CN116093385A - Multi-point voltage-based fuel cell anode nitrogen concentration estimation method - Google Patents

Multi-point voltage-based fuel cell anode nitrogen concentration estimation method Download PDF

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CN116093385A
CN116093385A CN202211708168.9A CN202211708168A CN116093385A CN 116093385 A CN116093385 A CN 116093385A CN 202211708168 A CN202211708168 A CN 202211708168A CN 116093385 A CN116093385 A CN 116093385A
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cathode
nitrogen
cavity
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谢佳平
朱维
唐伟
沈军
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Haidriver Qingdao Energy Technology Co Ltd
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Abstract

The invention discloses a fuel cell anode nitrogen concentration estimation method based on multipoint voltage, which comprises the steps of firstly, respectively acquiring the voltage of a single cell at an anode inlet and an anode outlet based on a multipoint voltage monitoring method aiming at the characteristic of large active area of a commercial-size fuel cell, and taking the voltage as a feedback signal; then dividing the fuel cell into two half cells based on a discretization method, wherein an anode inlet half cell consists of an anode inlet cavity and a cathode outlet cavity; the anode outlet half cell consists of an anode outlet cavity and a cathode inlet cavity; and introducing a gas dynamic equation and a voltage equation to accurately solve the nitrogen concentration at the outlet of the anode. Aiming at the problem of uneven distribution of components in a commercial-size fuel cell, the scheme provides a nitrogen concentration estimation method of the commercial-size fuel cell, which is suitable for the commercial-size graphite plate fuel cell.

Description

Multi-point voltage-based fuel cell anode nitrogen concentration estimation method
Technical Field
The invention belongs to the field of fuel cell anode nitrogen concentration estimation, and particularly relates to a fuel cell anode nitrogen concentration estimation method based on multipoint voltage.
Background
The fuel cell converts chemical energy from hydrogen and oxygen supplied from a hydrogen supply and an air supply, respectively, to electrical energy, and then generates oxidation-reduction reactions. The hydrogen supply subsystem of a fuel cell system directly affects the efficiency of the system and the life of the stack. As nitrogen, water vapor and hydrogen are transported across the membrane during operation of the fuel cell, nitrogen on the cathode side diffuses from the cathode to the anode, resulting in a decrease in the anode hydrogen concentration. In practical systems, however, a hydrogen recycling scheme is employed for cost savings, which can lead to nitrogen accumulation on the anode side, resulting in reduced fuel cell performance.
The existing nitrogen gas estimation method is used for homogenizing the nitrogen gas concentration inside the fuel cell, and the problem of in-plane heterogeneity of the commercial size fuel cell is not considered, so that a novel nitrogen gas concentration estimation method is needed to accurately describe the nitrogen gas concentration of each single cell.
Disclosure of Invention
The invention provides a fuel cell anode nitrogen concentration estimation method based on multipoint voltage, which aims at the characteristics of a commercial-size fuel cell engine and provides an anode outlet position nitrogen concentration estimation method based on a multipoint voltage monitoring method, so that the problem of online observation of anode nitrogen concentration in the running process of the commercial-size fuel cell engine system is solved.
The invention is realized by adopting the following technical scheme: a fuel cell anode nitrogen concentration estimation method based on multipoint voltage comprises the following steps:
step A, a multipoint voltage monitoring method is adopted to obtain multipoint voltage data of the fuel cell;
step B, establishing a gas dynamic model and a gas transmembrane transport model based on the multipoint voltage data;
dividing an anode and a cathode of a fuel cell into two cavities respectively, wherein the two cavities comprise an anode inlet cavity, an anode outlet cavity, a cathode inlet cavity and a cathode outlet cavity, the anode inlet cavity and the cathode outlet cavity form a half cell, the anode outlet cavity and the cathode inlet cavity form a half cell, the two half cells are connected in parallel on a circuit, and are connected in series on a gas circuit; respectively constructing gas dynamic models of four cavities, and constructing a gas transmembrane transport model based on multipoint voltage data;
step C, constructing an exhaust model and a voltage model according to the gas dynamic model and the gas transmembrane transport model;
step D, solving the nitrogen concentration at the outlet of the anode:
(1) Calculating the nitrogen concentration in the anode cavity of the single-chip battery: firstly, respectively calculating the permeation nitrogen amount and permeation steam amount in two cavities of a cathode inlet cavity and a cathode outlet cavity, and the purging amount of nitrogen and steam; then calculating the current nitrogen amount in the anode flow channel based on the permeated nitrogen amount and the purging amount of the nitrogen, and calculating the current amounts of the nitrogen and the steam by integrating the accumulation rate and the purging rate per unit time and adding the integrated accumulation rate and the purging rate to the initial amount;
(2) And obtaining the nitrogen concentration of the anode outlet of each cell to obtain the weighted nitrogen concentration of the commercial-size fuel cell stack, thereby realizing the estimation of the nitrogen concentration.
7. The method for estimating the anode nitrogen concentration of a fuel cell based on a multipoint voltage according to claim 1, wherein: in the step B, the constructed gas dynamic model of the four cavities is as follows:
(1) Gas dynamic model of anode inlet chamber:
Figure BDA0004025483410000021
Figure BDA0004025483410000022
Figure BDA0004025483410000023
Figure BDA0004025483410000024
wherein ,
Figure BDA0004025483410000025
is the hydrogen pressure in the anode inlet chamber, V an Is the volume of the anode, R is the ideal gas constant, T fc Is the temperature of the galvanic pile>
Figure BDA0004025483410000026
Is the molar flow of hydrogen into the anode inlet chamber,/->
Figure BDA0004025483410000027
Is the molar flow of hydrogen, i, from the anode inlet chamber to the anode outlet chamber 1 Is the current of half cell at anode inlet, F is Faraday constant, A is active area of cell, N is number of cells,/L>
Figure BDA0004025483410000028
Is the molar flow of hydrogen permeated from the anode to the cathode in the anode inlet cavity;
Figure BDA0004025483410000029
is the nitrogen pressure in the anode inlet chamber,/-)>
Figure BDA00040254834100000210
Is the molar flow of nitrogen permeated from the cathode to the anode in the anode inlet chamber, +.>
Figure BDA00040254834100000211
Is the nitrogen molar flow from the anode inlet cavity to the anode outlet cavity;
Figure BDA00040254834100000212
Is the water vapor pressure in the anode inlet chamber,/-, in the anode inlet chamber>
Figure BDA00040254834100000213
Is the molar flow of water vapor from anode to cathode in the anode inlet cavity,/i>
Figure BDA00040254834100000214
Is the molar flow of water vapor from the anode inlet cavity to the anode outlet cavity; p (P) an,ch1 Is the gas pressure of the anode inlet chamber;
(2) Anode outlet chamber gas dynamic model:
Figure BDA00040254834100000215
Figure BDA00040254834100000216
Figure BDA00040254834100000217
Figure BDA00040254834100000218
wherein ,
Figure BDA00040254834100000219
is the hydrogen pressure in the anode outlet cavity, +.>
Figure BDA00040254834100000220
Is a discharge anodeHydrogen molar flow of i 2 Is the current of half-cell at the anode outlet, +.>
Figure BDA00040254834100000221
Is the molar flow of hydrogen permeated from the anode to the cathode in the anode outlet cavity;
Figure BDA00040254834100000222
Is the nitrogen pressure in the anode outlet cavity, +.>
Figure BDA00040254834100000223
Is the molar flow of nitrogen permeated from the cathode to the anode in the anode outlet cavity, +.>
Figure BDA00040254834100000224
Is the molar flow of the nitrogen discharged;
Figure BDA00040254834100000225
Is the water vapor pressure in the anode outlet cavity,
Figure BDA00040254834100000226
is the molar flow of water vapor from anode to cathode in the anode outlet cavity, +.>
Figure BDA00040254834100000227
Is the molar flow of water vapor from the anode inlet cavity to the anode outlet cavity; p (P) an,ch2 Is the gas pressure of the anode outlet cavity;
(3) Gas dynamic model in cathode inlet chamber:
Figure BDA0004025483410000031
Figure BDA0004025483410000032
Figure BDA0004025483410000033
Figure BDA0004025483410000034
Figure BDA0004025483410000035
wherein ,
Figure BDA0004025483410000036
is the oxygen pressure in the cathode inlet chamber, V ca Is the volume of the anode, ">
Figure BDA0004025483410000037
Is the molar flow of oxygen into the cathode inlet chamber,/->
Figure BDA0004025483410000038
Is the molar flow of oxygen from the cathode inlet chamber to the cathode outlet chamber;
Figure BDA0004025483410000039
is the nitrogen pressure in the cathode inlet chamber,/-)>
Figure BDA00040254834100000310
Is the molar flow of air into the cathode inlet chamber,
Figure BDA00040254834100000311
is the nitrogen molar flow from the cathode inlet cavity to the cathode outlet cavity;
Figure BDA00040254834100000312
Is the water vapor pressure in the cathode inlet chamber,/-, in the cathode inlet chamber>
Figure BDA00040254834100000313
Is a cathode inlet cavity to a cathode outlet cavityWater vapor molar flow rate;
Figure BDA00040254834100000314
Is the hydrogen pressure in the cathode inlet chamber,/-)>
Figure BDA00040254834100000315
Is the molar flow of hydrogen from the cathode inlet chamber to the cathode outlet chamber; p (P) ca,ch3 Is the gas pressure of the cathode inlet chamber;
(4) Gas dynamic model in cathode outlet cavity:
Figure BDA00040254834100000316
Figure BDA00040254834100000317
Figure BDA00040254834100000318
Figure BDA00040254834100000319
Figure BDA00040254834100000320
wherein ,
Figure BDA00040254834100000321
is the oxygen pressure in the cathode outlet cavity, +.>
Figure BDA00040254834100000322
Is the molar flow of oxygen into and out of the reactor, < + >>
Figure BDA00040254834100000323
Is the cathodeNitrogen pressure in the outlet cavity, +.>
Figure BDA00040254834100000324
Is the molar flow of the nitrogen discharged;
Figure BDA00040254834100000325
Is the water vapor pressure in the cathode outlet cavity,/->
Figure BDA00040254834100000326
Is the molar flow rate of the discharged water vapor;
Figure BDA00040254834100000327
Is the hydrogen pressure in the cathode outlet chamber,/-)>
Figure BDA00040254834100000328
Is the molar flow of the discharged hydrogen; p (P) ca,ch4 Is the gas pressure of the cathode outlet chamber.
Further, in the step B, a gas transmembrane transport model established based on the multipoint voltage data is as follows:
Figure BDA0004025483410000041
Figure BDA0004025483410000042
Figure BDA0004025483410000043
Figure BDA0004025483410000044
Figure BDA0004025483410000045
Figure BDA0004025483410000046
wherein ,
Figure BDA0004025483410000047
is the permeability coefficient of hydrogen, ">
Figure BDA0004025483410000048
Is the permeability coefficient of nitrogen, c ca Is the cathode water concentration, c an,ch1 Is the water concentration of the anode inlet cavity, c an,ch2 Is the water concentration of the anode outlet cavity, n d Is the electroosmosis resistance coefficient, D w Is the reverse osmosis coefficient.
Further, in the step C, the constructed exhaust model is as follows:
Figure BDA0004025483410000049
Figure BDA00040254834100000410
Figure BDA00040254834100000411
Figure BDA00040254834100000412
Figure BDA00040254834100000413
purge flow of gas
Figure BDA00040254834100000414
Can be combined with anode in the outlet cavityGas pressure (P) an,ch2 ) And the gas pressure (P) outside thereof an,out ) The difference between them is compared, C is the purge gain value, n an Is the total amount of gas in the anode:
Figure BDA00040254834100000415
Figure BDA00040254834100000416
Figure BDA00040254834100000417
purge flow of gas
Figure BDA00040254834100000418
Is->
Figure BDA00040254834100000419
and
Figure BDA00040254834100000420
The exhaust flows of the three gases are summed.
Further, in the step C, the constructed voltage model is as follows:
Figure BDA00040254834100000421
Figure BDA0004025483410000051
wherein ,Vfc1 and Vfc2 Is the voltage at the anode inlet and anode outlet of a fuel cell obtained by using multiple points of voltage, a 0 Is the gas pressure parameter, P sat Is the pressure of the air at the point of the air,
Figure BDA0004025483410000052
and
Figure BDA0004025483410000053
The oxygen concentration in the chamber 3 and in the chamber 4, respectively, < >>
Figure BDA0004025483410000054
Is the open circuit voltage, v, calculated from Nernst's equation act Is the loss of activation voltage, v ohm Ohmic voltage loss due to the resistance of the polymer film to the cells, v conc Is the concentration voltage loss caused by the concentration drop of the reactant during the reaction.
Further, in the step D, it is assumed that the partial pressure of nitrogen in the anode outlet cavity of the first cell is
Figure BDA0004025483410000055
The partial pressure of nitrogen in the anode outlet chamber 2 of the j-th cell is +.>
Figure BDA0004025483410000056
Then there are:
Figure BDA0004025483410000057
Figure BDA0004025483410000058
wherein ,
Figure BDA0004025483410000059
is a nitrogen concentration weighted value.
Compared with the prior art, the invention has the advantages and positive effects that:
according to the scheme, the commercial-size fuel single cell is divided into four cavities, the gas concentration changes in the cavities are calculated respectively, the expression of the dynamic relationship between the nitrogen concentration and the voltage is established, the nitrogen concentration at the corresponding position is represented by the multi-point voltage data, the nitrogen concentration at the anode outlet position of the commercial-size fuel cell is estimated more accurately, the problems of stack performance reduction and the like caused by inaccurate estimation are avoided, the nitrogen concentration at the outlet is used as a control variable, more accurate gas control can be realized, and further the purification of the anode in the fuel cell is helped to be controlled accurately.
Drawings
FIG. 1 is a schematic diagram of a multi-point voltage sampling in accordance with an embodiment of the present invention;
FIG. 2 is a model diagram of an embodiment of the present invention;
FIG. 3 is a flow chart of nitrogen concentration estimation according to an embodiment of the present invention;
fig. 4 is a control flow chart in an embodiment of the present invention.
Detailed Description
In order that the above objects, features and advantages of the invention will be more readily understood, a further description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as described herein, and thus the present invention is not limited to the specific embodiments disclosed below, in which commercial dimensions refer to active area dimensions of commercial fuel cells, as opposed to small-scale fuel cells for laboratory use.
In order to achieve the above object, the present embodiment proposes a fuel cell anode nitrogen concentration estimation method based on a multipoint voltage, the basic principle of which is as follows:
a multi-point voltage monitoring method is first implemented on a commercial-size fuel cell to obtain the voltages at the cell anode inlet and anode outlet, respectively. And establishing an anode two-cavity gas dynamic model and a gas transmembrane transport model. And establishing a voltage model according to the multi-point voltage data, and respectively calculating the nitrogen partial pressure and the nitrogen concentration of the two cavities. According to the invention, by combining the acquired voltage information of a plurality of positions with the information of the fuel cell anode inlet flow, pressure, relative humidity, fuel cell temperature, current and the like provided by the fuel cell test bench, the model is built, and the dynamic relationship between the nitrogen partial pressure and the voltage can be built by building the model, so that the nitrogen concentration of the anode outlet of each cell is acquired, and the weighted nitrogen concentration of the commercial-size fuel cell stack is obtained.
As shown in fig. 3, the method specifically comprises the following steps:
step A, obtaining multipoint voltage data of a commercial-size fuel cell based on a multipoint voltage monitoring method;
step B, establishing a gas dynamic model and a gas transmembrane transport model based on the multipoint voltage data;
step C, constructing an exhaust model and a voltage model according to the gas dynamic model and the gas transmembrane transport model;
and D, solving the nitrogen concentration at the outlet of the anode.
In step S1, a multi-point voltage monitoring method for a commercial-size fuel cell as shown in fig. 1 is first established, that is, voltage data is monitored at different positions of the cell, and in this embodiment, an anode inlet sampling point and an anode outlet sampling point are taken as examples, and specific multi-point voltage acquisition points are arbitrary.
In step S2, as shown in fig. 2, the anode and the cathode of the fuel cell are respectively divided into two cavities, and the two divided cavities are connected in series on the gas path and connected in parallel on the circuit, so that the fuel cell includes four cavities, namely, an anode inlet cavity 1, an anode outlet cavity 2, a cathode inlet cavity 3 and a cathode outlet cavity 4. Hydrogen firstly passes through the anode inlet cavity 1, reacts in the anode inlet cavity 1 and then enters the anode outlet cavity 2; the air passes through the cathode inlet cavity 3, reacts in the cathode inlet cavity 3 and then enters the cathode outlet cavity 4. The anode inlet cavity 1 and the cathode outlet cavity 4 form a half cell, the anode outlet cavity 2 and the cathode inlet cavity 3 form a half cell, and the voltage of the two half cells is obtained by a multipoint voltage monitoring method.
Considering that the two half batteries are connected in parallel on a circuit and connected in series on a gas circuit, a gas dynamic model of four cavities is constructed:
1) The gas dynamic model in the cavity 1 is as follows:
Figure BDA0004025483410000061
Figure BDA0004025483410000062
is the hydrogen pressure in the chamber 1, V an Is the volume of the anode, R is the ideal gas constant, T fc Is the temperature of the galvanic pile>
Figure BDA0004025483410000063
Is the molar flow of hydrogen into the chamber 1, < >>
Figure BDA0004025483410000064
Is the molar flow rate of hydrogen, i, from chamber 1 to chamber 2 1 Is the current of half cell at anode inlet, F is Faraday constant, A is active area of cell, N is number of cells,/L>
Figure BDA0004025483410000065
Is the molar flow of hydrogen in the chamber 1 that permeates from the anode to the cathode.
Figure BDA0004025483410000066
Figure BDA0004025483410000067
Is the nitrogen pressure in the chamber 1, +.>
Figure BDA0004025483410000068
Is the molar flow of nitrogen permeated from the cathode to the anode in the chamber 1,/the cathode is>
Figure BDA0004025483410000071
Is the molar flow of nitrogen from chamber 1 to chamber 2.
Figure BDA0004025483410000072
Figure BDA0004025483410000073
Is the water vapor pressure in the cavity 1, < >>
Figure BDA0004025483410000074
Is the molar flow of water vapor in the cavity 1 from anode to cathode, +.>
Figure BDA0004025483410000075
Is the molar flow of water vapor from chamber 1 to chamber 2.
Figure BDA0004025483410000076
P an,ch1 Is the gas pressure of the chamber 1.
2) The gas dynamic model in the cavity 2 is as follows:
Figure BDA0004025483410000077
Figure BDA0004025483410000078
is the hydrogen pressure in the chamber 2, +.>
Figure BDA0004025483410000079
Is the molar flow rate of hydrogen out of the anode, i 2 Is the current of half-cell at the anode outlet, +.>
Figure BDA00040254834100000710
Is the molar flow of hydrogen in the chamber 2 that permeates from the anode to the cathode.
Figure BDA00040254834100000711
Figure BDA00040254834100000712
Is the nitrogen pressure in the chamber 2, +.>
Figure BDA00040254834100000713
Is the molar flow of nitrogen permeated from the cathode to the anode in the chamber 2,/the cathode is>
Figure BDA00040254834100000714
Is the molar flow of nitrogen that is discharged.
Figure BDA00040254834100000715
Figure BDA00040254834100000716
Is the water vapor pressure in the cavity 2, < >>
Figure BDA00040254834100000717
Is the molar flow of water vapor in the cavity 2 from anode to cathode,/i>
Figure BDA00040254834100000718
Is the molar flow of water vapor from chamber 1 to chamber 2.
Figure BDA00040254834100000719
P an,ch2 Is the gas pressure of the chamber 2.
3) The gas dynamic model in the cavity 3 is as follows:
Figure BDA00040254834100000720
Figure BDA00040254834100000721
is the oxygen pressure in the chamber 3, V ca Is the volume of the anode, ">
Figure BDA00040254834100000722
Is the molar flow of oxygen into the chamber 3, < >>
Figure BDA00040254834100000723
Is the molar flow of oxygen from chamber 3 to chamber 4.
Figure BDA00040254834100000724
Figure BDA00040254834100000725
Is the nitrogen pressure in the chamber 3, +.>
Figure BDA00040254834100000726
Is the molar flow of air into the cavity 3, < >>
Figure BDA00040254834100000727
Is the molar flow of nitrogen from chamber 3 to chamber 4.
Figure BDA00040254834100000728
Figure BDA0004025483410000081
Is the water vapor pressure in the cavity 3, < >>
Figure BDA0004025483410000082
Is the molar flow of water vapor from chamber 3 to chamber 4. />
Figure BDA0004025483410000083
Figure BDA0004025483410000084
Is in the cavity 3Hydrogen pressure of>
Figure BDA0004025483410000085
Is the molar flow of hydrogen from chamber 3 to chamber 4.
Figure BDA0004025483410000086
P ca,ch3 Is the gas pressure of the chamber 3.
4) The gas dynamic model in the cavity 4 is as follows:
Figure BDA0004025483410000087
Figure BDA0004025483410000088
is the oxygen pressure in the cavity 4, +.>
Figure BDA0004025483410000089
Is the molar flow of oxygen into the exhaust.
Figure BDA00040254834100000810
Figure BDA00040254834100000811
Is the nitrogen pressure in the chamber 4, +.>
Figure BDA00040254834100000812
Is the molar flow of nitrogen that is discharged.
Figure BDA00040254834100000813
Figure BDA00040254834100000814
Is the water vapor pressure in the cavity 4, < >>
Figure BDA00040254834100000815
Is the molar flow rate of the discharged water vapor.
Figure BDA00040254834100000816
Figure BDA00040254834100000817
Is the hydrogen pressure in the chamber 4, +.>
Figure BDA00040254834100000818
Is the molar flow of hydrogen that is discharged.
Figure BDA00040254834100000819
P ca,ch4 Is the gas pressure of the chamber 4.
Step S3: and establishing a gas transmembrane transmission model based on the multipoint voltage data.
Figure BDA00040254834100000820
Figure BDA00040254834100000821
Figure BDA00040254834100000822
Figure BDA00040254834100000823
Figure BDA00040254834100000824
Figure BDA00040254834100000825
Figure BDA0004025483410000091
Is the permeability coefficient of hydrogen, ">
Figure BDA0004025483410000092
Is the permeability coefficient of nitrogen, c ca Is the cathode water concentration, c an,ch1 Is the water concentration of the anode cavity 1, c an,ch2 Is the water concentration, n, of the anode cavity 2 d Is the electroosmosis resistance coefficient, D w Is the reverse osmosis coefficient.
Step S4: according to the built gas dynamic model and the built gas transmembrane transport model, building an exhaust model;
Figure BDA0004025483410000093
Figure BDA0004025483410000094
Figure BDA0004025483410000095
Figure BDA0004025483410000096
Figure BDA0004025483410000097
purge flow of gas
Figure BDA0004025483410000098
Can be matched with the gas pressure (P) in the anode outlet cavity 2 an,ch2 ) And the gas pressure (P) outside thereof an,out ) The difference between them is compared, C is the purge gain value, n an Is the total amount of gas in the anode.
Figure BDA0004025483410000099
Figure BDA00040254834100000910
Figure BDA00040254834100000911
Purge flow of gas
Figure BDA00040254834100000912
Is->
Figure BDA00040254834100000913
and
Figure BDA00040254834100000914
The exhaust flows of the three gases are summed.
Step S5: and building a voltage model according to the built gas dynamic model and the built gas transmembrane transmission model.
For this purpose, it is necessary to establish the relationship between the internal pressure, flow rate, temperature, current and voltage of the fuel cell, and the like, and the relationship between the oxygen partial pressure, the hydrogen partial pressure, the cell temperature, the oxygen concentration, the current and voltage is revealed:
Figure BDA00040254834100000915
Figure BDA00040254834100000916
wherein Vfc1 and Vfc2 Is the voltage at the anode inlet and anode outlet of a fuel cell obtained by using multiple points of voltage, a 0 Is the gas pressure parameter, P sat Is the pressure of the air at the point of the air,
Figure BDA00040254834100000917
and
Figure BDA00040254834100000918
The oxygen concentration in the cavity 3 and the cavity 4 respectively;
Figure BDA00040254834100000919
Is the open circuit voltage, v, calculated from Nernst's equation act Is the loss of activation voltage, v ohm Ohmic voltage loss due to the resistance of the polymer film to the cells, v conc Is the concentration voltage loss caused by the concentration drop of the reactant during the reaction.
Step S6: calculate the nitrogen concentration in the anode outlet chamber 2:
according to the gas dynamic model, the gas transmembrane transport model and the voltage model, the gas parameters in the model are provided by parameter fitting or a bench. According to the collected multipoint voltage data, the nitrogen concentration at the downstream of the anode is calculated according to the following specific principle:
firstly, the amount of permeated nitrogen and the amount of permeated steam in two cavities of the cathode are calculated respectively, and the purging amounts of the nitrogen and the steam are calculated. The current amount of nitrogen in the anode flow channel is then calculated based on the amount of permeated nitrogen and the purge amount of nitrogen. The current amounts of nitrogen and steam were calculated by integrating the accumulation rate and purge rate per unit time and adding the initial amounts using the gas dynamic model, the gas transmembrane transport model, and the voltage model described above. By the method, the nitrogen concentration at the outlet position of the anode can be estimated more accurately, the problem of inaccurate estimation of the nitrogen concentration in the fuel cell with commercial size is avoided, possible serious faults of the fuel cell are avoided, and the estimation accuracy of the nitrogen concentration is effectively improved.
Step S7: the nitrogen concentration at the anode outlet of each cell was obtained to obtain a weighted nitrogen concentration for a commercial size fuel cell stack.
Assuming that the partial pressure of nitrogen in the anode outlet cavity 2 of the first cell is
Figure BDA0004025483410000101
The partial pressure of nitrogen in the anode outlet chamber 2 of the j-th cell is +.>
Figure BDA0004025483410000102
Figure BDA0004025483410000103
Figure BDA0004025483410000104
Determining a weighted value of anode outlet nitrogen concentration for a commercial fuel cell stack
Figure BDA0004025483410000105
Whether or not threshold X is reached, when->
Figure BDA0004025483410000106
And when the hydrogen discharge valve is started, the opening frequency of the hydrogen discharge valve is increased by 25%, and the threshold X is obtained through calibration.
The multipoint voltage obtained by the invention is used as the feedback quantity of the fuel cell gas purification, thereby helping to accurately control the purification of the anode in the fuel cell and improving the hydrogen utilization rate, and the specific control process is shown in figure 4.
The present invention is not limited to the above-mentioned embodiments, and any equivalent embodiments which can be changed or modified by the technical content disclosed above can be applied to other fields, but any simple modification, equivalent changes and modification made to the above-mentioned embodiments according to the technical substance of the present invention without departing from the technical content of the present invention still belong to the protection scope of the technical solution of the present invention.

Claims (6)

1. A fuel cell anode nitrogen concentration estimation method based on a multi-point voltage, comprising the steps of:
step A, a multipoint voltage monitoring method is adopted to obtain multipoint voltage data of the fuel cell;
step B, establishing a gas dynamic model and a gas transmembrane transport model based on the multipoint voltage data;
dividing an anode and a cathode of a fuel cell into two cavities respectively, wherein the two cavities comprise an anode inlet cavity, an anode outlet cavity, a cathode inlet cavity and a cathode outlet cavity, the anode inlet cavity and the cathode outlet cavity form a half cell, the anode outlet cavity and the cathode inlet cavity form a half cell, the two half cells are connected in parallel on a circuit, and are connected in series on a gas circuit; respectively constructing gas dynamic models of four cavities, and constructing a gas transmembrane transport model based on multipoint voltage data;
step C, constructing an exhaust model and a voltage model according to the gas dynamic model and the gas transmembrane transport model;
step D, solving the nitrogen concentration at the outlet of the anode:
(1) Calculating the nitrogen concentration in the anode cavity of the single-chip battery: firstly, respectively calculating the permeation nitrogen amount and permeation steam amount in two cavities of a cathode inlet cavity and a cathode outlet cavity, and the purging amount of nitrogen and steam; then calculating the current nitrogen amount in the anode flow channel based on the permeated nitrogen amount and the purging amount of the nitrogen, and calculating the current amounts of the nitrogen and the steam by integrating the accumulation rate and the purging rate per unit time and adding the integrated accumulation rate and the purging rate to the initial amount;
(2) And obtaining the nitrogen concentration of the anode outlet of each cell to obtain the weighted nitrogen concentration of the commercial-size fuel cell stack, thereby realizing the estimation of the nitrogen concentration.
2. The method for estimating the anode nitrogen concentration of a fuel cell based on a multipoint voltage according to claim 1, wherein: in the step B, the constructed gas dynamic model of the four cavities is as follows:
(1) Gas dynamic model of anode inlet chamber:
Figure FDA0004025483400000011
Figure FDA0004025483400000012
Figure FDA0004025483400000013
Figure FDA0004025483400000014
wherein ,
Figure FDA0004025483400000015
is the hydrogen pressure in the anode inlet chamber, V an Is the volume of the anode, R is the ideal gas constant, T fc Is the temperature of the galvanic pile>
Figure FDA0004025483400000016
Is the molar flow of hydrogen into the anode inlet chamber,/->
Figure FDA0004025483400000017
Is the molar flow of hydrogen, i, from the anode inlet chamber to the anode outlet chamber 1 Is the current of half cell at anode inlet, F is Faraday constant, A is active area of cell, N is number of cells,/L>
Figure FDA0004025483400000018
Is anode penetration into the anode inlet cavityHydrogen molar flow of the cathode;
Figure FDA0004025483400000019
is the nitrogen pressure in the anode inlet chamber,/-)>
Figure FDA00040254834000000110
Is the molar flow of nitrogen permeated from the cathode to the anode in the anode inlet chamber, +.>
Figure FDA00040254834000000111
Is the nitrogen molar flow from the anode inlet cavity to the anode outlet cavity;
Figure FDA00040254834000000112
Is the water vapor pressure in the anode inlet chamber,/-, in the anode inlet chamber>
Figure FDA00040254834000000113
Is the molar flow of water vapor from anode to cathode in the anode inlet cavity,/i>
Figure FDA00040254834000000114
Is the molar flow of water vapor from the anode inlet cavity to the anode outlet cavity; p (P) an,ch1 Is the gas pressure of the anode inlet chamber;
(2) Anode outlet chamber gas dynamic model:
Figure FDA0004025483400000021
Figure FDA0004025483400000022
Figure FDA0004025483400000023
Figure FDA0004025483400000024
wherein ,
Figure FDA0004025483400000025
is the hydrogen pressure in the anode outlet cavity, +.>
Figure FDA0004025483400000026
Is the molar flow rate of hydrogen out of the anode, i 2 Is the current of half-cell at the anode outlet, +.>
Figure FDA0004025483400000027
Is the molar flow of hydrogen permeated from the anode to the cathode in the anode outlet cavity;
Figure FDA0004025483400000028
is the nitrogen pressure in the anode outlet cavity, +.>
Figure FDA0004025483400000029
Is the molar flow of nitrogen permeated from the cathode to the anode in the anode outlet cavity, +.>
Figure FDA00040254834000000210
Is the molar flow of the nitrogen discharged;
Figure FDA00040254834000000211
Is the water vapor pressure in the anode outlet cavity,/->
Figure FDA00040254834000000212
Is the molar flow of water vapor from anode to cathode in the anode outlet cavity, +.>
Figure FDA00040254834000000213
Is the molar flow of water vapor from the anode inlet cavity to the anode outlet cavity; p (P) an,ch2 Is the gas pressure of the anode outlet cavity;
(3) Gas dynamic model in cathode inlet chamber:
Figure FDA00040254834000000214
Figure FDA00040254834000000215
Figure FDA00040254834000000216
Figure FDA00040254834000000217
Figure FDA00040254834000000218
wherein ,
Figure FDA00040254834000000219
is the oxygen pressure in the cathode inlet chamber, V ca Is the volume of the anode, ">
Figure FDA00040254834000000220
Is the molar flow of oxygen into the cathode inlet chamber,/->
Figure FDA00040254834000000221
Is the molar flow of oxygen from the cathode inlet chamber to the cathode outlet chamber;
Figure FDA00040254834000000222
Is the nitrogen pressure in the cathode inlet chamber,/-)>
Figure FDA00040254834000000223
Is the molar flow of air into the cathode inlet chamber,/->
Figure FDA00040254834000000224
Is the nitrogen molar flow from the cathode inlet cavity to the cathode outlet cavity;
Figure FDA00040254834000000225
Is the water vapor pressure in the cathode inlet chamber,
Figure FDA00040254834000000226
is the molar flow of water vapor from the cathode inlet cavity to the cathode outlet cavity;
Figure FDA00040254834000000227
Is the hydrogen pressure in the cathode inlet chamber,/-)>
Figure FDA00040254834000000228
Is the molar flow of hydrogen from the cathode inlet chamber to the cathode outlet chamber; p (P) ca,ch3 Is the gas pressure of the cathode inlet chamber;
(4) Gas dynamic model in cathode outlet cavity:
Figure FDA0004025483400000031
Figure FDA0004025483400000032
Figure FDA0004025483400000033
Figure FDA0004025483400000034
Figure FDA0004025483400000035
wherein ,
Figure FDA0004025483400000036
is the oxygen pressure in the cathode outlet cavity, +.>
Figure FDA0004025483400000037
Is the molar flow of oxygen into the exhaust,
Figure FDA0004025483400000038
is the nitrogen pressure in the cathode outlet chamber, +.>
Figure FDA0004025483400000039
Is the molar flow of the nitrogen discharged;
Figure FDA00040254834000000310
Is the water vapor pressure in the cathode outlet cavity,/->
Figure FDA00040254834000000311
Is the molar flow rate of the discharged water vapor;
Figure FDA00040254834000000312
Is the hydrogen pressure in the cathode outlet chamber,/-)>
Figure FDA00040254834000000313
Is the molar flow of the discharged hydrogen; p (P) ca,ch4 Is the cathode outletGas pressure of the chamber.
3. The method for estimating the anode nitrogen concentration of a fuel cell based on a multipoint voltage according to claim 2, wherein: in the step B, a gas transmembrane transport model established based on the multipoint voltage data is as follows:
Figure FDA00040254834000000314
Figure FDA00040254834000000315
Figure FDA00040254834000000316
Figure FDA00040254834000000317
Figure FDA00040254834000000318
Figure FDA00040254834000000319
wherein ,
Figure FDA00040254834000000320
is the permeability coefficient of hydrogen, ">
Figure FDA00040254834000000321
Is the permeability coefficient of nitrogen, c ca Is the cathode water concentration, c an,ch1 Is the water concentration of the anode inlet cavity, c an,ch2 Is the water concentration of the anode outlet cavity, n d Is the electroosmosis resistance coefficient, D w Is the reverse osmosis coefficient.
4. A fuel cell anode nitrogen concentration estimation method based on a multipoint voltage according to claim 3, wherein: in the step C, the constructed exhaust model is as follows:
Figure FDA00040254834000000322
Figure FDA00040254834000000323
Figure FDA0004025483400000041
Figure FDA0004025483400000042
Figure FDA0004025483400000043
purge flow of gas
Figure FDA0004025483400000044
With the gas pressure P in the anode outlet cavity an,ch2 And the gas pressure P outside thereof an,out The difference between them is compared, C is the purge gain value, n an Is the total amount of gas in the anode.
5. The method for estimating anode nitrogen concentration of fuel cell based on multipoint voltage according to claim 4, wherein: in the step C, the constructed voltage model is as follows:
Figure FDA0004025483400000045
Figure FDA0004025483400000046
wherein ,Vfc1 and Vfc2 Is the voltage at the anode inlet and anode outlet of a fuel cell obtained by using multiple points of voltage, a 0 Is the gas pressure parameter, P sat Is the pressure of the air at the point of the air,
Figure FDA0004025483400000047
and
Figure FDA0004025483400000048
The oxygen concentration in the chamber 3 and in the chamber 4, respectively, < >>
Figure FDA0004025483400000049
Is the open circuit voltage, v, calculated from Nernst's equation act Is the loss of activation voltage, v ohm Ohmic voltage loss due to the resistance of the polymer film to the cells, v conc Is the concentration voltage loss caused by the concentration drop of the reactant during the reaction.
6. The method for estimating anode nitrogen concentration of fuel cell based on multipoint voltage according to claim 5, wherein: in the step D, it is assumed that the partial pressure of nitrogen in the anode outlet cavity of the first cell is
Figure FDA00040254834000000410
The partial pressure of nitrogen in the anode outlet chamber 2 of the j-th cell is +.>
Figure FDA00040254834000000411
Then there are:
Figure FDA00040254834000000412
Figure FDA00040254834000000413
wherein ,
Figure FDA00040254834000000414
is a nitrogen concentration weighted value. />
CN202211708168.9A 2022-12-29 2022-12-29 Multi-point voltage-based fuel cell anode nitrogen concentration estimation method Pending CN116093385A (en)

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CN117895033A (en) * 2024-02-21 2024-04-16 北京卡文新能源汽车有限公司 Nitrogen cumulative concentration calculation method, device, equipment and medium

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CN115207417A (en) * 2022-06-17 2022-10-18 同济大学 Large-area fuel cell current density distribution calculation method
CN115472876A (en) * 2022-08-30 2022-12-13 北京科技大学 Fuel cell stack anode nitrogen concentration estimation method based on voltage change characteristics

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Publication number Priority date Publication date Assignee Title
CN115207417A (en) * 2022-06-17 2022-10-18 同济大学 Large-area fuel cell current density distribution calculation method
CN115472876A (en) * 2022-08-30 2022-12-13 北京科技大学 Fuel cell stack anode nitrogen concentration estimation method based on voltage change characteristics

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117895033A (en) * 2024-02-21 2024-04-16 北京卡文新能源汽车有限公司 Nitrogen cumulative concentration calculation method, device, equipment and medium

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