DE102015210836A1 - A diagnostic method for determining a condition of a fuel cell stack - Google Patents

Abstract

The invention relates to diagnostic methods for determining a state of a fuel cell stack (10) having a plurality of individual cells (11), each comprising a first catalytic electrode arranged in a first electrode space (12) and a second catalytic one arranged in a second electrode space (13) Electrode, which are separated by an ion-conductive membrane (14). It is provided that the determination of the state comprises a determination of a diffusion and / or permeation-driven stream of molecular hydrogen through the membrane (14) or a variable equivalent thereto.

Description

The invention relates to a diagnostic method for determining a state of a fuel cell stack which has a plurality of individual cells, each individual cell each comprising a first catalytic electrode arranged in a first electrode space and a second catalytic electrode arranged in a second electrode space, and an ionically conductive membrane containing the separates two electrode spaces from each other. The invention further relates to a configured for carrying out the method fuel cell system and a vehicle with such.

Fuel cells use the chemical transformation of a fuel with oxygen to water to generate electrical energy. For this purpose, fuel cells contain as core component the so-called membrane electrode assembly (MEA) for membrane electrode assembly, which is a microstructure of an ion-conducting (usually proton-conducting) membrane and in each case on both sides of the membrane arranged catalytic electrode (anode and cathode). The latter usually comprise precious metals supported on an electrically conductive carbon-based material, in particular platinum. In addition, gas diffusion layers (GDL) can be arranged on both sides of the membrane-electrode assembly on the sides of the electrodes facing away from the membrane. Between the individual membrane electrode assemblies bipolar plates (also called flow field plates) are usually arranged, which ensure a supply of the individual cells with the operating media, ie the reactants, and usually also serve the cooling. In addition, the bipolar plates provide for an electrically conductive contact between the membrane-electrode units. As a rule, a fuel cell stack is formed by a plurality of series-arranged fuel cells whose electrical powers add up.

During operation of the fuel cell, the fuel, in particular hydrogen H ₂ or a hydrogen-containing gas mixture, is supplied to the anode via an anode-side flux field of the bipolar plate, where an electrochemical oxidation of H ₂ to H ⁺ takes place with emission of electrons. Via the electrolyte or the membrane, which separates the reaction spaces gas-tight from each other and electrically isolated, takes place (water-bound or anhydrous) transport of protons H ⁺ from the anode compartment in the cathode compartment. The electrons provided at the anode are supplied to the cathode via an electrical line. The cathode is supplied via a cathode-side flow field of the bipolar plate oxygen or an oxygen-containing gas mixture (for example, air), so that a reduction of O ₂ to 2O ^2- taking the electrons takes place. At the same time, the oxygen anions in the cathode compartment react with the protons transported via the membrane to form water.

Fuel cells are subject to increasing aging during their lifetime. This relates on the one hand to the catalytic electrodes as a result of agglomeration or loss of the catalytic material (usually platinum) and corrosion of the carbon-based catalyst support. All of these degradation phenomena lead to a decrease in the active catalytic surface area (ECSA) for electrochemical active surface area. In addition, the polymer electrolyte membranes are also subject to aging in the form of material dilution or even perforation. Also, the proton conductivity of the membrane and the ionomers present in the catalytic electrodes may decrease over time. The diagnosis of fuel cells is a core task for the dissemination of fuel cells. While individual cells can be diagnosed very well, for example by cyclic voltammetry (CV), the diagnosis of fuel cell stacks with a large number of single cells connected in series is difficult. Cyclic voltammetry regulates the voltage and measures the current. In a series connection of cells can thus not regulate the voltage of each cell. Furthermore, different effects overlap, which lead to different causes of the measured current. A solution to consider the individual phenomena differentiated and thus separately detect different state parameters of electrodes and membrane, would be desirable.

Imanashi et al. ( H. Imanashi, K. Manabe, T. Ogawa & Y. Nonobe: Developement of Electric Power Contraol Uses the Capacitance Characteristics Often He Fuel Cell, SAE International Journal of Engines 4 (1), 2011, 1879-1887 ) describe the determination of the double-layer capacity of a fuel cell stack by means of a voltage-controlled cyclic voltammogram.

Brightman et al. ( E. Brightman, G. Hinds & R. O'Malley: In situ measurements of active catalyst surface area in fuel cell stacks, Journal of Power Sources 242, 2013, 244-254 ) describe a galvanostatic method to determine the active catalyst surface area (ECSA) of a fuel cell stack or individual cells. For this purpose, the cell or the stack is subjected to a constant positive or negative current density and based on the slope of the resulting cell voltage, the double-layer capacitance and ECSA determines. In order to minimize the influence of hydrogen permeation through the membrane (H ₂ crossover), it is proposed to choose a high current density, so that the comparatively slow hydrogen transfer can be neglected compared with the rapid charge or discharge. Furthermore, the falsifying influence of hydrogen penetration is minimized by a low concentration of hydrogen on the anode side.

The diagnostic methods presented above are aimed primarily at detecting the state of the catalytic electrodes. A consideration of the condition of the membrane does not take place here.

The invention is based on the object of proposing a method which allows an assessment of the aging state of the polymer electrolyte membrane of a fuel cell. In particular, the method should also be applicable to a fuel cell stack in the compressed state (in situ) and, ideally, also be feasible in the context of on-board diagnostics.

This object is achieved by a method having the features of claim 1.

The invention thus relates to a diagnostic method for determining a condition of a fuel cell stack having a plurality of single cells. Each individual cell comprises a first catalytic electrode arranged in a first electrode space and a second catalytic electrode arranged in a second electrode space and an ion-conducting membrane which separates the first and the second electrode spaces from one another. According to the invention, the state determination comprises a determination of a diffusion-driven and / or permeation-driven stream of molecular hydrogen through the membrane or of an equivalent size to the stream.

In the context of the invention, a variable equivalent to the material flow is understood to mean a quantity which allows a calculation of the material flow, in particular, is proportional to the flow of material.

It has been found that the flow of hydrogen through the membrane is a conditional parameter that very well describes the state of aging of polymer electrolyte membranes. Although the membrane is to separate the operating gases in the two electrode spaces from each other, yet molecular hydrogen passes through the membrane, in the case of normal operation of the fuel cell from the fuel-side anode compartment into the air-side cathode compartment. As the membrane ages, the flow of material across the membrane increases. On the one hand, the material flow is due to diffusion due to different partial pressures (p *) between the anode and cathode sides (p * _An ≠ p * _Kat ). Since usually the hydrogen partial pressure on the anode side is greater, thus hydrogen passes as a result of diffusion from the anode to the cathode side. In addition, the material flow can occur as a result of permeation, that is, due to a difference in the absolute pressure in the two electrode spaces (p _An ≠ p _cat ). If a permeation stream is present, ie the permeation flow is not equal to zero, it is possible to conclude what is known as pitting in the membrane.

In a preferred embodiment of the method, the determination of the molecular stream of molecular hydrogen comprises the detection of an electrical pumping current which is required to counteract the diffusion and / or permeation-driven stream of molecular hydrogen through the membrane. Here, therefore, the detected electrical pumping current represents the equivalent size to the material flow. The electrical pumping current correlates directly with the size of the H ₂ -offowstream through the membrane. In addition, it can be detected directly via the electrical circuit present in fuel cells or fuel cell stacks.

Preferably, to determine the material flow of hydrogen through the membrane or the electric pumping current of the first electrode chamber with hydrogen and the second electrode chamber is acted upon with an inert gas or is already due to the operating point in such a state. Under these conditions, the second electrode acts as a working electrode and the first electrode as a hydrogen reference electrode or counter electrode. (All present voltage specifications therefore refer to the half-cell voltage with respect to the hydrogen reference electrode.) It is initially irrelevant whether the electrode referred to as "first electrode" or "second electrode" is the cathode or anode of the fuel cell in normal operation. In this state, a current is impressed on the fuel cell stack, such that the second catalytic electrode is switched to anode potential, so that in the second electrode space existing, molecularly previously migrated through the membrane hydrogen is oxidized and then the resulting protons migrate back into the first electrode space. The required pumping current is measured. In this way, the electric pumping current can be determined in a procedurally simple manner, which must be used to counteract the diffusion and / or permeation-driven flow of hydrogen through the membrane.

In a preferred embodiment, the current is impressed voltage or current, such that a predetermined temporal voltage curve (the target voltage) passes through a voltage maximum and the current is measured at the time of the maximum voltage. The advantage of this design is that at the time of the voltage maximum, the voltage gradient dU / dt is equal to zero, and thus the capacitive current which flows at the electrodes to build up a capacitive double layer is equal to zero. Thus, the measured current is not affected by the capacitive current. In particular, the current is detected in each case when individual cell voltages of individual diagnostic units, each comprising one or more individual cells of the fuel cell stack, pass through a voltage maximum. In this case, a diagnostic unit in each case comprise one or more individual cells of the fuel cell stack. This approach allows diagnosis of individual diagnostic units or even single cells of the fuel cell stack.

According to a further preferred embodiment of the invention, the impressing of the current takes place in such a way that the maximum voltage is reached as quickly as possible, in particular at the latest after 5 seconds, preferably at the latest after 3.5 seconds and particularly preferably after 2 seconds after the beginning of the current application. In this way the measurement becomes particularly robust and precise. With the start of the charging of the bilayers, the initially quite stationary concentration gradient and thus the H ₂ material flow changes. Since this and the associated back pump current can be different for each cell, but the cells are connected in series and therefore the total current in each cell is the same, the bilayers are charged at different rates, that is, the voltages diverge. This effect is stronger, the greater the proportion of the pumping current on the impressed total current. The slower it is loaded, the larger this proportion, the more inhomogeneous the stack behaves and the harder it is to comply with the voltage limits mentioned below. By quickly reaching the maximum voltage, the proportion of pumping current is kept low until this time.

Furthermore, it is preferably provided that the current is impressed in a voltage-controlled manner such that a predetermined temporal voltage curve at least temporarily assumes a half-cell voltage in the range from 0.4 to 0.8 volts, in particular from 0.4 to 0.6 volts, and the current measured in this voltage range. Exceeding the lower limit of 0.4 volts per cell ensures that no adsorbate of hydrogen is present at the electrodes, so that the measured current is not distorted by the amount of electricity used for the hydrogen oxidation of the H adsorbate. Compliance with the upper limit of the half-cell voltage of 0.8 volts, in particular 0.6 volts, prevents oxidation of the catalytic material of the electrodes and thus degradation thereof.

Particularly preferably, the two measures mentioned above are combined, that is, it is a voltage profile predetermined whose maximum voltage in a range of 0.4 to 0.8 volts, in particular from 0.4 to 0.6 volts, so that the current measurement at the time of the voltage maximum in this voltage range. As a result of the combination of the two measures, on the one hand the detection of the capacitive current and on the other hand the detection of the adsorbate current is suppressed. Thus, the measured current is composed only of the pumping current to be determined and an overlay by an electrical short-circuit current through the membrane.

In many cases, the electrical short-circuit current is negligibly small and need not be considered separately. A preferred embodiment of the method provides, however, that the state determination further comprises a determination of the electrical short-circuit current through the membrane and the measured current is corrected by this short-circuit current, so as to obtain the desired pumping current. In this way the accuracy of the method with respect to the pumping current is improved. In addition, the diagnostic method is supplemented by the determination of a further parameter, namely the electrical short-circuit current.

The method according to the invention can, of course, be carried out as an off-board method, for example as part of a workshop interval. In this case, the first and the second electrode space are preferably continuously purged with preconditioned gases, that is to say hydrogen on the one hand and inert gas on the other hand. Preferably, environmental parameters, such as temperature, pressure and humidity of the gases are kept constant here.

Preferably, however, the method is carried out as an on-board method and the pumping current is detected during a suitable operating mode of the fuel cell stack, in particular within a standby mode. The standby mode is ideal for carrying out the method, since in standby mode no power request is made to the fuel cell stack. Further, in standby mode, usually the air supply to the cathode is turned off while the anode gas recirculation is maintained. Thus, there is a consumption of atmospheric oxygen at the cathode, so that finally at the cathode substantially nitrogen is present as an inert gas and hydrogen at the anode. In this case, to carry out the method, the anode is operated as a hydrogen reference electrode and the actual cathode switched to anode potential, so that it acts as a working electrode and oxidized passing through the membrane hydrogen and migrate the resulting protons through the membrane back to the anode. Onboard diagnostics enable close monitoring of the fuel cell stack even outside of the workshop.

In principle, the diffusion and / or permeation-driven material flow of molecular hydrogen through the membrane or the corresponding electrical pumping current can be detected in any direction. In a preferred embodiment of the method, during normal operation of the fuel cell stack, the first electrode space corresponds to the anode space provided with the fuel and the first catalytic electrode of the anode arranged therein, while the second electrode space is the air-supplied cathode space during normal operation and the second catalytic electrode arranged therein corresponds to the cathode , In this way, the advantageous side effect is achieved to counteract the unwanted hydrogen flow through the membrane during operation of the fuel cell, in particular in the previously described standby mode.

The determination of the diffusion- and / or permeation-driven mass transport of molecular hydrogen through the membrane can be carried out for the entire fuel cell stack or for individual diagnostic units thereof, comprising one or more individual cells. In the latter case, it is necessary for the individual cell or the diagnostic unit comprising a plurality of individual cells each to have its own electrical cell voltage tap, which enables an individual measurement of the voltage. If the determination is made for the entire fuel cell stack, that is to say over all individual cells, the mass transport or pumping current is recorded as an average over all cells.

In an advantageous embodiment of the method, the state determination further comprises a determination of a double-layer capacitance of at least one of the catalytic electrodes, wherein the double-layer capacitance is determined as a function of the determined material flow or the electrical pumping current. Various methods for determining the double-layer capacity are known. However, to date it has not been possible to determine the mass transfer of hydrogen through the membrane in compressed fuel cell stacks and to eliminate the detected double-layer capacity from the effects of mass transfer.

According to a further embodiment of the invention, the state determination further comprises a determination of an active catalyst surface of at least one of the catalytic electrodes, which is determined as a function of the determined material flow or electrical pumping current and the determined double-layer capacitance.

The electrical double-layer capacitance and the active catalyst surface allow conclusions about the state of the catalytic electrodes, in particular on an agglomeration or a loss of the catalytic material and / or a degradation of the catalyst support material. On the basis of the inventively determined material flow of molecular hydrogen through the membrane and optionally the detection of the short-circuit current through the membrane thus the double-layer capacitance and the active catalyst surface of the catalytic electrodes can be determined in a series of two or three consecutive test measurements. Optionally, the state determination may further comprise determining the proton conductivity of the membrane and, optionally, ion-conducting polymers within the electrodes in a separate measurement. The detection of the various state variables will be explained in the embodiments.

In the context of the invention, for the measurements required for determining the pumping current, the electric short-circuit current, the double-layer capacitance and / or the active catalyst surface, the conditions in the first and second electrode spaces can be adjusted in a targeted manner in order to visualize the desired measured quantities. In particular, pressure, temperature, gas flow and / or gas composition are adjusted. This is easily possible in off-board diagnostics. In the case of execution as an on-board diagnosis, this setting of the measurement conditions preferably takes place as a function of the operating point or state of the fuel cell stack.

In a preferred embodiment, the determinations of the pumping current, the electric short-circuit current, the double-layer capacitance and / or the active catalyst surface or the partial measurements required for these quantities are carried out independently of time and in any order. The determination of the time and the sequence takes place in particular as a function of an operating point and / or state of the fuel cell stack, for example, an external power demand on this. In this way, the required partial measurements of the successive sizes can be performed independently. This procedure allows, in particular, the implementation of the diagnostic method by means of an on-board diagnosis, whereby the individual acquisitions are intelligently coordinated with the current operating situation.

Another aspect of the invention relates to a fuel cell system configured to carry out the method according to the invention. The fuel cell system comprises in particular a fuel cell stack and a control device for the same, which is set up to carry out the method according to the invention. For this purpose, the controller has a computer readable program algorithm executing the method. Furthermore, the control device can have characteristic curves and / or characteristic maps from which corresponding output values, for example control values for controlling various components of the fuel cell system, are determined as a function of input values.

Another aspect of the invention relates to a vehicle having such a fuel cell system. Preferably, this is a vehicle having at least one electric motor as a traction motor, with which alone or in combination with an internal combustion engine, the vehicle is driven.

Further preferred embodiments of the invention will become apparent from the remaining, mentioned in the dependent claims characteristics.

The various embodiments of the invention mentioned in this application are, unless otherwise stated in the individual case, advantageously combinable with each other.

The invention will be explained below in embodiments with reference to the accompanying drawings. Show it:

1 a block diagram of a fuel cell system according to a preferred embodiment of the invention;

2 a measuring arrangement for carrying out the diagnostic method according to a first embodiment;

3 a measuring arrangement for carrying out the diagnostic method according to a second embodiment;

4 a measuring arrangement for carrying out the diagnostic method according to a third embodiment;

5 time profiles of the voltage and the current density during the measurement of the diffusion and / or permeation-driven material flow;

6 Timing of the voltage and the current density during the measurement of the double capacitance and the ECSA and

7 a decision algorithm for coordinating the data acquisition for performing the diagnostic method.

1 shows a total of 100 designated fuel cell system according to a preferred embodiment of the present invention. The fuel cell system 100 is part of a not further illustrated vehicle, in particular an electric vehicle having an electric traction motor, by the fuel cell system 100 is supplied with electrical energy.

The fuel cell system 100 comprises as a core component a fuel cell stack 10 containing a plurality of stacked single cells 11 having. Every single cell 11 each includes an anode compartment 12 and a cathode compartment 13 that of an ion-conductive Polymer electrolyte membrane 14 are separated from each other (see detail). The anode and cathode compartment 12 . 13 each comprises a catalytic electrode, the anode or the cathode (not shown), which catalyzes the respective partial reaction of the fuel cell reaction. The anode and cathode electrodes comprise a catalytic material, such as platinum, supported on an electrically conductive high surface area support material, such as a carbon based material. Between two such membrane-electrode assemblies is also one each with 15 indicated bipolar plate arranged, which the supply of the operating media in the anode and cathode spaces 12 . 13 serves and also the electrical connection between the individual fuel cells 11 manufactures.

To the fuel cell stack 10 to supply with the operating gases, the fuel cell system 100 on the one hand, an anode supply 20 and on the other hand, a cathode supply 30 on.

The anode supply 20 includes an anode supply path 21 which feeds an anode operating medium (the fuel), for example hydrogen, into the anode spaces 12 of the fuel cell stack 10 serves. For this purpose, the anode supply path connects 21 a fuel storage 23 with an anode inlet of the fuel cell stack 10 , The anode supply 20 further includes an anode exhaust path 22 containing the anode exhaust gas from the anode chambers 12 via an anode outlet of the fuel cell stack 10 dissipates. The anode operating pressure on the anode sides 12 of the fuel cell stack 10 is about an actuating means 24 in the anode supply path 21 adjustable. In addition, the anode supply can 20 as shown, a fuel recirculation line 25 comprising the anode exhaust path 22 with the anode supply path 21 combines. The recirculation of fuel is common in order to return and utilize the fuel, which is mostly used in excess of stoichiometry, in the stack. In the fuel recirculation line 25 is another adjusting agent 26 arranged, with which the recirculation rate is adjustable.

The cathode supply 30 includes a cathode supply path 31 which is the cathode spaces 13 of the fuel cell stack 10 supplying an oxygen-containing cathode operating medium, in particular air which is drawn in from the environment. The cathode supply 30 further includes a cathode exhaust path 32 , which the cathode exhaust gas (in particular the exhaust air) from the cathode compartments 13 of the fuel cell stack 10 dissipates and optionally this feeds an exhaust system, not shown.

For conveying and compressing the cathode operating medium is in the cathode supply path 31 a compressor 33 arranged. In the illustrated embodiment, the compressor 33 designed as a mainly electric motor driven compressor whose drive via a with a corresponding power electronics 35 equipped electric motor 34 he follows. The compressor 33 may also be through a in the cathode exhaust path 32 arranged turbine 36 (optionally with variable turbine geometry) are supported by a common shaft (not shown) driven. The turbine 36 represents an expander, which causes an expansion of the cathode exhaust gas and thus a reduction of its pressure.

The cathode supply 30 may also according to the illustrated embodiment, a wastegate line 37 having the cathode supply line 31 with the cathode exhaust gas line 32 connects, so a bypass of the fuel cell stack 10 represents.

The wastegate pipe 37 allows the operating pressure and / or the mass flow of the cathode operating medium in the fuel cell stack in the short term 10 reduce without the compressor 33 shut down. One in the wastegate pipe 37 arranged adjusting means 38 allows control of the amount of the fuel cell stack 10 immediate cathode operating medium. All adjusting means 24 . 26 . 38 of the fuel cell system 100 can be designed as controllable or non-controllable valves or flaps or as additional compressors. Corresponding further actuating means can be in the lines 21 . 22 . 31 and 32 be arranged to the fuel cell stack 10 isolate from the environment and ensure controllability of the system.

The fuel cell system 100 also has a humidifier module 39 on. The humidifier module 39 on the one hand is in the cathode supply path 31 arranged so that it can be flowed through by the cathode operating gas. On the other hand, it is so in the cathode exhaust path 32 arranged so that it can be flowed through by the cathode exhaust gas. The humidifier 39 typically has a plurality of water vapor permeable membranes formed either flat or in the form of hollow fibers. In this case, one side of the membranes is overflowed by the comparatively dry cathode operating gas (air) and the other side by the comparatively moist cathode exhaust gas (exhaust gas). Driven by the higher partial pressure Water vapor in the cathode exhaust gas transfers to the cathode operating gas via the membrane, which is humidified in this way.

Various other details of the anode and cathode supply 20 . 30 are in the simplified 1 not shown for reasons of clarity. Thus, in the anode and / or cathode exhaust path 22 . 32 a water separator may be installed to condense and drain the product water resulting from the fuel cell reaction. Finally, the anode exhaust gas line 22 into the cathode exhaust gas line 32 lead, so that the anode exhaust gas and the cathode exhaust gas are discharged via a common exhaust system.

2 shows a total with 200 designated arrangement for carrying out the diagnostic method according to the invention in a first embodiment of the invention. Here is with 10 again denotes the fuel cell stack, the example here only as a single cell with an anode compartment 12 and a cathode compartment 13 is shown. The order 200 includes a power supply 40 that via load cable 41 with pole terminals of the fuel cell stack 10 connected is. A current sensor (ammeter) 42 allows the detection of an electric current I, with which the fuel cell stack 10 is applied or which of the stack 10 is produced. A voltage sensor (voltmeter) 43 allows the detection of a voltage U, with which the fuel cell stack 10 is applied or which is generated by this. The order 200 further includes a diagnostic device 44 , The diagnostic device 44 receives the data lines interrupted here with those with the current sensor 42 detected current intensity or density I and those with the voltage sensor 43 detected stack voltage U. If the fuel cell stack 10 has a single cell detection, by means of which the single-cell voltages of individual cells or combinations of individual cells can be measured, so these variables U _i in the diagnostic device 44 The index i is a single diagnostic unit of the stack 10 which consists of a single cell or a combined number of single cells.

In 2 has the diagnostic device 44 the function of data acquisition (I, U, U _i ) on and a setpoint generator, which via the control line to the power supply 40 or the load 45 is transferred, and optionally a control of the setpoint. Optionally, the diagnostic device 44 have a component protection function by monitoring the voltages and possibly the power supply 40 or the load 45 off.

In the 2 The arrangement shown is suitable for carrying out the measurement of the electric short-circuit current (but with a different gas feed), the electrical pumping current and the galvanic charging for determining the double-layer capacitance and the ECSA. If, in addition, the determination of the proton conductivity of the membrane and electrode ionomers is carried out, the power supply is 40 by an electrical load 45 replaces or additionally has a load function.

3 shows a diagnostic device 200 in a second embodiment. In the 3 shown arrangement differs from the 2 essentially in that the diagnostic device 44 is replaced by two functional units. These include on the one hand a data acquisition device 46 into which the measured data I, U and / or U _i are received via the signal lines, and on the other hand a control device 47 , which via the control line the power supply 40 or the load 45 with a setpoint. Optionally, the control device 47 via the current sensor 42 read current detected I, if necessary, to allow control of current or voltage.

In the in 3 the embodiment shown assumes the data acquisition device 46 the functions of data collection and evaluation, while the control device 47 as setpoint generator for the power supply 40 or the load 45 optionally with a corresponding control function. In addition, the controller may have a component protection function by connecting the power supply 40 or the load 45 to protect the stack 10 off.

Yet another variant of the diagnostic arrangement 200 is in 4 shown. Here is one of the two load cables 41 between power supply 40 / Load 45 and the current sensor 42 a relay 48 arranged. This is done by the controller 47 controlled to allow an interruption of the circuit for component protection. The arrangement according to 4 also contains a separate setpoint generator 49 which is the power adapter 40 or the load 45 with a corresponding setpoint controls and optional controls.

Hereinafter, the implementation of the diagnostic method according to a preferred embodiment and using the diagnostic device according to 2 explained in more detail.

• 1. Elektrischer Kurzschlussstrom durch die Membran (→ I_short)
• 2. Wasserstoff-Stoffstrom durch die Membran (H₂-Crossover) (→ I_H2)
• 3. Kapazität der Doppelschicht in der Katalysatorschicht (→ I_cdl)
• 4. Aktive Katalysatoroberfläche (ECSA) (→ I_ad)
• 5. Protonenleitfähigkeit der Membran.

The diagnostic method presented here preferably includes the determination of the following state variables of a fuel cell, which are essential and intrinsic for the fuel cell stack's performance and its degradation:

• 1. Electrical short-circuit current through the membrane (→ I _short )
• 2. Hydrogen flow through the membrane (H ₂ crossover) (→ I _H2 )
• 3. Capacity of the double layer in the catalyst layer (→ I _cdl )
• 4. Active Catalyst Surface (ECSA) (→ I _ad )
• 5. Proton conductivity of the membrane.

As part of the diagnosis, the above state determinations 1 to 4 build on each other in the form of a concatenation of three measurements (see equation 1). The results of measurements 1 to 3 serve to correct the subsequent measurement. In contrast, the measurement 5 is an independent measurement independent of the other measurements and serves to complete the diagnosis. I _measurement = I _{short, i} + I _{H2, i} + I _{cdl, i} + I _{ad, i} (1)

In the equations used herein, index i represents the ith diagnostic unit of the fuel cell stack. This may comprise a single cell or a combination of several individual cells or the entire stack. If more than one cell are combined in one diagnostic unit, the information always refers to the mean value per individual cell of the diagnostic unit.

1. Measurement of the electrical short-circuit current (I _{short, i} )

Although the membrane of a fuel cell is designed as an insulator, naturally it has only a finite resistance to the electron conduction, so that leakage currents occur. The electrical short-circuit current may be negligible, especially in brand-new fuel cells. However, it may become relevant when the membrane has aged. The electrical short-circuit current I _{short, i is} determined according to equation 2, in which R _{short, i is} the ohmic resistance of the membrane against electron conduction and U _{i is} the single-cell voltage. I _{short, i} = R _{short, i} · U _i (2)

The measurement of the short-circuit current across the membrane, for example, using the system in 2 by taking both electrode spaces 12 . 13 be subjected to identical gas conditions as possible. For example, both the first and the second electrode space 12 . 13 each with pre-conditioned air, preconditioned oxygen or nitrogen defined temperature, pressure, humidity and composition applied and rinsed continuously in the preferred case. Under these conditions, there should be no material flow across the membrane 14 that is, the kinetic current is zero. To measure the short-circuit current is at the fuel cell stack 10 a low voltage of, for example, 0.1 volts per single cell via the power supply 40 created and the current I _measured and the voltages of the diagnostic units U _i detected. Due to the selected conditions, the current flowing during this measurement corresponds to the short-circuit current I _meas = I _{short, i} . Equation (2) can now be used to calculate the electrical resistance of the membrane R _{short, i} . The knowledge of these values makes it possible to correct the later measurements together with the then measured time curves U _i (t) at any time by the then flowing short-circuit currents I _{short, i} (t).

For this purpose, the specific electrical resistances R _{short, i of} the individual diagnostic units or of the entire stack 10 saved.

2. Measurement of the diffusion- and / or permeation-driven material flow of H ₂ through the membrane (I _{H2, i} )

Although the membrane 14 The operating gases should be separated materially, molecular hydrogen passes through the membrane in the other electrode space. In the case of different H ₂ partial pressures (p * _H2 ) in the electrode spaces 12 . 13 this is diffusion-driven in the direction of the lower H ₂ partial pressure. At different absolute pressures in the electrode spaces 12 . 13 There is a permeation-driven flow through the membrane on that side of the electrode with the lower absolute pressure. The mass flow of molecular hydrogen through the membrane is detected in the form of an electrical pumping current, which is required to counteract the diffusion and / or permeation driven material flow. For this purpose, the first electrode space 12 with hydrogen H ₂ and the second electrode space 13 with an inert gas, here nitrogen N ₂ , charged and continuously purged, the gases in terms Temperature, pressure and humidity are preconditioned. The conditions are kept constant. Due to the higher H ₂ partial pressure in the first electrode space 12 a diffusion-driven substance transport takes place from the first into the second electrode space 13 , If in addition the absolute pressures in the electrode spaces 12 . 13 differ, it comes (in the case of a defective membrane) in addition to a permeation in the direction of the lower absolute pressure. First, here is a matching absolute pressure in both electrode spaces 12 . 13 be set.

Under the conditions mentioned is the fuel cell stack 10 over the power supply 40 imprinted a current, such that in the second electrode space 13 arranged catalytic electrode (working electrode) with respect to the first electrode space 12 arranged and acting as a hydrogen reference electrode acting electrode is connected to the anode potential. In this way, hydrogen, which is located in the second electrode space 13 is located at the second catalytic electrode to protons H ⁺ oxidized, which in turn into the first electrode space 12 migrate back and reduced there to H ₂ at the first electrode. The measured pumping current I _H2 attributable to the H ₂ substance flow is composed, according to Equation 3, on the one hand of a diffusion component D _H2 and a permeation component P _H2 . Here, Δp * means the H ₂ partial pressure difference between the first and second electrode spaces 12 . 13 Δp is the absolute pressure difference between the first and second electrode spaces 12 . 13 and d _mem the thickness of the membrane 14 , If, as in the present measurement, the absolute pressure in the first and second electrode space 12 . 13 are the same, the permeation is equal to zero.

However, the measured current contains not only components which are due to the pumping current I _H2 , but also potential components of the short-circuit current I _short , the capacitive current I _cdl , which is necessary for charging the double-layer capacitance at the electrodes, and an oxidation current I _Ad , which is used for the oxidation of hydrogen adsorbed on the electrodes (see equation 1). In order to exclude the latter two variables, the current is preferably impressed voltage, wherein a predetermined time waveform U _soll in the voltage range of 0.4 to 0.6 volts per cell passes through a voltage maximum. 5 exemplarily shows such a curve of the target voltage V _set as a function of time. The nominal voltage curve U is _intended by the diagnostic device 44 to the power supply 40 , which acts as an actuator, passed. Controlled variable is the average cell voltage U. In order to measure the H ₂ material flow as accurately as possible, the voltage is applied to the fuel cell stack in such a way that the voltage peak of the individual diagnostic units that is as clear as possible and achievable as quickly as possible is formed. It sets a measuring current I _measurement , whose course in 5 is also shown. In the context of the invention, the measuring current I _measurement is preferably determined for each diagnostic unit at the time at which its voltage curve U _{i has reached} its maximum (in this case approximately between 4 and 7 seconds). _Namely, according to Equation 4, in which C _i denotes the double-layer capacitance at the second catalytic electrode, the capacitive current I _{cdl, i} equals zero when the temporal voltage change is zero, that is, at the voltage _maximum .

Further, since no H-adsorbate is present at the second catalytic electrode above a half cell voltage of about 0.4 volts, the oxidation current I _Ad in the selected measurement range is also zero. Thus, by detecting the measurement current at a time when the voltage change is zero and the voltage is above 0.4 volts, the capacitive current I _cdl and the oxidative current I _{Ad become} zero, so that the _measurement current I _Meas Equation 1 is composed only of the short-circuit current I _short and the pump current I _H2 . Thus, the measurement current only has to be corrected by the short-circuit current I _{short, i in} order to obtain the pump current I _{H2, i} . This short-circuit current is determined according to equation (2) from the stored values R _{short, i} and the voltage measured voltage U _i .

In 5 In addition to the desired current profile U _soll , the voltages U _{i of} the individual diagnostic units are also shown. It can be seen that their courses are sometimes significantly different both from each other and from the mean U _soll . The measured current density I _measurement decreases monotonically in the time ranges of the voltage maxima, so that there are appreciable differences in the current density I _Mess and thus in the pump current I _H2 at the voltage maxima present in each case.

Since the above-described measurement of the pumping current I _H2 at the same absolute pressures in the two electrode spaces 12 . 13 was carried out, the detected pumping current corresponds exclusively to the diffusion-driven H ₂ -stoffstrom. In order to determine also the permeation rate, the described measurement can be repeated under conditions in which the absolute pressure on the side of the H ₂ reference electrode in the first electrode space 12 is greater than the absolute pressure in the second electrode space 13 , The pumping current detected in this way thus contains portions of the diffusion flow and portions of the permeation flow. By deducting the previously determined diffusion fraction, the permeation component can thus be determined. If this is not equal to zero, a perforation (pitting) of the membrane can be concluded.

3. Measurement of the double-layer capacitance (C _i )

The bilayer capacitance C _i is a measure of the total free surface area of the catalytic electrodes comprising the conductive support material as well as the particulate catalytic material (typically platinum) present thereon.

The measurement takes place under the same measuring conditions on the fuel cell stack 10 as described above under 2., that is, under continuous loading of the first electrode space with hydrogen and the second electrode space 13 with nitrogen and at constant temperature, humidity and pressure of the operating gases. For the determination of the double-layer capacity of the fuel cell stack 10 with a constant, low current density, for example of the order of 0 to 30 mA / cm ² cell membrane surface, applied. The corresponding current nominal course I _soll is in 6 shown. The illustrated voltage profiles U _{Mess, i of} the diagnostic units or their mean value U _{Mess appear} . Up to a range of about 0.3 to 0.4 volts per cell, the various voltages increase almost linearly. Beyond this range, the stresses also increase almost linearly, but with a much greater slope. In the entire measuring range, an electrical charge of the catalytic electrodes takes place, that is, it flows capacitive current I _cdl . In the voltage range up to approx. In addition, oxidation of the hydrogen previously adsorbed on the catalyst noble metal of the catalytic electrode is effected at 0.4 volt per cell. Due to the additional electrical current required for the oxidation, the voltage initially increases with the lower slope. Beyond 0.3 to 0.4 volts per cell, the adsorbed hydrogen is completely oxidized, resulting in the larger slope. Beyond 0.6 volts per cell, the formation of oxides of the catalyst material gradually begins, so that the measurement is stopped at this position to protect the cells. In the range of 0.4 to 0.6 volts per cell thus the oxidative current I _{ad, i is} equal to zero. In this range, the voltage change, that is, the maximum temporal voltage gradient (dU / dt) _{max is} measured. The constant impressed current I _soll (= I _measurement ) is now individually corrected for each diagnostic unit by the previously determined pumping current I _{H2, i} and the short-circuit current I _{short, i} and divided by the maximum voltage gradient (dU / dt) _max , according to equation 5 to obtain the double-layer capacitance C _i .

4. Measurement of active catalyst surface area (ECSA)

The knowledge of the ECSA gives immediate information about the active surface of the catalyst material (ECSA) available for the electrochemical processes in the fuel cell. The ECSA is reduced on the one hand by loss / migration of the catalytic material and on the other hand by agglomeration of the catalyst particles with increasing fuel cell life.

The ECSA can be determined by recording the amount of hydrogen adsorbed on the noble metal catalysts typical for fuel cells, which in turn is determined by the amount of charge required for their oxidation, ie the integral of the oxidation current I _ad . Namely, in a certain half-cell voltage range (0 to 0.4 volts per cell) hydrogen adsorbed on the noble metal catalysts is present, the amount of adsorbate decreasing with increasing half-cell voltage. By applying an anodic current to the working electrode (second electrode in the second electrode space 13 ) the adsorbed hydrogen is oxidized. By integrating the current that has flowed in the relevant potential range, the flow that has flowed can be calculated and the surface area-specific charge constant in the amount of 210 μC / cm ² platinum on the active surface. Thus, the measurement described for determining the double-layer capacitance can be used. In particular, starting from a stationary state in which a complete catalyst coverage with H ₂ adsorbate is present, a constant current corresponding to a current density of 0 to 30 mA / cm ² membrane area is impressed (see 6 ). In a predetermined Halbzellspannungsbereich in which the oxidation of adsorbed hydrogen takes place, in particular from 0 to 0.4 volts per cell, the total charge flowed in this voltage range during the measurement is corrected - corrected by the previously determined capacitive current I _{cdl, i} , the pump current I _{H2, i} and the short-circuit current I _{short, i} - integrated. According to equation 6 below, this integral is divided by the hydrogen-specific charge constant of 210 μC / cm ^{2 in} order to determine the active catalyst surface per geometric surface area (ECSA, also known as the roughness factor).

5. Determination of proton conductivity of the ionomer of the polymer electrolyte membrane and the catalytic electrodes

For this measurement, in turn, a structure according to one of 2 to 4 used, with the power supply 40 through a load 45 is replaced or has an additional load function. The diagnostic units to be examined continue to be continuously purged with preconditioned gases, in particular H ₂ and N ₂ . This is the fuel cell stack 10 imprinted a current having an alternating current component with varying frequency. The voltage response U _{i of} the diagnostic units to this current excitation is measured in terms of their amplitude and phase.

The proton conductivity of the membrane can be read directly in the high-frequency part of the impedance response of the individual diagnostic units, namely where the imaginary part of the response, that is to say the phase shift thereof, becomes zero.

The conductivity of the electrode ionomers is usually determined by a model-based evaluation, for example an equivalent circuit diagram. This usually includes at least the electrical short-circuit resistance R _{short, i} and the double-layer capacitance C _i . In conventional methods, these two variables must be modeled or fit. Due to the fact that both said quantities have already been determined in the context of the diagnostic method according to the invention, these can be specified in the model for determining the conductivity of the electrodeionomers, so that their modeling can be omitted and the fit quality of the remaining free parameters (essentially this the sought electrode conductivity) can be improved.

The procedure described above thus makes it possible, in a single measuring arrangement, to measure the electric short-circuit current, to measure the hydrogen mass flow by diffusion with or without permeation, to determine the double-layer capacitance and the ECSA and to proton conductivity of the membrane and electrode ionomers. The measurements are done in situ, ie on the complete fuel cell stack 10 However, by way of an off-board diagnosis, that is, using a diagnostic device, as for example in the 2 to 4 is shown.

In principle, however, there is also the advantageous option of carrying out the diagnostic method in particular with all of the individual measurements described in the context of an on-board diagnosis, that is to say in the normal environment of the fuel cell, in particular in a motor vehicle. Since the measurements described the admission of the fuel cell stack 10 through an external power source, this may be in place of the power supply 40 / Load part 45 of the 2 to 4 by an electrical energy storage, in particular a high-voltage battery or a capacitor, as well as an intermediate DC / DC converter. Furthermore, the majority of the measurements requires a reference electrode supplied with H ₂ and a working electrode acted upon by an inert gas (for example N ₂ atmosphere). Under these conditions, the fuel cell stack can 10 provide no power, so the measurements are performed only in suitable operating modes in which there is no power requirement to the fuel cell stack, such as after discharging the fuel cell stack in standby mode of start / stop functionality or after switching off the fuel cell system 100 , In both cases, there is an interruption of the air supply via the cathode air supply 30 (please refer 1 ), so that in the cathode compartments 13 present atmospheric oxygen is consumed by the fuel cell reaction and finally the cathode compartments 13 are substantially filled with nitrogen. The diagnosis can be made on the entire stack to obtain averaged single cell values or, if the fuel cell stack 10 has a corresponding single cell detection, receiving data on the individual diagnostic subunits, the one or more individual cells 11 as cell packets.

Thus, the first catalytic electrode becomes 12 , which in normal operation of the fuel cell stack 10 operates as an anode, connected as a hydrogen reference electrode and the second catalytic electrode of the cathode compartment 13 operated as a partially anodically connected working electrode.

• • Messung parasitärer Ströme I_para über die Membran, welche sich aus dem Wasserstoff-Stoffstrom über die Membran (Diffusion und gegebenenfalls Permeation) I_H2 sowie den elektrischen Kurzschlussstrom I_short zusammensetzt (I_para = I_short + I_H2)
• • Messung der Kapazität der Doppelschichten in den Elektroden C_i
• • Messung der aktiven Katalysatoroberfläche ECSA.

Similar to the offboard diagnostics described above, the onboard diagnostics described here are aimed at detecting the following parameters:

• Measurement of parasitic currents I _para across the membrane, which is composed of the hydrogen mass flow via the membrane (diffusion and optionally permeation) I _H2 and the electrical short-circuit current I _short (I _para = I _short + I _H2 )
• Measurement of the capacitance of the bilayers in the electrodes C _i
• • Measurement of the active catalyst surface ECSA.

An exemplary coordination algorithm for determining these values is in 7 shown.

Here is block 310 the normal operation of the fuel cell system in which the fuel cell stack 10 via the anode and cathode gas supply 20 . 30 is supplied with hydrogen or air and generates an electric power.

block 320 denotes the diagnostic method for determining the state of the fuel cell stack outside normal operation 310 ,

In the coordination block 321 the determination and coordination of necessary measurements takes place. In particular, contains block 321 the logic needed to determine which parameter most needs to be determined. The block 321 also determines how these parameters can best be determined. This applies in particular to the breakdown of the parasitic currents of the pumping current and the short-circuit current. Furthermore, the coordination block contains 321 a logic to quickly return to normal operation at power requirement of the vehicle 310 to return.

The block 322 serves to establish the measuring conditions. In order to carry out the individual measurements, on the one hand, the fuel cell stack 10 be discharged, that is, which are degraded in normal operation in the individual cells present electrochemical potentials. Furthermore, as defined operating or measuring conditions must be set. In particular, the first catalytic electrode (the anode in the anode space 12 ) are supplied with hydrogen to serve as a reference electrode. This is about the usual anode gas supply 20 represented. Furthermore, the second catalytic electrode (the cathode) must be acted upon as an anodically switched working electrode in particular with an inert gas atmosphere. This is after switching off the air supply via the cathode gas supply 30 possible, because then in the cathode rooms 13 existing residual oxygen is consumed by means of the fuel cell reaction. Thus, an essentially nitrogen atmosphere can be found in the cathode spaces 13 to be obtained. Furthermore, the block 322 the setting of predetermined temperatures, humidities, gas mass flows and absolute and partial pressures in the electrode spaces 12 . 13 to adjust.

The block 323 is used to measure the parasitic current I _para , which is composed according to equation 7 from the hydrogen _pump current I _H2 and the short-circuit current I _short . The present onboard diagnosis differs from offboard diagnostics in that the short circuit current in onboard mode can not or can not always be determined and therefore the measurements can not be corrected directly by the electrical short circuit current. For this reason, initially only the parasitic currents are measured together. For this purpose, as described above under point 2 and based on 5 shown, the second catalytic electrode (cathode in normal operation) compared to the reference electrode connected to anode potential, wherein galvanostatic or potentiostatic a voltage curve U _{soll is applied} with a fast and defined maximum in the range of 0.4 to 0.6 volts per individual cell and the current is measured at the time of the voltage maximum. The measured value I _para recorded here is buffered. I _para = I _short + I _H2 (7)

In the block 324 the measurement of the double-layer capacitance C (in 7 abbreviated to CDL) and the active catalyst surface ECSA. This again takes place as described under points 3 and 4 by subjecting the working electrode to a predetermined low nominal current density I _soll and detecting the maximum voltage gradient (dU / dt) _max or by integrating the current density in the region from 0 to 0.4 volts per cell. The corresponding values are calculated according to the following equations 8 and 9 with correction of the parasitic current and buffered.

A reliable value for the short-circuit current I _short can come from different sources. For example, it can be determined as part of an offboard workshop diagnosis as described under point 1. However, it is also conceivable to measure the short-circuit current in a non-operating state of the fuel cell stack, in which both electrode spaces are filled with the same operating gases, for example before a so-called air-air start after a longer shutdown of the stack. It is also possible to carry out and combine several measurements of the parasitic current under different operating conditions. If the conditions are deliberately varied, it is possible to _deduce the short-circuit current I _short via the variation of the measured values for the parasitic current I _para , since it is known from theoretical considerations how the hydrogen stream reacts to changes.

As soon as a reliable value for the short-circuit current is present, the desired quantities can be displayed in the block 325 finally be calculated. For this, those in the blocks 323 and 324 cached measured values via the coordination block 321 to the block 325 which performs the final calculation and storage.

The method described above is characterized in that all measurements can be carried out independently of each other, although the calculation of the final values builds on each other. This allows an intelligent strategy to perform the measurements of individual quantities as needed or possible, even though measurements of other sizes are not yet possible. Thus, a fuel cell stack can also be diagnosed outside a workshop stay comprehensively and with a hitherto impossible accuracy.

LIST OF REFERENCE NUMBERS

100

 The fuel cell system

10

 fuel cell stack

11

 single cell

12

 first electrode space / anode space

13

 Second electrode space / cathode space

14

 Polymer electrolyte membrane

15

 bipolar

20

 anode supply

21

 Anode supply path

22

 Anode exhaust gas path

23

 fuel tank

24

 actuating means

25

 Brennstoffrezirkulationsleitung

26

 actuating means

30

 cathode supply

31

 Cathode supply path

32

 Cathode exhaust path

33

 compressor

34

 electric motor

35

 power electronics

36

 turbine

37

 Waste gate line

38

 actuating means

39

 humidifier

200

 diagnostic system

40

 power adapter

41

 Lastkabel

42

 current sensor

43

 voltage sensor

44

 diagnostic device

45

 load

46

 Data acquisition device

47

 control device

48

 relay

49

 Setpoint generator

300

 diagnostic algorithm

310

 Normal operating mode

320

 diagnostic mode

321

 coordination block

322

 Block for the production of measuring conditions

323

 Block for measuring the parasitic currents

324

 Block for measuring the double-layer capacity and active catalyst area

325

 Block to calculate the final parameters

I _{mess, i}

 Measuring current of the i-th diagnostic unit

I _{short, i}

 Short-circuit current of the i-th diagnostic unit

I _{H2, i}

 Pumping current of the i-th diagnostic unit

I _{cdl, i}

 Capacitive current of the i-th diagnostic unit

I _{Ad, i}

 Adsorption current of the i-th diagnostic unit

I _para

 parasitic current

U _shall

 Target voltage curve

U _Mess

 measuring voltage

U _i

 measured voltage of the i-th diagnostic unit

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited non-patent literature

• H. Imanashi, K. Manabe, T. Ogawa, & Y. Nonobe: Developement of Electric Power Contraol and the Capacitance Characteristics often he Fuel Cell, SAE International Journal of Engines 4 (1), 2011, 1879-1887. [0005]
• E. Brightman, G. Hinds & R. O'Malley: In Situ Measurements of Active Catalyst Surface Area in Fuel Cell Stacks, Journal of Power Sources 242, 2013, 244-254 [0006]

Claims (12)

Diagnostic method for determining a state of a fuel cell stack ( 10 ) containing a plurality of single cells ( 11 ), each comprising one in a first electrode space ( 12 ) and a first electrode in a second electrode space ( 13 ) arranged second catalytic electrode through an ion-conductive membrane ( 14 ) are separated from each other, characterized in that the state determination is a determination of a diffusion and / or permeation-driven stream of molecular hydrogen through the membrane ( 14 ) or a size equivalent thereto. A diagnostic method according to claim 1, characterized in that the determination of the molecular stream of molecular hydrogen comprises the detection of an electric pumping current (I _H2 ), which is required to the diffusion and / or permeation-driven flow of molecular hydrogen through the membrane ( 14 ) counteract. Diagnostic method according to one of the preceding claims, characterized in that for determining the material flow of the first electrode space ( 12 ) with hydrogen and the second electrode space ( 13 ) is or is subjected to an inert gas and the fuel cell stack ( 10 ) is impressed such that the second catalytic electrode is connected to anode potential, so that in the second electrode space ( 13 ) is oxidized and into the first electrode space ( 12 ), and the required electrical pumping current (I _H2 ) is measured. Diagnostic method according to claim 3, characterized in that the current is impressed such that a predetermined temporal voltage curve (U _setpoint ) for the stack voltage passes through a voltage maximum and the current is measured at the time of the voltage maximum. Diagnostic method according to claim 4, characterized in that in each case the current is detected when individual cell voltages (U _i ) of individual, one or more individual cells of the fuel cell stack ( 10 ) pass through a voltage maximum across diagnostic units. Passes through at least Diagnostic method according to one of claims 3, 4 or 5, characterized in that the current is impressed in such a way that a predetermined temporal voltage curve (U _soll) second, a voltage in the range of 0.4 to 0.8 V per cell, and the Electricity in this area is measured. Diagnostic method according to one of claims 2 to 6, characterized in that the method is carried out as an on-board method and the pumping current (I _H2 ) during a standby mode of the fuel cell stack ( 10 ) is detected. Diagnostic method according to one of the preceding claims, characterized in that the determination of the diffusion and / or permeation-driven mass transport of molecular hydrogen through the membrane ( 14 ) for the entire fuel cell stack ( 10 ) or for individual diagnostic units, comprising one or more individual cells ( 11 ), is carried out. Diagnostic method according to one of claims 2 to 8, characterized in that the state determination further comprises a determination of an electrical short-circuit current (I _short ) through the membrane ( 14 ) and to obtain the pump current (I _H2 ), the measured current (I _mess ) is corrected by the short-circuit current (I _short ). Diagnostic method according to one of the preceding claims, characterized in that the state determination further comprises a determination of a double-layer capacitance (C _i ) of at least one of the catalytic electrodes, which is determined depending on the material flow or the determined electric pump current (I _H2 ). Diagnostic method according to claim 10, characterized in that the state determination further comprises a determination of an active catalyst surface (ECSA) of at least one of the catalytic electrodes, which is determined in dependence on the determined electric pumping current (I _H2 ) and the determined double-layer capacitance (C _i ). Diagnostic method according to one of claims 9 to 11, characterized in that the determinations of the pumping current (I _H2 ), the electrical short-circuit current (I _short ), the double-layer capacitance (C _i ) and / or the active catalyst surface (ECSA) or for these sizes required partial measurements independent of time and in any order depending on an operating point or state of the fuel cell stack ( 10 ) be performed.

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