mentioned, is concentrated in
the air supply manifold volume, while hydrogen
accumulation is concentrated in the hydrogen humidifier
volume). The heat capacity of the pipeline system is not
included in the model since it results negligible with
respect to the heat capacity of the other plant
components.
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4 Dynamic simulations
Preliminary simulations are performed to investigate the
system performance during cold start up and variable
load operation, in order to simulate the provision of grid
ancillary services.
4.1 Cold start up
Cold start up is simulated to understand how long does
it take the plant to reach nominal operating conditions
when started after a long shut-down period.
It is assumed that the plant is off and all the
components and the cooling fluid are at ambient
temperature (20°C). The FC plant is switched on and the
power demand is increased according to a warm up
procedure, defined to allow the plant itself to reach the
nominal point (detailed in Table 1) as fast as possible
while maintaining all the operating parameters within a
range of values defined to limit cells degradation.
Table 1. Plant nominal operating point
Parameter
Nominal value
Current density
1 A/cm2
Stack temperature
65°C
Coolant temperature gain over the
stack
10 °C
Air ratio to stoichiometry
2
Hydrogen ratio to stoichiometry
1.5
Air backpressure
1.35 bar
Average air relative humidity
100%
Average hydrogen relative
humidity
100%
Warm up initial state considers that the air
compressor is switched on at its nominal power (giving
the nominal air ratio to stoichiometry at nominal
operating conditions) and the backpressure valve is
regulated to obtain the nominal air backpressure. The
coolant flow rate is set at the nominal value aiming at
fast heating of humidifiers. The liquid ring compressor
is also operated at its nominal point.
The FC is switched on at its minimum load, with a
current density of 200 mA/cm2, equal to 20% of the
nominal value. The current density is then increased up
to the nominal value, with a rate of increase limited by
two temperature constrains (defined to limit cell
degradation): for each average temperature of the
coolant along the stack and for each temperature of the
air at stack inlet, a maximum current density is allowed
to keep the membrane correctly humidified.
When current density, reactants humidify and stack
temperature reach their setpoint, controls are activated
to keep, respectively, reactants ratio to stoichiometry,
reactants humidity and coolant temperature at the
desired values. The external cooler is activated to
remove the excess heat.
Fig. 2 shows how the current density varies over
time during plant warm up. The average temperature of
the coolant over the stack and the temperature of the air
at stack inlet are shown in the same figure.
The current density remains at the minimum value
for about 450 seconds (> 7 minutes), when the average
coolant temperature reaches the minimum value that
allows the current to increase. The system reaches the
nominal current in 1560 seconds (26 minutes). It takes
another 15 minutes for all parameters to reach the
nominal point, as shown in Fig. 3, being hydrogen ratio
to stoichiometry and hydrogen relative humidity the last
parameters to reach the nominal point.
Fig. 2 – Current density, average coolant temperature and air
temperature at FC inlet over time in cold start up.
Fig. 3 – Relative humidity, ratios to stoichiometry and
average coolant temperature profile over time during cold
start up vs. setpoints.
Air and fuel ratio to stoichiometry have their
maximum at start up, when the current density is at the
minimum. Then, they decrease when the current density
increases.
Immediately after start up, when the stack is cold,
air relative humidity is above 100% while hydrogen
relative humidity is about 100%. Then, while increasing
the current density, both air and hydrogen average
relative humidity decrease because the stack
temperature increases faster with respect to the
humidifiers temperature, influencing the gas water
content at stack inlet (air and hydrogen leave the
humidifiers at the same temperature of the sprayed
water, saturated with water). Finally, the humidifiers
0 500 1000 1500 2000 2500
time [s]
0
200
400
600
800
1000
1200
Current density [mA/cm
2
]
0
10
20
30
40
50
60
70
Temperature [°C]
Current density [mA/cm
2
]
T coolant average [°C]
T air FC inlet [°C]
0 500 1000 1500 2000 2500
0
50
100
150
200
Relative humidity [%]
Air RH [%]
H2 RH [%]
RH setpoint [%]
0 500 1000 1500 2000 2500
10
20
30
40
50
60
70
Temperature [°C]
0
5
10
15
Ratio to stoichiomentry
T coolant avg [°C]
T coolant avg setpoint [°C]
Air stoichiometry
Air stoichiometry setpoint
Fuel stoichiometry
Fuel stoichiometry setpoint
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temperature increases and the average relative humidity
reaches the 100% setpoint.
A sensitivity analysis has been performed to
determine which parameters mostly influence the warm-
up duration. Firstly, a sensitivity analysis on the initial
temperature is performed: it is indeed possible that
ambient temperature is higher in summer or that the
warmup procedure starts from a higher temperature
because the plant remained off only for a short period.
Then, by the FC point of view, an analysis is performed
to assess the impact of the cells overall heat transfer
capacity and of the cells heat capacity. Finally, at a
system level, the analysis focuses on the impact of (i)
the length of the pipes connecting the components, (ii)
the amount and initial temperature of the water in the
humidifiers (mainly in the air humidifier, since the
current ramp up depends on the air temperature at stack
inlet) and (iii) the overall heat transfer capacity in the
heat exchangers used to heat up the humidifier water.
The cases under investigation and the associated
time required for the current density to reach
1000 mA/cm2 are reported in Table 2, in comparison
with the reference case.
Table 2 - Sensitivity analyses: warm up duration and
percentage reduction with respect to the reference case.
Case
t [min]
Δt [%]
Reference case
26.0
-
Initial temperature 30 °C
12.8
-50.8%
Initial temperature 40 °C
3.2
-87.7%
Doubled cells overall heat
transfer coefficient
25.5
-1.9%
Halved cells heat capacity
24.8
-4.6%
Halved pipes length
23.8
-8.5%
Halved amount of water in the
humidifiers tanks
16.9
-35.0%
Initial temperature of water in
humidifiers tanks 30°C
15.0
-42.3%
Initial temperature of water in
humidifiers tanks 40°C
6.6
-74.6%
Doubled overall heat transfer
coefficients in heat exchangers
for humidifier water
25.3
-2.7%
Results show that, when the system is kept at higher
temperature, the start-up time significantly reduces,
reaching the nominal current density in 12.8 and 3.2
minutes when started from 30°C and 40°C respectively.
Indeed, the current density remains constant at 200
mA/cm2 for 7.5 minutes in the reference case, for 1.3
minutes when the system starts from 30°C while it can
increase immediately when it starts from 40°C. The
reason is the thermal inertia of the water in the
humidifier tanks, that takes about 4 minutes to heat up
from 20°C to 30°C, subtracting heat from the coolant
fluid and delaying the current increase.
Looking at the FC stack parameters, the impact on
the start-up time of the cells overall heat transfer
capacity and of the cells heat capacity are not
significant.
On a system level, impact of the length of the pipes
connecting the plan components is quite limited. On the
contrary, a reduction of 50% in the amount of water in
the humidifier tanks have an important impact on the
start-up time, with a reduction slightly below
10 minutes. Indeed, in this case a lower amount of heat
would be transferred from the coolant fluid to the
humidifiers water tanks in order to reach the target air
temperature. Thus, the current density could increase
faster because both coolant and humidifiers
temperature, and consequently the air temperature at
stack inlet, also increase faster. The strong impact of the
heat duty required by the water in the humidifiers tanks
on the start-up time is confirmed by the 11 minutes start-
up time reduction in the case where the humidifier water
temperature at the beginning of the warm up procedure
is 30°C, i.e. 10°C higher with respect to the reference
case. This time reduction is only 2.2 minutes less with
respect to the time reduction obtained by increasing the
temperature of all the system components to 30°C,
showing the effectiveness of heating up only the water
in the humidifier tank to speed up the warm up process.
Finally, a change in the overall heat transfer
coefficients in humidifiers heat exchangers does not
affect significantly the warm up time. It has to be
highlighted that, in this case, the current increase rate is
always limited by the coolant temperature rise, since
more heat is transferred to the water in the humidifiers
tanks and the air temperature increases faster at the
expense of the average coolant temperature. For the
same reason, the current density remains constant at the
initial 200 mA/cm2 for a longer time with respect to the
reference case (660 seconds instead of 450 seconds).
4.2 Load following operation
In order to provide ancillary services, the FC power
plant must operate dynamically, following the load
request within few minutes. Thus, the plant will operate
most of the time at partial load and the plant
optimization has to consider operation at any current
density.
Simulation following a hypothetic fluctuation of the
load are performed. The gross power generated by the
FC power plant is varied every 15 minutes, analysing
the entire range of operation for the stack, from 20 kWel
to 100 kWel, as depicted in Fig. 4.
Fig. 4 – FC gross power demand profile
Fig. 5 shows how the stack gross power, the current
density and the voltage vary over time, proving that the
system is able to follow the load demand. In Fig. 6,
details on performance at stepwise power changes from
20 kWel to 100 kWel and from 100 kWel to 20 kWel are
presented. The rate of change of the FC gross power is
limited at 2 kWel/s, to limit stack degradation while
0 15 30 45 60 75 90 105
time [min]
0
50
100
Gross power
demand [kW]
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respecting the desired ramp target (ramp-up rate
delivering 50 kWel within 20 seconds and 100 kWel
within 60 seconds). To avoid air and fuel starvation,
flow rates of air and fuel at FC stack inlet are increased
few seconds before current ramp-up and only at the end
of current ramp-down. Both in ramp-up and ramp-down
the system takes about 40 seconds to reach the power
setpoint.
Fig. 5 – FC current density, voltage and gross power profile
during variable load operation.
Fig. 6 - FC gross power profile for step-wise changes from
nominal to minimum load (left side) and from minimum to
nominal load (right side).
Preliminary design evaluations provide gross and net
plant efficiency up to 64% and 49% respectively (see
Fig. 7). The net efficiency at minimum load operation
(~ 42%) is negatively influenced by the air compressor
baseload; indeed the air ratio to stoichiometry is
controlled through the compressor rotational speed only
when the plant operates close to the nominal load, while
moving to lower load the compressor reaches its
minimum power and air purge is required. The adoption
of a compressor controllable over the entire range of
plant operation would increase the plant net efficiency.
Further improvements will come from design
optimization and experience from the pilot unit.
Fig. 7 – FC gross efficiency and plant net efficiency profile
during variable load operation.
5 Conclusions and future work
A dynamic model of a 100 kWel PEM FC power
plant has been developed, including sub-models of the
main plant components. Simulations of plant cold start-
up and load following operation have been performed.
Preliminary cold start-up simulations show that the
system reaches the nominal current density in 26
minutes when started from 20°C. However, when the
system is kept at higher temperature, the start-up time
significantly reduces, being 12.8 and 3.2 minutes when
started from 30°C and 40°C respectively. A sensitivity
analysis shows that the components which more
significantly limit the plant dynamic are the humidifiers.
Thus, possible options to reduce the start-up time are
decreasing the amount of the water in the humidifier
tanks, decreasing the humidifiers size or preheating the
water.
Simulations of plant variable load operation show
that the system is able to follow the power demand and
is able to ramp up and down between the minimum and
the maximum load in 40 seconds, fully reaching the
target set by the project.
These simulations results contribute to determine the
plant preliminary operating strategy and allows to
identify the more critical aspects and investigate
possible evolutions of the design.
During the first period of operation of the 100 kWel
GRASSHOPPER pilot plant, experimental operational
data will be collected and used to validate the model,
aiming at gaining further insight on the plant dynamics
and also at optimizing the system for MW-scale.
This work was developed within the project GRASSHOPPER,
which has received funding from the Fuel Cells and Hydrogen
2 Joint Undertaking under grant agreement No 779430. This
Joint Undertaking receives support from the European Union’s
Horizon 2020 research and innovation programme, Hydrogen
Europe and Hydrogen Europe research.
References
1. European Commission, “A Clean Planet for all. A
European long-term strategic vision for a prosperous,
modern, competitive and climate neutral economy,”
Com(2018) 773, p. 114, 2018.
2. Grasshopper project website: www.grasshopper.eu
3. S. Campanari, G. Guandalini, J. Coolegem, J. ten Have,
P. Hayes, A. H. Pichel, JEECS, doi 10.1115/1.4042923
(2019)
4. E. Crespi, G. Guandalini, J. Coolegem, M. Martín, S.
Gössling, P. Beckhaus, S. Campanari, Modelling and
optimization of a flexible PEMFC power plant for grid
balancing purposes, A1302, in Proceedings of
European Fuel Cell Forum (EFCF) 2019, 2-5 July,
Lucerne, Switzerland (2019)
5. M. J. Khan, M. T. Iqbal, Fuel Cell, 4, 463-475 (2005)
6. M. R. Malekbala, Thermal Science, 9, 6 (2015)
7. M. Cary, Proceedings of the Institution of Mechanical
Engineers, Part D, 215, 813-825(2001)
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i [mA/cm
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Efficiency [%]
Gross efficiency
Net efficiency
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