METHOD OF TESTING AN ELECTROCHEMICAL DEVICE
FIELD OF THE INVENTION
The present invention relates to various methods and associated apparatus for testing
an electrochemical device. Certain aspects of the invention relate to the testing of a fuel
cell, but others are applicable to a range of devices, including (but not limited to) fuel
cells and double-layer capacitors
BACKGROUND OF THE INVENTION
1. Testing procedures
Proton Exchange Membrane (PEM) Fuel Cell testing is wide ranging in terms of
measured properties, and testing techniques. Testing objectives may include identifying
specific properties, evaluating overall performance, or determining the state of a
functioning fuel cell for control purposes. Measured fuel cell properties include individual
loss terms, membrane hydration, and specific electrochemical properties such as the
charge transfer resistance. A number of material properties, such as the membrane
ionic resistance, have been measured ex situ using a variety of techniques [1, 2, 3].
However, most fuel cell testing is conducted on fully assembled, functioning cells or
stacks. A review of current testing and analysis techniques used (including modelling) is
given below.
The most common method of testing and characterising a PEM fuel cell is to obtain its
steady state voltage versus current (VI) curve. The VI curve is generally obtained by
holding the fuel cell operating conditions constant (such as the temperature, gas
stoichiometry, and humidity) and measuring the voltage at set current values. The
resulting VI curves are characterised by either mechanistic [4, 5] or empirical [6, 7]
model equations, in order to obtain a general mathematical description of the fuel cell's
performance.
Analysis of the VI curves and resulting model equations has also allowed individual loss
terms to be inferred, such as the activation polarisation (initial steep decline of the VI
curve), overall ohmic resistance (linear part of the VI curve), and mass transport loss

(near the end of the VI curve). The way in which these loss terms (and hence VI curves)
are affected by different operating conditions has also been studied, including the impact
of different airflow rates or humidity levels [8]. A thorough VI evaluation requires
accurate control over the stack power output and operating conditions. As a result, this
fuel cell testing method is confined to a lab environment rather than an application
setting.
AC impedance testing or Electrochemical Impedance Spectroscopy, (EIS) is also
commonly employed for determining properties of a fuel cell. The technique consists of
imposing a small AC sinusoidal current (or voltage) onto the fuel cell. The complex
impedance is then derived by measuring the phase and amplitude of the corresponding
voltage (or current) response. This test method has been conducted on a passive (non-
functioning) fuel cell and an active (functioning) fuel cell, in which case an AC
perturbation is superimposed onto DC load. Frequencies used typically range from
10mHz to 100kHz, in order to obtain a full spectrum of the AC impedance. In addition
the fuel cell can be held at a number of different current densities for each impedance
sweep to identify certain properties [9, 10].
It has been suggested that AC impedance testing is superior to steady state VI curve
evaluation for separating out and identifying the different loss mechanisms of a fuel cell
due to the association of loss mechanisms with certain frequency ranges [11]. For
example, the charge transfer resistance has been associated with the high frequency
region, while the mass transport losses are generally associated with lower frequency
regions. [12].
Thus far, AC impedance testing has only been conducted on individual cells, and is
aimed at obtaining discrete cell properties, rather than evaluating cell performance or
functionality Although complex test equipment is required, AC impedance testing has
been suggested for stack testing (in which case AC impedance is carried out on each
cell) in an application setting, thus providing information for active control and
assessment of the fuel cell [13,14].
Current interrupt or current pulse methods have been proposed as a potentially simpler
technique for obtaining some fuel cell characteristics. These methods do not require an
AC signal or measurement of the phase and magnitude of an AC response, which

requires complex equipment. By examining the voltage transient generated when a
functional fuel cell is subjected to a step change in current, the fuel cell resistance and
other properties have been derived [15,16]. The ohmic resistance seems to be the main
property identified by this technique.. However, other loss terms have been identified
when a functioning Molten Carbonate Fuel Cell had been subjected to a current interrupt
test [17]. A variation of this method involves subjecting a functioning fuel cell to a short
duration current pulse [18]. In general, these testing methods, like AC impedance, are for
determining specific fuel cell properties (primarily the resistance) rather than evaluating
the general performance or functionality. Current interrupt techniques have also been
suggested for implementation into a commercial application, through the use of a shunt
[19].
In general, current fuel cell testing methods either evaluate fuel cell performance by
simply running the stack over its operational range, or evaluate specific properties of the
fuel cell using a few electronic test methods. Identification of a single loss term
(although indicative) cannot be used to judge the full functionality of the cell. In other
words, there is no link from identification of a single fuel cell parameter, to the impact this
has in terms of total performance. Thus far, the only method of obtaining fuel cell
functional information has been to operate the fuel cell at a number of operating points,
and thus obtain its VI curve. However, this testing has not been implemented in an
application setting, and essentially is restricted to a lab type environment.
The vast majority of the testing methods and analysis are based on a single cell, hence
only the characteristics of a single cell are found. If a test is implemented on a stack,
such as current interrupt test, only properties of the stack as a whole can be found, such
as the overall resistance A VI evaluation can evaluate all cells in a stack (with all cells
being monitored) however, as stated above, this is a technique used only in a lab type
environment.
2. Equivalent Circuit Models and methods for obtaining the circuit parameters
2.1 Introduction to Equivalent Circuit Models
Equivalent circuit modelling is a common way of representing an electrochemical device,
such as a battery or an electrolysis cell. As fuel cell technology has progressed recently,
more attention has been given to equivalent circuit modelling of fuel cells. The resulting

equivalent circuit models are used for a number of purposes such as predicting a fuel
cell's dynamic response under a load change. The circuit models and their
corresponding circuit parameters have been determined using a variety of techniques,
such as AC impedance (or Electrochemical Impedance Spectroscopy), current interrupt
methods, and steady state VI evaluation. Much of the underlying theory and many of the
techniques used are common to electrochemical cells in general.
2.2 Existing fuel cell equivalent circuit models (Active models)
One of the simplest and commonly used fuel cell equivalent circuit models (ECM's), is
shown in figure 1a [16]. This model is often referred to as the Randels equivalent circuit,
and is a simple representation of any electrochemical cell. The model encapsulates the
main properties of a fuel cell, which are the ohmic (or internal) resistance (Rint), activation
loss (or charge transfer resistance, Ract), capacritive effect (C), and potential (E) due to
the electrochemical reactions. While this model has been used for simulating the
dynamic response of a fuel cell under a load change [20, 21], it is a simplistic
representation, and captures just the main dynamics of a fuel cell
One for the most commonly used ECM is shown in figure 1b, where the anode, cathode,
and electrolyte properties have been separated [15]. The total resistance is divided
between the ionic resistance of the membrane (Reie), and the resistances associated
with the anode (Ra) and cathode (Re). The fuel cell capacitance is divided between the
two charge layers created at the electrolyte/cathode interface (Cc), and the
electrolyte/anode interface (Ca), (double charge layer effect). The fuel cell potential has
also been divided between the half-cell reactions occurring at the anode and cathode. A
number of current interrupt tests are proposed for parameter identification, however, as
stated by Larminie, unique determination of anode and cathode properties can not be
achieved by this technique alone. Although circuit component values are given for a
number of different fuels, only an ideal voltage response to the current interrupt test had
been presented, with no comparison to experimental results.
O'Hayre et al [22] used a similar model to that sliown in figure 1b, however the electrode
resistances are attributed to the activation loss present at the anode and cathode, and a
single potential term was placed at the anode (-figure 1c). The activation resistances at
the electrodes were voltage dependant (encapsulating the non-linearity of the activation
loss) and for simulation purposes were actually modelled as voltage dependant current

sources. An additional resistor that connected the membrane of one cell to the
membrane of an adjacent cell was added when a stack was being modelled. This
additional resistor modelled lateral ionic conduction, a phenomenon that occurs when
cells are in a planar configuration (common membrane electrolyte, with the cells
externally connected in series. AC impedance and steady state VI curve testing was
employed to derive the circuit parameters of the circuit model. In addition to these
typical experiments, a number of open circuit experiments involving different planar
configurations enabled losses at the cathode, and the magnitude of the lateral ion
conduction to be identified. A simulation of the resulting ECM using P-Spice compared
well with experimental results. However, only a steady state comparison between
experimental and modelled results was made, negating the effect of the capacitors
present in the model.
2.3 Existing fuel cell equivalent circuit models (Passive models)
In order to represent an additional loss attributed to limited mass transport (diffusion)
present at the oxygen electrode (cathode), Wagner used an ECM containing an
additional RC parallel branch (figure 2a) [9, 10]. Derivation of the model was achieved
though AC impedance testing (electrochemical impedance spectroscopy), some of which
was conducted while the fuel cell was in a passive state, with either oxygen or hydrogen
present at both electrodes. Model validation was accomplished by comparing the AC
impedance spectrum of a single cell with a simulated spectrum However, this validation
is somewhat unclear, as the capacitors in the ECM were replaced with constant phase
elements and no circuit component values have been given.
One of the more complex models has been used by Li et al [11] (and references therein)
which is the transmission line model of a single electrode. The electrode is modelled
with an electronic resistance rail (Reie), connected with capacitors (C) in parallel, to an
ionic resistance rail (Rionic). Only three Rala - C - Rionic legs are shown in figure 2b),
however, Li et al used a series of 40 when simulating the AC impedance response of the
model. The objective of the paper was to investigate the ionic resistance as a function of
distance. This function was found for a variety of electrodes by trial and error, using a
comparison of the AC impedance spectrum to verify the function found.
Comparing the AC impedance spectrum between a fuel cell and model simulation is the
most common way of verifying the validity of a particular ECM. The comparison of an

AC impedance response is most often carried out directly, although the use of a Fourier
transform of the impedance has also been suggested [23].
2.4 Equivalent circuit models of Double-layer capacitors (DLC)
The fuel cell models reviewed thus far, along with the techniques employed for circuit
parameter identification, are primarily derived from the work conducted for a general
electrochemical cell containing chemical reactants, such as a battery or an electrolysis
cell. However, another electrochemical device that is very similar in construction to a
fuel cell, and which exhibits a similar behaviour (particularly when a fuel cell is in a
passive/non-functioning state) is a double-layer capacitor (DLC), also known as an
electrochemical super capacitor, or super capacitor.
The basic construction of any DLC consists of two electrodes, separated by an
electrolyte that contains free moving ions. Very large capacitances can be achieved due
to the double charge layer formed at the electrode/electrolyte interface. This layer,
where the charge separation between the ions in the electrolyte and the charge on the
electrodes is very small, gives the electrolyte membrane a very large dielectric effect,
thus making the capacitance of the whole device very large
Activated carbon is most commonly used for the electrodes, as it is non-reactive, and
large surface areas can be achieved. This is the same electrode material used in a PEM
fuel cell. Usually, DLCs contain an organic based electrolyte, as this enables higher
voltages to be used. However, aqueous H2S04 is also been used (similar to the acid
present in a PEM fuel cell) and a small number of DLCs employing Nafion (a polymer
membrane common in PEM fuel cells) have been realised and their properties tested
[24, 25]
While the construction of a DLC is very similar to other electrochemical cells (such as
fuel cells and batteries), a DLC can be distinguished based on the type of processes
occurring within it. In a DLC, only non-faradic processes can occur, such as the
movement and adsorption of ions, whereas with other electrochemical cells, faradic
processes also occur, i e electrochemical reactions due to a charge transfer between
the electrolyte and the electrode. It has been reported that certain DLC capacitors store
charge due in part to faradic processes (limited electrochemical reactions), however this
is a minor effect compared to the charge stored from non-faradic processes. Due to the

physical similarity between a PEM fuel cell and a DLC, it is fruitful to consider the circuit
models and testing techniques used for these devices, particularly due to the fu&l cell
experimental methods considered below.
A DLC does not behave as an ideal capacitor; hence much work has been devoted to
understanding and modelling the way in which the charge is stored, particularly with
respect to the double charge layer. Along with a number of theoretically based
mathematical models, a number of complex ECMs models have been proposed [25, 27],
most of which contain numerous resistor and capacitor branches connected in parallel.
However, a simple two branch model, as used by Goalous et al [28], has been sho\yvn to
predict the essential characteristics of a DLC (see figure 3a).
The model contains a resistor (Rp) that accounts for the leakage current (or self-
discharge), and two resistor and capacitor branches (Ri Ci R2 C2), which are able to
model the dynamic response of a DLC Although an inductor (L) is shown, its value
tends to be very low, and is only considered if high frequencies are being modelled. A
feature of the model is the variable capacitance value of capacitor C1. This well-known
characteristic is due to the way a DLC stores charge, resulting in a capacitance value
that increases linearly with voltage.
The methods employed for deriving DLC circuit parameters can roughly be divided into
two groups, those employing AC techniques, and those employing DC techniques- AC
methods (Electrochemical Impedance Spectroscopy) have been widely used [25, 26, 29]
and are very similar to those discussed in relation to fuel cells, thus the discussion below
will examine the DC methods.
The DC methods used are all very similar, and include measuring the transient voltage
response to an imposed constant current charge, discharge, or sequence of
charge/discharge steps. Goalous et al identified the R-C values based on the fact they
possessed different time constants. This enabled two distinct voltage transients "to be
identified, and the circuit parameters could be obtained with minimal computation.
Zubieta et al used a similar technique in finding the parameters to a 3 R-C branch model
(figure 3b). Determination of the parameters using this method requires the initial
voltage of the DLC to be zero (hence the initial voltage of the capacitors in the model will
also be zero). In the case of Zubieta et al, the DLC was held at short circuit for a -week

for the zero initial voltage condition to be satisfied. While many of these DC type tests
have been carried out, they are all quite similar, with the test and corresponding analysis
being conducted across only one cell [27, 28, 30, 31].
2.5 Summary of methods to determine circuit parameters
In equivalent circuit modelling, the experimental methods and corresponding techniques
used for parameter identification are only implemented on a single cell. Therefore, to
test a stack, individual test on each cell would be required. Fuel cell circuit models and
corresponding parameters are generally verified by comparing the simulated and
experimental AC impedance spectrum or steady state VI data. DC techniques (such as
applying a constant current) are used for validating super capacitors models along with
AC methods.
SUMMARY OF THE INVENTION
Fuel Cell Testing Procedure < ~-N
A first aspect of the invention provides amethod of testiaq_aJuel cell, the method ,
including charging the fuel celhjuring a charge periodjdischarging the fuel cell during a /
discharge period, and monitoring the response of the fuel cell during at least part of the/
discharge period. /
A second aspect of the invention provides a method of testing a fuel cell, the method
including charging the fuel cell during a charge period; and after the charge period
making the fuel cell open-circuit and monitoring the open-circuit response of the fuel cell.
The first and second aspects of the invention each obviate the need for complex test
equipment required to generate and measure compjgxjgst signals, such as sine waves ""oTv^ryingfrequency, a series of current pulses, or a current ramp.
The monitored response of the proposed testing procedure, is typically a voltage
transient or a specific part of the voltage transient behaviour such as a rate change in
voltage, or a step change in voltage resulting from a discrete change in the
charge/discharge test condition. The monitored response can also included a current
transient and/or any part of the current behaviour through the fuel cell during any part of

the testing procedure. In general, the response can be anything that gives information
about the fuel cell as a result of the testing protocol imposed. I
The response of the fuel cell may also be monitored during at least one other period/
The other period(s) may include the charge period and/or the discharge period and/or an
initial period prior to any charge/discharge test process, and/or a self-recharge perioa
after the discharge period. Monitoring during two or more periods provides additionalV
information that can be used to provide a more complete picture of the physical /
nature/condition of the cell. For instance monitoring during the initial period can be used /
to determine initial equivalent circuit conditions indicative of an initial value of a timel
varying circuit condition (such as voltage) I
Typically, the response of the fuel cell is measured during discharge into a test circuit including one or more passive test components, such as (but not limited to) resistors and
capacitors. The benefits of using simple circuit components of known values is
recognised, as no complex test circuitry is required. Measuring the response of the
passive test component(s) also provides additional information. In the preferred test
described below, the response of the components would include the voltage across Rue
during the charge up and the voltage across R2TC during the discharge. In this case
monitoring R2TC during the discharge does not provide additional information, as this
equals the voltage across the stack. However, if the fuel cell were discharge into a j
R2TCC2TC then monitoring the voltage across R2TC would provide additional information. /
Passive fuel cell test
A third aspect of the invention provides a method of testing a fuel cell, the method
including testing the fuel cell when the fuel cell is in a passive state in which substantially
no electrochemical reactions are occurring in the fuel cell.
The third aspect of the invention recognizes the benefits in testing a passive fuel cell. As
no substantial electrochemical reactions are taken place, the fuel cell can be charged
and/or discharged in predominately a capacitor sense. In other words, faradic reactions
do not occur, leaving only non-faradic processes.

The method is simpler than previous methods which require the fuel cell to be in an
operative state with fuel and oxidant being passed though the cell and electrochemical
reactions taking place. As a consequence, the passive fuel cell test could be
implemented on a manufacturing line or in a stand-by power system (as stored hydrogen ,
would otherwise have to be used, compromising back-up run time). In both cases the
fuel cell is in a passive state Testing a passive fuel cell also enables different
characteristics of the fuel cell to be examined as the test results are not affected by
electrochemical reactions taking place during the test. As a consequence, aspects more
closely related with the fuel cell's physical condition or construction may be found.
Condition of the fuel cell
The methods of the first, second and third aspects of the invention may be used to
assess certain aspects of a fuel cell, such as it's ability to function. Testing and
measuring the electrical properties of a passive fuel cell (which behaves predominantly
in a capacitive sense) could be related to the performance of the fuel cell when active.
For example, if the passive test indicated a large capacitance of a cell, (indicating more
surface area), this would indicate more reaction sites when active, thus increased
performance. The passive test results could thus be related to the level of functionality
of an active cell, and thus may be used to measure the level of health of a fuel cell.
Clearly it is recognised that not all factors affecting fuel cell performance can be found
using a passive test. The test process only probes the electrical nature of the cell itself,
thus only testing the physical properties of a cell. Aspects such as mass transport,
flooding, or gas flow field effects, are simply not present. However, as changes in the
condition of the fuel cell occur predominantly at the cell level, (such as degradation, or
dehydration) the results from successive passive tests could be used to predict a change
in the cell's state in an application setting.
The relationship between the passive test results and the active functionality of the fuel
cell can be found by a comparative analysis of the passive results. By directly inspecting
the results of a charge/discharge test (like those discussed above), a qualitative (or
comparative) measure of cell properties can be gained, thus a correlation between the
passive and active functionally of the stack could be found.

In one example, the direct results from the passive test could include a step change in
cell voltage during part of the discharge period, or the rate of change in cell voltage
during an open circuit period. In one fuel cell tested, it has been found that these
measurements correlate with the active cell performance. Other testing methods require
further computation of the fuel cell response, such as calculation of the fuel cell
resistance from AC impedance or current interrupt techniques. The physical quantities
once calculated, such as the resistance, are then used as an indicator of fuel cell
performance or condition. However, other factors in addition to the quantity calculated,
may affect the condition of the fuel cell. Hence an advantage in the above method is a
possible direct correlation between the results of the passive fuel cell test, and the active
performance.
Multiple devices
A fifth aspect of the invention provides a method of testing two or more electrically
connected electrochemical devices, the method including applying a single stimulus to
the end terminals of the connected devices, and independently monitoring the response
of each of the devices to the stimulus.
The fifth aspect of the invention enables a number of devices to be tested efficiently,
since only a single stimulus and a single test circuit is required for all devices. The
devices may be connected serially, in parallel, or a combination thereof.
The response of the device is typically monitored by measuring and storing a series of
voltage readings. These voltage readings (measured across each electrically connected
device) may then be further analyzed, if desired, to assess the condition of the device as
described in the section above.
Algorithm for acquiring Model parameters of a device
A sixth aspect of the invention provides a method of testing an electrochemical device,
the method including obtaining test data from the device; obtaining two or more circuit
values of an equivalent circuit model parameter; calculating a respective set of

simulation data for each parameter value; comparing each set of simulation data with the
test data, and selecting one of the parameter values based on the comparison.
The sixth aspect of the invention provides a systematic method of utilising the test data
to arrive at accurate values of equivalent circuit model parameters. The test data is
typically the measured response of the device when subjected to a test protocol, such as
one of the methods of the first or second aspects of the invention. The simulation data is
then calculated (e.g. using an electrical circuit simulation program such as PLECS) by
simulating the test protocol acting on an equivalent circuit model of the device.
The equivalent circuit parameters may be indicative of the value of a circuit component
(for instance a resistor or capacitor), or conditions indicative of an initial value of a time
varying circuit condition, such as the initial voltage of a capacitor.
A seventh aspect of the invention provides a method of testing an electrochemical
device, the method including obtaining test data from the device; and calculating
parameters of an equivalent circuit model from the test data; wherein the parameters
include
a. one or more values, each being indicative of the value of a circuit
component in an equivalent circuit model, and
b one or more conditions, each condition being indicative of an initial value
of a time varying circuit condition.
The seventh aspect of the invention provides an alternative testing method, which
calculates both circuit component values (for instance resistance and/or capacitance
values) and initial condition values (for instance initial voltage values) associated with the
equivalent, circuit model. This can be contrasted with conventional methods which
require (or assume) the initial conditions to be zero, for example, requiring the initial
voltage of DLC to be zero, thus all initial voltage conditions of the model will be zero.
The sixth and seventh aspects of the invention may be performed on a variety of
devices, including (but not limited to) a fuel cell or double-layer capacitor (DLC).
Provided the equivalent circuit model is derived based on the physical nature of the
device being tested, the equivalent circuit parameter values will typically relate to

physical properties of the device. This enables the values to be used directly in
assessing the physical condition/state of the device. Current equivalent circuit mode* Is
are either constructed to predict the terminal behaviour of a device, with no physical
significance given to the components (particularly with respect to a DLC's). Whereas
other equivalent circuits attempt to relate circuit components to physical properties (such
as the fuel cell models), but do not fully predict the dynamic behaviour of the device.
BRIEF DESCRIPTION OF TH^DRAWINGS
Embodiments of the invention will now be described by way of example with reference to
the accompanying drawings, in which:
Figure 1 shows a set of known equivalent circuit models for an active fuel cell
Figure 2 shows a set of known equivalent circuit models for a passive fuel cell
Figure 3 shows a set of known equivalent circuit models for double layer capacitors
(DLCs)
Figure 4 shows testing apparatus for performing the invention
Figure 5a) is a flow diagram showing the test protocol
Figure 5b) shows the test circuit
Figure 6 shows a single cell voltage response when a single cell is subjected to the test
protocol (electrodes of one cell attached to test circuit) and the corresponding modelled
results
Figure 7 shows the stack terminal voltage response when the stack is subjected to the
test protocol (stack terminals attached to test circuit);
Figure 8 shows the individual cell response when the stack is subjected to the test
protocol (test circuit attached to stack terminals)
Figure 9 shows the VI performance of the active stack
Figure 10 shows an equivalent circuit model of a passive fuel cell
Figure 11 shows the experimental and modelled data of the individual cell response to
the test protocol
Figure 12 shows the best fit of a standard equivalent model (see insert) to the
experimental test data

Figure 13 shows the best fit of a standard equivalent model (see insert) to the
experimental data
Figure 14 shows an overview of the algorithm employed for circuit parameter
determination.
DESCRIPTION OF PREFERRED EMBODIMENTS
3. Testing Procedure
3.1 Introduction
A new testing method is proposed, which provides results that can indicate the relative
performance of the individual cells within a fuel cell stack The performance information
is not obtained by operating the stack, but testing the stack while it is in a passive, non-
functioning state. The test method and analysis is relatively simple, enabling it to be
implemented in a number of situations. The testing method is described below with
reference to a particular fuel cell. However the method may also be used to test other
electrochemical devices such as Double Layer Capacitor (DLC).
3.2 Fuel cell Testing
The testing method is implemented while the fuel cell is in a passive (non-functioning)
state No hydrogen is present in the stack, with both the anode and cathode
compartments containing air As a result, no potential can be formed across any of the
cells. While the fuel ceil stack is in this passive state, each cell predominately behaves
as a DLC due to the similar physical structure between the two devices (as previously
described in section 2.4). In both cases, a double charge layer can be formed at the
electrode/electrolyte interface.
Using an electrical probing protocol shown in figure 5a), the fuel cell stack is effectively
charged and discharged during the test procedure (exploiting the capacitive property of a
passive fuel cell) The resulting transient voltage response of each individual cell in the
stack is recorded and analysed to assess physical/electrical properties of the cells, and
hence indicate the functionality of the stack.
The electrical probing protocol is carried out by the test system, shown in figure 4. The
test system includes a test circuit shown in detail in figure 5b) that can either apply a

voltage to the stack in order to charge it, maintain the stack at open circuit, or allow a
charge on the stack to be dissipated through a resistor. The test system also contains a
data acquisition and controller module that measures the individual cell voltages and
stack terminal voltage during the test procedure. The data acquisition and controller
module also monitors and controls the test circuit. A PC based supervisor/analyser
downloads a specific test protocol to the data acquisition and controller module, and
analyses the test results to assess the stack.
The test protocol subjects the stack to a sequence of DC electrical conditions at the
stack terminals, thereby charging and discharging the stack. The specific test protocol
described here consists of five distinct periods,
1. The initial voltages of the cells and stack terminals are measured from time to until
time t|.
2. The stack is then charged up using a constant voltage source in series with the
resistor R1Tc, over a time period from ti to t2
3. At time t2, the voltage source is disconnected, and the fuel cell remains at open
circuit until time t3.
4. The remaining charge held by the fuel cell is then dissipated through the resistor
R2TC m the time period t3 to U.
5. The stack is once again held at open circuit, with the voltage of the cells and stack
being recorded until time t5 is reached, at which point the test procedure ends.
The data acquisition and controller module sets the time values to - ts (by controlling the
switches Sue and S2TC), and it also sets the value of the regulated voltage source.
Along with the voltages of the stack and cells being monitored throughout the test
process, the voltage across Rnc is also monitored, thereby measuring the current
flowing through the stack during the charge step. The details of the test protocol and
other experimental details are described below.
3.4 Specific Experimental Embodiment
The testing procedure has been implemented on a small PEM fuel cell stack
manufactured by MerCorp. The stack contained 6 cells stacked in series, each with an
active area of 32cmz and a Nation based membrane. The stack design is completely
symmetrical i.e. the gas flow-field design and electrode structures for the anode and
cathode are identical. The test circuit component values were Rue = 100Q and R2TC =

4.9Q, with Vrc being set at a variety of values depending on what test was being
implemented. For data acquisition and control, an HP 349 70A Data Acquisition/Switch
Unit was used, which contains an internal digital multi-meter for measurement purposes.
The Data Acquisition/Switch Unit contained an HP 34901A 20-Channel Multiplexer card
(enabling all of the cell voltages, stack terminals and the voltage across RITC to be
measured) as well as a HP 34907A Multifunction Module (which provided outputs for
control of the test circuit). A P4m 2GHz notebook computer running Matlab 6.5 R13 was
used for supervisor/analyser purposes. The HP Data Acquisition/Switch unit was
programmed directly in the Matlab environment, and communicated via an RS232
connection Matlab was also used for analysing the voltage data, which was sampled at
1Hz
3.5 Fuel cell test results
The general effect the testing protocol has on a fuel cell can be most easily observed by
examining the response of a single cell Thus, the test circuit was connected across cell
#3 only, and the results (using VTC = 0.05V) are shown in figure 6.
The five parts of the test protocol creates five regions, which have been labelled as the
initial steady state, charge up, natural decay, discharge, and self-recharge. A brief
description of the phenomena occurring in the fuel cell and corresponding voltage
response in each of the regions is given below.
1. Initial steady state (to - ti): The stack is maintained at open circuit, and any
potential that may initially be across the cell is recorded. In this case there is
approximately 0 V across the cell initially.
2. Charge up (1, -12): In this region, a voltage is applied across the cell (acting as a
capacitor) in series with resistor Rnc as illustrated by figure 5b with Sue closed.
This results in an exponential type rise in the stack potential. The rise in the stack
voltage is not a pure exponential function, as the fuel cell, (like a DLC) does not
behave as an ideal capacitor.
3. Natural Decay (t2 - U)- The voltage decays in an exponential type manner as a
result of S1Tc being opened. The voltage decay is due to electronic conductance of
the membranes, (as the membranes are not perfect electronic insulators) and charge
redistribution within the membrane. The presence of membrane electronic
conduction can also be observed in the charge up region, as voltage across the fuel

cell does not approach the applied voltage. Charge redistribution in the membrane is
also responsible for the decay in voltage. As H+ ions will continue to move from the
negative to the positively charged electrode, this effectively increases the dielectric
constant of the membrane, thus reducing the potential across the cell (assuming the
charge remains near a fixed value).
4. Discharge (t3 - t»): The remaining charge on the fuel cell is rapidly discharged
through the resistor R2TC As the value of R2TC is small, the fuel cell is effectively
short-circuited during this period, resulting in the voltage across the fuel cell
approaching zero.
5. Self recharge (t, - tB): After the short is removed, the potential across the stack
builds back up, and then begins to decay as in the natural decay region. This self-
recharge is believed to be caused by a residual charge being held by the membrane
even when there is little or no charge present on the electrodes. The residual charge
is caused by the H+ ions having a slow relaxation time, i.e. the distribution of H+ ions
will still be non-uniform in the membrane for some time after the charge on the
electrodes has been reduced to zero. The non-uniformity in the H* distribution
causes a potential across the cell to build once the short across the fuel cell has
been removed After a maximum voltage is. reached in the natural recharge region,
the charge across the fuel cell stack then naturally decays as in the natural decay
region. Once again charge redistribution can explain the self recharge, as ions will
continue to move to an equilibrium value, thus decreasing the effective dielectric
constant of the membrane, and causing a rise in the potential (providing some
electronic charge remains on the electrodes).
Note that if the test protocol were implemented across the entire stack, i.e. if the test
circuit was connected across the stack terminals, the same transient voltage behaviour
would be exhibited. This is shown in figure 7, where the same test procedure was
implemented across the stack, with VTC = 0.109V. The combined behaviour of many
cells stacked in series (6 in this case) happens to be the same as one cell on its own.
However, when the test is implemented across the stack terminals, and the voltage
across each cell is monitored, the voltage transient behaviour exhibited by each cell is
quite different, as shown in figure 8.
The voltage response of each cell shown in figure 8 has been taken from the same test
as the result of the stack voltage. The sum of the cell voltages adds to give the stack

terminal voltage response shown in figure 7. The wide range of cell voltage responses is
caused by each cell possessing different capacitance, electronic conductance values
etc. For example, Cell 5 exhibits a particularly low electronic conduction (a quality
desirable in a cell), which is the reason the initial voltage was comparatively high at the
start of the test, i.e. there is still a remaining charge across the cell from the previous
day's operation The variation of electrical properties amongst the cells, together with
the cells interacting during the test process (as they are connected in series), produces ,
the large range in voltage transient behaviour observed.
The different cell behaviours observed by the passive fuel cell test have been found to
correlate with the individual cell performance (or their state of health) when the stack is
active. In other words, the varied voltage response between the cells is caused by the
same physical differences that cause the cells to function at different levels of health. As
a result, the passive fuel cell test can be used for predicting the comparative functionality
of individual cells within the stack. To demonstrate this, the fuel cell was operated after
the passive test was conducted, and a correlation can be established between the
operational functionality of each cell in the stack, and certain regions of the passive fuel
cell test results
3.6 Active Stack experimental details
In order to relate the outcome of the passive test to the functionality of the fuel cell, the
operating conditions and acquisition of the VI curves were obtained in a way that limited
changes to the state of the fuel cell. Thus a VI curve was obtained as soon as a certain
degree of steady state had been achieved, ensuring the physical condition of the active
fuel cell was as close as possible to the condition at which the passive fuel ceil test was
conducted. Due to these restrictions on the operation of the fuel cell stack, only low
currents, and low powers were achieved. In addition, the stack was known to have
performa'nce issues, thus also contributing the low power levels achieved.
The VI curve of the fuel cell was taken at a stack temperature of 26.5°C, compared with
23.5CC for the passive fuel cell test. The air (constant airflow rate of 1.3 l/min) was
bubbled through distilled water, and entered the fuel cell at a temperature of 25°C,
preventing possible dehydration. The Hydrogen (dead-ended, dry) and air were both
slightly above atmospheric pressure, as they exited the fuel cell stack via a water column
of equal height, ensuring near equal pressures at the anode and cathode.

Before the VI curves were obtained, the stack was allowed to come to a steady state
defined as a change in voltage of less than 1.2 * 10"3 V/s on any particular cell. This
was achieved by operating the stack minimally, at a number of different currents, with
steady state being achieved approximately 400s from when hydrogen first entered the
stack. A constant current load was used to obtain the VI curves. Three voltage readings
of each cell were taken (over a period of 6 seconds) for a given current value, and the
voltage readings were taken in order of increasing current. The resulting VI curves of
each cell are shown in figure 9.
The VI curves in figure 9 show that each cell in the stack functions with a different level
of performance or health. The healthiest cells produce a high voltage at a given current,
thus, a simple way of quantifying the health of a cell is to use the voltage of the cell at a
current of 0.56 A (listed below in table 1). As was claimed in a previous section above,
the results of the passive fuel cell test can be used to indicate the performance (or
health) of the cells. This prediction has been found by examining two areas of the
passive fuel cell test results; the voltage rate of change (gradient) just after time t2, and
the size of the voltage step that occurs at t3. These two quantities are shown for cell 5 in
figure 8, and a list of the gradient, voltage step size, and the corresponding functional
cell voltage of each cell are listed below in table 1.

Table 1 shows that cells possessing a smaller gradient at t2l and a smaller voltage step
at t3, correlate to healthier cells. Cells 4, 5 and 6 are very similar in their performance,
so they present some discrepancy in the performance measurement. The process of
conducting a passive test on the fuel cell, running the fuel cell, then comparing the

performance with the gradient and voltage step has been repeated many times on this
particular stack. Always a correlation could be seen between the passive and active set
of results; however this was not always as clear as the correlation shown in table 1.
Clearly, other operation factors can influence the performance of the cells but will not
affect the results of the passive test (such as gas flow, and possible flooding of the cell).
These aspects can influence the strength of the correlation observed. For the MerCorp
stack, there were usually certain cells that performed very well, with the remainder of the
cells performing marginally. The distinction between the groups of good cells and bad
cells could always be identified from the passive tests.
It is interesting to observe the range in electronic conductivity of various cells, which can
be inferred by the final voltage value of the charge up region of the passive results (the
lower the voltage, the higher the electronic conductivity). While this would have an
impact on cell performance (allowing a greater amount of parasitic current to flow), it
cannot be used as an indicator of cell performance, as shown by the results.
Other areas of the passive test results could be investigated in order to reveal more
about the condition of the fuel cell and how it will function when active.
3.7 Passive Testing and Active Correlation Summary
A new method of testing a proton exchange fuel cell has been proposed which is based
on testing the fuel cell while in a passive state Results of the passive test indicate the
comparative health or functionality of individual cells when the fuel cell stack is active.
Cell heath status can be inferred directly from the behavioural trend of the test results,
and requires minimal computational effort. The passive test is executed on the entire
stack, as the test circuit is attached to the stack terminals. By recording the voltage
transient on each cell during one test procedure, a comparative assessment can be
made on each cell Previous electronic test methods were either conducted on a single
cell in order to identify its properties, or only net stack properties could be obtained if the
test was conducted on the stack. This new approach has a number of possible uses.
Due to its simplicity, it could be easily used in an application setting, particularly for a fuel
cell stand-by system, where the fuel cell stack is in a passive state for most of the time.
This test would provide a simple way to predict the performance of the stack before it
becomes active The test could also be employed as a quick check from a production
line, enabling a quick indication of cell performance.

4. Equivalent circuit modelling
4.1 Introduction
Directly analysing the results of the passive test as shown in section 3, shows the
potential value of the passive fuel cell test and how it can relate to the fuel cell
characteristics and active functionality. A potentially more insightful method of analysing.
the results is to use an equivalent circuit model (ECM) as described in the prior art of
section 2. Based only on the fuel cell being in a passive state, an ECM is investigated
including a circuit parameter determination method.
4.1A Results and discussion
The passive test method outlined above was implemented on a single cell with the test
circuit being attached across cell #3 only. The values of the test circuit for this
experiment were RiTC = 100Q, R2TC = 4.9S2 and VTC = 0.05V. The resulting voltage
behaviour of cell 3 during the test procedure is shown in figure 7.
4.1 B Explanation of results and formulation of ECM
The phenomena occurring in the cell during various parts of the test procedure, and how
a corresponding passive fuel cell ECM (shown in figure 10) was inferred, is explained
below.
Charge up (ti -12): The first part of the curve is typical of a capacitor being charged with
a constant voltage source in series with a resistor (Rnc) Hence the ECM contains a
capacitor, C-|.
Natural Decay (t2 -13): In the natural decay region (fuel cell at open circuit), the voltage
declines as though the capacitor, Ci, is being discharged through a resistor. As a result,
the ECM contains a resistor Rp, in parallel with Ci, representing the electronic
conduction of the membrane. The resistance RP must not be confused with the
membrane resistance presented in the other fuel cell models, as this resistance
represents the conduction of H+ ions through the membrane, not electrons.
Discharge (t3 - t»): In the Discharge region, the voltage across the cell rapidly
approaches zero as expected, due to the charge in the cell being dissipated through
resistor Rzrc- As the resistor value R2TC is small, the cell is effectively short-circuited
during this period.

Self recharge (U - ts): When the stack is then open circuited after this rapid discharge
(time = U), the voltage across the cell rises to a maximum value before decaying, hence
this region is called the self recharge region. As stated in a previous section it is
believed that this phenomenon is caused by the free moving ions in the membrane.
When the cell is charged, the ions are forced away from the positive electrode and
towards the negative electrode, thus creating the typical double charge layer at the
electrolyte/electrode interface Even though the charge of the electrodes can be
reduced to zero rapidly (by shorting the cell), the uneven distribution of the ions in the
membrane takes more time to reach a uniform distribution through diffusion. The
uneven ion distribution still present when the short is removed forces a charge to build
up on the electrodes. In order to model the self-recharge effect in the ECM, a capacitor
and resistor in series (C2 R2) are placed in parallel across the first capacitor Ci. A
possible interpretation of R2 C2 based on the explanation given above is that R2 is
somehow related to the resistance of the ions in the membrane, and C2 is related to the
added capacitance (dielectric effect) of the free moving ions. The final component of the
model is resistor R-i, which is attributed to ohmic losses in the fuel cell, due to the
electrodes, contact resistance etc.
4.2 Formulation of the Fuel Cell Equivalent Circuit Model
The goal when formulating an Equivalent Circuit Model (ECM) of the fuel cell is to derive
the model from a physical standpoint of the fuel cell. This way, physical meaning can be
placed on the circuit model parameters. To formulate the ECM, basic elements of the
fuel cell (in a passive state) are considered. Initially, the electrodes (without a
membrane) are considered, which in a PEM fuel cell are essentially two high surface-
area conductors placed parallel to one another. This clearly means that a capacitor
would have to be placed across the terminals of an equivalent circuit model. Thus, the
fuel cell equivalent circuit model (shown in figure 10) has a capacitor Ci across the cell
terminals. The capacitance value of Ci would be related to surface area and the
separation of the electrodes. The membrane affects the characteristics of the cell
(when in a passive state) in a number of ways. Firstly, the membrane is not a perfect
electronic insulator, thus a resistor RP is added across Ci. The resistance RP must not be
confused with the membrane resistance presented in the other fuel cell models, as this
resistance represents the conduction of H+ ions through the membrane, not electrons.
The values of RP will depend on a number of things, not only the membrane, but also if
the electrodes happen to be touching in an area due to some defect etc. The affect the

membrane has on the total capacitance of the cell would be to increase it. Due to the
mobile ions, (and the formation of a double charge layer), the membrane has a very
large dielectric effect. Thus, in the equivalent circuit model, an additional capacitor C2 is
added in parallel to represent this increase in capacitance. In addition, as ions are
subject to resistance in the membrane, a resistor, R2 is placed in series with the
capacitor. Finally, if many cells are to be connected, there will be electrical resistance
between each cell,'thus a resistor R1 is placed in series with the circuit.
The passive fuel cell model shown in figure 10 is very similar to the existing model of a
DLC, the only difference being the placement of a resistor R1 (see figure 3a), and the
non-variability of G|. Based on the reasoning given above, placement of R1 must be the
first component in the circuit models (compared to the placement in a standard DLC
ECM), as any current travelling through RP due to a charge, must pass through R-i. In
DLC models, the variability in C1 (due to the double charge layer) is also present in the
passive model of a fuel cell However, given the reasoning above, it would make more
sense if the non-variability were placed on C2, as C2 was attributed membrane
properties The similarity between the passive fuel cell model and that of a DLC can be
attributed to the fact that the fuel cell has the same basic construction as a DLC. In
addition, as air is present at both of the fuel cell electrodes, and the test voltage is well
below the level needed to electrolyse water (present in the membrane), no
electrochemical reactions can occur during the test procedure. This leaves only faradic
processes to occur in the fuel cell, which are the only processes that occur in a DLC.
The model shown in figure 10 has been derived considering just the basic physical
nature of a fuel cell, thus is relatively simple. A more complex model (such as one
including voltage dependence capacitance) may be used, however the model is found to
adequately model a passive fuel cell as shown is the next section.
4.3 Verification of the Passive Fuel Cell Equivalent Circuit ModelA circuit simulation
program, PLECS (operating in the Matlab Simulink environment), was used to simulate
the passive fuel cell model with circuit parameters shown in table 2 (derivation of circuit
model values is described in section 4.5). Comparing the simulation and experimental
results (experimental details given in section 3.4 3.5), it can be seen that the modelled ,
data fits the experimental data with a good degree of accuracy (see figure 6). Hence the
equivalent circuit model, inferred from considering the physical nature of a passive fuel
cell, provides a good model of a passive fuel cell.


The way the circuit model is able to reproduce the voltage transient behaviour of a
passive fuel cell test is briefly described below, with consideration being given to the
physical interpretation of the circuit model components (as described in section 4.2).
1 Initial steady state: The Initial voltage values assigned to capacitors Ci and C2 in
the circuit model, simulate the initial potential measured across the passive cell.
2. Charge up (ti - t2): In the charge up region, the voltage across the cell rises in an
exponential like manner. The circuit model reproduces this voltage transient as
capacitor d is charged through the resistor Rue + RL The rise in voltage across the
cell is not purely exponential, and the presence of R2 C2 and RP results in the ;
modelled voltage rise not being a purely exponential also.
3 Natural Decay (t2 - U)' The Natural decay in cell voltage is due to the internal
conduction through the membrane, as well as the continued movement of H+ ions in
the membrane (as explained in section 3.5). The circuit model captures these two
characteristics by having capacitor Ci being discharged through resistor RP, and Ci
being discharge into C2 through resistance R2.
4 Discharge (t3 - t»): In the discharge region, the cell is connected across the
discharge resistor R2TC and the potential drops rapidly in an exponential like manner.
The circuit model captures this behaviour due to capacitor Ci being discharge
through R2Tc thus the voltage across model reduces to a value close to zero.
However, the charge on C2 remains to some extent due the added resistance of R2.
5. Self recharge (t* - ts): In the self recharge region, the potential across the cell builds
to a maximum then decays as in the Natural Decay region. As explained in section
3.5, this voltage transient is due to a residual charge being held in the membrane.
The equivalent circuit model reproduces this transient voltage behaviour as capacitor
C2 discharges into Ci through R2, thus increasing the potential across the cell as

observed. As the resistor RP will continue to conduct, the potential across Ci will
build to a maximum before decaying, thus reproducing the complete voltage
transient observed in the Self-recharge region.
4.4 Discussion 7
There are significant differences between the newly proposed ECM of a passive fuel cell /
(which is very similar to a DLC model) and fuel cell models proposed previously. Firstly, none of the existing fuel cell circuit models (passive or active) include electronic />
conduction of the membrane, which would be an additional loss term in an active fuel cell. It may be that the effect of membrane electronic conduction is only noticeable in the passive tests described, and other loss mechanisms, particularly hydrogen crossover, would mask the effects of the electronic conduction in an active fuel cell. As stated in
section 3 4, the passive fuel cell test cannot test all properties of the fuel cell, and I
molecular Hydrogen crossover is one such property. However, electronic conduction of/
the membrane would always be present, even if it were very small, and may indicate
other physical aspects of the fuel cell.
In all existing circuit models (excluding the very simple) at least two capacitors are
placed in series, and are attributed to the individual charge layers present at the anode
and cathode. This interpretation cannot be given to the passive fuel cell ECM, as the
capacitors present in the model are placed in parallel. An alternative interpretation of the
two capacitors has been proposed, in which one capacitor (Ci) representing the
capacitance of the electrodes only, and the other capacitor (C2) representing the added
capacitance provided by the ions in the membrane (providing a dielectric effect).
Clearly, only a passive model of a fuel cell is being proposed, thus differences are
expected when comparing existing circuit models that are largely based on an active fuel ,
cell. However, the validity of the existing models, (particularly when reduced to a
passive model) are explored in section 4.8.
4.5 Method for obtain the model values
PLECS, an electrical circuit simulator program that operates in the Matlab Simulink
environment, is used for obtaining the circuit simulation results. To derive the circuit
parameters, an algorithm was written in Matlab that uses the simulation results generate
by PLECS. A simplified overview of the algorithm depicted in figure 14, shows there are
two main parts, one for finding the circuit component values, the other for calculating the

initial voltage condition of the capacitors in the model. The circuit model parameters are
calculated by repeatedly stepping through each parameter, and successively selecting a
value that reduces the error (in the least squares sense or by using another error
calculation) between the simulated and experimental results. One method of selecting a
new circuit value is to generate a set of possible values for a particular circuit parameter,
simulate the model a number of times using each possible value, and then compare the
error each simulation gives.
The set of values can be generated by multiplying the existing parameter value, say R2,
by a spread vector, i.e.
R2x (0 75, 0.90, 0.99, 1.00, 1.01, 1.10, 1.25)
This gives 6 new values of R2, plus the original value, i.e. n + 1. The set of R2 values
this generates will consist of a large number centred on the original value, with a few
more out lying. This pattern of possible values makes the algorithm converge to a
solution. Changing the spread vector would change the algorithm convergence time and
accuracy. For example, the addition of 0.995, and 1.005 would achieve a better fit,
however the algorithm would take longer to converge.
The circuit is then simulated with each new value of the parameter. With each
simulation of the circuit, the error between the actual test data and the modelled test
data is recorded A new parameter value is then chosen, based on the smallest error
between the simulated and test data.
The same process is carried out for finding the initial voltage condition of the capacitors
as for finding the circuit component values. The spread vector used for generating the
set of circuit component values does not have to be the same as the one used for
generating the set of initial voltage condition values, hence n and m values are given in
the algorithm diagram. If the model of figure 10 is used, then only one initial condition
needs to be found for a cell, which is the voltage of C2 (the initial voltage of Ci is
measured directly at to). However, if a different model is used, more than one initial
condition may need to be found. Alternatively, when the initial values of the whole stack
are needed, there are 6 C2 values to find. As the algorithm determines the initial voltage

condition of the model capacitors, this overcomes one of the problems with current
methods of parameter identification, i.e. requiring an initial potential of OV.
The algorithm converges to a solution when the original value for all parameters
produces the smallest error. Using the spread vector given above, this implies that the
algorithm converges to a solution when any change in any one of the variables by 1%,
produces a larger error between the simulated and experimental data. A better fit
between the simulated and experimental results can be achieved by reducing the 1%
tolerance (thus changing the spread vector), but the 1% value was found to be an
adequate compromise between solution accuracy and computation time. In addition, the
circuit model used is still rather basic; hence, an identical fit (thus a unique solution) may
not exist. The proposed method of finding the circuit parameters is flexible, in that any
circuit model can be employed, including models containing voltage dependent
capacitors.
4.6 Whole stack simulation
To further verify the equivalent circuit model, the test procedure was implemented on the
entire stack (test circuit connected to the stack terminals) and the voltage response of
each cell measured. The corresponding 6 celled stack model (using the parameters in
Table 3) was simulated using PLEC, and the simulated (dashed line) and experimental
(solid line) results are compared in figure 11.

The advantage of obtaining the circuit parameters with the method described in section
4.5 is that it can be easily extended to find the parameters of each individual cell from
the data shown in figure 11. This saves having to do individual tests on each cell, then
individually obtaining the parameters of each cell. There are 30 circuit values to find, (5

condition of the model capacitors, this overcomes one of the problems with current
methods of parameter identification, i.e. requiring an initial potential of OV.
The algorithm converges to a solution when the original value for all parameters
produces the smallest error. Using the spread vector given above, this implies that the
algorithm converges to a solution when any change in any one of the variables by 1%,
produces a larger error between the simulated and experimental data. A better fit
between the simulated and experimental results can be achieved by reducing the 1%
tolerance (thus changing the spread vector), but the 1% value was found to be an
adequate compromise between solution accuracy and computation time. In addition, the
circuit model used is still rather basic; hence, an identical fit (thus a unique solution) may
not exist. The proposed method of finding the circuit parameters is flexible, in that any
circuit model can be employed, including models containing voltage dependent
capacitors.
4.6 Whole stack simulation
To further verify the equivalent circuit model, the test procedure was implemented on the
entire stack (test circuit connected to the stack terminals) and the voltage response of
each cell measured. The corresponding 6 celled stack model (using the parameters in
Table 3) was simulated using PLEC, and the simulated (dashed line) and experimental
(solid line) results are compared in figure 11.

The advantage of obtaining the circuit parameters with the method described in section
4.5 is that it can be easily extended to find the parameters of each individual cell from
the data shown in figure 11. This saves having to do individual tests on each cell, then
individually obtaining the parameters of each cell. There are 30 circuit values to find, (5

for each of the 6 cells), and the computation time simply increases compared to finding
the values of a single cell. Using the same convergence criteria, the circuit parameters
were obtained (shown in table 3) and the simulation of the circuit with these parameters
is also shown in figure 11. As can be seen, the simulated model results compare very
well with the data from the stack.
4.8 Simulation of existing fuel cell models
It is interesting to compare how well the other models proposed in the literature are able
to simulate the results of the passive fuel cell test as shown in figure 11. Hence, the
same algorithm was employed to find the best solution of two additional fuel cell models,
shown in figure 12 and 13. In both cases, the fuel cell model simulated is based on the
common ECM shown in figure 1 b. However, as a passive fuel cell is being modelled, the
voltage sources have either been regarded as an open circuit (shown in figure 12) or a
closed circuit, (figure 13). In addition, a resistor representing the electronic conduction
has been added, as this property has not been included in the original ECM of figure 1b.
The model shown in figure 13 most probably represents a fuel cell in a passive state
according to the reasoning behind the parameters in the original model, as the capacitor
properties (Ca Cc) are still present for a passive fuel cell (representing the double charge
layer at the anode and cathode), as is the with the ionic resistance (R|nt) of the
membrane. However, the other resistance present in figure 12 (Ra Re), are generally
attributed to the activation loss (charge transfers resistance), a phenomena that occurs
only during electrochemical reactions, hence, not present while a fuel cell is in a passive
state.



Upon first glance, the ECM in figure 12 and 13 may seem to capture the general
behaviour of the passive fuel cell, however there are significant discrepancies. In figure
12, (which is the better fit of the two models) a major discrepancy is observed at the start
of the charge region (ti). The model results showed a very large voltage step at ti
(difficult to see in the graph shown), which is not present in the experimental results.
Also the initial steady state region of this simulation could not be matched to the
experimental data In addition, the model that would most represent the fuel cell in a
passive state based on the physical interpretation given to its components (shown in
figure 13) does not comprehensively capture the behaviour of the passive fuel cell.
4.9 Conclusion
A new equivalent circuit model has been proposed for modelling a passive PEM fuel cell
The model is similar to a DLC model apart for the placement of the resistor attributed to
ohmic losses, and a constant capacitance is used, unlike the voltage dependent
capacitance typically employed for a DLC (however a variable C may be attributed to
C2). The ECM has been validated in two ways. Firstly, by identifying the similarity
between a fuel cell and DLC. This similarity is in the physical construction of the two
devices and in the types of processes occurring in each device (i.e. only faradic
processes, no electrochemical reactions). Comparing simulated and experimental test
results has also validated the model. Not only did the model reproduce the behaviour of
a single cell, but of many cells in series. A further confirmation of the model was shown
when two additional passive ECMs (reduced from active stack models) could not
simulate the response of the stack.

A new method of obtaining the circuit parameters of an equivalent circuit model has
been proposed. The method employs an iterative algorithm, and compares passive fuel
cell test results with simulation data. The algorithm is based on the results produced by
the test procedure, and relies on the test procedure producing a unique set of voltage
transits for each cell, from which a best-fit solution is obtained. The test procedure is
different to other DC tests previously carried out, as it contains a number of different
steps, which broadly may be stated in the following:
1. A procedure where the fuel cell stack is charged (in a capacitor sense with known
external charge conditions)
2 The charged fuel cell is then allowed to interact with a number of additional passive
circuit devices (in the detailed embodiment, open circuit -> R2TC -^ open circuit),
which produces additional voltage transient behaviour.
3. An ECM with a unique set of parameters can reproduce the voltage behaviour from
this test, hence an algorithm to find the parameters can be realised.
Although least squares fitting techniques have been used previously, they have only
been employed match simulated and experimental AC impedance spectroscopy data.
This testing procedure and corresponding technique to obtain the circuit parameters can
be applied to an entire stack. All previous methods for finding the circuit parameters of a
stack (or DLC) can only be implemented on a single cell. The new method proposed
allows all circuit parameters of each cell in a stack to be obtained from only 1 test, which
takes in the order of minutes complete. Due to these advantages, the passive test and
circuit model analysis technique could have a number of uses. For example, a problem
in manufacturing could be identified by conducting a passive fuel cell test off the
production line, in conjunction with a circuit model analysis.
While the present invention has been illustrated by the description of the embodiments
thereof, and while the embodiments have been described in detail, it is not the intention
of the Applicant to restrict or in any way limit the scope of the appended claims to such
detail. Additional advantages and modifications will readily appear to those skilled in the
art Therefore, the invention in its broader aspects is not limited to the specific details,
representative apparatus and method, and illustrative examples shown and described.

Accordingly, departures may be made from such details without departure from the spirit
or scope of the Applicant's general inventive concept*

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WE CLAIM :
1. A method of testing a fuel cell, the method comprising charging the fuel
cell during a charge period; discharging the fuel cell during a discharge
period; and monitoring the response of the fuel cell during at least part of
the discharge period; and calculating one or more equivalent circuit values in
accordance with the monitored response of the passive fuel cell, characterized in
that the one or more equivalent circuit values comprise a first resistance value as
a first component in an equivalent circuit model that represents electrical
resistance between each fuel cell and fixed first capacitance value representing a
capacitance across terminals of the fuel cell.
2. A method as claimed in claim 1 wherein the response of the fuel cell is
monitored by monitoring a step change in the voltage across the fuel cell
during the at least part of the discharge period.
3. A method as claimed in claim 1, comprising making the fuel cell open-
circuit after the charge period, and monitoring the open-circuit
response of the fuel cell.
4. A method as claimed in claim 1 wherein the fuel cell is discharged
during the at least part of the discharge period through one or more
passive test components.

5. A method as claimed in claim 3 wherein the open- circuit response of the
fuel cell is monitored by monitoring the rate of change of voltage across
the fuel cell.
6. An apparatus configured to perform the method as claimed in claim 1.
7. A method as claimed in claim 1 wherein the one or more equivalent
circuit values comprise a second resistance value that represents a
resistance of a membrane of the fuel cell, a third resistance value that
represents a resistance to the movement of ions in the membrane, and
a second capacitance value representing a dielectric effect of the
membrane.
8. A method as claimed in claim 1 wherein the equivalent circuit values
comprise a second resistance value that represents a resistance of a
membrane of the fuel cell and the first capacitance value is in parallel
with the second resistance value.

9. A method as claimed in claim 1 wherein the equivalent circuit values
comprise a third resistance value in series with a second capacitance
value, where the third resistance value represents a resistance to the
movement of ions in the membrane and the second capacitance value
represents the dielectric effect of the membrane, wherein the first
capacitance value is in parallel with a series arrangement of the third
resistance value and second capacitance value.

ABSTRACT

TITLE "A METHOD OF TESTING A FUEL CELL"
The invention relates to a method of testing a fuel cell, the method
comprising charging the fuel cell during a charge period; discharging the
fuel cell during a discharge period; and monitoring the response of the
fuel cell during at least part of the discharge period; and calculating one or
more equivalent circuit values in accordance with the monitored response of the
passive fuel cell, characterized in that the one or more equivalent circuit values
comprise a first resistance value as a first component in an equivalent circuit
model that represents electrical resistance between each fuel cell and fixed first
capacitance value representing a capacitance across terminals of the fuel cell.