质子交换膜电池的建模与控制

1、质子交换膜电池建模及控制,报告人：彭飞,主要内容,基本原理,Anode： Cathode：,质子交换膜燃料电池系统框图,质子交换膜燃料电池实际模型,主要内容,质子交换膜电池总体模型,质子交换膜电池总体模型,Stack Voltage Model,Larminie,J. and Disks,A.2000 Fuel System Explained Stack output Voltage： (2-1),Stack Voltage Model,Amphlett,J.C.,Baument,R.M. Performance modeling of the Ballard Mark IV solid p

2、olymer electrolyte fuel cell,(2-2),Stack Voltage Model,Activation overvoltages: Lee,J.H.,Lalk,T.R.,and Appleby,A.J.1998 The relationship between the activation overvoltage and the current density is described by the Tafel equation, which is approximated by (2-3) The values of and their dependency on

3、 oxygen partial pressure and temperature can be determined from nonlinear regression of experimental data.,Stack Voltage Model,Ohmic overvoltage (2-4) Mann RF,Amphlett JG,Hooper MAI,Jensen HM,Peppley BA,Roberge PR.2006 J POWER SOURCES (2-5) Where represents the membrane water content. Its value vari

4、es between 0 and 14 , which correspond to relative humidity (RH) of 0% and 100%, respectively.,Stack Voltage Model,Concentration overvoltage Guzzella,L.,1999,Control Oriented Modelling of Fuel-Cell Based Vehicles. (2-6) Where are constants that depend on temperature and reactant partial pressure and

5、 can be determined empirically.,Stack Voltage Model,Nonlinear regression of experimental data,Stack Voltage Model,Stack Voltage Simulink Model,Stack Voltage Model,Some data of Simulink 1.System parameters of the Ballard 5kW PEMFC,Stack Voltage Model,Operation condition of the Ballard 5kW PEMFC,Stack

6、 Voltage Model,Stack Voltage Model,Stack Voltage Model,Stack Voltage Model,Stack Voltage Model,Cathode Flow Model,Cathode Flow Model,This model captures the cathode air flow behavior, and is developed using the mass conservation principle and the thermodynamic and psychrometric properties of air. Se

7、veral assumptions are made: (1) All gases obey the ideal gas law; (2) The temperature of the air inside the cathode is equal to the stack temperature; (3) The properties of the flow exiting the cathode such as temperature, pressure, and humidity are assumed to be the same as those inside the cathode

8、; (4) When the relative humidity of the gas exceeds 100%, vapor condenses into the liquid form. The liquid water does not leave the stack and will either evaporate when the humidity drops below 100% or accumulate in the cathode;,Cathode Flow Model,Cathode Flow Model,(2-9),(2-10),(2-11),Cathode Flow

9、Model,Anode Flow Model,Anode Flow Model,(2-14),(2-15),Membrane Hydration Model,The membrane hydration model captures the effect of water transport across the membrane. Spring ,T.E.,Zawodzinsiki,T,A.,and Gottesfeld,S.,1991,Polymer Electrolyte Fuel Cell Nguyen,T.V.,and White,R.E.1993, A Water and Heat

10、 Management Model for PEMFC The water transport across the membrane is achieved through two distinct phenomena: (1)the electro-osmotic drag phenomenon: due to the water molecules dragged across the membrane from anode to cathode by the protons (2) back-diffusion: the gradient of water concentration

11、across the membrane.,Membrane Hydration Model,Membrane Hydration Model,Dutta,S.,Shimpalee,S. and Van Zee,J.W.,2001,Numerical prediction of mass-exchange between cathode and anode channels in PEM fuel cell The coefficients vary with membrane water content , which is calculated from the average of the

12、 water content at the anode and cathode.,(2-16),Membrane Hydration Model,(2-18),(2-19),(2-20),Compressor Model,A lumped rotational model is used to represent the dynamic behavior of the compressor.,Where is the ratio of the specific heats of air (=1.4), is the constant-pressure specific heat capacit

13、y of air(=1004),Compressor Model,Supply / Return Manifold Model,The cathode supply manifold (SM) includes pipe and stack manifold volumes between the compressor and the fuel cells.,(2-27),Hydrogen Flow,Since pressurized hydrogen is used, the anode hydrogen flow can be regulated by a servo valve to a

14、chieve very high loop bandwidth. The goal of the hydrogen flow control is to minimize the pressure difference across the membrane. Since the valve is fast, it is assumed that the flow rate of hydrogen can be directly controlled based on the feedback of the pressure difference.,(2-28),High oxygen exc

15、ess ratio,(2-29),High oxygen excess ratio,Jay T. Pukrushpan ,Huei Peng,Anna G.Stefanopoilou,2004 ,Control-Oriented Modeling and Analysis for Automotive Fuel Cell System,It can be seen that the optimal oxygen excess ratio varies between 2.0 and 2.4, and decreases slowly when the stack current increas

16、es. Note that the results may also be influenced by factors not included in the model, such as stack flooding.,主要内容,Control System Formulation,The LTI system analysis in MATLAB/SIMULINK control system toolbox is used to linearize the model. The nominal operating point is: The linear model is:,Control System Formulation,Control System Formulation,Output variable：,Input variable：,State variable：,The linear model has seven states while the nonlinear model has nine states. The state removed is the mass of wat