CN117195530A - Modeling optimization method of fuel cell cooling system simulation model - Google Patents
Modeling optimization method of fuel cell cooling system simulation model Download PDFInfo
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- CN117195530A CN117195530A CN202311116006.0A CN202311116006A CN117195530A CN 117195530 A CN117195530 A CN 117195530A CN 202311116006 A CN202311116006 A CN 202311116006A CN 117195530 A CN117195530 A CN 117195530A
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- 239000000446 fuel Substances 0.000 title claims abstract description 94
- 238000001816 cooling Methods 0.000 title claims abstract description 90
- 238000004088 simulation Methods 0.000 title claims abstract description 49
- 238000000034 method Methods 0.000 title claims abstract description 46
- 238000005457 optimization Methods 0.000 title claims abstract description 18
- 238000005070 sampling Methods 0.000 claims abstract description 32
- 230000004044 response Effects 0.000 claims abstract description 30
- 238000004364 calculation method Methods 0.000 claims abstract description 29
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- 238000011161 development Methods 0.000 claims description 4
- 230000008569 process Effects 0.000 description 10
- 239000007789 gas Substances 0.000 description 6
- 238000009423 ventilation Methods 0.000 description 6
- 239000000110 cooling liquid Substances 0.000 description 5
- 230000008901 benefit Effects 0.000 description 4
- 238000003487 electrochemical reaction Methods 0.000 description 4
- 239000007788 liquid Substances 0.000 description 4
- 239000012530 fluid Substances 0.000 description 3
- 230000004913 activation Effects 0.000 description 2
- 238000006243 chemical reaction Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000017525 heat dissipation Effects 0.000 description 2
- 230000002427 irreversible effect Effects 0.000 description 2
- 238000012544 monitoring process Methods 0.000 description 2
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
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- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 description 1
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- 239000003795 chemical substances by application Substances 0.000 description 1
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Abstract
The application discloses a modeling optimization method of a fuel cell cooling system simulation model, which specifically comprises the steps of firstly establishing the fuel cell cooling system simulation model, determining input and output variables of the model, and distributing probability distribution associated with standard deviation for each variable by adopting a Monte Carlo calculation method; the Monte Carlo calculation method adopts a Latin hypercube sampling mode, sets the upper and lower limit ranges of input and output variables, uniformly samples the input and output variables, and generates sampling data; based on the sampling data, creating a response surface model of the fuel cell cooling system, fitting an input and output relation by a polynomial function, and determining various coefficients of the polynomial function by adopting a least square method; adding a first-order delay link for characterizing system characteristics at the rear end of the response surface model, setting reasonable initial values and delay time, and realizing the creation of a complete proxy model; the method realizes model simplification, reduces simulation calculation time of the model and improves calculation efficiency.
Description
Technical Field
The application relates to the field of fuel cell control, in particular to a modeling optimization method of a fuel cell cooling system simulation model.
Background
The fuel cell uses hydrogen and oxygen as fuel, converts chemical energy in the fuel into electric energy through electrochemical reaction, has the advantages of high energy conversion efficiency, low operation noise, no environmental pollution and the like, and is widely applied to the fields of stationary power generation, new energy automobiles and the like. The fuel cell itself is a nonlinear, strongly coupled, complex dynamic system, and in particular the cooling system of the fuel cell involves coordinated operation of numerous components, which is more complex. In order to make intensive studies on a fuel cell cooling system, a simulation model that accurately describes the performance and the trend of variation thereof is established. However, in practical application, the simulation model of the cooling system is found to have the defects of relatively complex model, low calculation speed, no real-time operation function and the like.
In the prior art, the improvement of the simulation model precision and the matching of the operation conditions of the fuel cell cooling system are also limited in the establishment process of the fuel cell simulation model, the optimization of the model is not concerned, the simulation calculation time of the model is reduced, the protection of the physical equation and the modeling process of the model is not concerned, the proxy model based on a response surface is not developed, the proxy model is not used in the analysis and the research of the fuel cell cooling system, and the simulation model with a real-time operation function is not developed.
Disclosure of Invention
According to the problems existing in the prior art, the application discloses a modeling optimization method of a fuel cell cooling system simulation model, which specifically comprises the following steps:
establishing a fuel cell cooling system simulation model comprising a fuel cell stack model, a water pump model, a radiator fan model, a deionizer model, a filter model and an expansion water tank model according to an actual fuel cell cooling system;
determining boundary conditions of a simulation model of a fuel cell cooling system, taking a water pump rotating speed, a fan rotating speed and a pile current as input variables, taking a pile water inlet temperature, a pile water outlet temperature and a pile water flow as output variables, adopting a Monte Carlo calculation method to distribute probability distribution associated with standard deviation for each variable, adopting a Latin hypercube sampling mode, setting upper and lower limit ranges of the input variables and the output variables, uniformly sampling the input variables and the output variables, and generating sampling data;
based on the sampling data, a response surface model of the fuel cell cooling system is created, the response surface model fits an input and output relation through a polynomial function, each coefficient of the polynomial function is determined by adopting a least square method, a first-order delay link for representing the system characteristics is added at the rear end of the response surface model, a reasonable initial value and delay time are set, and a proxy model of the fuel cell cooling system is built.
And (3) performing virtual operation on the fuel cell cooling system in the early design stage, analyzing and researching the performance and the variation trend of the fuel cell cooling system, verifying the design scheme and guiding the development and the application of the fuel cell cooling system.
The input and output variables of the response surface model of the fuel cell cooling system are the same as the boundary dimensions of the simulation model of the fuel cell cooling system.
The response surface model determines polynomial coefficients by a least square method, and fits a numerical relationship between input and output.
The sampling data are acquired by a fuel cell cooling system simulation model, and various test data are obtained in a virtual mode.
The first-order delay link characterizes the dynamic characteristics of a real fuel cell cooling system, and reasonable initial values and delay time are required to be set according to the real fuel cell cooling system.
The response surface model is a proxy model for converting a complex simulation model into a numerical relation by utilizing virtual data obtained by the simulation model or test data of an actual fuel cell cooling system, and based on the obtained sampling data, a response surface model of the fuel cell cooling system is created, the response surface model is a polynomial model for describing algebraic relation between input and output, and a polynomial function between a plurality of inputs and a plurality of outputs is mapped, and a calculation formula is as follows:
where NMonomials is the term of the polynomial, coef is the fitting coefficient, offset is the offset, and orders is the order of the polynomial. Wherein the fitting coefficients are determined by the least squares method.
By adopting the technical scheme, the modeling optimization method of the fuel cell cooling system simulation model provided by the application has the advantages that the model is simplified, the simulation calculation time of the model is reduced, and the calculation efficiency is improved by establishing the fuel cell cooling system proxy model based on the response surface model on the premise that the model has higher precision; abundant test data are obtained by adopting a virtual means, so that necessary test times can be reduced, and test cost can be reduced; an online model with a real-time computing function is provided, and full virtual verification is performed in the early stage of design development and is used for real-time control of a system. The method can simplify the model, reduce the simulation calculation time of the model and improve the calculation efficiency on the premise of ensuring that the model has higher precision; intellectual property can be protected, and physical equations and modeling processes of the model are hidden; the adoption of the virtual means to obtain abundant test data has great significance in reducing the test cost.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings may be obtained according to the drawings without inventive effort to those skilled in the art.
FIG. 1 is a flow chart of the method of the present application
FIG. 2 is a graph showing comparison of the results of the temperature of the water inlet of the electric pile in the present application
FIG. 3 is a graph showing comparison of the results of the temperature of the water outlet of the electric pile in the present application
FIG. 4 is a graph showing the comparison of the results of the flow rate of the electric pile in the present application
FIG. 5 is a graph comparing the calculated time-consuming results of the raw fuel cell cooling system simulation model and the proxy model of the present application
FIG. 6 is a schematic diagram of a cooling system for a raw fuel cell according to the present application
FIG. 7 is a diagram showing the construction of a response surface according to the present application
FIG. 8 is a schematic representation of a fuel cell cooling system according to the present application
In fig. 6: 1. water pump 2, expansion tank 3, radiator fan 4, filter 5, deionizer 6, cooling path inlet temperature sensor 7, fuel cell stack 8, cooling path outlet temperature sensor
Detailed Description
In order to make the technical scheme and advantages of the present application more clear, the technical scheme in the embodiment of the present application is clearly and completely described below with reference to the accompanying drawings in the embodiment of the present application:
the modeling optimization method of the fuel cell cooling system simulation model shown in fig. 1 specifically comprises the following steps: the heat in the fuel cell stack comprises irreversible heat of electrochemical reaction and joule heat information, and the heat generated in the working process needs to be cooled by a cooling system and is taken out through cooling water circulation. For a fuel cell with a plurality of cells connected in series, the calorific value calculation formula is:
wherein Q is the instant heating power of the electric pile; v (V) 0 Reference voltage for a single cell; v (V) cell The instant voltage of the single-chip battery is; i cell The current is the system instant current; n is the total number of the galvanic pile; i is the current per unit activation area; a is the activation area of the galvanic pile.
The fuel cell cooling system comprises key components such as a water pump, a radiator fan, a deionizer, a filter, an expansion tank and the like. The cooling system of the fuel cell can generate a large amount of heat after working, and the cooling system is required to adjust the internal temperature of the fuel cell, so that the fuel cell is ensured to work in a proper temperature range all the time. The water pump provides a power source for the fuel cell cooling system to meet the heat dissipation requirement of the fuel cell cooling system. The rotating speed of the water pump determines the flow rate of the cooling liquid so as to control the temperature difference between the water inlet and the water outlet of the electric pile. The calculation formula of the output pressure of the water pump is as follows:
P out ＝P in +Δp (3)
wherein P is in Is the inlet pressure (barA) of the water pump, delta P is the pressure difference, P out Is the water pump outlet pressure (barA).
The power provided by the water pump for the fluid is as follows:
wherein Q is the water pump flow (L/min), and eff is the water pump efficiency.
The output flow of the water pump is determined by the rotation speed and the lift of the water pump, and the corresponding water pump flow is output by searching the working point in the MAP. And according to the water pump performance curve graph and the test data, establishing a relation among the lift, the flow and the rotating speed and a relation among the efficiency, the flow and the rotating speed, inputting the relation into a water pump model, and establishing a complete water pump model.
The main function of the cooling fan is to take away the heat of the cooling liquid in the circulating pipeline through the operation of the fan, and the heat dissipation capacity of the cooling fan is related to the air flow and the cooling liquid flow, and the cooling capacity and the cooling liquid flow jointly determine the temperature of the inlet of the cooling circuit of the electric pile. The projection area of the fan on the radiator is a ventilation surface of the radiator, and the speed of air passing through the ventilation surface is as follows:
in the method, in the process of the application,is the air velocity (m/s), V at the radiator inlet fan Is the additional speed (m/s) of the fan when it is running.
The effective area expression of the ventilation surface is:
wherein D is ext Is the outer diameter (m), D of the radiator fan int Is the inner diameter (m) of the radiator fan. The amount of heat exchange over the ventilation area is therefore:
wherein q is lh For the flow rate of the cooling liquid, R h Is the height (m) of the radiator, R l Is the length (m) of the heat sink.
Both the filter and the deionizer were modeled with symmetrical thermo-hydraulic orifices having laminar or turbulent flow characteristics, and the opening and closing process was accomplished based on the characteristic critical flow rates provided and the corresponding pressure drops. And determining the density and viscosity of the reference fluid according to the functional relation between the calibrated pressure drop and the flow of the experimental data, thereby realizing the virtual calibration and modeling process of the flow resistance characteristics of the filter and the deionizer.
The expansion tank is a heat accumulating type energy accumulator, and the hydraulic balance is maintained by considering the heat exchange between gas and liquid. The heat exchange between liquid and gas is:
hgf＝tcgf*(T g -T l ) (8)
wherein hgf is the heat flow rate between the gas and the fluid, tcgf is the heat conductivity between the gas and the liquid, T g And T l The temperatures of the gas phase and the liquid phase, respectively (c).
According to the system flow chart, the parts in the cooling system are connected, a simulation model of the fuel cell cooling system is built, virtual operation of the fuel cell cooling system can be realized in advance, and the performance and the change trend of the fuel cell cooling system can be analyzed and researched.
In the actual use process of the model, the problems of complex model, slow calculation speed and insufficient confidentiality of the model are found, and in order to solve the problems, a fuel cell cooling system agent model meeting the requirements needs to be established.
Determining the boundary of a simulation model of a fuel cell cooling system, acquiring key input and output data such as the rotation speed of a water pump, the rotation speed of a fan, the current of a galvanic pile, the temperature of a galvanic pile water inlet, the temperature of a galvanic pile water outlet, the flow rate of the galvanic pile and the like by using a Monte Carlo calculation method and a Latin hypercube sampling mode, and establishing a proxy model based on a response surface after generating sampling data. The response surface is utilized to finish model reduction, so that a complex physical model can be simplified and packaged, and the simulation calculation time of the model is reduced.
Monte Carlo is a calculation method based on random numbers, and the core content is that by generating random samples, the frequency of occurrence of events is utilized as an approximation of the occurrence probability of the events. The probability distribution of solving the problem is obtained through sampling a large number of random samples, and the average value of the probability distribution approaches to a true value as the number of the samples is larger.
The sampling data is obtained by a Latin hypercube sampling method, which is a method for approximate random sampling from multivariate parameter distribution, and belongs to a layered sampling technology, wherein the Latin hypercube sampling method is used for replacing random sampling in a Monte Carlo calculation method. The Latin hypercube sampling method has the core content that input probability distribution is layered, the probability density range is between (0 and 1), and the layering is that an accumulated curve is divided into equal intervals on the accumulated probability density. The sampling method has the advantage that random sampling is carried out from each interval of the divided input distribution, so that samples in each interval are ensured to be collected. Compared with a random sampling method, the Latin hypercube sampling method is used, and the sample can more accurately represent the distribution condition of the median of the input probability distribution.
The response surface model is a proxy model for converting a complex simulation model into a numerical relation by utilizing virtual data obtained by the simulation model or test data of an actual system. Here, based on the acquired sampling data, a response surface model of the fuel cell cooling system is created. The response surface model is a polynomial model describing algebraic relationships between inputs and outputs, and can map polynomial functions between multiple inputs and multiple outputs. The calculation formula is as follows:
where NMonomials is the term of the polynomial, coef is the fitting coefficient, offset is the offset, and orders is the order of the polynomial. Wherein the fitting coefficients are determined by the least squares method.
Since the temperature in the fuel cell cooling system is a key variable affecting the performance of the system and the hysteresis of the temperature is large, a phenomenon that the output lags the current input of the system exists in the actual system, so that corresponding dynamic characteristics are necessary to be introduced in the modeling process of the model to characterize the phenomenon. The dynamic characteristics of the system are represented by adding a first-order delay link, reasonable initial values and delay time are set, the real dynamic characteristics of the system are simulated, and algebraic circulation phenomenon possibly caused by the introduction of a proxy model can be avoided.
Examples:
a modeling optimization method and a flow of a fuel cell cooling system simulation model are shown in a figure 1, and the specific implementation mode is as follows:
the heat in the fuel cell stack includes electrochemical reaction irreversible heat, joule heat, and the like. For a fuel cell stack composed of a plurality of single units in series, based on the actual number of fuel cell stack sections and the electrochemical reaction process, calculating the heat released by the reaction under different currents, and combining the formula (1) and the formula (2) to complete the modeling of the fuel cell stack 7
And (3) establishing a relation between the pressure and the flow of the water pump according to the formula (3) and the formula (4), and then inputting MAP data among the lift, the flow and the rotating speed and MAP data among the lift, the flow and the efficiency into a water pump model to complete modeling of the water pump 1.
The expansion tank is a heat accumulating type energy accumulator, and the modeling of the expansion tank 2 is completed by combining the formula (8) in consideration of heat exchange between gas and liquid.
And (3) establishing a quantity relation between the speed of the cooling fan model and the effective area of the ventilation surface according to the formula (5) and the formula (6), and calculating the heat exchange quantity of the cooling fan model on the ventilation surface by combining the formula (7) to complete modeling of the cooling fan 3.
And a symmetrical thermal hydraulic orifice model is adopted, and the functional relation between pressure drop and flow is calibrated according to experimental data, so that the flow resistance characteristics of the filter and the deionizer are determined, and the modeling of the filter 4 and the deionizer 5 is completed.
A cooling path inlet sensor 6 module is added to the left side of the fuel cell stack 7 for monitoring the temperature at the cooling path inlet of the fuel cell stack, and a cooling path outlet sensor 8 module is added to the right side of the fuel cell stack 7 for monitoring the temperature at the cooling path outlet of the fuel cell stack.
The above modules are connected and combined together to form the complete fuel cell stack cooling system simulation model shown in fig. 6.
Determining the boundary of a simulation model of the fuel cell cooling system, taking the rotation speed of a water pump, the rotation speed of a fan and the current of a galvanic pile as input variables, taking the temperature of a galvanic pile water inlet, the temperature of a galvanic pile water outlet and the flow of the galvanic pile water as output variables, and distributing probability distribution associated with standard deviation for each variable by adopting a Monte Carlo calculation method.
The Monte Carlo calculation method adopts a Latin hypercube sampling mode, sets the upper and lower limit ranges of input and output variables, uniformly samples the input and output variables, and generates sampling data.
Based on the sampled data, a response surface model of the fuel cell cooling system as shown in fig. 7 is created, the response surface model fits the input and output relationships by a polynomial function, and the coefficients of the polynomial function are determined in conjunction with equation (9) and using a least squares method.
And a first-order delay link for representing the characteristics of the system is added at the rear end of the response surface model, reasonable initial values and delay time are set, the real dynamic characteristics of the system are simulated, and the creation of the complete fuel cell cooling system proxy model shown in fig. 8 is realized.
As can be seen from fig. 2, 3 and 4, the simulation model of the cooling system of the primary fuel cell and the simplified proxy model have the same variation trend in the key parameters of the temperature of the water inlet of the electric pile, the temperature of the water outlet of the electric pile, the water flow of the electric pile and the like, and the average error with higher precision is within 4%. As can be seen from fig. 5, the calculation time of the simulation model of the cooling system of the primary fuel cell is 49.6 seconds, while the calculation time of the proxy model is only 0.1 seconds, and the real-time online calculation capability is provided. The results can be summarized, by the modeling optimization method and the modeling optimization flow of the fuel cell cooling system simulation model, the proxy model established based on the response surface can realize model simplification on the premise of ensuring that the model has higher precision, so that the simulation calculation time of the model is greatly reduced, and the calculation efficiency is improved. An online model with a real-time computing function is provided, and full virtual verification is performed in the early stage of design development and is used for real-time control of a system.
The foregoing is only a preferred embodiment of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art, who is within the scope of the present application, should make equivalent substitutions or modifications according to the technical scheme of the present application and the inventive concept thereof, and should be covered by the scope of the present application.
Claims (7)
1. A modeling optimization method of a fuel cell cooling system simulation model, characterized by comprising:
establishing a fuel cell cooling system simulation model comprising a fuel cell stack model, a water pump model, a radiator fan model, a deionizer model, a filter model and an expansion water tank model according to an actual fuel cell cooling system;
determining boundary conditions of a simulation model of a fuel cell cooling system, taking a water pump rotating speed, a fan rotating speed and a pile current as input variables, taking a pile water inlet temperature, a pile water outlet temperature and a pile water flow as output variables, adopting a Monte Carlo calculation method to distribute probability distribution associated with standard deviation for each variable, adopting a Latin hypercube sampling mode, setting upper and lower limit ranges of the input variables and the output variables, uniformly sampling the input variables and the output variables, and generating sampling data;
based on the sampling data, a response surface model of the fuel cell cooling system is created, the response surface model fits an input and output relation through a polynomial function, each coefficient of the polynomial function is determined by adopting a least square method, a first-order delay link for representing the system characteristics is added at the rear end of the response surface model, a reasonable initial value and delay time are set, and a proxy model of the fuel cell cooling system is built.
2. The modeling optimization method of a fuel cell cooling system simulation model according to claim 1, characterized by: and (3) performing virtual operation on the fuel cell cooling system in the early design stage, analyzing and researching the performance and the variation trend of the fuel cell cooling system, verifying the design scheme and guiding the development and the application of the fuel cell cooling system.
3. The modeling optimization method of a fuel cell cooling system simulation model according to claim 1, characterized by: the input and output variables of the response surface model of the fuel cell cooling system are the same as the boundary dimensions of the simulation model of the fuel cell cooling system.
4. The modeling optimization method of a fuel cell cooling system simulation model according to claim 1, characterized by: the response surface model determines polynomial coefficients by a least square method, and fits a numerical relationship between input and output.
5. The modeling optimization method of a fuel cell cooling system simulation model according to claim 1, characterized by: the sampling data are acquired by a fuel cell cooling system simulation model, and various test data are obtained in a virtual mode.
6. The modeling optimization method of a fuel cell cooling system simulation model according to claim 1, characterized by: the first-order delay link characterizes the dynamic characteristics of a real fuel cell cooling system, and reasonable initial values and delay time are required to be set according to the real fuel cell cooling system.
7. The modeling optimization method of a fuel cell cooling system simulation model according to claim 1, characterized by: the response surface model is a proxy model for converting a complex simulation model into a numerical relation by utilizing virtual data obtained by the simulation model or test data of an actual fuel cell cooling system, and based on the obtained sampling data, a response surface model of the fuel cell cooling system is created, the response surface model is a polynomial model for describing algebraic relation between input and output, and a polynomial function between a plurality of inputs and a plurality of outputs is mapped, and a calculation formula is as follows:
where NMonomials is the term of the polynomial, coef is the fitting coefficient, offset is the offset, and orders is the order of the polynomial. Wherein the fitting coefficients are determined by the least squares method.
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