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III. MODEL FORMULATION
The output voltage of a single celi can be defined as the result of the following expression [1,3,9]:
Vrc=En,„-V„-VMl-V,m (4)
In the eąuation above, is the thermodynamic potential of the celi and it represents its
reversible voltage; Vact is the voltage drop due to the activation of the anodę and cathode (also known as activation overpotential), a measure of the voltage drop associated with the electrodes; is the ohmic voltage drop (also known as ohmic overpotential), a measure of the ohmic voltage drop resulting from the resistances of the conduction of protons through the solid electrolyte and the electrons through its path; and Vcon represents the voltage drop resulting from the reduction in concentration of the reactants gases or, altematively, from the transport of mass of oxygen and hydrogen (also known as concentration overpotential). There is another voltage drop associated to the internal currents and/or the fuel crossover [9]. This voltage drop is considered in the model, using a fixed current density even at no-load operation (represented by /„). The first term of (4) represents the FC open Circuit voltage (without load), while the three last terms represent reductions in this voltage to supply the useful voltage across the celi electrodes, Wc, for a certain operation current. Each one of the terms of (4) is discussed and modeled separately in the subsections that follow. Also, the following sections show the dynamie behavior of fuel cells and the equations for electrical power generation.
3.1. Celi reversible voltage
The reversible voltage of the celi (Em™*/) is the potential of the celi obtained in an open Circuit thermodynamic balance (without load). In this model, Esemst is calculated starting from a modified version of the equation of Nernst, with an extra term to take into account changes in the temperaturę with respect to the standard reference temperaturę, 25°C [1]. This is given by:
(5)
AG
" 2.F"
where AG is the change in the free Gibbs energy (J/mol); F is the constant of Faraday (96.487 C); AS is the change of the entropy (J/mol); R is the universal constant of the gases (8.314 J/K.mol); while Ph2 and Po2 are the partial pressures of hydrogen and oxygen (atm), respectively. Variable T denotes the celi operation temperaturę (K) and Tref the reference temperaturę. Using the standard pressure and temperaturę (SPT) values for AG, AS and Tref, (5) can be simplified to [ 1 ]:
(6)
ENems, = 1.229 - 0.85.10_3.(r - 298.15) + 4.31.10~5.T. |In (pHi ) + ^ In (p0j )
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