Supplementary
Information
for
A Comparative
Techno-Economic
Analysis
of
Renewable
Hydrogen
Production
Using
Solar
Energy
Electronic
Supplementary
Material
(ESI)
for
Energy
&
Environmental
Science.
This
journal
is
©
The
Royal
Society
of
Chemistry
2016
Methods
Photoelectrochemical
Systems
Costs
Window
Considerations
Poly(methyl
methacrylate
(Plexiglass®),
as
has
been
used
in
previous
studies,
was
not
recommended
by
an
industry
supplier,
based
on
chemical
compatibility
with
the
operating
conditions
of
this
design.
1,2
Systems
operating
in
alkaline
media
will
require
an
alternative
to
glass
(unstable),
such
as
an
ethylene
tetrafluoroethylene
(ETFE,
Fluon®
from
Asahi
Glass)-coated
glass
or
another
alkaline-stable
material
that
is
transparent
to
solar
illumination;
this
requirement
would
likely
increase
the
window
component
cost.
PEC
Membrane
Considerations
A
density
of 2 g – cm
-3
(based
on
acid
functionalized
membranes
3
),
a thickness
of 5
mil
(~127
microns)
and
a cost
of $2000/kg
was
used
to
calculate
the
$ - m
-2
PEC
for
Nafion
based
on
a Nafion
area
requirement
of
10%
of the
PEC
area.
Type
4 PEC
Concentrating
Optics
Considerations
A
variety
of
concentrating
optics
can
provide
non-
or
minimal
tracking
10x
light
concentration:
compound
parabolic
concentrators
(CPC),
Fresnel
lenses,
dielectric
totally
internally
reflecting
concentrators
(DTIRC)
and
prismatic
concentrators.
4
Commercial
availability
of
low-concentrating
optics
for
solar
applications
is
limited
to
two-dimensional
compound
parabolic
troughs,
prismatic
concentrators
and,
on
small-scale,
three-dimensional
parabolic
concentrators.
Concentrator
areal
costs
could
only
be
obtained
for
CPCs,
and
the
two-dimensional
trough
architecture
provided
the
lowest
costs,
$48
m
-2
.
1,5
A relatively
low
volume
(highest
volume
quote
available)
quote
for
three-dimensional
compound
parabolic
concentrators
(13x
concentration
ratio)
of
$1.9
x 10
5
m
-2
,
which
is four
orders
of magnitude
larger
than
the
two-dimensional
analog
used
in the
study.
PV-E
Sizing
The
photovoltaic
electrolysis
system
was
sized
such
that
the
photovoltaic
array
would
produce
the
exact
amount
of
energy
needed
to produce
the
desired
hydrogen
output,
10,000
kg/day,
and
the
electrolysis
units
were
sized
to
accept
the
maximum
instantaneous
power
output
by
the
photovoltaics,
assumed
to
be
1000
W
p
m
-2
.
For
the
base-case
economics,
this
arrangement
provided
the
lowest
cost
configuration
because
the
capital
cost
required
to
add
more
photovoltaics
is greater
than
the
capital
cost
reduction
associated
with
fewer
electrolyzer
units.
A
basic
calculation
that
demonstrates
this
follows.
The
base-case
photovoltaic
area
per
electrolyzer
stack
is
7.6
x 10
4
m
2
/stack.
In
the
limit
of
removing
a single
electrolyzer
stack
(500
kg
H
2
/day
capacity),
one
would
need
~7.6
x 10
4
m
2
of additional
photovoltaic
area,
which
would
be
an
additional
$3.9
MM
of
capital
(base-case
values),
while
the
removal
of
a
single
electrolyzer
stack
would
result
in
a
$0.98
MM
reduction
in
capital.
Thus,
the
capital
cost
of
the
additional
photovoltaic
arrays
outweighs
that
of
the
electrolysis
units.
This
simple
analysis
does
not
consider
the
value
of
the
extra
electricity
produced
by
the
additional
photovoltaic
area
that
could
be
sold
to
the
grid
and/or
used
onsite.
Capacity
Factor
The
maximum
capacity
factor
values
were
calculated
based
on
hourly
radiant
energy
density
data
for
each
month
from
2005-2010
for
Daggett,
CA
6
.
The
global
tilted
radiant
energy
density
data
was
used
for
all
systems
except
the
Type
4 system,
which
used
the
direct
tilted
radiant
energy
density
data
calculated
from
the
direct
normal
radiant
energy
density
data
available.
Equation
1 was
used
to
calculate
the
capacity
factor
where
each
monthly
averaged
hourly
radiant
energy
density
profile
was
multiplied
by
the
number
of days
in that
month
and
summed
for
all
hours
in
that
month
and
months
in
that
year
to
obtain
the
maximum
amount
of
solar
power
that
could
possibly
be
absorbed
per
m
2
.
This
value
was
divided
by
the
peak
irradiance
summed
over
all
wavelengths
(1000
W-m
-2
)
and
the
number
of
hours
in
a
year.
퐶푎푝푎푐푖푡푦
퐹푎푐푡표푟
푦푒푎푟
=
12 푀표푛푡ℎ푠
∑
푗
=
1
24 ℎ푟푠
∑
푖
=
1
푅
adiant energy density
ℎ푟,푚표푛푡ℎ
(
푊
‒
ℎ푟
푚
2
)
∗
퐷푃푀
(
푑푎푦푠
푚표푛푡ℎ
)
(
1000
푊
푚
2
)
(
8760
ℎ푟푠
푦푒푎푟
)
(1)
The
direct
tilted
radiant
energy
density
for
the
Type
4
system
was
calculated
assuming
100%
collection
of
all
direct
incident
light,
though
this
is
unlikely
because
of
the
lack
of
tracking
for
the
10x
concentrator
system
7
.
The
direct
normal
radiant
energy
data
were
adjusted
based
on
the
solar
azimuthal
and
zenith
angles
to
obtain
the
direct
tilted
radiant
energy
density
based
on
Equations
2 and
3 (collected
from
ref.
8
for
34N,
116W
and
GTM
offset
= -7
hrs
on
the
15
th
of each
month).
Here,
θ
is
the
tilt
angle
(set
to
the
latitude,
34°),
θ
z
is
the
solar
zenith
angle,
β
is the
panel
tilt
angle,
γ
s
is
the
solar
azimuth
angle
and
γ
is
the
panel
azimuth
angle
(set
to
180°
for
optimal
solar
collection
in
the
northern
hemisphere).
퐷푇퐼
=
cos
(
Θ
)
퐷푁퐼
(2)
cos
(
Θ
)
=
cos
(
Θ
푧
)
cos
(
훽
)
+
sin
(
Θ
푧
)
푠푖푛(훽)푐표푠
(
훾
푠
‒
훾)
(3)
The
base-case
capacity
factor
for
the
Type
4
system
was
calculated
based
on
the
ratio
of
the
maximum
operating
factors
and
the
base-case
operating
factor
for
the
non-concentrating
systems
(Equation
4).
표푓푎푐
푇푦푝푒 4 푏푎푠푒
‒
푐푎푠푒
=
표푓푎푐
푎푙푙 표푡ℎ푒푟푠 푏푎푠푒
‒
푐푎푠푒
표푓푎
푐
푇푦푝푒 4 푚푎푥
표푓푎
푐
푎푙푙 표푡ℎ푒푟푠 푚푎푥
(4)
The
maximum
capacity
factors
for
the
non-concentrated
and
concentrated
(Type
4)
systems
were
0.245
and
0.224,
respectively.
The
base-case
capacity
factor
for
the
Type
4 system
was
calculated
to be
0.186.
Figure
S 1:
Radiant
energy
density
versus
the
time
of
day
for
(a)
global
tilted
solar
irradiation
and
(b)
direct
tilted
solar
irradiation
The
value
used
for
the
base-case
of
the
non-concentrated
systems
is different
than
other
recently
reported
AC
capacity
factors
for
photovoltaics
in
the
southwestern
U.S.
9
.
The
photovoltaic
AC
capacity
factor
is
equivalent
to the
capacity
factor
used
in
this
study
because
it
does
not
include
AC-DC
conversion
losses
and
thus
is
higher
than
DC
capacity
factors.
As
indicated
in ref.
9
the
high
AC
capacity
factors
for
photovoltaic
installations
are
due
to
an
oversizing
of the
installed
photovoltaic
capacity
as
compared
to
the
inverter
capacity.
Because
the
capacity
rating
is based
on
the
inverter
capacities
in these
systems,
the
oversized
photovoltaic
array
artificially
makes
the
capacity
factor
higher
than
physically
possible
based
on
integration
of
the
solar
resource
in those
regions.
Financial
Calculations
Many
cost
estimates
for
system
components
were
taken
from
reports/quotes
in the
past.
These
were
future
valued
to
2014
$ by
Equation
5 using
an
inflation
rate
of
1.9%.
퐹푢푡푢푟푒 푉푎푙푢푒
(
2014 $
)
=
푅푒푝표푟푡푒푑 푉푎푙푢푒
(
#### $
)
(
1
+
0.019
)
2014
‒
####
(5)
Solar
Area
Calculations
The
area
required
for
the
solar
absorbing
component
of
the
system
was
calculated
based
on
the
following
equation.
퐴푟푒푎
(
푚
2
)
=
10000
(
푘푔
퐻
2
푑푎푦
)
1.2 푥
10
8
(
퐽
푘푔
퐻
2
)
1000
(
푊
푝
푚
2
)
휂
푆푇퐻
3600
(
푠
ℎ푟
)
24
(
ℎ푟
푑푎푦
)
표푓푎
푐
푠표푙푎푟
(6)
Number
of
PEM
Electrolyzer
Stack
Calculations
푁푢푚푏푒푟 표푓 푆푡푎푐푘푠
=
10000
(
푘푔
퐻
2
푑푎푦
)
500
(
푘푔
퐻
2
푠푡푎푐푘
)
표푓푎
푐
푒푙푒푐푡푟표푙푧푒푟
(7)
Discussion
Calculations
Carbon
Tax
To
calculate
the
carbon
tax
($
kg
-1
H
2
)
for
the
base-case
Type
3 and
4 PEC
systems,
Equation
9 was
used
with
the
SMR
CO
2
intensity
taken
from
industrial
data.
10
The
target
systems
were
assumed
to have
a CO
2
intensity
of zero.
퐶푎푟푏표푛 푇푎푥
(
$
푡 퐶
푂
2
)
=
푇푎푟푔푒푡 푆푦푠푡푒푚
(
$
푘푔
퐻
2
)
‒
푆푀푅
(
$
푘푔
퐻
2
)
푆푀푅 퐶푂
2
퐼푛푡푒푛푠푖푡푦
(
푡 퐶
푂
2
푘푔
퐻
2
)
(8)
The
CO
2
intensity
of
grid
electrolysis
was
calculated
from
the
total
CO
2
associated
with
electricity
generation
11
and
the
total
electricity
produced
12
in
the
U.S
in 2012
,
in
conjunction
with
an
electrolysis
efficiency
of
66%
(50
kWH/kg
H
2
)
10
.
CO
2
Electrochemical
Reduction
Product
CO
2
Cost
Equivalence
The
CO
2
cost
equivalence
for
a
variety
of
known
CO
2
electrochemical
reduction
products
on
Cu
was
calculated
by
first
determining
the
current
market
value
in
$/ton
product.
13
A mass
change
fraction
was
then
calculated
for
each
product
based
on
the
carbon
and
oxygen
content
retained
from
CO
2
in
the
product
molecule.
The
CO
2
equivalence
value
is
then
given
by
multiplying
the
product
market
value
by
the
mass
fraction
value. This
calculation,
Equation
9,
assumes
100%
utilization
of
CO
2
.
퐶푂
2
퐸푞푢푖푣푎푙푒푛푐푒
(
$
푡표푛
퐶푂
2
)
=
푃푟표푑푢푐푡 푉푎푙푢푒
(
$
푡표푛
)
×
# 표푓 퐶 푖푛 푝푟표푑푢푐푡
×
12
(
푔
푚표푙
)
+
# 표푓 푂 푖푛 푝푟표푑푢푐푡
×
16
(
푔
푚표푙
)
# 표푓 퐶 푖푛 푝푟표푑푢푐푡
×
44
(
푔
푚표푙
)
CO
2
Mass
Transport
Limitations
Liquid
phase
mass
transport
of
CO
2
to a submersed
electrode
surface
can
limit
the
maximum
achievable
rate
of
reaction.
The
aqueous
mass
transport
limited
flux
of
CO
2
into
the
liquid
is
~10
-6
mol
m
-2
s
-1
.
14
The
equivalent
current
density
is
dependent
on
the
number
of
electrons
used
per
CO
2
in
the
reduction
process,
mA
cm
-2
.
Assuming
an
8 electron
reduction
of
# 표푓 푒푙푒푐푡푟표푛푠 푝푒푟
퐶푂
2
푚표푙푒푐푢푙푒
×
10
‒
2
CO
2
gives
a
limiting
current
density
of
~10
-1
mA
cm
-2
,
which
is
approximately
3
orders
of
magnitude
lower
than
the
limiting
current
density
for
a tandem
junction
cell.
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