DE102006035741A1 - Method of determining the current density distribution in a stack of fuel cells using a magnetotomography process - Google Patents

Abstract

The method involves using magnetic field sensors (35) which measures values of a magnetic field (30) generated by the current flow (20) in the fuel cell stack (10). A feed line and return line are provided for the cell stack current and these are arranged in parallel to the extent possible. Those sections where it is not possible or sensible to arrange the lines in parallel are taken into account partly or completely in a reconstruction volume for the current density distribution.

Description

The The invention relates to a method for determining the current density distribution in a fuel cell stack of one or more fuel cells, in which magnetic field sensors are used, the values of the Measure current flow in the fuel cell stack generated magnetic field.

Fuel cell stacks, also referred to as fuel cell stacks are used in fuel cell systems used. These fuel cell systems with fuel cell stacks greater power can for the Drive and power supply of motor vehicles and stationary power supplies be used. For The operation of these fuel cell stacks makes sense, the current density distribution to be able to determine in the fuel cell stacks. For this determination are different Known method.

At first were This method used an invasive determination of the current density distribution in single cells and stacks. For example, there are a proposal from Jürgen Stumper et al., "In situ methods for the determination of current destructions in PEM fuel cells, in: Electrochimica Acta, Vol. 43, No. 23 (1998), pages 3773 to 3783.

such invasive method for determining the current density distribution in fuel cell stacks however have disadvantages. It is each an intervention respectively a manipulation in the fuel cell stack required. This can cause repercussions the measurement on the operation and also to falsification of the measurement results through the manipulation. Furthermore As the need for precise resolution increases, so too does the wiring overhead for the individual measurements considerably, so that their scope is limited for economic reasons is. Invasive determination methods have therefore only for research or for the development of fuel cell stacks proved to be suitable, not for a continuous measurement during of the operation or for Service intervals.

R. Satija, DK Jacobson, M. Arif, SA Werner, "In situ neutron imaging techniques for evaluation of water management systems in operating PEM fuel cells", in:
Journal of Power Sources 129 (2004), pages 238 to 245, another proposal is known. They describe a method that visualizes the distribution of water in a fuel cell using neutrons. However, using the neutron source makes this process expensive and unwieldy. In addition, this method does not measure the current density distribution itself, but only the water distribution in a fuel cell. This can then be deduced within certain limits on the current density distribution.

In contrast, have proven to be very practical magnetotomographic methods, in particular from the EP 1 254 376 B1 are known. These magnetotomographic methods allow a noninvasive measurement of the differential current density distribution in a fuel cell stack. Further, on the EP 1 254 376 B1 Karl-Heinz Hauer, Lars Kühn, Roland Potthast, "On uniqueness and non-uniqueness for current reconstruction from magnetic fields"
in: Inverse Problems 21 (2005), pages 955 to 967 as well
Karl-Heinz Hauer, Roland Potthast, Torsten Wuester, Detlef Stolten, "Magnetotomography - A New Method for Analyzing Fuel Cell Performance and Quality",
in: Journal of Power Sources (2005), pages 67-74.

In magnetotomographic methods, such as in EP 1 254 376 B1 For example, magnetic field sensors are used which measure the values of a magnetic field generated by the flow of current in the fuel cell stack. The internal currents in a fuel cell stack create a magnetic field outside of the fuel cell stack. Magnetic field sensors now measure this magnetic field located outside the fuel cell stack. Based on these measurements, the current density distribution within the fuel cell stack is now closed and these values taken. The result is a non-invasive method in which no or at least significantly less measuring wires and the like must be performed in the fuel cell stack.

This Although this proposed method offers excellent basic Possibilities, however, leaves still room for improvement open.

task In contrast, the present invention is a generic method for determining the current density distribution in a fuel cell stack to suggest the still improved provisions of the current density distribution with a magnetotomographic method allows.

This object is achieved in a generic method in that Hinleiter and return conductors for the flow in the fuel cell are stacked that the Hinleiter and return conductors for the current in the fuel cell stack are laid largely parallel, and that those portions of Hinleiter and / or return conductors, where a parallel installation is not useful or possible, wholly or partially with in a reconstruction volume for the current density distribution are included.

As the inventors have realized, that is from the EP 1 254 376 B1 known methods, inter alia, limited by the influence of the feeders on the magnetic field to differential measurements. As a result of the steps according to the invention, in addition to determining the change in the current density distribution (differential measurement), it is now also possible to determine the absolute current density distribution.

With the steps according to the present invention become the values of the magnetic field measured by the magnetic field sensors in a special test arrangement with suitable installation of leaders and return leaders for the Electricity will be absorbed and subsequently taken into account the experimental design and geometry of Zuleiterverlegung in a Current density distribution to be converted and converted Data afterwards in a further step to an absolute current density distribution be modified.

The Hinleiter and return conductor are also referred to as feeders and arresters. It is about each around the main connection cable to the fuel cell stack.

The Modifications allow for An absolute measurement of the current density distribution was considered necessary Scaling and one too for Absolute measurements necessary significant increase in the accuracy of the reconstruction as well as an increase the accuracy in the detection of the magnetic field measurements. Some the modifications are also for the usual today Differential measurements applicable.

All in all Thus, considerable advantages arise, since for the first time a meaningful and reliable Determination of the absolute current density distribution is possible.

The Invention is not limited to a certain number of fuel cells limited in a fuel cell stack. It can be relative many lines or just a few, depending on the purpose. The invention can also be used when the fuel cell stack in extreme cases only consists of a single fuel cell, the Number of single cells is therefore only one.

Around To determine the current density distribution, one speaks of a "reconstruction" of this initially unknown current density distribution.

For the absolute reconstruction the current density distribution is preferably a scaling advantageous introduced. This happens in particular in that first a distortion or Elongation of the determined from the data of the magnetic field sensors current density distribution and this information is subsequently modified the actual reconstruction of the measured values by means of scaling is used.

By some further preferred modifications are much more accurate Measurements possible, in some alternatives also extensions of the measuring possibilities.

The in the conversion of data from the magnetic field sensors in the sought Current density distribution occurring distortions, caused by about the Regularization of the matrix or generally due to the applied Procedures can be through the scaling will be compensated.

To is for the reconstruction area (the fuel cell) has a known (for Example homogeneous) current density distribution assumed. The associated magnetic field is calculated in space and then in the actual algorithm fed to the conversion of magnetic fields into current densities. The resulting Current density distribution shows process-related deviations from the original current density distribution. By comparing original current density distribution and reconstructed current density distribution can different scaling factors are determined.

For example, a location-independent factor c _{α can be determined} from the quotient of the norm of both current density distributions:

Alternatively, for each discrete volume element in the reconstruction area, one factor may be formed from the assumed and reconstructed streams. This results in not only a single factor C _α but a correction matrix Ca from individual correction factors for each volume ment.

A for the Determination of the absolute current density distribution very meaningful and desired possibility to improve the accuracy of the reconstruction may be preferred be achieved in that with the magnetic field sensors magnetic fields known current density distribution can be measured that the measured Values with the theoretically calculated values of the same current density distribution and that from the comparison correction data for measurement errors or measurement misregistrations of the magnetic field sensors are determined.

Thereby arises namely the advantage that the position of the magnetic field sensor relative to the measurement object (So the fuel cell stack with the fuel cells) clearly be specified and further taken into account.

• • Die Messung aller drei Komponenten erfolgt nicht mehr in einem einzigen Punkt
• • Die genaue rechtwinkelige Ausrichtung der Sensoren ist bedingt durch die geometrischen Abmessungen schwierig. Die Sensoren weisen eine Verdrehung bzw. Verkippung gegeneinander und gegen das Messobjekt auf.

Furthermore, it seems advantageous to measure all 3 components of the magnetic field surrounding the fuel cell. Commercially available magnetic field sensors, for example Honeywell HMC1001 or HMC 1002, measure only one or two components of the magnetic field at a time. To measure all three components, several sensors must be combined. This creates the following situation:

• • All three components are no longer measured in a single point
• • The exact right-angled orientation of the sensors is difficult due to the geometric dimensions. The sensors have a rotation or tilting against each other and against the measurement object.

Both Effects have a direct influence on the measurement accuracy with which the magnetic field is detected and thus on the quality of the current density reconstruction.

Of the Influence of these effects is especially important in absolute reconstructions harmful. In differential reconstructions now fall through the difference formation Part of the effects of these effects.

The The invention also relates in particular to the position and Orientation of the magnetic field sensors (of the sensor, if only one) only component of the magnetic field is detected) in the coordinate system to determine. For this purpose, a conductor loop which is precisely aligned with the measurement object is used (For example, made of copper wire or printed on a circuit board for printed Circuits) known geometry (for example, triangle, circle, square) charged with a well-known current. The resulting magnetic field is measured and compared with the theoretically calculated magnetic field. By a fit will be for every sensor is the offset in x, y, z direction and the twist or tilting of the sensor in the coordinate system calculated so that listed below Functional g is minimal. additionally let to the mentioned geometry sizes determine the offset and gain. The information obtained is used to correct the magnetic field measured values used.

In establishing the system of equations for the absolute unknown discrete currents in the reconstruction volume, equations for the divergence freedom div (I) = 0 in each point can be considered in addition to the equations for the magnetic field strength. I = A -1 · H equations for magnetic fields F · I = f equations for freedom from divergence

The Divergence equation div (I) = 0 corresponds to the discrete lattice Node rule, that is the fact that at each node the sum of the flows are the same the sum of the inflowing streams is. The divergence condition can be determined by the equation system F · I = f be taken into account.

In Absolute reconstructions is especially at the node where the power feeder is is positioned, the sum of the currents flowing into the cell is the same the total current of the cell or the stack. The same applies to the node where the current conductor is positioned.

• • Das Erdmagnetfeld
• • Der Einfluss der Zuleiter

When measuring the magnetic fields of the fuel cell, two effects are disturbing.

• • The Earth's magnetic field
• • The influence of the Zuleiter

The Earth's magnetic field can be assumed to be constant (or at Zero current measured) and the actual magnetic field measured values subtracted from.

There are different approaches to taking account of the influence of the feeder. It is usual that only differential reconstructions are carried out. This means that two follow each other de magnetic field measurements at different fuel cell operating parameters are performed. If both measurements are taken at the same total current, the same points are chosen at which the magnetic field is measured and the cables are not moved, the difference of both magnetic field measurements results in the differential magnetic field B _diff . B _diff is caused by the change of the current density distribution in the fuel cell due to the change of the operating parameters.

A reconstruction of the current density distribution on the basis of the differential _{magnetic field} B _diff thus results in the change of the current density distribution due to the change of the operating parameters. However, in this case, no statement can be made about the absolute value of the current density in the fuel cell. B 1 = B earth + B electric wire + B Brennstoffzelle_Messung1 B 2 = B earth + B electric wire + B Brennstoffzelle_Mestung2 B diff = B 1 - B 2 = B1 Brennstoffzelle_Mestung1 - B Brennstoffzelle_Messung2

A Statement about however, the absolute value of the current density becomes possible when the return conductor for the Electricity are provided and laid largely parallel.

there is preferably provided that those sections of Hinleiter and / or return conductors, at where a parallel installation is not meaningful or possible, wholly or partially included in the reconstruction volume become. In particular, you can while return conductor be laid so that only the area between the terminals of the fuel cell stack is not laid parallel to the corresponding opposite pole.

It is then possible, that with largely parallel laying the conductor piece between the two connections of the fuel cell stack by one or more additional Degrees of freedom is included in the equation system.

Especially it is preferred if the return conductor for the current in the fuel cell stack coaxial and thus minimize the resulting magnetic field.

in the Following are some aspects of the basic concept based on the drawing and preferred embodiments shown. Show it:

1 a schematic representation of the streamlines, the magnetic field and the sensor arrangement in a fuel cell stack, wherein various edge effects are neglected;

2 schematically a conductor loop with a fuel cell on a measuring table;

3 schematically a representation of Zuleitern and arresters in an xy plane; and

4 Structure of a fuel cell stack in one embodiment.

In the 1 is a fuel cell stack 10 shown. This has several fuel cells 11 on, which are also referred to as single cells. Through the fuel cells 11 in the fuel cell stack 10 current flows 20 that flows through streamlines inside the fuel cell stack 10 is indicated.

The inside of the fuel cell stack 10 flowing electricity 20 automatically leads to a magnetic field 30 outside the fuel cell stack 10 ,

To determine the current density distribution in the fuel cell stack 10 becomes the external magnetic field 30 of the fuel cell stack to be examined in a plane at the point x = x ₀ in the y and in the z direction measured (B _y and B _z ). Hence, the current density distribution J (x _0, y, z) inside the fuel cell stack 10 be determined.

The basis for this calculation are, as usual, the Maxwell equation and the material equation, the relationships between the magnetic flux density, the magnetic field strength and the current density distribution inside the fuel cell stack 10 result.

In the 2 is schematically a conductor loop with a fuel cell stack 10 with different fuel cells 11 on a measuring table 40 shown. Also indicated is a coordinate system x, y, z and a supply line with two twisted lines 21 . 22 ,

In the 3 is shown schematically as in the reconstruction or determination of current density distributions from the data of magnetic field sensors 35 can be proceeded.

So it is possible the electricity 20 in each branch of the discretized volume, but this is only very simplified. A base vector can be seen, as seen in the direction of the xy plane. The base vector also includes currents flowing into the two top surfaces or end plates of the fuel cell stack 10 flow. This will do that for the bestim However, the system of equations to be solved for the unknown currents is very large.

mit zum Beispiel n = 16However, it is possible to significantly reduce the dimension of the system of equations by defining basic elements. In addition, the base elements may also contain other edge information that may lead to improved reconstruction. The current reconstruction then does not take place by determining the unknown currents in the discretized grid, but by determining the coefficients c _{k of} the basis vectors J _k .

with for example n = 16

The basis vectors must be chosen appropriately. One way is it to each element in the xy plane ( 3 ) assign a unit current, for example 1A. Assuming that the anterior and posterior surface of the surface can conduct infinitely well then for each element a current distribution in the three-dimensional network can be calculated. These current distributions correspond to the respective base elements.

In the 4 schematically a structure is presented, with which also a measurement of the absolute current density in the fuel cell stack 10 based on the data of the magnetic field sensors 35 becomes possible. It should be noted that the illustration is purely schematic.

The proposed experimental setup makes use of the fact that the closely parallel leads 21 and return conductor 22 no significant magnetic field affecting the fuel cell magnetic field 30 superimposed, generate. The only exception is the area below the fuel cell, in which the magnetic field of the return conductor 22 undisturbed with the magnetic field 30 superimposed on the fuel cell. The current generating this magnetic field is thereby incorporated into the reconstruction region (left part of FIG 4 ) is included as an additional degree of freedom, that is, in the reconstruction becomes the return conductor 22 , corresponding to all other surface elements, a current based on that of the magnetic field sensors 35 assigned magnetic field data.

The method is not limited to the corresponding part of the return conductor 22 to include in the model only with a single degree of freedom. It can be introduced for more accurate current modeling also more than a new degree of freedom. The location of the return conductor 22 is not limited to the specified location. The return conductor 22 can also be next to or above the fuel cell 11 or the fuel cell stack 10 be guided. go conductor 21 and return conductor 22 do not necessarily have to be run in parallel. If they are not performed in parallel, the areas of the return conductor should have a significant impact on the fuel cell magnetic field 30 have to be included in the reconstruction area. In general, for stability reasons, it is advisable to keep the reconstruction area as small as possible.

10

Fuel cell stack

11

fuel cells

20

electrical electricity

21

go conductor

22

return conductor

30

magnetic field

35

magnetic field sensors

40

measuring table

Claims (16)

Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ), in which magnetic field sensors ( 35 ), the values of the current flow ( 20 ) in the fuel cell stack ( 10 ) generated magnetic field ( 30 ), characterized in that 21 ) and return conductors ( 22 ) for the stream ( 20 ) in the fuel cell stack ( 10 ), that the leaders ( 21 ) and return conductors ( 22 ) for the flow in the fuel cell stack ( 10 ) are largely parallel, and that those sections of Hinleiter ( 21 ) and / or return conductors ( 22 ), in which a parallel installation is not meaningful or possible, are wholly or partly included in a reconstruction volume for the current density distribution. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to claim 1, characterized in that Hinleiter ( 21 ) and return conductors ( 22 ) so that only the area between the terminals of the fuel cell stack ( 10 ) is not laid parallel to the corresponding opposite pole. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to claim 1 or 2, characterized in that at substantially parallel laying the conductor piece between the two terminals of the fuel cell stack ( 10 ) is included in the equation system by one or more additional degrees of freedom. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to one of the preceding claims, characterized in that initially a distortion or elongation of the data from the magnetic field sensors ( 35 ) and this information is subsequently used to modify the actual reconstruction of the measured values by means of scaling. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to claim 4, characterized in that the total flow of the fuel cell stack ( 10 ) and used for scaling. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to one of the preceding claims, characterized in that a vectorial basis of basis vectors for the unknown current density is introduced and to calculate the unknown current density the coefficients of the basis vectors are calculated so that a reduction of the dimension of the system of equations I = A ^-1 × H he follows. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to one of the preceding claims, characterized in that with the magnetic field sensors ( 35 ) Magnetic fields ( 30 ) of a known current density distribution are measured, that the measured values are compared with the theoretically calculated values of the same current density distribution, and that from the comparison correction data for measurement errors or measurement error arrangements of the magnetic field sensors ( 35 ). Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to claim 7, characterized in that the translational shift in all three coordinate directions or in selected coordinate directions to a reference point or reference object are determined from the comparison. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to claim 7 or 8, characterized in that from the comparison, the rotation and tilt of the magnetic field sensors ( 35 ) to a reference object. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to claim 7, 8 or 9, characterized in that from the comparison offset and gain of the magnetic field sensors ( 35 ) or the downstream evaluation unit (measuring amplifier, AD converter) are determined. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to any one of claims 7 to 10, characterized in that the comparison of the magnetic field sensors ( 35 ) measured magnetic field data with the theoretically expected data component by component for each magnetic field component is separated. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to one of claims 7 to 11, characterized in that the comparison of the magnetic field sensors ( 35 ) measured magnetic field data with the theoretically expected data for all magnetic field components (H _x , H _y , H _z ) is done together. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to one of claims 7 to 12, characterized in that the obtained correction factors are stored and applied to later obtained measured values. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to one of the preceding claims, characterized in that the equation system I = A ^-1 × H is supplemented with equations for the node rule in each node of the reconstruction volume and that the supplemented system of equations is solved instead of the original system of equations for the determination of the unknown current density distribution. Method for determining the current density distribution in a fuel cell stack ( 10 ) from one or more fuel cells ( 11 ) according to one of the preceding claims, characterized in that Hinleiter ( 21 ) and return conductors ( 22 ) for the flow in the fuel cell stack ( 10 ) are coaxial and thus minimize the resulting magnetic field. Method for determining the current density distribution in a fuel cell stack ( 10 ) from egg ner or more fuel cells ( 11 ) according to one of the preceding claims, characterized in that the feeds are carried out in coaxial design.