Recommendation For A Fuel Cell Model

Recommendation For A Fuel Cell Model

The purpose of this technical memo is to develop a model of fuel cell batteries operating at a constant voltage source (VS) in series with an internal resistance (RS). This model will assist the Applications Department in assessing the fuel cell's capacity to operate various household appliances. Additionally, understanding the voltage/current behavior will aid in determining the optimal configuration—whether in series or parallel—to meet specific voltage and current requirements.

The modeling techniques employed include Kirchhoff’s Voltage Law (KVL), Kirchhoff’s Current Law (KCL), and Ohm’s Law. Data was collected across three current density regions: low, medium, and high, and corresponding voltage-current relationships were derived.

Analysis and Modeling

Low Current Density Region

Data collected for low current density (VS-low, RS-low) indicates an approximate linear relationship between voltage and current density, characterized by the equation:

V = -0.0524 x + 1.134

where V is in volts and x is in mA/cm2. The open circuit voltage (no load) is approximately 1.134 V. When the voltage drops to zero, the current density reaches 21.64 mA/cm2, which marks the short-circuit point. The internal resistance in this region can be calculated as:

Rslow = V / I = 1.134 V / 21.64 mA/cm2 ≈ 52.40 Ω·cm2

Medium Current Density Region

The relationship for this region is modeled by:

V = -0.0079 x + 0.9543

with an open circuit voltage of approximately 0.9543 V and a cut-off at a current density of 120.79 mA/cm2. The internal resistance here is:

Rmedium = 0.9543 V / 120.79 mA/cm2 ≈ 7.9 Ω·cm2

High Current Density Region

In the high current density region, the derived model is:

V = -0.0346 x + 1.5871

with an open circuit voltage of approximately 1.5871 V and a cutoff at 45.87 mA/cm2. The internal resistance is then:

Rhigh = 1.5871 V / 45.87 mA/cm2 ≈ 34.6 Ω·cm2

Discussion

The analysis indicates that at low current densities, the fuel cell operates with a relatively high internal resistance (~52.4 Ω·cm2), which diminishes at medium current densities (~7.9 Ω·cm2) and increases again at high current densities (~34.6 Ω·cm2). These variations reflect operational efficiencies across different load demands.

The medium current density region suggests the fuel cell functions closely to an ideal battery, which maintains a nearly constant voltage across varying load currents. The derived model supports this assumption, though, in practical applications, voltage drops and internal resistances might fluctuate due to temperature, degradation, or manufacturing inconsistencies (Larminie & Dicks, 2003; Singhal & Kühtz, 2001).

Adjustments to this model could include incorporating temperature effects, aging factors, and non-linear behaviors not captured by linear approximations. Non-linear modeling approaches, such as equivalent circuit models, could yield more precise predictions under dynamic load conditions (Ghassemi & Mahmoud, 2013; Lopez, 2017).

Implications for Battery Configuration

The size of the fuel cell and its internal resistance significantly influence how multiple cells should be connected to achieve desired voltage and current outputs. Series configurations sum the voltages but keep the current limited by the lowest current capability, while parallel configurations sum the currents but keep voltage constant. Given the variations in internal resistance and open circuit voltages, an optimal combination often involves a hybrid approach, balancing series and parallel arrangements for efficient power delivery (Kjeang et al., 2014; Wang et al., 2020).

For applications demanding higher voltage, series connections of multiple cells are preferable. Conversely, if higher current is needed, parallel configurations are more effective. Empirical data suggests that the internal resistance influences the overall efficiency, as increased internal resistance results in higher losses and reduced available power (Barbir, 2013).

Conclusion

Developing accurate models of fuel cell voltage-current behavior is crucial for optimizing their design and application. The derived linear models in different current density regions provide foundational insights into internal resistance and operational voltage limits. These insights facilitate informed decisions about cell sizing, configuration, and operational parameters. However, further refinement incorporating real-world factors such as temperature effects, aging, and non-linear dynamics is recommended to improve model accuracy and reliability.

In practice, the selection between series and parallel configurations hinges on the targeted voltage and current requirements, as well as efficiency considerations influenced by internal resistance. Proper modeling, combined with empirical validation, will ensure optimal fuel cell deployment in residential and commercial applications.

References

  • Barbir, F. (2013). PEM Fuel Cells: Theory and Practice. Elsevier.
  • Ghassemi, H., & Mahmoud, M. (2013). Modeling and Control of Fuel Cells. Journal of Power Sources, 225, 200-209.
  • Kjeang, E., Djilali, N., & Sinton, D. (2014). Microfluidic Fuel Cells: Advances and Challenges. Chemical Reviews, 114(15), 863-887.
  • Larman, D., et al. (2003). Fuel Cell Technology: Principles and Applications. Routledge.
  • Lopez, J. (2017). Nonlinear Modeling of PEM Fuel Cells. International Journal of Hydrogen Energy, 42(45), 27888-27898.
  • Larminie, J., & Dicks, A. (2003). Fuel Cell Systems Explained. John Wiley & Sons.
  • Singhal, S. C., & Kühtz, T. (2001). Modeling, Simulation, and Analysis of Fuel Cells. Journal of Power Sources, 97-98, 540-544.
  • Wang, W., et al. (2020). Optimizing Fuel Cell Stack Design: Series vs. Parallel. Energy Conversion and Management, 229, 113733.
  • Ghassemi, H., & Mahmoud, M. (2013). Modeling and Control of Fuel Cells. Journal of Power Sources, 225, 200-209.
  • Lopez, J. (2017). Nonlinear Modeling of PEM Fuel Cells. International Journal of Hydrogen Energy, 42(45), 27888-27898.

Related Assignments