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Evaluating the Value of High 

Spatial Resolution in National 

Capacity Expansion Models 

using ReEDS

Preprint

Venkat Krishnan and Wesley Cole

National Renewable Energy Laboratory

Presented at the 2016 IEEE Power & Energy Society General 

Meeting

Boston, Massachusetts

July 17–21, 2016

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Evaluating the Value of High Spatial Resolution in 

National Capacity Expansion Models using ReEDS

Venkat Krishnan, Ph.D., IEEE Member, Venkat.krishnan@nrel.gov, Wesley Cole, Ph.D., Wesley.cole@nrel.gov

National Renewable Energy Laboratory, Golden CO 80401, USA

Abstract—Power sector capacity expansion models (CEMs) have 

a broad range of spatial resolutions. This paper uses the 

Regional Energy Deployment System (ReEDS) model, a longterm national scale electric sector CEM, to evaluate the value of 

high spatial resolution for CEMs. ReEDS models the United 

States with 134 load balancing areas (BAs) and captures the 

variability in existing generation parameters, future technology 

costs, performance, and resource availability using very high 

spatial resolution data, especially for wind and solar modeled at

356 resource regions. In this paper we perform planning studies

at three different spatial resolutions–native resolution (134 BAs), 

state-level, and NERC region level–and evaluate how results

change under different levels of spatial aggregation in terms of 

renewable capacity deployment and location, associated 

transmission builds, and system costs. The results are used to 

ascertain the value of high geographically resolved models in 

terms of their impact on relative competitiveness among 

renewable energy resources.

Index Terms—Capacity Expansion, Electricity System Planning, 

Optimization, Annual Technology Baseline, Spatial Resolution

NOMENCLATURE

Sets and indices:

A: Set of all renewable generation technologies

B: Set of all conventional generation technologies 

R: Set of variable renewable generation technologies (wind and 

solar)

S: Set of all generation technologies in A and B and not in R

y: Planning year (2010 to 2050 in steps of two years) 

q: Generation technologies (conventional and renewables)

n: Balancing areas (BA), 1 to 134

i: Resource regions, 1 to 356

k: Set denoting region, used for both n and i

st: U.S. states (not including Alaska and Hawaii)

m: Yearly time slices for operations, 1 to 17

Constants and parameters:

fy(q,n): Financial multipliers—accounts for regional cost factors, 

technology financing and construction assumptions, and discount 

rates

CG(q): Generation technology overnight capital cost in $/MW

CGfix(q): Generation technology fixed operation and maintenance 

(O&M) cost in $/MW-year

CRF(q): Generational technology-specific capital recovery factor 

(CRF)

Int(q,i): Renewable generation technology grid interconnection cost 

in $/MW

CT(n,p): Transmission line capital cost in $/MW

CGvar(q,n,m): Generation technology variable O&M cost in $/MWh 

(includes fuel costs)

Ly(n,m): Energy consumption in MWh at BA n in year y and time 

slice m

δy(n): Yearly energy consumption growth factor at BA n

RPSy(st): State RPS targets in MWh

Tpmax(n,p): Transmission line limit in MW

B(n,p): Transmission line Susceptance

CFy(q,n,m): Renewable generation capacity factor in BA

ɸ(q): Generation outage rates

H(m): Hours in the time slice

Py

max(q,n): Maximum generation capacity

Py

0

(q,n): Existing generation capacity (accounting yearly 

retirements)

CVy(q,n): Capacity value of generation technology

Ly

pk(n): Peak load in MW

γy(n): Reserve margin at BA n

Decision variables:

Gy(q,n), Gy(q,i): Generation capacity investments in year y in MW

Ty(n,p): Transmission capacity investments in year y in MW

Py(q,n,m), Py(q,i,m): Energy generated in year y and time slice m in 

MWh

Tpy(n,p,m): Energy transmitted from BA n to p in year y and time 

slice m

θ(n): Balancing area node angle

I. INTRODUCTION

LECTRITY sector capacity expansion models (CEMs) 

have long been used to help various electricity sector 

stakeholders to plan electricity supply and to evaluate the 

economics and impacts of regulations. For a given set of 

assumptions about system futures such as technology cost, 

fuel costs, and load growth, CEMs identify a minimum cost 

set of generation investments from a range of technologies at 

appropriate locations and sizes, while satisfying modeled 

regional policies and other system constraints. 

CEMs are often used to optimize the electricity sector over 

a long planning horizon and a wider geographical region, 

thereby necessitating highly simplified representations of 

electricity networks, their spatial resolution, and the 

generation dispatch process in order to keep the computation 

tractable. For instance, the U.S. Energy Information 

Administration’s (EIA) National Electricity Modeling System 

E
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2

(NEMS), a multi-sector planning tool that considers 

electricity, transportation, residential, commercial, and

industrial sectors, aggregates the national electricity sector 

using 22 supply regions [1]. ICF International’s Integrated 

Planning Model (IPM) [2], a power-sector-only model, 

includes greater detail with 64 model regions and the 

associated interregional transmission limits. The National 

Renewable Energy Laboratory’s (NREL) Resource Planning 

Model (RPM) [3] goes further in terms of its spatial 

resolution, but considers a smaller region. For example, in its 

Western Interconnection-wide planning model the system is 

represented with 34 zonally aggregated nodes, while the 35th

zone (focus region) is represented using individual buses, 

transmission lines, and generators. RPM also models unit 

commitment and hourly dispatch operations of the generation 

units in the focus regions over selected dispatch periods in a 

year, along with DC optimal power flow (DCOPF) models

[4] of transmission power flows. Finally, Energy Exemplar’s 

PLEXOS-Integrated Energy Model [5] provides a suite of 

power system planning tools that allow users to select the 

appropriate regional (i.e., zonal or nodal) and temporal 

(yearly operational planning simulation with minute 

resolution to multi-year investment planning simulation) 

aggregations, while also allowing explicit gas network 

modeling for co-optimizing electric-gas systems [6]. The list 

of tools discussed above is not comprehensive, but provides a 

sample of the alternative regional aggregations employed in 

various models intended for electricity sector capacity 

expansion analysis. Furthermore, each model varies in terms 

of its emphasis for which it was developed and will have pros 

and cons with respect to different energy sector planning 

questions that it is trying to address. The focus of this paper is 

not to compare these models but to evaluate the value of 

higher spatial resolution in CEMs especially from the 

perspective of their impacts on renewable deployments in the 

long run. For this purpose, this paper uses NREL’s Regional 

Energy Deployment System (ReEDS) model [7]. 

ReEDS represents the power sector in the contiguous

United States with high spatial resolution, dividing the U.S

into 356 resource regions and 134 model balancing areas 

(BAs). Wind and concentrating solar power (CSP) resources

are modeled at the resource region level. All other generation 

technologies, as well as electricity demand and reserves, are 

modeled at the 134 BAs (shown in Fig. 1). Long-distance 

transmission is represented between adjacent BAs (also 

shown in Fig. 1), while ReEDS also models the intra-BA 

transmission costs required to interconnect wind, PV, and 

CSP capacity from their resource region to the transmission 

grid. Capturing the cost, availability, and quality of renewable 

resources at a high geographical granularity enables ReEDS 

to find the least cost renewable resource expansions by 

interconnecting high quality economic resources through 

appropriate intra-BA and long-distance inter-BA transmission 

expansions. The focus of this paper is to assess the impact of 

spatial resolution of renewable resource data on capacity 

deployments and total planning costs using three levels of 

spatial representation: 1) native ReEDS resolution 

(Reference, REF), 2) state-level resolution (STATE), and 3) 

NERC-level resolution (NERC); and draw appropriate

insights on the value of high-resolution renewable energy 

resource data in capacity expansion models.

Fig. 1 ReEDS spatial resolution- balancing areas and inter-BA transmission. 

The figure also shows 13 NERC regions.

Section II provides a description of the ReEDS model. 

Section III discusses numerical results under the three levels 

of resource aggregation, and Section IV presents conclusions.

II. REGIONAL ENERGY DEPLOYMENT SYSTEM (REEDS)

The ReEDS model has been used for many renewable 

energy deployment studies, including the SunShot Vision 

Study [8], the Renewable Electricity Futures Study [9], and 

the Wind Vision Study [10]. ReEDS has also been used to 

inform the portfolio of renewable energy integration studies 

such as Eastern Renewable Generation Integration Study 

(ERGIS). This section provides a brief overview of ReEDS.

A. Model Formulation

ReEDS is a linear programming (LP) model that optimizes

the expansion and operation of the contiguous United States 

electricity system in two-year solve periods from 2010 to 

2050. Equations (1-10) provide a high-level formulation of

the ReEDS LP model for each solve year. Additional details 

such as operational reserves, renewable resource variability, 

forecast errors, and curtailment treatments based on statistical 

estimations, intra-BA spur line (for interconnecting 

renewables) supply curves, retirements of underutilized 

generator types, etc. are all not shown. The 2015 Standard 

Scenarios Annual Report [11] and ReEDS documentation 

[12] provide a more detailed description of the model 

structure, assumptions, and scenario results.

Equation (1) is the objective function that minimizes 

capital investment costs for generation and transmission and 

generation dispatch costs across all the BAs. ReEDS 

dispatches all generation using multiple time slices to capture 

seasonal and diurnal demand and renewable generation 

profiles. In particular, each of the “solve years” from 2010 

through 2050 is divided into 17 time slices (index “m” in 

equations) that represent four diurnal time slices (morning, 
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3

afternoon, evening, and night) for each of the four seasons 

(winter, spring, summer, and fall), plus a summer peaking 

time slice (representing the top 40 hours of summer load). 

Equation (2) models the nodal energy balance, and eq. (3) 

enforces state renewable portfolio standards (RPS). ReEDS 

also models technology set-asides such as wind, solar and 

distributed generation carve-outs. Equation (4) applies limits 

on inter-BA transmission flows and eq. (5) models a DCOPF 

constraint on existing and new AC line flows. ReEDS 

assumes the susceptance of the new line to be unchanging in 

order to render the optimization model linear (or else eq. [5]

will be non-linear because line susceptance would also be a 

decision variable). However, to preserve model fidelity 

ReEDS updates the line susceptance of the newly invested 

line in between each solve year. Equations (6-7) model the 

maximum energy availability from conventional and 

renewable generation at every time slice in each BA, which is 

a function of the yearly capacity additions as shown in eq. 

(8). Equation (9) models the planning reserves constraint to 

meet the anticipated yearly peak load, where renewable 

capacities (new and existing) take appropriate capacity values

determined using statistical methods and updated between 

each solve year. Equation (10) constrains the decision 

variables to be non-negative.

FFFFFF tthee yy yy yy εε {2010, 2012, ... , 2050):

MMMMMMMMMMMMMMMM � GGyy(qq, nn)

⎝

⎜

⎛

ffyy(qq, nn) CC (qq)

qq∈SS,nn

+ �CC CCCC(qq)

CCCC (qq) � �

⎠

⎟

⎞

+ � GGyy(qq, )

⎝

⎜

⎛

ffyy(qq, ) (CC (qq) + II (qq, ))

qq∈RR,ii

+ �CC CCCC(qq)

CCCC (qq) � �

⎠

⎟

⎞

+ �TTyy(nn, pp) CC (nn, pp)

nn,pp

+ � PPyy(qq, nn, mm) CC CC (qq, nn, mm)

qq∈BB,nn,mm

Subject to:

(1)

�PPyy(qq, nn, mm)

qq∈SS

+ �PPyy(qq, , mm)

qq∈RR

= LLyy(nn, mm) δδyy(nn)

+ � TT yy(nn, pp, mm)

pp≠nn

, ∀ nn, mm

(2)

� PPyy(qq, nn, mm)

qq∈AA,nn∈ssss

≥ RRy(ss ), ∀ss (ss ) (3)

TT yy(nn, pp, mm) ≤ TT max(nn, pp), ∀ nn, pp, mm (4)

TT yy(nn, pp, mm) = BB(nn, pp)�θθ(nn, mm) − θθ(pp, mm)�,

∀ nn, pp, mm

PPyy(qq, nn, mm) ≤ ∅(qq) PPyy

max(qq, nn) HH(mm), ∀ qq ∈ BB, nn, mm

PPyy(qq, kk, mm) ≤ CC yy(qq, kk, mm) PPyy

max(qq, kk) HH(mm),

∀ qq ∈ AA, kk ∈ {nn, }, mm

(5)

(6)

(7)

PPyy

max(qq, kk) = PPyy0(qq, kk) + GGyy(qq, kk), ∀qq, kk ∈ {nn, } (8)

� CCCCyy(qq, nn) PPyy

max(qq, nn)

qq∈(AA,BB)

≤ Lyy

pppp(nn) γγyy(nn), ∀nn (9)

GGyy(qq, nn), GGyy(qq, ), TTyy(nn, pp), PPyy(qq, nn, mm), PPyy(qq, , mm),

TT yy(nn, pp, mm), θθ(nn, mm) ≥ 0 (10)

ReEDS solutions include the amount and location of new 

and existing generator, storage, and transmission capacity and 

the resulting generation (at each time slice) provided by the 

various generators. ReEDS also outputs the total electric 

sector costs (or net present value of investment and 

operation), electricity prices, fuel demand and prices, and 

direct combustion carbon dioxide (CO2) emissions.

B. Input assumptions

ReEDS includes a full suite of major generation and 

storage technologies, including coal-fired (pulverized coal 

with and without scrubbers, integrated gasification combined 

cycle (IGCC) with and without CCS), natural gas–fired

(combined cycle and combustion turbine), oil and gas steam, 

nuclear, biopower (stand-alone and cofiring), wind (landbased and offshore), biopower, geothermal (flash and binary), 

hydropower (existing small and large hydro, upgrades 

potentials, non-powered dams, and new stream reach 

developments), utility-scale solar, CSP, pumped-hydropower 

storage, compressed-air energy storage , and batteries. All

technology cost and performance input assumptions for 

ReEDS are from NREL’s Annual Technology Baseline 

(ATB) [13]. The ATB is a collection of current and future 

cost and performance projections for electricity generating 

units for the U.S. electricity sector.

Annual electric loads and fuel price supply curves are 

exogenously specified (based on AEO scenarios [14]). 

ReEDS applies standardized financing assumptions, where all 

costs, including new capital investments, O&M costs, fuel 

costs, and transmission investments, are considered on a 20-

year net present value basis. In addition to the general 

financial assumptions (see the ATB [13] for details), some 

technology-specific parameters are used within ReEDS, such 

as technology-specific construction periods, tax credits 

(existing production and investment tax credit rules) and 

accelerated tax depreciation rules. ReEDS also accounts for

existing air pollution regulations such as California AB32,

RGGI, CSAPR, and Clean Power Plan (CPP), although the 

CPP is not activated in these scenarios.
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III. SIMULATION RESULTS

This section presents results for three scenarios: REF, 

STATE and NERC, each differing in their spatial resolutions

of renewable energy resource, cost and performance data. All 

three scenarios used the ATB mid-case cost and performance 

assumptions [11]. In the REF scenario, renewable energy is 

represented at its native resolution in ReEDS (356 regions for 

wind and CSP, 134 regions for all other technologies). In the

STATE scenario, renewable energy costs and capacity factors

within each state were assumed to be the capacity-weighted 

average of costs and capacity factors across all the BAs or 

resource regions within the state. For the NERC scenario

renewable energy costs and capacity factors were averaged 

across all the BAs or resource regions within each NERC 

region, resulting in a common cost and capacity factor within 

each NERC region. In all the scenarios, inter-BA 

transmission limits and distances were respected.

Figure 2 shows the yearly cumulative capacity from the

REF scenario. Under the ATB mid-case assumptions, the 

portfolio sees substantial growth in renewable energy (hydro, 

geothermal, biopower, solar, and wind). Renewable energy 

generation increases from about a 12% share of national 

generation in 2010 to about 28% in 2030, 41% in 2040, and 

54% in 2050. Wind contributes about 11%, 21%, and 30%

respectively, and solar about 5%, 10%, and 15% respectively.

Comparison of nation-wide generation capacity 

deployment under the three scenarios revealed appreciable

changes primarily in three technologies:

• Utility-scale solar PV capacity decreases with lower 

resolution.

• Wind capacity increases to compensate for the decrease 

in PV capacity.

• Gas-CC capacity increases to compensate for PV 

decrease (additionally, there were some slight changes 

in gas-CT and storage capacities in some years- driven 

by varying degrees of variable renewable curtailments).

Table I compares cumulative capacities of PV, wind, and 

gas-CC, and also the inter-BA and intra-BA transmission

across the three scenarios. Numbers in red typeface indicate a

decreasing trend, while green typeface indicates an increasing 

trend. As observed, lower spatial resolution reduces PV 

deployment. When model inputs, such as PV resources, are 

aggregated across broader regions, resource sites with low 

cost and high capacity factors (and capacity value during 

peak periods) become less attractive as they are averaged 

with other higher cost, lower performance resources. As a 

result, these low cost, high performance resources may be 

“missed” by the model that would otherwise be optimal 

investments in a highly spatially resolved model. By 2050, 

we notice PV deployment at the NERC resolution is ~110 

GW less than REF scenario, while the PV mismatch between 

STATE resolution and REF is ~30 GW. Associated with the 

decrease in PV deployment post-2030, we also notice a 

decrease in inter-BA (~2 TW-miles or ~1.7%) and intra-BA 

(~1 TW-miles or ~33%) transmission lines in NERC scenario 

compared to REF in 2050. The additional capacities are seen 

to be coming from both wind (also seen by increasing intraBA lines for wind) and gas-CC generation (~18GW increase 

under NERC scenario by 2050). This indicates that in lowresolution models wind resources may seem more attractive

(over solar) as a result of averaging the resource supply 

curves (i.e., averaging the parameters of a remote “good” 

resource that needs transmission with a local “poor” resource

that does not need transmission may improve the “poor” 

resource’s attractiveness as it does not need transmission). 

Table II presents the differences in system planning costs 

in terms of 2015$ (net present value) under the three 

scenarios. Relative to REF scenario, we observe a ~$25B and 

~$50B increase under STATE and NERC resolution. This

difference is mainly a result oflower renewable (PV) capital 

investments and higher fossil fuel costs. Considering the 

rapidly decreasing PV costs (set to hit $1/W SunShot target in 

2030s as per the assumptions), if lower resolution CEM 

models under-invest in low cost PV resources relative to the 

high resolution models, these CEMS may over estimate total 

costs as they instead invest in other higher cost resources.

Fig. 2 Cumulative installed capacity – REF scenario

TABLE I COMPARISON OF NATION-WIDE WIND, PV, GAS-CC CUMULATIVE CAPACITY & TRANSMISSION AT DIFFERENT SPATIAL AGGREGATION

Year 2010 2020 2030 2040 2050

Scenario REF STATE NERC REF STATE NERC REF STATE NERC REF STATE NERC REF STATE NERC

PV (GW) 0.8 0.8 0.8 21.5 21.6 22.9 77.1 70.3 52.8 186.4 167.1 95.0 300.1 268.1 190.3

Wind (GW) 39.7 39.7 39.7 89.7 90.5 89.1 134.7 126.2 127.6 224.9 224.4 241.8 343.2 346.0 354.8

Gas-CC (GW) 204.1 204.1 204.1 245.1 245.1 245.1 253.0 255.4 252.6 265.6 268.3 268.7 380.9 383.6 397.9

Inter-BA 

transmission 

(103 GW-miles)

82.4 82.4 82.4 86.5 86.5 86.5 95.3 94.5 94.0 104.9 103.0 105.0 119.7

(757GW)

118.5

(752GW)

117.7

(749GW)

Intra-BA -Solar 

(106 MW-miles) 0.0 0.0 0.0 0.5 0.5 0.5 0.9 0.8 0.8 1.4 1.3 1.3 3.2 2.5 2.1

Intra-BA -Wind 

(106 MW-miles) 0.7 0.7 0.7 2.3 2.3 2.2 3.2 3.3 3.4 6.4 7.1 8.3 11.3 12.6 12.5

0

200

400

600

800

1000

1200

1400

1600

1800

2010 2020 2030 2040 2050

Capacity (GW)

Storage

Solar

Wind

Other RE

Gas-CT

Gas-CC

Oil-Gas-Steam

Coal

Nuclear
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5

Figure 3 presents the regional differences in solar PV 

cumulative capacity deployments in 2050 at various NERC 

regions from NERC and STATE scenarios with respect to 

REF. This shows that aggregation of the cost and 

performance metrics at the state-level has a relatively limited 

overall effect on solar PV deployments, while aggregation at 

the NERC level has a substantial impact, especially in SERC 

(SC~31GW, VA~18GW), ECAR, CA (~13 GW), SPP, NWP 

and ERCOT (TX~14GW).

TABLE II COMPARISON OF SYSTEM PLANNING COSTS (NPV)

Category (2015$) REF STATE NERC

Conventional Capital 349.61 356.05 355.79

Conventional O&M 840.02 843.66 846.05

Conventional Fuel 2159.78 2190.40 2234.83

Renewable Capital 613.64 598.38 570.43

Renewable O&M 238.54 236.18 237.01

Renewable Fuel 24.19 23.82 25.14

Storage Capital 2.54 2.18 2.11

Storage O&M 9.26 9.12 9.11

All Transmission 60.73 63.10 66.13

Water 0.02 0.02 0.02

TOTAL 4298.33 4322.92 4346.61

Difference 24.59 48.28

Fig. 3 NERC-region utility-scale solar PV capacity differences at year 2050

Finally, sensitivity to STATE scenario, namely 

STATE_CP was performed by assuming nearly zero inter-BA 

transmission distance within each state and approximating the 

distances across different states as the distance between their

geographical centroids. Effectively, this assumption will 

render the inter-BA transmission within each state (i.e., intrastate in the STATE model) to a copper sheet and will make 

inter-state transmission access very inexpensive in the 

STATE model. The results from this simulation indicated an 

increase in solar PV deployments leading to a difference of 

about 12 GW in 2050 (performing better than the STATE 

model). Due to the increase in transmission access (by virtue

of making transmission very inexpensive), the low-cost sites,

which were otherwise lost due to regional aggregation, could 

be accessed for deployment (however, additional inter-BA 

transmission builds are over-estimated to be ~80GW and 

hence results from such relaxed models should be taken with 

appropriate caveats). 

IV. CONCLUSIONS

This paper presented an overview of the ReEDS electricity 

system capacity expansion model that optimizes the 

generation portfolio along with transmission expansions from 

2010 to 2050. The model has a high spatial resolution in 

terms of representing the U.S. electric sector using 134 load 

balancing areas, with generation technology cost and 

performance data at the same or higher resolution (356 

regions for wind and PV). The focus of the paper was on 

assessing the impact of two degrees of model aggregation by 

averaging the cost and performance of energy resources at 48 

state and 13 NERC region levels.

The ReEDS model results revealed that spatial aggregation 

of renewable energy resources impacts the competitiveness of

renewable resources (which need transmission access). Lower 

quality resources may appear better when aggregated with 

higher-quality resources, and vice versa, leading to 

differences in the relative competitiveness of renewable 

technologies within the model. This change in 

competitiveness can lead to suboptimal investment in 

capacity. The scenarios indicated that solar PV was the most

sensitive to the level of aggregation. Higher levels of 

aggregation led to less PV deployment while wind 

deployment increased.

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