DE102023107057A1 - POLYMER ELECTROLYTE FUEL CELL POLARIZATION CURVE - Google Patents

Abstract

The invention relates to a method, comprising: determining first physical parameters (500, 502, 504, 506) of at least one polymer electrolyte fuel cell (10) at a specific point in time on the basis of electrical and thermodynamic conditions to which the at least one polymer electrolyte fuel cell (10) is exposed during operation subject to the at least one polymer electrolyte fuel cell (10) up to the specified point in time; anddetermining first data representing at least a portion of a polarization curve (28) of the at least one polymer electrolyte fuel cell (10) at the particular point in time based on the first physical parameters (500, 502, 504, 506).

Description

The present invention relates to a method for determining data representing at least a portion of a polarization curve of a polymer electrolyte fuel cell. In particular, the present invention relates to a controller for controlling electrical and thermodynamic conditions to which a polymer electrolyte fuel cell is subject during operation of the polymer electrolyte fuel cell, the controller being set up to carry out the method.

Polymer electrolyte fuel cells are subject to an aging process, which leads to a change in the polarization curve of the polymer electrolyte fuel cell during the operation of a polymer electrolyte fuel cell.

A method according to the invention comprises determining first physical parameters of at least one polymer electrolyte fuel cell at a specific point in time on the basis of electrical and thermodynamic conditions to which the at least one polymer electrolyte fuel cell is subject during operation of the at least one polymer electrolyte fuel cell up to the specific point in time and determining first data which represent at least a portion of a polarization curve of the at least one polymer electrolyte fuel cell at the particular point in time based on the first physical parameters.

In this context, the phrase “at least one polymer electrolyte fuel cell” as used in the context of the present description and the claims is to be understood in particular as a stack of polymer electrolyte fuel cells connected in series. Furthermore, the wording “electrical and thermodynamic conditions” as used in the context of the present description and the claims is to be understood in particular as operating parameters. For example, the thermodynamic conditions can be an operating temperature, an operating temperature range, an operating pressure, an operating pressure range, a mass flow and/or a mass flow range of an air supply, a hydrogen supply and/or a coolant supply of the at least one polymer electrolyte fuel cell and/or or a relative humidity or a relative humidity range of the air supply and/or the hydrogen supply of the at least one polymer electrolyte fuel cell. Furthermore, the electrical conditions can include an operating voltage, an operating voltage range, an operating current intensity, or an operating current intensity range of the at least one polymer electrolyte fuel cell.

Furthermore, the term "physical parameters" as used in the context of the present description and the claims, in particular the layer thicknesses of the membrane-electrode assembly, such as the thicknesses of the catalyst layers, the thicknesses of the gas diffusion layers, the thicknesses of the microporous layers and the thicknesses of the membranes, the rupture and "pinhole" probability distribution of the membranes, the size distribution of the catalyst particles, the hydrophobicity/hydrophilicity of the catalyst layers, gas diffusion layers and microporous layers, the contact resistances of the bipolar plates and the electrical and protonic resistances. Furthermore, the term “polarization curve” as used in the context of the present description and the claims is to be understood in particular as a curve describing the dependency of the electrical voltage generated by the at least one polymer electrolyte fuel cell between anode and cathode on the current density.

When determining the first data, which represents at least a section of the polarization curve of the at least one polymer electrolyte fuel cell, it can be taken into account that an influence of a change in a first of the first physical parameters on a course of the polarization curve in the section of a change in a second of the first physical parameters depends.

The method may further include changing at least one first electrical or thermodynamic condition to which the at least one polymer electrolyte fuel cell is subject during operation of the at least one polymer electrolyte fuel cell from the specific point in time, based on the first physical parameters and/or the first data.

For example, the first physical parameters and/or the first data can be used to determine a degradation state of the at least one polymer electrolyte fuel cell and (taking into account the current degradation state) to take measures with the aim of slowing down further degradation. Furthermore, the degradation status can also be used to identify errors or causes of errors.

The method can also quantify, based on the first physical parameters and/or the first data, a first effect of changing the at least one first elec cal or thermodynamic condition for aging-related changes in the polarization curve from the specific point in time, a quantification, based on the physical parameters and/or the data, of a second effect of changing at least one second electrical or thermodynamic condition on aging-related changes in the polarization curve from the specific point in time, and determining, using an evaluation metric, that the first impact is preferable to the second impact.

For example, the effect of different operating strategy changes on the degradation can be simulated and an operating strategy change can be selected that proves to be advantageous with regard to future degradation.

Alternatively, various operating strategies can be simulated with regard to the associated degradation when the at least one polymer electrolyte fuel cell is designed and both the design of the at least one polymer electrolyte fuel cell and the operating strategy used can be optimized.

For example, the method can also determine second physical parameters of the at least one polymer electrolyte fuel cell at the specific point in time on the basis of the electrical and thermodynamic conditions that differ from the electrical and thermodynamic conditions to which the at least one polymer electrolyte fuel cell is subject during operation of the at least one polymer electrolyte fuel cell up to the subject to a specific point in time, determining second data representing at least the portion of the polarization curve of the at least one polymer electrolyte fuel cell at the specific point in time based on the second physical parameters and comparing the first data and the second data.

The electrical and thermodynamic conditions can then be adjusted taking into account a result of the comparison. By adapting the electrical and thermodynamic conditions, an improved operating strategy can be achieved with regard to the degradation to be expected during operation.

A control device for controlling electrical and thermodynamic conditions to which at least one polymer electrolyte fuel cell is subject during operation of the at least one polymer electrolyte fuel cell can be set up to carry out the method.

Furthermore, a computer program can include instructions which, when the program is executed by a computer, cause the computer to carry out the method.

The method can be based on a semi-empirical description of the degradation mechanisms to which the at least one polymer electrolyte fuel cell is exposed (in particular during operation). Depending on the value of the input variables, different degradation mechanisms (of varying degrees) can be activated. The degradation mechanisms can be represented by empirical equations, the form of which corresponds to the underlying physical causal relationships. Output variables of these empirical equations can be the physical parameters of the at least one polymer electrolyte fuel cell, for example catalyst particle size distributions, diffusion coefficients or layer thicknesses.

The input variables thus control the modeling of the aging process of the polymer electrolyte fuel cell based on the implemented degradation mechanisms, which is reflected in a change in the physical parameters. Because the input variables are mapped to physical parameters, the (complex) interactions of the various degradation mechanisms can be taken into account (in a relatively simple way). The polarization curve can then be determined on the basis of the physical parameters. For example, the physical parameters can be converted into the calibration parameters of the polarization curve by suitable correlations. For this purpose, a parametric description of the polarization curve, which represents the polymer electrolyte fuel cell that has not yet aged, can be adjusted to the initial state using a calibration based on the physical parameters. The calibration can also be determined using "machine learning" algorithms.

• 1 eine schematische Darstellung einer Polymerelektrolytbrennstoffzelle;
• 2 eine schematische Darstellung eines Polymerelektrolytbrennstoffzellenstapels;
• 3 eine schematische Darstellung des Ablaufs eines computerimplementierten Verfahrens zur Bestimmung der Polarisationskurve der Polymerelektrolytbrennstoffzelle;
• 4 eine schematische Darstellung des Einflusses einer Degradation der Polymerelektrolytbrennstoffzelle auf die durch das Verfahren bestimmte Polarisationskurve; und
• 5 ein Steuergerät zur Steuerung elektrischer und thermodynamischer Gegebenheiten, denen die Polymerelektrolytbrennstoffzelle während des Betriebs unterliegt, zeigt.

The invention is explained below in the detailed description using exemplary embodiments, reference being made to drawings in which:

• 1 a schematic representation of a polymer electrolyte fuel cell;
• 2 a schematic representation of a polymer electrolyte fuel cell stack;
• 3 a schematic representation of the sequence of a computer-implemented method for determining the polarization curve of the polymer electrolyte fuel cell;
• 4 a schematic representation of the influence of degradation of the polymer electrolyte fuel cell on the polarization curve determined by the method; and
• 5 shows a controller for controlling electrical and thermodynamic conditions encountered by the polymer electrolyte fuel cell during operation.

The same or functionally similar elements are identified by the same reference symbols in the drawings.

1 12 shows a schematic representation of a polymer electrolyte fuel cell 10. The polymer electrolyte fuel cell 10 comprises a cathode 12, a cathode-side catalyst layer 14, a polymer membrane 16, an anode-side catalyst layer 18 and an anode 20. As in FIG 2 As shown, a plurality of polymer electrolyte fuel cells 10 can be arranged in a stack, with a bipolar plate 24 being arranged between two polymer electrolyte fuel cells 10 arranged next to one another.

3 FIG. 12 shows a schematic representation of the course of a computer-implemented method for determining the polarization curve of the polymer electrolyte fuel cell 10. As indicated by dashed lines, the method is divided into three stages. In the first stage, the electrical and thermodynamic conditions to which the polymer electrolyte fuel cell 10 is subject from a point in time t0 to a point in time t1 are entered and evaluated. The electrical conditions may include the polymer electrolyte fuel cell voltage 98, for example. The thermodynamic conditions can include, for example, the temperature 90, the pressure 92 and the mass flow 94 of the air, hydrogen and coolant path. The thermodynamic conditions can also include the relative humidity 96 of the air and hydrogen path. Furthermore, the occurrence or the frequency of certain events can be taken into account, e.g ) and event-based state changes (start-stop cycles, air-air starts, stops, etc.).

The operating mode in which the polymer electrolyte fuel cell 10 is located at a specific point in time can be derived from the electrical and thermodynamic conditions and the event-based state changes. For example, it can be derived from the electrical and thermodynamic conditions and the event-based state changes that the polymer electrolyte fuel cell 10 is in normal operation 100 at a specific point in time, that relative humidity is low 102, that temperature is high 104, that open-circuit voltage 106 there is a high voltage 108, there is a potential change 110, the relative humidity is high 112, there is an air-to-air start or stop 114, the stoichiometry is low 116, or there is flooding 118.

• • die Schichtdicken 500 der Membran-Elektroden-Einheit der Polymerelektrolytbrennstoffzelle 10 (jeweils für die Anode 20 und die Kathode 12, bspw. die Katalysatorschichtdicke, die Gasdiffusionsschichtdicke, die Dicke der mikroporösen Schicht; die Membrandicke, etc.);
• • die Riß- und „Pinhole“-Wahrscheinlichkeitsverteilung 502 der Membran 16;
• • die Katalysatorpartikelgrößenverteilung 504;
• • die Hydrophobizität / Hydrophilität der Katalysatorschichten 14 und 18;
• • die Kontaktwiderstände der Bipolarplatte 24 (jeweils für die Anode 20 und die Kathode 12); und
• • die elektrischen und protonischen Widerstände.

In the second stage, the degradation mechanisms are modeled. For example, semi-empirical equations can be used to derive a change in the physical parameters of the polymer electrolyte fuel cell 10 from the sequence of operating modes. The following physical parameters can be considered, for example:

• • the layer thicknesses 500 of the membrane-electrode assembly of the polymer electrolyte fuel cell 10 (each for the anode 20 and the cathode 12, for example the catalyst layer thickness, the gas diffusion layer thickness, the thickness of the microporous layer; the membrane thickness, etc.);
• • the rupture and "pinhole" probability distribution 502 of the membrane 16;
• • the catalyst particle size distribution 504;
• • the hydrophobicity/hydrophilicity of the catalyst layers 14 and 18;
• • the contact resistances of the bipolar plate 24 (respectively for the anode 20 and the cathode 12); and
• • the electrical and protonic resistances.

In order to determine the values of the physical parameters changing as a result of the degradation, the following degradation mechanisms or combinations of degradation mechanisms are activated in the degradation model representing the second stage, depending on the operating state. The interdependence of the individual mechanisms is particularly evident in the air-air start and stop, since correlations such as the speed of the H ₂ /air front can be significant there.

When relative humidity is low 102 or temperature is high 104, oxygen 200 permeates membrane 16, activating a degradation mechanism 300 that results in a decrease in membrane thickness and membrane 16 degradation. This causes an increase in hydrogen and oxygen transport 400 and a reduction in proton conductivity 402.

If there is an open circuit voltage 106 or a high voltage 108, this leads to a change in the oxygen concentration 202 and the potential 204 at the cathode-side catalyst layer 14, whereby both the degradation mechanism 300 and the degradation mechanism 302 ("Ostwald Ripening") are activated, which leads to a dissolution 404 of the catalyst contributes. Degradation mechanism 302 can also be activated by the oxygen concentration 206 or the water content 208 at the cathode-side catalyst layer 14 . The water content 208 on the cathode-side catalyst layer 14 can also activate the degradation mechanism 304 (carbon corrosion), which also contributes to the dissolution 404 of the catalyst.

If there is an air-air start or a stop 114, if the stoichiometry is low 116 or if there is flooding 118, the current 210 is inverted, which activates degradation mechanism 306 (carbon corrosion in the gas diffusion layer) in addition to degradation mechanism 304, thereby activating oxygen diffusivity 406 reduced, affecting the effective diffusion coefficient 506 .

• • Kohlenstoffkorrosion. Bei entsprechenden elektrischen Potentialen reagiert der Kohlenstoff innerhalb der Polymerelektrolytbrennstoffzelle zu CO₂. Dies führt zu einem Abbau der katalytischen Schichten und zu einem Verlust der Katalysatorpartikel. Die Reaktionsgleichungen werden mittels Arrhenius und Bulter-Volmer Gleichungen empirisch berechnet und es wird eine Partikelgrößenverteilung manipuliert, sodass der Verlust an Katalysatorpartikeln modelliert wird. Dieser Mechanismus führt zu einer Reduktion der aktiven katalytischen Fläche und somit zu einem Anstieg der Austauschstromdichte.
• • Partikel-Agglomeration, „Ostwald Ripening“, Katalysatorauflösung. Hier werden ebenfalls Gleichungen ähnlich zur Kohlenstoffkorrosion verwendet und die Partikelgrößenverteilung manipuliert. Die aktive katalytische Fläche wird reduziert und die Austauschstromdichte steigt.
• • Chemische Alterung der Membran 16. Durch Radikalenangriff wird die Membran 16 chemisch abgebaut. Hierzu wird die Radikalenbildung modelliert, um den Abtrag darzustellen. Die Protonenleitfähigkeit steigt durch die dünnere Membran 16, aber auch die H₂ und O₂ Leckage steigt an, was zu einer höheren Leckagestromdichte führt.
• • Mechanische Alterung: Durch Temperatur- und Feuchtezyklen kann sich die Membran 16 ausdehnen oder schrumpfen. Hierdurch entstehen Spannungen in den Katalysatorschichten 14 und 18 und der Membran 16. Diese führen zu Ermüdungserscheinungen, welche z. B. durch „Linear-elastic fracture mechanics“ beschrieben werden können. Hierzu kann z. B. der Paris' Law Ansatz herangezogen werden. Durch die Risse steigt die Leckage von H₂ über die Membran 16 an und die Protonenleitfähigkeit nimmt zu.
• • Korrosion der Bipolarplatte 24. Die Korrosion wird durch die saure Umgebung und das elektrische Potential getrieben und kann im Wesentlichen durch die Fenton-Reaktion beschrieben werden, welche empirisch modelliert wird. Die bei der Fenton-Reaktion entstehenden Metallionen führen zu Korrosion und einem verstärkten chemischen Abbau der Membran 16. Diese Effekte werden modelliert, wobei Korrekturfaktoren bei Anwesenheit von Radical Scavengern angewendet werden können. Die Korrosion führt zu einem erhöhten Kontaktwiderstand.
• • Verlust von Hydrophobizität: Mit der Zeit wird das PTFE aus den beschichteten Gasdiffusionschichten herausgewaschen. Dies führt zu einem verminderten Stofftransport, welche durch eine Diffusionsgleichung beschrieben wird.

When modeling the degradation mechanisms, the physical relationships are retained - ie the form of the equation (Arrhenius equation, diffusion equation, etc.) is retained - the values required for the equations, on the other hand, are derived empirically. In the case of an electrochemical process, for example, equations in the form of the Arrhenius or Butler-Volmer equation are used and the parameters are pre-calibrated according to literature data. In the case of mechanical degradation phenomena, mechanical stresses are calculated and approaches from material fatigue are used. For example, degradation mechanisms in the second stage can be modeled as follows:

• • Carbon corrosion. With appropriate electrical potentials, the carbon within the polymer electrolyte fuel cell reacts to form CO ₂ . This leads to degradation of the catalytic layers and loss of catalyst particles. The reaction equations are calculated empirically using Arrhenius and Butter-Volmer equations and a particle size distribution is manipulated so that the loss of catalyst particles is modeled. This mechanism leads to a reduction in the active catalytic area and thus to an increase in the exchange current density.
• • Particle agglomeration, "Ostwald Ripening", catalyst dissolution. Equations similar to carbon corrosion are also used here and the particle size distribution is manipulated. The active catalytic area is reduced and the exchange current density increases.
• • Chemical aging of the membrane 16. The membrane 16 is chemically degraded by radical attack. For this purpose, the formation of radicals is modeled in order to represent the erosion. The proton conductivity increases due to the thinner membrane 16, but the H ₂ and O ₂ leakage also increases, which leads to a higher leakage current density.
• • Mechanical aging: The membrane 16 can expand or shrink as a result of temperature and humidity cycles. This creates stresses in the catalyst layers 14 and 18 and the membrane 16. This leads to fatigue, which z. B. can be described by "Linear-elastic fracture mechanics". For this purpose z. B. the Paris' Law approach can be used. The leakage of H ₂ across the membrane 16 increases due to the cracks and the proton conductivity increases.
• • Corrosion of the bipolar plate 24. The corrosion is driven by the acidic environment and the electric potential and can essentially be described by the Fenton reaction, which is empirically modeled. The metal ions formed during the Fenton reaction lead to corrosion and increased chemical degradation of the membrane 16. These effects are modeled, correction factors being able to be applied when radical scavengers are present. The corrosion leads to increased contact resistance.
• • Loss of Hydrophobicity: Over time, the PTFE leaches out of the coated gas diffusion layers. This leads to reduced mass transport, which is described by a diffusion equation.

In the third stage, the polarization curve of the polymer electrolyte fuel cell 10 is calculated. To take the degradation into account, the physical parameters 500, 502, 504 and 506 from the degradation model can be converted into calibration parameters (leakage current density 600, ohmic loss 602, loss of active catalytic surface 604 and diffusion losses 606) of the calculation formulas of the polarization curve calculation. Suitable correlations can be calibrated when converting the physical parameters into the calibration parameters. The calibration can also be carried out using "machine learning" algorithms, which are trained, for example, with existing calibrations.

By using empirical equations and doing without complex systems of equations, the computational effort involved in carrying out the method can be reduced. By dividing it into a degradation core model and physical variables 500-506, the core model can be retained regardless of the method used to calculate the polarization curve, and other models of the polarization curve of any complexity can be used. Furthermore, the approach can be applied to stacks, cells or cell segments.

Due to the pre-calibration based on literature data, the model can easily be transferred and applied to other systems using a (relatively) small amount of reference data. This requires no more than two polarization curves; a polarization curve representing the initial state and a polarization curve representing the aged state plus the underlying load spectrum. The model quality can also be improved by using polarization curves lying in between in time. Furthermore, the complex interactions of the degradation mechanisms can be mapped through the description of the physical quantities.

4 shows a schematic representation of the influence of degradation of the polymer electrolyte fuel cell 10 on the polarization curve 28 determined by the method.

5 FIG. 1 shows a controller 30 for controlling electrical and thermodynamic conditions to which the polymer electrolyte fuel cell 10 is subjected during operation. The control unit can be provided with a computer program which includes instructions which, when the program is executed, cause the method to be carried out. In particular, the control unit 30 can be set up to adapt at least a first electrical or thermodynamic condition to which the polymer electrolyte fuel cell 10 is subject during operation from the specific time t ₁ in order to extend the service life of the polymer electrolyte fuel cell 10 .

Reference List

10

polymer electrolyte fuel cell

12

cathode

14

catalyst layer

16

membrane

18

catalyst layer

20

anode

22

Polymer electrolyte fuel cell stack

24

bipolar plate

26

polarization curve (initial)

28

Polarization curve (after aging of the polymer electrolyte fuel cell)

30

control unit

90

temperature

92

Print

94

mass flow

96

Relative humidity

98

Tension

100

normal operation

102

Deviation (low relative humidity)

104

deviation (high temperature)

106

Deviation (open circuit voltage)

108

deviation (high voltage)

110

Deviation (change of potential)

112

Deviation (high relative humidity)

114

Air to air start or stop

116

Deviation (low stoichiometry)

118

flooding

200

oxygen passing through the membrane

202

oxygen concentration

204

potential

206

oxygen concentration

208

water content

210

current (inverted)

300

Decrease in membrane thickness and deterioration of the membrane

302

"Ostwald Ripening"

304

carbon corrosion

306

Carbon corrosion in the gas diffusion layer

400

oxygen transport

402

proton conductivity

404

dissolution (catalyst)

406

oxygen diffusivity

500

layer thicknesses

502

Crack and "pinhole" probability distribution

504

catalyst particle size distribution

506

diffusion coefficient

600

leakage current density

602

ohmic loss

604

Loss of active catalytic area

606

diffusion losses

Claims (10)

Method comprising: Determining first physical parameters (500, 502, 504, 506) of at least one polymer electrolyte fuel cell (10) at a specific point in time on the basis of electrical and thermodynamic conditions to which the at least one polymer electrolyte fuel cell (10) is subjected during operation of the at least one polymer electrolyte fuel cell (10) to subject to at the specific time; and Determining first data representing at least a portion of a polarization curve (28) of the at least one polymer electrolyte fuel cell (10) at the specific point in time based on the first physical parameters (500, 502, 504, 506). procedure after claim 1 , the thermodynamic conditions being an operating temperature (90), an operating temperature range, an operating pressure (92), an operating pressure range, a mass flow (94) and/or a mass flow range of an air supply, a hydrogen supply and/or a Coolant supply of the at least one polymer electrolyte fuel cell (10) and/or a relative humidity (96) or a relative humidity range of the air supply and/or the hydrogen supply of the at least one polymer electrolyte fuel cell (10). procedure after claim 1 or 2 , wherein the electrical conditions include an operating voltage (98), an operating voltage range, an operating current, or an operating current range of the at least one polymer electrolyte fuel cell (10). Procedure according to one of Claims 1 until 3 , wherein when determining the first data, which represents at least a section of the polarization curve (28) of the at least one polymer electrolyte fuel cell (10), it is taken into account that an influence of a change in a first of the first physical parameters (500, 502, 504, 506) on a course of the polarization curve (28) in the section depends on a change in a second of the first physical parameters (500, 502, 504, 506). Procedure according to one of Claims 1 until 4 , further comprising: Changing at least one first electrical or thermodynamic condition to which the at least one polymer electrolyte fuel cell (10) is subject during operation of the at least one polymer electrolyte fuel cell (10) from the specific point in time on the basis of the first physical parameters (500, 502, 504, 506) and/or the first data. procedure after claim 5 , further comprising: quantifying, based on the first physical parameters (500, 502, 504, 506) and/or the first data, a first effect of changing the at least one first electrical or thermodynamic condition on aging-related changes in the polarization curve (28). the specific point in time; quantifying, based on the physical parameters (500, 502, 504, 506) and/or the data, a second effect of a change in at least one second electrical or thermodynamic condition on aging-related changes in the polarization curve (28) from the specific point in time; and determining, using an evaluation metric, that the first impact is preferable to the second impact. Procedure according to one of Claims 1 until 4 , further comprising: determining second physical parameters of the at least one polymer electrolyte fuel cell (10) at the specific point in time on the basis of the electrical and thermodynamic conditions differing from the electrical and thermodynamic conditions to which the at least one polymer electrolyte fuel cell (10) during operation of the at least one polymer electrolyte fuel cell (10) subject to such time; determining second data representing at least the portion of the polarization curve (28) of the at least one polymer electrolyte fuel cell (10) at the determined point in time based on the second physical parameters; and comparing the first data and the second data. procedure after claim 7 , further comprising: adjusting the electrical and thermodynamic conditions taking into account a result of the comparing. Control device (30) for controlling electrical and thermodynamic conditions to which at least one polymer electrolyte fuel cell (10) is subject during operation of the at least one polymer electrolyte fuel cell (10), wherein the control device (30) is set up, a method according to one of the Claims 1 until 6 to perform. A computer program comprising instructions which, when executed by a computer, cause the computer to perform a method according to any one of Claims 1 - 8th to perform.

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