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1
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Supplementary
Information
-
Ruggles, T.H. & Virgüez, E., et al.
Planning reliable wind
-
and solar
-
based electricity systems
Tyler H. Ruggles
1+*
, Edgar Virgüez
1+*
, Natasha Reich
2
, Jacqueline Dowling
1
, Hannah Bloomfield
3
, Enrico
G.A. Antonini
1,4
,5
, Steven J. Davis
6
, Nathan S. Lewis
2,
7
, Ken Caldeira
1,
8
*
1
Carnegie Science; Stanford, California, United States.
2
Division of Chemistry and Chemical Engineering, California Institute of Technology; Pasadena, California, United States.
3
School of
Engineering, Newcastle University; Newcastle, England.
4
CMCC Foundation, Euro
-
Mediterranean Center on Climate Change
;
Lecce,
A
pulia
,
Italy
.
5
RFF
-
CMM European Institute on Economics and the Environment; Milan, Lombardy, Italy
.
6
Department of Earth System Science,
Stanford
University,
Stanford
;
Stanford
,
California, United States.
7
Beckman Institute, California Institute of Technology; Pasadena, California, United States.
8
Gates Venture
s
; Kirkland, Washington, United States.
+
These authors contributed equally (equally contributing first
authors)
* Corresponding authors:
-
Tyler H. Ruggles (truggles@carnegiescience.edu)
-
Edgar Virgüez (evirguez@carnegiescience.edu)
-
Ken Caldeira (kcaldeira@carnegiescience.edu)
This document contains:
-
Supplementary Equations S1
-
S23 (pages 3
-
6)
-
Supplementary Table
s
S1
(
page 2
) and S2 (page
23
)
-
Supplementary Figures
S
1
-
S1
4
(
pages
8
-
22
)
-
References
(page
2
4
)
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2
of
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4
Supplementary
Information
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Ruggles, T.H. & Virgüez, E., et al.
Model
f
ormulation
The model formulation is presented below and supplements the higher
-
level model description in the main text.
Table
S
1 | Model formulation
Symbol
Unit
Description
푥
푡표
푦
label only
Energy from ‘x’ to ‘y’ (grid to battery, battery to grid, grid to
H
2
, H
2
to grid)
푡
h
Time step, starting from 1 and ending at T
푐
푐푎푝
(
$
푘푊
푒
)
for generation and
electrolysis facility,
(
$
푘푊
ℎ
푒
)
for battery storage,
(
$
푘푊
ℎ
퐿퐻푉
)
for H
2
storage,
(
$
푘푊
퐿퐻푉
)
for fuel cell
(Overnight) capital cost
푐
푓푖푥푒푑
푂
&
푀
(
$
푦푟
푘푊
푒
)
for generation,
(
$
푦푟
푘푊
ℎ
푒
)
for storage
Fixed operating and
maintenance (O&M) cost
푐
푓푖푥푒푑
(
$
ℎ
푘푊
푒
)
for generation,
(
$
ℎ
푘푊
ℎ
푒
)
for storage
Fixed cost
푐
푣푎푟
(
$
푘푊
ℎ
푒
)
Variable cost (natural gas with CCS)
푓
unitless
Capacity factor (generation technology, f = 1 for all t for natural
gas)
ℎ
h/yr
Number of hours per year
푖
unitless
Discount rate
푛
years
Asset lifetime
훥푡
h
Time step size, i.e., 1 hour in the model
퐶
푘푊
푒
푘푊
ℎ
푒
(generation / storage)
Capacity
퐷
푡
푘푊
푒
Dispatch at time step t from generation or energy storage
assets
푀
푡
푘푊
푒
Electricity load at time step t
푢
푡
푘푊
푒
Curtailed power
푆
푡
푘푊
ℎ
푒
푘푊
ℎ
퐿퐻푉
(battery / H
2
)
Energy in battery or H
2
storage at end of time step t
퐿
푡
푘푊
ℎ
푒
Energy supply shortfall at time step t (lost load)
퐿퐿
푡표푡
푘푊
ℎ
푒
Total energy supply shortfall
퐿퐿
푓푟푎푐
unitless
Total energy supply shortfall divided by total load
훾
1/
yr
Capital recovery factor
훿
1/
h
Storage decay rate (energy loss per hour) expressed as fraction
of energy in storage
휂
unitless
Round
-
trip efficiency (all energy storage assets)
휏
h
Storage charging duration
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Ruggles, T.H. & Virgüez, E., et al.
The fixed hourly costs (Eq.
S
1) for the generation assets (wind, solar, and natural gas), the battery storage
asset, and the energy conversion assets
(electrolysis facility and fuel cell) were calculated considering capital
investment (
푐
푐푎푝
)
and fixed annual operation and maintenance costs (
푐
푓푖푥푒푑
푂
&
푀
)
. We partitioned the capital
investment over the lifetime of the associated asset using an annual capital recovery factor (Eq.
S
2).
푐
푓푖푥푒푑
=
훾
푐
푐푎푝
+
푐
푓푖푥푒푑
푂
&
푀
ℎ
(
푆
1
)
훾
=
푖
(
1
+
푖
)
푛
(
1
+
푖
)
푛
−
1
(
푆
2
)
The power capacities of wind generation (
퐶
푤푖푛푑
), solar generation (
퐶
푠표푙푎푟
), and natural
-
gas
-
fired generation
(
퐶
푛푎푡
푔푎푠
) were constrained to be greater than or equal to zero (Eq.
S
3).
퐶
푤푖푛푑
≥
0
,
퐶
푠표푙푎푟
≥
0
,
퐶
푛푎푡
푔푎푠
≥
0
(
푆
3
)
The associated dispatched power flows (
퐷
푡
) at each time step (
푡
) were constrained by the capacities (Eqs.
S
4 &
S
5). For wind and solar, the capacity is multiplied by the capacity factor for that time step (
푓
푡
).
0
≤
퐷
푡
,
푛푎푡
푔푎푠
≤
퐶
푛푎푡
푔푎푠
(
푆
4
)
0
≤
퐷
푡
,
푤푖푛푑
≤
퐶
푤푖푛푑
푓
푡
,
푤푖푛푑
,
0
≤
퐷
푡
,
푠표푙푎푟
≤
퐶
푠표푙푎푟
푓
푡
,
푠표푙푎푟
(
푆
5
)
In the
Solar+wind+battery+DG
scenario, the total dispatch of natural gas was constrained to supplying less
than or equal to 5% of total energy demand during the initial optimizations (Eq.
S
6). This 5% constraint was
removed during the operational tests of the
Solar+wind+battery+DG
systems.
∑
퐷
푡
,
푛푎푡
푔푎푠
푡
∑
푀
푡
푡
≤
5%
(
푆
6
)
Lost load per time step (
퐿
푡
)
did not have an associated capacity constraint and was forced to equal zero for
all time steps during the system planning phase (Eq.
S
7).
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퐿
푡
=
0
(
푆
7
)
The energy capacities of
battery storage (
퐶
푏푎푡푡
) and the power capacity of conversion technologies, i.e.,
electrolysis facility (
퐶
푒푙푒푐푡푟표푙푦푠푖푠
) and fuel cell (
퐶
푓푢푒푙
푐푒푙푙
) were also constrained to be greater than or equal
to zero (Eq.
S
8).
퐶
푏푎푡푡
≥
0
,
퐶
푒푙푒푐푡푟표푙푦푠푖푠
≥
0
,
퐶
푓푢푒푙
푐푒푙푙
≥
0
(
푆
8
)
The battery charging and discharging rates were limited by the energy storage capacity and the power
-
to
-
energy ratio (
휏
푏푎푡푡
)
, which was 4 for the modeled Li
-
ion technology (Eqs.
S
9 &
S
10).
0
≤
퐷
푡
,
푔푟푖푑
푡표
푏푎푡푡
≤
퐶
푏푎푡푡
휏
푏푎푡푡
(
푆
9
)
0
≤
퐷
푡
,
푏푎푡푡
푡표
푔푟푖푑
≤
퐶
푏푎푡푡
휏
푏푎푡푡
(
푆
10
)
The rates for charging and discharging the hydrogen storage were limited by the power capacities of the
conversion technologies (electrolysis facility and fuel cells) (Eqs.
S
11 &
S
12).
0
≤
퐷
푡
,
푔푟푖푑
푡표
퐻
2
≤
퐶
푒푙푒푐푡푟표푙푦푠푖푠
(
푆
11
)
0
≤
퐷
푡
,
푏푎푡푡
푡표
퐻
2
≤
퐶
푓푢푒푙
푐푒푙푙
(
푆
12
)
The stored energy in the grid battery and hydrogen storage (when included in the scenario) were less than or
equal to their energy storage capacities (Eq.
S
13), with the total dischargeable energy limited by the decay
rates of the stored energy (Eq.
S
14).
0
≤
푆
푡
,
푏푎푡푡
≤
퐶
푏푎푡푡
,
0
≤
푆
푡
,
퐻
2
≤
퐶
퐻
2
(
푆
13
)
0
≤
퐷
푡
,
푏푎푡푡
푡표
푔푟푖푑
≤
푆
푡
,
푏푎푡푡
(
1
−
훿
푏푎푡푡
)
훥푡
,
0
≤
퐷
푡
,
퐻
2
푡표
푔푟푖푑
≤
푆
푡
,
퐻
2
(
1
−
훿
퐻
2
)
훥푡
(
푆
14
)
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Energy balance was maintained for all time steps for the electricity node and, when applicable, for the
hydrogen node. The grid battery storage assets maintained energy balance, including balancing at the start and
end of each simulation, according to Eq.
S
15 and Eq.
S
16, where time steps range from
1
through
T
.
푆
1
,
푏푎푡푡
=
(
1
−
훿
푏푎푡푡
)
푆
푇
,
푏푎푡푡
훥푡
+
휂
푏푎푡푡
퐷
푇
,
푔푟푖푑
푡표
푏푎푡푡
훥푡
−
퐷
푇
,
푏푎푡푡
푡표
푔푟푖푑
훥푡
(
푆
15
)
푆
푡
+
1
,
푏푎푡푡
=
(
1
−
훿
푏푎푡푡
)
푆
푡
,
푏푎푡푡
훥푡
+
휂
푏푎푡푡
퐷
푡
,
푔푟푖푑
푡표
푏푎푡푡
훥푡
−
퐷
푡
,
푏푎푡푡
푡표
푔푟푖푑
훥푡
푡
∈
1
,
...
,
(
푇
−
1
)
(
푆
16
)
The hydrogen energy balance used in the
Solar+wind+battery+H
2
scenario is described in Eqs.
S
17 &
S
18,
similar to Eqs.
S
15 &
S
16 used for battery storage.
푆
1
,
퐻
2
=
(
1
−
훿
퐻
2
)
푆
푇
,
퐻
2
훥푡
+
휂
퐻
2
퐷
푇
,
푔푟푖푑
푡표
퐻
2
훥푡
−
퐷
푇
,
퐻
2
푡표
푔푟푖푑
훥푡
(
푆
17
)
푆
푡
+
1
,
퐻
2
=
(
1
−
훿
퐻
2
)
푆
푡
,
퐻
2
훥푡
+
휂
푒푙푒푐푡푟표푙푦푧푒푟
퐷
푡
,
푔푟푖푑
푡표
퐻
2
훥푡
−
퐷
푡
,
퐻
2
푡표
푔푟푖푑
훥푡
푡
∈
1
,
...
,
(
푇
−
1
)
(
푆
18
)
Grid energy balance was maintained by balancing all sources (generation, discharge from the grid battery
and conversion from H
2
via the fuel cell, and lost load per time step) against all sinks (load, battery charging
and conversion to H
2
via the electrolysis facility, and generation curtailment) (Eq.
S
1
9
).
(
퐷
푡
,
푤푖푛푑
+
퐷
푡
,
푠표푙푎푟
+
퐷
푡
,
푛푎푡
푔푎푠
)
훥푡
+
퐷
푡
,
푏푎푡푡
푡표
푔푟푖푑
훥푡
+
휂
푓푢푒푙
푐푒푙푙
퐷
푡
,
퐻
2
푡표
푔푟푖푑
훥푡
+
퐿
푡
훥푡
=
푀
푡
훥푡
+
퐷
푡
,
푔푟푖푑
푡표
푏푎푡푡
훥푡
+
퐷
푡
,
푔푟푖푑
푡표
퐻
2
훥푡
+
푢
푡
훥푡
(
푆
19
)
The lost load per time step was constrained to zero during the initial optimizations for all time steps (Eq.
S
7).
The total lost load over the duration of the modeled system operations is referred to as lost load (
퐿
퐿
푡표푡
)
throughout the text (Eq.
S
20) and is often referred to as a percent of electricity load (
퐿
퐿
푓푟푎푐
)
(Eq.
S
21).
퐿
퐿
푡표푡
=
∑
퐿
푡
훥푡
푡
(
푆
20
)
퐿
퐿
푓푟푎푐
=
∑
퐿
푡
푡
∑
푀
푡
푡
(
푆
21
)
The model minimized the system cost for each initial simulation (Eq.
S
22) by optimizing the installed
generation, conversion, and battery storage asset capacities and dispatch during each 4
-
hour time step, while
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lost load was constrained to zero. When planned systems were being tested for resource adequacy, asset
capacities were held constant and only the dispatch of each technology was varied in the cost
-
minimization
process. The cost of lost load during tests, $
10/kWh, was substantially greater than all other variable costs.
Thus, the lost load in each test was effectively minimized. Despite this, lost load was often greater than zero
during these tests.
푆푦푡푒푚
푐표푠푡
=
∑
푐
푓푖푥푒푑
,
푡푒푐
ℎ
퐶
푡푒푐
ℎ
푡푒푐
ℎ
+
∑
푐
푣푎푟
,
푛푎푡
푔푎푠
퐷
푡
,
푛푎푡
푔푎푠
푡
푇
+
∑
푐
푣푎푟
,
푙푙
퐿
푡
푡
푇
(
푆
22
)
The average cost of electricity, i.e., the levelized cost of electricity (LCOE), was calculated as the system
cost divided by the supplied load for each simulation (Eq.
S
23).
퐿푒푣푒푙푖푧푒푑
푐표푠푡
표푓
푒푙푒푐푡푟푖푐푖푡푦
(
퐿퐶푂퐸
)
=
푆푦푠푡푒푚
푐표푠푡
∑
푀
푡
푡
(
푆
23
)
M
odel limitations
There are a number of limitations specific to the employed modeling approach.
Our analysis relied on a
wind power model that provides the wind turbine capacity factors from wind speeds at 100
-
m height
obtained from the ERA5 reanalysis. Wind speeds of reanalysis datasets can, however, display a range of biases
and errors that result
from terrain orography, poor coverage of assimilated inputs, model resolution, and
physical parametrization
1,2
. Despite these potential biases, wind speed and generation obtained from
reanalysis data show relatively high correlations with observed values
3
. While the typical biased
-
low wind
capacity factor could affect absolute measures, the model preserves wind patterns of interest to our analysis,
such as 24
-
hour and longer wind drought (Figure S1
3
). This wind power model allows us to incorporate up to
40 years of weather data and capture extremes and seasonal/inter
-
annual variability, which are independent of
any bias in capacity factor values.
The selection of the top 25% of grid cells by resource, and their aggregation over a large area, creates a
smoothing effect on the resulting wind and solar generation profiles. In highly decarbonized power systems
without cheap dispatchable generators or o
ther mechanisms that provide grid flexibility, and where
geographic variety is allowed, relatively high value is placed on sites where generation correlates with residual
demand, as opposed to sites with just high capacity factors
4
. Real
-
world siting decisions would require
detailed analyses with more granular power system models to exploit the variation in timing of wind and solar
generation, which may lead to a more efficient asset allocation.
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The synthetic electricity profile used in this analysis is based on historical electricity use patterns. Growth in
the electrification of end uses, such as transportation through battery electric vehicles (BEV) and heating
through the use of heat pumps, wi
ll change when and how we use electricity. An increase in these and other
loads will pose new challenges and opportunities for system planners. For example, the prevalent use of heat
pumps could change the time when peak electricity demand occurs
5
. Changes in amount and timing of
demand may ease the incorporation of greater quantities of wind and solar generation
6
. But there is
substantial uncertainty regarding future electrification rates
7
. Electrification will likely change which weather
events are the leading cause of lost load events in our models (Figure S12). Adding more flexible loads, such
as BEVs or hydrogen production, which can shift load by multiple hours or longer during severe
weather
events, could ease grid strain and lessen lost load.
The evolving market of power
-
to
-
H
2
-
to
-
power technologies consists of a variety of hydrogen production,
storage, and consumption technologies. The different attributes of each technology with respect to efficiency,
capital costs, lifetimes, etc. will yield trade
-
offs in cost and performance
that influence the optimal system
configurations. We limited our study to a single set of technology costs and characteristics. These
assumptions do not affect the main conclusions of the study, which are driven by geophy
sical properties and
related weather variability (i.e., resource droughts). Consequently, incorporating more data
-
years into the
planning process will lead to increased capacity of some technologies to address the increase in modeled
weather variability, a
nd will result in systems with higher resource adequacy.
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Figure
S1 |
Technologies included in each of the illustrative electricity systems scenarios:
Solar+wind+battery
(
top
)
,
Solar+wind+battery
+DG
(middle)
,
and
Solar+wind+battery+H
2
(
bottom
)
.
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Figure
S
2
|
Lost load by build and test year
.
Lost load is shown for the
Solar+wind+battery
(top) and
Solar+wind+battery+H
2
(bottom) systems, each planned using
on a single year of input data and tested for resource
adequacy tests using a single year of operational data (
O
yrs
=1
years
). The planning year is shown along the x
-
axis, and the
operational year along the y
-
axis, with the coloring corresponding to the lost load from each specific planning and
operating year combination. The histogram to the right (above) shows the mean lost l
oad for each row (column) in the
matrix.
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Figure
S
3
| Lost load by the strength of system build.
Lost load is shown as
P
yrs
increased for the three modeled
scenarios. Lost load values are distributed into three categories based on the years included in
planned systems. Planned
systems based exclusively on the high
-
resource years resulted in low resource adequacy. In contrast, systems were more
reliable when planned using at least a single year from the low
-
resource year category.
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Figure
S
4
| Identifying critical weather moments.
Specific weather events during the planning year exert a large
influence over the optimal asset capacities in the system builds. These weather events can be identified from the model
results by
selecting
the time slice with the highest shadow price (or dual value) for electricity. The day with the highest
shadow price is listed for each of the 42
P
yrs
=1
-
year
systems for the
Solar+wind+battery+
DG
scenario
in the 42 subpanels
.
The f
ive
horizontal
bands
per sub
panel each
represent
one
day worth of daily averaged demand, wind, and solar values
.
Thus, five days are represented per year from the leading two days through the lagging two days and
are centered on the
day with the highest shadow price. Red coloring indicates the daily average value for
when
that profile was experiencing
higher than
seasonally
normal values, while blue coloring indicates lower than
seasonally
normal values. For many years,
the day with the highest shadow price was during a sustained wind lull (blue for wind column),
whereas
the demand and
solar profiles show less obvious
trends.
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Figure
S
5
|
Variability in annual mean capacity factors.
The variability for the modeled solar and wind resources in
the U.S. are shown along with the variability in the annual mean values for the modeled electricity demand in the U.S.
The
mean demand is 304 GW with a relative standard deviation of 1.29%. The mean wind capacity factor is 0.285, with
a relative standard deviation of 4.82%. The mean solar capacity factor is 0.265, with a relative standard deviation of
1.49%.
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Figure
S
6
|
Annual mean solar and wind capacity factors are shown for the modeled data.
The coloring
corresponds to the planning year and operating year categorization
developed for Figure 4 in the
Critical weather years
section of the Results
. The categorization of years is not identical across the three scenarios (i.e., the markers often have
different colors
among
the different panels).
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Figure S
7
|
Unique years per optimization.
Box and whisker plot showing the number of unique weather years
included in each
system planning optimization. Because the included years were selected with replacements from the 42
possible years, single years could be selected multiple times. The same seed was used for the random selection process;
thus. the distribution is identical
for all three modeled scenarios. The mean
number of unique years per optimization
is
shown by the circle, with the median represented by the black line. The box shows the 25%
-
75% range, and the
whiskers show 5%
-
95%.
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Ruggles, T.H. & Virgüez, E., et al.
Figures
S
8
-
S10 show the resulting asset capacities and the levelized cost of electricity for a sensitivity study comparing
the time step resolution used in the initial optimization and system planning phase of the study. The three scenarios were
run using 1
-
hour, 2
-
hour, 3
-
hour, and 4
-
hour timesteps. The displayed values are the mean values from ensembles of
100 cases for
P
yrs
equal to 1, 3, and 5
years
and ensembles of 50 cases for
P
yrs
= 10
years
. The mean asset capacities and
their trends shown in Figures
S
8
-
S9 are similar, comparing the results between modeled runs with different time step
resolutions; in most cases, the mean capacity values are different by less than 5%. The notable exceptions to this are the
storage capacities for the
Solar+wind+battery+
DG
and
Solar+wind+battery+H
2
systems where the trends are remarkably
similar, yet the absolute values are higher when there is finer temporal resolution and lower when there is greater
temporal smoothing
,
which diminishes the value of short
-
duration energy s
torage. The discrepancies in the mean
levelized cost of electricity values are even smaller and are all less than 3%
, when
comparing the values between
ensembles that used the same
P
yrs
value and different temporal resolutions (Fig S10).
The similarities observed between asset capacities for systems modeled at different temporal resolutions and between
levelized cost of electricity values for systems modeled at different temporal resolutions show that it is not
meteorological variability o
n the 1
-
to 4
-
hour scale that influences the system builds and costs. The similarities further
suggest that the results and trends discussed in the main text, which used a temporal resolution of 4 hours, will hold for
models with finer temporal resolution.
The exception to this is that battery storage is noticeably less valuable in systems
where it is sized primarily for smoothing short
-
duration energy fluctuations, such as the
Solar+wind+battery+
DG
and
Solar+wind+battery+H
2
systems. In contrast, for the
Solar+wind+battery
systems, the battery storage was sized to deal with
longer
-
duration resource lulls because of the lack of firm generation resources. The battery capacities in the
Solar+wind+battery
systems are sized to supply > 7 hours of mean
U.S.
demand
for
P
yrs
=1
year
compared to the other two
scenarios where battery storage was sized closer to supplying 1 hour of mean
contigious U.S.
demand for
P
yrs
=1
year
.
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Figure S
8
|
Temporal resolution and asset capacities for the
Solar+wind+battery
systems
.
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Figure S
9
|
Temporal resolution and asset capacities for the
Solar+wind+battery+
DG
systems
.
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Ruggles, T.H. & Virgüez, E., et al.
Figure S
10
|
Temporal resolution and asset capacities for the
Solar+wind+battery+H
2
systems
.
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Figure S1
1
|
Temporal resolution and levelized cost of electricity for all three scenarios.
The mean costs shown
are similar regardless of the temporal resolution.
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Ruggles, T.H. & Virgüez, E., et al.
Figure S1
2
|
Dispatchable generation
dispatch.
The
dispatchable generation
dispatch
, modeled as natural gas,
during
the initial optimization and system building step for the
Solar+wind+battery+
DG
scenarios for
all 42
P
yrs
=1
systems is
shown based on
their 4
-
hour timesteps. 79.4% of hours exhibited zero natural gas dispatch and are not shown. When
natural gas was used, the mean generation was 24.2% of mean demand, the 90
th
percentile was at 49.3%, and the
maximum dispatch was 108.9%. It is clear that natural gas generation is not being used as a stable base load generator
supplying 5% of demand
at
every time step. Instead, it is used when power from wind, solar, and battery assets is
insufficient.