This Proton Exchange Membrane (PEM) fuel cell system model was developed by Virginia Tech (VT) in collaboration with NREL in 2001/2002. The VT model is a semi-empirical model that accounts for the thermal management and water balance in the system. The model provides hot- and cold-start effects on vehicle fuel economy, power limitations due to temperature, and a water balance for reactant humidification. The system operates on pure hydrogen.
Figure 1 shows a schematic of the model. The relevant components are a compressor, reactant humidifiers, a fuel cell stack, a condenser and water separator, a pressure release device and a cooling circuit including a pump, water reservoir and radiator.
The inlet gases are humidified in separate humidifiers. The stack outlet gases are assumed to be fully saturated (i.e., RH = 100%). The cathode exhaust is cooled in the condenser where part of its water content is condensed out and recovered for reuse in the humidification process. The system operating pressure varies as a function of the fuel cell load.
Figure 1. Schematic view over the fuel cell system model.
At each time step during a drive cycle, the power demand of the drive cycle translates into a vehicle power request. The control strategy of the vehicle determines how much power to request form the fuel cell system and the battery. Then the models supply the power requested to the vehicle that may, or may not, meet the drive cycle power demand due to power limiting effects in the system.
The fuel cell system model includes two major parts: the electrochemistry model and the thermal model. The electrochemistry model relates the operating conditions (temperature, pressure, relative humidity, etc.) to a fuel cell stack voltage and current. The vehicle power request translates into a net power request to the fuel cell system. To start the solution simulation, the iterative solver uses an initial condition that related the net power request to a gross power request. The inputs to the electrochemistry model are the gross power request and the fuel cell stack temperature and the outputs are:
1. heat generated by the fuel cell reaction within the stack
2. gross fuel cell system power at the present operating conditions
3. parasitic power required to run the fuel cell system at the present gross power operating point.
The thermal model uses the result of the electrochemistry model to estimate the operating temperatures in the fuel cell system. In addition, some of the temperatures, eg. fuel cell stack and water reservoir temperatures, are provided by a delayed feedback loop. At each time step, the results of the previous time step (or initial conditions) are used in the thermal model. Using the information of the water balance and temperature from the previous time step and the thermal system characteristics, the thermal model performs mass and energy balances on the fuel cell system components. The outputs of the thermal model are information on
1. water balance
2. parasitic power load
3. cathode operating conditions
4. humidification and condensation
5. heat rejection requirements.
With the information of the gross power operating point and the parasitic power required from the electrochemistry and thermal models, a net power operating point is established. During each time step, the iterative solver repeats the electrochemical and thermal calculations to refine the gross power input to meet the requested net power output of the fuel cell system. Internal to the iterative solver, logic steps that refine the solution to different goals in order to meet different operating scenarios.
The fuel cell system model has the ability to converge to three different goals upon a net power request. Goal 1 is to generate the net power requested, goal 2 is to generate a power that has been limited duel to operating conditions and goal 3 is to generate zero gross power.
Following additions of the VT model have been done:
The impacts of elevation and oxygen concentration can now be evaluated under real driving conditions. The vehicle speed has been linked to the heat transfer processes in the radiator and the condenser, and the fuel cell model equations have been updated to include inlet ambient pressure as a variable. These improvements are significant because they allow the tool to analyze the impact of altitude and ambient temperature on fuel cell vehicle performance and fuel economy.
Load the fc_vt_compact_r1_in and you will have a compact hybrid vehicle with a 50kW fuel cell system and 6 Ah Li-ion battery pack. Its control strategy is to let the fuel cell system be on at all times except when the key is manually turned off.
Under Variable button, there are a number of fuel cell system parameters that either can be kept as default or set to a new value. The parameters are
fuel cell stack characteristics such as
fc_min_cell_volts- the minimum cell voltage
fc_min_temp_for_heat_rejection- the minimum temperature for heat rejection of the fuel cell stack
fc_target_anode_inlet_humidity, fc_target_cathode_outlet_humidity- the desired relative humidity of the anode/cathode
fc_allowable_temp_rise- the maximum temperature difference across the fuel cell stack
or thermal system characteristics such as
fc_system_coolant_capacity- system cooling medium capacity [liter]
fc_radiator_frontal_area- frontal area of the radiator [m^2]
fc_condenser_frontal_area- frontal area of the condenser [m^2]
The parameters shown under the Variable button can also be edited in system_characteristics.m
For more information, please go to
S. Gurski, Cold Start Effects on Performance and Efficiency for Vehicle Fuel Cell System, Master of Science Thesis, Virginia Polytechnic Institute and State University, (2002), http://scholar.lib.vt.edu/theses/available/etd-12192002-162600/ and http://scholar.lib.vt.edu/theses/available/etd-12192002-162600/unrestricted/sgurski@vt.edu_thesis.pdf.pdf
J. Laramie and A. Dicks, Fuel Cell Systems Explained, John Wiley & Sons, Ltd, 2002
KH 08/28/03