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An Embedded Frequency Response Analyzer forFuel Cells Monitoring and Characterization

Martin Ordonez,Member, IEEE, Maximiliano O. Sonnaillon,Member, IEEE, John E. Quaicoe,SeniorMember, IEEE, and Mohammad T. Iqbal

Abstract—This paper presents an embedded frequency re-sponse analyzer (EFRA) for Fuel Cells (FC) based on arobust measurement technique with simple implementation.Frequency response analysis technique provides valuable in-formation of different electrochemical processes that occurinside the FC. The measurement system is implemented on alow-cost Digital Signal Processor (DSP) to perform frequencyresponse and impedance tracking. The small size and lowpower consumption allows this special device to be embeddedinto the FC controller or the power conditioning stage. Thesystem is capable of measuring automatically the frequencyresponse of the FC at different operating points, even when theFC is operating with load. These measurements can be usedto characterize the FC at design stage and to perform on-linemonitoring of the FC state during continuous operation. Theproposed instrument uses the lock-in amplification technique,which allows very accurate and precise measurements evenin the presence of high noise levels. The proposed hardwareand signal processing technique are described in this paperincluding experimental result of a 1.2kW Proton ExchangeMembrane Fuel Cell (PEMFC) system.

Index Terms—Fuel cell, frequency response, impedance,lock-in, monitoring.

I. I NTRODUCTION

Fuel Cells (FC) are power sources that convert electro-chemical energy into electrical and thermal energy in a cleanand efficient manner. Fuel cells have the potential to meet anew generation of energy conversion standards comprisinghigh efficiency, low emissions, and quiet operation. A basicFC arrangement is like a battery consisting of anode andcathode electrodes linked by electrolyte. However, unlikebatteries, FCs can operate continuously while they areexternally fed with reactant (fuel) [1].Frequency Response Analysis (FRA) provides a powerful

Manuscript received March 1, 2009; revised April 14, 2009. Accepted forpublication July 2, 2009. This work was supported by the Natural Sciencesand Engineering Research Council (NSERC) and the Atlantic InnovationFund (AIF), Canada.

The authors are with the Faculty of Engineering and Applied Science,Memorial University of Newfoundland, St. Johns, NL A1B 3X5,Canada(e-mail: mordonez@ieee.org).

Copyright (c) 2009 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to pubs-permissions@ieee.org.

technique to characterize dynamic systems and it is usedin wide variety of applications. FRA is applied to iden-tify parameters of mechanical systems [2], electromagneticsystems [3] and electrochemical systems [4], [5], and it issuccessfully employed to detect different types of abnormaloperating conditions in electric motors [6], [7].FRA technique measures the impedance of a system at dif-ferent frequency values within a given spectrum of interest.The instrument injects a small perturbation signal to theFC and perform measurements of the voltage and currentresponse [8]. When applied to FCs, this technique allowsthe characterization of different electrochemical processesthat are produced at different timescales. For example, ina Proton Exchange Membrane Fuel Cell (PEMFC), thehigh-frequency response depends mainly on the electrodekinetic response, while the low-frequency response can beattributed to water management [9]. By computing the realand imaginary components of the impedance, the parametersof an equivalent electrical circuit of the system can beidentified [10]. In addition, since the AC perturbation signalhas small amplitude, it can be superimposed on a DCsignal allowing the measurement of the system at differentoperating points.Measurement instruments for FC characterization that arecommercially available [11], mainly focus on electro-chemistry techniques such as impedance spectroscopy andvoltammetry. The main drawbacks of these instruments arelack of flexibility and high cost. Such instruments cannot bereprogrammed to perform custom automated tests. Further-more, an electronic load module is also required as part ofthe measurement device resulting in a bulky system.Special systems have been presented in the literature toperform FRA in FCs. In [4] a measurement system based inFast Fourier Transform (FFT) has been developed. FFT lacksof noise immunity and good resolution in low frequencies.In [5] two different techniques are proposed to indentify theparameters of a simplified equivalent circuit of the FC. Theequivalent circuit is explained with relevant electrochemicaldetails. The presented measurement methods require intro-ducing big perturbations to the FC due to limitations in noiseimmunity.

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This paper presents a novel measurement device basedon lock-in amplification technique (LIA) and a low-costDigital Signal Processor (DSP). The proposed instrumentperforms FRA at programmable operating points whileproviding high noise immunity. The main advantages of theproposed system, in comparison with previously publishedsystems and comercial instruments are: robustness/noiseimmunity, simplicity, automatic operation, low-cost, low-power consumption and small size. Furthermore, due to thesimple hardware architecture, it can be integrated as partof the FC control system or embedded in the FC powerconditioning stage. The superior noise immunity providedby the measurement technique allows precise measurementsof the frequency response by injecting very small pertur-bation signals to the FC. Such arrangement allows real-time monitoring and diagnosis of a real FC application. Theproposed Embedded Frequency Response Analyzer (EFRA)is useful in the diagnosis of possible failures or performanceevaluation during the operation of the FC.Figure 1 shows two potential configurations of the systemusing the proposed EFRA. Figure 1(a) shows the EFRAembedded into the power conditioning system. The EFRAalgorithms can be implemented in the same processorthat controls the power conditioning stage, for digitallycontrolled systems [12]. In this configuration, the EFRAis linked with the FC controller, which regulates the FCoperating parameters based on the on-line measurements.The EFRA measurements can also alert the power con-ditioning to prevent system failures. Figure 1(b) showsanother configuration, where the EFRA is embedded inthe FC system controller. Here the EFRA measures andregulates automatically the FC variables to ensure optimalFC operating conditions. It can also prevent FC damages incase of system failures or incorrect FC operating conditions.This special device can be integrated or embedded as part ofFC power systems in a wide variety of applications such astransportation [13], [14], [15], stationary power generation[16], [17], hybrid energy sources [12], and portable powerapplications [18].

II. M EASUREMENTTECHNIQUE

The proposed system uses a measurement technique knowas lock-in amplification (LIA), or synchronous detection,which allows accurate and precise AC measurements, evenin the presence of high noise levels. Power electronicsconversion stages that extract power from FCs generatesignificant levels of noise due to high voltage and currentslew-rates involved in switches commutations. The lock-in amplification technique, has been proven to provide thesuperior noise immunity required to measure small signalsin switching converters [3], [7].A LIA uses a reference signal that can be generated by

Fig. 1. Possible applications of the proposed EFRA: FRA embedded ina) the power conditioning system, and b) FC system.

the same instrument or can be generated externally. In thiswork, the reference is generated by the instrument, whichis embedded in the system. The general expression for theinternal reference is,

r(t) = sin(2πf0t) (1)

The LIA input signal i(t) is composed of a sinusoidalsignal of frequencyf0 with arbitrary amplitudeA andphaseθ, added to a generic functionn(t) that representsnoise, harmonic distortion, or DC component presentin the signal. In the embedded FRA presented in thispaper, the DC component inn(t) is mainly produced bythe FC operating point, and is much larger than the ACsignal to measure. Other typical noise components arehigh-frequency switching noise and line-frequency rippleproduced by single-phase inverters connected to the FC.

i(t) = A sin(2πf0t + θ) + n(t) (2)

A digital LIA amplifies and digitizes this signal. The DSPsoftware multiplies the input signal by the in-phase andquadrature (shifted 90 degrees) components of the referenceas given by,

Pp(ti) = i(ti)×rp(ti) =

=1

2A cos(θ) −

1

2A cos(4πf0ti + θ) + np(ti) (3)

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Pq(ti) = i(ti)×rq(ti) =

=1

2A sin(θ) +

1

2A sin(4πf0ti + θ) + nq(ti) (4)

where rp and rq represent the references in-phase andquadrature respectively (sine and cosine functions),np andnq represent the noise functions after the products, and theith sampling instant is represented byti.

By filtering the AC components and keeping only theaverage value (the DC signal), two signals with the in-phaseand quadrature components of the input signal are obtainedas

x = 2P p ≈ A cos(θ) (5)

y = 2P q ≈ A sin(θ) (6)

If effective low-pass filtering techniques are used, the lock-in technique will provide excellent accuracy and noiseimmunity, even when the noise signals (np andnq) are muchlarger than DC components that have the useful information(x and y). Thus, the magnitude and phase of the input signalcan be computed as

M =√

x2 + y2 = A (7)

Ph = tan−1

(y

x

)

= θ (8)

where tan−1(y/x) computes the inverse tangent functionof y/x and takes into account the signs of both variables inorder to give the correct quadrant.

III. SYSTEM IMPLEMENTATION

A prototype of the proposed instrument was implementedusing a low-cost fixed-point DSP (TMS320LF240xA). Sincefixed-point DSPs are commonly used in power electronicsapplications, this system can be easily embedded in the FCcontroller or the power conditioning stage.

A. Software and Hardware Description

Figure 2 shows a conceptual block diagram of theproposed system. The DSP generates a current referencethat is composed of a small AC signal superimposedon a DC operating point. This reference signal feeds aclosed-loop current regulator that controls the AC loadingcondition of the FC. Since the AC perturbation is small,the current regulator power rating is a just a few mWper kW of the FC rated power. The low power currentregulator is implemented with an operational amplifierdriving a MOSFET working in the active region. Currentmeasurement is performed using a precision sensingresistor. A conceptual representation of the AC perturbationintroduced by the instrument is presented in Fig. 3, wherethe small current regulator is connected directly to the

Referencesignal

Lock-in

Impedancecomputation

DCGain

Output voltagemeasurement

Currentregulator

Controllableresistive load

Direct MethanolFuel Cell

Currentsensingresistor

Currentmeasurement

Non-volatileMemory

Lock-in

Digital processing

Fig. 2. Conceptual block diagram of the embedded instrument.

DC/DCor

DC/AC

Load

Regulator

Unreg. HPDC

+ small AC

Fuel Cell

Unreg.

HPDC

small

AC+DC

Reg. HP

DC or AC

Fig. 3. Conceptual block diagram of the small AC perturbation injectedin the FC system.

output of the FC. In order to avoid current clipping, theinstrument also extracts a small DC level as indicated inFig. 3. The High Power DC (HPDC), unregulated (Unreg.)and regulated (Reg.) power flow are also indicated in thefigure.

Measured signals (current and voltage) are amplifiedusing low-noise and wide bandwidth operational amplifiers.The bandwidth of the signal conditioning must be wideenough to avoid phase shifts that may lead to errors in theimpedance measurements.The current and voltage measurements are digitized usingthe DSP on-chip analog-to-digital converters (ADC) at asampling rate of 50kHz. Each ADC conversion generatesan interrupt that runs the following routines:

• Current reference generation: the DSP computes thecurrent reference value and sends it to a digital-to-analog converter.

• Lock-in algorithm computation: two identical lock-inalgorithms are computed, as shown in Fig. 4. With thecurrent and voltage measurements, the DSP computesthe electrical impedance at the measured frequency andstores it in memory.

The lock-in block implements the mathematical operationsdescribed in the previous section. First, the input signal (volt-age or current) is multiplied by the in-phase and quadratureinternal references. After that, the average value is obtainedby filtering the AC components. The AC spectrum is mainly

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Input signal(voltage or

current)

MAFLPF

X

Y

Outputs

Fig. 4. Lock-in amplification block diagram.

composed by three different components:• Component atf0: it is produced by the product of

the input DC component (DC operating point) and theinternal reference.

• Component at2f0: it is produced by the product ofthe injected AC perturbation signal and the internalreference.

• Components at any other frequencies: components thatare not synchronized withf0 can be considered asnoise. Examples of this type of noise are the switchingnoise of power converters and any other measurementnoise.

When the reference frequency (f0) is low (e.g. 0.1Hz),the first two components are difficult to eliminate, becausetraditional filtering techniques require very long settlingtimes. This would result in unacceptable measurement timesto characterize the FC. In the proposed system, the filteringtime is significantly reduced by using a synchronous MovingAverage Filter (MAF) as the low pass filter (LPF). The MAFlength is programmed based on the reference frequency tofit exactly an integer number of cycles. If the MAF lengthis TMAF , it is computed as:

TMAF =k

f0

(9)

Ideally, the frequency response of the resulting MAFcompletely eliminates any frequency component off0

and its harmonics as indicated in Fig. 5. It is critical toselect TMAF andf0 to meet (9), in order to enhance theeffectiveness of the filter. Experimental results show anexcellent performance of this filter. The number of cycles(k) is chosen to improve the filtering of other frequencycomponents. Higher values ofk will result in improvednoise immunity but higher measurement times.

The outputs of the LIA are two DC values that corre-spond to the in-phase and quadrature values of the inputsignal. From the measured voltage and current, the compleximpedance is computed as:

Z(ω0) = R(ω0) + jX(ω0) (10)

−35

−30

−25

−20

−15

−10

−5

0

Mag

nitu

de (

dB)

Frequency (Hz)

f0

2f0

3f0 ....

Fig. 5. MAF filtering characteristics.

Precision

resistor

Current

regulator

DSP chip

(bottom)Instrumentation

(bottom)

CAN bus

DAC

Serial

Peripheral

Interfase

Analog

ADC input

signals

Fig. 6. DSP board and instrumentation prototype.

R(ω0) = Re

V (ω0)

I(ω0)

=VXIX + VY IY

IX2 + IY

2(11)

X(ω0) = Im

V (ω0)

I(ω0)

=VY IX − VXIY

IX2 + IY

2(12)

whereVX , VY , IX andIY are the in-phase and quadraturecomponents of the measured voltage and current, respec-tively. The instrument takes the impedance measurementsat several frequencies (N ), configured by the user, in orderto obtain the frequency response in the required frequencyrange. The connection between the instrument and otherequipment is performed through a CAN bus that ensuresrobust high-speed data transmission under noisy electricalenvironments [19]. A picture of the system prototype isshown in Fig. 6.

B. Measurement Sequence

The implemented prototype operates in stand alone modeand performs the measurements automatically. A PC isonly used to configure the measurement parameters and

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to download the measurement data through the CAN bus.The definition of the measurement parameters is as follows:

N : Number of frequency pointsfmin : Minimum freq. valuefmax : Maximum freq. valuekmin : Minimum number of cycles each frequency point

is measured.Tmin : Minimum time each frequency is measured.

Defines minimum value ofk as a function off0. This isimportant to limit the minimum measurement time for highreference frequencies.

Tmax : Maximum time each frequency is measured.Defines maximum value ofk as a function off0. This isimportant to limit the maximum measurement time for lowreference frequencies.

Twait : Settling time the DSP waits before each frequencymeasurement. This is intended to avoid the influence of tran-sient dynamics that can occur when the reference frequencyis changed.

The procedure required to measure the frequency responseof the FC is described as follows:

1) The user generates a configuration file that stores themeasurement parameters. These parameters are sentto the DSP through the CAN bus. The PC softwarecomputes theN frequency values distributed logarith-mically within the specified frequency range.

2) The DSP starts the measurement process triggered byan external signal (push button, digital input or CANmessage).

• First, the no-load voltage is measured by settingto zero the current reference.

• The current reference is set to a fixed DC valueand the DC impedance is measured.

• Finally, the DSP starts theN -point frequencyresponse measurement. Before measuring eachfrequency point, the DSP waits a settling timeto avoid measurement errors due to current andvoltage transients.

3) When the EFRA finishes the frequency scan, it storesthe measured values in memory and waits for a newmeasurement. The data is stored in memory until it isdownloaded to the PC through the CAN bus.

C. Design Considerations

Some design aspects should be considered to ensuresuccessful operation of the instrument. One importantaspect is the bandwidth of the power converter in relation tothe AC perturbation frequency range. When an AC currentperturbation is introduced to the FC system, it is expectedthat a small AC voltage ripple will develop across the outputimpedance of the FC. It is desirable to have a bandwidth in

the power converter that exceeds the intermediate frequencymeasured by the instrument. For instance, for the analyzedcase example in this paper, the intermediate frequency is inthe vicinity of (fmin + fmax)/2 = 2.5kHz (Recall that theFC output impedance is maximum at this frequency). Sincethe frequency response of the FC is well below typicalswitching frequencies, it is straightforward to achieve ahigher bandwidth in the power converter. Such bandwidthhelps to inherently reduce or eliminate potential audiosusceptibility issues. Nevertheless, by selecting the numberof cycles kmin, the measurement of the FC impedanceis performed by injecting a very small perturbation thatis almost imperceptible to the power converter whilemaintaining a high degree of accuracy in the measurement(low signal to noise capability).Another important aspect is the signal conditioning ofthe measured variables. The effect of aliasing has to beconsidered to prevent alterations of the results, speciallyunder noisy environment. By considering the maximumfrequency value expected during tests, a passive anti-aliasingfilter is required to be included as part of the design andis located at the input of the ADC. The passive filtershave precision resistors and capacitors to ensure matchingbetween cutoff frequencies of each acquisition channel.The selection of the current sensor technology dependson the power rating of the power generation system.Measurement of low current using shunts present a numberof advantages including low cost, low power dissipationand high accuracy (excellent linearity). When the powerrating of the system increases, the use of shunt may becomeimpractical due to the lack of isolation between the EFRAand the power stage, as well as its size increase. In suchscenario the use of hall effect sensor becomes an idealsolution to replace the shunt counterpart. The cost of a halleffect sensor in high power application becomes only asmall fraction of the overall cost of the system.

IV. EXPERIMENTAL RESULTS AND VALIDATION : FUEL

CELL ELECTRICAL EQUIVALENT CIRCUIT

A comprehensive review of the many models developedfor FCs has been presented in the literature [20], includingthe main technical challenges [21], and dominant powerconversion technologies [22]. The electrical behavior ofpolymer electrolyte FCs can be analyzed in terms of anelectric model [23] and also using alternative approaches,such as neural networks [24]. What follows is a descriptionof the basic features needed to understand the electricalcharacteristics of the FC, considering the well establishedequivalent circuit shown in Fig. 7 and Fig. 8.

In Fig. 7, the electrochemical and thermal behavior ofthe FC is modeled using the following components:E

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is the equivalent internal potential or open circuit outputvoltage. For a Direct Methanol Fuel Cell (DMFC), thetheoretical voltage (E) in Fig. 7 is given as a function ofthe methanol and oxygen feed concentrations by the Nernstequation [1]. The theoretically predicted value lies around1.2V for a single cell. However, typically, the practicalopen circuit output voltage remains below 0.8V, and thevoltage drops further as current is drawn from the cell.Eo is standard reference potential at 1 ATM and 25. fE

is a non-linear potential associated to chemical reactantvariations and fuel/oxidant delay and is a function of thecell internal temperature and the output current. In thismodel, the activation voltage dropVAct(T ) corresponds tothe activation of the anode and cathode, which dependsprimarily on the cell temperature, the catalyst effectiveness,and the active areas of the electrodes. The effect of theoutput current associated with the activation voltage dropis modelled byRAct. ROhmic represents the voltage dropdue to the resistance of the electrodes (electrons) and mem-brane (protons). The concentration voltage drop reflects thedecreases in the concentrations of the reactants within theelectrodes, for example, methanol at the anode and oxygenat the cathode in a DMFC. This is included in the modelasRConc. Finally, the thermodynamic block represents theslow thermal dynamic behavior of the FC (T ) as a functionof ambient temperature, output current, output voltage, andinternal potential. The thermal mass of the FC is large dueto the combined product of the masses of the different com-ponent of the assembly and their respective heat capacities.The electrochemical reaction produces heat in addition toelectricity. The power loss of the FC can be estimated bysimply multiplying the output current times the differencebetween the output voltage and the ideal Nernst voltage. Thecloser the output voltage is to the Nernst voltage, the betteris the efficiency of the electrochemical power conversion.The FC thermal behavior can be described as a temperaturegradient produced by the power losses along the equivalentthermal resistances (distributed) of the assembly and theambient temperature, as well as air flow conditions. In thiswork, the focus is on the electrical behavior of the FC andits output impedance characteristics.

As can be seen in Fig. 7, the model shows an intricatenon-linear dependence on temperature and reactants behav-ior. Nevertheless, when the FC is operated with fixed operat-ing conditions (i.e., fixed temperature, fuel concentration andair flow), the model of Fig. 7 can be significantly simplifiedusing the circuit in Fig. 8.

The several factors that cause voltage drop or irreversibil-ity, namely activation losses (Tafel equation), fuel crossoverand corrosion, internal currents, ohmic losses, and masstransport are conceptually represented in a simple generalequation (13) [1]. The influence of these factors results in

Fig. 7. Fuel cell equivalent circuit.

Fig. 8. Simplified equivalent model of the Fuel Cell.

the FC polarization (voltage vs. current).

Vo = E − ∆VOhmic − ∆VAct − ∆VTrans (13)

The second term in (13),∆VOhmic, represents the voltagedrop due to the electrodes and membrane resistance. Thethird term of the equation,∆VAct, corresponds to theactivation of the anode and cathode. Finally,∆VTrans isdue to decreases in the concentrations of the reactants.

In the equivalent circuit shown in Fig. 8, the ohmic lossis represented byROhmic, while the activation and masstransport losses are combined asRa. AlthoughRa exhibitsa complex dependence on the current drawn from the cell, itcan be considered as approximately constant under mediumand high loading conditions. The electrodes capacitanceC,known as the double layer capacitance, acts in parallel withRa. The double layer capacitance is a characteristic of anyinterface between an electron conducting phase and an ionconducting phase. It arises from the fact that (in the absenceof a Faradaic process) charge cannot cross the interface whenthe potential across it is changed [25]. The key componentfor the FC dynamic behavior is the large capacitance (C) ofthe cell [26].

The action of the cell capacitance in conjunction with∆VAct and∆VTrans is described using Kirchhoff’s current

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law as follows:

d(∆VAct + ∆VTrans)

dt= io

1

C−

∆VAct + ∆VTrans

RaC(14)

where io is the FC output current, andRa is a non-linear resistor that produces both∆VAct and∆VTrans dropsduring steady state operation.

For a given set of operating conditions (i.e., specifiedtemperature, fuel concentration and air flow), the parametersin the model will remain approximately constant, exceptfor Ra at low current densities. A change in the operatingconditions produces a change in the values of the modelparameters.The impedance measurement technique was preliminaryevaluated in Matlab using different test circuits. Those testcircuits were reproduced experimentally and measured withthe EFRA to validate its performance. In order to provide ameaningful validation, the selected experimental test circuitrepresents the simplified equivalent model of the FC. Forthis purpose a discrete passive network was implemented.Even though FCs are highly non-linear systems, a linearelectrical equivalent circuit represents approximately FCselectrical behavior when operated with small signal at aquiescent operating point. For this reason, the instrumentwas first evaluated using a known network that matchesthe FC equivalent electrical model, as shown in Fig. 8. Theresults using the EFRA for the electrical equivalent circuitin Fig. 8 were compared to both the theoretical behaviorof the network as well as the response using a CommercialFrequency Response Analyzer (CFRA) [11]. Figure 9 showsthe bode plot (magnitude and phase frequency response)and Fig. 10 the Nyquist impedance diagram for the FCelectrical equivalent circuit. The test parameters employedin the measurement are shown in Table I, where both theEquivalent Series Resistance (ESR) of the capacitor andthe Equivalent Series Inductance (ESL) of the connectionare indicated. The measurement configuration are outlinedin Table II. As can be noted in Fig. 9 and Fig. 10 theEFRA accurately fits the response obtained with the CFRA.Moreover, when the parasitic value of the capacitor andthe connection are included in the electrical equivalentcircuit, both analyzers have good match with the theoreticalfrequency response and impedance diagram.

V. EXPERIMENTAL RESULTS: PROTON EXCHANGE

MEMBRANE FUEL CELL

The proposed EFRA is used to perform frequency re-sponse analysis of a Ballard Nexa 1.2kW PEMFC system[27] operating with a fixed fuel pressure of 1.6 barg andvariable air flow rate (automatically controlled by the sys-tem). The experimental measurements consist of extractinga fixed DC current superimposed by a small AC signal

0

1

2

3

Mag

nitu

de (

dB)

EFRACFRAIdeal+parasiticsIdeal

10−1

100

101

102

103

−20

−10

0

10

Frequency (Hz)P

hase

(de

gree

s)

Fig. 9. Bode plot of the test circuit using the Embedded FRA (EFRA),commercial FRA (CFRA), and ideal response.

1 1.2 1.4 1.6 1.8 2−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Real (Ω)

Imag

inar

y (Ω

)

EFRACFRAIdeal

f = 0.1 Hz

f =5 kHz

Fig. 10. Nyquist impedance plot of the test circuit: Embedded FRA(EFRA), Commercial FRA (CFRA), and ideal response.

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TABLE ITEST CIRCUIT PARAMETERS

Circuit parameters V alue

Ra 1.07 ΩRohmic 1.00 Ω

C 36 mFESR 8.0 mΩESL 5.0 µH

TABLE IIMEASUREMENTCONFIGURATION FOR THETEST CIRCUIT

FRA parameters V alue

N 25 pointsfmin 0.1 Hzfmax 5 kHz

k 50 cyclesTmin 10 sTmax 20 sTwait 1 s

with variable frequency. The DC current sets the operatingpoint of the FC, and the AC signal is used to measure theimpedance of the FC at different frequencies. The measuredfrequency response is used to compute the parameters of theFC equivalent circuit.

The frequency response of the PEMFC at three differ-ent operating points was performed using the parametersof Table III. Figure 11 shows the magnitude and phaseof the frequency response. Figure 12 shows the resultingimpedance diagram. It can be noted in this plot that theimpedance values for low frequencies vary significantly atdifferent operating points.

From the Nyquist impedance plot in Fig. 12, theparameters of the FC equivalent electrical circuit canbe obtained as follows. Since the charge double layercapacitorC has large impedance for low frequencies, the

TABLE IIIMEASUREMENTCONFIGURATION FOR THEFC TEST

FRA parameters value

N 30 pointsfmin 0.1 Hzfmax 5 kHz

k 50 cyclesTmin 10 sTmax 20 sTwait 1 s

−6

−3

0

3

6

Mag

nitu

de (

dB)

IDC

= 1.25A

IDC

= 2A

IDC

= 3A

10−1

100

101

102

103

−40

−20

0

20

40

60

Frequency (Hz)P

hase

(de

gree

s)

Fig. 11. Bode plot of a PEMFC using the EFRA for three operatingpoints.

0 0.5 1 1.5 2 2.5 3 3.5−1

−0.5

0

0.5

1

1.5

Real (Ω)

Imag

inar

y (Ω

)

IDC

= 1.25A

IDC

= 2A

IDC

= 3A

f = 0.1 Hz

f = 5 kHz

Fig. 12. Nyquist impedance plot of a PEMFC using the EFRA for threeoperating points.

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TABLE IVESTIMATION OF THE EQUIVALENT CIRCUIT PARAMETERS

IDC ROhmic Ra

1.25 A 220 mΩ 3335 mΩ2 A 220 mΩ 2030 mΩ3 A 220 mΩ 1430 mΩ

low frequency points (0.1 Hz) in the Nyquist impedanceplot indicates approximately the sum ofRa and ROhmic.On the other hand,C presents very low impedance at highfrequencies. Particularly, when the imaginary component isequal to zero at high frequencies, the impedance diagramindicates ROhmic value, which is equal for the threeevaluated operating points. Hence, by evaluating twospecific frequencies, these important parameters can beestimated using the EFRA providing a valuable tool foron-line monitoring, diagnosis, and characterization of FC.Table IV shows the estimated values for the evaluatedoperating points.Since the actual minimum and maximum frequenciesrequired to measureRa and ROhmic are unknown, aninitial frequency scan is necessary to narrow thefmin

to fmax range and accelerate subsequent measurements.The ability to measure the entire frequency response ofthe FC allows to estimate other parameters and fit morecomplex models. For example, whilefmin and fmax

allows to estimateRa andROhmic, the value of the doublelayer capacitorC can be estimated by measurementsin the medium frequency range. Such ability permitsdetermining dynamic characteristics of the FC which arehighly dominated by the double layer capacitance.

Finally, Fig. 13 shows the AC components of the outputvoltage for currents of different frequencies extracted bytheEFRA. It can be noted that the FC output voltage containsripple as well as noise due to the load and the auxiliaryequipment, which is also supplied by the FC (e.g. air blowerand electronic control board). As the frequency of the sinu-soidal current extracted by the EFRA aproaches the existentripple, the signal to noise ratio decreases dramatically (heresignal is considered as the AC voltage component of thesame frequency as the EFRA current). As predicted by thelock-in amplification theory, the proposed instrument wasable to obtain accurate and precise measurements even inthe presence of high noise levels. In the presented measure-ments, the RMS value of the extracted AC current is 50mA,which represents a signal 60 times smaller than the DCoperating point (in the case ofIDC = 3A). This fact showsthat the embedded instrument is able to precisely measurethe magnitude and phase of the AC signal in presence of

Fig. 13. EFRA current extraction waveform (Ch1) and PEMFC output volt-age waveform (Ch2): a) Current extraction frequency below ripple voltagefrequency, b) current extraction frequency close to ripplevoltage frequency,and c) current extraction frequency beyond ripple voltage frequency.

noise levels at least 60 times higher. The AC signal level canbe further reduced if required and the noise immunity canbe increase as much as desired by incrementing the numberof averaged cycles (k).

FCs are non-linear systems that present a differentfrequency response and impedance characteristic underdifferent operating conditions. A change in loadingcondition results in a new operating point in the FC. Inthis work, the impedance measurements are performed ata quiescent operating point to reflect the FC status undera certain loading condition and FC input parameters. FRAtechnique is based on steady state operation, and this workaims to detect operating conditions with small changes overtime or under repetitive changes. A sudden load change mayinterfere with the measurement process. Since the controlleris aware of the output loading condition, the measurementcan be restarted with the new operating point in the FC. Ifperiodical changes in loading conditions occurs (i.e., 120Hzripple current from an inverter) the instrument is capableof measuring the average state successfully. This is due tothe fact that the measurement is based on the AC currentperturbation that is injected and controlled by the EFRA.

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In order to avoid erroneous measurement in the vicinity ofripple current frequencies (e.g., 120Hz and harmonics ininverter applications), the number of pointsN should beselected to avoid hitting the low frequency ripple currentand harmonics or by using a large number of pointN .The data acquisition of the FC output voltage is performedby measuring the voltage ripple that includes the small ACperturbation generated by the EFRA. In order to optimizethe resolution of the measured signals, the instrumenttakes the voltage measurement and subtracts its largeDC component using a DAC and a difference amplifier.This technique is similar to the one typically used inoscilloscopes to measure small AC signals on top of largeDC components. As a result, only the AC components areamplified and converted using a 10-bit ADC. It is worthmentioning that LIA technique can operate with much lowerresolutions (<5-bit) by increasing the minimum numberof cycles (kmin) the lock-in averages. Hence, there is atrade-off between resolution and S/N ratio in the measuredsignals and the measurement time.

VI. CONCLUSION

A measurement instrument for FC monitoring andcharacterization based on a low cost DSP was presentedin this paper. Due to its simple hardware architecture andlow power consumption, it can be easily integrated as partof the FC control system or embedded in the FC powerconditioning stage. Such arrangement allows performingreal-time monitoring and diagnosis of a real FC application.A robust digital lock-in amplification technique providesthe required accuracy to the measurements under noisyelectrical environments. Hence, the embedded instrumentcan be used on-line, while a power electronics stage isextracting power from the FC. The proposed embeddedinstrument can be used in the diagnosis of possible failuresor in the evaluation of the FC performance during itsoperation. As well, the proposed instrument allows theequivalent circuit parameters of the FC to be estimated.Since the complete frequency response can be accuratelymeasured, parameters of more complex equivalent circuitscan be also obtained to identify conditions not reflectedin simple models. This extends the potential features ofthe on-line FRA technique and broadens its range ofapplications.

ACKNOWLEDGMENTS

The authors would like to thank the Natural Sciencesand Engineering Research Council (NSERC), Canada andAtlantic Innovation Fund (AIF) ACOA for the financial

support towards this research. Help and support providedby Dr. P. Pickup of the Department of Chemistry, MemorialUniversity of Newfoundland is also greatly acknowledged.

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Martin Ordonez (S’02-M’09) was born inNeuquen, Argentina. He received the Ing. de-gree in electronics engineering from the NationalTechnological University (UTN-FRC), Cordoba,Argentina, in 2003, and the Masters and Ph.D.degrees in electrical engineering from MemorialUniversity, Canada, in 2006 and 2009 respec-tively. Dr. Martin Ordonez is currently an As-sistant Professor within the Faculty of Engineer-ing and Applied Science, Memorial University,Canada.

His industrial experience in power conversion includes research anddevelopment at Xantrex Technology Inc./Elgar ElectronicsCorp., DeepElectronica de Potencia, and TRV Dispositivos. His research interestincludes characterization and utilization of renewable power sources, powerconversion architectures and control, and high-performance power elec-tronics topologies. His current research activities are supported by theIndustrial Research and Innovation Fund (IRIF). Dr. Ordonez teachinginterest includes design-oriented courses such as analog electronics andpower electronics.During his graduate studies, he was awarded with the David DunsigerAward for excellence in the Faculty of Engineering and Applied Science(2009), the Birks Graduate Medal (2006) and as a Fellow of theSchoolof Graduate Studies (2009 and 2005), Memorial University, for leadership,contributions to the student community, and academic excellence.

Maximiliano O. Sonnaillon (M’07) was bornin Parana, Argentina, in 1979. He received theElectronics Engineering degree (cum laude) fromNational Technological University (UTN), Ar-gentina, in 2002, the Masters degree in Elec-trical Engineering from National University ofRio Cuarto (UNRC), Argentina, in 2005; andthe Ph.D. in Engineering from Balseiro Institute,Argentina, in 2007. In 2003 he received thenational award “Prize to the Best Graduates inEngineering at Argentine Universities”, from the

National Academy of Engineering, Argentina. He is currently working asa Senior Research and Development Engineer for Elgar Electronics, SanDiego, California, USA, where he develops advanced programmable powersupplies based on digital control and state-of-the-art power electronics.His research interests include electric machines, power electronics, controlsystems and digital signal processing. His research has been supported bythe National Scientific and Technological Research Council(CONICET),Argentina.

John E. Quaicoe (S’75-M’76-SM’93) receivedthe B.Sc. degree from the University of Scienceand Technology, Kumasi, Ghana in 1973, and theM.A.Sc. and Ph.D. degrees from the University ofToronto, Canada in 1977 and 1982 respectively,all in electrical engineering. In 1982 he joinedthe Faculty of Engineering and Applied Scienceat Memorial University of Newfoundland, wherehe is presently the Dean (pro tem). His under-graduate and graduate teaching activities are inthe areas of electric circuit analysis, electronic

circuit analysis and design, energy systems, power electronics and powerelectronic systems, including modeling, analysis, control and design ofpower converters for various applications. Dr. Quaicoe wasthe recipient ofthe Presidents Award for Distinguished Teaching at Memorial University ofNewfoundland for 2001 and the IEEE Canada Outstanding Educator Medalfor 2002. His research activities include inverter modulation and controltechniques, utility interface systems and power quality, and uninterruptiblepower supplies. His recent research programs include the development ofpower electronic systems and control strategies for fuel cells and windgeneration systems. He is a member of the Association of ProfessionalEngineers and Geoscientists of Newfoundland and Labrador.

M. Tariq Iqbal received the B.Sc.(EE) degreefrom the University of Engineering and Technol-ogy, Lahore in 1986, the M. Sc. Nuclear Engineer-ing degree from the Quaid-e-Azam University,Islamabad in 1988 and the Ph.D. degree in Elec-trical Engineering from the Imperial College Lon-don in 1994. From 1988 to 1991 and again from1995 to 1999 he worked at the Pakistan Instituteof Engineering and Applied Science, Islamabad,Pakistan. From 1999 to 2000 he worked as anAssociate Professor at IIEC, Riphah International

University. Since 2001 he is working at Faculty of Engineering andApplied Science, Memorial University of Newfoundland. Presently he isan Associate Professor. His teaching activities cover a range of electricalengineering topics including electronics devices, control systems, renewableenergy systems and power electronics. Currently, his research focuses onmodeling and control of renewable energy systems with interests in theareas of design of control systems and comparison of controlstrategies ofhybrid energy systems.

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