CN113299951B - Method for observing cathode pressure and flow of proton exchange membrane fuel cell - Google Patents

Method for observing cathode pressure and flow of proton exchange membrane fuel cell Download PDF

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CN113299951B
CN113299951B CN202110462076.6A CN202110462076A CN113299951B CN 113299951 B CN113299951 B CN 113299951B CN 202110462076 A CN202110462076 A CN 202110462076A CN 113299951 B CN113299951 B CN 113299951B
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observer
cathode
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CN113299951A (en
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江维海
李丞
孙铂奇
朱仲文
李晓伟
聂振华
王森
周炼
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Caac Yangzhou Automotive Engineering Research Institute Co ltd
China Automotive Technology and Research Center Co Ltd
CATARC Tianjin Automotive Engineering Research Institute Co Ltd
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China Automotive Technology and Research Center Co Ltd
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04298—Processes for controlling fuel cells or fuel cell systems
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    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
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    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
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    • H01M8/0438—Pressure; Ambient pressure; Flow
    • H01M8/04395—Pressure; Ambient pressure; Flow of cathode reactants at the inlet or inside the fuel cell
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
    • H01M8/04298—Processes for controlling fuel cells or fuel cell systems
    • H01M8/04313—Processes for controlling fuel cells or fuel cell systems characterised by the detection or assessment of variables; characterised by the detection or assessment of failure or abnormal function
    • H01M8/0438—Pressure; Ambient pressure; Flow
    • H01M8/04425—Pressure; Ambient pressure; Flow at auxiliary devices, e.g. reformers, compressors, burners
    • H—ELECTRICITY
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    • H01M—PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
    • H01M8/00—Fuel cells; Manufacture thereof
    • H01M8/04—Auxiliary arrangements, e.g. for control of pressure or for circulation of fluids
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Abstract

The invention provides a method for observing cathode pressure and flow of a proton exchange membrane fuel cell, which comprises the following steps: s1: establishing a lumped parameter model of a fuel cell air system; s2: based on the model, designing an adaptive observer to observe the pressure of a cathode cavity and the flow of a cathode inlet; s3: the observer design process considers the temperature difference between the inlet and the outlet of the manifold, which is caused by the intercooler, so as to ensure the convergence of the observer; s4: measurable signals of the fuel cell system are input into an observer, and real-time accurate observation of cathode flow and pressure is realized through real-time iterative operation. The method for observing the cathode pressure and the flow of the proton exchange membrane fuel cell has the advantages of convenient arrangement of a sensor for signal acquisition, strong realizability, effective increase of the observation precision and control effect of transient working conditions during high fuel cell power point migration.

Description

Method for observing cathode pressure and flow of proton exchange membrane fuel cell
Technical Field
The invention belongs to the technical field of fuel cells, and particularly relates to a method for observing cathode pressure and flow of a proton exchange membrane fuel cell.
Background
With the increasing severity of energy and environmental problems, new energy vehicles have attracted people's attention, and compared with pure electric vehicles, fuel cell vehicles have the advantages of short hydrogenation time, long driving range and the like. However, the mass production and application of fuel cell vehicles are still limited by a plurality of technical difficulties, for vehicle products, reliability and durability are important indexes for evaluating vehicle performance, the fuel cell needs to respond to the rapid change of power demand under the dynamic working condition of the vehicle rapidly to ensure the dynamic requirement of the vehicle, and simultaneously, the flow of hydrogen and air is required to be accurately controlled to ensure the economic requirement, the phenomenon of oxygen starvation caused by insufficient air supply affects the service life, and the internal reaction efficiency is reduced due to the excessively low cathode pressure. Therefore, in order to be able to accurately control the cathode inlet air flow and the cathode cavity pressure, feedback control is required, however, the above physical quantities cannot be directly measured by the sensors, and an observer needs to be designed to estimate them in real time.
Disclosure of Invention
In view of the above, the present invention aims to realize real-time and accurate estimation of cathode cavity pressure and inlet stack air flow through a design observer, and indirectly estimate two physical quantities, i.e., inlet and outlet stack flow and cathode cavity pressure, which cannot be directly measured or have difficulty in measurement by a sensor, according to measurable signals such as inlet manifold inlet flow, inlet and outlet temperatures, manifold internal pressure, and the like. The air flow of the inlet of the reactor and the pressure of the cathode cavity are used as important state parameters and control feedback quantity of the fuel cell, and the method is important in the key technical fields of fault diagnosis, state detection, air system decoupling control and the like.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
the method realizes real-time observation in the driving process, provides a technical basis for state detection and accurate control of the fuel cell, and comprises the following specific steps:
1) establishing a lumped parameter model of a fuel cell air system;
2) based on the model, designing an adaptive observer to observe the pressure of a cathode cavity and the flow of a cathode inlet;
3) the observer design process considers the temperature difference between the inlet and the outlet of the manifold, which is caused by the intercooler, so as to improve the observation precision, and simultaneously, the observer parameters are analyzed and designed through the convergence, so that the convergence of the observer is ensured;
4) measurable signals of the fuel cell system (including air compressor outlet temperature and flow, cathode inlet temperature and manifold internal pressure) are input into an observer, and real-time accurate observation of cathode flow and pressure is realized through real-time iterative operation.
In the step 1), a control-oriented fuel cell air system lumped parameter model is built according to a mass conservation law, an ideal gas equation and an assumed condition and by considering the temperature difference between an inlet and an outlet of a manifold.
The assumed conditions of the model specifically include:
the air in the manifold is considered as an ideal gas;
the pressure, temperature and concentration of the gas component are uniformly distributed;
the cathode inlet flow is proportional to the pressure differential;
irrespective of the thermodynamic process, an adiabatic system is considered.
The construction of the fuel cell air system lumped parameter model needs to consider the temperature difference between an inlet and an outlet of a manifold, and the state space equation is as follows:
x＝P sm y＝P sm
Figure BDA0003042659440000021
Figure BDA0003042659440000022
wherein P is sm Is a state variable and an output quantity, u is an input quantity, including an inlet temperature T of an air inlet pipe sm,in Outlet temperature T of air inlet pipe sm,out And air compressor flow
Figure BDA0003042659440000023
R is a gas constant, V sm Is the volume of the inlet pipe, M a The molar mass of the air is the mass of the air,
Figure BDA0003042659440000031
is the cathode inlet flow.
In the step 2), the adaptive observer is designed based on the model to observe the pressure of the cathode cavity and the inlet flow of the cathode, and the inlet flow of the cathode is measured
Figure BDA0003042659440000032
Cathode cavity pressure P as a time-varying parameter ca The observer is obtained by calculation according to the inlet flow and the pressure of the air inlet pipe, and the specific observer formula is as follows:
Figure BDA0003042659440000033
Figure BDA0003042659440000034
Figure BDA0003042659440000035
Figure BDA0003042659440000036
wherein g is ca,in For the flux coefficient of the reactor inlet, A, B, C and phi are coefficient matrixes, Y is an intermediate variable, L and gamma are observer gains, and sigma is an arbitrary positive definite diagonal matrix.
In the step 3), the convergence analysis is performed by analyzing and designing the observer parameters, the state variables and the time-varying parameter estimation errors through the convergence analysis, and the method specifically comprises the following steps:
3) first, it is necessary to define
Figure BDA0003042659440000037
And
Figure BDA0003042659440000038
the relation of (1):
Figure BDA0003042659440000039
4) the above formula is derived:
Figure BDA00030426594400000310
wherein
Figure BDA00030426594400000311
The derived consensus can be expanded into the following form:
Figure BDA00030426594400000312
according to the state space equation and the observer formula, the transformation and the adjustment can be in the following form:
Figure BDA00030426594400000313
since the parameter θ changes relatively slowly, its derivative can be approximated to zero, and the above equation can be simplified to the following form:
Figure BDA00030426594400000314
if it can be guaranteed that A + LC < 0, i.e. L < 0, then η converges to 0.
3) Due to the fact that
Figure BDA0003042659440000041
From the observer formula, the parameter estimation error can be derived
Figure BDA0003042659440000042
The dynamic equation of (c):
Figure BDA0003042659440000043
since sigma is a positive definite diagonal matrix, if observer gain gamma > 0, then
Figure BDA0003042659440000044
Convergence to 0, with Y being a bounded variable, can be guaranteed
Figure BDA0003042659440000045
Also converging to 0.
Compared with the prior art, the method for observing the cathode pressure and the flow of the proton exchange membrane fuel cell has the following advantages:
1) the invention reduces the requirement on the precision of the model by introducing the self-adaptive rate, and the model for designing the observer adopts the simplified air system model, thereby effectively improving the operation speed and meeting the real-time requirement of control.
2) The observer designed by the invention provides a parameter range for ensuring the convergence of the observer through convergence analysis, and can ensure the stability of the observation process under any working condition through parameter design, thereby meeting the safety requirement of a fuel cell system.
3) The observer designed by the invention has less input quantity, and the sensor used for signal acquisition is convenient to arrange and has strong realizability.
4) The invention considers the temperature difference between the outlet and the inlet of the air compressor of the air system, increases the collection of the temperature of the outlet of the air compressor on the basis of collecting the temperature of the inlet, and simultaneously uses the temperature and the temperature as the input quantity of the observer, thereby eliminating the observation deviation based on single temperature and effectively increasing the observation precision.
5) The invention observes the cathode pressure and the cathode inlet flow in real time through the observer, and provides technical support for realizing the functions of fuel cell state detection, fault diagnosis and the like.
6) The cathode pressure and the inlet flow observed by the observer can be used as feedback control quantities, so that the control effect of the transient working condition during the power point migration of the fuel cell is effectively improved.
Drawings
FIG. 1 is a schematic view of an observer system according to the present invention;
FIG. 2 is a schematic diagram of an internal algorithm structure of an observer according to the present invention;
FIG. 3 is FCU controller hardware in an example of the invention;
FIG. 4 is a hardware-in-the-loop system architecture for a test observer of the present invention;
FIG. 5 is a hardware-in-the-loop experiment platform control interface according to the present invention;
FIG. 6 is a test condition for an example of the present invention;
FIG. 7 is an observation of inlet flow in an example of the present invention;
FIG. 8 is a cathode chamber pressure observation in an example of the invention;
FIG. 9 is a graph of observer-based control of oxygen ratio in an example of the present invention.
Detailed Description
Unless defined otherwise, technical terms used in the following examples have the same meanings as commonly understood by one of ordinary skill in the art to which the present invention belongs. The test reagents used in the following examples, unless otherwise specified, are all conventional biochemical reagents; the experimental methods are conventional methods unless otherwise specified.
The invention is described in detail below with reference to embodiments and the accompanying drawings.
FIG. 1 shows a system for observing cathode pressure and flow of a PEM fuel cell constructed according to an embodiment of the present invention, the fuel cell air system in this example mainly includes an air compressor, an intercooler, a humidifier, a condenser, a back pressure valve, and various sensors, the observation method requires a temperature sensor, a pressure sensor and a flow sensor to be installed in the fuel cell air system, and a flow sensor is installed at the inlet of the air compressor for measuring the inlet air flow of the air intake manifold, a pressure sensor is installed at the inlet of the air compressor for measuring the pressure in the air intake manifold, two temperature sensors are respectively installed at the outlet and the inlet of the air compressor for measuring the temperature difference generated after the air passes through the intercooler, as shown in figure 1, an observer acquires the measuring signals of the sensors, and (4) calculating in real time through internal operation to obtain estimated values of the air flow of the reactor inlet and the pressure of the cathode cavity.
In this example, before designing the observer, a lumped parameter model of the fuel cell air system needs to be constructed, the model is a control-oriented model, in order to meet the real-time requirement of the observer, the model needs to be simplified, and the following assumptions are included in the simplification process:
1) the air in the manifold is considered as an ideal gas;
2) the pressure, temperature and concentration of the gas component are uniformly distributed;
3) the cathode inlet flow is proportional to the differential pressure;
4) irrespective of the thermodynamic process, an adiabatic system is considered.
Based on the hypothesis, a fuel cell air system model is established, and comprises an air inlet manifold model, an exhaust manifold model and a cathode cavity model, wherein the air inlet manifold model comprises an air compressor sub-model, a reactor inlet sub-model and a manifold internal pressure dynamic model, and a state space equation can be described as follows:
Figure BDA0003042659440000061
Figure BDA0003042659440000062
Figure BDA0003042659440000063
wherein
Figure BDA0003042659440000064
Is the outlet flow (kg/s) f of the air compressor cp (. for) representing air compressor MAP, ω is air compressor speed (rpm), k is pressure ratio, k is P a /P sm ，P a Is atmospheric pressure (1.013X 10) 5 Pa)，P sm Is the intake manifold pressure (Pa).
Figure BDA0003042659440000065
For the flow rate of the inlet, the nonlinear model can be simplified into a linear equation (3), g, about the pressure difference because the pressure difference between two sides of the inlet is small ca,in For the inlet flow coefficient, it can be determined by parameter identification, P ca Is the cathode chamber pressure. V sm Is the intake manifold volume (m) 3 )，M a The molar mass of air (28.84g/mol), R is the gas constant (8.314J/(K. mol)), and T sm Is the intake manifold temperature (K). The invention considers the temperature difference between the inlet and the outlet when establishing the intake manifold model, and converts the equation (1) into the following form:
Figure BDA0003042659440000066
wherein T is sm,in Is the intake manifold inlet temperature, T sm,out Is the intake manifold outlet temperature.
The exhaust manifold model can be divided into a stack outlet sub-model, a back pressure valve model and a manifold internal pressure dynamic sub-model. Wherein the reactor outlet model is similar to the reactor inlet model and is described by a linear equation related to the pressure difference between the cathode cavity and the exhaust manifold; the back pressure valve is constructed in the form of a butterfly valve, and its model can be described by using a nozzle model with variable effective cross-sectional area. Its state space equation can be described as:
Figure BDA0003042659440000071
Figure BDA0003042659440000072
Figure BDA0003042659440000073
Figure BDA0003042659440000074
Figure BDA0003042659440000075
wherein
Figure BDA0003042659440000076
Is the flow rate of the outlet of the reactor, g ca,out Is the flow coefficient of the outlet, P rm To be the exhaust manifold pressure,
Figure BDA0003042659440000077
back pressure valve flow, W correction factor, T rm As the temperature of the exhaust pipe is taken,
Figure BDA0003042659440000078
is the opening (rad) of the back pressure valve, a 1 And a 2 Is a coefficient of opening, V rm Is the exhaust manifold volume.
The cathode cavity model can describe the dynamic change of the cathode cavity pressure according to the reactor inlet sub-model, the reactor outlet sub-model and the oxygen consumption sub-model, and the state space equation can be described as follows:
Figure BDA0003042659440000079
Figure BDA00030426594400000710
wherein T is ca Is the cathode chamber temperature, V ca Is the volume of the cathode cavity,
Figure BDA00030426594400000711
in order to achieve the oxygen consumption per second,
Figure BDA00030426594400000712
is the oxygen molar mass (32g/mol), n is the membrane electrode number, I st The current of the cell stack (A) and F are the Faraday constants (96485C/mol).
According to the fuel cell air system model established in the present example, a state observer is designed, and for convenience of description, the intake manifold model is first written in the form of a state space equation:
Figure BDA0003042659440000081
wherein the state variable x ═ P sm Input quantity of
Figure BDA0003042659440000082
Time varying parameter
Figure BDA0003042659440000083
A＝0，
Figure BDA0003042659440000084
C＝1。
Fig. 2 is a schematic diagram of the internal structure of the observer, and the specific structural form is as follows:
Figure BDA0003042659440000085
Figure BDA0003042659440000086
Figure BDA0003042659440000087
Figure BDA0003042659440000088
wherein L and gamma are observer gains, and sigma is a positive definite diagonal matrix, and state variable estimation errors and parameter estimation errors are defined to be in the following forms respectively:
Figure BDA0003042659440000089
Figure BDA00030426594400000810
to verify the convergence of the adaptive observer, a test is first defined with respect to
Figure BDA00030426594400000811
And
Figure BDA00030426594400000812
the relation of (c):
Figure BDA00030426594400000813
derived from the above formula
Figure BDA00030426594400000814
In conjunction with equations (16) and (17), the above equation can be written as follows:
Figure BDA00030426594400000815
substituting equations (12), (13) and (15) into equation (21) can result in
Figure BDA00030426594400000816
Since the parameter changes relatively slowly, its derivative can be approximated to zero, and the above equation can be simplified to the following form:
Figure BDA0003042659440000091
if it can be guaranteed that A + LC < 0, η converges to 0 and at the same time
Figure BDA0003042659440000092
According to equation (14), convergence of the parameter estimation error can be ensured by the following equation:
Figure BDA0003042659440000093
since sigma is a positive definite diagonal matrix, if observer gain gamma > 0, then
Figure BDA0003042659440000094
Convergence to 0, with Y being a bounded variable, can be guaranteed
Figure BDA0003042659440000095
Also converging to 0.
In order to verify the effect of the observer of the invention, a fuel cell model was constructed using MATLAB/Simulink and verified by hardware-in-the-loop (HIL) experiments. The testing environment is built based on Veristand of NI, controller hardware is shown in figure 3, TC277D is used as an operation core, data communication modules such as AD and CAN are integrated, functions such as PWM input and output, high-low side driving, high-voltage acquisition and LIN communication are achieved, the hardware-in-loop testing system is shown in figure 4, and a hardware-in-loop experiment platform control interface is shown in figure 5. The fuel cell air system model and observer parameters are given in table 1, the target current and cathode cavity pressure given by experimental conditions are shown in fig. 6, the target current is varied in steps between 100 and 150A, the target pressure is varied in steps between 2 and 2.2bar, the corresponding observed result of the inlet flow is shown in fig. 7, the observed result of the cathode cavity pressure is shown in fig. 8, the measured values of the flow and pressure sensors are approximately represented by hardware-in-loop model output values, and compared with the estimated value of the observer, the observed result has higher observed accuracy in both steady-state and transient conditions and has higher transient accuracy compared with the observer based on single temperature input. Under the transient condition that the target current is changed from 140A to 130A in a step mode and the target pressure is changed from 2.1bar to 2.05bar in a step mode, the observation value has better following effect as seen from a partially enlarged view. To further verify the beneficial effect of the observer on the control of the cathode air system, fig. 9 compares the control effect of the oxygen ratio with or without the observer, and the control method based on the observer has better transient control accuracy under transient operating conditions.
TABLE 1 model and observer parameters
Figure BDA0003042659440000096
Figure BDA0003042659440000101
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the invention, so that any modifications, equivalents, improvements and the like, which are within the spirit and principle of the present invention, should be included in the scope of the present invention.

Claims (3)

1. A method for observing the cathode pressure and flow of a proton exchange membrane fuel cell is characterized in that: the method comprises the following steps:
s1: establishing a lumped parameter model of the fuel cell air system;
s2: based on the model, designing an adaptive observer to observe the pressure of a cathode cavity and the flow of a cathode inlet;
s3: the observer design process considers the temperature difference between an inlet and an outlet of the manifold, which is caused by the intercooler, so that the convergence of the observer is ensured;
s4: inputting a measurable signal of the fuel cell system into an observer, and realizing real-time accurate observation of cathode flow and pressure through real-time iterative operation;
the construction of the fuel cell air system lumped parameter model needs to consider the temperature difference between an inlet and an outlet of a manifold, and the state space equation is as follows:
x＝P sm y＝P sm
Figure FDA0003811752240000011
Figure FDA0003811752240000012
wherein P is sm Is the state variable and the output quantity, u is the input quantity,
T sm,in is the inlet temperature of the air inlet pipe,
T sm,out is the temperature at the outlet of the air inlet pipe,
Figure FDA0003811752240000013
is the flow rate of the air compressor,
r is the gas constant, and R is the gas constant,
V sm is the volume of the air inlet pipe,
M a the molar mass of the air is the mass of the air,
Figure FDA0003811752240000014
is the cathode inlet flow rate;
in S2, the adaptive observer is designed based on the model to observe the cathode cavity pressure and the cathode inlet flow rate, and the cathode inlet flow rate is measured
Figure FDA0003811752240000021
Cathode cavity pressure P as a time varying parameter ca The observer is obtained by calculation according to the inlet flow and the pressure of the air inlet pipe, and the specific observer formula is as follows:
Figure FDA0003811752240000022
Figure FDA0003811752240000023
Figure FDA0003811752240000024
Figure FDA0003811752240000025
wherein g is ca,in For the flux coefficient of the reactor inlet, A, B, C and phi are coefficient matrixes, Y is an intermediate variable, L and gamma are observer gains, and sigma is an arbitrary positive definite diagonal matrix;
in S3, the convergence analysis of the observer parameters, state variables, and time-varying parameter estimation errors is designed through convergence analysis, which includes the following specific steps:
1) first, it is necessary to define
Figure FDA0003811752240000026
And
Figure FDA0003811752240000027
the relation of (c):
Figure FDA0003811752240000028
2) the above formula is derived:
Figure FDA0003811752240000029
wherein
Figure FDA00038117522400000210
The derived consensus can be expanded into the following form:
Figure FDA00038117522400000211
according to the state space equation and the observer formula, the transformation and the adjustment can be in the following form:
Figure FDA00038117522400000212
since the parameter θ changes relatively slowly, its derivative can be approximated to zero, and the above equation can be simplified to the following form:
Figure FDA00038117522400000213
if the A + LC is less than 0, namely L is less than 0, then eta converges to 0;
due to the fact that
Figure FDA00038117522400000214
Deducing parameter estimation error according to observer formula
Figure FDA00038117522400000215
The dynamic equation of (c):
Figure FDA00038117522400000216
since sigma is a positive definite diagonal matrix, if observer gain gamma > 0, then
Figure FDA0003811752240000031
Convergence to 0, with Y being a bounded variable, can be guaranteed
Figure FDA0003811752240000032
Also converging to 0.
2. The method for observing the cathode pressure and flow of a proton exchange membrane fuel cell according to claim 1, wherein: in S1, the total parameter model builds a control-oriented fuel cell air system lumped parameter model according to the mass conservation law, the ideal gas equation and the assumed conditions, and according to the manifold inlet-outlet temperature difference, where the model assumed conditions specifically include: the air in the manifold is considered an ideal gas; the pressure, temperature and concentration of the gas component are uniformly distributed; the cathode inlet flow is proportional to the pressure differential; irrespective of the thermodynamic process, an adiabatic system is considered.
3. The method for observing the cathode pressure and flow of a proton exchange membrane fuel cell according to claim 1, wherein: the measurable signals in S4 include air compressor outlet temperature and flow, cathode inlet temperature, and manifold pressure.
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