of 32
JOUL, Volume
4
Supplemental Information
Role of Long-Duration Energy Storage
in Variable Renewable Electricity Systems
Jacqueline A. Dowling, Katherine Z. Rinaldi, Tyler H. Ruggles, Steven J. Davis, Mengyao
Yuan, Fan Tong, Nathan S. Lewis, and Ken Caldeira
1. Model formulation
1.1. Nomenclature
Symbol
Unit
Description
g
kW
Generation technology (wind, solar)
v
kW
Energy conversion (electrolyzer, fuel cell)
s
kWh
Energy storage (PGP storage, battery storage)
f roms
kW
Discharge from energy storage
tos
kW
Charge to energy storage
t
h
Time step, starting from 1 and ending at
T
c
capital
$/kW for generation
or conversion
$/kWh for storage
(Overnight) capital cost
c
fixed
$/kW/h for generation
or conversion
$/kWh/h for storage
Fixed cost
c
fixed O&M
$/kW/yr
Fixed operating and maintenance (O
&
M) cost
c
var
$/kWh
Variable cost
f
-
Capacity factor (generation technology)
h
h/year
Average number of hours per year
i
-
Discount rate
n
yrs
Project life
t
h
Time step size, i.e., 1 hour in the model
C
kW for generation or
conversion
kWh for storage
Capacity
D
t
kW
Dispatch at time step t
M
t
kWh
Demand at time step t
S
t
kWh
Energy remaining in storage at time step t
1/yr
Capital recovery factor
1/h
Storage decay rate, or energy loss per hour
expressed as fraction of energy in storage
-
Storage charging e
ffi
ciency
h
Storage charging duration
Table S1: Model nomenclature
1.2. Cost calculations
Fixed cost of generation and conversion technologies (wind, solar, electrolyzer,
fuel cell):
c
g,v
fixed
=
c
g,v
capital
+
c
g,v
fixed O&M
h
2
Fixed cost of energy storage (PGP storage, battery storage):
c
s
fixed
=
c
s
capital
h
Capital recovery factor:
=
i
(1 +
i
)
n
(1 +
i
)
n
1
1.3. Constraints
Capacity:
0
C
g,v,s
8
g, v, s
Dispatch:
0
D
g
t
C
g
f
g
8
g, t
0
D
v
t
C
v
8
v, t
0
D
to s
t
C
s
s
8
s, t
0
D
textfroms
t
C
s
s
8
s, t
0
S
s
t
C
s
8
s, t
0
D
from s
t
S
s
t
(1
s
)
8
s, t
Storage energy balance:
S
1
=(1
s
)
S
t
t
+
s
D
to s
T
t
D
from s
T
t
8
s
S
t
+1
=(1
s
)
S
t
t
+
s
D
to s
t
t
D
from s
t
t
8
s, t
2
1
,...,
(
T
1)
System energy balance:
X
g
D
g
t
t
+
D
from s
t
t
=
M
t
+
D
to so
t
t
8
g, t
1.4. Objective function
minimize(system cost)
system cost
=
X
g
c
g
fixed
C
g
+
X
g
(
P
t
c
g
var
D
g
t
T
)+
X
v
c
v
fixed
C
v
+
X
s
c
s
fixed
C
s
+
P
t
c
to s
var
D
s
t
T
+
P
t
c
from s
var
D
s
t
T
3
2. Supplemental experimental procedures
2.1. Model limitations
The linear model considers scenarios with perfect foresight, perfectly e
ffi
cient
markets, and no transmission losses. Despite these simplifications, key findings
of our study are in accord with and build on a similar European electricity
system that included transmission modeling.
1
Simulations for the West, East,
and Texas Interconnects further show the robustness of our results (Figure S7).
The system was confined solely to the electricity sector and did not consider
conversion of electricity into fuel to serve other sectors such as transportation
or heating. We did not include carbon capture with natural gas because the
regulatory and legislative environment considered is confined to zero-carbon and
renewable electricity sources (Table S2). We evaluate the system over an hourly
timescale. Other technologies, including perhaps batteries, are assumed to pro-
vide short term (minutes to hours) smoothing of power variability. Additionally,
although we include a project lifetime and self-discharge rate for batteries, we
do not track battery deterioration due to cycling. Previous studies of electric-
ity systems for the U.S. with high variable renewable penetration depend on
future projections, consider shorter time periods, do not satisfy hourly demand
with the statutorily required resource availability, and/or use highly complex
models.
2
2.2. Storage technology costs
In Table S3 we list cost and performance metrics for a variety of energy
storage technologies. This table builds o
ff
of the compiled information in Luo
et al.
3
for the more mature technologies: pumped hydropower, compressed air
energy storage, flywheels, capacitors, and lead-acid batteries; original works are
cited in the table itself. More rapidly developing technologies, such as Li-ion
batteries, redox flow batteries, and PGP cite more recent literature including
references
4,5
and those listed for the base case in Table 1. For some storage
technologies (pumped hydropower, compressed air, redox flow, and PGP) the
power and energy capacities for a given project can be sized independently. For
these technologies, and all of the others, we provide the total capital cost divided
by the power and again by the energy capacity of typical systems characterized
in the literature in Figure 1. In these cases, the flexibility of independently
sizing power and energy capacities for a given project for the LDS candidates is
not shown in this table. The values depicted in Figure 1 are shown in Table S3.
The increased flexibility of the four LDS technologies: pumped hydropower
storage (PHS), compressed air energy storage (CAES), redox flow batteries (po-
tentially because of the ability to separate power and energy capacities), and
PGP is shown in Table S3 where capital costs are split into power-related capi-
tal costs and energy-related capital costs. The costs of PHS projects are highly
site and project specific;
6
depending on the local geology, a dam capable of
storing one quantity of water in one valley, could potentially store a very dif-
ferent quantity in another valley necessitating caution when extrapolating PHS
costs. The conversion of pressurized air to power in a CAES systems relies on
4
multiple stages of air expansion with some involving gas turbines.
7
This makes
CAES inconsistent with with the zero carbon emissions and 100% RE goal of
this analysis. Despite this, we include CAES in Table S4. We emphasize that
either gas produced from a carbon neutral process would be needed for the tur-
bine or carbon capture and storage of the CO
2
from the exhaust. Either option
would increase the presented CAES costs.
5
3. Supplementary figures and tables
State
Max renewable
requirement
Electricity sector
end-state
Virginia
8
100% RE by 2050
a
100% RE-only by 2050
a
Maine
9
80% RE by 2030
100% RE-only by 2045
Hawaii
10
100% RE by 2050
100% RE-only by 2045
New Mexico
11
80% RE by 2040
Zero-carbon by 2045
New York
12
70% RE by 2030
Zero-carbon by 2040
b
California
13
60% RE by 2030
Zero-carbon by 2045
Nevada
14
50% RE by 2030
Zero-carbon by 2045
c
Washington
15
only zero-carbon requirements
Zero-carbon by 2045
Puerto Rico
16
100% RE by 2050
100% RE-only by 2050
Washington D.C.
17
100% RE by 2032
100% RE-only by 2032
Table S2:
100% clean power state laws: renewable vs. zero-carbon requirements.
Several states and jurisdictions have mandated the adoption of 100% clean electricity systems
by 2030-2050. The term ‘zero-carbon’ is broader than renewable energy (RE), as it gener-
ally includes technologies like nuclear and large-scale hydropower, for example, that are not
strictly renewable by policy definition in most state Renewable Portfolio Standards (RPS).
RE technologies include wind, solar, batteries, renewable hydrogen, and others. Natural gas
with CCS is currently not eligible as a "zero-carbon resource" for meeting clean energy man-
dates in states like California (although the CEC is actively discussing their eligibility for
this purpose.)
18
Natural gas with CCS may be permitted in net "zero-emissions" electricity
systems in states like New York. Most states with 100% clean power laws have mandated
the adoption of primarily RE technologies prior to zero-carbon or RE-only electricity system
end-states. RPS are also used to specify the capacities of certain RE technologies such as
wind, solar, and energy storage to be deployed. Iowa was the first state to establish an RPS
and since then, more than half of states have established RE targets.
19
While most state RE
targets are between 10% and 45%, 14 states—California, Colorado, Hawaii, Maine, Maryland,
Massachusetts, Nevada, New Mexico, New Jersey, New York, Oregon, Vermont, Virginia,
Washington, as well as Washington, D.C., Puerto Rico, and the Virgin Islands—have require-
ments of 50% or greater.
19
a
Virginia’s RE targets apply to ‘Phase I’ and ‘Phase II’ investor-owned utilities.
b
New York’s goal involves reducing 100% of the electricity sector’s greenhouse gas emissions
by 2040 as compared to 1990 levels.
c
Nevada’s 50% RE by 2030 target is binding; its 100% zero-carbon by 2050 target is non-
binding.
6
Demand
Solar
Wind
Median
50%
100%
Figure S1:
Resource and demand variability.
The temporal variability of wind (blue) and
solar (yellow) supply and electricity (black) demand over the contiguous United States from
1980-2018. Variability is shown over a) daily averaged, seasonal, b) hourly summer (June,
July, and August), and c) hourly winter (December, January, February) timescales. The dark
lines represent the median value, the darker shading represents the 25
th
to 75
th
percentile
of data, and the lighter shading represents the 0
th
to 100
th
percentile of data. All data is
normalized to its respective 39 year mean. See methods section on wind and solar capacity
factors for more details. Data used in our analysis is displayed here. The plotting code is
adapted.
20
7
storage
technology
total capital
cost ($/kW)
total
capital cost
($/kWh)
typical
energy/
power
typical
round-trip
e
ffi
ciency
RTE (%)
typical
lifetime
(years)
flywheel
250-350
7
1,000-
5,000
7
1
7,21
90–95
7
15
7
capacitor
200-400
7
500-1,000
7
1–1
7
60-70
7
5
7
lead–acid
300-600
7
200-400
7
<
1-
10
7,22
70-80,
7
63-90,
22
75–80
23
5-15
7
Li-ion
280-513,
488-980,
898-1,874
24
295-540,
e
257-517,
e
237-494
e
24
1,
2,
4
24
86-90
24
10
24
redox
flow
a
(vana-
dium)
1,027-1,155,
1,788-1,956
5
4,106-4,620,
447-489
5
0.25,
4
5
70-78,
76-79
5
20
5
pumped
hydropower
a
2,500-
4,300,
25
2,000-
4,000,
21
975
26
5-100,
7
97.5
26
1-24+,
7
6-10,
25
10,
21
10
26
70-85,
7
70-80
21
40-60,
7
50
f
compressed
air
a
400-800,
7
800-1,000,
21
650
26
2-50,
7
16
26
1-24,
7
40
26
42,
7
45-60
21
20-40,
7
30
f
power-to-
gas-to-
power
a
6,500-6,600,
b
5,300-11,000
c
5.6-8.8,
b
4.6-14
c
740-
1,200
b
electro-
lyzer 70,
d
fuel
cell 70,
d
RTE 49
d
electro-
lyzer 12.5,
d
cavern
30,
d
fuel
cell 20
d
Table S3: Technical characteristics of energy storage technologies with cost values reported
as total capital costs divided by typical power and energy capacities.
a
Technologies with more easily separated power and energy capacities and costs; values for
the split costs for these technologies are include in Table S4.
b
Characteristics for the specific PGP system used in this analysis and optimized using one
year of 2018 demand and resource data and again with 6 years of 2013-2018 data.
c
These values consider the two scenarios in the
b
note and the original uncertainty in fuel cell
capital costs of 4,600-10,000$/kW instead of using the base case value of 5,854 $/kW. The
PGP systems were not re-optimized based on the low and high fuel cell values.
d
References in Table 1.
e
Values originally reported based on nameplate energy storage, converted to usable energy by
dividing by sqrt(0.9), where 90% is approximately the round-trip e
ffi
ciency.
f
Exact values used in Figure 7b.
8