CN113609792B - Multidisciplinary modeling method based on power flow - Google Patents
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Abstract
The invention discloses a multidisciplinary modeling method based on power flow. Taking a power system of a hydrogen fuel cell automobile as a specific research object, starting from a power system energy supply device, and establishing an electrochemical mechanism model of the hydrogen fuel cell; the internal electrochemical reaction dynamics and electrochemical thermodynamic mechanism of the fuel cell are researched by constructing a voltage output model, the internal association mechanism of the electrode back pressure and the effective partial pressure of the gas is analyzed by constructing a back pressure regulating model, the former model which directly takes the gas flow or the effective partial pressure as output is replaced, and the dynamic accurate regulation of the output performance of the fuel cell is realized; aiming at the energy consumption of the power system load of the hydrogen fuel cell automobile, a resistance model of each part of the power system load is established and fused into a dynamic load model of the power system. The invention takes the power as a tie, and realizes the cooperative analysis of the driving force and the resistance of the hydrogen fuel cell automobile and the energy supply and the energy consumption of a power system.
Description
Technical Field
The invention belongs to the field of complex product multidisciplinary modeling, and particularly relates to a multidisciplinary modeling method based on power flow.
Background
The reserved quantity of the motor vehicles in China in 2020 reaches 3.72 hundred million, and is increased by 3.56% compared with 2019, wherein the reserved quantity of the new energy automobile is increased by 29.18% compared with 2019, and is increased to 492 ten thousand. At present, the related matching technology of the pure electric automobile is mature, but the electric energy of the pure electric automobile is completely dependent on the power grid supply, so the environmental protection degree of the pure electric automobile is dependent on the environmental protection of a power generation mode, and at present, the traditional thermal power generation is mainly used in China, the pollution is large, in addition, the development of the pure electric automobile is facing the bottleneck under the restriction of the lithium battery technology; the hydrogen fuel cell has high energy density and larger lifting space, and along with the development of the matched technologies such as vehicle-mounted hydrogen supply, liquid hydrogen storage and transportation and the like, the hydrogen fuel cell automobile has the technical advantage of being more environment-friendly and has wider development prospect.
The performance deficiency of the hydrogen fuel cell power system seriously hinders the progress of the hydrogen fuel cell automobile with practical commercial value in China, but the hydrogen fuel cell automobile power system has complex structure, wide related subject field and multiple technical difficulties, and needs to be researched by means of a digital prototype technology to shorten the research and development period and reduce the research and development cost. By researching the modeling method of the hydrogen fuel cell automobile power system, a power system model capable of accurately and efficiently solving various characteristics of the power system can be established.
Disclosure of Invention
In order to solve the problems in the background technology, the invention provides a modeling method of a hydrogen fuel cell automobile power system based on power flow. The energy supply of the power system needs to be regulated according to the energy consumption, and starts from the two aspects of energy supply and energy consumption, simultaneously, a hydrogen fuel cell model and a power system load model are established, and the cooperative solution of the energy supply and the energy consumption of the power system is realized, so that the energy output characteristic of the power system is truly and comprehensively reflected.
Establishing a voltage output model by researching an electrochemical reaction mechanism of the hydrogen fuel cell; and establishing a back pressure regulating model by researching a back pressure regulating mechanism of the fuel cell, and fusing the two models according to the internal logic of the electrochemical of the fuel cell to obtain the electrochemical mechanism model of the hydrogen fuel cell facing the voltage output characteristic. And establishing a dynamic load model of the power system according to the dynamics of the automobile and the kinematics of the automobile aiming at the energy consumption of the load part of the power system.
The modeling method of the hydrogen fuel cell automobile power system based on power flow adopts the following technical scheme:
the hydrogen fuel cell automobile power system model comprises a hydrogen fuel cell electrochemical mechanism model and a power system load model; the electrochemical mechanism model of the hydrogen fuel cell mainly comprises an electrochemical electromotive force model, an activation polarization overvoltage model, a concentration polarization overvoltage model, an ohmic polarization overvoltage model and a back pressure regulating model; electrochemical mechanism model V of hydrogen fuel cell out The calculation formula of (2) is as follows:
V out ＝E Nernst -V act -V conc -V ohm
wherein ,ENernst Is an electrochemical electromotive force model, V act To activate the polarization overvoltage model, V conc For concentration polarization overvoltage model, V ohm An ohmic polarization overvoltage model;
the power system load model mainly comprises a road resistance model, an air resistance model, an acceleration resistance model and a transmission efficiency model; power system load model F t The calculation formula of (2) is as follows:
F t ＝F r +F w +F a +F η
wherein ,Fr For road resistance model, F w Is an air resistance model, F a To accelerate the composition of the resistance model, F η Is a transmission efficiency module.
The electrochemical electromotive force model E Nernst The calculation formula of (2) is specifically as follows:
wherein Δg is the amount of change in gibbs free energy; f is Faraday constant; Δs is the variation of standard molar entropy; r is a universal gas constant;is an effective partial pressure of hydrogen; />Is an effective partial pressure of oxygen; n is the number of mobile electrons; t (T) st Is the fuel cell operating temperature; t (T) ref Is the reference temperature.
The activated polarization overvoltage model V act The calculation formula of (2) is specifically as follows:
wherein ,Tst Is the fuel cell operating temperature; t (T) ref Is the reference temperature; p (P) c Back pressure for the cathode of the battery;saturated vapor pressure; i is the external circuit current density; x is x 1 ,x 2 …x 14 All are electrochemical correlation coefficients.
Effective partial pressure of HydrogenAnd effective partial pressure of oxygen->The method is obtained by constructing a backpressure regulating model:
wherein ,Pa Back pressure for the anode of the battery; m is m 1 ,m 2 …m 5 All are electrochemical correlation coefficients.
The concentration polarization overvoltage model V conc The calculation formula of (2) is specifically as follows:
wherein R is a universal gas constant; t (T) st Is the fuel cell operating temperature; f is Faraday constant; i is the current in the circuit; i lim Is the limiting current of the fuel cell.
The ohmic polarization overvoltage model V ohm The calculation formula of (2) is specifically as follows:
wherein I is the current in the circuit; s is the effective activation area of the proton exchange membrane;R c equivalent impedance for the external circuit of the fuel cell; l is the proton exchange membrane thickness; gamma is the correlation coefficient of the resistivity of the proton exchange membrane;
wherein v is the water content of the proton exchange membrane, and the calculation formula is as follows:
P c lambda is the cathode back pressure of the battery c Is the stoichiometric ratio of the cathode reactant of the battery, and k is the water content correlation coefficient of the proton exchange membrane.
The output parameter of the electrochemical mechanism model of the hydrogen fuel cell is the output power P of the hydrogen fuel cell eout ：
P eout ＝V out ×I
The specific construction process of the road resistance model, the air resistance model, the acceleration resistance model and the transmission efficiency model in the power system load model is as follows:
1) Road resistance model F r Is constructed by the following steps:
1.1 Moment calculation is carried out by taking the middle point of the contact surface between the front wheel and the rear wheel of the automobile and the road as the center, and the normal reaction force of each wheel in the running process of the automobile is calculated by the following specific formula:
wherein G is the total weight of the automobile; b 1 Distance from the front wheel to the center of gravity of the vehicle; b 2 Distance from the rear wheel to the center of gravity of the vehicle; l is the distance between the front wheel and the rear wheel; alpha is the gradient angle of the road; h is a g Distance from the center of gravity of the vehicle to the wheel axle; u is the running speed of the automobile; f (F) zw1 and Fzw2 Respectively, are air lift forces acting on the vehicle body and positioned above the grounding points of the left front wheel and the left rear wheel, F zw3 and Fzw4 Respectively acting on the car body and positioned above the grounding points of the right front wheel and the right rear wheel; t (T) f1 and Tf2 Respectively is left front,Rolling resistance moment couple, T on left rear wheel f3 and Tf4 Rolling resistance even moment on the right front wheel and the right rear wheel respectively; t (T) jw1 and Tjw2 Moment of inertia and moment of couple on the left front wheel and the left rear wheel respectively, T jw3 and Tjw4 The inertia resistance couple moment is respectively arranged on the right front wheel and the right rear wheel; f (F) z1 and Fz2 Normal reaction forces of the left front wheel and the left rear wheel of the automobile respectively; f (F) z3 、F z4 Normal reaction forces of the right front wheel and the right rear wheel respectively; m is the total mass of the automobile;
wherein ,T f(1,2,3,4) ＝Gr s fcosα，/>
wherein ,rs Is the radius of the wheel; c (C) lf and Crf The air lift coefficients of the front wheel and the rear wheel are respectively; i w The moment of inertia of each wheel; a is the windward area; ρ a Is the air density; f is the coefficient of rolling resistance,f 0 ,f 1 ,f 4 to influence the natural coefficient of rolling resistance of the tyre;
1.2 According to F obtained in step 1.1) z1 ,F z2 ,F z3 ,F z4 Calculating the sum F of normal reaction forces applied to each tire of the automobile z The specific formula is as follows:
F z ＝F z1 +F z2 +F z3 +F z4
＝Gcosα-C lf Aρ a u 2 -C rf Aρ a u 2
1.3 A road resistance model F is calculated by the following formula r ：
2) Air resistance model F w Is constructed by the following steps:
wherein ,Fw Is air resistance; c (C) D Is the air resistance coefficient.
3) Acceleration resistance model F a Is constructed by the following steps:
wherein ,Fa Is acceleration resistance; i w The moment of inertia of each wheel; r is (r) s Is the radius of the wheel;
4) Transmission efficiency model F η Is constructed by the following steps:
wherein T is motor torque; i.e 0 Is the transmission ratio of the main speed reducer; η (eta) T Is the transmission efficiency of the power system.
5) According to the calculation formula of each load resistance in the power system, a power system load model F is obtained t ：
The power system load model F t The output parameters of (a) are acceleration a, speed u and power system consumption powerWherein the acceleration a,The speed u is the output parameter of the acceleration resistance model
1) The calculation formula of the acceleration a is as follows:
wherein a is acceleration generated by the power system; η (eta) T The transmission efficiency of the power system is achieved; p (P) e For driving power of the power system, i.e. equal to the output power of the hydrogen fuel cell, P e ＝P eout ＝V out ×I；
2) The calculation formula of the speed u is as follows:
wherein ,t0 Is the initial time; u (u) 0 For initial speed, i.e. t 0 The running speed of the car at the moment.
3) Power system power consumptionThe calculation formula of (2) is as follows:
the invention has the beneficial effects that:
1. compared with the traditional model which takes the flow rate of the reaction gas or the effective partial pressure as the input, the model takes the back pressure of the anode and the cathode as the input, thereby being more in line with the actual situation in the fuel cell production application and obtaining more accurate solving results.
2. Through the established electrochemical mechanism model of the hydrogen fuel cell and dynamic load model of the power system, the cooperative analysis of driving force and resistance of the hydrogen fuel cell automobile and energy supply and energy consumption of the power system by taking power as a tie is realized.
Drawings
FIG. 1 is a diagram of a hydrogen fuel cell electrochemical mechanism model;
fig. 2 is a model diagram of the electrochemical energy electromotive force part.
Fig. 3 is a model diagram of an active polarization overvoltage portion.
Fig. 4 is a model diagram of the concentration polarization overvoltage section.
Fig. 5 is a model diagram of an ohmic polarization overvoltage portion.
Fig. 6 is a voltage output model diagram.
Fig. 7 is a model of hydrogen fuel cell backpressure regulation.
FIG. 8 is a dynamic load model of the powertrain system.
Fig. 9 is a road resistance portion model diagram.
Fig. 10 is an air resistance section model diagram.
Fig. 11 is a partial model diagram of acceleration resistance.
Detailed Description
The invention is further described below with reference to the drawings and examples.
The invention includes a hydrogen fuel cell electrochemical mechanism model and a dynamic system dynamic load model. The hydrogen fuel cell electrochemical mechanism model is modeling of a power system energy supply device, and the power system dynamic load model is modeling of energy consumption of a power system load. The cooperative analysis of driving force and resistance of the hydrogen fuel cell automobile and energy supply and energy consumption of a power system by taking power as a tie is realized through an electrochemical mechanism model of the hydrogen fuel cell and a dynamic load model of the power system.
As shown in fig. 1, the electrochemical mechanism model of the hydrogen fuel cell comprises a voltage output model and a back pressure regulating model. The voltage output model takes the operating temperature, current, effective hydrogen partial pressure, effective oxygen partial pressure and cathode back pressure of the fuel cell as input parameters, and takes the output voltage of the fuel cell as output parameters. Compared with the existing hydrogen fuel cell related model, the hydrogen fuel cell voltage output model disclosed by the invention has the advantages that the factors such as the effective partial pressure of the reaction gas, the running temperature of the cell, the chemical metering ratio of the reaction gas, the humidity in the cell and the like are all calculated in detail, and the considered fuel cell influence factors are more comprehensive, so that the solving result of the output voltage is more accurate.
As shown in FIG. 6, the voltage output model includes an electrochemical electromotive force model Enernst, an activated polarization overvoltage model V act Concentration polarization overvoltage model V conc And ohmic polarization overvoltage model V ohm ：
1) The electrochemical electromotive force model energy is shown in fig. 2:
the content of Func1 in FIG. 2 is
2) Activated polarization overvoltage model V act As shown in fig. 3:
in FIG. 3, func1 has a content of x 2 (T st -T ref ) The method comprises the steps of carrying out a first treatment on the surface of the Func2 content isFunc3 content is->Func4 content is->Func5 content is->Func6 content is->Func7 content is->Func8 content is->
wherein ,x1 ,x 2 …x 14 Is x 1 ＝0.279；x 2 ＝0.00085；x 3 ＝0.00004308；x 4 ＝1.01325；x 5 ＝0.5；x 6 ＝8.63811；x 7 ＝0.5736；x 8 ＝0.00058；x 9 ＝0.00018；x 10 ＝0.166；x 11 ＝0.1173；x 12 ＝0.01618；x 13 ＝0.00001618；x 14 ＝10。
3) Concentration polarization overvoltage model V conc As shown in fig. 4:
in FIG. 4, func1 has the following content
4) Ohmic polarization overvoltage model V ohm As shown in fig. 5:
wherein v is the water content of the proton exchange membrane, and the calculation formula is as follows:
wherein the actual value of k is k= 6.3348.
In FIG. 5, func1 has the following contentFunc2 content is->Func3 content isFunc4 content is->Func5 content is->Func6 content isFunc7 content is->Func8 content isFunc9 content is->Func10 content is
The back pressure regulating model takes the back pressure of the anode and cathode, the current and the operating temperature of the fuel cell as inputs, takes the effective partial pressure of hydrogen and oxygen as outputs, analyzes the internal correlation mechanism of the back pressure of the electrode and the effective partial pressure of the gas, replaces the former model which directly takes the flow of the gas or the effective partial pressure as the output, accords with the actual application scene of the hydrogen fuel cell better, and realizes the more accurate regulation of the output performance of the fuel cell. The backpressure-regulating model is shown in fig. 7:
in FIG. 7, func1 has the following contentFunc2 content is->Func3 content isFunc4 content is->Func5 content is->
wherein ,m1 ,m 2 …m 5 The values of (2) are as follows:
m 1 ＝3.7619；m 2 ＝0.291；m 3 ＝0.832；m 4 ＝1.635；m 5 ＝1.334。
as shown in fig. 8, the dynamic load model of the power system comprises a road resistance model, an air resistance model and an acceleration resistance model. The driving power, the initial speed, the road parameters and the like of the power system are taken as inputs, and the acceleration, the current speed and the resistance power are taken as outputs. The individual and complete modeling of the individual part of the resistance of the hydrogen fuel cell car power system load is performed by the relation between the power system driving power and the power consumption of the individual part of the resistance.
The Func1 content in FIG. 8 is a model of transmission efficiencyAnd (5) calculating parts.
The road resistance model is shown in fig. 9:
in FIG. 9, func1 has a content of Gcos α -C Lf Aρ a u 2 -C rf Aρ a u 2 The method comprises the steps of carrying out a first treatment on the surface of the Func2 content is
wherein ,f0 ,f 1 ,f 4 The actual values of (2) are as follows: f (f) 0 ＝0.0076；f 1 ＝0.000056；f 4 ＝0
Air resistance model F w As shown in fig. 10:
acceleration resistance model F a As shown in fig. 11:
the output parameter of the acceleration resistance model is F a 、a、u。
The invention provides a multi-model integrated modeling method for a power system, which is integrated into the power system model according to the logic relation and the mutual feedback information flow direction between an electrochemical mechanism model of a hydrogen fuel cell and a dynamic load model of the power system, and describes the simulation calculation flow of the hydrogen fuel cell automobile. When the simulation of the power system of the hydrogen fuel cell automobile is carried out, the output power can be obtained by multiplying the output voltage of the electrochemical mechanism model of the hydrogen fuel cell by the circuit current. In the power system with independent power supply of the hydrogen fuel cell, the output power of the hydrogen fuel cell is used as the input parameter of the dynamic load model of the power system, so that the simulation analysis of the power system can be carried out. The powertrain dynamics load model may calculate the current power consumption and power demand of the powertrain. The electrochemical mechanism model of the hydrogen fuel cell needs to adjust the output power based on the electrochemical mechanism model, and transmits the output power of the hydrogen fuel cell to the load model of the power system, and the current acceleration and the current speed of the automobile are calculated by combining the driving power and the resistance power, so that iterative operation is formed.
Claims (4)
1. The modeling method of the hydrogen fuel cell automobile power system based on power flow is characterized in that the hydrogen fuel cell automobile power system model comprises a hydrogen fuel cell electrochemical mechanism model and a power system load model;
the electrochemical mechanism model of the hydrogen fuel cell mainly comprises an electrochemical electromotive force model, an activation polarization overvoltage model, a concentration polarization overvoltage model, an ohmic polarization overvoltage model and a back pressure regulating model; electrochemical mechanism model V of hydrogen fuel cell out The calculation formula of (2) is as follows:
V out ＝E Nernst -V act -V conc -V ohm
wherein ,ENernst Is an electrochemical electromotive force model, V act To activate the polarization overvoltage model, V conc For concentration polarization overvoltage model, V ohm An ohmic polarization overvoltage model;
the electrochemical electromotive force model E Nernst The calculation formula of (2) is specifically as follows:
wherein Δg is the amount of change in gibbs free energy; f is Faraday constant; Δs is the variation of standard molar entropy; r is a universal gas constant;is an effective partial pressure of hydrogen; />Is an effective partial pressure of oxygen; n is the number of mobile electrons; t (T) st Is the fuel cell operating temperature; t (T) ref Is the reference temperature;
the activated polarization overvoltage model V act The calculation formula of (2) is specifically as follows:
wherein ,Tst Is the fuel cell operating temperature; t (T) ref Is the reference temperature; p (P) c Back pressure for the cathode of the battery;saturated vapor pressure; i is the external circuit current density; x is x 1 ,x 2 …x 14 All are electrochemical correlation coefficients;
the concentration polarization overvoltage model V conc The calculation formula of (2) is specifically as follows:
wherein R is a universal gas constant; t (T) st Is the fuel cell operating temperature; f is Faraday constant; i is the current in the circuit; i lim Is the limiting current of the fuel cell;
the ohmic polarization overvoltage model V ohm The calculation formula of (2) is specifically as follows:
wherein I is the current in the circuit; s is the effective activation area of the proton exchange membrane; r is R c Equivalent impedance for the external circuit of the fuel cell; l is the proton exchange membrane thickness; gamma is the correlation coefficient of the resistivity of the proton exchange membrane;
wherein v is the water content of the proton exchange membrane, and the calculation formula is as follows:
P c lambda is the cathode back pressure of the battery c The stoichiometric ratio of the cathode reactant of the battery is that k is the water content correlation coefficient of the proton exchange membrane;
the power system load model mainly comprises a road resistance model, an air resistance model, an acceleration resistance model and a transmission efficiency model; power system load model F t The calculation formula of (2) is as follows:
F t ＝F r +F w +F a +F η
wherein ,Fr For road resistance model, F w Is an air resistance model, F a To accelerate the composition of the resistance model, F η Is a transmission efficiency module;
the specific construction process of the road resistance model, the air resistance model, the acceleration resistance model and the transmission efficiency model in the power system load model is as follows:
1) Road resistance model F r Is constructed by the following steps:
1.1 Moment calculation is carried out by taking the middle point of the contact surface between the front wheel and the rear wheel of the automobile and the road as the center, and the normal reaction force of each wheel in the running process of the automobile is calculated by the following specific formula:
wherein G is the total weight of the automobile; b 1 Distance from the front wheel to the center of gravity of the vehicle; b 2 Distance from the rear wheel to the center of gravity of the vehicle; l is the distance between the front wheel and the rear wheel; alpha is the gradient angle of the road; h is a g Distance from the center of gravity of the vehicle to the wheel axle; u is the running speed of the automobile; f (F) zw1 and Fzw2 Respectively, are air lift forces acting on the vehicle body and positioned above the grounding points of the left front wheel and the left rear wheel, F zw3 and Fzw4 Respectively is that the wheels are respectively grounded at the front right and the rear right of the vehicle bodyAir lift above the point; t (T) f1 and Tf2 Rolling resistance moment of couple, T on left front and left rear wheels respectively f3 and Tf4 Rolling resistance even moment on the right front wheel and the right rear wheel respectively; t (T) jw1 and Tjw2 Moment of inertia and moment of couple on the left front wheel and the left rear wheel respectively, T jw3 and Tjw4 The inertia resistance couple moment is respectively arranged on the right front wheel and the right rear wheel; f (F) z1 and Fz2 Normal reaction forces of the left front wheel and the left rear wheel of the automobile respectively; f (F) z3 、F z4 Normal reaction forces of the right front wheel and the right rear wheel respectively; m is the total mass of the automobile;
wherein ,T f(1,2,3,4) ＝Gr s fcosα，/>
wherein ,rs Is the radius of the wheel; c (C) lf and Crf The air lift coefficients of the front wheel and the rear wheel are respectively; i w The moment of inertia of each wheel; a is the windward area; ρ a Is the air density; f is the coefficient of rolling resistance,f 0 ,f 1 ,f 4 to influence the natural coefficient of rolling resistance of the tyre;
1.2 According to F obtained in step 1.1) z1 ,F z2 ,F z3 ,F z4 Calculating the sum F of normal reaction forces applied to each tire of the automobile z The specific formula is as follows:
F z ＝F z1 +F z2 +F z3 +F z4
＝Gcosα-C lf Aρ a u 2 -C rf Aρ a u 2
1.3 A road resistance model F is calculated by the following formula r ：
2) Air resistance model F w Is constructed by the following steps:
wherein ,Fw Is air resistance; c (C) D Is the air resistance coefficient;
3) Acceleration resistance model F a Is constructed by the following steps:
wherein ,Fa Is acceleration resistance; i w The moment of inertia of each wheel; r is (r) s Is the radius of the wheel;
4) Transmission efficiency model F η Is constructed by the following steps:
wherein T is motor torque; i.e 0 Is the transmission ratio of the main speed reducer; η (eta) T The transmission efficiency of the power system is achieved;
5) According to the calculation formula of each load resistance in the power system, a power system load model F is obtained t ：
2. According to claimThe modeling method of the hydrogen fuel cell automobile power system based on power flow, which is characterized by comprising the following steps ofAnd effective partial pressure of oxygen->The method is obtained by constructing a backpressure regulating model:
wherein ,Pa Back pressure for the anode of the battery; m is m 1 ,m 2 …m 5 All are electrochemical correlation coefficients.
3. The modeling method for a power flow-based hydrogen fuel cell automobile power system of claim 1, wherein the output parameter of the electrochemical mechanism model of the hydrogen fuel cell is the output power P of the hydrogen fuel cell eout ：
P eout ＝V out ×I。
4. The modeling method for a hydrogen fuel cell vehicle power system based on power flow according to claim 1, wherein the power system load model F t The output parameters of (a) are acceleration a, speed u and power system consumption powerThe acceleration a and the speed u are output parameters of an acceleration resistance model:
1) The calculation formula of the acceleration a is as follows:
wherein a is acceleration generated by the power system; η (eta) T The transmission efficiency of the power system is achieved; p (P) e For driving power of the power system, i.e. equal to the output power of the hydrogen fuel cell, P e ＝P eout ＝V out ×I；
2) The calculation formula of the speed u is as follows:
wherein ,t0 Is the initial time; u (u) 0 For initial speed, i.e. t 0 The running speed of the automobile at the moment;
3) Power system power consumptionThe calculation formula of (2) is as follows:
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