CN114530618A - Random optimization algorithm-based fuel cell and air compressor matching modeling method - Google Patents

Random optimization algorithm-based fuel cell and air compressor matching modeling method Download PDF

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CN114530618A
CN114530618A CN202210058602.7A CN202210058602A CN114530618A CN 114530618 A CN114530618 A CN 114530618A CN 202210058602 A CN202210058602 A CN 202210058602A CN 114530618 A CN114530618 A CN 114530618A
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焦魁
宫智超
王博文
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Abstract

The invention discloses a fuel cell air compressor self-adaptive matching modeling method based on a random optimization algorithm, wherein a set of parameters to be determined in an air compressor simulation model is represented by alpha, and a set of parameters to be determined in a fuel cell stack simulation model is represented by beta. And taking the parameters to be determined as input, and the predicted air compressor power, the fuel cell voltage, the reversible voltage and the electric pile power as output, and constructing a fitness function in a random optimization algorithm by using the system efficiency. And searching the optimal solution of alpha and beta to maximize the constructed fitness function F, and completing the self-adaptive matching of the fuel cell and the air compressor in any system output power interval. A good match of the air supply system to the fuel cell is the object and final goal of the invention. In the research process of the traditional matching strategy, a large number of experiments or simulation operations are required to try to complete the matching process, and a large amount of manpower and experiment expenses are required to be consumed. The invention has high matching efficiency, and the whole optimization process can be automatically realized by utilizing the written program.

Description

Random optimization algorithm-based fuel cell and air compressor matching modeling method
Technical Field
The invention belongs to the field of fuel cells, and particularly relates to a modeling method for adaptively matching an air compressor in a fuel cell system and an air supply subsystem.
Background
Polymer Electrolyte Membrane Fuel Cells (PEMFCs) generate electrical energy through an electrochemical reaction of hydrogen and oxygen, and are considered to be one of the most potential automotive energy conversion devices due to their advantages of zero pollution, low energy consumption, long range, and the like. An integrated automotive fuel cell system includes an air supply subsystem, a hydrogen supply subsystem, a temperature and humidifier subsystem, and a fuel cell stack. An air compressor (air compressor for short) is the most important component in an air supply subsystem, and has an important influence on the performance of a fuel cell system. The air compressor is a mechanical device with relatively slow response, large time delay is generated in the air supply process, and when the load working condition is suddenly changed, the cathode is possibly interrupted to lack oxygen, so that the output voltage of the battery is further reduced, and the service life of the fuel battery is even accelerated to be shortened. In the operation process of the fuel cell system, a reasonable matching state of air supply pressure and flow of the air compressor needs to be ensured, so that the fuel cell system keeps a high-efficiency operation state. The matching between the air compressor and the fuel cell is mainly that the air compressor provides a proper amount of compressed air for the fuel cell at a certain rotating speed according to different output power requirements of the fuel cell, so that the fuel cell system has higher output efficiency.
In order to obtain a high-performance fuel cell system, some researchers have studied a design method of a fuel cell gas supply system controller to control an oxygen excess ratio of a gas supply system in a short time. The main object of these studies is (fuel cell) stack transient control during short-term conditions, without full life-cycle stack and system studies from the design and matching of air supply systems. The invention provides a method for establishing a system self-adaptive matching mathematical model of an air compressor and a fuel cell by combining a random optimization algorithm under different output powers and taking the highest efficiency of the fuel cell system as a target for the first time, thereby providing a design target for the design and optimization of a centrifugal air compressor.
Disclosure of Invention
The invention aims to provide a method for modeling an air compressor (in an air supply subsystem) and a fuel cell system in a self-adaptive matching mode based on a random optimization algorithm. In the running process of the vehicle-mounted fuel cell system, reasonable air supply pressure, rotating speed and flow of the air compressor are matched according to the state of the battery, so that the fuel cell system keeps a high-efficiency running state.
A fuel cell and air compressor matching modeling method based on a random optimization algorithm relates to an air compressor simulation model and a fuel cell stack simulation model, and establishes a self-adaptive matching relation between the two simulation models.
The method specifically comprises the following steps: the set of parameters to be determined related in the air compressor simulation model is represented by alpha, and the parameters to be determined are input; the predicted air compressor power is output, and the function expression of the air compressor simulation model is as follows:
Pcp＝CM(α) (1)
the set of parameters to be determined related in the fuel cell stack simulation model is represented by beta, and the parameters to be determined are input; the fuel cell voltage, the reversible voltage and the fuel cell stack power predicted by the fuel cell stack simulation model are output, and the function expression of the fuel cell stack simulation model is as follows:
(V,Erev,Pfc)＝FM(β) (2)
the output power of the fuel cell system is the difference between the output power of the fuel cell stack and the consumed power of the air compressor:
(V,Erev,Pfc)＝FM(β) (3)
and constructing a fitness function in the random optimization algorithm according to the output efficiency of the PEMFC system, adding a punishment constraint condition into the fitness function, and eliminating individuals which do not meet the constraint condition and are generated in the random optimization algorithm. The penalty constraint condition comprises a polymer electrolyte membrane fuel cell system output power interval and a cathode stoichiometric ratio, and the cathode stoichiometric ratio interval is set as follows: 1.2-4.0. The output power interval of the polymer electrolyte membrane fuel cell system is set according to the upper and lower boundary powers of the interval and the expression of a fitness function F:
Figure BDA0003468448010000021
in the formula, STcIs the cathode stoichiometric ratio; pupper boundaryAnd Plower boundaryAnd upper and lower boundary powers representing an output power interval of the fuel cell system.
And searching the optimal solution of alpha and beta by using a random optimization algorithm so as to minimize the constructed fitness function F. And the obtained alpha is the optimizing result of the working condition parameters of the air compressor, and the obtained beta is the optimizing result of the operating parameters of the fuel cell stack, so that the self-adaptive matching process of the fuel cell and the air compressor in different output power intervals is completed.
Further: available stochastic optimization algorithms include: genetic algorithms, random particle swarm algorithms, and simulated annealing algorithms.
The invention has the characteristics and beneficial effects that: the self-adaptive optimization matching method can optimize and estimate parameters to be determined of the fuel cell and the air compressor related in the vehicle-mounted polymer electrolyte membrane fuel cell system model by combining the fuel cell-air compressor system simulation model and the random optimization algorithm, so that matching of the fuel cell and the air compressor in any system output power interval is completed. The good matching of the air supply system and the fuel cell is the fundamental aim and the final aim of the system design and development, and the method does not need deep experience knowledge of a model of a user; meanwhile, the efficiency is very high, and the whole optimization matching process can be automatically realized by using a written program; the research process of the traditional matching strategy requires a researcher to perform a large number of experiments or simulation operations, and the matching process is completed according to a large number of attempts, which consumes a large amount of manpower and experiment expenses.
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Fig. 1 shows simulation results of the embodiment of the present invention without using the adaptive matching method.
FIG. 2 shows simulation results after the embodiment of the present invention adopts the adaptive matching method.
Figure 3 shows the matching results of the current density I of the fuel cell at different output powers according to the embodiment of the present invention.
Fig. 4 shows the matching result of the air compressor rotation speed N under different output powers according to the embodiment of the present invention.
FIG. 5 shows the output air pressure p of the air compressor under different output powers according to the embodiment of the present inventioncpThe matching result of (1).
FIG. 6 shows mass flow m of air compressor under different output powers according to the embodiment of the present inventioncpThe matching result of (1).
Detailed Description
The method and modeling calculation process of the present invention are further described by the following specific examples, which should be construed as illustrative and not limiting, and the scope of the present invention is not limited thereby.
The fuel cell stack simulation model and the air compressor simulation model in the embodiment are non-limiting, and the states of the fuel cell and the air compressor are matched under the condition of full output power of the PEMFC system by optimizing parameters to be determined in the simulation model.
The specific process for realizing the adaptive matching of the two simulation models in the embodiment is as follows:
the set alpha of the parameters to be determined in the air compressor simulation model and the parameter beta to be determined in the fuel cell stack simulation model can be expressed as follows:
α＝(N,pcp,mcp) (5)
β＝(I) (6)
wherein N is the rotating speed p of the air compressorcpIs the pressure ratio m of the air compressorcpAnd I is the mass flow of the air compressor, and I is the starting current density of the fuel cell.
Taking a set alpha of parameters to be determined of the air compressor simulation model as input, taking the power of an air compressor as output, and taking a function expression of the air compressor simulation model as follows:
Pcp＝CM(α) (1)
taking a set beta of parameters to be determined related in a fuel cell stack simulation model as input, taking fuel cell voltage, reversible voltage and fuel cell stack power predicted by a cell model as output, wherein a function expression of the fuel cell stack simulation model is as follows:
(V,Erev,Pfc)＝FM(β) (2)
the system output power is the difference between the output power of the fuel cell and the parasitic power consumption of the air compressor:
P＝Pfc-Pcp (3)
the method constructs a fitness function in a random optimization algorithm according to the output efficiency of a fuel cell system of a simulation model, wherein the fitness function has an expression as follows:
Figure BDA0003468448010000041
in the formula Plower boundaryThe lower boundary power of the required power interval; pupper boundaryThe upper bound power of the power interval. With Plower boundaryAnd Pupper boundaryTaking 20kW and 25kW as examples for operation, calculating to enable the constructed fitness function F to be maximum by utilizing a genetic algorithm tool in Matlab, and obtaining the estimation results of the parameters to be determined of the fuel cell and air compressor simulation model as follows:
N＝31139r min-1,pcp＝1.2441atm,mcp＝12.5684g s-1,I＝2321.1A m-2。
using the same method for Plower boundaryAnd Pupper boundaryAnd (3) carrying out value taking for multiple times, and calculating parameters to be determined to obtain an efficiency optimization result of the fuel cell system under full power, as shown in figure 2.
Fig. 1 and fig. 2 show the simulation result without optimization matching and the simulation result after optimization matching by using the method, respectively. According to the simulation result, the fuel cell system efficiency which is not optimized is 0.7353, and the efficiency after optimization matching is 0.7882, taking the output power of the fuel cell system as 4.99kW as an example. Through calculation, the system efficiency after optimization and matching is improved by 3.8 percent in the full-power range of the fuel cell system, so that the system output performance can be effectively improved, and extra consumption is avoided. Therefore, the method has high practical value in optimizing and matching.
Fig. 3 shows the results of matching the current densities of fuel cells with I at different output powers.
Fig. 4 shows the matching result of the air compressor rotation speed N under different output powers.
FIG. 5 shows the air pressure p of the air compressor at different output powerscpThe matching result of (1).
FIG. 6 shows mass flow m of air compressor at different output powerscpThe matching result of (1).
Through comparison, it can be seen that through the effective adaptive matching optimization of the two models, the efficiency of the PEMFC system is greatly improved, the output performance of the system can be effectively improved, and extra consumption is avoided. The effectiveness of the optimized matching method provided by the invention is proved.
In this embodiment, the calculation process using the PEMFC system simulation model is as follows:
output power of fuel cell stack:
Pfc＝V×N×I×Aact (7)
wherein V represents the fuel cell output voltage; n represents the number of fuel cells in the fuel cell stack, and the numerical value of this example is 370; i represents a current density; a. theactThe activation area is shown, and the value is 300cm-2。
The output voltage of the fuel cell can be expressed as:
V＝Erev-ηohm-ηact,a-ηact,c (8)
in the formula ErevRepresents a reversible voltage; etaohmOhmic losses representing voltage; etaactThe voltage activation loss is expressed, and the ohmic loss and the activation loss include voltage loss due to the reactant concentration and water loss.
The reversible voltage is obtained by the nernst equation:
Figure BDA0003468448010000051
in the formula ErevIs a reversible voltage; Δ G is the Gibbs free energy change; f is a Faraday constant; Δ S is entropy change; r is an ideal gas constant; t is the working condition temperature; t is a unit ofrefIs a reference temperature;
Figure BDA0003468448010000052
the anode catalytic layer hydrogen pressure and the cathode catalytic layer oxygen pressure are respectively.
Ohmic loss calculation:
Figure BDA0003468448010000053
in the formula etaohm,P、ηohm,porAnd ηohm,mOhmic losses caused by the polar plate, the porous medium layer and the proton exchange membrane respectively; i is the current density;
Figure BDA0003468448010000054
the surface resistances are respectively used for transmitting electrons for the flow channel polar plate and each layer of the porous medium;
Figure BDA0003468448010000055
respectively the area resistance of the catalytic layer and the proton exchange membrane for transferring the protons.
Solution calculation of activation loss:
Figure BDA0003468448010000056
Figure BDA0003468448010000061
wherein etaact,a、ηact,cRespectively generation by generationSurface anode and cathode activation overpotentials; α is the charge transfer coefficient; n is the number of electrons transmitted in a unit reaction; j is a unit of a group0,refIs a reference current density;
Figure BDA0003468448010000062
reference hydrogen concentration and reference oxygen concentration, respectively.
The air compressor simulation model applied in the embodiment is established according to the mass flow characteristic of the air compressor, and the molar flow (mol s) of oxygen at the inlet of the single battery of the air compressor simulation model-1) Calculating the formula:
Figure BDA0003468448010000063
in the formula (I), the compound is shown in the specification,
Figure BDA0003468448010000064
representing the oxygen flow at the inlet of the fuel cell; m is a unit ofair(kg s-1) Representing the mass air flow output by the air compressor; mair(kg mol-1) Represents the air molar mass; and N represents the number of single batteries in the electric pile.
And applying polynomial fitting to deduce a functional relation among the oxygen flow, the pressure ratio and the rotating speed according to a large amount of sample data. In order to improve the accuracy of fitting, the rotating speed and the pressure of the sample are both subjected to centralization treatment, and a fitting formula is as follows:
Figure BDA0003468448010000065
it should be noted that the fitting result includes the surge operating region and the excess maximum flow region, so the surge line and the maximum flow line are fitted to the boundary of the air compressor:
Figure BDA0003468448010000066
the functional relationship among the efficiency of the air compressor, the oxygen flow rate ratio and the rotating speed is as follows:
Figure BDA0003468448010000067
the compression process of the centrifugal air compressor is regarded as an isentropic process, and the power of the air compressor is calculated as follows:
Figure BDA0003468448010000071
in the formula, cp(J kg-1K-1) γ represents a specific heat capacity coefficient of air.
The invention utilizes the fuel cell stack simulation model and the air compressor simulation model to realize the matching of the vehicle-mounted polymer electrolyte membrane fuel cell system to the fuel cell and the air compressor in any system output power interval by optimizing and estimating the parameters to be determined of the two simulation models.
The analysis and calculation are based on a self-adaptive optimization matching method, and parameters to be determined related to a PEMFC system simulation model can be optimized and estimated by combining a fuel cell-air compressor system simulation model and a random optimization algorithm, so that matching of the fuel cell and the air compressor in any system output power interval is completed. The good matching of the air supply system and the fuel cell is the fundamental aim and the final aim of the system design and development, and the method does not need deep experience knowledge of a model of a user; meanwhile, the efficiency is very high, and the whole optimization matching process can be automatically realized by using a written program; the research process of the traditional matching strategy requires a researcher to perform a large number of experiments or simulation operations, and the matching process is completed according to a large number of attempts, which consumes a large amount of manpower and experiment expenses.

Claims (3)

1. A fuel cell and air compressor matching modeling method based on a random optimization algorithm relates to an air compressor simulation model and a fuel cell stack simulation model, and is characterized in that: establishing a self-adaptive matching relation between an air compressor simulation model and a fuel cell stack simulation model, expressing a set of parameters to be determined related in the air compressor simulation model by alpha, and taking the parameters to be determined as input; the predicted air compressor power is output, and the function expression of the air compressor simulation model is as follows:
Pcp＝CM(α) (1)
in the formula, PcpThe power of the air compressor; the set of parameters to be determined related in the fuel cell stack simulation model is represented by beta, and the parameters to be determined are input; the fuel cell voltage, the reversible voltage and the fuel cell stack power predicted by the fuel cell stack simulation model are output, and the function expression of the fuel cell stack simulation model is as follows:
(V,Erev,Pfc)＝FM(β) (2)
wherein V is the fuel cell voltage; erevIs a Nernst voltage; pfcPower for the fuel cell stack;
the output power of the fuel cell system is the difference between the output power of the fuel cell stack and the consumed power of the air compressor:
P＝Pfc-Pcp (3)
wherein, P is the power of the fuel cell system; pfcIs fuel cell stack power; pcpIn order to consume the power of the air compressor,
constructing a fitness function in a random optimization algorithm by using the output efficiency of the polymer electrolyte membrane fuel cell system, and adding a punishment constraint condition into the fitness function, so as to eliminate individuals which do not meet the constraint condition and are generated in the random optimization algorithm, wherein the punishment constraint condition comprises an output power interval of the polymer electrolyte membrane fuel cell system and the stoichiometric ratio of a cathode, and the stoichiometric ratio interval of the cathode is set as: 1.2-4.0, setting the upper and lower boundary power of the interval according to the requirement in the output power interval of the fuel cell system, and expressing the fitness function:
Figure FDA0003468441000000011
in the formula, STcIs the cathode stoichiometric ratio; pupper boundaryAnd Plower boundaryUpper and lower boundary powers representing an output power interval of the fuel cell system,
and searching for optimal solutions of alpha and beta by using a random optimization algorithm to minimize the constructed fitness function F, wherein the obtained alpha is an optimization result of the working condition parameters of the air compressor, and the obtained beta is an optimization result of the operating parameters of the fuel cell stack, so that the self-adaptive matching process of the fuel cell and the air compressor in different output power intervals is completed.
2. The fuel cell and air compressor matching modeling method based on the stochastic optimization algorithm as claimed in claim 1, wherein the method comprises the following steps: the function expression of the set alpha of the parameters to be determined related in the air compressor simulation model is as follows:
α＝(N,pcp,mcp) (5)
wherein: n is the rotating speed p of the air compressorcpIs the pressure ratio m of the air compressorcpMass flow of the air compressor; the functional expression of the set beta of the parameters to be determined related in the fuel cell stack simulation model is as follows:
β＝(I) (6)
wherein: and I is the starting current density of the fuel cell.
3. The fuel cell and air compressor matching modeling method based on the stochastic optimization algorithm as claimed in claim 1, wherein the method comprises the following steps: the stochastic optimization algorithm comprises: genetic algorithms, random particle swarm algorithms, and simulated annealing algorithms.
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