CN115911468A - Operation condition optimizing method for improving power generation efficiency of fuel cell - Google Patents

Operation condition optimizing method for improving power generation efficiency of fuel cell Download PDF

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CN115911468A
CN115911468A CN202211354433.8A CN202211354433A CN115911468A CN 115911468 A CN115911468 A CN 115911468A CN 202211354433 A CN202211354433 A CN 202211354433A CN 115911468 A CN115911468 A CN 115911468A
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fuel cell
stack
power generation
generation efficiency
power
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卫东
马玉河
崔健
向志平
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China Jiliang University
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    • Y02E60/50—Fuel cells

Abstract

An operating condition optimizing method for improving the power generation efficiency of a fuel cell. The method comprises the following steps: the theoretical model of the power generation efficiency of the proton exchange membrane fuel cell is analyzed, and the power generation efficiency of the electric pile is gradually reduced along with the increase of the output power of the fuel cell. Under the condition of meeting the requirement of stable operation of a load, when the output power of the galvanic pile operates according to the power required by the load and the minimum total internal resistance of the fuel cell is taken as a control target, the Lagrange multiplier method is used for obtaining the working temperature, the working humidity and the output voltage when the total internal resistance of the galvanic pile is minimum under the current power output, and the power generation efficiency of the fuel cell can be improved under the working condition. And substituting the obtained working temperature, working humidity and output voltage into a theoretical model of the power generation efficiency of the fuel cell to calculate the power generation efficiency of the fuel cell under the current power output.

Description

Operation condition optimizing method for improving power generation efficiency of fuel cell
The technical field is as follows:
the invention belongs to the field of power generation efficiency of proton exchange membrane fuel cells, and relates to an operation condition optimizing method for improving the power generation efficiency of a fuel cell.
Background art:
with the reduction of fossil fuel reserves and the increasing severity of environmental pollution problems, the development of clean energy has become a hot topic affecting the development of socioeconomic development. The fuel cell power generation technology is based on chemical energy conversion, the power generation efficiency and the output power of the fuel cell are higher than those of the traditional thermal power generation, and the pollution of the fuel cell emission is small, so the fuel cell is considered as the best choice for future power generation. Among many Fuel cells, proton Exchange Membrane Fuel Cells (PEMFC) have been widely used in many practical applications, such as vehicles, ships, airplanes, and micro-grids, because of their advantages of high energy conversion efficiency, cleanliness and no pollution.
A proton exchange membrane fuel cell is a power generation device that converts hydrogen energy into electrical energy. Since hydrogen is an expensive source and is difficult to store, the cost of the entire fuel cell is high in practical use. Therefore, with the rapid expansion of the application range of the PEMFC power generation technology, the requirements of the industry on the PEMFC not only stay in the fuel cell stack to quickly and stably meet the load requirements in different ranges, but also require the fuel cell to have higher power generation efficiency, thereby playing the role of energy saving and consumption reduction. However, the power generation efficiency of the pem fuel cell stack gradually decreases with the increase of the output power of the stack, and how to balance the negative correlation between the output power and the power generation efficiency to make the output power of the stack meet the load requirement and have higher power generation efficiency has become a key object for research by experts and scholars in the new energy field.
The invention content is as follows:
in order to solve the above problems of the power generation efficiency of the proton exchange membrane fuel cell, the present specification proposes an optimization method of operating conditions for improving the power generation efficiency of the fuel cell. The method is characterized in that: the theoretical model of the generating efficiency of the proton exchange membrane fuel cell is analyzed, and the generating efficiency of the electric pile is gradually reduced along with the increase of the output power of the fuel cell. Under the condition of meeting the requirement of stable operation of a load, when the output power of the galvanic pile operates according to the power required by the load and the minimum total internal resistance of the fuel cell is taken as a control target, the Lagrange multiplier method is used for obtaining the working temperature, the working humidity and the output voltage when the total internal resistance of the galvanic pile is the minimum under the power output required by the load, and the power generation efficiency of the fuel cell can be improved under the working condition. The method comprises the following specific steps:
the method comprises the following steps: electric power generation efficiency eta of fuel cell stack stack Is represented by formula (1):
Figure BDA0003919581260000011
in the formula (1), the acid-base catalyst,
Figure BDA0003919581260000012
hydrogen molar mass, kg/mol; n is the number of the battery pieces; u is the output voltage of the electric pile, V; f is a Faraday constant; />
Figure BDA0003919581260000013
Is hydrogen with low heat value;
step two: due to the influence of the polarization overvoltage loss, the actual output voltage of the fuel cell stack is lower than the theoretical voltage value under the actual working state of the fuel cell, so that the actual output voltage of the fuel cell stack is shown as the formula (2):
Figure BDA0003919581260000021
in the formula (2), E ocv Is the stack open circuit voltage, V; r f To activate internal resistance, R m Is ohmic internal resistance, R d Is concentration internal resistance, omega cm 2 (ii) a Alpha is an electrochemical reaction rate parameter; n is the number of transferred electrons of the electrochemical reaction; f is a Faraday constant; r is an ideal gas constant; i.e. i 0 Is T 0 Exchange current density at temperature i is T stack Current density at temperature, A/cm 2 ；T 0 Is the standard temperature, T, of the stack stack The working temperature of the galvanic pile, K; delta is the thickness of the diffusion layer, mu m; c g Is the total concentration of reactants, mol/L; d eff Is the water migration coefficient of the running state, J/(K.mol); t is t m Is the thickness of the proton exchange membrane, mu m; a is electrochemical reaction area, cm 2 ；λ m The water content of the proton exchange membrane; alpha is alpha 1 ～α 7 Are all model empirical parameters;
in summary, the combination of formulas (1) and (2) can obtain the power generation efficiency η of the fuel cell stack Is represented by formula (3):
Figure BDA0003919581260000022
step three: the relation between the actual output current density i and the output voltage U of the galvanic pile is shown as the formula (4):
i＝P/(UA) (4)
substituting expression (4) of current density into fuel cell power generation efficiency eta stack In the expression (3), the fuel cell power generation efficiency η can be obtained stack An expression relating to the operating temperature, the operating humidity, and the output voltage is expressed by the following equation (5):
Figure BDA0003919581260000023
the theoretical model analysis of the fuel cell power generation efficiency shown in the formula (5) shows that the power generation efficiency of the fuel cell stack gradually decreases with the increase of the output power of the fuel cell stack under the condition that the operating temperature, the operating humidity and the output voltage of the fuel cell are constant. Under the condition of meeting the requirement of stable operation of a load, when the output power of the electric pile operates according to the power required by the load and the total internal resistance of the fuel cell is the minimum control target, the optimal operation condition exists so that the power generation efficiency of the fuel cell is improved.
Step four: total internal resistance R of the galvanic pile stack As optimization target, total internal resistance R stack The expression of (b) is shown in formula (6); constraint function
Figure BDA0003919581260000031
As a constraint on which the constraint function->
Figure BDA0003919581260000032
The expression of (b) is shown in formula (7); and introducing a Lagrange multiplier method to carry out operation condition optimization solution.
Figure BDA0003919581260000033
Figure BDA0003919581260000034
When the temperature is higher than the set temperature
Figure BDA0003919581260000035
The output power of the electric pile is operated according to the power required by the load, and the function R of the total internal resistance is obtained stack In a constraint function>
Figure BDA0003919581260000036
Constructing an auxiliary-calculation real number lambda according to a core formula of a Lagrange multiplier method, so that the gradient sum of the real number lambda and the gradient sum is zero, wherein the expression is shown as formula (8):
Figure BDA0003919581260000037
step five: the gradient in formula (8) may be determined by the total internal resistance R stack And a constraint function
Figure BDA0003919581260000038
Respectively to temperature T stack Humidity RH stack And the output voltage U is obtained by calculating the partial derivative, and the formula (8) can be written into the form of the following components;
Figure BDA0003919581260000039
Figure BDA00039195812600000310
Figure BDA00039195812600000311
step six: when the output power of the electric pile runs according to the power required by the load, the operating condition at which the total internal resistance of the fuel cell is minimum needs to satisfy the equations (9) to (11) which are all equal to 0. Therefore, the four equations of equations (7), (9), (10) and (11) are connected into a lagrange equation set, and the nonlinear programming problem with constraint conditions becomes a problem for solving the nonlinear equation set.
Figure BDA00039195812600000312
When all the equations of the nonlinear equation set are established, the solved solution set is the solution set at the position where the total internal resistance of the cell stack is minimum. Since the system of equations is a multi-element nonlinear system of equations, newton's iteration method is used for the solution. The temperature T obtained by solving at this time stack Humidity RH stack And the output voltage U is an optimum operating condition of the stack at the power output required by the load, which improves the stack power generation efficiency of the fuel cell. The obtained temperature T stack Humidity RH stack And substituting the output voltage U into the formula (5) to calculate the power generation efficiency of the fuel cell.
Description of the drawings:
FIG. 1 shows the curve of the power generation efficiency of a galvanic pile along with the output power of the galvanic pile
FIG. 2U-I curve of fuel cell
The specific implementation mode is as follows:
in order to clearly explain the technical features of an operation condition optimizing method for improving the power generation efficiency of a fuel cell, the present invention will be explained in detail by the following embodiments in conjunction with the accompanying drawings. The implementation process of the invention comprises the following steps:
the method comprises the following steps: electric power generation efficiency η of fuel cell stack stack Is represented by formula (1):
Figure BDA0003919581260000041
in the formula (1), the reaction mixture is,
Figure BDA0003919581260000042
the hydrogen gas inlet flow rate is kg/s; n is the number of the battery pieces; p is the output power of the galvanic pile, W; />
Figure BDA0003919581260000043
Is hydrogen with low heating value;
in the formula (1), the hydrogen gas inlet flow rate is related to the output current, and the hydrogen gas inlet flow rate
Figure BDA0003919581260000044
Is represented by formula (2):
Figure BDA0003919581260000045
in the formula (2), the reaction mixture is,
Figure BDA0003919581260000046
the hydrogen gas inlet flow rate is kg/s; />
Figure BDA0003919581260000047
Hydrogen molar mass, kg/mol; i is the output current of the electric pile, A; f is a Faraday constant;
the expression of the fuel cell output power P in the formula (1) is shown by the formula (3):
P＝UI (3)
in summary, the fuel cell power generation efficiency η is obtained by combining the expressions (1) to (3) stack The specific expression of (2) is shown in formula (4):
Figure BDA0003919581260000048
step two: according to the U-I curve of the fuel cell shown in the attached figure 2 and different stages and characteristics of polarization, polarization of the fuel cell stack is divided into active polarization loss, ohmic polarization loss and concentration polarization loss. Dividing the equivalent internal resistance into activation internal resistances R by analyzing the causes and characteristics of polarization loss generated in different current density sections f In ohmResistance R m Concentration internal resistance R d . Due to the influence of the polarization overvoltage loss, the actual output voltage of the fuel cell stack is lower than the theoretical voltage value under the actual working state of the fuel cell, so that the actual output voltage of the fuel cell stack is as shown in formula (5):
Figure BDA0003919581260000051
in the formula (5), E ocv Is the stack open circuit voltage, V; r f To activate internal resistance, R m Is ohmic internal resistance, R d The concentration internal resistance is omega cm 2 (ii) a Alpha is an electrochemical reaction rate parameter; n is the number of transferred electrons of the electrochemical reaction; f is a Faraday constant; r is an ideal gas constant; i.e. i 0 Is T 0 Exchange current density at temperature i is T stack Current density at temperature, A/cm 2 ；T 0 Is the standard temperature, T, of the stack stack The working temperature of the galvanic pile, K; delta is the thickness of the diffusion layer, mu m; c g Is the total concentration of reactants, mol/L; d eff The water migration coefficient is the water migration coefficient of the running state, J/(K.mol); t is t m Is the thickness of the proton exchange membrane, mu m; a is electrochemical reaction area, cm 2 ；λ m The water content of the proton exchange membrane; tau is the mole number of the transferred ions, mol; d λ Is the water migration coefficient of the initial state, J/(K.mol); beta is the conductivity coefficient; alpha is alpha 1 ～α 7 、γ 1 ～γ 4 、β 1 ～β 4 Are all model empirical parameters;
in summary, the combination of formulas (4) and (5) can obtain the power generation efficiency η of the fuel cell stack Is represented by formula (6):
Figure BDA0003919581260000052
step three: the relation between the actual output current density i and the output voltage U of the electric pile is shown in formula (7):
i＝P/(UA) (7)
substituting expression (7) of current density into fuel cell power generation efficiency eta stack In the expression (6), the fuel cell power generation efficiency η can be obtained stack The expression formula of the relation with the working temperature, the working humidity and the output voltage is shown as the formula (8):
Figure BDA0003919581260000061
by analyzing the theoretical model of the power generation efficiency of the fuel cell shown in equation (8), under the condition that the operating temperature, the operating humidity and the output voltage of the fuel cell are constant, the power generation efficiency of the fuel cell stack gradually decreases along with the increase of the output power of the fuel cell stack, as shown in fig. 1. Under the condition of meeting the requirement of stable operation of a load, when the output power of the electric pile operates according to the power required by the load and the total internal resistance of the fuel cell is the minimum control target, the optimal operation condition exists so that the power generation efficiency of the fuel cell is improved.
Step four: the total internal resistance R of the galvanic pile stack As optimization target, total internal resistance R stack The expression of (b) is shown as formula (9); constraint function
Figure BDA0003919581260000062
As a constraint on which the constraint function->
Figure BDA0003919581260000063
Is represented by formula (10); and introducing a Lagrange multiplier method to carry out operation condition optimization solution.
Figure BDA0003919581260000064
Figure BDA0003919581260000065
When in use
Figure BDA0003919581260000066
The output power of the electric pile is operated according to the power required by the load, and the function R of the total internal resistance is obtained stack In a constraint function>
Figure BDA0003919581260000067
And constructing an auxiliary real number lambda according to a core formula of a Lagrange multiplier method by using the minimum value below, so that the gradient sum of the two is zero. The expression is shown in formula (11):
Figure BDA0003919581260000068
step five: the gradient in formula (11) can be determined by the total internal resistance R stack And a constraint function
Figure BDA0003919581260000069
Respectively to temperature T stack Humidity RH stack And the output voltage U is obtained by calculating the partial derivative, and the formula (11) can be written into the form of the following components;
Figure BDA00039195812600000610
Figure BDA0003919581260000071
/>
Figure BDA0003919581260000072
step six: when the output power of the electric pile is operated according to the power required by the load, the operating condition at which the total internal resistance of the fuel cell is minimum needs to satisfy the equations (12) to (14) which are all equal to 0. Therefore, the four equations (10), (12), (13) and (14) are combined into a lagrangian equation system, and then the nonlinear programming problem with the constraint condition becomes a problem for solving the nonlinear equation system.
Figure BDA0003919581260000073
When all the equations of the nonlinear equation set are established, the solved solution set is the solution set at the position where the total internal resistance of the cell stack is minimum. Since the system of equations is a multi-element nonlinear system of equations, newton's iteration method is used for the solution. The temperature T obtained by solving at this time stack Humidity RH stack And the output voltage U is an optimum operating condition of the stack at the power output required by the load, which improves the power generation efficiency of the fuel cell. The obtained temperature T stack Humidity RH stack And substituting the output voltage U into the formula (8) to calculate the power generation efficiency of the fuel cell.

Claims (3)

1. An operating condition optimizing method for improving power generation efficiency of a fuel cell, comprising:
the theoretical model of the generating efficiency of the proton exchange membrane fuel cell is analyzed, and the generating efficiency of the electric pile is gradually reduced along with the increase of the output power of the fuel cell; under the condition of meeting the requirement of stable operation of a load, when the output power of the galvanic pile operates according to the power required by the load and the total internal resistance of the fuel cell is the minimum as a control target, obtaining the working temperature, the working humidity and the output voltage when the total internal resistance of the galvanic pile is the minimum under the current power output by using a Lagrange multiplier method, and improving the power generation efficiency of the fuel cell under the working condition; the method comprises the following specific steps:
the method comprises the following steps: electric power generation efficiency η of fuel cell stack stack Is represented by formula (1):
Figure FDA0003919581250000011
in the formula (1), the reaction mixture is,
Figure FDA0003919581250000012
hydrogen molar mass, kg/mol; n is the number of the battery pieces; u is the output voltage of the electric pile,v; f is a Faraday constant; />
Figure FDA0003919581250000013
Is hydrogen with low heat value;
step two: due to the influence of the polarization overvoltage loss, the actual output voltage of the fuel cell stack is lower than the theoretical voltage value under the actual working state of the fuel cell, so that the actual output voltage of the fuel cell stack is shown as the formula (2):
Figure FDA0003919581250000014
in the formula (2), E ocv Is the stack open circuit voltage, V; r is f To activate internal resistance, R m Is ohmic internal resistance, R d Is concentration internal resistance, omega cm 2 (ii) a Alpha is an electrochemical reaction rate parameter; n is the number of transferred electrons of the electrochemical reaction; f is a Faraday constant; r is an ideal gas constant; i.e. i 0 Is T 0 Current density at temperature i is T stack Current density at temperature, A/cm 2 ；T 0 Is the standard temperature of the stack, T stack The working temperature of the galvanic pile, K; delta is the thickness of the diffusion layer, mu m; c g Is the total concentration of reactants, mol/L; d eff Is the water migration coefficient of the running state, J/(K.mol); t is t m Is the thickness of the proton exchange membrane, mu m; a is electrochemical reaction area, cm 2 ；λ m The water content of the proton exchange membrane; alpha (alpha) ("alpha") 1 ～α 7 Are all model empirical parameters;
in summary, the combination of formulas (1) and (2) can obtain the power generation efficiency η of the fuel cell stack Is represented by the following formula (3):
Figure FDA0003919581250000015
step three: the relation between the actual output current density i and the output voltage U of the galvanic pile is shown as the formula (4):
i＝P/(UA) (4)
substituting expression (4) of current density into fuel cell power generation efficiency eta stack In the expression (3), the fuel cell power generation efficiency η can be obtained stack An expression relating to the operating temperature, the operating humidity, and the output voltage is expressed by the following equation (5):
Figure FDA0003919581250000021
the theoretical model of the power generation efficiency of the fuel cell shown in the formula (5) is analyzed, so that the power generation efficiency of the galvanic pile is gradually reduced along with the increase of the output power of the galvanic pile under the condition that the working temperature, the working humidity and the output voltage of the fuel cell are constant; under the condition of meeting the stable operation of the load, when the output power of the galvanic pile operates according to the power required by the load and the minimum total internal resistance of the fuel cell is taken as a control target, the optimal operation condition exists to improve the power generation efficiency of the fuel cell;
step four: the total internal resistance R of the galvanic pile stack As an optimization target, total internal resistance R stack The expression of (b) is shown in formula (6); constraint function
Figure FDA0003919581250000022
As a constraint on which the constraint function->
Figure FDA0003919581250000023
The expression of (b) is shown in formula (7); introducing a Lagrange multiplier method to carry out operation condition optimization solution;
Figure FDA0003919581250000024
Figure FDA0003919581250000025
when the temperature is higher than the set temperature
Figure FDA0003919581250000026
The output power of the electric pile is operated according to the power required by the load, and the function R of the total internal resistance is obtained stack In a constraint function
Figure FDA0003919581250000027
Constructing an auxiliary-calculation real number lambda according to a core formula of a Lagrange multiplier method, so that the gradient sum of the two is zero, wherein the expression is shown as a formula (8):
Figure FDA0003919581250000028
step five: the gradient in formula (8) may be determined by the total internal resistance R stack And a constraint function
Figure FDA0003919581250000029
Respectively to temperature T stack Humidity RH stack And the output voltage U is obtained by calculating the partial derivative, and the formula (8) can be written into the form of the following components;
Figure FDA0003919581250000031
/>
Figure FDA0003919581250000032
Figure FDA0003919581250000033
step six: when the output power of the galvanic pile runs according to the power required by the load, the operating conditions at the minimum position of the total internal resistance of the fuel cell need to satisfy the conditions that the expressions (9) to (11) are all equal to 0; therefore, the four equations of the formulas (7), (9), (10) and (11) are connected into a Lagrange equation set, and the nonlinear programming problem with constraint conditions becomes a problem of solving the nonlinear equation set;
Figure FDA0003919581250000034
when all equations of the nonlinear equation set are established, the solved solution set is the solution set at the minimum position of the total internal resistance of the galvanic pile; because the equation set is a multi-element nonlinear equation set, a Newton iteration method is used for solving; the temperature T obtained by solving at this time stack Humidity RH stack And the output voltage U is an optimum operating condition of the stack at the power output required by the load, which improves the stack power generation efficiency of the fuel cell.
2. The method of claim 1, wherein: combining the theoretical model of the generating efficiency of the galvanic pile with an expression of the output power of the galvanic pile to obtain an expression of the generating efficiency of the galvanic pile related to the output power of the galvanic pile:
Figure FDA0003919581250000035
3. the method of claim 1, wherein: fuel cell operating temperature T determined by Lagrange multiplier method stack And operating humidity RH stack And the output voltage U is the optimum operating condition of the electric pile under the power output required by the load, and the obtained temperature T stack Humidity RH stack And substituting the output voltage U into the formula (5) to calculate the power generation efficiency of the fuel cell under the current power output.
CN202211354433.8A 2022-11-01 2022-11-01 Operation condition optimizing method for improving power generation efficiency of fuel cell Pending CN115911468A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117048435A (en) * 2023-10-11 2023-11-14 南方电网电力科技股份有限公司 Coordinated control method for power supply of multiple fuel cells and related device

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117048435A (en) * 2023-10-11 2023-11-14 南方电网电力科技股份有限公司 Coordinated control method for power supply of multiple fuel cells and related device
CN117048435B (en) * 2023-10-11 2024-01-26 南方电网电力科技股份有限公司 Coordinated control method for power supply of multiple fuel cells and related device

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