I have an engineering project, it’s about making a spreadsheet of the numbers given and solve to get to the solution and a technical memo about 3 pages.Date: 11/06/2013
Project: Recommendation for a Fuel Cell Model
Subject: Model of the voltage/current behavior for the correct configuration Fuel cell batteries
Prepare by: Development Department of a Fuel Cell Company
Introduction
The purpose of this technical memo is to perform themodel batteries, at a constant voltage source (V_{S}) in series with an internal resistance (R_{S}). This model will be used by the Applications Department to determine the ability of the fuel cell to operate various home appliances. In addition, the model of the voltage/current behavior will also be used to find the best configuration for cells arranged in series and parallel to deliver the necessary voltage and current.
Field Procedures
The techniques that we will be using for this fuel cell modeling are:
Kirchhoff’s voltage law (KVL)
 Kirchhoff’s current law (KCL)
Data and Graph:Model for low current density region, V_{Slow}, R_{Slow}
Data Graph V&I/Cm^{2}
Current Density  Voltage 


mA/Cm^{2}  Volt  
0.0  1.24  
0.2  1.14  
0.5  1.09  
1.0  1.00  
2.0  0.99  
4.0  0.89  
6.0  0.87 
Calculation
According to the graph V& I/cm^2, the derive equation is y =0.0524x + 1.134 where y=V (Volts) and X= I/Cm^2. The open circuit voltage (no laod )is Y=V=1.134 volts
The cutoff point for this equation occur when Y=0 and we have X=I/cm^2=21.64 mA/cm^2 which correspond the short circuit current per unit of area. Rslow=1.134V/(21.64 mA/Cm^2)
=52.40 ohms/Cm^2. To calculate the internal resistance we need to know the size of the Fuel cell.
Data and GraphModel for medium current density region, V_{Smed}, R_{Smed}
Data graph V&I/Cm^{2}
Current Density  Voltage 


mA/Cm2  Volt  
8  0.92  
10  0.84  
12  0.83  
14  0.89  
16  0.82  
18  0.82  
20  0.79  
Calculation
According to the graph V& I/cm^2, the derive equation is y =0.0079x+0.9543 where y=V (Volts) and X= I/Cm^2. The open circuit voltage (no laod )is Y=V=0.9 543 volts and the cutoff point for this equation is x=120.79 mA/cm^{2}. The resistance internal Rsmedium=7.9 Ohm/cm^{2}.
Data and GraphModel for high current density region, V_{Shigh}, R_{Shigh}
Data Graph V&I/Cm^{2}
Current Density  Voltage 


mA/Cm^2  Volt  
22  0.8  
24  0.73  
26  0.74  
28  0.65  
30  0.52  
32  0.5  
34  0.38  
Calculation
According to the graph V& I/cm^2, the derive equation is y =0.0346x+1.5871 where y=V (Volts) and X= I/Cm^2. The open circuit voltage (no laod )is Y=V=1.5871 volts and the cutoff point for this equation is x=45.87 mA/cm^{2}. The resistance internal Rs high=34.6 Ohm/cm^{2}.
Discussion
If we refer to the original graph, we can say that the calculation reflect exactly the region of low current density which is 21.64 mA/cm^{2}, then the medium region present the high current density 120.79 mA/cm^{2}. For that precise region we may suggest that the fuel cell function as an ideal battery. For the ideal battery, for any current, the voltage remaining fixed. Can the medium region data reflect what we expecting? Any data correction can be made? For the high currents density, the calculation show
45.87 mA/cm^{2} which is acceptable for the size/area for the fuel cell chosen.
Conclusion
During the modeling for fuel cell battery, it is important to knownthe value of the voltage across the fuel cell an open circuit and the value of the current when we short the circuit. Those two values help us to calculate the internal resistance of the battery. According to the calculation, the size or the area of the cell is important to know before provide which configuration to choose. The two extreme configurations that can useful are series and parallel. The approach techniques used are
Kirchhoff’s voltage law (KVL)
 Kirchhoff’s current law (KCL)
Ohm ‘s law