#  Optimal transmission expansion minimally reduces decarbonization costs of
U.S. electricity ††thanks: First version: February 21. This version: . The
authors would like to acknowledge all contributors to Switch 2.0, the open-
source capacity expansion model we use in this work, as well as Catalyst
Cooperative’s Public Utility Data Liberation (PUDL) Project
(https://catalyst.coop/pudl/), which is a key input into PowerGenome. Partial
funding for this project was provided by the Sloan Foundation via the
Environmental Defense Fund’s Model Intercomparison Project. Comments welcome.

Rangrang Zheng, Greg Schivley, Patricia Hidalgo-Gonzalez,
Matthias Fripp, Michael J. Roberts University of Hawai’i, Email:
<EMAIL_ADDRESS>University, Email:
<EMAIL_ADDRESS>of California San Diego,
<EMAIL_ADDRESS>Defense Fund, Email:
<EMAIL_ADDRESS>of Hawai’i, Email<EMAIL_ADDRESS>
###### Abstract

Solar and wind power are cost-competitive with fossil fuels, yet their
intermittent nature presents challenges. Significant temporal and geographic
differences in land, wind, and solar resources suggest that long-distance
transmission could be particularly beneficial. Using a detailed, open-source
model, we analyze optimal transmission expansion jointly with storage,
generation, and hourly operations across the three primary interconnects in
the United States. Transmission expansion offers far more benefits in a high-
renewable system than in a system with mostly conventional generation. Yet
while an optimal nationwide plan would have more than triple current
interregional transmission, transmission decreases the cost of a 100% clean
system by only 4% compared to a plan that relies solely on current
transmission. Expanding capacity only within existing interconnects can
achieve most of these savings. Adjustments to energy storage and generation
mix can leverage the current interregional transmission infrastructure to
build a clean power system at a reasonable cost.

Keywords: Decarbonization, renewable energy, intermittency, transmission,
trade, optimization

JEL Classification:  Q42, Q52

##  1 Introduction

Although solar and wind power are affordable and likely central to efforts to
decarbonize the world economy, their variability presents a considerable
challenge to existing systems dominated by easily controllable thermal power
plants. Interregional transmission can help smooth imbalances in supply and
demand over space while transferring power from places relatively rich in
solar and wind resources to places with poorer options. For example, compared
to other regions, the desert Southwest receives more solar radiation, while
the Great Plains have abundant wind resources. These aspects of solar and wind
contrast sharply with existing generation. Thermal power plants perform nearly
the same wherever they are placed. It is unclear how suitable existing
transmission lines are for the emerging energy system with different
interregional and intertemporal gains from trade. At the same time, extreme
weather events and reliability impacts (e.g., heat waves and wildfires in
California and winter storms in Texas) have increased discussion of the need
for strong connections between U.S. grids.

Existing interregional transmission capacity was not built with a high-
renewable future in mind, and building new transmission lines is costly
economically, logistically, environmentally, and politically. Historically,
building new transmission lines has often been fraught with controversies
about where to site transmission lines, how to finance them, and how costs
should be allocated to buyers, sellers, and electricity customers. While
enhanced trade between regions generally benefits all sides, individual
stakeholders, such as existing transmission line owners and locally advantaged
existing generators, can lose rents amid enhanced competition (Hausman, 2024).
New transmission lines might also pass through regions that do not benefit
from them, and these communities may understandably resist their siting,
especially when transmission line construction has considerable environmental
and biodiversity impacts (Biasotto and Kindel, 2018; Marshall and Baxter,
2002; Söderman, 2006; Hyde, Bohlman and Valle, 2018). In addition, ERCOT, the
Texas-only interconnect, is especially isolated and likely to resist
connections with other regions given its unique market structure and aversion
to oversight from the Federal Energy Regulatory Commission (FERC). These
challenges cast doubt on the likelihood that interregional transmission will
expand in line with conventional measures of benefits and costs.

When these challenges are paired with a perception that transmission expansion
is an essential part of the decarbonization puzzle (Brown and Botterud, 2021;
Pacala et al., 2021; Moch and Lee, 2022; Joskow, 2020; Davis, Hausman and
Rose, 2023), it highlights the importance of evaluating the benefits and costs
of interregional transmission upgrades, taking into account the full portfolio
of alternatives, both within and between the existing interconnects. If future
transmission expansion is uncertain, some may wonder whether near-term
investments in solar, wind, and other infrastructure will be compromised if
transmission expansion does not proceed as expected. While there is a
significant body of literature addressing the optimal design of electricity
systems for the U.S. (Brown et al., 2018; Mai et al., 2018; Jayadev, Leibowicz
and Kutanoglu, 2020), few studies consider 100% decarbonization. Even fewer
studies have evaluated the value of transmission in a 100% decarbonization
future. Given the scale and useful lifetimes of these investments, it is
important to consider the rapidly falling costs of storage and other
technologies that could serve as substitutes.

Findings from existing work about transmission are divergent. Using a modified
version of OSeMOSYS (Howells et al., 2011), (Jayadev, Leibowicz and Kutanoglu,
2020) illustrate the limited value of long-distance transmission in the least
cost scenario with no carbon policy applied. In contrast, the recent study by
(Brown and Botterud, 2021) finds that interregional transmission upgrades in a
zero-carbon electricity system can reduce the average cost of decarbonized
power from over $100 per MWh to about $70 per MWh. However, this measure
compares ideal “greenfield" transmission systems and pays no attention to
existing transmission capacities. Moreover, it does not consider seasonal
balancing options, such as green hydrogen, nuclear power or carbon capture and
storage (CCS) paired with natural gas generation. Moderate deployment of these
technologies can both lower the cost of decarbonization and greatly diminish
the value of added transmission, even if these emerging technologies are
costly.

Our work contributes to the literature by evaluating transmission value in
least-cost, zero-emissions, and socially-optimal scenarios, while building
from existing infrastructure, including transmission. It accounts for how a
broad range of technologies, including renewables, batteries, hydrogen,
nuclear, and CCS, can substitute for transmission using a model with high
temporal and spatial resolution of weather and associated supply and demand.

Our main finding is that an optimal nationwide zero-emissions plan would more
than triple current interregional transmission, which validates the
conventional wisdom that much more is needed. However, we find that such a
system would cost only 4% less than a well-designed zero-emissions system with
no new interregional transmission, as a complex array of substitutes from
storage to generation mix adjustments can limit excess costs.

##  2 Current and idealized future systems

The value of expanding transmission depends on what already exists, including
generation and transmission infrastructure. It also depends on the resource
availability to build and connect new generation and on expected future
demand. The existing grid evolved from primarily local power provision to
increasingly interconnected regions. At first, transmission was used mainly to
transport power from remote generating plants to urban customers (Decker,
2021). Over time, it became clear that efficiency would be enhanced by
connecting population centers to exploit economies of scale with large “base
load" power plants that could operate continuously at full capacity (e.g.,
coal and nuclear), paired with smaller local ramping and peaking power plants
that could accommodate time-varying demand (Masters, 2013). A larger, more
connected grid also has more inertia and stability in the face of demand
shocks, severe weather events, plant outages, and, increasingly, renewable
energy intermittency. As a result of these economic forces, regions are more
interconnected today than a century ago. Still, the U.S. grid remains highly
fragmented, with three nearly disjoint sections, the Eastern, Western, and
ERCOT interconnections (panel b of Figure 1), and varying degrees of
connectivity between regions within each of these interconnects.

The existing transmission system was not designed for the future, which will
likely employ much more solar, wind, batteries, and other forms of storage,
given their low and declining costs and lack of CO2 and other pollution
emissions. However, long-duration storage remains expensive, so there is an
ongoing debate about what the future generation mix should look like (Jacobson
et al., 2018; Pursiheimo, Holttinen and Koljonen, 2019; Qazi, 2022), and how
the degree of interregional transmission expansion could factor into the
generation mix (Staadecker et al., 2023), its geographic disposition, and
overall cost. The future energy system is also policy-dependent. It will hinge
on subsidies for clean energy, taxes or other restrictions on carbon dioxide
and other pollutant emissions, local market rules and structures, and
decisions by state and federal regulators.

To obtain a sense of what an idealized future system could look like, we used
Switch (Fripp, 2012; Johnston et al., 2019; Staadecker et al., 2023; Hidalgo-
Gonzalez, Johnston and Kammen, 2021; Sánchez-Pérez et al., 2022), a state-of-
the-art, open-source power-system planning model, paired with PowerGenome
(https://github.com/PowerGenome/PowerGenome), an open-source platform that
compiles comprehensive weather and utility system data, to develop a least-
cost plan for a zero-carbon power system for the continental United States in
2050. The model co-optimizes potential new generation capacities, storage,
interregional transmission, and hourly chronological operation of the system
for all 8,760 hours, which is essential for finding true least-cost high-
renewable systems given their weather-driven variability and critical
dependence on storage and transmission. Technology and fuel cost assumptions
are derived mainly from the National Renewable Energy Laboratory’s Annual
Technology Baseline (National Renewable Energy Laboratory, 2022). This
idealized system of the future, portrayed in panel c of Figure 1, is dominated
by solar and wind generation, possesses ample storage in the form of batteries
and green hydrogen, and increases interregional transmission capacity by over
200%.

This idealized, zero-emissions system is 68% more costly per MWh than the
least-direct-cost system that excludes any account of external CO2 emissions
costs. At a markedly lower cost (45% above least-cost, excluding emissions’
costs), we could achieve roughly 95% decarbonization, a level of
decarbonization consistent with the Environmental Protection Agency’s
estimated social cost of carbon dioxide of $190 per ton. The difference in
cost and emissions between the socially optimal and zero-emissions scenarios
is mainly derived from natural gas with carbon capture and storage (CCS)
replacing hydrogen. Note that these costs pertain only to generation and
transmission and do not account for local distribution costs, which can
comprise almost half of the retail electricity costs for residential customers
today (Borenstein, Fowlie and Sallee, 2021). Hence, these decarbonization
costs are a considerably smaller share of retail prices. However, these
idealized systems optimize interregional transmission, roughly tripling it,
including building new connections between the three interconnects.

##  3 Scenarios considered

Each scenario jointly optimizes generation and storage capacities,
transmission, and hourly chronological operation of the system over 52 weeks,
subject to emissions and transmission constraints of the given scenario. We
use 942 clusters of candidate renewable energy projects, corresponding to
approximately 21 TW of potential capacity, with each cluster’s variable
capacity factors derived from weather data synchronized with demand. Both
weather and demand are based on 2012; details are provided in methods.

To show how interregional transmission influences the cost of decarbonization,
we built a series of scenarios with different restrictions on emissions and
transmission expansion. These include three emissions scenarios: (i) a _least-
direct-cost_ system that ignores external costs of CO2 and other pollution
emissions; (ii) a _socially-optimal system_ that assumes a CO2 price of $190
per ton; and (iii) a _zero-emissions system_ with no CO2 emissions. All three
of these scenarios use the same projected demand for 2050, which is 74%
greater than today’s demand, roughly accounting for the growth of electric
vehicles, partial electrification of heat, and electrification of some
industrial activities. For each of these three emissions scenarios, we
consider three transmission scenarios: (a) _existing_ transmission in 2022;
(b) optimized expansion _within interconnects_ , but no expansion between
interconnects; and (c) _fully-optimized_ expansion of transmission between
regions both within and between interconnects. Crossing the emissions
scenarios and transmission scenarios gives a total of nine scenarios labeled
below.

LE | Least-direct-cost, existing trans.
---|---
LI | Least-direct-cost, within-interconnect trans.
LO | Least-direct-cost, fully-optimal trans.
SE | Socially-optimal, existing trans.
SI | Socially-optimal, within-interconnect trans.
SO | Socially-optimal, fully-optimal trans.
ZE | Zero-emissions, existing trans.
ZI | Zero-emissions, within-interconnect trans.
ZO | Zero-emissions, fully-optimal trans.

The main figures in this manuscript focus on LE, LO, ZE, and ZO and we report
results for the other scenarios in the supplement since they are similar to
the cases shown here. In each case, all other aspects of the system are co-
optimized, subject to transmission constraints. Existing and candidate
generation technologies include solar, wind, batteries, hydrogen, natural gas
with and without carbon capture, battery storage, nuclear, pumped-storage
hydroelectric power, pre-existing hydroelectricity, and distributed solar.
Hydrogen production can be produced endogenously via electrolysis and later
used for generation via fuel cell, and thus serves as a form of long-term
storage. The model accounts for all systems’ operations and maintenance costs,
including existing transmission lines. By optimizing all options in
conjunction with different transmission constraints, we see how portfolio
adjustments compensate for less-than-ideal expansion of long-distance
transmission.

##  4 Results

This paper uses average load-weighted, long-run marginal cost as the
“wholesale cost" metric (the dual of the load-serving constraint in the
optimization model). This roughly corresponds to demand-weighted locational
marginal prices in wholesale power markets, assuming markets are perfectly
competitive and in long-run equilibrium. This metric includes rents to scarce
resources and can thus differ slightly from engineering-based measures of
levelized cost. Note, however, that we do not account for reserves, excess
capacity payments for obsolete or partially obsolete assets, within-region
congestion costs, or any sub-optimal investment or operation of the system.
The costs also correspond to a single weather year.

Optimizing transmission for the least-direct-cost system minimally reduces the
average wholesale cost of power from 37.4 $/MWh under existing transmission to
37.0 $/MWh, a savings of just 0.3% (Overall LE - Overall LO in Figure 2, panel
a). This difference is barely visible in the graph due to its small size.
Optimally expanding transmission within interconnects reduces overall cost by
0.2 $/MWh, or about half the savings from fully-optimal transmission. Although
the least-direct-cost scenarios do not take into account emissions and assume
inexpensive future natural gas following NREL-ATB projections, they still
include a nearly five-fold expansion of solar and wind capacity relative to
2022 levels and reduce electricity sector CO2 emissions by 6.9 to 7.8%
relative to 2022. These emission reductions occur despite 74% growth in
overall demand and thus result in over 50% reduction in emissions intensity
(CO2 per MWh delivered) compared to 2022. Furthermore, the projected growth in
demand embodies substantial growth of electric vehicles and electrification of
heat, such that economy-wide emissions reductions would likely be much
greater; a precise calculation is beyond the scope of this study.

Optimizing transmission for the zero-emissions system reduces the average
wholesale cost of power from 64.8 $/MWh under existing transmission to 62.2
$/MWh, a savings of 4% (Overall ZE - Overall ZO in Figure 2). Optimally
expanding transmission within interconnects, but not between them, reduces
cost by 3.2% (not shown). The relative savings of expanded transmission are
greater in the high-renewable zero-emissions system than in the least-direct-
cost system with about one-third the amount of wind and solar. And because the
direct costs are far higher, net transmission savings are fairly substantial.
As shown in Figure 5, optimal transmission scenarios reduce prices slightly
throughout the distribution.

The overall cost of decarbonization, defined as the difference between the
average marginal cost of a zero-emissions system and a least-direct-cost
system, is 25.2–27.4 $/MWh, or 68–73% of the least-direct-cost system,
depending on the transmission scenario. If emissions are valued at $190/tCO2,
the avoided harm in the zero-carbon case is much greater than the extra direct
costs in the power system. We find that full decarbonization has total
societal costs—including both direct costs and emission impacts—that are
57%–59% below the least-direct-cost case. If, instead of full decarbonization,
societal costs are minimized, direct costs increase by 34–36% relative to the
least-direct-cost scenario, electricity sector emissions fall by 95.5 to 95.7%
relative to 2022, and societal savings rise to 66%. These estimates do not
include economic and emissions savings in transportation, heating, and
industrial sectors of the economy that would be substantially electrified
(supplement Table A1).

The costs of decarbonization and benefits of optimal transmission vary across
regions. In Figure 2 panel a, regions are ordered from least to greatest cost
in the scenario with zero emissions and existing transmission (ZE). These
costs vary from about $47/MWh in TRE_WEST, which encompasses southwestern
Texas, to about $91/MWh in NYCM, which contains New York City and Long Island.
It is clear from the map (panel b) that the transmission benefit for
decarbonization varies across regions; in a few cases, expanding transmission
increases the decarbonization cost (shades of red). The precise calculation
for each point is the demand-weighted average hourly marginal cost for each
region under each scenario. Because the model optimizes the system’s capital
and chronological operation, and capital decisions are nearly continuous at
the regional scale, the average marginal cost equals the average cost,
including positive or negative economic rents to infra-marginal or stranded
generation and transmission. We report on rents below and show how
transmission changes their allocation, which may be relevant to the political
economy of transmission expansion and of generation plants siting.

To fully decarbonize using only existing transmission, investments in storage
must increase by 21%, generation by 9%, and hydrogen electrolysis by 0.6%
relative to the fully-optimized transmission scenario (Figure 3, panel a ). If
transmission can expand optimally only within interconnects, generation and
storage capacities change minimally relative to the fully optimized
transmission scenario, while hydrogen is minimally used regardless of
transmission. In the socially optimized system, limiting to existing
transmission causes storage and generation expenditure to increase by 23% and
5%, while hydrogen is minimally used regardless of transmission (shown in the
supplement in Table A1 and Figure A4). In general, the mix of generation is
similar regardless of transmission but uses slightly more nuclear and solar
and less wind when transmission is constrained (panels c and d of Figure 3).
These compensating adjustments in generation and storage expansions are
somewhat more expensive than the optimized transmission expansions that they
replace (Figure 3, panel a). The adjustments are modest, however, relative to
the 15-fold increase in renewables and other capacity increases needed for
decarbonization.

Generation capacities and their geographic locations, including those for
solar, wind, batteries, hydrogen, nuclear, and other sources, are generally
similar regardless of transmission expansion and vary mainly with the degree
of decarbonization. We illustrate these differences in Figure 4, which plots
capacities in each region and type when only existing transmission is used
against capacities when interregional transmission is fully optimized. The
similarity of these generation mixes has a practical implication for planning:
it suggests that generation expansion should proceed similarly regardless of
inter-regional transmission expansion, especially during the early to
intermediate stages of decarbonization. In the supplement Figure A5, we show
similar comparisons for the socially optimum scenarios that assume a carbon
price of $190/ton.

In addition to the technologies shown, the model includes options for carbon
capture and storage (CCS) paired with natural gas and coal generation
facilities. These technologies are only selected in the socially optimal
scenarios, with details provided in the supplement (Figure A4).

Transmission expansion will have little influence on price variability, while
the extent of decarbonization will significantly increase price variability
(Figure 5). In competitive markets, wholesale prices equal marginal cost, the
distributions of which we can infer from model’s dual variables associated
with each hour’s balancing constraint. We show these distributions as
cumulative densities because they tend to have significant mass points at
zero, and especially large ones in high-renewable scenarios. In the supplement
we use multiple bar plots to show the density functions, which may be more
intuitive. We discuss likely real-world departures from competitive markets
below.

The marginal-cost distributions for the least-direct-cost scenarios have about
90 percent of MWh between 20 and 40 dollars per MWh. About 2 percent of MWh
have a marginal cost of zero or nearly so ($<$ $1/MWh), and about five percent
have marginal costs above 40 dollars per MWh. The zero marginal-cost times
occur during curtailment events (wind and/or solar energy are discarded). The
influence of transmission on the marginal cost distribution is so small that
it is difficult to discern in the graph.

In contrast, the high-renewable scenarios, including both zero-emissions and
socially-optimal scenarios with a $190/tCO2, have starkly greater variability,
with 28 to 48 percent of delivered MWh having a zero or near-zero marginal
cost ($<$ $1/MWh). The large share of “free" energy occurs because solar and
wind capacities are optimally built out to help serve demand on days with low
to medium wind and sunlight and high demand. These times are seasonal, tending
to occur in late fall and winter. As a result, there are often surpluses
during other seasons, especially spring and summer, when wind and sunlight are
more abundant, leading to many stretches of time with zero marginal cost.
During these times, renewables are curtailed because there is more energy in
batteries than could be depleted before being fully charged again with excess
wind and solar, and electrolysis capacity is fully utilized.

In zero-emissions scenarios, the spread of marginal cost above near-zero is
smooth and broad, with about 25 percent of marginal costs spread evenly
between $10 and $100 per MWh, and the marginal cost of most other energy
spread evenly between $100 and $200 per MWh. Extreme marginal costs above
$1000/MWh are rare. The main effect of transmission is to slightly increase
the frequency of hours in the $30 to $80 and $100 and $200 range. Again, the
influence of transmission is modest. In the socially optimal scenarios,
marginal costs above near-zero are more concentrated in the $75 to $200 range.
Like the other cases, the influence of transmission on the distribution of
marginal costs is minimal.

The extreme variability of marginal cost in high-renewable scenarios,
especially the high frequency of zero-marginal-cost energy, suggests that
flexible demand could be especially valuable in these systems, as indicated by
(Imelda, Fripp and Roberts, 2022).

Transmission expansion increases economic rents for some resource owners while
reducing them for others (Figure 6). If resource owners are paid a price equal
to the the incremental cost of power in each region and hour, then all
variable and fixed costs are recovered in long-run equilibrium, which is what
our model assumes. In addition, some owners of scarce resources glean rent
above their total costs. The potential rents we can identify in this study
pertain to heterogeneous solar and wind resources and potentially constrained
transmission resources. Areas with unusually large or well-timed amounts of
solar radiation or winds earn rent (above competitive profit) because they
provide more value than marginal resources. Our model indicates that these
rents tend to be highest in the zero-emissions scenarios.

Transmission expansion increases rents for some resources and regions and
decreases them for others. For example, a region that has high-quality wind or
solar resources gains from expanded transmission and trade with regions that
have worse wind and solar resources, while a region that has lower-quality
wind and solar resources may lose out when enhanced transmission instills
greater competition from neighboring areas.

Combining rent and cost changes, which mostly benefit consumers, all regions
gain from transmission expansion. However, since some resource owners lose
rents relative to the no-expansion case, diverging stakeholder interests could
hamper efforts to expand transmission. Figure 6 illustrates these divergent
interests for solar and wind resources, which are most prevalent and have
greater rent than in the zero-emissions scenarios. The graph shows gains and
losses in solar, wind, nuclear, and transmission rent. The coastal regions and
South tend to lose solar and wind rent with transmission expansion, while
Arizona, Ohio, and Michigan gain solar rent, and the Rocky Mountains,
Oklahoma, and upper Great Plains gain wind rent. Nuclear plants mostly lose
rent, as sunk costs from existing plants earn less revenue when transmission
is optimized, enhancing competition from renewables.

Hourly operational detail in ERCOT shows how transmission expansion can aid
resiliency during the most constrained times (Figure 7). The model optimizes
hourly operations and interregional flows in each region, revealing how the
system achieves balance. Here we consider a costly day in the most isolated
region, TRE, the Eastern part of ERCOT, which has most of the interconnect’s
generation and demand. In two of the four scenarios (LO, ZE), the day depicted
(December 13th, 2050, based on actual weather data in 2012), is the most
expensive in the region. This is a cold day in early winter near the solstice,
when solar resources would generally be more limited, with unusually little
wind.

Compared with the least-cost scenarios, decarbonization is achieved via
substantially greater capacities of solar and wind paired with significant use
of batteries and hydrogen, which replaces natural gas and some old-vintage
coal. The deficit from renewable energy is mostly counterbalanced with natural
gas in the least-cost scenarios and with imports, battery storage, and
hydrogen in the zero-emissions scenarios. Notably, even the least-direct-cost
scenarios use batteries to help serve the net peak at 7pm, when wind and solar
power fall to near-zero.

The effects of optimizing transmission are subtle and difficult to discern in
the least-direct-cost scenarios. In these scenarios, some power is imported
from the Western part of ERCOT (TRE_WEST) at 1pm and 3pm of December 13th,
2050 when transmission is fixed (panel a), but less is imported under optimal
transmission, because, in this case, more natural gas capacity is built so the
region can export more on other days. The generation mix is largely the same
when transmission is fully optimized (panel b), except there is slightly more
gas generation and less battery use during the evening peak. The peak hour
marginal cost falls from about $20,000 to about $16,000 when optimizing
transmission.

The zero-emissions scenarios (c and d) show a somewhat greater influence from
optimizing transmission. Generation mixes are similar regardless of
transmission, but there is noticeably more battery use and slightly less wind
in the scenario with existing transmission. And while imports help, especially
in the optimal transmission scenario, it is interesting that imports occur
midday to help replenish batteries, and much less during the expensive evening
peak. The peak marginal cost of about $22,000 per MWh falls to about $7,000
with expanded transmission. And where the nighttime hours after the peak stay
elevated at $5,000 per MWh with existing transmission, marginal cost falls
back to very low levels when transmission is optimally expanded.

Although we do not consider demand response or demand-side flexibility in this
study, this difficult day in ERCOT suggests it could be valuable. In all
scenarios, hours up to 5pm are very low cost or free. Adjustments in EV
charging, thermal storage or pre-heating in buildings, or even modest
thermostat adjustments during the critical peak, would reduce required
hydrogen or battery capacity, saving substantial costs. Even existing demand
responses by some industrial customers could make a difference. Such demand
responses would likely reduce transmission value, too.

##  5 Discussion

More than 2 TW of solar, wind, and storage capacity was waiting for
interconnection to the U.S. grid at the end of 2022, a staggering quantity
equal to multiple times existing capacity. The U.S. electricity sector would
take a healthy step toward decarbonization if all of it were built, connected
to the grid, and managed efficiently. Still, the wait times are substantial,
and many proposed projects are never completed (Rand et al., 2023). Full
decarbonization will require even more growth of renewable energy capacity by
2050, especially with higher demand from electric vehicles and electrification
of heat and industry. Many kinds of local transmission upgrades are critical
to connect these resources, including spur lines to the locations of new
generation facilities, and grid-enhancing technologies that can help to
maximize the use of existing transmission lines within and between regions.
The Federal Energy Regulatory Commission is considering the nature and extent
of transmission upgrades needed, and how best to manage a considerable queue
of clean energy resources.

This study does not focus on these immediate transmission challenges of grid
interconnection and optimal power flow (which considers exact existing lines,
their impedances, currents, voltage limits, and real and reactive power
flows). However, it does account at least approximately for the cost of spur
lines and transmission upgrades to connect new solar and wind installations to
the grid. Rather, considered the costs and benefits of transmission expansion
and large-scale energy flows between large regions, which could allow more
power to be traded over greater distances but could face considerable social,
political, and environmental challenges. This research question and scope can
be adequately addressed using capacity expansion models as we do in this work.

While the optimal expansion of interregional transmission would require more
than a three-fold increase relative to what presently exists, we find that the
net benefits of this expansion are small relative to the overall cost of a
decarbonized system. Alternatives to expanded transmission are multifaceted
and include greater renewable generation capacity, battery storage, and
hydrogen electrolysis paired with fuel cell power generation. While expanded
transmission might improve resiliency in some locations, the overall
distribution of marginal costs (i.e., competitive wholesale prices) is similar
regardless of interregional transmission expansion.

One caveat is that some kinds of transmission might be expanded at lower cost
using various grid enhancing strategies111https://www.energy.gov/oe/grid-
enhancing-technologies-improve-existing-power-lines to improve power flow, or
by employing new high-capacity conductors in existing right-of-ways
(Chojkiewicz et al., 2024), which could halve the cost of expanding existing
lines. It is also conceivable that storage costs could fall more than
projected. Such technologies could only serve to expand the portfolio of
options available to integrate clean energy affordably.

Another caveat to these findings is that they generally assume economic
efficiency or perfectly competitive outcomes. During congested times,
transmission and generation capacity owners may possess considerable market
power, and be tempted to withhold generation or transmission to raise
wholesale prices and profits (Borenstein, Bushnell and Wolak, 2002). Greater
transmission capacity could, therefore, have the added benefit of increasing
competition. At the same time, those earning substantial scarcity and/or
market-power rents may resist expansion efforts that would reduce such rents.
Transmission expansion may need to be expanded much more than otherwise
optimal if the goal is to attenuate market power.

Perhaps a greater limitation of this study is that it does not account for
demand-side adjustments that could substitute for transmission, storage, and
generation. Such responses could be achieved through strategic timing of
electric vehicle charging, vehicle-to-grid technologies, improved building
insulation, thermal storage, smart control of building HVAC and water heating
systems, thermostat adjustments during extreme weather events, and industrial
demand shifting, some of which already exist. Given the extraordinary growth
in marginal cost variability in the decarbonization scenarios, it seems likely
that utilities, industry, communities, and opportunistic intermediaries will
find ways to exploit growing wholesale price differentials. If they do,
interregional transmission growth could be worth less than we estimate. Future
research could consider how optimal transmission upgrades and expansion
interact with demand response and distributed resources from local to
interregional scales. A robust demand-side market that is responsive to real-
time marginal costs would have the added benefit of reducing potential market
power during congested times.

##  6 Methods

The paper reports results from Switch, a structured power system planning
model with input data compiled by PowerGenome. Both Switch and PowerGenome are
open-source platforms with online documentation. We provide a brief
characterization of the model here.

### Limitations

Three main aspects are important to discuss in the context of transmission
line expansion. First, in this study, we model transmission capacity in an
aggregated manner to represent important energy flows between load zones. Our
approach models the transfer capability of the electrical network but does not
directly represent the physics of AC optimal power flow. Hence, our findings
should not be taken as a claim that there is no need to worry about
transmission expansion within individual regions in 2050. Our work sheds light
on what are the most important electricity transfers between regions and
interconnects to achieve zero emissions in 2050. Our findings speak to the
lack of need and minimal economic impact of deploying “energy corridors”
between interconnects as opposed to speaking about the value of specific
transmission lines, for which power flow modeling would be required with an
accurate model of the transmission network (e.g., California should be modeled
with its approximately 9,000 buses). Second, our study, while high-resolution,
considers only a single weather year and coincident demand. We do not account
for reserves or for extreme weather events that do not occur in a typical
year. Appropriate account of reserves and extreme events in reliable high-
renewable environments requires the compilation of many years of high-
resolution weather. It would also be important to include a careful account of
demand response in such a study.

### Switch Characterization of the Planning Problem

Our analysis uses Switch (Fripp, 2012; Johnston et al., 2019), which is an
open source capacity expansion model that minimizes the net present value
(NPV) of costs for an electricity grid across all investment periods and
timepoints. It optimizes both the investment and operational costs subject to
constraints such as emissions limits or prices, or other policies, such as
Renewable Energy Portfolio Standards (RPS).

Switch has a modular structure. Core modules define the time and spatial scale
for the power system as well as an hourly load-balancing constraint and cost-
minimizing objective function, both of which is initially empty. Additional
modules define physical components and add their costs to the objective
function and their power contribution to the load balance. Other modules
define constraints or costs to reflect policy choices, such as renewable
portfolio standards or carbon caps. The modules we used in this study are
described briefly below.

#### Timescales

Timescales defines the time horizon for the investment planning and energy
balancing. Under the Switch modeling toolkit, the time resolution has a three-
level hierarchy that accounts for the temporal dimension at various scales:
periods, time series, and time points. Periods are a set of multi-year
timescales that describe the times when the investment decisions are made. In
this model, to focus squarely on the question of transmission, we assume just
one investment period that stretches 10 years from 2041 to 2050 and refer it
as period 2050. The next level of granularity is the time series. This denotes
blocks of consecutive time points within a period. An individual time series
could represent a single day, a week, a month, or an entire year, or even a
mix of blocks of different lengths. The length of time that energy may be
stored is typically limited to the time series, which means that the amount of
energy storage at the beginning of the time series is constrained to equal the
ending amount at the end of the time series. (Hydrogen is an exception, as
explained below.) There are 52 time series in this study, each one week long,
with hourly time points from each week, comprising all 8760 hours in a year.
Having 52 one-week time series instead of one time series of length 8760 saves
considerably on computational cost while losing little practical precision,
since battery storage and most hydroelectric resources cannot be economically
used for long-duration storage that exceeds a week.

#### Financial

The financial module defines the base year for the NPV calculation, the
discount rate applied, and interest rate used for financing capital
investments. The base year in this study is year 2022 with the interest and
discount rates set to 5% (real). The cost-minimizing objective function is
defined in this module.

#### Generation

The generation modules define generation build-out options (both new and
existing) and electricity dispatch, including fuel costs, variable O&M, and
overnight build costs. Solar and wind installations have no fuel costs, but
have variable capacity factors associated with each candidate project that
account for hourly resource availability at that site. Switch has separate
modules for storage, hydro and endogenous hydrogen production and storage
because of their unique operation and function. The storage module defines
energy storage assets, optimizes new power and energy capacity, and optimizes
their operation (charging and discharging). The hydro module enforces minimum
and average flows for hydro resources for each time series. Newly built
hydrogen generators can be implemented as generators that require the supply
of hydrogen as an external fuel. In addition, Switch includes a module that
produces hydrogen endogeneously. In this module, Switch optimizes the amount
of electrolyzer, fuel cell, liquifier and hydrogen storage tank needed to be
built and used for every model region. Storage tanks are sized to accommodate
a whole year of hydrogen production and thereby facilitate seasonal storage,
which is the predominant use.

#### Transmission

The Transmission module represents the expansion and operation of the
transmission assets using a transport model. In addition to optimized
transmission expansion which allows additional capacity along any potential
corridors, this module offers the option for users to disable expansion of any
corridor using a binary parameter – trans_new_build_allowed. This flexibility
allows us to consider scenarios without expansion or with partial expansion
(e.g., within interconnects but not between).

#### Policies

The policies subpackage has modules that enforce energy policy constraints
such as RPS and carbon targets or carbon prices. The three decarbonization
scenarios in our study are defined via the carbon policies module. (i) a
least-direct-cost system that ignores external costs of CO2 and other
pollution emissions; (ii) a socially-optimal system that assigns a cost of
$190 per tonne of CO2 emitted; and (iii) a zero-emissions system with an
emission cap of zero at 2050.

### PowerGenome and Principal Data Sources

One of the most difficult parts of running electricity capacity expansion
models is assembling all the data. PowerGenome (Schivley, 2020) serves as a
platform to generate inputs files for power system optimization
models—including Switch, GenX, Temoa and USENSYS. The source data comes from a
number of different resources, including EIA, NREL, and EPA.

#### Model Regions

The extent of geographic coverage and number of regions is one of the first
decisions to make when running an electricity planning model. Model regions in
PowerGenome are derived from IPM regions. To align with the new-build resource
cost multipliers for Electricity Market Module (EMM) regions in EIA’s NEMS
model, we group the IPM regions into 26 model regions in this study. These
regions conjoin existing sub-regional balancing authorities. Region names are
determined by matching the actual names listed in EIA’s Open Data query search
against each map and then looking at example API urls. Data on existing
generating units, cost estimates for new generating units, transmission
constraints between regions, hourly load profiles and hourly generation
profiles for wind & solar to construct the optimization problem, are all
parsed by these regions. The sources of these data are presented below.

#### Existing and Candidate Generators

Existing generating units are from the latest version of form EIA-860 (U.S.
Energy Information Administration, 2021), 2021 supplemented with 860m from
June 2023. The cost and heat rates of new-build resources are provided by
NREL’s Annual Technology Baseline (ATB) 2022 (National Renewable Energy
Laboratory, 2022). Renewable resources are generally location-specific, with
unique generation profiles and interconnection costs. Rather than representing
all potential new-build renewable resources as individual sites, PowerGenome
lets the user specify how much capacity of each resource type should be
available for consideration in a model region and how many clusters the
resource should be represented by. We use 942 clusters of candidate renewable
energy projects, corresponding to approximately 21 TW of potential capacity.
High-resolution weather data provided by Vibrant Clean Energy for 2012 (the
year upon which our demand data is based) is used to construct hourly variable
capacity factors for each cluster.

#### Transmission lines

Existing transmission capacities between IPM regions are from EPA. Model
regions in our study can consist of one or more individual IPM regions. When
two or more IPM regions are combined to make a Switch model region, the
transmission capacity between individual IPM regions is also combined.
Transmission lines in this study are defined as connections between major
metros in each region, with additional backbone networks connecting major
metros within a region (if there is more than one). Costs and line loss use
transmission line segments created with a least cost path method described in
Appendix F of (Patankar et al., 2023).

#### Demand

Hourly demand starts with NREL EFS profiles (National Renewable Energy
Laboratory, 2019). Stock values (historical) and hourly demand profiles of
electrified end-use technologies like transportation, water heating, and space
heating/cooling (derived from NREL EFS data) are subtracted from the 2019 EFS
profiles. The remaining demand is inflated using sector-specific growth rates
from EIA AEO 2022 (Nalley and LaRose, 2022). The future hourly demand from
electrified end-use technologies are added back in using future stock values
(from the REPEAT (Rapid Energy Policy Evaluation and Analysis Toolkit, 2022)
scenario IRA_MID) and hourly demand profiles derived from EFS.

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Figures

Figure 1: Demand, generation, and transmission capacities in existing and
idealized future zero-emission electricity systems. Panel a shows weekly
demand as modeled for 2022 and 2050. These demand data are derived from 2012
to synchronize with the weather data but are re-scaled to 2022 and projected
to 2050 levels. Panel b shows 2022 generation capacities and inter-regional
transmission. Note that total transmission capacity is less than 1 GW between
the East and WECC. Panel c shows a least-cost, zero-emissions system for 2050
without superfluous constraints on the generation mix or transmission
expansion. Figure 2: Cost per MWh for the different emissions and transmission
scenarios. Panel a shows the demand-weighted average marginal cost for each
region in 2050 in four scenarios, least-direct-cost (triangles) and zero-
emissions scenarios (circles), each with existing (blue) and optimized (red)
transmission. Comparing circles to triangles of the same color gives the
region’s cost of decarbonization, with blue indicating the cost without
transmission expansion (difference A) and red indicating the cost with
optimized transmission expansion (difference B). Comparing the same shapes of
different colors gives the net savings from expanded transmission. Panel b
shows a map of the difference in differences (A-B): the cost savings ($/MWh)
from fully decarbonizing using optimal transmission instead of using only
existing transmission. Figure 3: Comparing component costs and capacities. The
graphs compare costs, generation mixes, and transmission capacities across six
scenarios, LE (least-direct-cost with existing transmission), LI (least-
direct-cost with optimal within-interconnect transmission), LO (least-direct-
cost with optimal fully-optimized transmission), ZE (zero-emissions with
existing transmission), ZI (zero-emissions with optimal within-interconnect
transmission), and ZO (zero-emissions with optimal fully-optimized
transmission). Panel a shows broadly categorized cost components; panel b
shows total transmission capacity in each scenario (GW-miles); panel c shows
total generation capacities (TW) in each scenario; and panel d shows the share
of dispatch (source of energy consumed) in each scenario. Figure 4: Comparison
of regional capacities across transmission scenarios. These scatter plots show
how transmission expansion influences the mix of generation capacities across
regions. It plots generation capacities in each region and type when only
existing transmission is used against capacities when interregional
transmission is fully optimized. Panel a shows the relationship under least-
direct-cost scenarios, and panel b shows the relationship under zero-emissions
scenarios. Different types of generation are plotted in different colors.
Figure 5: Distribution function of marginal cost. This graph shows the
distribution functions or (cumulative density functions) for hourly marginal
cost across all MWh in all continental U.S. regions in 2050. To construct
these, we account for the MWh of demand in each region/hour. Six scenarios are
depicted: least-direct-cost, with existing and optimal transmission (LE & LO),
zero-emissions with existing and optimal transmission (ZE & ZO), and socially
optimal, with an assumed price of CO2 emissions of $190 per ton, which
achieves roughly 89% reduction of emissions from the electricity sector
relative to 2022. All scenarios assume 74% demand growth relative to 2022 and
conservative projections from NREL-ATB. Figure 6: Rent changes when going from
existing to optimal transmission in zero-carbon scenarios. Each graph shows
the rent change to a resource when going from the ZE scenario to the ZO
scenario. The rents accrue to infra-marginal wind and solar resources that are
more valuable than marginal sources, existing nuclear facilities (costs are
assumed sunk), and constrained transmission resources that receive surplus
congestion rents. Panel a shows transmission expansion benefits solar and wind
producers in regions unusually rich in these resources relative to their
neighbors, while reducing rents in neighboring areas; it also shows that
existing nuclear typically loses with transmission expansion since it becomes
less competitive. Panel b shows the change in rents to transmission lines.
Expanded transmission links typically lose rent as congestion charges decline.
New transmission links have zero rent because expansion is optimized. Existing
but non-expanded lines also tend to lose rent as congestion charges decline.
The rare exceptions where transmission rents rise are cases where existing
transmission is marginally overbuilt and losses are reduced. Figure 7: Hourly
generation, dispatch, transmission, and marginal cost in TRE during the most
costly sample day. The graphs show hourly dispatch, inflows, outflows, and
marginal cost in four scenarios for the TRE region, the Eastern part of ERCOT
in Texas, on the sample day with the highest demand-weighted average marginal
cost. Panels a and b show the least-direct-cost systems under existing and
optimized transmission (LE and LO), and panels c and d show the zero-emissions
systems under existing and optimized transmission (ZE and ZO).

Optimal transmission expansion minimally reduces decarbonization costs of U.S.
electricity
Appendix

Rangrang Zheng, Greg Schivley, Patricia Hidalgo-Gonzalez,
Matthias Fripp, Michael J. Roberts

Supplemental Analysis

Here we describe mathematical structure of Switch in more detail and present
additional results, with an emphasis on comparing the least-direct-cost (LX)
scenarios with the _socially optimal_ (SX) scenarios that minimize costs
subject to a carbon emissions price of $190 per ton rather than forcing zero
emissions. This price leads to 90 to 95% emissions reductions relative to 2022
levels in most cases, even with a 75% growth in electricity production. We
refer to these scenarios as socially optimal because they equate the marginal
cost of abatement to the Environmental Protection Agency’s marginal social
cost of emissions (i.e., the estimated marginal benefit of abatement).

## Switch Formulations

Here we provide a brief overview of the mathematical formulation of Switch
2.0, the model used for our research. More complete documentation of the
software can be found in (Johnston et al., 2019). Switch 2.0 has a modular
architecture that reflects the modularity of actual power systems. Most power
system operators follow rules that maintain an adequate supply of power, and
most individual devices are not concerned with the operation of other devices.
Similarly, core modules in Switch define spatially and temporally resolved
balancing constraints for energy and reserves, and an overall social cost.
Separate modules represent components such as generators, batteries or
transmission links. These modules interact with the overall optimization model
by adding terms to the shared energy and reserve balances and the overall cost
expression. Switch 2.0 supports co-optimization of multiple investment
periods, but we have omitted those definitions here, since we use a single
stage for this study (2041-2050). We have likewise omitted details on spinning
reserves and unit commitment, which were not used for this study.

### Objective function

The objective function is defined by the financials module. It minimizes the
net present value of all investment and operation costs:

$\displaystyle
Min\Biggl{\\{}\sum_{c^{\text{f}}\in\mathcal{C}^{\text{fixed}}}c^{\text{f}}+\sum_{t\in\mathcal{T}_{p}}w_{t}^{\text{year}}\sum_{c^{\text{v}}\in\mathcal{C}^{\text{var}}}c_{t}^{\text{v}}\Biggr{\\}}$
(1)

Function 1 sums over sets of fixed costs $\mathcal{C}^{\text{fixed}}$ and
variable costs $\mathcal{C}^{\text{var}}$. Each fixed cost component
${c^{\text{f}}\in\mathcal{C}^{\text{fixed}}}$ is a Pyomo object, indexed by
investment period and specified in units of $/year. This object may be a
variable, parameter or expression (calculation based on other components). The
term $c^{\text{f}}$ is the fixed cost that occurs during our study period.
Each variable cost component $c^{\text{v}}$ is indexed by timepoint ($t$) and
specified in units of $/hour. Modules add components to the fixed and variable
cost sets to represent each cost that they introduce. Hence, the exact
equation will depend on which modules are selected by the user. In most runs,
fixed costs in $\mathcal{C}^{\text{fixed}}$ include capital repayment for
investments at a fixed financing rate over the lifetime of each asset, sunk
costs from existing infrastructure, as well as fixed operating and maintenance
(O&M) costs. Variable costs in $\mathcal{C}^{\text{var}}$ typically include
fuel costs and variable O&M. The weight factor $w_{t}^{\text{year}}$ scales
costs from a sampled timepoint to an annualized value.

### Operational Constraints

Power Balance: Specifies that power injections and withdrawals must balance
during each time point $t$ in each zone $z$. As with the objective function,
plug-in modules add model objects to $\mathcal{P}^{\text{inject}}$ and
$\mathcal{P}^{\text{withdraw}}$ to show the amount of power injected or
withdrawn by each system component during each timepoint. For this study,
production components include renewable and conventional generators,
batteries, hydrogen fuel cells, and inbound transmission flows. Withdrawals
include customer loads, battery charging, hydrogen electrolysis and
refrigeration, and outbound transmission flows.

$\displaystyle\sum_{p^{\text{i}}\in\mathcal{P}^{\text{inject}}}p^{\text{i}}_{z,t}~{}~{}~{}=\sum_{p^{\text{w}}\in\mathcal{P}^{\text{withdraw}}}p^{\text{w}}_{z,t},$
$\displaystyle\forall z\in\mathcal{Z},\forall t\in\mathcal{T}$ (2)

Dispatch: Power generation from a source $g$ (e.g., a power plant) must fall
below its installed capacity $K_{g}^{\text{G}}$ during time point $t$
multiplied by a capacity factor $\eta_{g,t}$, that may vary with exogenous
factors like solar radiation or wind speed.

$\displaystyle 0\leq P_{g,t}\leq\eta_{g,t}K_{g}^{\text{G}},$
$\displaystyle\forall g\in\mathcal{G},\forall t\in\mathcal{T}$ (3)

Transmission Flows: Transmission flows $F_{\ell,t}$ along a corridor $\ell$
are constrained by the installed capacity $K_{\ell}^{\text{L}}$ on that
corridor. Additional constraints (not shown) define the flow out of a corridor
to take a smaller value than flow into the corridor, reflecting transmission
losses.

$\displaystyle 0\leq F_{\ell,t}\leq K_{\ell}^{\text{L}},$
$\displaystyle\forall\ell\in\mathcal{L},\forall t\in\mathcal{T}_{p}$ (4)

Power System Construction: Eqs. (5) and (6) define installed capacity for
generation projects $K_{g}^{\text{G}}$ and transmission lines
$K_{\ell}^{\text{L}}$ as the sum of capacity additions during the study
($B_{g}^{\text{G}}$ or $B_{\ell}^{\text{L}}$) and preexisting capacity of the
same type in the same location ($k_{g}^{\text{G}}$ or $k_{\ell}^{\text{L}}$).

$\displaystyle K_{g}^{\text{G}}=B_{g}^{\text{G}}+k_{g}^{\text{G}},$
$\displaystyle\forall g\in\mathcal{G}$ (5) $\displaystyle
K_{\ell,p}^{\text{L}}=B_{\ell}^{\text{L}}+k_{\ell,y}^{\text{L}},$
$\displaystyle\forall\ell\in\mathcal{L}$ (6)

Some generation projects (the set $\mathcal{G^{\text{rc}}}$) also have caps on
installed capacity $\overline{k^{\text{G}}_{g}}$. These may be plants of a
type that cannot be built in the future or renewable projects with limits on
available land.

$\displaystyle K_{g}^{\text{G}}\leq\overline{k^{\text{G}}_{g}},$
$\displaystyle\forall g\in\mathcal{G^{\text{rc}}}$ (7)

Additional terms define behavior of storage facilities (charging, state of
charge, round-trip losses), fuel consumption (full load heat rate times power
production) and hydrogen facilities (production and storage of hydrogen and
conversion back to electricity). For complete details on Switch’s mathematical
formulation, see the Supplementary Material of (Johnston et al., 2019) at
https://ars.els-cdn.com/content/image/1-s2.0-S2352711018301547-mmc1.pdf.

Supplemental Figures

Figure A1: Demand, generation, and transmission capacities in existing and
idealized socially optimum electricity systems. Panel a shows 2022 generation
capacities and inter-regional transmission. Panel b shows an optimized,
socially-optimal system for 2050 without constraints on the generation mix or
transmission expansion. It is important to note the substantial difference in
scale of generation capacities for 2022 and 2050. Figure A2: Cost per MWh for
different emissions and transmission scenarios. Panel a shows the demand-
weighted average marginal cost for each region in 2050 in four scenarios,
least-direct-cost (triangles) and socially-optimal scenarios (circles), each
with existing (blue) and optimized (red) transmission. Comparing square to
triangles of the same color gives the region’s cost of decarbonization, with
blue indicating the cost without transmission expansion (difference A) and red
indicating the cost with optimized transmission expansion (difference C).
Comparing the same shapes of different colors gives the net savings from
expanded transmission. Panel b shows a map of the difference in differences
(A-C): the cost savings ($/MWh) from optimizing transmission under full
decarbonization relative to using only existing transmission. Figure A3: Count
percentage of marginal cost. This graph shows the count percentage for hourly
marginal cost across all MWh in all continental U.S. regions in 2050. Six
scenarios are depicted: Panel a shows the system of least-direct-cost, with
existing and optimal transmission (LE & LO); Panel b shows the system of zero-
emissions with existing and optimal transmission (ZE & ZO); Panel c shows the
system of socially optimal, with an assumed price of CO2 emissions of $190 per
ton, which achieves roughly 89% reduction of emissions from the electricity
sector relative to 2022. Figure A4: Comparing component costs and capacities.
The graphs compare costs, generation mixes, and transmission capacities across
six scenarios, LE (least-direct-cost with existing transmission), LI (least-
direct-cost with optimal within-interconnect transmission), LO (least-direct-
cost with optimal fully-optimized transmission), SE (socially-optimal with
existing transmission), SI (socially-optimal with optimal within-interconnect
transmission), and SO (socially-optimal with optimal fully-optimized
transmission). Panel a̱ shows broadly categorized cost components; panel ḇ
shows transmission capacity in each scenario (GW-miles); panel c̱ shows
generation capacities (TW) in each scenario; and panel ḏ shows the share of
dispatch (source of energy consumed) in each scenario.  Figure A5: Comparison
of regional capacities across transmission scenarios. These scatter plots show
how transmission influences the mix of generation capacities across regions.
Each panel shows optimized region-level generation capacities under existing
transmission plotted against generation capacities under fully optimized
transmission. Panel a shows the relationship under least-direct-cost
scenarios, and panel b shows the relationship under socially-optimal
scenarios. Different types of generation are plotted in different colors.
Figure A6: Rent changes when going from existing to optimal transmission in
socially optimal scenarios. Each graph shows the change in rents to a resource
when going from the SE scenario to the SO scenario. The rents accrue to infra-
marginal wind and solar resources that are more valuable than marginal
sources, to existing nuclear facilities (costs are assumed sunk), and to
constrained transmission resources that receive surplus congestion rents.
Panel a shows transmission expansion benefits solar and wind producers in
regions unusually rich in these resources while hurting producers in other
regions; it also shows that existing nuclear generally gains with transmission
expansion since it can enjoy higher capacity factors. Panel b shows the change
in rents to transmission lines when going from the SE scenario to the SO
scenario. Figure A7: Hourly generation, dispatch, transmission, and marginal
cost in TRE during the most costly sample day. The graphs show hourly
dispatch, inflows, outflows, and marginal cost in four scenarios for the TRE
region, which is the Eastern part of ERCOT in Texas, on the sample day with
the highest demand-weighted average marginal cost – Dec 13th, 2050. Panels c
and d show the socially-optimal systems under existing and optimized
transmission (SE and SO).

Supplemental Table

| Least-direct-cost | Zero-emissions | Socially-optimal
---|---|---|---
| LE | LI | LO | ZE | ZI | ZO | SE | SI | SO
O&M | 4.2 | 4.2 | 4.2 | 1.8 | 1.4 | 1.4 | 5.5 | 4.9 | 4.6
Fuel | 35.3 | 34.9 | 34.5 | 4.8 | 3.6 | 3.7 | 15.9 | 13.8 | 13.3
Storage | 1.4 | 1.3 | 1.3 | 15.8 | 14.2 | 13.0 | 7.4 | 6.37 | 6.0
Generation | 36.3 | 35.6 | 35.4 | 100.1 | 92.9 | 91.9 | 77.6 | 74.6 | 73.9
Transmission | 3.1 | 4.0 | 4.3 | 3.1 | 9.1 | 9.8 | 3.1 | 8.4 | 9.3
Hydrogen | 0.4 | 0.3 | 0.3 | 22.7 | 22.5 | 22.5 | 0.2 | 0 | 0
Subtotal | 80.6 | 80.2 | 79.9 | 148.3 | 143.8 | 142.4 | 109.6 | 108.1 | 107.0
Emissions Cost | 272.3 | 272.0 | 269.8 | 0 | 0 | 0 | 13.3 | 11.6 | 11.6
Total | 352.8 | 352.2 | 349.7 | 148.3 | 143.8 | 142.4 | 123.0 | 119.7 | 118.6
Table A1:  Cost components for all nine scenarios. The table reports the
annualized costs in billions of 2022 dollars for each scenario, discounted at
5% (real) from the 2041-2050 investment period, to the present. Graphical
displays of these numbers are in Figures 3 and A3. The _Least-direct-cost_
scenarios minimize the net present value of all costs excluding emissions; the
_Zero-emissions_ scenarios force zero emissions; and the _Socially-optimal_
scenarios optimize CO2 emissions assuming a social cost of $190 per ton.
Scenarios LE, SE, ZE restrict transmission capacities to their current level,
but do account for maintenance of those lines; scenarios LI, SI, ZI optimize
transmission capacities _within_ existing interconnects, but do not disallow
new transmission between interconnects; scenarios LO, SO, ZO fully optimize
transmission within and between interconnects. Emissions costs multiply metric
tons of emissions by $190/tCO2.