32 Techno-Economic Analysis of a Hybrid Solar-Hydrogen-Biomass …
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and Wind turbine. The output power of the fuel cell is proportional to the rate of
hydrogen consumption (m H 2 ) (Kabza 2016):
P FC = N · I FC · E FC
(32.14)
N is the number of cells, and I FC is the current flow of cells. E FC refers to the
electromotive energy of fuel cell which is calculated as follows:
I FC =
2F
s A
mol
N[−] · υ[−] · M
g
mol
·
m H 2
g
s
(32.15)
E FC [V] = E 0 − b(log(i) + 3) − R ohmic i − me
8i
(32.16)
where, F is Faraday constant; υ is the stoichiometry of the reaction; M is the molecular
mass of hydrogen; i is the current flow density which is a function of the reaction
area (A) as follows:
i = I/A
(32.17)
And b is the Tafel slope:
b =
1
2
nF
RT
(32.18)
n is the number of exchanged electrons in the reaction; T is the working temperature
of fuel cells. Generally, the range of working temperature of PEM (Polymer Electrode
Membrane) Fuel cells is between 353.15[K] (80[°C]) to 393.15[K](120[°C]).
In Eq. (32.16), E 0 is the open circuit voltage (OCV). This value is dependent on
the working cell temperature:
E 0 = −G/nF
(32.19)
G[kJ/mol] = 0.052T[K] − 244.277[
J
mol
]
(32.20)
When working temperature increases, the absolute value of Gibbs free energy
decreases. The ohmic loss in Eq. (32.16) can be calculated by using the below
equations
R ohmic = r m [ cm]L mem [cm]
(32.21)
where, r m refers to the specific resistivity for the flow of hydrated protons, and L mem
is the thickness of the polymer membrane as given in (Laoun 2016).