# To design any system the basic it is key to meet all the critical requirements. Fuel cells are a rather clean source of power as compared to other similar sources of power.

RECOMMENDATION: MODELLING OF A NON-LINEAR FUEL CELL
NAME:
COURSE:
COLLEGE:
INSTRUCTOR:
INSTITUTION:

RECOMMENDATION FOR A FUEL CELL MODEL
To design any system the basic it is key to meet all the critical requirements. Fuel cells are a rather clean source of power as compared to other similar sources of power. The system to be designed in this case should be very cheap, efficient, and less costly and have more than one application (Choi, 2003). To achieve the maximum results I am, in my project, using the three kinds of fuel systems designs. I shall employ the sample results to develop the fuel cell that will provide sufficient amount of current and less voltage, more voltage and less current and a combination of fuel cells that will serve a specific basic purpose. This will be effectively attained by carrying out experiments and comparing them with the actual then determine the required region for each model. This in turn calls for the design of a model for low current density, a medium current density and a consequent high current density (Hayre, 2006). By applying these three basic designs, I am placed in a better position to develop a single non-linear fuel cell battery that will serve a wide range of functions.
Before we commence analyzing each of the designs, the basic principle upon which we base our argument for selection is the type of electrodes and the electrolyte to be used. Each model is selected independent of the other, and to meet our high current demand we intend to connect them in parallel as current will add up.

Current density voltage Resistance deviation
4 0.94 0.235 0.08
6 0.93 0.155 0.0325
8 0.98 0.1225 0.0335
10 0.89 0.089 0.015667
12 0.88 0.073333 0.009762
14 0.89 0.063571 0.009196
16 0.87 0.054375 0.006597
18 0.86 0.047778 0.005778
20 0.84 0.042 0.003364
22 0.85 0.038636 0.006553
24 0.77 0.032083 #REF!

In my model, the high current density model is the fuel cell of 22mA/cm2, the model with medium current density 12mA/cm2, and the low current density model is 4mA/cm2. Their respective currents are, 0.85 volts, 0.88 volts and 0.93 volts. The disparity between the currents is relatively minimal, hence a relatively flat curve results providing more stable current and voltage over a wide region of operation (Proceedings / 2. European Solid Oxide Fuel Cell Forum. 1996). The use of the three fuel cells, means we are operating at a multiple power level which consequently calls for an efficient control system. It is necessary to have such a system that will ensure there is sufficient air supply and fuel for continual constant power generation. To limit the current disturbance a feed forward loop is connected to the control circuit. The major components of the control unit are the anti-windup scheme and the dynamic constraint unit (Zhao, 2011). To obtain an efficient and stable system, the sensing and actuating components must be designed with the precision and accuracy required. The actuation process is accomplished by controlling the cell operating voltage, and the rate at which air flows, while the sensing component is made up of a temperature sensor, through a thermocouple, it is also prudent to include a pressure and flow rate measuring device to keep in check the various measurements.
To select the three models, we put into consideration the respective parameters of the three models (Hayre, 2006). We needed each model to have minimal current deviation from the other. We selected the low current design, at 22mA/squared cm and the high current density model at 6mA/cm2 with a voltage deviation of (0.93-0.85) 0.8 volts. This is a manageable deviation. By connecting the three cases in series, we will get a current of, (22 + 12 + 6) 40 mA/cm2 and constant voltage of 0.89 volts. The fuel cell can operate up to a specific limiting current density, beyond which its

The low current density design have a relatively higher operating efficiency this saves energy in terms of the amount of energy lost in terms of heat dissipation. This is mainly as a consequence of the need of the cell area. To operate in this region, a large active cell is necessary. This is due to the large surface area needed to generate the required amount of electricity. In this state the membrane resistance is nearly constant and does not depend on the oxidizing components hence much more efficient (Sheng, 2007).

In the case of a high current density fuel cell, the membrane is usually dried out, we hence selected a current density corresponding to a relatively wet cell membrane. This was determined using the voltage level. The voltage of 0.93 volts is the better option of all the list given.

While selecting the medium current density design, I opted to consider the current density that offers the least deviation from the higher and lower limit, with regards to the voltage generate. The deviation was determined to be: (0.93-0.88) 0.05 volts and (0.88-0.85) 0.03volts respectively. This is much more reasonable as compared with the other records.

The voltage levels for each sampled design can be calculated as:
V=E-iR –w exp(z-i)
This formulae is best applied when we factor in the loss of voltage from the cell due to kinetic, ohmic and transport limitations. This works on the assumption that there is minimal anode polarization and there is manageable mass loss on the cathode rod.
The cell efficiency can be calculated using the current and voltage efficiency.
Current efficiency =theoretical amount of reactant required to produce a given current/actual amount of reactant consumed
Voltage efficiency= actual cell voltage/ reversible potential
Hence overall energy efficiency =current efficiency*voltage efficiency
These formulae can be applied to determine the different efficiency levels, among medium, low and high current density regions in fuel cells.
References
Choi, Y. (2003). Optimized fuel cell grade hydrogen from methanol.
Haddad, A., Bouyekhf, R., Moudni, A., & Wack, M. (n.d.). Non-linear dynamic modeling of proton exchange membrane fuel cell. Journal of Power Sources, 420-432.
Hayre, R. (2006). Fuel cell fundamentals. Hoboken, NJ: John Wiley & Sons.
Hoogers, G. (2003). Fuel cell technology handbook. Boca Raton, Fla.: CRC Press.
Liu, J. (2007). A structure-based model for cathode catalyst layer of polymer electrolyte membrane fuel cell. Burnaby B.C.: Simon Fraser University.
Proceedings / 2. European Solid Oxide Fuel Cell Forum. (1996). Oberrohrdorf: European SOFC Forum.
Ragb, O., Zhao, D., Yu, D., & Zhu, Q. (2011). Comparison study of different non-linear feed-forward controllers for oxygen starvation control of PEM fuel cell stacks. International Journal of Modeling, Identification and Control, 352-352.
Sheng, M. (2007). Non-linear model reduction and control of molten carbonate fuel cell systems with internal reforming.