Environmental Engineering Reference
In-Depth Information
acquired by sensors located in the experimental plant introduced in the previous
sections. These calculations are also valid for the other case study analyzed in the
next chapter.
The stack efficiency is calculated by the following equation:
g
stack
¼
V
V
id
ð
6
:
1
Þ
where V is the measured output stack voltage and V
id
is the reversible open circuit
stack voltage (1.23 V), given by -DG
f
/2F (see
Sect. 3.1
), while the theoretical or
thermodynamic stack efficiency is given by the Eqs.
6.3
-
6.9
.
As discussed in
Sect. 4.2
, during stack operation a partial hydrogen purge is
necessary, then it is possible to define a fuel utilization efficiency (g
util
) as ratio
between mass of fuel reacted in the stack and mass of fuel entering the stack. It can
be experimentally set by fixing the opening time and the opening frequency of the
anode purge valve. The efficiency losses due to all the auxiliary components (air
compressor, water pump, cable resistance, other electrical, and minor components)
necessary to the stack operation can be taken into account by an experimental
coefficient (g
abs
) expressed as ratio between power at DC-DC converter inlet and
stack power. The total efficiency of the fuel cell system is then calculated by the
following equation:
g
FCS
¼
g
th
g
util
g
stack
g
abs
ð
6
:
2
Þ
which expresses the ratio between the power at DC-DC converter input and the
theoretical power associated with the fuel entering the stack. The experimental
determination of DC-DC converter (g
DC
) and electrical drive (g
ED
) efficiency is
also performed. Both are calculated as ratio between outlet and inlet power of the
devices. The electrochemical efficiency of storage batteries is defined as ratio
between the integral of the instantaneous current during a discharge and the same
integral during a charge, if the status of the battery before and after the calculation
is the same:
R
t
d
I
d
dt
0
g
batt
¼
ð
6
:
3
Þ
R
t
c
I
c
dt
0
where I
d
and I
c
are the battery current during the discharge and charge periods,
respectively, while t
d
and t
c
are the lengths of these periods. The determination of
this efficiency for a specific type and sample of battery, with reference to a par-
ticular driving cycle, requires the experimental evaluation of the battery state of
charge (SOC), which is based on specific tests which are beyond the scope of this
case study. On the other hand, for lead-acid batteries, used in this case study, it has
