of 11
Planning
reliable
wind- and solar-based
electricity
systems
Tyler H. Ruggles
a
,
1
,
*
, Edgar
Virgüez
a
,
1
,
*
, Natasha
Reich
b
, Jacqueline
Dowling
a
,
Hannah
Bloomfield
c
, Enrico
G.A. Antonini
a
,
d
,
e
, Steven
J. Davis
f
, Nathan
S. Lewis
b
,
g
,
Ken Caldeira
a
,
h
,
*
a
Department
of Global
Ecology,
Carnegie
Science,
Stanford,
CA, United
States
b
Division
of Chemistry
and Chemical
Engineering,
California
Institute
of Technology,
Pasadena,
CA, United
States
c
School
of Engineering,
Newcastle
University,
Newcastle,
England,
UK
d
CMCC
Foundation,
Euro-Mediterranean
Center
on Climate
Change,
Lecce,
Apulia,
Italy
e
RFF-CMM
European
Institute
on Economics
and the Environment,
Milan,
Lombardy,
Italy
f
Department
of Earth
System
Science,
Stanford
University,
Stanford,
CA, United
States
g
Beckman
Institute,
California
Institute
of Technology,
Pasadena,
CA, United
States
h
Gates
Ventures,
Kirkland,
WA, United
States
ARTICLE
INFO
Keywords:
Low
carbon
electricity
systems
Cost-optimization
Weather
Resource
adequacy
Reliability
ABSTRACT
Resource
adequacy,
or ensuring
that electricity
supply
reliably
meets demand,
is more challenging
for wind- and
solar-based
electricity
systems
than fossil-fuel-based
ones. Here, we investigate
how the number
of years of past
weather
data used in designing
least-cost
systems
relying
on wind,
solar, and energy
storage
affects
resource
adequacy.
We find that nearly
40 years of weather
data are required
to plan highly
reliable
systems
(e.g., zero
lost load over a decade).
In comparison,
this same adequacy
could be attained
with 15 years of weather
data
when additionally
allowing
traditional
dispatchable
generation
to supply
5 % of electricity
demand.
We further
observe
that the marginal
cost of improving
resource
adequacy
increased
as more years,
and thus more weather
variability,
were considered
for planning.
Our results
suggest
that ensuring
the reliability
of wind-
and solar-
based systems
will require
using considerably
more weather
data in system
planning
than is the current
prac
-
tice. However,
when considering
the potential
costs associated
with unmet
electricity
demand,
fewer planning
years may suffice
to balance
costs against
operational
reliability.
1. Introduction
Electricity
systems
that rely predominantly
on variable
renewable
resources
will require
different
approaches
to ensure
acceptable
reserve
margins
and resource
adequacy
(i.e., a median
loss-of-load-expectation
of zero [
1
]) than those used for systems
that rely on firm, dispatchable
generation.
The historical
approach
to planning
(i.e., identifying
the
required
capacities
necessary
to reliably
supply
electricity)
and regula
-
tory approval
for systems
based on fossil fuel resources
generally
uses
averaged
demand
and generation
data to establish
a safety or
reserve
margin
of generating
capacity
[
2
].
With increasing
generation
from wind and solar resources,
innova
-
tive system
planners
are pursuing
methods
to constitute
new safety
margins
(e.g., flexible
reserve
margins)
in their planning
processes
[
3
].
New planning
processes
are critical
because
these resources
exhibit
substantial
variability
on timescales
that range from seconds
to years,
introducing
new challenges
[
2
,
4
,
5
]. Thus, a better representation
of the
spatiotemporal
variability
of wind and solar resources
is required
[
6
,
7
].
The reliability
of wind-
and solar-based
electricity
systems
has been
studied
by characterizing
extreme
events
that jeopardize
the systems
ability
to meet demand
at all times.
Some of these studies
focus on the
characterizations
of events
with low availability
of wind or solar re
-
sources
[
8
,
9
], weather
patterns
that pose high stress on the system
[
10
,
11
], or the influence
of regional
geophysical
resource
variability
on the
necessary
adjustments
for wind and solar-based
electricity
systems
to
operate
reliably
[
12
15
]. Additionally,
climate
change
may introduce
further
variability
in the future
than in the 20th century
[
16
,
17
].
Given inter-annual
variability
of wind and solar resources
[
4
,
18
,
19
]
and occasional
wind or solar
droughts
[
6
,
9
], the reliability
of elec
-
tricity
systems
based
on such resources
may be improved
by
*
Corresponding
authors
at: Carnegie
Science,
Stanford,
CA, United
States.
E-mail
addresses:
truggles@carnegiescience.edu
(T.H. Ruggles),
evirguez@carnegiescience.edu
(E. Virgüez),
kcaldeira@carnegiescience.edu
(K. Caldeira).
1
These
authors
contributed
equally
(equally
contributing
first authors).
Contents
lists available
at
ScienceDirect
Advances
in Applied
Energy
journal
homep
age:
www.el
sevier.com/l
ocate/adapen
https://doi.org/10.1016/j.adapen.2024.100185
Received
26 March
2024; Received
in revised
form 1 August
2024; Accepted
3 August
2024
Advances
in
Applied
Energy
15
(2024)
100185
Available
online
10
August
2024
2666-7924/©
2024
The
Author(s).
Published
by
Elsevier
Ltd.
This
is
an
open
access
article
under
the
CC
BY
license
(
http://creativecommons.org/licenses/by/4.0/
).
incorporating
multiple
years of weather
data into models
used for
planning.
Indeed,
studies
have shown
that electricity
systems
that rely
primarily
on variable
renewable
generation,
and are designed
to be
100 % reliable
based on a single year of resource
and demand
data, may
have very different
generation
capacities
and lower system
costs when
compared
to systems
designed
to remain
reliable
over multiple
years of
varying
weather
[
20
23
]. Similarly,
systems
that are planned
including
weather
years with extreme
weather
events
will have higher
costs
compared
to systems
that are planned
based on average
weather
years.
The former
systems
may operate
more reliably
in years with other
extreme
events
[
20
].
Studies
have thus analyzed
the operational
characteristics
necessary
to firm an electricity
system
based
on wind and solar resources
(e.g.,
necessary
energy
storage
requirements)
[
24
], how to optimize
the use of
existing
capacities
(e.g., economic
dispatch
models)
[
24
], and how to
optimize
capacity
building
over a defined
period
of time (e.g., capacity
expansion
models)
[
25
,
26
]. However,
previous
work in the long-term
system
planning
space,
where
capacity
expansion
models
are appli
-
cable,
has largely
neglected
an analysis
of how resource
adequacy
im
-
proves
as models
are optimized
over longer
periods
of time. Thus, the
trade-off
between
increasing
systems
cost and their improved
reli
-
ability
has not been quantified
to our knowledge,
nor have studies
quantified
the benefits
of representing
more weather
years for systems
with different
technical
characteristics.
Here, we assess
the trade-offs
among
cost, asset capacities,
and the
resource
adequacy
of idealized
solar-
and wind-based
electricity
sys
-
tems, as well as the incremental
cost of increasing
resource
adequacy
as
a function
of the number
of years of weather
data used in electricity
system
planning.
We used the ERA5 dataset
of historical
weather
data
from 1979 to 2020 to derive
wind and solar resource
profiles
at 4-hour
time steps for each of 42 calendar
years over the contiguous
United
States
(hereafter
referred
to as the U.S.) [
27
]. We calculated
plausible
synthetic
electricity
demand
profiles
for each weather
year [
28
],
including
diurnal
patterns
of non-heating
and non-cooling
loads and the
influence
of temperature
variation
on electrical
heating
and cooling.
Next,
we determined
least-cost
system
configurations
(i.e., planned
systems)
using a macro-scale
energy
model
based on different
numbers
of years of weather
data. The model
identified
the least-cost
electricity
system
and the costs of building,
operating,
and maintaining
system
assets while it ensured
that 100 % of demand
was supplied
in each time
step of the planning
years. The number
of years of weather
data used to
plan the different
least-cost
systems
was varied
from 1 to 40 years. As a
greater
number
of years of weather
data were used to plan systems,
more
weather
variability
was considered.
Lastly,
we tested
(i.e., operated
systems)
the resource
adequacy
of the designed
systems
over 10
randomly
selected
years of weather
data not used for planning.
This
process
allowed
the assessment
and comparison
of the annual
hours of
lost load, asset capacities,
and system
costs for 114,600
operational
years as a function
of the number
of years of weather
data that were used
to plan the electricity
system.
We repeated
this analysis
for three illustrative
electricity
system
scenarios
representing
different
plausible
electricity
systems.
First, we
model
a scenario
with exclusively
solar and wind power
generation
in
conjunction
with battery
storage
(
Solar
+
wind
+
battery
). This is the most
limiting
scenario
because
the only dispatchable,
albeit highly
energy-
constrained,
technology
is battery
storage.
While
future
continent-
scale energy
systems
will undoubtedly
contain
a wider array of gener
-
ation and storage
technologies,
the
Solar
+
wind
+
battery
scenario
illus
-
trates
a technology
set that has been studied
and currently
exists in
certain
micro-grid
and island
regions
where
combustion
fuels may be
costly
and difficult
to acquire
[
29
,
30
]. The second
scenario
uses solar
and wind generation,
battery
storage,
and dispatchable
generation
(DG)
(modeled
as natural
gas-fired
generation)
constrained
to meet no more
than 5 % of the total energy
demand
(
Solar
+
wind
+
battery
+
DG
). This
scenario
illustrates
a limiting
low-carbon
emission
scenario
with low
capital
cost, flexible,
firm generation
that can buffer the system
from the
most severe
instances
of weather
variability.
Flexible,
dispatchable
generation
has been shown
to substantially
reduce
electricity
costs in
systems
heavily
dependent
on variable
renewable
generation
[
31
].
Additionally,
considering
the useful
lifetime
of gas plants
being built
today,
it is possible
many regional
to continental
power
systems
will
transition
through
a low-emission
state with substantial
solar and wind
generation
and constrained
rates of natural
gas dispatch
[
32
]. The third
scenario
includes
solar and wind generation,
battery
storage,
and access
to a hydrogen
power-to-gas-to-power
system
to provide
seasonal
or
long-duration
energy
storage
(
Solar
+
wind
+
battery
+
H
2
). Long-duration
energy
storage
(LDES)
is considered
a potential
key technology
in
future
net-zero
emissions
energy
systems.
LDES has been shown
to in
-
crease
the utilization
of wind and solar assets while decreasing
the cost
of electricity
in low- and zero-emission
electricity
systems,
compared
to
systems
without
such technologies
[
33
,
34
]. Inter-annual
weather
vari
-
ability
may affect systems
containing
LDES differently
than systems
with
shorter
duration
energy
storage,
such as the
Solar
+
wind
+
battery
sce
-
nario. This is because
LDES can operate
on a seasonal
cycle as opposed
to
daily weather
cycles,
which
drive the behavior
of shorter
duration
en
-
ergy storage.
2. Experimental
procedures
The Experimental
Procedures
section
describes
the model,
critical
model
inputs,
and the steps in the study workflow,
and is split into
multiple
sections.
First, an overview
of the model
is presented
in the
Macro-scale
energy
model
section,
while a full mathematical
formula
-
tion of the model
is presented
in the
Model
formulation
section
of the
Supplementary
Material.
Second,
the data used to define
the inputs
is
described
in the
Model
inputs
section.
Lastly,
the
Scenarios
of input
weather
data
section
presents
the methodology
for selecting
the specific
sets of input data used for system
planning.
2.1.
Macro-scale
energy
model
A reduced-order,
parsimonious,
macro-scale
energy
model
(MEM)
was used to represent
a continental-scale
electricity
system
across
the U.
S. [
33
,
35
38
]. The model
assumed
lossless
transmission
from generation
to load across
the U.S., and hence had a single node with the U.S. as the
load-balancing
region.
A least-cost
optimization
was performed
using a
linear
program
that solved
for the installed
capacities
and dispatch
of
the system
assets.
At each 4-hour
time step, energy
was balanced
in the
model,
with the electricity
load supplied
equal to the dispatched
power
plus the dispatched
stored
energy.
Ramp rates were not constrained
for
any modeled
technology.
2.2.
Model
inputs
The model
was based on existing
technologies
and current
cost es
-
timates
(
Table 1
). Calculation
of the parameters
in
Table 1
can be found
in the
Model
formulation
section
of the Supplementary
Material
(Table
S1). The fixed capital
investment
for each system
component
represented
the purchase
cost and installation
of each component,
including
all ancillary
components
and needs during
installation
such as
instrumentation,
piping,
electrical,
buildings,
and service
facilities
[
39
].
The resulting
fixed hourly
cost included
the fixed capital
investment
plus
fixed annual
operation
and maintenance
costs. Variable
operation
and
maintenance
costs and variable
fuel costs were included
as appropriate.
Batteries
were assumed
to have a 1 % per month
self-discharge
rate and
a 1:4 power-to-energy
ratio. This ratio was based on market
trends
for
Li-ion
systems
that have been paired
with solar PV to reduce
solar
curtailment
and better
align power
output
with electricity
system
de
-
mand
[
40
42
]. Proton
exchange
membrane
(PEM)
electrolyzers
were
used to convert
electricity
into hydrogen.
Wind and solar resources
were represented
by 4-hourly
time series of
capacity
factors
derived
from the ERA5 weather
reanalysis
data [
28
].
T.H. Ruggles
et al.
Advances
in
Applied
Energy
15
(2024)
100185
2
Solar capacity
factors
were calculated
using a horizontal
single-axis
tracking
system
with a tilt ranging
from 0
to 45
. The solar panel
power
output
was calculated
based
on the in-plane
irradiance
and
module
temperature
[
50
]. Wind capacity
factors
were calculated
based
on a representative
wind turbine
with a 100 m hub height
and a 1.6 MW
nameplate
capacity
[
51
53
]. The turbines
had a cut-in speed of 3 m s
-1
, a
maximum
output
at 12 m s
-1
, and a cut-out
speed of 25 m s
-1
. Annual
mean capacity
factors
were calculated
for each ERA5 grid cell. Aggre
-
gate time series were then produced
using an area-weighted
average
of
the 25 % of these ERA5 cells that had the highest
annual
capacity
fac
-
tors. This aggregation
smoothed
the resource
profiles
by averaging
over
a quarter
of the U.S. cells, thus producing
a less variable
profile
while
using the most productive
regions.
This historical
weather
dataset
had a
mean wind capacity
factor (CF) of 29 % and solar CF of 26 %, which
are
comparable
to the U.S. mean wind CF of 35 % and solar CF 25 % for
installed
projects
[
54
]. Within
our 42-year
dataset,
the variability
in the
mean of the annual
capacity
factors,
calculated
using relative
standard
deviation,
for wind generation
was 4.80 %, and 1.49 % for solar elec
-
tricity
generation
(Fig. S5).
A synthetic
demand
profile
was used to preserve
any correlations
between
wind and solar availability
and electricity
load. The methods
developed
by Waite
and Modi in their study of future
peak electricity
demands
and load profiles
were used to calculate
plausible
electricity
demand
across
the U.S. [
55
]. Waite and Modi constructed
a predictor
of
historical
electricity
demand
as a function
of temperature
based on U.S.
building
stock information
and U.S. Census
American
Community
Sur
-
vey Data 2010. Their predictors
minimize
the sum of squares
between
the predicted
monthly
electricity
usage
and actual
2010 monthly
state-level
electricity
usage for each building
class. A plausible
hourly
electricity
load for a 2010-type
building
stock from years 1979 through
2020, concurrent
with the wind and solar profiles,
was calculated
using
this approach
in conjunction
with historical
hourly
ERA5 temperatures.
The calculations
were performed
at the census
tract level, then aggre
-
gated to obtain
a total for the U.S.
2.3.
Scenarios
of input
weather
data
We first designed
system
builds
by optimizing
asset capacities
and
dispatch
using different
lengths
of input weather
data assembled
by
concatenating
randomly
sampled
years from the 42-year
dataset
(
P
years
=
1, 2, 3, 4, 5, 7, 10, 15, 25, and 40). In this design
phase,
we constrained
the model
to meet electricity
demand
in each time step, resulting
in
100 % resource
adequacy.
We then tested
the performance
and evalu
-
ated the resource
adequacy
of each designed
system
against
10-year-
long input weather
and demand
data (operation
years:
O
years
=
10)
built by concatenating
randomly
sampled
years from the years not used
for planning.
These tests used a dispatch-only
mode in which
the asset
capacities
were fixed.
Thus,
some systems
could
not supply
all the
demanded
electricity,
leading
to lost load. These steps are illustrated
in
Fig. 1
.
The specific
years of input data were selected
using a bootstrapping
resampling
method
where
years
were selected
randomly
with re
-
placements
from the 42-year
data set (1979-2020).
The case with the
longest
weather
record
(
P
years
=
40) typically
sampled
25 to 28 distinct
weather
years (Fig. S7). There were always
>
10 non-overlapping
years
available
for inclusion
in the
O
years
. The cases with the shortest
weather
record
(
P
years
<
10) had almost
always
distinct
years.
The random
selection
process
that determined
the years in each
simulation
allowed
modeling
many different
possible
systems
for each
scenario
P
years
, with the set of simulations
that had the same
P
years
value
designated
as an ensemble.
Ensembles
of 500 systems
were modeled
for
P
years
10, ensembles
of 150 systems
were modeled
for
P
years
=
15 and
for
P
years
=
25, and ensembles
of 20 systems
were modeled
for
P
years
=
40, for a total of 3,820
systems.
Afterward,
lost load tests were per
-
formed
over
O
years
=
10 of weather
data for each system
resulting
in
testing
over 114,600
operational
years for all systems
and all three
scenarios.
3. Results
&
discussion
The Results
&
Discussion
section
describes
the main results
of the
study and discusses
their relevance
in a global
context.
Characteristics
of
the planned
systems
are described
in the
System
costs and capacities
section,
followed
by an analysis
of the lost load resulting
from testing
the
planned
systems
in the
Resource
adequacy
section.
Next, the tradeoff
between
system
costs and resource
adequacy
is analyzed
in the
Marginal
Table
1
Techno-economic
values
for electricity
technologies.
Economic
parameter
Solar PV
[
43
]
Wind
[
43
]
Combined-cycle
gas
turbine
[
43
]
Utility-scale
battery
storage
[
44
]
Electrolysis
facility
[
45
]
Salt cavern
H
2
storage
[
46
,
47
]
Molten
carbonate
fuel
cell [
48
,
49
]
Fixed capital
cost
(
$
KW
e
)
1,300
1,300
950
370
(
$
yW
e
)
1,100
0.21
(
$
kWHh
e
)
5,000
Fixed O
&
M cost
(
$
yrkW
e
)
15
26
12
12
36
0.016
(
$
yrkWh
e
)
43
Lifetime
(
yr
)
25
25
30
10
7 stack, 40 BoP, 15
compressor
30
20
Heat rate
(
Btu
KWh
)
-
-
6,370
-
-
-
-
Fixed hourly
cost
*
(
$
hkW
e
)
0.015
0.016
0.010
0.0074
(
$
hkWh
e
)
0.021
3.7e-6
(
$
hkWh
LKH
)
0.058
Relative
efficiency
-
-
54 %
90 % round-trip
70 % (LHV)
0.01 % per year
70 %
Variable
O
&
M cost
(
$
kWh
e
)
0
0
0.0019
0 (applied
in fixed
O
&
M)
0
0
0
Variable
fuel cost
**
(
$
kWh
e
)
-
-
0.019
-
-
-
-
Total variable
cost
***
(
$
kWh
e
)
0
0
0.0210
0
0
0
0
*
Calculations
are based on our assumed
discount
rate of 7 %.
**
The variable
fuel cost for the combined-cycle
plant is based on $3/MMBtu
natural
gas.
***
Calculations
are based on the variable
O
&
M and variable
fuel cost.
T.H. Ruggles
et al.
Advances
in
Applied
Energy
15
(2024)
100185
3
costs of avoided
lost load
section.
Finally,
a detailed
analysis
of the
specific
years of data used for planning
versus
the years used for testing
is presented
in the
Critical
weather
years
section.
This section
is fol
-
lowed
by a
Discussion
where
all the results
are interpreted.
3.1.
System
costs
and capacities
Resource
adequacy
during
the operating
years improved
as more
years of weather
data (
P
years
) were used to plan the system.
But this
increase
in reliability
came at the expense
of an increase
in the levelized
cost of electricity
(LCOE),
regardless
of the technologies
available
(
Fig. 2
a
c). Due to the lack of dispatchable
generation,
Solar
-
+
wind
+
battery
systems
were particularly
sensitive
to wind and solar
variability,
with an overall
higher
LCOE.
They exhibited
rapid increases
in LCOE
as
P
years
increased
(
Fig. 2
a). In contrast,
when dispatchable
generation,
modeled
as natural
gas-fired
generation,
was permitted
to
supply
up to 5 % of electricity
demand
(
Fig. 2
b), the dispatchable
gen
-
eration
was used during
~20 % of the hours.
This dispatchable
gener
-
ation largely
compensated
for weather
variability
and limited
the
average
increase
in LCOE for reliable
Solar
+
wind
+
battery
+
DG
systems
to just 3.0 % between
P
years
=
1 and
P
years
=
40 (
Fig. 2
b). Due to the
availability
of dispatchable
stored
hydrogen,
the planned
Solar
-
+
wind
+
battery
+
H
2
systems
were less costly
than
Solar
+
wind
+
battery
systems
,
yet were more costly than the
Solar
+
wind
+
battery
+
DG
systems
(
Fig. 2
c).
In least-cost
idealized
systems,
the availability
of dispatchable
gen
-
eration
(e.g., natural
gas) substantially
reduced
wind and solar capac
-
ities and decreased
curtailment.
For example,
when
systems
were
planned
using one year of weather
data (
P
years
=
1), the average
wind and
solar generation
capacities
were 37 % and 43 % greater
in
Solar
-
+
wind
+
battery
systems
than in
Solar
+
wind
+
battery
+
DG
systems,
respectively
(
Table
2
). Meanwhile,
60 % of available
wind and solar
generation
was curtailed,
on average,
in the
Solar
+
wind
+
battery
sys
-
tems, as compared
to 38 %, on average,
in
Solar
+
wind
+
battery
+
DG
systems.
As
P
years
increased,
capacities
of different
technologies
did not in
-
crease
uniformly.
In
Solar
+
wind
+
battery
systems
(
Fig. 2
d), average
solar
and battery
capacities
increased
by 71 % and 110 % between
P
years
=
1
and
P
years
=
40, respectively,
but wind capacities
decreased
by 18 %. For
P
years
=
1, these systems
had substantial
variability
in their planned
asset
capacities
indicating
that optimal
system
builds
were strongly
affected
by the different
weather
years (
Table 2
). The observed
increase
in solar
capacity
and decrease
in wind capacity
is supported
by Rinaldi
et al.
[
36
] who find severe,
persistent
wind droughts
across
the U.S. have
historically
occurred
much more frequently
than severe,
persistent
solar
droughts.
Thus, when planning
over increasing
numbers
of years, there
is a higher
probability
of sampling
a year with a severe,
persistent
wind
drought
that necessitates
expanding
solar and battery
capacities
to make
up for the wind generation
shortfall.
In addition
to lower frequencies
of
severe,
persistent
resource
droughts,
the inter-annual
variability
of total
solar availability
is much lower than for wind (Fig. S5).
Solar
+
wind
+
battery
+
DG
(
Fig. 2
e) systems
exhibited
relatively
little
change
in the mean values
of asset capacities
as
P
years
increased,
and
show the system
optimization
is not greatly
sensitive
to the weather
inputs.
The exception
to this insensitivity
is that the dispatchable
gen
-
eration
capacity
increased
by 39 % between
P
years
=
1 and
P
years
=
40 (with
a corresponding
decrease
in utilization
rate;
Fig. 2
e). The relative
insensitivity
of asset capacities
for
Solar
+
wind
+
battery
+
DG
systems
to
P
years
is further
supported
by the smaller
spread
in asset capacities
for
P
years
=
1 compared
to the
Solar
+
wind
+
battery
systems
(
Table 2
). In the
Solar
+
wind
+
battery
+
H
2
scenario,
as
P
years
increased
from 1 to 40 years,
wind,
solar,
and electrolyzer
capacities
remained
relatively
constant
(each changed
by less than 15 %;
Fig. 2
f) due to the availability
of dis
-
patchable
stored
hydrogen.
In contrast,
the hydrogen
storage
and fuel
cell capacities
increased
substantially,
by 62 % and 45 %, respectively
(
Fig. 2
f), which
is consistent
with studies
showing
that longer
modeled
time horizons
increase
the value of long-duration
storage
[
13,15,33
].
Additionally,
battery
capacity
decreased
by 41 %
representing
the
largest
relative
decrease
in asset capacity
among
the systems
evaluated.
Figs. S8 through
S11 compare
asset capacities
and system
costs for
systems
initialized
using 1-, 2-, 3-, and 4-hour
time step resolution.
These model
results
are remarkably
insensitive
to the tested
differences
in resolution,
similar
to the findings
of Pfenninger
[
26
] and Gonzato
[
56
]. This insensitivity
is because
the weather
events
that most strongly
Fig. 1.
Schematic
analysis
workflow.
The analysis
workflow
is split into three steps. In the first step, data is selected
for use as input data for the system
planning
model.
Sets of input data are created
of varying
lengths,
including
random
weather
years from the 42 years of historical
weather
data. In the second
step, the least-
cost systems
are planned
using their input data and require
zero lost load. The asset capacities
and system
costs are the main parameters
of interest
from the second
step. In the final step, the planned
systems
are tested
by operating
each of them on 10 years of historical
data that were specifically
not used during
the system
planning
process.
Asset capacities
are held fixed during
this last step; thus, lost load results
when planned
systems
are incapable
of meeting
100 % of elec
-
tricity
demands.
T.H. Ruggles
et al.
Advances
in
Applied
Energy
15
(2024)
100185
4
influence
system
builds
for the capacity
expansion-type
model
used in
this study are multi-hour
or longer
events
as opposed
to shorter-duration
(hour
length)
fluctuations
in resource
availability
or demand,
which
would
be smoothed
by 4-hour
averaging.
3.2.
Resource
adequacy
Least-cost
systems
planned
using
a single
year of weather
data
(
P
years
=
1) frequently
failed to meet electricity
demand
when operated
over ten randomly-selected,
out-of-sample
years
of weather
data
(
Fig. 2
). The lost load in operational
years (
O
years
) was calculated
as a
percentage
of mean demand
(i.e., (total demand
total supplied
de
-
mand)/total
demand).
This resulted
in 0.082 % lost load for
Solar
-
+
wind
+
battery
, 0.0074
% for
Solar
+
wind
+
battery
+
DG
, and 1.00 % for
the
Solar
+
wind
+
battery
+
H
2
scenarios
(
Fig. 2
g
i). The black line repre
-
sents the average
lost load over each ensemble,
while the color-shaded
areas indicate
the fraction
of simulations
corresponding
to specific
lost
load levels.
For example,
the dark blue area represents
the lost load for
the half of the operational
simulations
with the least lost load per
ensemble
as we increase
the number
of years of input data.
Incorporation
of a second
year of weather
data in system
planning
(incrementing
from
P
years
=
1 to
P
years
=
2) decreased
lost load in all sys
-
tems by
>
50 %, with the largest
decrease
(61 %) observed
for
Solar
-
+
wind
+
battery
+
DG
systems.
Notably,
100 % resource
adequacy
was not
obtained
in half of the decade-long
operational
tests (
O
years
=
10) until
P
years
=
15 for the
Solar
+
wind
+
battery
+
DG
scenario,
and until
P
years
=
40
for the
Solar
+
wind
+
battery
and
Solar
+
wind
+
battery
+
H
2
scenarios.
For
reference,
due to selecting
years with replacement,
the
P
years
=
40 simu
-
lations
were planned
with at most 29 distinct
years of weather
data,
leaving
13 or more out-of-sample
years for operating
each system
(Fig. S7). In general,
severe
wind droughts
with 24-hour
average
wind
power
output
near 10 % of nameplate
capacity
were prevalent
during
the most extreme
lost load events
regardless
of season.
Moreover,
these
events
were exacerbated
during
hotter
months
(April through
October),
Fig. 2. System
costs,
capacities,
and lost load.
The top panels
(a,b,c)
show the mean levelized
cost of electricity
as the number
of years used in system
planning
(
P
years
) increases.
These panels
reflect
only the planned
systems.
Across
all studied
systems,
as
P
years
increased,
mean costs increased.
The middle
panels
(d,e,f)
show
how the mean asset capacities
changed
as
P
years
increased.
Across
the three studied
scenarios,
as
P
years
increased,
the planned
systems
increasingly
favored
different
technologies,
with some asset capacities
increasing
while others
remained
relatively
unchanged
or decreased.
Plotted
values
are the mean values
from the ensemble
of planned
least-cost
systems.
The bottom
panels
(g,h,i)
show the lost load (unsupplied
demand)
from operational
resource
adequacy
tests as the number
of years of
weather
data used in system
planning,
P
years
, increased.
Each planned
system
was tested
over ten randomly
selected
years of weather
data not previously
seen by the
model
for system
operation
(
O
years
=
10 years).
Lost load decreased,
and thus reliability
increased,
in each system
as
P
years
increased.
Including
even a second
year of
weather
data into system
planning
halved,
on average,
the amount
of unsupplied
demand
during
system
operation
tests.
T.H. Ruggles
et al.
Advances
in
Applied
Energy
15
(2024)
100185
5