ANALYSIS AND MODELING OF A LT-PEM FUEL CELL

ANALYSIS AND MODELING OF A LT-PEM FUEL CELL

Nguyen Ha Hiep

candidate of technical sciences, Le Quy Don Technical University,

Vietnam, Hanoi

Trinh Xuan Long

candidate of technical sciences, Le Quy Don Technical University,

Vietnam, Hanoi

ABSTRACT

The paper presents an analysis of the operation of fuel cells and the results of their simulation using the program MATLAB/Simulink. The main characteristics of fuel cells are determined.

Keywords: fuel cell, LT-PEM, anode, cathode, Nerst equation, polarization curve.

Introduction

Fuel cells are electrochemical devices that convert chemical energy in fuels into electrical energy directly and heat with high efficiency. Proton exchange membrane fuel cells (PEMFC) are a type of fuel cell being developed mainly for transport applications, as well as for stationary and portable applications. They work at a lower temperature (less than 100 °C), called an LT-PEM fuel cell. A schematic diagram of the LT-PEM fuel cell is shown in Figure 1 [1].

Figure 1. Schematic of LT-PEM fuel cell

The following reactions in LT-PEM fuel cells [2]:

Anode: H₂ (g) → 2H⁺ + 2e^-

Cathode: 1/2O₂ (g) + 2H⁺ + 2e^- → H₂O (l)

Overall: H₂ (g) + 1/2O₂ (g) → H₂O (l) + electric energy + waste heat

Reactants are transported by diffusion and convection to the catalyzed electrode surfaces where the electrochemical reactions occur.

Materials and methods of research

This electric energy is called the enthalpy of formation ∆H, which can be divided into thermal energy, represented by specific entropy ∆S kJ/mol.K, multiplied by operational absolute temperature T, and useful work called Gibbs free energy ∆G kJ/mol, which can be extracted as electrical energy. So, the total energy is [3]:

The maximum electrical work (W_el) obtainable in a fuel cell operating at constant temperature and pressure is given by the change in Gibbs free energy (∆G) of the electrochemical reaction [2]:

where n = 2 is the number of electrons participating in the reaction, F is Faraday's constant (96487 coulombs/g-mole electron), and E is the ideal potential of the cell.

The potential given by the fuel cell can be calculated as follow:

This value must be adapted to get the effects of the changes in operational temperature, and partial pressures of reactants and products from its reference value (T_ref = 25 ^oC, P_ref = 1 atm). The effect of changing temperature on potential is calculated by considering that ∆H, and ∆S are constant as follow [3]:

The Gibbs free energy change of reaction can be expressed by the equation [3]:

where ∆G^o = -237.17 kJ/mol is Gibbs free energy in the standard condition, and R gas constant 8.3143 J/mol.K.

The Nerst equation for voltage [4]:

The activation loss is given by a semi empirical equation [4]

where ξ_i are parametric coefficients, i_FC is the cell current, and C_O2 is the oxygen's concentration mol/cm³ on the catalytic interface which equals:

The ohmic loss is given by [3]:

where R_c is the constant part of cell’s resistance, and R_m depends on the temperature and on a parameter Ψ which represents membrane hydration level, and R_m is given by:

where l is the membrane thickness (Nafion 117), A the cell active area cm², ρ_m specific membrane resistance Ω.cm which is:

The concentration loss is given by [4]:

where B, V -  the factor depends on the fuel cell type and operating conditions; j is the current density mA/cm², j = i_FC/A; j_L is the limiting current density j_L = 1500 mA/cm².

Therefore, the equation defines the fuel cell voltage as:

Results and discussion

In this work, analysis and modeling of fuel cells with a power of 1.26 kW, and a voltage of 24 V were carried out. The nominal current will be I_nom = 52.5 A. Nominal cell voltage accepted, V_cell.nom = 0.57 V. The number of cells N = 24/0.57 = 42. Therefore, the nominal current density j_nom = 0.79 A/cm² and the cell active area A = 66.7 cm². Other parameters of fuel cells are given in Table 1 [3,4].

Table 1.

Parameters of a LT-PEM fuel cell

Based on the data in Table 1, using the program MATLAB/Simulink, we built a fuel cell polarization curve (Figure 2) and Volt-Ampere characteristic of LT-PEM fuel cell (Figure 3). They indicate the performance of the investigation fuel cells.

Figure 2. LT-PEM fuel cell polarization curve

Figure 3. Volt-Ampere characteristic of LT-PEM fuel cell

Conclusions

Analysis and modelling of LT-PEMFC with a power of 1.26 kW, and a voltage of 24 V were carried out. The nominal current of 52.5 A, the cell active area of 66.7 cm², the cell number of 42 are determined.

Fuel cell polarization curve and Volt-Ampere characteristic of LT-PEM fuel cell are described. They can be used when choosing fuel cells for a vehicle.

References:

1. P V Belyaev et al (2018). The research of compensation for changes in air flow rate by increasing the oxygen concentration of oxidant in a fuel cell J. Phys.: Conf. Ser. 1050 012011
2. Fuel cells Handbook ed. S. Edition (2004). EG&G Technical Services, Inc.
3. Saeed, E. W., & Warkozek, E. G. (2015). Modeling and Analysis of Renewable PEM Fuel Cell System. Energy Procedia, 74, 87–101. doi:10.1016/j.egypro.2015.07.527.
4. Ansari, S. A., Khalid, M., Kamal, K., Abdul Hussain Ratlamwala, T., Hussain, G., & Alkahtani, M. (2021). Modeling and Simulation of a Proton Exchange Membrane Fuel Cell Alongside a Waste Heat Recovery System Based on the Organic Rankine Cycle in MATLAB/SIMULINK Environment. Sustainability, 13(3), 1218. doi:10.3390/su13031218.