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Understanding PEM fuel cell dynamics: The reversal curve
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
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Understanding PEM fuel cell dynamics: The reversal curve ~ a Arias a, Patrick Trinke b, Ivonne Karina Pen Richard Hanke-Rauschenbach b,*, Kai Sundmacher a,c a
Max Planck Institute for Dynamics of Complex Technical Systems, Department Process Systems Engineering, Sandtorstr. 1, D-39106 Magdeburg, Germany b University of Hannover, Electric Energy Storage Systems, Appelstr. 9A, D-30167 Hannover, Germany c €tsplatz 2, Otto-von-Guericke-University Magdeburg, Department Process Systems Engineering, Universita D-39106 Magdeburg, Germany
article info
abstract
Article history:
In this contribution the reversal line, a new voltageecurrent (Uei) characteristic curve, is
Received 26 August 2016
proposed to analyze the transient behavior after an arbitrary load step. The response of a
Received in revised form
differential polymer electrolyte membrane (PEM) fuel cell to the changes in current,
24 April 2017
voltage, resistance and power is evaluated, and the existence of the curve is established.
Accepted 12 May 2017
Furthermore, the influence of the starting point and the relative humidity is investigated.
Available online xxx
By using this approach, it is possible to predict the trajectory followed after any load step in the Uei plane and to anticipate infeasible load steps as well as the presence and magnitude
Keywords: PEM fuel cell
of overshoots or undershoots in the cell response. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Dynamics Load step Transient response
Introduction Numerous studies have been carried out on PEM fuel cell dynamics. The influence of the operation parameters on the transient behavior after a load change has gained the attention of many researchers. Different models and model modifications have been proposed [1e16] since Amphlett et al. published one of the first attempts to mathematically represent and predict the transient behavior of a PEM fuel cell stack [17]. In parallel, experimental investigations on the response of PEM fuel cells to load changes, either steps [16,18e36] or modified sinusoidal functions [37,38], have been carried out. A
concise, yet thorough, literature survey on transient response of PEM fuel cells under dynamic load conditions can be found guy et al. [30]. Additionally, in a recent paper of Moc¸ote Banarjee and Kandlikar delivered a review on proton exchange fuel cell dynamics focusing on the long duration transients [39]. The application of a step function to one of the four possible control modes (current, voltage, resistance and power) allows us to identify different dynamic processes occurring within the cell. In every work published until now, either current [2,3,5,10,11,15e17,20e22,25e29,31,32,35,40,41], voltage [1,8,18,24,33e35,39], power [9] or resistance [19,43,42] steps have been exclusively investigated as input variables.
* Corresponding author. E-mail address: [email protected] (R. Hanke-Rauschenbach). http://dx.doi.org/10.1016/j.ijhydene.2017.05.087 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. ~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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The response of the cell exhibited, in most of the cases, undershoots or overshoots depending on the direction of the step. The existence of these deviations has been attributed to the changes in the saturation conditions [39] and to the differences among the characteristic time constants of the transport phenomena at the cell level [44]. Furthermore, the overshoots and undershoots can be reduced if the operation conditions are modified accordingly [1,5,8,16,22,24,25,29,31]. Likewise, depending on the load speed and the amplitude of the signal, the intensity of the under- or overshoot can be manipulated [3,15,27,35,37]. On the contrary, in the works of Lee et al. [33] and Zhang et al. [34] no undershoots nor overshoots were reported, while Peng et al. [8] and Shen et al. [29] showed that they could be eliminated. The electric power produced by the fuel cell is the control mode with the highest technical relevance. However, this control scenario has been rarely discussed and the transient response of the cell (Uei) after a step function has not been yet reported. Likewise, a unified description for the four possible control modes has not been proposed. Therefore, in this work, an experimental analysis of the cell response after several load steps for the four control modes has been carried out. Consequently, the different trajectories followed during the transient as well as the presence of undershoots and overshoots have been systematically investigated. A new Uei characteristics, called the reversal curve in the following, has been found. This curve, in context with the steady-state curve and the instantaneous characteristic line, allows predicting the trajectories followed after a load step and to identify infeasible steps, which under non-dynamic conditions are easily achievable. The article is organized as follows: the experimental setup, the PEM fuel cell hardware and the conditioning procedure are described in section Experimental setup. In section Results and discussion, the experimental results are presented and discussed. Within this section, the reversal curve, which emerges after analyzing altogether the load steps from a fixed starting point, is introduced together with the new approach. Finally, remarks and conclusions are given in section Conclusions.
Test rig and equipment The test rig used to carry out the experiments on the PEM fuel cell is presented in Fig. 1. Dry gases were fed to the system and mass flow controllers EL-FLOW® from Bronkhorst High-Tech B.V. were used to dose them. Previous to the cell inlet, the gases were humidified in bubblers covered by a jacket, in which, heated water was fed at the desired temperature. A JULABO F32 heating circulator, allowed us to control indirectly the temperature within the bubblers by heating and pumping the water to the jacket. After the bubblers, the gases were continuously heated at 10 K above the cell temperature to account for possible heat losses and avoid water condensation. Since gas saturation was not necessarily reached in the bubblers, Vaisala dew point meters (DMT340 Series) were connected right before the cell inlet to measure and monitor the water content of the fed gases. The differential cell used in our experiments had an active area of 3.8 cm2 and was characterized by a stripe-like catalytic region that, with an accordingly high stoichiometric coefficient, allowed us to neglect the concentration and temperature gradients along the flow channel; a similar design was used previously by Kirsch et al. [45]. The cell and the quickConnect fixture, which controlled the cell temperature and the contact pressure, were produced by Baltic Fuel Cells GmbH. A Hoecherl & Hackl GmbH electronic load, from the ZS series, was used to evaluate the different control modes (125 A and 5 V). This load was selected because it allows to carry out the four types of steps, namely: current, voltage, resistance and power. Furthermore, it is possible to control the load speed in such a way that a rapidly changing load requirement can be simulated (response time is lower than 3 ms). However, an additional device is required to evaluate the electrochemical impedance spectra (EIS) because the load does not have a frequency response analyzer (FRA). To fulfill this requirement, a Modulab system from Solartron Analytical with an internal booster of 2 A was used. Since the load changes are considerably fast and cannot be evaluated at a reasonable sampling rate by the load software, a Cleverscope CS328A-FRA oscilloscope was used to investigate the excitation signal and the cell response.
Cell conditioning
Experimental setup Materials The gases used during the experiments were provided by Westfalen AG. At the anode, hydrogen with a grade purity N5.0 was used, while at the cathode synthetic air was fed by mixing oxygen N4.5 and nitrogen N5.0. The three layers membrane electrode assembly (MEA) and the gas diffusion layers (reference H600 STD and SGL 25 BC, respectively) were provided by Solvicore GmbH & Co. KG. The thickness of the reinforced Nafion membrane was 20e25 mm. Both sides were coated with PtC; the catalyst loading at the anode was 0.3 mg/ cm2 and at the cathode 0.55 mg/cm2. All results presented here were obtained with the same MEA.
When the cell is connected for the first time to the test rig, a conditioning procedure is required to start the cell, clean the active area from contaminants and ensure reproducibility of the experiments. Since the starting point is an air/air system, the cell was electrically shorted to avoid any potential variation or carbon corrosion when the hydrogen was fed to the anode side. The cleaning was carried out independently at each electrode but the concept behind it was the same: first, cycling the electrode potential in such a way that the contaminants can be reduced and oxidized and, second, producing high amounts of water that washed out the contaminants. Furthermore, to avoid any degradation between experiments the cell was kept electrically shorted and pure nitrogen, instead of air, was fed to the cathode.
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 1 e Scheme of the test rig.
Results and discussion In the following, the experimental procedures and the results for the differential cell are presented. In all cases pure hydrogen was fed to the anode, while synthetic air was dosed to the cathode. Both flows were kept constant during all experiments. As an initial step, the operation conditions (Table 1) were chosen and the polarization curve, here called the steady-state curve, was measured. For this, a constant voltage was applied and the steady-state current after a couple of hours was recorded. A starting point Ps was selected and from there, current, voltage, resistance and power steps were carried out. An example of a downwards (with respect to the starting point in
Table 1 e Operation conditions of the differential PEM fuel cell. Property Cell temperature Outlet pressure at anode and cathode Anode flow rate Cathode flow rate Dew point temperature at anode and cathode inlet
Value 353.15 K 1.2 bar 100 sccm 350 sccm 323.15 K
the Uei plane) load step is presented in Fig. 2. The sampling rate was 3 ms and the experiment times were variable, depending purely on the time required to achieve the steady state that was known from the steady-state curve. In some cases, the experiments lasted longer than two and a half hours; here, only the first 100 s are presented. Four different load steps are depicted, one for each control mode, all of them have the same starting and final points. As can be observed, three different Du and Di can be identified in the figures; Du0 and Di0 are the difference between the initial voltage/current and the immediate response of the cell; Du00 and Di00 represent the difference between the initial state and the minimum/ maximum voltage/current achieved after the step. Finally, Du000 and Di000 are the difference between the initial steady-state and the final steady-state. In the case of current control (Fig. 2a) Di0 , Di00 and Di000 are the same, since they are defined by the input parameters. However, following the voltage decrease (Du0 ), a slight undershoot in the voltage can be observed (Du00 ); similar results have been already presented by Refs. [5,15,18,22,25,26,31,32,35,41]. Loo et al. sustained that the undershoot is caused by the delayed response of the membrane resistance to a step increase in the current density [5]. For the voltage control case, Fig. 2b, the opposite occurs; Du0 , Du00 and Du000 have the same value and, after the current
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 2 e Downwards load steps. Sample rate 3 ms. (a) Current control. (b) Voltage control. (c) Resistance control. (d) Power control.
overshoot due to the step (Di0 ), an undershoot (Di00 ) is present in the response. Such an experimental finding has not been yet presented in the literature; however, an analogous result was published in the modeling work of Wang and Wang [1], where after an upward voltage step, a current undershoot followed by an overshoot was observed at dry-cathode conditions. In the results presented for a resistance step in Fig. 2c, an undershoot in the voltage and an overshoot followed by an undershoot in the current response are observed and the minimum values (Du00 ,Di00 ) occur at the same time. Zenith et al. [43] evaluated an analogous system in which, after a decrease in the load resistance, only an overshoot in the current and an undershoot in the voltage were observed. When comparing the resistance control to the current and voltage modes, it can be seen that the system shows an equivalent behavior in the current and voltage responses, although the magnitudes are different. Finally, evaluating the response after the power downwards step, Fig. 2d, an undershoot in the voltage and an overshoot in the current are found; the latter is qualitatively different from the previous cases but is in agreement with the
results of Hamelin [23], who measured the response of a PEM fuel cell stack to fast commutations. An upwards step starting from Ps for the four control modes is presented in Fig. 3. Again, three Du and Di can be identified and the initial and final states are the same for all control modes. The results are qualitatively opposite to the ones presented in Fig. 2. For current and resistance control, an overshoot in the cell voltage is present, in accordance with [25,26,31] while for voltage and resistance modes a combination of undershoot and overshoot in the current response is observed, as was reported in Ref. [1]. Yet, after the power step, the qualitative behavior of the current is, once more, atypical and a single undershoot is observed [23]. Nevertheless, when evaluating the results in Figs. 2 and 3, it can be seen that the system response depends on the step direction. Current, voltage and resistance modes show qualitatively equivalent but quantitatively different behavior, although the initial and final points are the same. Furthermore, the intensity of the overshoots and undershoots varies with the control mode and, in this specific case, the power controller shows the highest deviation between Di0 and Di00 or Du0 and Du00 .
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 3 e Upwards load steps, sample rate 3 ms. (a) Current control. (b) Voltage control. (c) Resistance control. (d) Power control.
To have a better understanding of the results, several current steps were carried out from Ps. The measured (Du0 ,Di0 ) and (Du00 ,Di00 ) pairs for each step are depicted in Fig. 4, together with the steady-state curve. As can be seen, if the (Du00 ,Di00 ) pairs are connected, they form a monotonically descending curve, which is referred here as the reversal curve. In the same manner, the initial response line is formed by the (Du0 ,Di0 ) pairs that represent the points at which the desired current level is achieved. Each of the trajectories followed after a step can be described as: from the starting point Ps to the initial response point (Du0 ,Di0 ), then to the reversal point (Du00 ,Di00 ) and finally to the steady-state curve at the desired load level. Both curves depend on the initial point and the experimental conditions, as will be shown later. Before discussing the reversal line and its application to the prediction of the trajectories followed after an arbitrary load step, it is worth to raise some comments on the initial response line. Zenith and Skogestad [42] defined a so-called instantaneous characteristic line as the locus of all points that can be reached instantaneously in the Uei plane. It is a straight line that passes through Ps with the negative value of the membrane resistance to proton conduction and other
Fig. 4 e Experimental steady-state curve, initial response line and reversal curves after several current load steps from Ps.
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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resistances in series with it, rM, as slope [42]. In order to determine the high frequency resistance, the potentiostatic impedance spectra at Ps was measured with 10 mV of amplitude, between 1 Hz and 100 kHz. Based on the value obtained, rM ¼ 0.21 Ucm2, the instantaneous characteristic line was constructed. According to the theory, the measured (Du0 ,Di0 ) pair should correspond or approximate to the instantaneous characteristic line, since they represent the response of the cell once the desired load level is achieved. Fig. 5 gives a comparison between the initial response line and the calculated instantaneous characteristic line. As can be observed, there is a high deviation between the two curves. To understand better what happened during the steps, one of the measured trajectories is presented as a red curve (markers are measured points Dt ¼ 0.1 ms). Immediately after the jump, in the first recorded 0.1 ms, the instantaneous characteristic line is followed; as the time passes, the trajectory deviates considerably. When the desired current level is reached (Du0 ,Di0 ), there is almost 30 mV of difference between both lines. The higher the magnitude of the load step, the higher the deviation with respect to the instantaneous characteristic line, since with increasing amplitude, the load requires a longer period to achieve the new set point and complexer electrochemical dynamics arise, such as the double-layer charging/discharging, charge transfer process, gas diffusion through the porous layer and membrane hydration. Among all the dynamic phenomena occurring in the cell, the doublelayer discharge has the smallest time constant. To determine the characteristic time of the double-layer capacitance, tc ¼ 0.318 ms, the frequency at which the phase angle is minimal can be read directly from the Bode plot.
If the transient of the controlled variable and the response of the cell are considered, it is evident that the step in our experiment is not immediate, because it takes around 1.1 ms (see tc in Fig. 6). Moreover, compared with tc, the time required by the load is considerably longer and this difference explains the deviation between the instantaneous characteristic point and the measured initial response value. If the load were faster, the initial response would lay closer to the instantaneous characteristic line. Since the initial response line depends on the load and does not represent the authentic behavior of the cell, from now on only the instantaneous characteristic line will be considered. In the following, the reversal curve introduced in Fig. 4 is discussed in detail. The reversal curve arises purely as the cell response to the different dynamics occurring at the electrochemical level. A theory that explains or considers the reversal curve has not been presented so far. Nevertheless, reversal points are visible in the results presented by Refs. [1,5,10,11,15,31,35,43]. Cho et al. [31] explained the reversal point they observed as the point in which the membrane water content is recovered after a downwards step. The first interesting feature of the reversal curve becomes visible when resistance, power and voltage steps from Ps are carried out. The resulting (Du00 ,Di00 ) pairs for all control modes lie on the reversal curve obtained exclusively for current control, see Fig. 7. This means that the curve does not depend on the control mode or step amplitude. Thus, it is possible to determine Di0 and Di00 or Du0 and Du00 for an arbitrary load step just by selecting the desired starting point, measuring the high frequency resistance and performing a few constant current steps. With this approach, the trajectories followed in the Uei plane and the presence of undershoots, overshoots or both
Fig. 5 e Comparison between the instantaneous characteristic line based on the EIS measurement and the experimental instantaneous response measured at a sample rate of 100 ms.
Fig. 6 e Comparison of the characteristic mean time (tc) for the double layer capacitance based on the EIS measurement and the time required for the load (tl) to attain the desired operating point during an upward current control step.
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 7 e Experimental reversal curve after several load steps from Ps. can be predicted. Additionally, it is possible to foresee the magnitudes of the overshoots and undershoots for the four different control modes. In Fig. 8 the trajectories followed after an instantaneous step for each of the four control modes are depicted. As can be observed, the starting and final points are the same for all of them. However, the trajectories are completely different. Furthermore, independently on the control mode, the steadystate performance is always higher than the performance during the transient. After a current step, there is a single undershoot in the voltage response, while a combination of overshoot and undershoot is the current response to a voltage step. For resistance and power modes, the voltage and the current are the response of the cell. As has been discussed, the response after a resistance step is qualitatively equivalent to voltage and current steps, which means that a combination of overshoot and undershoot in the current and an undershoot in the voltage occur. In the case of power mode, an overshoot in the current and an undershoot in the voltage are the anticipated cell response. With increasing step amplitude, the overshoots and undershoots magnitudes increase, as was reported by Refs. [3,5,15,35]. According to Loo et al. [5], since the membrane resistance does not change instantaneously, the ohmic overpotential increases proportionally. An additional attribute of this approach is that it allows anticipating infeasible load steps. As can be seen in Fig. 7, the instantaneous line intercepts the voltage axis at a value slightly higher than 720 mV. If an instantaneous voltage step between Ps and Pf (Ucell 720 mV) is carried out, the cell response would drive the current to negative values; for such a step it is better to choose a different control mode. A similar case occurs when the membrane resistance is high due to low water content or high thickness. The slope of the instantaneous characteristic line can be so steep, that there is a current step amplitude at which the cell response drives the voltage to negative values, as experienced by Wang and Wang [3,15]. Therefore, in such a case, the voltage control mode
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would be recommendable to avoid conditions that might lead to cell degradation. As described before, the trajectory followed after a load step passes first from the starting point to the instantaneous characteristic line, then to the reversal curve and finally to the steady-state curve. However, it is still not defined, what occurs when the isolines describing the trajectories cross the instantaneous characteristic line but do not intercept the reversal line. Such a situation can arise under power control because the power isolines are hyperbolic in the Uei plane, as presented in Fig. 9a. When the step is carried out, the voltage and the current density of the cell oscillate between extremely high and low values until the controller is able to achieve the demanded load point. All these oscillations can be very harmful to the cell and the electronic components. They occur in less than one second and will definitively produce a shut down of the peripheral system. Additional experiments were carried out to measure the instantaneous characteristic line and the reversal curve for different starting points and humidification levels. In Fig. 10 some of the results are presented to exemplify the influence of the starting point and operation conditions. Fig. 10a presents the scenario already discussed in Fig. 7, while in Fig. 10b the starting point is modified to higher voltage levels, keeping the same operation conditions. The resulting instantaneous characteristic line is steeper due to the decrease in the water membrane content, thus increasing the membrane resistance. For this scenario, the probability of encountering an infeasible current or power steps is high because, with increasing current density, the difference among the curves is higher. In Fig. 10c, the temperature at the bubblers is increased and the dew point was TDP ¼ 343.15 K Ps2 was selected in such a way that the load current corresponded to Ps1, however the cell voltage was higher due to the improvement in the humidification level. As in the previous case, the reversal curve is located below the steady-state curve while the instantaneous characteristic line is above; this implies that, after a downwards step, the performance of the cell will be higher than the steady-state maximum power, as suggested by Zenith and Skogestad [42]. In all the scenarios evaluated, the instantaneous characteristic line lays always above of the reversal curve for currents higher than the starting point and the opposite happens for lower currents. Thus, the trends presented in Figs. 2 and 3 can be extrapolated to any instantaneous step performed in this system. Nevertheless, the intensities of the overshoots and undershoots are closely dependent on the starting point and operation conditions [31]. Moreover, the presence of overshoots and undershoots will depend on the load controller speed and the sampling rate of the data recorder. If the load controller is slow, the velocity of processes intrinsically fast, such as the discharge of the double-layer capacitance, would decrease; giving time to the gas diffusion and water transport to react and reduce the overshoots and undershoots, as shown by Ref. [37]. On the contrary, if the load is fast but the sampling frequency is low, as in Refs. [29,33,34], even if undershoots or overshoots are happening, they will not be observable; especially, when the dynamics are very fast due to high stoichiometric coefficients and good humidification.
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 8 e Comparison of the trajectories followed after an instantaneous load step depending on the controlled variable. (a) Current control. (b) Voltage control. (c) Resistance control. (d) Power control.
Fig. 9 e (a) An infeasible power step due to the absence of intersection between the reversal curve and the power isoline. (b) Cell response during the power step. ~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 10 e Comparison of the instantaneous characteristic line and reversal curve for different starting points and relative humidities. (a) Ps, dew point temperature is 323.15 K. (b) Ps1, dew point temperature is 323.15 K. (c) Ps2, dew point temperature is 343.15 K.
Finally, Cho et al. [31] observed a voltage undershoot, followed by an overshoot after a downwards current step and associated the latter with the membrane hydration time. However, in the several steps carried out in this work such a response was not ascertained since, in the design of the experiments, reactants starvation and cell flooding were avoided.
Conclusions A new approach to analyze the PEM fuel cell transient behavior has been introduced. It is based on experimental findings after carrying out several load steps for the four control modes (current, voltage, power and resistance). It has been shown that the reversal curve together with the instantaneous characteristic line and the steady-state curve, allows predicting the existence of overshoots and undershoots as well as anticipating infeasible load changes. Depending on the exact location of the curves and on the desired load level, a specific type of controller might behave erratically. It has been demonstrated that the location and slope of the curves are affected by the starting point and the operation conditions. Additionally, it has been shown that the qualitative behavior after an arbitrary load steps can be easily anticipated, depending on whether it is an upwards or downwards step.
Acknowledgments The authors gratefully acknowledge the financial support from the German Federal Ministry of Education and Research (BMBF) under the project GECKO, Grant No. 03SF0454B.
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~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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[16] Latha K, Vidhya S, Umamaheswari B, Rajalakshmi N, Dhathathreyan KS. Tuning of PEM fuel cell model parameters for prediction of steady state and dynamic performance under various operating conditions. Int J Hydrogen Energy 2013;38(5):2370e86. [17] Amphlett JC, Mann RF, Peppley BA, Roberge PR, Rodrigues A. A model predicting transient responses of proton exchange membrane fuel cells. J Power Sources 1996;61(1):183e8. [18] Weydahl H, Møller-Holst S, Hagen G, Børresen B. Transient response of a proton exchange membrane fuel cell. J Power Sources 2007;171(2):321e30. [19] Corbo P, Migliardini F, Veneri O. Experimental analysis of a 20 kWe PEM fuel cell system in dynamic conditions representative of automotive applications. Energy Convers Manag 2008;49(10):2688e97. [20] Pei P, Yuan X, Gou J, Li P. Dynamic response during PEM fuel cell loading-up. Materials 2009;2(3):734. [21] Tang Y, Yuan W, Pan M, Li Z, Chen G, Li Y. Experimental investigation of dynamic performance and transient responses of a kW-class PEM fuel cell stack under various load changes. Appl Energy 2010;87(4):1410e7. [22] Qu S, Li X, Ke C, Shao Z-G, Yi B. Experimental and modeling study on water dynamic transport of the proton exchange membrane fuel cell under transient air flow and load change. J Power Sources 2010;195(19):6629e36. [23] Hamelin J, Agbossou K, Laperrire A, Laurencelle F, Bose TK. Dynamic behavior of a PEM fuel cell stack for stationary applications. Int J Hydrogen Energy 2001;26(6):625e9. [24] Kim S, Shimpalee S, Van Zee JW. The effect of stoichiometry on dynamic behavior of a proton exchange membrane fuel cell (PEMFC) during load change. J Power Sources 2004;135(12):110e21. [25] Yan Q, Toghiani H, Causey H. Steady state and dynamic performance of proton exchange membrane fuel cells (PEMFCs) under various operating conditions and load changes. J Power Sources 2006;161(1):492e502. [26] Edwards RL, Demuren A. Regression analysis of PEM fuel cell transient response. Int J Energy Environ Eng 2016:1e13. [27] Yan X, Hou M, Sun L, Cheng H, Hong Y, Liang D, et al. The study on transient characteristic of proton exchange membrane fuel cell stack during dynamic loading. J Power Sources 2007;163(2):966e70. [28] del Real AJ, Arce A, Bordons C. Development and experimental validation of a PEM fuel cell dynamic model. J Power Sources 2007;173(1):310e24. [29] Shen Q, Hou M, Yan X, Liang D, Zang Z, Hao L, et al. The voltage characteristics of proton exchange membrane fuel cell (PEMFC) under steady and transient states. J Power Sources 2008;179(1):292e6. guy P, Ludwig B, Steiner N. Influence of ageing on the [30] Moc¸ote dynamic behaviour and the electrochemical characteristics
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~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Understanding PEM fuel cell dynamics: The reversal curve ~ a Arias a, Patrick Trinke b, Ivonne Karina Pen Richard Hanke-Rauschenbach b,*, Kai Sundmacher a,c a
Max Planck Institute for Dynamics of Complex Technical Systems, Department Process Systems Engineering, Sandtorstr. 1, D-39106 Magdeburg, Germany b University of Hannover, Electric Energy Storage Systems, Appelstr. 9A, D-30167 Hannover, Germany c €tsplatz 2, Otto-von-Guericke-University Magdeburg, Department Process Systems Engineering, Universita D-39106 Magdeburg, Germany
article info
abstract
Article history:
In this contribution the reversal line, a new voltageecurrent (Uei) characteristic curve, is
Received 26 August 2016
proposed to analyze the transient behavior after an arbitrary load step. The response of a
Received in revised form
differential polymer electrolyte membrane (PEM) fuel cell to the changes in current,
24 April 2017
voltage, resistance and power is evaluated, and the existence of the curve is established.
Accepted 12 May 2017
Furthermore, the influence of the starting point and the relative humidity is investigated.
Available online xxx
By using this approach, it is possible to predict the trajectory followed after any load step in the Uei plane and to anticipate infeasible load steps as well as the presence and magnitude
Keywords: PEM fuel cell
of overshoots or undershoots in the cell response. © 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Dynamics Load step Transient response
Introduction Numerous studies have been carried out on PEM fuel cell dynamics. The influence of the operation parameters on the transient behavior after a load change has gained the attention of many researchers. Different models and model modifications have been proposed [1e16] since Amphlett et al. published one of the first attempts to mathematically represent and predict the transient behavior of a PEM fuel cell stack [17]. In parallel, experimental investigations on the response of PEM fuel cells to load changes, either steps [16,18e36] or modified sinusoidal functions [37,38], have been carried out. A
concise, yet thorough, literature survey on transient response of PEM fuel cells under dynamic load conditions can be found guy et al. [30]. Additionally, in a recent paper of Moc¸ote Banarjee and Kandlikar delivered a review on proton exchange fuel cell dynamics focusing on the long duration transients [39]. The application of a step function to one of the four possible control modes (current, voltage, resistance and power) allows us to identify different dynamic processes occurring within the cell. In every work published until now, either current [2,3,5,10,11,15e17,20e22,25e29,31,32,35,40,41], voltage [1,8,18,24,33e35,39], power [9] or resistance [19,43,42] steps have been exclusively investigated as input variables.
* Corresponding author. E-mail address: [email protected] (R. Hanke-Rauschenbach). http://dx.doi.org/10.1016/j.ijhydene.2017.05.087 0360-3199/© 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. ~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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The response of the cell exhibited, in most of the cases, undershoots or overshoots depending on the direction of the step. The existence of these deviations has been attributed to the changes in the saturation conditions [39] and to the differences among the characteristic time constants of the transport phenomena at the cell level [44]. Furthermore, the overshoots and undershoots can be reduced if the operation conditions are modified accordingly [1,5,8,16,22,24,25,29,31]. Likewise, depending on the load speed and the amplitude of the signal, the intensity of the under- or overshoot can be manipulated [3,15,27,35,37]. On the contrary, in the works of Lee et al. [33] and Zhang et al. [34] no undershoots nor overshoots were reported, while Peng et al. [8] and Shen et al. [29] showed that they could be eliminated. The electric power produced by the fuel cell is the control mode with the highest technical relevance. However, this control scenario has been rarely discussed and the transient response of the cell (Uei) after a step function has not been yet reported. Likewise, a unified description for the four possible control modes has not been proposed. Therefore, in this work, an experimental analysis of the cell response after several load steps for the four control modes has been carried out. Consequently, the different trajectories followed during the transient as well as the presence of undershoots and overshoots have been systematically investigated. A new Uei characteristics, called the reversal curve in the following, has been found. This curve, in context with the steady-state curve and the instantaneous characteristic line, allows predicting the trajectories followed after a load step and to identify infeasible steps, which under non-dynamic conditions are easily achievable. The article is organized as follows: the experimental setup, the PEM fuel cell hardware and the conditioning procedure are described in section Experimental setup. In section Results and discussion, the experimental results are presented and discussed. Within this section, the reversal curve, which emerges after analyzing altogether the load steps from a fixed starting point, is introduced together with the new approach. Finally, remarks and conclusions are given in section Conclusions.
Test rig and equipment The test rig used to carry out the experiments on the PEM fuel cell is presented in Fig. 1. Dry gases were fed to the system and mass flow controllers EL-FLOW® from Bronkhorst High-Tech B.V. were used to dose them. Previous to the cell inlet, the gases were humidified in bubblers covered by a jacket, in which, heated water was fed at the desired temperature. A JULABO F32 heating circulator, allowed us to control indirectly the temperature within the bubblers by heating and pumping the water to the jacket. After the bubblers, the gases were continuously heated at 10 K above the cell temperature to account for possible heat losses and avoid water condensation. Since gas saturation was not necessarily reached in the bubblers, Vaisala dew point meters (DMT340 Series) were connected right before the cell inlet to measure and monitor the water content of the fed gases. The differential cell used in our experiments had an active area of 3.8 cm2 and was characterized by a stripe-like catalytic region that, with an accordingly high stoichiometric coefficient, allowed us to neglect the concentration and temperature gradients along the flow channel; a similar design was used previously by Kirsch et al. [45]. The cell and the quickConnect fixture, which controlled the cell temperature and the contact pressure, were produced by Baltic Fuel Cells GmbH. A Hoecherl & Hackl GmbH electronic load, from the ZS series, was used to evaluate the different control modes (125 A and 5 V). This load was selected because it allows to carry out the four types of steps, namely: current, voltage, resistance and power. Furthermore, it is possible to control the load speed in such a way that a rapidly changing load requirement can be simulated (response time is lower than 3 ms). However, an additional device is required to evaluate the electrochemical impedance spectra (EIS) because the load does not have a frequency response analyzer (FRA). To fulfill this requirement, a Modulab system from Solartron Analytical with an internal booster of 2 A was used. Since the load changes are considerably fast and cannot be evaluated at a reasonable sampling rate by the load software, a Cleverscope CS328A-FRA oscilloscope was used to investigate the excitation signal and the cell response.
Cell conditioning
Experimental setup Materials The gases used during the experiments were provided by Westfalen AG. At the anode, hydrogen with a grade purity N5.0 was used, while at the cathode synthetic air was fed by mixing oxygen N4.5 and nitrogen N5.0. The three layers membrane electrode assembly (MEA) and the gas diffusion layers (reference H600 STD and SGL 25 BC, respectively) were provided by Solvicore GmbH & Co. KG. The thickness of the reinforced Nafion membrane was 20e25 mm. Both sides were coated with PtC; the catalyst loading at the anode was 0.3 mg/ cm2 and at the cathode 0.55 mg/cm2. All results presented here were obtained with the same MEA.
When the cell is connected for the first time to the test rig, a conditioning procedure is required to start the cell, clean the active area from contaminants and ensure reproducibility of the experiments. Since the starting point is an air/air system, the cell was electrically shorted to avoid any potential variation or carbon corrosion when the hydrogen was fed to the anode side. The cleaning was carried out independently at each electrode but the concept behind it was the same: first, cycling the electrode potential in such a way that the contaminants can be reduced and oxidized and, second, producing high amounts of water that washed out the contaminants. Furthermore, to avoid any degradation between experiments the cell was kept electrically shorted and pure nitrogen, instead of air, was fed to the cathode.
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 1 e Scheme of the test rig.
Results and discussion In the following, the experimental procedures and the results for the differential cell are presented. In all cases pure hydrogen was fed to the anode, while synthetic air was dosed to the cathode. Both flows were kept constant during all experiments. As an initial step, the operation conditions (Table 1) were chosen and the polarization curve, here called the steady-state curve, was measured. For this, a constant voltage was applied and the steady-state current after a couple of hours was recorded. A starting point Ps was selected and from there, current, voltage, resistance and power steps were carried out. An example of a downwards (with respect to the starting point in
Table 1 e Operation conditions of the differential PEM fuel cell. Property Cell temperature Outlet pressure at anode and cathode Anode flow rate Cathode flow rate Dew point temperature at anode and cathode inlet
Value 353.15 K 1.2 bar 100 sccm 350 sccm 323.15 K
the Uei plane) load step is presented in Fig. 2. The sampling rate was 3 ms and the experiment times were variable, depending purely on the time required to achieve the steady state that was known from the steady-state curve. In some cases, the experiments lasted longer than two and a half hours; here, only the first 100 s are presented. Four different load steps are depicted, one for each control mode, all of them have the same starting and final points. As can be observed, three different Du and Di can be identified in the figures; Du0 and Di0 are the difference between the initial voltage/current and the immediate response of the cell; Du00 and Di00 represent the difference between the initial state and the minimum/ maximum voltage/current achieved after the step. Finally, Du000 and Di000 are the difference between the initial steady-state and the final steady-state. In the case of current control (Fig. 2a) Di0 , Di00 and Di000 are the same, since they are defined by the input parameters. However, following the voltage decrease (Du0 ), a slight undershoot in the voltage can be observed (Du00 ); similar results have been already presented by Refs. [5,15,18,22,25,26,31,32,35,41]. Loo et al. sustained that the undershoot is caused by the delayed response of the membrane resistance to a step increase in the current density [5]. For the voltage control case, Fig. 2b, the opposite occurs; Du0 , Du00 and Du000 have the same value and, after the current
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 2 e Downwards load steps. Sample rate 3 ms. (a) Current control. (b) Voltage control. (c) Resistance control. (d) Power control.
overshoot due to the step (Di0 ), an undershoot (Di00 ) is present in the response. Such an experimental finding has not been yet presented in the literature; however, an analogous result was published in the modeling work of Wang and Wang [1], where after an upward voltage step, a current undershoot followed by an overshoot was observed at dry-cathode conditions. In the results presented for a resistance step in Fig. 2c, an undershoot in the voltage and an overshoot followed by an undershoot in the current response are observed and the minimum values (Du00 ,Di00 ) occur at the same time. Zenith et al. [43] evaluated an analogous system in which, after a decrease in the load resistance, only an overshoot in the current and an undershoot in the voltage were observed. When comparing the resistance control to the current and voltage modes, it can be seen that the system shows an equivalent behavior in the current and voltage responses, although the magnitudes are different. Finally, evaluating the response after the power downwards step, Fig. 2d, an undershoot in the voltage and an overshoot in the current are found; the latter is qualitatively different from the previous cases but is in agreement with the
results of Hamelin [23], who measured the response of a PEM fuel cell stack to fast commutations. An upwards step starting from Ps for the four control modes is presented in Fig. 3. Again, three Du and Di can be identified and the initial and final states are the same for all control modes. The results are qualitatively opposite to the ones presented in Fig. 2. For current and resistance control, an overshoot in the cell voltage is present, in accordance with [25,26,31] while for voltage and resistance modes a combination of undershoot and overshoot in the current response is observed, as was reported in Ref. [1]. Yet, after the power step, the qualitative behavior of the current is, once more, atypical and a single undershoot is observed [23]. Nevertheless, when evaluating the results in Figs. 2 and 3, it can be seen that the system response depends on the step direction. Current, voltage and resistance modes show qualitatively equivalent but quantitatively different behavior, although the initial and final points are the same. Furthermore, the intensity of the overshoots and undershoots varies with the control mode and, in this specific case, the power controller shows the highest deviation between Di0 and Di00 or Du0 and Du00 .
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 3 e Upwards load steps, sample rate 3 ms. (a) Current control. (b) Voltage control. (c) Resistance control. (d) Power control.
To have a better understanding of the results, several current steps were carried out from Ps. The measured (Du0 ,Di0 ) and (Du00 ,Di00 ) pairs for each step are depicted in Fig. 4, together with the steady-state curve. As can be seen, if the (Du00 ,Di00 ) pairs are connected, they form a monotonically descending curve, which is referred here as the reversal curve. In the same manner, the initial response line is formed by the (Du0 ,Di0 ) pairs that represent the points at which the desired current level is achieved. Each of the trajectories followed after a step can be described as: from the starting point Ps to the initial response point (Du0 ,Di0 ), then to the reversal point (Du00 ,Di00 ) and finally to the steady-state curve at the desired load level. Both curves depend on the initial point and the experimental conditions, as will be shown later. Before discussing the reversal line and its application to the prediction of the trajectories followed after an arbitrary load step, it is worth to raise some comments on the initial response line. Zenith and Skogestad [42] defined a so-called instantaneous characteristic line as the locus of all points that can be reached instantaneously in the Uei plane. It is a straight line that passes through Ps with the negative value of the membrane resistance to proton conduction and other
Fig. 4 e Experimental steady-state curve, initial response line and reversal curves after several current load steps from Ps.
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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resistances in series with it, rM, as slope [42]. In order to determine the high frequency resistance, the potentiostatic impedance spectra at Ps was measured with 10 mV of amplitude, between 1 Hz and 100 kHz. Based on the value obtained, rM ¼ 0.21 Ucm2, the instantaneous characteristic line was constructed. According to the theory, the measured (Du0 ,Di0 ) pair should correspond or approximate to the instantaneous characteristic line, since they represent the response of the cell once the desired load level is achieved. Fig. 5 gives a comparison between the initial response line and the calculated instantaneous characteristic line. As can be observed, there is a high deviation between the two curves. To understand better what happened during the steps, one of the measured trajectories is presented as a red curve (markers are measured points Dt ¼ 0.1 ms). Immediately after the jump, in the first recorded 0.1 ms, the instantaneous characteristic line is followed; as the time passes, the trajectory deviates considerably. When the desired current level is reached (Du0 ,Di0 ), there is almost 30 mV of difference between both lines. The higher the magnitude of the load step, the higher the deviation with respect to the instantaneous characteristic line, since with increasing amplitude, the load requires a longer period to achieve the new set point and complexer electrochemical dynamics arise, such as the double-layer charging/discharging, charge transfer process, gas diffusion through the porous layer and membrane hydration. Among all the dynamic phenomena occurring in the cell, the doublelayer discharge has the smallest time constant. To determine the characteristic time of the double-layer capacitance, tc ¼ 0.318 ms, the frequency at which the phase angle is minimal can be read directly from the Bode plot.
If the transient of the controlled variable and the response of the cell are considered, it is evident that the step in our experiment is not immediate, because it takes around 1.1 ms (see tc in Fig. 6). Moreover, compared with tc, the time required by the load is considerably longer and this difference explains the deviation between the instantaneous characteristic point and the measured initial response value. If the load were faster, the initial response would lay closer to the instantaneous characteristic line. Since the initial response line depends on the load and does not represent the authentic behavior of the cell, from now on only the instantaneous characteristic line will be considered. In the following, the reversal curve introduced in Fig. 4 is discussed in detail. The reversal curve arises purely as the cell response to the different dynamics occurring at the electrochemical level. A theory that explains or considers the reversal curve has not been presented so far. Nevertheless, reversal points are visible in the results presented by Refs. [1,5,10,11,15,31,35,43]. Cho et al. [31] explained the reversal point they observed as the point in which the membrane water content is recovered after a downwards step. The first interesting feature of the reversal curve becomes visible when resistance, power and voltage steps from Ps are carried out. The resulting (Du00 ,Di00 ) pairs for all control modes lie on the reversal curve obtained exclusively for current control, see Fig. 7. This means that the curve does not depend on the control mode or step amplitude. Thus, it is possible to determine Di0 and Di00 or Du0 and Du00 for an arbitrary load step just by selecting the desired starting point, measuring the high frequency resistance and performing a few constant current steps. With this approach, the trajectories followed in the Uei plane and the presence of undershoots, overshoots or both
Fig. 5 e Comparison between the instantaneous characteristic line based on the EIS measurement and the experimental instantaneous response measured at a sample rate of 100 ms.
Fig. 6 e Comparison of the characteristic mean time (tc) for the double layer capacitance based on the EIS measurement and the time required for the load (tl) to attain the desired operating point during an upward current control step.
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Fig. 7 e Experimental reversal curve after several load steps from Ps. can be predicted. Additionally, it is possible to foresee the magnitudes of the overshoots and undershoots for the four different control modes. In Fig. 8 the trajectories followed after an instantaneous step for each of the four control modes are depicted. As can be observed, the starting and final points are the same for all of them. However, the trajectories are completely different. Furthermore, independently on the control mode, the steadystate performance is always higher than the performance during the transient. After a current step, there is a single undershoot in the voltage response, while a combination of overshoot and undershoot is the current response to a voltage step. For resistance and power modes, the voltage and the current are the response of the cell. As has been discussed, the response after a resistance step is qualitatively equivalent to voltage and current steps, which means that a combination of overshoot and undershoot in the current and an undershoot in the voltage occur. In the case of power mode, an overshoot in the current and an undershoot in the voltage are the anticipated cell response. With increasing step amplitude, the overshoots and undershoots magnitudes increase, as was reported by Refs. [3,5,15,35]. According to Loo et al. [5], since the membrane resistance does not change instantaneously, the ohmic overpotential increases proportionally. An additional attribute of this approach is that it allows anticipating infeasible load steps. As can be seen in Fig. 7, the instantaneous line intercepts the voltage axis at a value slightly higher than 720 mV. If an instantaneous voltage step between Ps and Pf (Ucell 720 mV) is carried out, the cell response would drive the current to negative values; for such a step it is better to choose a different control mode. A similar case occurs when the membrane resistance is high due to low water content or high thickness. The slope of the instantaneous characteristic line can be so steep, that there is a current step amplitude at which the cell response drives the voltage to negative values, as experienced by Wang and Wang [3,15]. Therefore, in such a case, the voltage control mode
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would be recommendable to avoid conditions that might lead to cell degradation. As described before, the trajectory followed after a load step passes first from the starting point to the instantaneous characteristic line, then to the reversal curve and finally to the steady-state curve. However, it is still not defined, what occurs when the isolines describing the trajectories cross the instantaneous characteristic line but do not intercept the reversal line. Such a situation can arise under power control because the power isolines are hyperbolic in the Uei plane, as presented in Fig. 9a. When the step is carried out, the voltage and the current density of the cell oscillate between extremely high and low values until the controller is able to achieve the demanded load point. All these oscillations can be very harmful to the cell and the electronic components. They occur in less than one second and will definitively produce a shut down of the peripheral system. Additional experiments were carried out to measure the instantaneous characteristic line and the reversal curve for different starting points and humidification levels. In Fig. 10 some of the results are presented to exemplify the influence of the starting point and operation conditions. Fig. 10a presents the scenario already discussed in Fig. 7, while in Fig. 10b the starting point is modified to higher voltage levels, keeping the same operation conditions. The resulting instantaneous characteristic line is steeper due to the decrease in the water membrane content, thus increasing the membrane resistance. For this scenario, the probability of encountering an infeasible current or power steps is high because, with increasing current density, the difference among the curves is higher. In Fig. 10c, the temperature at the bubblers is increased and the dew point was TDP ¼ 343.15 K Ps2 was selected in such a way that the load current corresponded to Ps1, however the cell voltage was higher due to the improvement in the humidification level. As in the previous case, the reversal curve is located below the steady-state curve while the instantaneous characteristic line is above; this implies that, after a downwards step, the performance of the cell will be higher than the steady-state maximum power, as suggested by Zenith and Skogestad [42]. In all the scenarios evaluated, the instantaneous characteristic line lays always above of the reversal curve for currents higher than the starting point and the opposite happens for lower currents. Thus, the trends presented in Figs. 2 and 3 can be extrapolated to any instantaneous step performed in this system. Nevertheless, the intensities of the overshoots and undershoots are closely dependent on the starting point and operation conditions [31]. Moreover, the presence of overshoots and undershoots will depend on the load controller speed and the sampling rate of the data recorder. If the load controller is slow, the velocity of processes intrinsically fast, such as the discharge of the double-layer capacitance, would decrease; giving time to the gas diffusion and water transport to react and reduce the overshoots and undershoots, as shown by Ref. [37]. On the contrary, if the load is fast but the sampling frequency is low, as in Refs. [29,33,34], even if undershoots or overshoots are happening, they will not be observable; especially, when the dynamics are very fast due to high stoichiometric coefficients and good humidification.
~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
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Fig. 8 e Comparison of the trajectories followed after an instantaneous load step depending on the controlled variable. (a) Current control. (b) Voltage control. (c) Resistance control. (d) Power control.
Fig. 9 e (a) An infeasible power step due to the absence of intersection between the reversal curve and the power isoline. (b) Cell response during the power step. ~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y x x x ( 2 0 1 7 ) 1 e1 0
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Fig. 10 e Comparison of the instantaneous characteristic line and reversal curve for different starting points and relative humidities. (a) Ps, dew point temperature is 323.15 K. (b) Ps1, dew point temperature is 323.15 K. (c) Ps2, dew point temperature is 343.15 K.
Finally, Cho et al. [31] observed a voltage undershoot, followed by an overshoot after a downwards current step and associated the latter with the membrane hydration time. However, in the several steps carried out in this work such a response was not ascertained since, in the design of the experiments, reactants starvation and cell flooding were avoided.
Conclusions A new approach to analyze the PEM fuel cell transient behavior has been introduced. It is based on experimental findings after carrying out several load steps for the four control modes (current, voltage, power and resistance). It has been shown that the reversal curve together with the instantaneous characteristic line and the steady-state curve, allows predicting the existence of overshoots and undershoots as well as anticipating infeasible load changes. Depending on the exact location of the curves and on the desired load level, a specific type of controller might behave erratically. It has been demonstrated that the location and slope of the curves are affected by the starting point and the operation conditions. Additionally, it has been shown that the qualitative behavior after an arbitrary load steps can be easily anticipated, depending on whether it is an upwards or downwards step.
Acknowledgments The authors gratefully acknowledge the financial support from the German Federal Ministry of Education and Research (BMBF) under the project GECKO, Grant No. 03SF0454B.
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~ a Arias IK, et al., Understanding PEM fuel cell dynamics: The reversal curve, International Journal Please cite this article in press as: Pen of Hydrogen Energy (2017), http://dx.doi.org/10.1016/j.ijhydene.2017.05.087