CN109145363B - Transient modeling method for centrifugal air compressor in fuel cell system - Google Patents
Transient modeling method for centrifugal air compressor in fuel cell system Download PDFInfo
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Abstract
The invention discloses a transient modeling method of a centrifugal air compressor in a fuel cell system, which comprises the following steps: establishing a mass flow relation model of the air compressor, wherein the mass flow relation model comprises a mass flow characteristic curve of the air compressor; establishing an inertia model of the driving motor; and calculating three transient response parts of the compressor under the control strategy, so that the air compressor can meet the mass flow and the working pressure required by the fuel cell stack. The model identifies the functions of the pressure intensity, the rotating speed and the flow rate of the compressor based on the mass flow database, and then the inertial model of the coupling driving motor is used for constructing a complete air compressor model, so that the actual air inlet condition of the system under the variable load working condition can be truly described, and the performance of the air compressor under different control strategies can be simulated. The simulation accuracy is ensured, the calculation efficiency is improved, and the simulation device can be better combined with a fuel cell system. Has important significance for optimizing the air inlet control strategy of the air compressor.
Description
Technical Field
The invention belongs to the field of fuel cells, and particularly relates to a transient modeling method of a centrifugal air compressor containing a control strategy in a proton exchange membrane fuel cell system.
Technical Field
Proton Exchange Membrane Fuel Cells (PEMFCs) have the advantages of high energy density, high energy conversion efficiency, zero emission and the like, and are considered as one of clean energy sources in the future transportation industry. A sufficient supply of reactant gas is one of the preconditions for the normal and stable operation of the fuel cell stack, and the air supply system includes an air cleaner, an air compressor, an intercooler, a humidifier, and the like. The air firstly passes through a filter to remove particulate impurities, then passes through a compressor for pressurization, an intercooler for cooling and a humidifier for humidification, and then enters the electric pile. In the air supply system, due to the transient response delay of the air compressor, when the load current suddenly changes, the air supply quantity is necessarily delayed from the actual demand quantity, which means that the phenomenon of insufficient oxygen in the electric pile can occur, so that the output voltage is reduced, and the service life of the electric pile is even shortened. Therefore, air is usually supplied with a certain excess factor (ratio of intake air amount to actual consumption), and increasing the air excess factor contributes to improvement of output performance, but also increases energy consumption of the air compressor, resulting in reduction of net power of the system, and overall, the higher the excess air factor is, the better.
Air compressors suitable for use in fuel cells are diverse, such as Roots blower, scroll compressor, screw compressor, and the like. The turbine compressor belongs to a centrifugal compressor, and mainly comprises an air inlet chamber, an impeller, a diffuser, a bend, a reflux device and a volute chamber. The air compressor is used as a component with larger inertia, and the transient response capacity of the air compressor directly determines the actual supply condition of air, so that the transient response capacity of the system is influenced. In addition, the energy consumption of the compressor is also a concern. If the gas flow condition in the air compressor is to be accurately described, a geometric model of the air compressor including the blades needs to be constructed, and simulation calculation is performed by a hydrodynamic method, but the method has the advantages of more parameters, complex model, low calculation efficiency and incapability of being coupled with an air inlet control strategy, so that the method is difficult to be applied to an actual system.
The invention provides a simplified transient air compressor model comprising a control strategy, a function of compressor pressure, rotating speed and flow is identified based on a mass flow database, and then an integral air compressor model is constructed by coupling an inertia model of a driving motor, so that the actual air inlet condition of a system under a variable load working condition can be truly described, and the performance of an air compressor under different control strategies can be simulated. The method has important significance for optimizing the control strategy of the air compressor, and obviously saves the bench experiment cost of the air compressor.
Disclosure of Invention
The invention aims to provide a modeling method of a transient air compressor comprising a control strategy, wherein a function of the pressure, the rotating speed and the flow of the compressor is identified based on a mass flow database, and then an integral air compressor model is constructed by coupling an inertia model of a driving motor, so that the performance of the air compressor under a steady-state working condition and the transient response capability of the air compressor under a variable-load working condition can be calculated.
The present invention is described and illustrated below. The establishment of the model comprises the establishment of a mass flow relation model of the air compressor, an inertia model of a driving motor and the calculation of transient response of the compressor under a control strategy, so that the air compressor meets the mass flow and the working pressure required by a fuel cell stack.
The boost ratio (ratio of outlet pressure to inlet pressure) and the rotation speed of the air compressor determine the mass flow rate, and the rotor of the air compressor is usually driven by a driving motor and is affected by the voltage of the motor end, so that the air compressor model needs to construct the relationship among the voltage of the driving motor, the rotation speed of the air compressor, the boost ratio of the air compressor and the mass flow rate. The method comprises the following specific steps: (1) The method comprises the steps of establishing a mass flow relation model of an air compressor, firstly fitting a mass flow characteristic curve of the air compressor, and correcting the temperature and the pressure of the rotating speed and the mass flow of the compressor as follows:
wherein θ represents a temperature correction coefficient, δ represents a pressure correction coefficient, m cp Represents mass flow of the air compressor, m air,cr Indicating the corrected air flow value.
Based on sample points in a mass flow curve of the disclosed centrifugal compressor, a relation formula of a boosting ratio, a rotating speed and a mass flow is constructed by utilizing binary quintic polynomial fitting, wherein the relation formula is as follows:
in the formula, x is the rotating speed subjected to center regularization treatment, and y is the rising speed subjected to center regularization treatmentPressure ratio, p 00 ,p 10 …p 14 ,p 05 Respectively representing polynomial fitting coefficients.
In the polynomial fitting, the surge operation area of the compressor and the operation area exceeding the maximum flow rate are removed, and the surge line and the maximum flow rate line also adopt a polynomial fitting method.
(2) Inertial model of driving motor
2.1 the inertial link calculation expression of the air compressor is as follows:
in J cp Representing the moment of inertia, ω, of the rotor portion of an air compressor cp Represents the angular velocity of the rotor, t represents time, τ cm Represents the driving torque of the driving motor, tau cp Representing the load moment of the compressor.
2.2 driving torque calculation expression of the driving motor is as follows:
middle kappa t Representing the torque constant, κ of the drive motor v Represents the voltage constant, eta of the driving motor cm Indicating the efficiency of the driving motor, R cm Representing armature resistance, omega of the motor cm Representing the angular velocity of the motor, v cm Representing the drive motor terminal voltage.
2.3 compressor angular speed versus drive motor angular speed relationship is as follows:
ω cp ＝rω cm (2-3)
where r represents the driving ratio of the compressor,
2.4 compressor load moment calculation expression is as follows:
p in the formula cp Representing the power of the air compressor, c p Represents the specific heat capacity, T, of air cp,in Represents the intake air temperature, eta cp Representing the efficiency of the air compressor, p cp,out 、p cp,in Respectively representing the air compressor outlet and inlet pressures, and gamma represents the specific heat ratio coefficient of air.
The outlet temperature of the gas compressed by the air compressor is as follows:
based on steps (1) and (2), a complete air compressor model can be constructed. The mass flow rate of the compressor can be calculated given the speed and step-up ratio, but the mass flow rate and operating pressure required to make the air compressor meet the fuel cell stack requirements are related to control strategy issues.
(3) Calculating transient response of compressor under control strategy
When the air compression rotating speed is fixed, the driving moment is equal to the load moment of the air compressor, so that the stable voltage of the driving motor is solved:
p in the formula cp Represents the power, eta of the air compressor cm Indicating the efficiency of the air compressor,
comparing the mass flow of the air compressor obtained by real-time monitoring with the mass flow required by the electric pile, and taking the difference value of the mass flow and the mass flow as the deviation value of proportional integral derivative control (PID), thereby calculating the control quantity:
in the middle of
Indicating the required air mass flow of the fuel cell stack, < >>
Represents the actual mass flow of the air compressor, e (t) represents the deviation, K p ，K I ，K D Respectively representing proportional, integral and differential coefficients, u (t) representing a control quantity, ++>
Represents the drive motor voltage after PID control.
And determining the working point of the air compressor according to the air supply demand of the electric pile, if the working point is positioned in a surge area or exceeds a maximum flow area, adjusting and improving the ratio of the outlet pressure to the inlet pressure of the air compressor to preferentially meet the demand of the mass flow, after determining the ratio, calculating the current actual mass flow according to the current rotating speed of the compressor, thereby comparing the calculated deviation and the control quantity with the demand value to obtain the new rotating speed and the mass flow of the air compressor, and repeatedly circulating until the actual mass flow and the demand value of the air compressor reach the set error, and calculating and controlling the performance of the air compressor under the steady-state working condition and the transient response capability of the air compressor under the variable load working condition.
The invention is characterized in that:
(1) The constructed transient centrifugal air compressor model overcomes the defects that model parameters exist in complex hydrodynamic analysis and the model parameters cannot be applied to an actual system, ensures simulation accuracy and improves calculation efficiency, and the compressor model is coupled with an air inlet control strategy, so that the model can be better combined with a fuel cell system.
(2) The model not only can simulate the performance of the compressor under the steady-state working condition, but also can simulate the transient response condition under the variable-load working condition, has strong applicability, and has important scientific significance and practical value.
(3) The model can simulate the actual air inlet condition under different control strategies, thereby optimizing the control strategy of the air inlet system, increasing the working reliability of the fuel cell system, and greatly reducing the bench experiment cost in the research and development process of the air compressor.
Drawings
Fig. 1 is a diagram of a centrifugal air compressor mass flow characteristic.
Fig. 2 is a control flow diagram of a centrifugal air compressor.
Fig. 3 is Matlab polynomial fitting results.
FIG. 4 is a performance of a compressor model under a PID control strategy.
FIG. 5 is a performance of a compressor model under an optimized PID control strategy.
Fig. 3 to 5 are all the effects of the present invention.
Detailed Description
The modeling process of the present invention is further illustrated by the following specific examples, which should be construed as illustrative, and not limiting the scope of the present invention.
The modeling method for transient state of centrifugal air compressor in fuel cell system includes modeling mass flow relation model of air compressor, inertial model of driving motor, and calculating transient state response of compressor under control strategy. The mass flow and the working pressure required by the fuel cell stack are met by the air compressor, and the specific steps are as follows:
(1) Establishing a mass flow relation model of an air compressor, and firstly fitting a mass flow characteristic curve of the air compressor
The change of working temperature and pressure can lead to the change of compressor performance, and the MAP of the compressor gives out the mass flow characteristic under specific working conditions, and the temperature and pressure correction is carried out on the rotating speed and the mass flow of the compressor as follows:
wherein θ represents a temperature correction coefficient
Delta represents the pressure correction coefficient +.>
m cp (kg s -1 ) Represents mass flow of the air compressor, m air,cr (kg s -1 ) Indicating the corrected air flow value.
Mass flow diagrams of the Rotrex C15-16 series centrifugal compressors can be obtained in the product instruction manual, as shown in fig. 1. Based on sample points in a mass flow curve of the disclosed centrifugal compressor, a relation formula of a boosting ratio, a rotating speed and a mass flow is constructed by utilizing binary quintic polynomial fitting, wherein the relation formula is as follows:
in the formula, x is the rotating speed subjected to center regularization, y is the boosting ratio subjected to center regularization, and p 00 ,p 10 …p 14 ,p 05 Respectively representing polynomial fitting coefficients.
In the polynomial fitting, the surge operation area of the compressor and the operation area exceeding the maximum flow rate are removed, and the surge line and the maximum flow rate line also adopt a polynomial fitting method.
(2) Inertial model of driving motor
2.1 the inertial link calculation expression of the air compressor is as follows:
in J cp (kg m 2 ) Representing the moment of inertia, ω, of the rotor portion of an air compressor cp (rad s -1 ) Represents the angular velocity of the rotor, t(s) represents time, τ cm (N m) represents the driving torque of the driving motor, τ cp (N m) represents the load moment of the compressor,
2.2 driving torque calculation expression of the driving motor is as follows:
middle kappa t Representing the torque constant, κ of the drive motor v Represents the voltage constant, eta of the driving motor cm Indicating the efficiency of the driving motor, R cm Representing armature resistance, omega of the motor cm (rad s -1 ) Representing the angular velocity of the motor, v cm (V) represents the drive motor terminal voltage.
2.3 compressor angular speed versus drive motor angular speed relationship is as follows:
ω cp ＝rω cm (2-3)
where r represents the driving ratio of the compressor,
2.4 compressor load moment calculation expression is as follows:
p in the formula cp (W) represents the power of the air compressor, c p (J kg -1 K -1 ) Represents the specific heat capacity, T, of air cp,in (K) Represents the intake air temperature, eta cp Representing the efficiency of the air compressor, p cp,out 、p cp,in (Pa) represents the air compressor outlet and inlet pressures, respectively, and γ represents the specific heat ratio coefficient of air.
The outlet temperature of the gas compressed by the air compressor is as follows:
based on the steps (1) and (2), a complete air compressor model can be constructed, and the mass flow of the compressor can be calculated under the condition of given rotating speed and boosting ratio, but the mass flow and the working pressure for enabling the air compressor to meet the requirements of the fuel cell stack are related to the control problem.
(3) Calculating transient response of compressor under control strategy
The rotation speed of the driving motor is controlled by the terminal voltage, so that the response of the air compressor is directly affected by how the terminal voltage changes.
When the air compression rotating speed is fixed, the driving moment is equal to the load moment of the air compressor, so that the stable voltage of the driving motor is solved:
p in the formula cp (W) represents the power of the air compressor, eta cm Indicating the efficiency of the air compressor,
comparing the mass flow of the air compressor obtained by real-time monitoring with the mass flow required by the electric pile, and taking the difference value of the mass flow and the mass flow as the deviation value of proportional integral derivative control (PID), thereby calculating the control quantity:
in the middle of
Indicating the air needed for a fuel cell stackMass flow rate,/->
Representing the actual mass flow of the air compressor, e (t) (kg s -1 ) Represent the deviation, K p ，K I ，K D Respectively representing proportional, integral and differential coefficients, u (t) (V) representing a control quantity, ++>
Represents the voltage of the driving motor after PID control,
the schematic diagram of the control flow of the air compressor is shown in fig. 2, the working point of the air compressor is determined according to the air supply requirement of the electric pile, if the working point is located in the surge area or exceeds the maximum flow area, the ratio of the outlet pressure to the inlet pressure of the air compressor is adjusted to preferentially meet the requirement of the mass flow, after the ratio is determined, the current actual mass flow is calculated according to the current rotating speed of the compressor, so that the deviation amount and the control amount are calculated and compared with the required value to obtain the new rotating speed and the mass flow of the air compressor, and the air compressor is reciprocally circulated until the actual mass flow and the required value of the air compressor reach the set error, and the performance of the air compressor under the steady-state working condition and the transient response capability of the air compressor under the variable load working condition can be calculated and controlled.
The following further describes the steps of the present invention with reference to specific examples, which relate to the following main parameters:
centrifugal air compressor parameters: moment of inertia (kg m) 2 ) Is 5 multiplied by 10 -5 Constant K of driving motor v ,K t 0.026 and 0.036 respectively, the efficiency of the driving motor is 0.97, the efficiency of the compressor is 0.8, the armature resistance (omega) of the motor is 0.01, and the driving ratio is 12.67;
the compressor inlet temperature (K) is 298.15, and the inlet pressure (atm) is 1.0;
the specific heat ratio coefficient of air is 1.40;
the current rotation speed (RPM) of the driving motor is 6000;
the current boost ratio of the air compressor is 1.2;
the fuel cell stack requires an air intake pressure (atm) of 1.2;
the number of unit cells of the fuel cell stack is 400;
cell reaction area (cm) 2 ) 200;
the air stoichiometric ratio was 2.0;
the current density of the fuel cell stack was selected from 1.0A cm -2 Becomes 1.5A cm -2 The response of the air compressor model at a time step is taken as an example.
(1) Calculating a current mass flow rate and a desired air mass flow rate of the fuel cell stack
The mass air flow required for the fuel cell stack is calculated according to faraday's law:
m is in air,req (kg s -1 ) Indicating the required air mass flow, I (A cm -2 ) Represents the current density, A (cm) 2 ) Represents the cell reaction area, ζ represents the air stoichiometric ratio, M air (g mol -1 ) Represents the molar mass of air, N stack Represents the number of single cells in the stack, F (C mol) -1 ) Representing the faraday constant.
According to the above, the current density was calculated to be 1.5A cm -2 When the mass air flow (kg s) required by the fuel cell stack -1 ) At 0.0572, the change in operating temperature and pressure will result in a change in compressor performance, and the MAP of the compressor will show mass flow characteristics for a particular operating condition. The mass flow of the compressor needs to be corrected first:
wherein θ represents a temperature correction coefficient
Delta represents the pressure correction coefficient +.>
m cp (kg s -1 ) Represents mass flow of the air compressor, m air,cr (kg s -1 ) Indicating the corrected mass airflow.
The air mass flow (kg s) in the MAP is calculated in turn based on the actual mass flow required by the fuel cell stack -1 ) 0.0563.
The current mass flow of the fuel cell stack needs to be calculated according to the current rotating speed and the boosting ratio, a mass flow characteristic diagram of the compressor needs to be fitted first, the sample points in the diagram 1 are utilized, the fitting is carried out through a polynomial fitting tool box in Matlab, and the fitting result is shown in the diagram 3. The specific expression is as follows:
m cp ＝p 00 +p 10 x+p 01 y+p 20 x 2 +p 11 xy+p 02 y 2 +p 30 x 3 +p 21 x 2 y+p 12 xy 2 +p 03 y 3
+p 40 x 4 +p 31 x 3 y+p 22 x 2 y 2 +p 13 xy 3 +p 04 y 4 +p 50 x 5 +p 41 x 4 y+p 32 x 3 y 2 +p 23 x 2 y 3 +p 14 xy 4 +p 05 y 5
in the formula, x is the rotating speed subjected to center regularization, y is the boosting ratio subjected to center regularization, and N cp (RPM) is the compressor speed, p ratio For the air boosting ratio, p represents a polynomial fitting coefficient, the coefficient values are shown in the following table, the standard deviation of the fitting result is 0.005529, and the determined coefficient is 0.9805, so that the fitting result has good fitness to the sample points.
The fitting of the surge line to the maximum flow line results are as follows:
surge line: p is p surging ＝1.009×10 4 m cp 3 +264.5m cp 2 +2.469m cp +1.032
Maximum flow line: p is p max_rate ＝445.9m cp 3 -68.58m cp 2 +5.975m cp +0.9028
Knowing the mass flow of the demand, judging whether the working point of the demanded compressor is in a surge area or exceeds a maximum flow area, if the working point is in the surge area, reducing the boosting ratio, and if the working point exceeds the maximum flow line, increasing the boosting ratio, so that the air compressor works normally. According to the required air mass flow, the surge line boosting ratio is 3.8057, the maximum flow line is 1.1013, the required boosting ratio is 1.20, and the value is between the surge line boosting ratio and the maximum flow line boosting ratio, so that the boosting ratio does not need to be adjusted.
The current rotation speed (RPM) of the driving motor is 6000, 76020 is obtained, the rotation speed is converted to a MAP, 77348 is obtained, and the current air mass flow (kg s) is obtained -1 ) 0.0224.
(2) Inertial model of driving motor
When the air compression rotating speed is fixed, the driving moment is equal to the load moment of the air compressor, and the stable voltage of the driving motor is not difficult to solve:
v in cm (V) represents the terminal voltage of the drive motor, P cp (W) represents the power of the air compressor, R cm Represents the armature resistance, eta of the motor cm Representing the efficiency of the air compressor, wherein kappa is in the middle t ，κ v Represents the constant, eta of the driving motor cm Indicating the efficiency of the drive motor omega cp (rad s -1 ) Represents the angular velocity, omega of the compressor cm (rad s -1 ) Indicating the angular velocity of the motor.
The power calculation expression of the air compressor is as follows:
in c p (J kg -1 K -1 ) Represents the specific heat capacity, T, of air cp,in (K) Represents the intake air temperature, eta cp Representing the efficiency of the air compressor, p cp,out ，p cp,in (Pa) represents the air compressor outlet and inlet pressures, respectively, and γ represents the specific heat ratio coefficient of air.
According to the current operation parameters of the compressor, the compressor power (W) is calculated to be 450.567, and the terminal voltage (V) of the driving motor is calculated to be 36.871.
(3) Calculating PID control quantity and transient response of compressor
Calculating deviation and control quantity according to the current mass flow of the compressor and the required mass flow:
in the middle of
Air mass flow indicative of fuel cell stack demand, +.>
Representing the actual mass flow of the air compressor, e (t) (kg s -1 ) Represent the deviation, K p ，K I ，K D Respectively representing proportional, integral and differential coefficients, u (t) (V) representing a control quantity, ++>
Represents the drive motor voltage after PID control.
The deviation is 0.0339, the value of the control quantity is related to the selection of PID parameters, in this example, K is taken p ＝1.2， K I ＝20，K D =20, thereby calculating a control amount of 0.4475 and a drive motor voltage (V) after pid control of 37.319.
The inertia links of the driving motor are as follows:
in J cp (kg m 2 ) Representing the moment of inertia, ω, of the rotor portion of an air compressor cp (rad s -1 ) Represents the angular velocity of the rotor, t(s) represents the response time, τ cm (N m) represents the driving torque of the driving motor, τ cp (N m) represents compressor load torque.
The driving torque calculation expression of the driving motor is as follows:
τ in cm (N m) represents the driving moment, κ t ，κ v Represents the constant, eta of the driving motor cm Indicating the efficiency of the driving motor, R cm Representing armature resistance, omega of the motor cm (rad s -1 ) Representing the angular velocity of the motor, v cm (V) represents the drive motor terminal voltage. The drive torque (N m) can then be determined as 0.7332 from the PID-controlled drive motor voltage.
The load moment calculation expression of the compressor is as follows:
τ in cp (N m) represents a load moment, P cp (W) represents the work of the air compressorRate, omega cp (rad s -1 ) Representing the angular velocity of the rotor, the calculated load moment (N m) is 0.7171.
The drive torque (N m) is known to be 0.7332 and the load torque (N m) is known to be 0.7171 so that the new compressor angular velocity (rad s) in the MAP can be calculated -1 ) 660.434, the compressor rotational speed (RPM) is 79906, and after temperature and pressure correction, the corresponding actual compressor rotational speed (RPM) is 78534, and the driving motor rotational speed (RPM) is 6198.
Fig. 3 to 5 are all implementation effects of the present invention, in which fig. 4 is a performance of the present model under a set of PID control strategies, and fig. 5 is a performance of the present model under an optimized PID control strategy.
Claims (1)
1. A transient modeling method for a centrifugal air compressor in a fuel cell system is characterized by comprising the following steps: the method comprises the steps of establishing a mass flow relation model of the air compressor, an inertia model of the driving motor and calculating transient response of the compressor under a control strategy, so that the air compressor meets mass flow and working pressure required by the fuel cell stack, and the method comprises the following specific steps of:
(1) The method comprises the steps of establishing a mass flow relation model of the air compressor, firstly fitting a mass flow characteristic curve of the air compressor, and correcting the rotating speed and the mass flow of the compressor in terms of temperature and pressure as follows:
wherein θ represents a temperature correction coefficient, δ represents a pressure correction coefficient, m cp Represents mass flow of the air compressor, m air,cr Indicating corrected air flow value, N cr Indicating corrected air compressor rotational speed, N cp Indicating the rotational speed of the air compressor,
based on sample points in a mass flow curve of the disclosed centrifugal compressor, a relation formula of a boosting ratio, a rotating speed and a mass flow is constructed by utilizing binary quintic polynomial fitting, wherein the relation formula is as follows:
in the formula, x is the rotating speed subjected to center regularization, y is the boosting ratio subjected to center regularization, and p 00 ,p 10 …p 14 ,p 05 Respectively represent the fitting coefficients of the polynomials,
in polynomial fitting, a surge working area and a working area exceeding the maximum flow rate of the compressor are removed, and a polynomial fitting method is adopted for a surge line and a maximum flow rate line;
(2) Inertial model of driving motor
2.1 the inertial link calculation expression of the air compressor is as follows:
in J cp Representing the moment of inertia, ω, of the rotor portion of an air compressor cp Represents the angular velocity of the rotor, t represents time, τ cm Represents the driving torque of the driving motor, tau cp Representing the load moment of the compressor,
2.2 driving torque calculation expression of the driving motor is as follows:
middle kappa t Representing the torque constant, κ of the drive motor v Represents the voltage constant, eta of the driving motor cm Indicating the efficiency of the driving motor, R cm Representing armature resistance, omega of the motor cm Representing the angular velocity of the motor, v cm Representing the terminal voltage of the drive motor,
2.3 compressor angular speed versus drive motor angular speed relationship is as follows:
ω cp ＝rω cm (2-3)
where r represents the driving ratio of the compressor,
2.4 compressor load moment calculation expression is as follows:
p in the formula cp Representing the power of the air compressor, c p Represents the specific heat capacity, T, of air cp,in Represents the intake air temperature, eta cp Representing the efficiency of the air compressor, p cp,out 、p cp,in Respectively representing the air compressor outlet and inlet pressures, gamma represents the specific heat ratio coefficient of air,
the outlet temperature of the gas compressed by the air compressor is as follows:
based on steps (1) and (2), a complete air compressor model can be constructed,
(3) Calculating transient response of compressor under control strategy
When the air compression rotating speed is fixed, the driving moment is equal to the load moment of the air compressor, so that the stable voltage of the driving motor is solved:
p in the formula cp The power of the air compressor is represented,
comparing the mass flow of the air compressor obtained by real-time monitoring with the mass flow required by the electric pile, and taking the difference value of the mass flow and the mass flow as the deviation value of proportional-integral-differential control, thereby calculating the control quantity:
in the middle of
Indicating the required air mass flow of the fuel cell stack, < >>
Represents the actual mass flow of the air compressor, e (t) represents the deviation, K p ，K I ，K D Respectively representing proportional, integral and differential coefficients, u (t) representing a control quantity, ++>
Represents the voltage of the driving motor after PID control,
and determining the working point of the air compressor according to the air supply demand of the electric pile, if the working point is positioned in a surge area or exceeds a maximum flow area, adjusting and improving the ratio of the outlet pressure to the inlet pressure of the air compressor to preferentially meet the demand of the mass flow, after determining the ratio, calculating the current actual mass flow according to the current rotating speed of the compressor, thereby comparing the calculated deviation and the control quantity with the demand value to obtain the new rotating speed and the mass flow of the air compressor, and repeatedly circulating until the actual mass flow and the demand value of the air compressor reach the set error, and calculating and controlling the performance of the air compressor under the steady-state working condition and the transient response capability of the air compressor under the variable load working condition.
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