4th IFAC Workshop on 4th Workshop on Engine Powertrain 4th IFAC IFACand Workshop on Control, Simulation and Modeling 4th IFAC Workshop on Engine and Powertrain Control, Simulation and Modeling Available online at www.sciencedirect.com August 23-26, 2015. Columbus, USA Engine and Powertrain Control, Simulation and Engine and Powertrain Control, OH, Simulation and Modeling Modeling August 23-26, 2015. Columbus, OH, USA August 23-26, 23-26, 2015. 2015. Columbus, Columbus, OH, OH, USA USA August
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Control by state observer of PEMFC Control by state observer of Control by state observer of PEMFC Control by state observer of PEMFC PEMFC anodic purges in dead-end operating mode anodic purges in dead-end operating mode anodic purges in dead-end operating mode anodic purges∗,∗∗in dead-end operating mode ∗,∗∗ ∗∗∗ Maxime Piffard ∗,∗∗ Mathias Gerard ∗,∗∗ Eric Bideaux ∗∗∗ ∗,∗∗ Mathias ∗,∗∗ Eric Bideaux ∗∗∗ Maxime Piffard Gerard ∗,∗∗ ∗∗∗ ∗,∗∗ ∗∗∗ MaximeRamon PiffardDa Mathias Gerard Eric Bideaux Bideaux Fonseca Paolo∗,∗∗ Massioni Maxime Piffard Mathias Gerard Eric ∗,∗∗ ∗∗∗ ∗,∗∗ ∗∗∗ Ramon Da Fonseca Massioni ∗,∗∗ Paolo ∗∗∗ Ramon Da Fonseca Paolo Massioni Ramon Da Fonseca Paolo Massioni ∗ ∗ CEA LITEN, F-38054 Grenoble, France (e-mail: ∗ LITEN, F-38054 Grenoble, France (e-mail: ∗ CEA CEA F-38054 maxime.piff
[email protected]) CEA LITEN, LITEN, F-38054 Grenoble, Grenoble, France France (e-mail: (e-mail: maxime.piff
[email protected]) ∗∗ maxime.piff
[email protected]) Alpes, F-38000 Grenoble, France maxime.piff
[email protected]) ∗∗ Univ. Grenoble ∗∗ Univ. Grenoble Alpes, F-38000 Grenoble, France ∗∗∗ ∗∗ Univ. Grenoble Alpes, National F-38000 des Grenoble, France Laboratory, Institut Sciences appliques de Univ. Grenoble Alpes, F-38000 Grenoble, France ∗∗∗ Ampere ∗∗∗ Laboratory, Institut des Sciences appliques de ∗∗∗ Ampere Ampere Laboratory, Institut National des Sciences appliques Lyon (INSA-Lyon), 69621National Villeurbanne cedex, France Ampere Laboratory, Institut National des Sciences appliques de de Lyon (INSA-Lyon), 69621 Villeurbanne cedex, France Lyon Lyon (INSA-Lyon), (INSA-Lyon), 69621 69621 Villeurbanne Villeurbanne cedex, cedex, France France
Abstract Abstract Abstract A Proton Exchange Membrane Fuel Cell (PEMFC) needs an active system to control all the Abstract A Proton Fuel (PEMFC) needs active to all the A Proton Exchange Exchange Membrane Fuel Cell Cellconditions, (PEMFC)especially needs an an in active system to control control all fuel the ancillaries and ensureMembrane optimal operating a fuelsystem cell vehicle. For the A Proton Exchange Membrane Fuel Cell (PEMFC) needs an active system to control all the ancillaries and ensure optimal operating conditions, especially in a fuel cell vehicle. For the fuel ancillaries and ensure optimal operating conditions, especially in a fuel cell vehicle. For the fuel cell systemand architecture, dead-end anodeconditions, is the cheapest architecture forcell thevehicle. hydrogen line and ancillaries ensure optimal operating especially in a fuel For the fuel cell is theand cheapest architecture for theif hydrogen line and cell system architecture, dead-end anode is cheapest architecture for line also system the onearchitecture, that leads to dead-end importantanode reversible irreversible degradations not appropriately cell system architecture, dead-end anode is the theand cheapest architecture for the theif hydrogen hydrogen line and and also the one that leads to important reversible irreversible degradations not appropriately also the one leads to important reversible and irreversible degradations if not appropriately managed. Tothat address the cost and durability issues on fuel cell vehicles, this study proposes a also the one that leads to important reversible and irreversible degradations if not appropriately managed. To the cost and on cell this study proposes aa managed. To address address the at cost and durability durability issues on fuel fuelsaturation cell vehicles, vehicles, thisanode studyside proposes state observer which aims estimating online issues the nitrogen in the in order managed. To address the cost and durability issues on fuel cell vehicles, this study proposes a state observer which aims at estimating online the nitrogen saturation in the anode side in order state observer which aims at estimating online the nitrogen saturation in the anode side in order to trigger the purge at a given criterion. This observer is based on a simple set of equations state observer which aims at estimating online the nitrogen saturation in the anode side in order to trigger the purge at a given criterion. This observer is based aa simple of equations to trigger the at criterion. This observer is on set of extracted from a detailed 2D-meshed model. Nitrogen buildup is on evaluated in set simulation with to trigger from the purge purge at a a given given criterion. ThisNitrogen observerbuildup is based based on a simple simple set of equations equations extracted a detailed 2D-meshed model. is evaluated in simulation with extracted from a detailed 2D-meshed model. Nitrogen buildup is evaluated in simulation with different road profiles with less than 5% error. Moreover the fuel cell system efficiency increases extracted fromprofiles a detailed 2D-meshed model. Nitrogen buildup is evaluated in simulation with different less 5% error. the fuel efficiency different road profiles with less than than 5%strategies, error. Moreover Moreover the mileage. fuel cell cell system system efficiency increases comparedroad to the otherwith existing purge so as the The observer canincreases also be different road profiles with less than 5% error. Moreover the fuel cell system efficiency increases compared to the other existing purge strategies, so as the mileage. The observer can also be compared to other existing purge so the mileage. observer also be used to develop other optimal strategies to minimize the irreversible degradations of the fuel compared to the theother otheroptimal existingstrategies purge strategies, strategies, so as asthe theirreversible mileage. The The observer can can alsofuel be used to develop to minimize degradations of the used to develop other optimal strategies to minimize the irreversible degradations of the fuel cell. used to develop other optimal strategies to minimize the irreversible degradations of the fuel cell. cell. cell. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Keywords: Keywords: Fuel Cell Vehicles, PEM, State observer, Anode purging Keywords: Fuel Cell Vehicles, PEM, State observer, Anode purging Fuel Fuel Cell Cell Vehicles, Vehicles, PEM, PEM, State State observer, observer, Anode Anode purging purging 1. INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION 1. INTRODUCTION Proton-exchange-membrane fuel cell (PEMFC) is the most Proton-exchange-membrane fuel is Proton-exchange-membrane fuel cell cell (PEMFC) (PEMFC) is the the most most promising technology for transportation applications due Proton-exchange-membrane fuel cell (PEMFC) is the most promising technology for transportation applications due promising technology for transportation applications due to the high power density and low operating temperatures. promising technology for transportation applications due to high and temperatures. to the high power powerasdensity density and low low operating operating temperatures. It the is considered an alternative to internal combustion to the high power density and low operating temperatures. It is considered as an alternative to internal combustion It is considered considered as an an alternative alternative to internal internal combustion engines as it provides the same mileage range with no It is as to combustion engines provides same range no engines asofit itgreenhouse provides the the same mileage range with no emissionsas gases on mileage site. A fuel cellwith system engines as it provides the same mileage range with no emissions of greenhouse gases on site. A fuel cell system emissions of greenhouse gases on site. A fuel cell system is composed of four mains supply sub-system: the air, hyemissions of of greenhouse gases on sub-system: site. A fuel the cell system is composed supply hyis composed of four four mains supplysupply sub-system: the air, air,(Fighydrogen, cooling and mains the electric sub-systems is composed of four mains supply sub-system: the air, hydrogen, cooling and the electric supply sub-systems (Figdrogen, cooling and the electric supply sub-systems (Figure 1). The fuel and cell the needs activesupply ancilliaries (compressor, drogen, cooling electric sub-systems (Figure 1). The cell active ancilliaries ure 1). valves, The fuel fuelpower cell needs needs activeto ancilliaries (compressor, pump, electronic) obtain a (compressor, high level of ure 1). The fuel cell needs active ancilliaries pump, valves, power electronic) to obtain aa (compressor, high pump, valves, power electronic) to obtain high level level of of efficiency (performance and durability). The optimization pump, valves, power electronic) to obtain a high level of efficiency (performance and durability). The optimization efficiency (performance and durability). The optimization of the system components and the control laws associated efficiency (performance and durability). The optimization of system components the laws of the system to components and the control control laws associated associated arethe essential reach theand targets of performances and of the system components and the control laws associated are essential to reach are essential to cell. reach the the targets targets of of performances performances and and lifetime of a fuel are essential to reach the targets of performances and lifetime lifetime of of aaa fuel fuel cell. cell. lifetime of fuel cell. To achieve the cost target for a PEMFC system, the deadTo achieve the cost target PEMFC system, the To achieve the cost architecture target for for a PEMFC system, the deaddeadendachieve anode the (DEA) is a simple solution since To cost target for aa PEMFC system, the deadend anode (DEA) architecture is a simple solution since end anode (DEA) architecture is a simple solution since only a pressure regulator at the inlet and a solenoid valve end anode (DEA) architecture is a simple solution valve since only pressure at aa solenoid only a outlet pressure regulator at the the inlet inlet and solenoid valve at thea areregulator required for anodeand side. The hydrogen only a pressure regulator at the inlet and a solenoid valve at the are required for hydrogen at the outlet outlet areanode required for the the anode anode side. The hydrogen injected in the is supposed to beside. fullyThe consumed in at the outlet are required for the anode side. The hydrogen injected in the anode is supposed to be fully consumed in injected in the anode is supposed to be fully consumed in DEA operations, which theoretically means 0% hydrogen injected in the anode is supposed to be fully consumed in DEA which means DEA operations, which theoretically theoretically means 0% 0% hydrogen hydrogen losses.operations, However nitrogen and water permeation through DEA operations, which theoretically means 0% hydrogen losses. However nitrogen and water permeation through losses. However nitrogen and water permeation through the membrane induce performance drops and irreversible losses. Howeverinduce nitrogen and waterdrops permeation through the membrane the membranedecreasing induce performance performance drops and and irreversible irreversible degradations, the efficiency. the membrane induce performance drops and irreversible degradations, decreasing the efficiency. degradations, decreasing decreasing the efficiency. efficiency. degradations, According to Strahl et al.the (2014), reversible degradations According Strahl et reversible According to Strahl et al. al. (2014), (2014), reversible degradations are due to to excess nitrogen and water in the degradations outlet anode According to Strahl et al. (2014), reversible degradations are due to excess nitrogen and water in the anode are due to excess nitrogen and water in the outlet outlet(stratianode side that lead to a lower hydrogen concentration are due to excess nitrogen and water in the outlet anode side that lead to a lower hydrogen concentration (stratiside that lead to a lower hydrogen concentration (stratiside that lead to a lower hydrogen concentration (strati-
Figure 1. Fuel Figure 1. Figure 1. Fuel Fuel 2013) Figure 1. Fuel 2013) 2013) 2013)
cell cell cell cell
with with with with
its its its its
four four four four
sub-systems sub-systems sub-systems sub-systems
(Fonseca, (Fonseca, (Fonseca, (Fonseca,
fication phenomena). The main consequence is a voltage fication main consequence is aa voltage fication phenomena). The main consequence is efficiency. voltage drop andphenomena). thus a lowerThe output power or a lower fication phenomena). The main consequence is a voltage drop and thus a lower output power or a lower efficiency. drop and thus a lower output power or a lower efficiency. The performance can be recovered by purging the androp and thus a lower output power or a lower efficiency. The performance can be by anThe outlet performance can accumulated be recovered recovered nitrogen by purging purging the anode to remove andthe water. The performance can be recovered by purging the anode to accumulated nitrogen water. ode outlet outlet irreversible to remove remove degradations accumulated could nitrogen and water. Moreover, be and accelerated ode outlet to remove accumulated nitrogen and water. Moreover, irreversible degradations could be accelerated Moreover, irreversible degradations could be accelerated during stratification effect. The accumulation of nitrogen Moreover, irreversibleeffect. degradations could be accelerated during stratification The of during stratification effect.outlet The accumulation accumulation of nitrogen nitrogen and water at the anode induces the presence of during stratification effect. The accumulation of nitrogen and water at the anode outlet induces the presence of and water water at the the anode anode outlet induces the that presence of oxygen (permeation through the induces membrane) can acand at outlet the presence of oxygen the that oxygen (permeation (permeation through the membrane) membrane) that can can acaccelerate the cathode through carbon corrosion. This measurement oxygen (permeation through the membrane) that can accelerate the carbon This measurement celerate the cathode cathode carbonetcorrosion. corrosion. This measurement is confirmed by Matsuura al. (2013), where a strong celerate the cathode carbon corrosion. This measurement is confirmed by Matsuura et al. (2013), where aa strong is confirmed confirmedis by by Matsuura Matsuura et al. al.cathode (2013),carbon where corrosion strong correlation developed between is et (2013), where a strong correlation is between cathode corrosion correlation is developed developed between cathode carbon corrosion and presence of oxygen in the anode side carbon after long purge correlation is developed between cathode carbon corrosion and and presence presence of of oxygen oxygen in in the the anode anode side side after after long long purge purge intervals. and presence of oxygen in the anode side after long purge intervals. intervals. intervals.
Copyright 2015 IFAC 237 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Copyright 2015 IFAC 237 Peer review© of International Federation of Automatic Copyright © 2015 IFAC 237 Copyright ©under 2015 responsibility IFAC 237Control. 10.1016/j.ifacol.2015.10.034
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Consequently, purge intervals must be calibrated to achieve a performance criterion and/or a lifetime criterion. Hydrogen loss may occur during purges according to the operating conditions and increase with short purge intervals. On the other hand, we have just seen that long purge intervals lead to irreversible degradations. Chen et al. (2013) have investigated the optimization of the purge strategy to reach these two objectives, taking into account actuators constraints (opening/closing delay). This study therefore show an optimal tuning of the purge interval/purge duration for a given operating power. However, the tuning is highly related to the operating conditions, and the optimality may not be obtained with varying-power. Ahluwalia and Wang (2007) has studied the build up of nitrogen for a 90kW automotive stack in recirculation mode. They found an optimum purge that minimizes the performance drop, mainly based on the nitrogen buildup. The optimal purge strategy is also link to the relative humidity, according to Nikiforow et al. (2013). Thus, knowing the internal parameters of the stack (nitrogen, humidity, liquid water) seems to be the first step to build an optimal purge strategy for a dynamic power cycle. Humidity sensors used in Farcas and Dobra (2014) are expensive for a widespread commercialization and the durability of such sensors is not appropriate for industrial fuel cells systems. Hydrogen concentration sensors are already used in recirculation mode and located in the recirculation loop. Their implementation is more difficult in DEA in a non-intrusive manner. Another solution is to use a model correlated with experimental measurements to fit precisely the studied stack (Chen et al., 2014; Steiner et al., 2011). This solution relies on a strong data base to deliver appropriate results.
a drop pressure coefficient and the geometry. Through the GDL (porous media), the diffusion flux computed by a R element is based on Stefan-Maxwell’s equations for the diffusion and on Darcy’s laws for the convective terms (gas and liquid phases). Through the membrane, the two mass transfer processes of water (diffusion and electro-osmose) are taken into account. 2.2 Membrane transport model Our study focuses on the nitrogen build up in the anode side, therefore we need to model the nitrogen permeation through the membrane, which is according to Matsuura et al. (2013), a function of λm the membrane water content and Tcell the cell temperature: ( ) KN2 (λm , Tcell ) = αN2 0.0295 + 1.21fv − 1.93fv2 × e−14 ( )] [ 1 1 E N2 (1) − × exp R Tref Tcell
where αN2 is a tuned scale factor fixed at 1.5 here, R is the universal gas constant, EN2 is the nitrogen molar energy (EN2 = 24 kJmol−1 ), Tref = 303 K and fv is the volume fraction of water in the membrane given by: λm Vw Vmb + λm Vw where Vmb = EW/ρdry is the dry membrane volume, EW the equivalent weight, ρdry the dry density of the membrane and Vw the molar volume of water. fv =
The key parameter of the nitrogen permeation is the membrane water content λm , given by:
The solution developed here is a state observer that combine a simplified physical model with online measurements to update the states estimation. The state observer delivers in real time the nitrogen buildup which can be used to trigger the purge at the right moment. The observer and associated purge strategy are tested and validated by simulation with a 2D dynamic model to simulate the fuel cell response.
) EW 1 ∑ λm = F dt (2) ρdry em S ∑ with F the algebraic sum of the different fluxes (backdiffusion and electro-osmosis) through the membrane. The electro-osmotic drag and the back diffusion flux are calculated with the following equations (Schott and Baurens, 2006):
2. FUEL CELL DYNAMIC MODEL DESCRIPTION
( ) I (3) Feo = 1.0 + 0.028λm + 0.0026λ2m F ) ρdry S ( Fd,i = 6.707e−8 λm + 6.387e−7 EW em ) ( −2416 (λm − λi ) (4) × exp T where I is the fuel cell current, F the Faraday constant and λi the membrane water content at the interface between the membrane and the electrode active area. λi is given by:
2.1 General model setting A detailed fuel cell model has been used in this study to simulate the stack and its system in a dead-end mode. This model has been described in several studies (Schott and Baurens, 2006; Gerard et al., 2010; Robin et al., 2013; Fonseca et al., 2014) and it is efficient to capture the dynamics of the local conditions of the fuel cell. It is 2D-meshed along the surface of the MEA (Membrane Electrode Assembly) and based on pseudo bond graph theory to describe transport phenomena, mass and energy balance, heat transfer through the channel, the GDL (Gas Diffusion Layer) and the membrane. The flow balances are represented by a multi-physic capacity (C). The C element calculates the effort variables (temperature, partial pressure). The transport of flow or heat is represented by a resistive element (R). Through the channel the R element calculates the flow variables by the difference of pressure, 238
ˆ (
λi = 0.043 + 17.81a − 39.85a2 + 36a3 where a = Pvap /Psat (T ).
(5)
2.3 Simulation of the stratification effect Only the fuel cell hydrogen sub-system is modeled with dead-end mode architecture. The other sub-sytems are
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239
The simplified model can be expressed in a continuous form but this continous form cannot be used in a real time target so the system is discretized in the 1st order as: nN2 ,a (k + 1) nH2 O,a (k + 1) (k + 1) n H2 O,c Figure 2. Example of simulated nitrogen accumulation through the anode channel length. The first element is the outlet, the tenth the inlet. Single-cell stack operating at 0.4 Acm−2 , 1.5 bars, 333 K. only considered as perfect inlets and outlets (inlet air flow, humidity and temperature, outlet air pressure, cooling circuit loop with perfect flow regulation). The hydrogen sub-system model is composed of a hydrogen vessel and a pressure regulator at the inlet and a solenoid valve at the outlet. The simulations are carried out with 10 meshes along the channel and the MEA surface, in order to capture the effects of heterogeneities inside the MEA. The cell voltage drops because of the accumulation at the anode outlet of nitrogen and liquid water (Figure 2). Purges (opening of the outlet valve) permit to recover the reversible degradations. 3. STATE OBSERVER 3.1 Choice of the state variables The state observer is built on the 2D model described previously. The internal parameter that interest us the most is the nitrogen buildup. Thanks to (1), nitrogen permeation could be estimated with the knowledge of stack temperature and membrane water content. The last is given by (2) that requires the electro-osmotic drag and the back diffusion flux. Thus the observer must estimate the water on both anode and cathode side to properly compute the two different water fluxes through the membrane. This statement lead us to choose the following state vector:
nN2 ,a n X = H2 O,a nH2 O,c λm
(6)
where nN2 ,a is the number of moles of nitrogen in the anode, nH2 O,a and nH2 O,c respectively the number of moles of water, liquid and vapor, in the anode and cathode side, and λm the membrane water content. We consider for both the anode and cathode side a unique volume gathering the channel and the active area. The hypothesis underlying here is the homogeneous repartition of the species in the electrodes and the membrane. 239
λm (k + 1)
= nN2 ,a (k) + ∆t [KN2 − Fpurge,N2 ] = nH2 O,a (k) +∆t [Fd,a − Feo − Fpurge,H2 O,a ] = nH[2 O,c (k) ] I + Fin − Fout +∆t Fd,c + Feo + 2F = λm[(k) ] EW (−Fd,a − Fd,c ) +∆t ρdry em S +∆t [−Fpurge,λm ] (7)
with ∆t the time step, KN2 , Feo , Fd,X the fluxes mentioned in section 2.2, Fin , Fout respectively the inlet and outlet water flux in the cathode channel. The system in (7) is modified with 3 corrective terms, Fpurge,X , to describe the average empirical decrease of the species X during the anodic purge. The magnitude of these corrective terms are constants, as an approximation of these terms in the same order of magnitude as the real behavior is sufficient since the observer will correct it online. It can be expressed in general as:
Fpurge,X =
{
fpurge,X 0
if Qao = 1 if Qao = 0
(8)
The input vector considered here in two parts: the purge command, Qao , as the input command and Tcooling and I, respectively the cooling temperature and current, as input “disturbances”. The purge command aims at switching the observer in purge mode, with the 3 corrective terms Fpurge,X . Cooling temperature and current are used to compute the equations with the actual operating conditions, assuming that relative humidity at the input cathode, cathode stoichiometry and pressures remain stable at a given value. Consequently we have:
U=
[
Qao Tcooling I
]
(9)
as an entrance to the system. An advantage of a state observer is to use online measurements to correct the model and estimate properly the states. However, in this case, it is hard to find relevant measurements that give us information on the internal states because of the coupling effects. Even if test benches are full of sensors, the goal is to limit as much as possible the use of expensive ones, like humidity sensors, to reduce the cost of the overall system. The only measurement used in this observer is the membrane ohmic resistance Rm , deduced from the output voltage and current, as explained in a further section. Rm is linked to the membrane water content by the equation:
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Rm =
1 em exp S 33.75λm − 21.41
(
1268 T
)
(10)
One should notice that the cooling temperature and the stack current are also measured online but used in this case as input disturbances. 3.2 UKF algorithm
Table 1. Operating conditions Parameter
Value
Pressure Inlet cathode humidity Inlet anode humidity Cooling temperature Cathode stoichiometry
1.5 bars 50 % 0% 343 K 2
3.4 Purge based on the observer
We have incomplete measurements for the observer (1 measure, 4 states). The model is also highly non linear and we need to specify linear inequality constraints to ensure the physical meaning of the estimation: the states (number of moles) are positive and limited by the channels’ volume. According to Simon (2009) and our specifications, we chose the Unscented Kalman Filter (UKF), which uses a statistical linearization called unscented transform, instead of Jacobians in the EKF. The states obtained after the unscented transform can be constrained, leading to the contrained UKF algorithm. For a complete description of the Unscented Kalman Filter, please refer to Terejanu (2011) and van der Merwe and Wan (2000). The final algorithm used in the observer is constrained UKF+EKF: constrained UKF for the prediction stage and EKF for the update stage. The EKF is appropriate for the update stage as the only measurement equation is 10, which is not highly non linear, so the use of the Jacobian still have sense. The gain is a lower computational load for this stage and thus a faster algorithm.
The observer allows us to know in real time the volumetric saturation of nitrogen in average in the fuel cell. For the sake of simplicity we arbitrarily choose an overall nitrogen saturation of 10% as the trigger level for the purge, which is a trade-off between performance and lifetime. The opening time should be defined according to the trigger level, the valve and the operating conditions (especially temperature). We used the 2D model, with purge flow equations, to determine the optimal opening time: 0.1 s is enough to remove only nitrogen without wasting hydrogen, whereas 0.15/0.25 s is needed if there is liquid water in the anode channel. The exact duration depends on the location of the liquid water along the channel. As it is impossible with the observer structure to locate precisely the liquid water in the channel, 0.25 s is a good compromise choice for lifetime criterion, whereas 0.10/0.15 s must be choosen to ensure the best performances. We choose an opening time of 0.25 s for all the simulations made in this study. 4. RESULTS
3.3 Measurement of the membrane ohmic resistance 4.1 Validation The membrane ohmic resistance is linked to the output voltage of the fuel cell with the equation: U = Erev + ηact − (Rm + Re ) I
(11)
with Erev the thermodynamical potential, Rm is the membrane resistance, Re is the electrical resistance of the stack (bipolar plates, GDL...) and ηact the over-potential. Concentration losses are taken into account with the modeling of the transport phenomena in the GDL that influences the partial pressure of species in the active area. As the electrical time constant is shorter than the physical one, it is thus possible to measure the membrane ohmic resistance with high frequency oscillations on U and I, and the knowledge of Re . A DC/DC converter is often used in a fuel cell system to protect the stack from reverse currents and adapt the output voltage to the external load. These DC/DC converters create high frequency oscillations in the stack current, which are used in Hinaje et al. (2009) to deduce the membrane ohmic resistance from the magnitudes ripples of the current and voltage. Other methods have been investigated by Cooper and Smith (2006) and they all provided at least 3.5% accuracy on the membrane ohmic resistance measurement, including the high frequency oscillations method. We therefore consider for this study that the membrane ohmic resistance is available with a 3 % accuracy. 240
The observer is tested in simulation and compared with a realistic 2D model. The model used is a single-cell stack with the operating parameters referenced in Table 1. A highway automotive cycle is used for the test. The profile has been re-sized to match the maximal output power of the simulated cell. The first test is made with exact operating condition parameters to validate the concept. As the observer is a strong reduction model of the 2D model, we expect performances drops. Our goal is to have a 5% accuracy on the estimated nitrogen saturation. Figure 3 shows the first third of the simulation. We can notice the good overall accuracy of the observer. The peaks that occur after the purges are due to minor differences between model and observer that take huge proportions with small values of nitrogen saturation. The relative humidity computed by the observer shows a good agreement with the simulated one, for each side (Figure 4). This is a relevant information for basic water management, even if it sounds hard to obtain precise estimations of relative humidity here since it is an inhomogeneous phenomena and this observer takes into account a unique volume. Related to the humidity, the liquid water is poorly estimated because liquid water appears where the relative humidity reaches 100%. Obviously a 100% RH can occur when the average humidity is below 100%, leading to a wrong estimation of the liquid water.
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241
4.2 Robustness analysis The robustness of the observer is then tested with the addition of uncertainties on different parameters: temperature, current, relative humidity, cathode stoichiometry and membrane ohmic resistance. The other parameters are supposed to be well defined, in particular the physical design of the stack (volume, membrane thickness, dry membrane density). The temperature is given by a sensor in the cooling line, with inhomogeneities along the length. An offset is added to the temperature, growing from −4 K up to 4 K during 200 s to model this uncertainty. The output current is measured by a sensor with a known precision of 1% and we expect a 3% accuracy for the membrane ohmic resistance measurement. A multiplicative noise, uniformly distributed, is used for both uncertainties. Inlet relative humidity and stoichiometry at the cathode side are supposed to be constant. However, the air cathode line is hard to manage properly due to the non linear behavior of the air compressor and the humidifier (Fonseca et al., 2014). We consider that the cathode stoichiometry has a 20% accuracy in a dynamic mode (we expect < 10% with appropriate control (Fonseca et al., 2014)) and admit that the inlet relative humidity can vary from nearly 0% up to 100% with a passive humidifier. Even if the passive humidifier is sized to deliver a 50% RH, the lack of control can lead to great variations with specific operating conditions (flooding for example). The simulated stack is run with perfect parameters. The observer error still remain below 5%, except for some current peaks, the same that occur during the validation simulation. Figure 3. Observer results with exact operating condition parameters. The first plot represents the average nitrogen saturation, model and observer. The second plot shows the relative error made between model and observer, with the 5% goal. The third plot represents the current delivered by the cell.
4.3 Comparison of different purge strategies efficiency Three different purge strategies are compared: a static purge at constant interval and opening time (100 s / 0.25 s); a current integration method (Tr = 7000 As); an observer based purge. The current integration method, presented in Chen et al. (2014), is based on the on-line integration of current: Tr =
ˆ
Istack (t) dt
(12)
with Tr in As. The value that Tr should reach to trigger the purge is determined with the specifications of the PEMFC and the associated operating conditions. It is a simpler way to implement an anodic purge for dynamic conditions. However, this method does not guarantee an appropriate control of the nitrogen buildup in the anode side, as shown in Figure 5.
Figure 4. Comparison of relative humidity estimations of the observer and the 2D model on the WLTC power cycle. 241
For the three methods with the same dynamic power cycle (highway automotive profile), the fuel cell system efficiency is compared (Table 2), given by the equation: η=
Eelec LHVH2 nH2 ,cons
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validate the observer and the associated strategy on a real fuel cell system. REFERENCES
Figure 5. Average nitrogen saturation for anode purging based on current-integration with time. Trigger criterion: 7000 As Table 2. Comparison of different purge strategies for highway automotive cycle Strategy
η
Static purge Current integration Observer
38.56% 54.80% 55.76%
with Eelec the electric energy produced by the fuel cell during the cycle, LHVH2 the hydrogen Low Heating Value and nH2 ,cons the total hydrogen consumed during the cycle. The observer based purge strategy shows the best performances. Even if the difference with the current integration is low, the observer based purge is always the best regardless the power cycles. Indeed, in this case, the current integration strategy is calibrated on this specific power cycle, but its trigger level must be adapted to another power cycle dynamic to ensure the same level of performances. 5. CONCLUSION This paper presented a state observer and its associated control to optimize the anodic purge strategy for a fuel cell system with dead-end architecture. The model of the observer is derivated from the simplification of the transport equations of a membrane model. The observer has been tested and validated by simulation with a dynamic fuel cell model. The results show a good accuracy of the observer with several power profiles even with uncertainties. Moreover, the observer command increases the fuel cell system efficiency and probably the durability, compared to the other existing purge strategies. Therefore, this work is of great interest to improve the management of fuel cell vehicles and their associated dynamic power profiles. However, improvements can be made concerning the opening time of the purge valve and the estimation of liquid water along the channels. A better estimation of liquid water will not only enhance the water management strategy but also help calibrating the opening time to match with the exact amount of species that must be purged, resulting in even better performances. Experiments are planned to 242
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