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

Abstract

The invention discloses an adaptive matching modeling method for a fuel cell air compressor based on a stochastic optimization algorithm. The set of parameters to be determined in the simulation model of the air compressor is represented by α, and the parameters to be determined in the simulation model of the fuel cell stack are represented by α. The set is denoted by β. Taking the parameters to be determined as input, and the predicted air compressor power, fuel cell voltage, reversible voltage, and stack power as output, the fitness function in the stochastic optimization algorithm is constructed based on the system efficiency. Find the optimal solution of α and β, make the constructed fitness function F maximum, and complete the adaptive matching of fuel cells and air compressors in any system output power range. A good match of the air supply system to the fuel cell is the object and ultimate goal of the present invention. The research process of traditional matching strategy requires a large number of experiments or simulation operations to complete the matching process, and consumes a lot of manpower and experimental funds. The invention has high matching efficiency, and the whole optimization process can be automatically realized by using the written program.

Description

Matching modeling method of fuel cell and air compressor based on stochastic optimization algorithm

technical field

The invention belongs to the field of fuel cells, and in particular relates to a modeling method for adaptively matching a fuel cell system and an air compressor in an air supply subsystem.

Background technique

Polymer electrolyte membrane fuel cells (PEMFCs), which generate electricity through the electrochemical reaction of hydrogen and oxygen, are considered to be one of the most potential automotive energy conversion devices due to their advantages of zero pollution, low energy consumption, and long range. The integrated vehicle fuel cell system includes an air supply subsystem, a hydrogen supply subsystem, a temperature and humidifier subsystem, and a fuel cell stack. As the most important component in the air supply subsystem, the air compressor (referred to as the air compressor) has an important influence on the performance of the fuel cell system. The air compressor is a relatively slow-response mechanical device, and there will be a large time delay during the air supply process. When the load condition changes suddenly, it may interrupt the cathode oxygen deficiency, which will further cause the battery output voltage to drop, and even Accelerated decay of fuel cell life. During the operation of the fuel cell system, it is necessary to ensure a reasonable matching state of the air supply pressure and flow of the air compressor, so that the fuel cell system can maintain a high-efficiency operating state. The matching between the air compressor and the fuel cell is mainly that the air compressor provides an appropriate amount of compressed air to the fuel cell at a certain speed according to the different output power requirements of the fuel cell, so that the fuel cell system has a high output efficiency.

In order to obtain a high-performance fuel cell system, some researchers are currently researching the design method of the fuel cell gas supply system controller to control the oxygen excess ratio of the gas supply system in a short time. The main object of these studies is the transient control of (fuel cell) stacks in short-term operating conditions, and there is no research on stacks and systems in the whole life cycle from the perspective of the design and matching of the air supply system. The good match between the air supply system and the fuel cell is the fundamental purpose and ultimate goal of the system design and development. The present invention proposes for the first time that under different output powers, aiming at the highest efficiency of the fuel cell system, the air compressor and the fuel cell are established in combination with the stochastic optimization algorithm. The system adaptively matches the mathematical model, thereby providing design goals for the design and optimization of centrifugal air compressors.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a method for adaptive matching modeling of an air compressor and a fuel cell system (in the air supply subsystem) based on a stochastic optimization algorithm. During the operation of the on-board fuel cell system, a reasonable air compressor supply pressure, rotation speed and flow rate are matched according to the battery state, so that the fuel cell system maintains a high-efficiency operating state.

The fuel cell and air compressor matching modeling method based on stochastic optimization algorithm involves an air compressor simulation model and a fuel cell stack simulation model, and establishes an adaptive matching relationship between the two simulation models.

Specifically: the set of parameters to be determined involved in the air compressor simulation model is represented by α, the parameter to be determined is the input; the predicted air compressor power is the output, and the function expression of the air compressor simulation model is:

P _cp =CM(α) (1)

The set of parameters to be determined involved in the fuel cell stack simulation model is represented by β, and the parameters to be determined are used as input; the fuel cell voltage, reversible voltage, and fuel cell stack power predicted by the fuel cell stack simulation model are output. The functional expression of the battery stack simulation model is:

(V,E _rev ,P _fc )=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 power consumption of the air compressor:

(V,E _rev ,P _fc )=FM(β) (3)

Based on the output efficiency of the PEMFC system, the fitness function in the stochastic optimization algorithm is constructed, and penalty constraints are added to the fitness function, and the individuals generated in the stochastic optimization algorithm that do not meet the constraints are eliminated. The penalty constraints include the output power range of the polymer electrolyte membrane fuel cell system and the stoichiometric ratio of the cathode, and the range of the stoichiometric ratio of the cathode is set as: 1.2-4.0. The output power interval of the polymer electrolyte membrane fuel cell system is based on the upper and lower boundary power of the interval set according to the demand, and the expression of the fitness function F:

In the formula, ST _c is the cathode stoichiometric ratio; P _{upper boundary} and P _{lower boundary} represent the upper and lower boundary powers of the output power range of the fuel cell system.

Using the stochastic optimization algorithm, find the optimal solution of α and β, so that the constructed fitness function F is the smallest. At this time, the obtained α is the optimization result of the operating parameters of the air compressor, and the obtained β is the optimization result of the operating parameters of the fuel cell stack, so as to complete the adaptive matching process of the fuel cell and the air compressor in different output power ranges. .

Further: Available stochastic optimization algorithms include: genetic algorithm, stochastic particle swarm optimization, and simulated annealing algorithm.

The features and beneficial effects of the invention are as follows: the proposed adaptive optimization matching method utilizes the combination of the fuel cell-air compressor system simulation model and the stochastic optimization algorithm, which can realize the matching of the methods involved in the vehicle-mounted polymer electrolyte membrane fuel cell system model. The parameters to be determined by the battery and the air compressor are optimized and estimated to complete the matching of the fuel cell and the air compressor in any system output power range. The good matching of the air supply system and the fuel cell is the fundamental purpose and ultimate goal of the system design and development. This method does not require the user to have in-depth experience and knowledge of the model; at the same time, the efficiency is very high. Automatic realization; the research process of traditional matching strategy requires researchers to conduct a large number of experiments or simulation operations, and complete the matching process according to a large number of attempts, which requires a lot of manpower and experimental funds.

Description of drawings

FIG. 1 is a simulation result of an embodiment of the present invention without using the adaptive matching method.

FIG. 2 is a simulation result after optimization by an adaptive matching method according to an embodiment of the present invention.

FIG. 3 is the matching result of the current density I of the fuel cell under different output powers according to the embodiment of the present invention.

FIG. 4 is the matching result of the rotational speed N of the air compressor under different output powers according to the embodiment of the present invention.

FIG. 5 is the matching result of the air compressor output air pressure p _cp under different output powers according to the embodiment of the present invention.

FIG. 6 is the matching result of the air compressor mass flow m _cp under different output powers according to the embodiment of the present invention.

Detailed ways

The method and modeling calculation process of the present invention will be further described below through specific embodiments. It should be noted that this embodiment is descriptive rather than restrictive, and does not limit the protection scope of the present invention.

The fuel cell stack simulation model and the air compressor simulation model in this embodiment are non-limiting. By optimizing the parameters to be determined in the simulation model, under the condition of the full output power of the PEMFC system, the fuel cell and air compressor status to match.

The specific process for realizing adaptive matching of two simulation models in this embodiment is as follows:

The set α of the parameters to be determined in the air compressor simulation model and the parameter β to be determined in the fuel cell stack simulation model can be expressed as:

α=(N,p _cp ,m _cp ) (5)

β=(I) (6)

Among them, N is the rotational speed of the air compressor, _pcp is the air compressor pressure ratio, _mcp is the air compressor mass flow, and I is the fuel cell startup current density.

Taking the set α of the parameters to be determined in the air compressor simulation model as the input, and the air compressor power as the output, the function expression of the air compressor simulation model is:

P _cp =CM(α) (1)

The set β of parameters to be determined involved in the fuel cell stack simulation model is used as input, the fuel cell voltage, reversible voltage, and fuel cell stack power predicted by the battery model are output, and the functional expression of the fuel cell stack simulation model is: :

(V,E _rev ,P _fc )=FM(β) (2)

The output power of the system is the difference between the output power of the fuel cell and the parasitic power consumption of the air compressor:

P=P _fc -P _cp (3)

In this method, the output efficiency of the fuel cell system of the simulation model is used to construct the fitness function in the stochastic optimization algorithm. The expression of the fitness function is:

In the formula, P _{lower boundary} is the lower boundary power of the required power interval; P _{upper boundary} is the upper boundary power of the power interval. Taking the values of P _{lower boundary} and P _{upper boundary} as 20kW and 25kW, respectively, as an example, use the genetic algorithm tool in Matlab to calculate the maximum fitness function F, and obtain the parameters of the fuel cell and air compressor simulation model to be determined. The estimated results are as follows:

N=31139r min ^-1 , p _cp =1.2441 atm, m _cp =12.5684 gs ^-1 , I=2321.1 A m ^-2 .

The same method is used to obtain the values of P _{lower boundary} and P _{upper boundary} multiple times, and the parameters to be determined are calculated to obtain the efficiency optimization result of the fuel cell system under full power, as shown in Figure 2.

Figures 1 and 2 are the simulation results without optimal matching and the simulation results after optimal matching using this method, respectively. Through the simulation results, it is found that taking the output power of the fuel cell system as an example of 4.99kW, the efficiency of the fuel cell system without optimization is 0.7353, and after optimization and matching, the efficiency is 0.7882. Through calculation, the system efficiency after optimization and matching can be increased by an average of 3.8% in the full power range of the fuel cell system, which is a very significant improvement, which can effectively improve the system output performance and avoid additional consumption. Therefore, using this method to optimize matching has high practical value.

Figure 3 shows the matching results of the current density of the fuel cell with I at different output powers.

Figure 4 shows the matching results of the air compressor rotational speed N under different output powers.

Figure 5 shows the matching results of air compressor air pressure p _cp under different output powers.

Figure 6 shows the matching results of the air compressor mass flow m _cp under different output powers.

By comparison, it can be seen that the effective adaptive matching optimization of the two models can greatly improve the efficiency of the PEMFC system, which can effectively improve the system output performance and avoid additional consumption. The effectiveness of the optimal matching method proposed by the present invention is proved.

The calculation process using the PEMFC system simulation model in the present embodiment is as follows:

Fuel cell stack output power:

P _fc =V×N×I×A _act (7)

In the formula, V represents the output voltage of the fuel cell; N represents the number of fuel cells in the fuel cell stack, and the value in this example is ₃₇₀ ; I represents the current ^density ;

The output voltage of the fuel cell can be expressed as:

V=E _rev -η _ohm -η _act,a -η _act,c (8)

In the formula, E _rev represents the reversible voltage; η _ohm represents the ohmic loss of the voltage; η _act represents the activation loss of the voltage. The ohmic loss and activation loss include the voltage loss caused by the concentration of reactants and water loss.

The reversible voltage is obtained from the Nernst equation:

分别为阳极催化层氢气压力和阴极催化层氧气压力。where E _rev is the reversible voltage; ΔG is the Gibbs free energy change; F is the Faraday constant; ΔS is the entropy change; R is the ideal gas constant; T is the operating temperature; T _ref is the reference temperature;

are the hydrogen pressure of the anode catalytic layer and the oxygen pressure of the cathode catalytic layer, respectively.

Ohmic loss calculation:

分别为流道极板和多孔介质各层传输电子的面电阻；

分别为催化层和质子交换膜内传输质子的面电阻。where η _ohm,P , η _{ohm, por} and η _ohm,m are the ohmic losses caused by the polar plate, the porous dielectric layer and the proton exchange membrane, respectively; I is the current density;

are the surface resistances of the flow channel plate and each layer of the porous medium transporting electrons, respectively;

are the sheet resistances of the transported protons in the catalytic layer and the proton exchange membrane, respectively.

Solving calculation of activation loss:

分别为参考氢气浓度和参考氧气浓度。where η _act,a and η _act,c represent the anodic and cathodic activation overpotentials, respectively; α is the charge transfer coefficient; n is the number of electrons transported in a unit reaction; j _0,ref is the reference current density;

are the reference hydrogen concentration and the reference oxygen concentration, respectively.

The air compressor simulation model used in this example is established based on the mass flow characteristics of the air compressor. The formula for calculating the molar flow rate (mol s ^-1 ) of oxygen at the inlet of the single cell of the air compressor simulation model is:

代表燃料电池入口的氧气流量；m_air(kg s^-1)代表空压机输出的空气质量流量；M_air(kg mol^-1)代表空气摩尔质量；N代表电堆中单体电池数量。In the formula,

represents the oxygen flow at the fuel cell inlet; m _air (kg s ^-1 ) represents the air mass flow output by the air compressor; M _air (kg mol ^-1 ) represents the air molar mass; N represents the number of single cells in the stack.

A polynomial fit was applied to derive the functional relationship between oxygen flow, pressure ratio and rotational speed from a large number of sample data. In order to improve the accuracy of fitting, the rotational speed and pressure of the sample are centralized, and the fitting formula is:

It should be noted that the above fitting results include the surge working area and the area exceeding the maximum flow rate, so the surge line and the maximum flow line are fitted for the air compressor boundary:

The functional relationship between air compressor efficiency, oxygen flow ratio and rotational speed:

The compression process of a centrifugal air compressor is regarded as an isentropic process, and the power calculation of the air compressor is as follows:

In the formula, _cp (J kg ^-1 K ^-1 ) is the specific heat capacity of air, and γ is the specific heat ratio coefficient of air.

The present invention utilizes the fuel cell stack simulation model and the air compressor simulation model to optimize and estimate the to-be-determined parameters of the two simulation models, so as to realize the on-board polymer electrolyte membrane fuel cell system in any system output power range, and the fuel cell And the matching of the air compressor.

The above analysis and calculation shows that based on the adaptive optimization matching method, combined with the system simulation model of the fuel cell-air compressor and the stochastic optimization algorithm, the parameters to be determined involved in the simulation model of the PEMFC system can be optimized and estimated, so as to complete the optimization and estimation of the parameters involved in the simulation model of the PEMFC system. Output power range, matching of fuel cells and air compressors. The good matching of the air supply system and the fuel cell is the fundamental purpose and ultimate goal of the system design and development. This method does not require the user to have in-depth experience and knowledge of the model; at the same time, the efficiency is very high. Automatic realization; the research process of traditional matching strategy requires researchers to conduct a large number of experiments or simulation operations, and complete the matching process according to a large number of attempts, which requires a lot of manpower and experimental funds.

Claims (3)

1. A fuel cell and air compressor matching modeling method based on a stochastic optimization algorithm, involving an air compressor simulation model and a fuel cell stack simulation model, characterized in that: establishing an air compressor simulation model and a fuel cell stack simulation model From the adaptive matching relationship, the set of parameters to be determined involved in the air compressor simulation model is represented by α, and the parameter to be determined is the input; the predicted air compressor power is the output, and the function expression of the air compressor simulation model is : P _cp =CM(α) (1) In the formula, P _cp is the power of the air compressor; the set of parameters to be determined involved in the fuel cell stack simulation model is represented by β, and the parameters to be determined are input; the fuel cell voltage predicted by the fuel cell stack simulation model, The reversible voltage and fuel cell stack power are output, and the functional expression of the fuel cell stack simulation model is: (V,E _rev ,P _fc )=FM(β) (2) where V is the fuel cell voltage; E _rev is the Nernst voltage; P _fc is the fuel cell stack power; The output power of the fuel cell system is the difference between the output power of the fuel cell stack and the power consumption of the air compressor: P=P _fc -P _cp (3) In the formula, P is the power of the fuel cell system; P _fc is the power of the fuel cell stack; P _cp is the power consumption of the air compressor, The fitness function in the stochastic optimization algorithm is constructed based on the output efficiency of the polymer electrolyte membrane fuel cell system, and penalty constraints are added to the fitness function, so that the individuals generated in the stochastic optimization algorithm that do not meet the constraints are eliminated. The penalty constraints include The output power range of the polymer electrolyte membrane fuel cell system and the stoichiometric ratio of the cathode, the stoichiometric ratio range of the cathode is set to: 1.2-4.0, the output power range of the fuel cell system is set according to the needs of the upper and lower boundary power of the range, and the expression of the fitness function Mode:

In the formula, ST _c is the cathode stoichiometric ratio; P _{upper boundary} and P _{lower boundary} represent the upper and lower boundary powers of the output power range of the fuel cell system, Use the stochastic optimization algorithm to find the optimal solutions of α and β, so that the constructed fitness function F is the smallest. At this time, the obtained α is the air compressor operating condition parameter optimization result, and the obtained β is the operation of the fuel cell stack. Parameter optimization results are used to complete the adaptive matching process of fuel cells and air compressors in different output power ranges. 2. The matching modeling method for a fuel cell and an air compressor based on a stochastic optimization algorithm according to claim 1, characterized in that: the set α of the parameters to be determined involved in the air compressor simulation model, the function expression of which is The formula is: α=(N,p _cp ,m _cp ) (5) Wherein: N is the rotational speed of the air compressor, p _cp is the air compressor pressure ratio, m _cp is the air compressor mass flow; the set β of the parameters to be determined involved in the fuel cell stack simulation model, its function expression for: β=(I) (6) Where: I is the starting current density of the fuel cell. 3 . The matching modeling method for fuel cells and air compressors based on a stochastic optimization algorithm according to claim 1 , wherein the stochastic optimization algorithm comprises: a genetic algorithm, a stochastic particle swarm algorithm, and a simulated annealing algorithm. 4 .

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