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Operated by the Alliance for Sustainable Energy, LLC

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Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

Advanced Methods for 

Incorporating Solar Energy 

Technologies into Electric 

Sector Capacity-expansion 

Models: Literature Review and 

Analysis

P. Sullivan, K. Eurek, and R. Margolis

Technical Report

NREL/TP-6A20-61185

July 2014
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Advanced Methods for 

Incorporating Solar Energy 

Technologies into Electric 

Sector Capacity-expansion 

Models: Literature Review and 

Analysis

P. Sullivan, K. Eurek, and R. Margolis

Prepared under Task No. SS13.1020

Technical Report

NREL/TP-6A20-61185

July 2014
NOTICE

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Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

16560, photo by Dennis Schroeder, NREL 17613, photo by Dean Armstrong, NREL 17436, photo by Pat Corkery, NREL 17721.
iii

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Acknowledgments

The authors would like to thank the following individuals for their helpful reviews of draft 

versions of this report: Chris Namovicz at the U.S. Energy Information Administration; Ana 

Mileva, Jimmy Nelson, and Josiah Johnston at the University of California Berkeley; Marshall 

Wise and Leon Clarke at Pacific Northwest National Laboratory; and Paul Denholm, Trieu Mai,

and Ann Brennan at the National Renewable Energy Laboratory. We would also like to thank 

Jarett Zuboy, independent consultant, for his expert editing and input. This work was supported 

by the U.S. Department of Energy under contract number DE-AC36-08GO28308.
iv

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Abbreviations/Acronyms

CGE Computable general equilibrium

CSP Concentrating solar power

DHI Diffuse horizontal irradiance

DLR German Aerospace Center

DNI Direct normal irradiance

DOE U.S. Department of Energy

ELCC Effective load-carrying capacity

EPA U.S. Environmental Protection Agency

EPRI Electric Power Research Institute

EU European Union

GHI Global horizontal irradiance

GIS Geographic information system

G-Rad Global Monitoring Division Radiation

IAEA International Atomic Energy Agency

IREC Interstate Renewable Energy Council

LDC Load duration curve

LOLP Loss of load probability

MCP Mixed complementarity problem

MISO Midcontinent Independent System Operator

NASA National Aeronautics and Space Administration

NERC North American Electric Reliability Corporation

NOAA National Oceanic and Atmospheric Administration

NREL National Renewable Energy Laboratory

NSRDB National Solar Radiation Database

PIK Potsdam Institute for Climate Impact Research

PNNL Pacific Northwest National Laboratory

PV Photovoltaic

QCP Quadratic complementarity problem

RReDC Renewable Resource Data Center

SAM System Advisor Model

SSE Surface meteorology and Solar Energy

TES Thermal energy storage

VRRE Variable resource renewable energy

WECC Western Electricity Coordinating Council
v

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Table of Contents

1 Introduction........................................................................................................................................... 1

2 Overview of Electric Sector Capacity-expansion Modeling............................................................. 6

3 General Methods for Modeling Non-dispatchable Technologies .................................................... 8

3.1 Screening Curves with Merit-order Dispatch................................................................................ 8

3.2 Renewable and Conventional Technology Portfolio Analysis Using Detailed Operational 

Modeling ..................................................................................................................................... 10

3.3 Renewable Technology Portfolio Analysis Using Conventional Technology Capacityexpansion Modeling .................................................................................................................... 11

3.3.1 Combining Capacity-expansion Modeling with Detailed Operational Modeling.......... 11

3.4 Renewable and Conventional Technology Capacity-expansion Modeling................................. 12

4 Determining Which Solar Technologies to Model........................................................................... 14

5 Choosing a Spatial Resolution.......................................................................................................... 16

6 Incorporating Solar Resource Assessments................................................................................... 20

6.1 Solar Radiation Data ................................................................................................................... 20

6.2 Assessing the Potential for Solar Power...................................................................................... 21

7 Accounting for Solar Generation Variability and Uncertainty ....................................................... 24

7.1 Dispatch (Value of Energy at Time Delivered)........................................................................... 25

7.2 Curtailment.................................................................................................................................. 30

7.3 Electric System Reliability.......................................................................................................... 31

7.3.1 Resource Adequacy: Effective Load-carrying Capacity ................................................ 31

7.3.2 Operating Reliability: Ancillary Service Requirements................................................. 32

8 Conclusions ........................................................................................................................................ 35

9 References .......................................................................................................................................... 36
vi

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List of Tables

Table 1. Models Discussed in this Report................................................................................................ 4

Table 2. Spatial Extent and Resolution of Selected Models................................................................. 18

Table 3. Description of Simplified Dispatch Periods for Selected Models ......................................... 29

List of Figures

Figure 1. Illustration of the screening curve method.............................................................................. 9

Figure 2. Illustration of a residual load duration curve......................................................................... 10

Figure 3. GridView-simulated national mean dispatch stack during 4 days in summer for a high 

solar penetration scenario................................................................................................................. 12

Figure 4. Map of the mean solar resource available to a PV system facing south and tilted at an 

angle equal to the latitude of the system......................................................................................... 16

Figure 5. Regional maps of selected electricity system models with United States (or similar) 

coverage.............................................................................................................................................. 19

Figure 6. Solar variability: 100 small PV systems throughout Germany, June 1995......................... 24

Figure 7. Visualization of dispatch periods for selected electricity system models ......................... 28

Figure 8. System load following and regulation. ................................................................................... 33
1

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1 Introduction

Global and U.S. electricity systems are evolving rapidly. In response, electric utilities, regulators, 

government agencies, and academic researchers are increasingly using capacity-expansion 

models to explore the potential mixes of electricity-generating technologies under various future

scenarios. Although solar energy provides only a small fraction of U.S. and global energy needs, 

recent technology cost reductions have driven rapid solar growth, and further solar cost 

reductions are targeted (Barbose et al. 2013; DOE 2012; IREC 2013).

1 As solar power becomes 

a more important contributor to the electricity system, capacity-expansion modeling will need to 

account accurately for the integration of solar technologies. Such analysis will help researchers 

and policymakers understand the implications of solar expansion.

Capacity-expansion models are used to develop scenarios of electricity system evolution that 

span large regions—from a single utility service territory to a group of countries—and decades 

of time. They explore the generating unit investments, transmission planning, and operational 

changes that might occur in response to shifting demand, unit retirements, and changes to 

regulation, legislation, and technology. The results illuminate the implications of potential policy 

and technology developments as well as the factors influencing the evolution of electricity 

systems over time.

The special characteristics of solar technologies require unique data and modeling capabilities 

and thus add complexity to capacity-expansion modeling. Whereas conventional thermal 

generators generally can be dispatched within some operational limits, solar-electricity output is 

subject to the external factor of solar irradiance. This irradiance is temporally variable and 

uncertain and geographically heterogeneous. The correspondingly variable and uncertain 

electricity output affects the operational dynamics of the entire electricity system, for example by

changing dispatch profiles and increasing the need for ancillary services. Because the economics

and performance of solar are strongly site dependent, solar installations also face unique issues 

related to transmission access, environmental impact, and public acceptance. Accounting for

these characteristics is important for understanding the economics of solar investments and, 

through capacity-expansion modeling, the potential for solar power within electricity systems.

This report highlights the major challenges of incorporating solar technologies into capacityexpansion models and shows examples of how specific models address those challenges. It is 

intended to help modelers consider ways to enhance their own models’ representations of solar to 

reflect the state-of-the-art. Following an overview of electric sector capacity-expansion modeling 

(Section 2), the report covers five important issues related to modeling solar technologies: 

understanding general methods for modeling non-dispatchable technologies (Section 3), 

determining which solar technologies to model (Section 4), choosing a spatial resolution (Section 

5), incorporating solar resource assessments (Section 6), and accounting for solar generation 

variability and uncertainty (Section 7). The key points are summarized here.

Each capacity-expansion model is unique and designed with its own priorities, objectives, and 

level of detail. Although no single model or modeling approach is superior for all circumstances,

 1 For example, the U.S. Department of Energy’s SunShot Initiative aims to reduce the price of U.S. solar energy 

systems by about 75% between 2010 and 2020 (DOE 2012).
2

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each one can provide a valuable perspective. With multiple viewpoints from different models,

researchers and analysts can better understand the dynamics of electricity systems, especially 

with respect to integrating solar technologies.

We survey four general methods for integrating non-dispatchable2 technologies like solar into 

capacity-expansion modeling, ranging from simple screening-curve calculations to simultaneous 

capacity-expansion modeling of dispatchable and non-dispatchable generators. A sophisticated

model would capture the complex relationships among unit dispatch, transmission, reliability and 

market rules, and capacity-investment decisions. Screening curves, which estimate the optimal 

system mix from the shape of the load-duration curve can provide a first-order approximation of 

capacity expansion and can be augmented to consider the impact that deployment of nondispatchable technologies can have on the system mix. Two intermediate methods use extant 

modeling practices to compare among discrete portfolios of non-dispatchable generators, 

providing substantial detail and subtlety beyond screening curves but not co-optimizing 

dispatchable and non-dispatchable investments. Most of the models discussed in this report fall 

into the fourth category, considering dispatchable and non-dispatchable generators—and often 

transmission—together. However, these models still differ from one another in their areas of 

emphasis and in their strategies for accommodating the complexities of integrating nondispatchable technologies.

Multiple solar technologies exist, and each has particular resource and operational 

characteristics. That there is such variety in solar generating technologies puts the burden on the 

model developer to select or combine technologies into a manageable subset. Central 

photovoltaic (PV) systems and concentrating solar power (CSP) systems without thermal energy

storage (TES) are common across models. Fewer include distributed PV and CSP with TES. In 

the literature we examined, concentrating PV is rarely represented.

Each capacity-expansion model has a particular spatial resolution—from one to hundreds of 

analytical regions. Tradeoffs between fine and coarse resolution make different choices 

appropriate for different applications.

Modelers can incorporate solar resource data into their capacity-expansion models; credible data 

sources and processing tools are available for this purpose. The resource data are often 

implemented as a supply curve defining the quantity of deployable solar capacity at a given 

resource quality. The quality is often inversely proportional to the cost of accessibility (that is, 

regions with the best solar resources are often farthest from electricity demand centers). 

Therefore, representing solar-related transmission costs is also important. While some models 

assign a simple transmission cost adder to imply that there are above-average transmission costs 

to access solar resources, the spatial heterogeneity of the resource means that a model can 

increase fidelity by constructing “accessibility supply curves” that approximate the distribution 

of potential sites for solar deployment and include the cost for building transmission to the sites.

 2 ‘Dispatchability’ refers to the ability of a generator to adjust output based on a signal or control from the system 

operator. Without the aid of dedicated storage, solar technologies lack dispatchability because their output depends 

on the intensity of sunlight which is variable and uncertain. As such, we classify solar technologies as ‘nondispatchable.’
3

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To reproduce realistic investment behavior, capacity-expansion models must account for the 

costs and benefits related to the variable and uncertain operational characteristics of solar 

technologies, especially the value of solar electricity. To balance accuracy and usability, 

modelers generally create simplified dispatch periods meant to capture correctly the relationship 

between solar electricity output, load, and conventional operations—while also allowing the 

model to account for the solar resource’s spatial heterogeneity, explore adequate time horizons, 

and maintain reasonable computational requirements. Thoughtful selection of chronological or 

non-chronological simplified dispatch periods and correction factors can provide a balance 

between accuracy and usability.

Effective capacity-expansion models also consider how solar deployment interplays with the 

electricity system’s resource adequacy and operating reliability. Advanced models account for a 

solar generator’s capacity value (and its erosion with increasing solar penetration) and 

contribution to resource adequacy as well as the improved capacity value of CSP with hybrid 

backup or TES. Finally, the variability and uncertainty of the solar resource adds to the system’s 

operating-reliability burden and costs associated with additional need for ancillary services. 

Some capacity-expansion models ignore these impacts and costs, whereas others incorporate 

them in various simplified forms. Models typically characterize PV as requiring higher ancillaryservice needs than CSP, even CSP without TES. Some of these operational characteristics 

remain difficult to address with current models and thus represent an area for future research.

Table 1 provides a brief description of each of the capacity-expansion models discussed in this 

report. While the list is not exhaustive, the included models cover a range of geographic regions

and sectoral scope, and they represent several modeling structures. Many of these models are 

designed primarily for research or long-term policy and technology analysis. We do not include 

the suite of commercial tools used by utilities and system planners for planning purposes. Mills 

and Wiser (2012) discuss several of these commercial models within a survey of utility 

procurement plans. In general, we choose models that are documented with some consideration 

of solar technologies. Some of these models were developed a decade or more in the past, have 

not been used widely, or are not actively maintained by their developers today. Still, each 

includes strategies for integrating solar technologies that provide insights useful for current solar 

modeling activities.
4

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Table 1. Models Discussed in this Report

Model Name Primary Reference Description Institution

EGEAS

(Electric Generation 

Expansion Analysis 

System)

Rastler (2011)

Dynamic programming model used for 

production costing and generationexpansion planning in the United States.

Electric Power 

Research 

Institute (EPRI)3

ENERGY 2020 SSI and PAC (n.d.)

System dynamics model that explores the 

energy supply/demand balance across 

multiple sectors and regions in North 

America.

Systematic 

Solutions Inc.

EPPA

(Emissions 

Prediction and Policy 

Analysis)

Morris (2008)

Computable general equilibrium (CGE) 

model that explores the interaction of 

multiple energy and non-energy sectors 

for multiple regions around the world.

Massachusetts 

Institute of 

Technology

GCAM

(Global Change 

Assessment Model)

PNNL (2012)

Partial-equilibrium model designed to 

examine long-term, large-scale changes 

in global and regional energy systems.

Pacific Northwest 

National 

Laboratory 

(PNNL)

IPM

(Integrated Planning 

Model)

EPA (2013)

Deterministic linear programming model 

of the electric-power sector for multiple 

regions in North America.

ICF International

LIMES-EU Haller et al. (2012)

Linear programming model of electricitysector evolution for Europe, the Middle 

East, and North Africa.

Potsdam Institute 

for Climate 

Impact Research 

(PIK)

MARKAL

(Market Allocation 

Model)

Loulou et al. (2004)

Linear programming model of both the 

supply and demand sides of the energy 

system with a flexible regional structure 

applicable to any spatial extent.

Brookhaven 

National 

Laboratory

NEMS

(National Energy 

Modeling System)

EIA (2013)

Economic equilibrium model for the multisector energy system of the United 

States.

U.S. Energy 

Information 

Administration

PERSEUS-RES-E Rosen (2007)

Linear programming model that optimizes 

the evolution of the electric power sector 

in Europe.

Universitätsverlag 

Karlsruhe 

(Germany)

PLEXOS LT Plan Energy Exemplar 

(2013)

Mixed-integer programming model that 

integrates long-term electric sector 

planning optimization with detailed 

operational optimization for regional 

systems.4

Energy Exemplar

ReEDS

(Regional Energy 

Deployment System)

Short et al. (2011)

Deterministic linear program optimization 

model of the deployment of electricgeneration technologies and transmission 

infrastructure throughout the contiguous 

United States.

National 

Renewable 

Energy 

Laboratory 

(NREL)

 3 EGEAS was originally developed for EPRI by the Massachusetts Institute of Technology and the Stone & Webster 

Engineering Corporation.

4 PLEXOS LT Plan has been used to model regions including New Zealand (MMA 2007), Australia (Lilley et al. 

2009; Malla 2012; Nweke 2012), and Spain (Panagiotakopoulou n.d.). 
5

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Model Name Primary Reference Description Institution

ReMIND-R Luderer et al. (2011)

General equilibrium model that optimizes 

the welfare of the integrated energyeconomy-environment system around the 

world. 

PIK

REMix

(Renewable Energy 

Mix for Sustainable 

Electricity Supply)

Scholz (2012)

Linear programming model that 

determines the cost-optimal electricity 

supply mix for the European Union (EU)

and North Africa.

German 

Aerospace 

Center (DLR)

RPM

(Resource Planning 

Model)

Mai et al. (2013a)

Mixed-integer linear programming model 

with high spatial and temporal resolution 

that can be used for mid- and long-term 

scenario planning of regional power 

systems.

NREL

RREEOM

(Regional 

Renewable 

Electricity Economic 

Optimization Model)

Budischak et al. 

(2013)

Optimization model for evaluating high 

renewable penetration with a reliable 

least-cost capacity mix for the PJM 

system in the eastern United States.

University of 

Delaware

SEDS

(Stochastic Energy 

Deployment System)

Short et al. (2006)

Stochastic simulation model of the U.S. 

energy markets designed to explore how 

the U.S. energy economy will evolve in 

response to the development of new 

technologies.

NREL

SWITCH-WECC5

(Solar, Wind, Hydro 

and Conventional 

Generators and 

Transmission)

Johnston et al. 

(2013)

Mixed-integer linear programming6 model 

for least-cost generation, storage, and 

transmission capacity expansion for the 

electric-power sector in western North 

America.

University of 

California, 

Berkeley

THEA

(The High temporal 

resolution Electricitymarket Analysismodel)

Nicolosi (2012)

Decomposed linear optimization model for 

investment planning of the electric-power 

sectors in Texas and Germany with hourly 

dispatch.

Universität zu 

Köln, Germany

US-REGEN

(United States 

Regional Economy, 

Greenhouse Gas, 

and Energy Model)

EPRI (2013)

CGE model that combines a mixed 

complementarity problem (MCP) 

macroeconomic model with a quadratic 

complementarity problem (QCP) electric

sector investment and dispatch model for 

the United States.

EPRI

WASP-IV

(Wien Automatic 

System Planning –

Version 4)

IAEA (2001)

Dynamic-programming model to analyze 

the economic optimal generation 

expansion plan for the electric power 

sector of a user-define spatial extent.

International 

Atomic Energy 

Agency (IAEA)7

 5 The version of SWITCH referenced here models the area associated with Western Electricity Coordinating Council 

(WECC) service territory. There also exists a version of SWITCH specifically for California (Fripp 2012).

6 The traditional mixed-integer linear programming formulation for SWITCH-WECC can be relaxed and run as a 

linear program as demonstrated by Mileva (forthcoming) and Nelson (2013).

7 WASP-IV was originally developed for IAEA by the Tennessee Valley Authority and Oak Ridge National 

Laboratory.
6

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2 Overview of Electric Sector Capacity-expansion 

Modeling

Capacity-expansion models, the subjects of this paper, are mathematical models that make 

generation (and often transmission) investment decisions based on system operation needs.8

Given a set of rules and objectives, the model will construct an electricity system from scratch or 

update one through time to meet evolving needs. Capacity-expansion models use three primary 

methods to determine which type of new capacity will be built: optimization, simulation, and 

equilibration. Optimization models typically select the least-cost method of meeting load while 

satisfying reliability and other requirements. Simulation models make investment decisions 

through a series of formulas: if an investment option is expected to garner sufficient revenue to 

support its capital and operating requirements, it is built; alternatively, a quantity of required 

capacity is subdivided across eligible technologies according to their relative costs (a marketshare algorithm). For example, SEDS (Short et al. 2006) uses logit functions to simulate the 

market share for competing technologies. Equilibrium models find a set of prices such that 

supply and demand across the set of relevant parameters (electricity, fuels) equilibrate. As an 

equilibrium model, EPPA (Morris 2008) includes CSP and PV technologies as imperfect 

substitutes for conventional generators to represent a set of aspects particular to variable 

renewables, including integration challenges. These three model types each have distinct 

advantages and disadvantages, but that discussion is outside the scope of this report; for more on 

model classification, see Mai et al. (2013b) and Van Beeck (1999).

Numerous studies have reviewed capacity-expansion planning in the electric sector, including 

methodologies and challenges. Phupha et al. (2012) discuss the major issues in developing an 

expansion plan, including forecasting demand, identifying technology options, evaluating 

technology economics, and addressing reliability. Van Beeck (1999) classifies different types of 

energy models according to their methodology (e.g., equilibrium, optimization, simulation), 

mathematical approach (e.g., linear programming, integer programming, dynamic programming),

and scope (e.g., geographic, temporal, sectoral). Palmintier (2013) outlines models specific to the

electric sector—both detailed operations and capacity-expansion—and organizes them by 

timeframe (milliseconds to years), modeling detail (system level to component level), and scope 

(type of questions to answer).

Early versions of older electric sector models (e.g., EGEAS, MARKAL, NEMS, and WASP) 

focus primarily on modeling the deployment of large, dispatchable thermal generating units 

fueled by coal, natural gas, and uranium. With the changing electric sector landscape, modeling 

teams have been either modifying existing models to better represent variable resource 

renewable energy (VRRE) technologies or constructing new models designed to consider

VRREs (e.g., ReEDS and SWITCH-WECC). Recent efforts also have begun exploring the 

challenges of integrating wind and solar technologies into the grid at high levels of market 

penetration: DOE (2008), DOE (2012), GE Energy (2010), Mills et al. (2009), NERC (2009),

NREL (2012), and Zavadil et al. (2004). 

 8 In addition to generation and transmission investments, these models can also consider investments in electricity 

storage, energy efficiency, and demand response. 
7

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Moving forward, there is a need for improved modeling of renewable impacts on the grid, 

including large-scale, high-resolution models that simultaneously consider capacity expansion 

and dispatch to inform long-term planning with wind and solar (Möst and Fichtner 2010; Nelson 

et al. 2012). Also not well explored are the effects of temporal resolution on high–renewable 

energy scenarios, the characterization of the variable and uncertain nature of VRREs within 

traditional capacity-expansion models, and the sensitivity of renewable capacity expansion to 

exogenous inputs, e.g., technology cost and performance characteristics (Kammen et al. 2011; 

Neuhoff et al. 2008; Nicolosi 2012). McCalley (2012) identifies a need for better long-term 

electric sector planning tools that consider co-optimization of transmission and generation, long 

time horizons, chronological dispatch with greater resolution, demand-side options, geographic

impacts on renewables, effects of cycling, ramping needs for VRREs, multiple-objective

optimization, and improved handling of uncertainty. 

Next-generation models will have an increased focus on evaluating uncertainty. Brun (2011)

discusses general areas of uncertainty in capacity-expansion modeling, including macroeconomic 

data, technological innovations, technology financing, climate dynamics, technical generator 

characteristics, regulations, and public opinion. Models address uncertainty using methods such 

as Monte Carlo simulation, scenario development and stochastic programming. As a simulation 

model, SEDS (Short et al. 2006) samples uncertain input parameters such as future technology 

costs, fuel prices, economic growth, and policies from probability distributions to produce 

probabilistic forecasts of electricity-supply infrastructure deployment. Milligan et al. (2012) 

discuss stochastic methods for planning and operating power systems with large amounts of 

wind and solar power. Drury et al. (2014) explore three types of uncertainties for residential 

customers investing in rooftop PV and the relative impacts of uncertainty mitigation. These 

uncertainties include interannual solar variability, PV technical performance and maintenance 

costs, and market risks.

With that overview as background, the next section discusses general methods for modeling nondispatchable electricity-generating technologies.
8

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3 General Methods for Modeling Non-dispatchable 

Technologies

Electric utilities, regulators, governments, academic researchers, and others are interested in 

understanding how new and growing generation technologies might interact with the traditional 

structure of the electricity system. Wind and solar power in particular, being non-dispatchable,9

are likely to require changes in how conventional technologies are valued and operated (NERC 

2009). This section discusses four methods researchers use to explore VRRE integration into 

electricity systems:

1. Screening curves with merit-order dispatch

2. Renewable and conventional technology portfolio analysis using detailed operational 

modeling

3. Renewable technology portfolio analysis using conventional technology capacityexpansion modeling

4. Renewable and conventional technology capacity-expansion modeling. 

The first method is the simplest, an analytical estimation of how VRRE deployment is likely to 

change the operation levels of the conventional fleet, and what that is likely to mean for VRRE 

investment attractiveness. Methods 2 and 3 use two categories of electricity system models that 

are not necessarily strong on VRRE modeling to provide some insight into VRRE impacts. The 

fourth method uses the category of full-featured capacity-expansion models on which this paper 

focuses.

3.1 Screening Curves with Merit-order Dispatch

A screening curve estimates the optimal generating mix for serving a load assuming the lowestcost units sufficient to meet demand are always selected for dispatch (merit-order). Given a load 

duration curve (LDC), a screening-curve algorithm can estimate how often each class of unit will 

run, based on marginal operating cost, and will select appropriate units for investment by 

optimizing capital and operating costs compared to expectation of hours operated (Figure 1). 

Screening curves do not consider plant startup costs, ramping constraints, or minimum 

turndown—or system considerations like transmission and ancillary services—and so only 

approximate actual unit commitment. Nevertheless, this first-order approximation can be useful 

for capacity-expansion planning.

 9 Both wind and solar power technologies depend on resource that is variable and uncertain. As such, we classify 

both as ‘non-dispatchable.’
9

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Figure 1. Illustration of the screening curve method 

Source: Zhang (2013)

While designed for systems comprising conventional generators, screening-curve methodologies 

can be revised to evaluate the effect of VRREs on the operation of the conventional fleet. 

Because wind and solar power have no fuel needs, they can be assumed to operate at near-zero 

marginal cost and therefore to be dispatched first in a merit-order dispatch stack. The VRREs 

thus can be treated as load modifiers, reducing the net demand variably across hours—based on 

the characteristics of the variable resources. The screening-curve calculator can then report the 

optimal shares of conventional generator types for dispatching to that adjusted (residual) LDC, 

compared to the fleet for the original LDC. Figure 2 gives an example of an adjusted LDC. 

Lamont (2008) notes that the load-modifier approach neither accounts for the optimal VRRE 

deployment (i.e., VRREs are added to the system without considering their economic 

competitiveness in relation to other generation technologies) nor offers explicit insight into the

marginal value of VRREs. Despite these shortcomings, comparing the screening-curve results 

with and without the VRREs can estimate the impact VRRE deployment might have on the 

electricity system such as fuel savings, emissions reductions, and a shift in generation mix 

toward more intermediate and peak-load capacity.
10

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Figure 2. Illustration of a residual load duration curve

Source: Ueckerdt et al. (2011)

Screening-curve estimates of optimal system mix can provide value, especially if augmented by 

consideration of reliability needs; compared to more complex methods, screening curves have 

much lower data and computing requirements. The screening-curve method could be useful, for 

example, to identify obvious technology choices or develop a large pool of candidate technology 

mixes over a range of input assumptions quickly. Screening-curve and LDC analysis was a key 

component, alongside dynamic programming in WASP-IV, of developing a system-expansion 

plan for Pakistan’s power system (Shinwari et al. 2012). EGEAS includes capacity-expansion 

planning tools ranging from simple screening curves to complex non-linear optimization and 

dynamic-programming models. A MISO energy-storage study used the dynamic-programming 

capabilities of EGEAS for the detailed model analysis but also applied screening curves to 

illuminate the decision making of the dynamic-programming tool by visualizing the marginalcost curves for different technologies (Rastler 2011).

3.2 Renewable and Conventional Technology Portfolio Analysis 

Using Detailed Operational Modeling

A step up in complexity and fidelity from screening curves is to use a chronological productioncost or unit-commitment model on a proposed system or ensemble of systems that include both 

renewable and conventional generators and transmission. GridView (ABB 2008), HiGRID 

(Eichman et al. 2013), PLEXOS,10 PROMOD (Ventyx 2012), and RREEOM (Budischak et al. 

2013)

11 are all detailed operational models that can evaluate a suite of predefined portfolios for 

operational details. Models like these can be used by electric utilities and other entities engaged 

in the integrated resource planning process for detailed investigation of how a particular 

investment likely will be used within a complex system.

 10 PLEXOS here is the production-cost model. This is different than PLEXOS LT-Plan, which uses the productioncost capabilities in a capacity-expansion tool. See PLEXOS for power systems at http://www.energyexemplar.com. 11 Most detailed operational models evaluate system operations for 1 year. As an exception, RREEOM compares the 

minimum-cost portfolios for a 4-year simulation of 1.7 billion combinations of renewable energy/storage technology 

portfolios such that renewable energy completely serves load for a threshold number of hours.
11

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Operating a production-cost model in place of a screening curve incorporates the operational 

details (startup cost, ramp rates, transmission considerations) that are overlooked in the 

screening-curve approximations. Studies evaluating the gap between screening curves and 

operational models have shown that screening curves do miss some subtleties of operation, 

especially relating to costs and prices, even if bulk-generation numbers are similar to those 

produced through detailed models (Staffell and Green 2012). Depending on the characteristics of 

interest, it may be worthwhile to take advantage of the flexibility, ease of use, and speed of 

screening curves to evaluate a large ensemble of system configurations. Analysis including 

revenue or operational details would benefit from detailed operational modeling. Like screening 

curves, this method only compares among predefined portfolios; it does not select or suggest 

optimal system configurations. For that, a capacity-expansion model is needed.

3.3 Renewable Technology Portfolio Analysis Using Conventional 

Technology Capacity-expansion Modeling

Capacity-expansion models extend the capabilities of the previous two methods in that the model 

itself constructs an internally consistent electricity system that meets demand and reliability 

requirements in a planned way, rather than relying on the user to enter predefined generating 

portfolios. If the model uses an optimization algorithm, it devises a solution based on some 

optimality objective such as cost minimization or profit maximization.

12 Capacity-expansion 

models also usually make investments over time to meet changing demands, which provide 

scenarios of system evolution compared to the snapshot results from the first two methods. If a 

capacity-expansion model does not have the capabilities to explicitly model VRREs, a set of 

candidate renewable portfolios can be prescribed and a balance-of-system built around each. If 

an optimization model is used, the result will be a discrete set of VRRE-driven conventional 

investment decisions, each optimal for the given VRRE portfolio. The resulting systems, costs, 

and operational behaviors can be compared across systems to evaluate the relative costs and 

impacts of each of the candidate portfolios. THEA (Nicolosi 2012) uses a residual-load approach 

(load minus generation from VRRE) to incorporating prescribed VRRE profiles, and then it uses 

capacity-expansion modeling to optimize conventional generation around that residual-load 

system.

3.3.1 Combining Capacity-expansion Modeling with Detailed Operational 

Modeling

Capacity-expansion models generally have simplified operation compared to the full productioncost models described in Section 3.2 because of concerns about high computational

requirements. Capacity-expansion models typically have reduced-resolution dispatch, for 

instance, with aggregate units and time blocks or only a subset of hours. In exchange for the 

reduced operational detail, capacity-expansion models gain long-term planning capabilities. A 

recent combination technique pairs capacity-expansion models (including those with prescribed 

VRRE portfolios described in this section as well as those with optimized VRRE portfolios 

described in Section 3.4) with production-cost models, producing investment scenarios in the 

former and dispatching them in the latter for increased operational information and validation 

(DOE 2012; Lew et al. 2013; NREL 2012). Figure 3 shows an example of a dispatch stack

 12 Models can use a variety of optimality objectives, but cost minimization is used commonly.
12

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produced from the GridView production cost model to validate a generation portfolio produced 

from ReEDS in a high solar penetration analysis (DOE 2012). Similarly, Ueckerdt et al. (2011) 

model capacity expansion using ReMIND-R and validate dispatchability using MICOES.

13

Nelson et al. (2012) use SWITCH-WECC to determine an investment portfolio and validate 

using a detailed operational model with two years of historical hourly data in weekly batches. As 

an extension, Mileva et al. (2013) use this validation routine for SWITCH-WECC to identify 

hours of capacity shortfalls, which are then added into the capacity-expansion optimization.

Poullikkas et al. (2011) optimize the capacity mix using WASP-IV and determine the optimal 

dispatch with IPP.

14

Figure 3. GridView-simulated national mean dispatch stack during 4 days in summer for a high 

solar penetration scenario

Source: DOE (2012)

3.4 Renewable and Conventional Technology Capacity-expansion

Modeling

The methods discussed so far compare user-defined electricity systems or VRRE portfolios, but

for many analysis questions the goal is an evenly balanced evaluation of all generationinvestment options. That explains the rise of capacity-expansion models with a robust 

representation of VRREs, a category that encompasses most of the models discussed in this 

report. Much of the rest of this report discusses what constitutes a robust representation, 

including resource-assessment needs, transmission analysis, spatial resolution, and operational 

detail that enable consideration of the impact of a generator’s variability and reliability on system 

operation.

Simultaneous consideration of conventional and renewable generators transfers the analytical

burden from analyst to model and enables systematic evaluation of how the complicating aspects 

of VRREs affect their value to the system. For solar power, these characteristics include:

 13 For a description of MICOES, see Harthan et al. (2011). 14 For a description of IPP, see Poullikkas (2009).
13

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• Solar generator technology (characteristics and performance)

• Solar resource accessibility (connecting solar to the transmission and distribution 

network)

• Solar output profile and smoothing through resource diversification

• Coincidence of residual peak load and solar plant output profiles

• Value of solar energy at the time it is available

• Ability of a solar system to replace conventional generation sources (capacity value)

• Operating reserve requirements induced by variable generation

• Inability to use solar energy (curtailments) due to oversupply of power (e.g., minimum 

stabilization levels for thermal generators).

Capturing all these factors in full detail is likely to result in a highly complex model with steep 

computational and data requirements. An effective, full-featured capacity-expansion model 

therefore requires a balance between model usability and absolute fidelity. The remainder of this 

report discusses a subset of modeling decisions an analytical team must make when

incorporating solar technologies into a model as well as existing techniques used in models to 

capture the characteristics listed above.
14

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4 Determining Which Solar Technologies to Model

Each solar technology has unique resource and performance characteristics that affect its

interaction with the electricity system. Capturing the full gamut of technology options in any 

single model would be unreasonable, so one role of the model developer is to capture a 

representative sample of the technologies available to enable the model to tackle its intended 

questions effectively. The two major categories of solar technologies are CSP and PV:

• CSP systems focus direct sunlight onto fluid at a focal point.15 The fluid typically

generates steam, which runs a turbine. There are multiple CSP technologies that differ in 

cost and performance characteristics and in their ability to store thermal energy for later 

use. CSP fields augmented with either TES or natural gas backup can allow the system to 

operate more like a traditional generator than a VRRE technology.

• PV systems are solid-state devices that convert sunlight (both direct and diffuse16) 

straight to electricity. As with CSP technologies, there is diversity in PV options that 

affects cost and performance, so a modeler must choose which specific configurations to 

represent. PV modules take multiple forms and can be manufactured from a range of 

semiconductor materials, although silicon is the most popular. PV modules are deployed 

in both small and large arrays, on buildings or on the ground. Large arrays can be

mounted on mechanical tracking systems that rotate the modules throughout the day to 

follow the sun’s trajectory and improve performance.

Other technologies that are not yet commercially available could also be incorporated into 

models. For example, integrated PV and compressed air energy storage systems could enable the 

PV to act as a dispatchable generator with cycling, regulation, and non-spinning reserve 

capabilities (Fthenakis et al. 2009).

Most models reviewed here represent PV and CSP without TES, because these technologies can 

be treated simply as load modifiers. Capturing the operational details of CSP with TES is more 

difficult, because the storage makes the generator dispatchable, which requires the addition of 

operational detail and increases computational burden. Although several models examined here 

consider this technology (e.g., GCAM, ReEDS, REMix, and SWITCH-WECC), a much smaller 

subset of models allows dynamic time shifting of CSP input energy via TES. ReEDS, REMix,

and SWITCH-WECC allow CSP with TES to dispatch within energy limits imposed by the solar 

multiple, hours of storage, and the time profile of the insolation.17

Models might choose to ignore certain solar technologies. For example, nascent technologies like 

concentrating PV that have not yet gained a significant foothold in the market are often excluded. 

Among the models considered, only SWITCH-WECC represents concentrating PV (Kammen et 

al. 2011). Moreover, if the spatial extent of interest does not have sufficient solar resource, then 

 15 Direct sunlight is referred to as direct normal irradiance or DNI. In the United States, the best direct sunlight 

exists in the Southwest.

16 Diffuse sunlight is referred to as diffuse horizontal irradiance or DHI. 17 Insolation is the amount of solar radiation striking a unit of surface area. In this report it is used interchangeably 

with the term “solar resource.”
15

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solar technologies are not likely to be economically viable. For instance, ReEDS does not model 

CSP in Canada, because the CSP resource (direct normal irradiance or DNI) in Canada is not 

generally considered to be economically viable (Martinez et al. 2013). Finally, central planning 

models typically do not endogenously consider residential rooftop PV systems in their 

investment decisions, because the central-planning decision criteria do not sufficiently capture 

residential rooftop market dynamics. However, a small subset of models mentioned here directly 

represents distributed rooftop PV. For example, SEDS (DeForest et al. 2011) includes a module 

for the buildings sector that endogenously models the supply-demand balance of energy 

resources (e.g., passive solar, rooftop PV) and end uses (e.g., heating, lighting) in commercial 

and residential buildings. SWITCH-WECC (Johnston et al. 2013) endogenously models rooftop 

PV deployment at 216 sites, limiting the total deployed capacity based on an assessment of 

available roof area and rooftop spacing ratios. Residential PV can also be added exogenously. 

For example, NREL accounts for distributed PV in ReEDS by entering the output from its 

SolarDS model (Denholm et al. 2009) into ReEDS. This approach has limited feedback between 

the dynamics of residential PV adoption behavior (SolarDS) and utility-scale decisions and 

electricity price (ReEDS). In contrast, endogenously modeling rooftop PV (central-planner style) 

co-considers rooftop PV adoption and investment decisions for the rest of the system, although 

this approach may not effectively capture individual consumer behavior.
16

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5 Choosing a Spatial Resolution

Spatial resolution in models can vary from a single region to hundreds of regions depending on 

the study area, level of detail desired, and model intent. Model size and complexity are generally 

limited by data and computational practicality; larger, more detailed models have larger upfront 

data and programming requirements and also generally take longer to execute. As such, scope 

and detail are the common tradeoffs in model design. Global and economy-wide models (e.g., 

GCAM and ReMIND-R) generally have far fewer regions than electricity system models,

because the additional model scope needed for geographical and sectoral expansiveness occupies 

some of the data and computational space that could have gone to geospatial detail. These 

models usually emphasize the larger relationships among large regions and across sectors rather 

than focusing on the details of any one region and sector. Models focusing solely on the electricpower sector (e.g., IPM, ReEDS and SWITCH-WECC), on the other hand, can represent more 

regions because the reduced model scope affords added complexity elsewhere. 

Energy-system models can gain benefits in model fidelity by increasing geospatial resolution,

because increased resolution can reveal resource, transmission, and market structures that 

spatially coarse models overlook. Especially for certain model types, additional resolution also

means an increased number of decisions, which can diversify outcomes, not only through 

technologies finding favorable niches in small regions, but also simply because more decision 

events with subtle differences 

(load levels, fuel prices, 

transmission connections) tend 

to spread results, reducing 

“knife-edge” or “winner-takeall” behavior (Short 2007). 

Considering renewable 

resources like solar power, the 

fact that resource quality and 

characteristics vary significantly 

by location means that greater 

spatial resolution can improve 

the fidelity of solar investment 

placement and plant 

performance. Figure 4 is a map 

of PV resource quality in the 

United States showing the 

dramatic regional differences in 

insolation across the country. 

Accounting for regional 

differences in resource quality 

can help solar technologies 

compete effectively in high-resource areas. Solar output profiles also vary from site to site, so 

models with large regions can miss the benefits accrued by spatially diversifying solar resources 

to smooth the solar output profiles (Tarroja et al. 2013). Models can—and often do—include 

Figure 4. Map of the mean solar resource available to a PV 

system facing south and tilted at an angle equal to the 

latitude of the system 

Source: Drury et al. (2012)
17

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constructs (e.g., resource supply curves) to provide sub-regional information about solar resource 

characteristics. Examples of models with regional supply curves are presented in Section 6.

Geographic resolution is not the only possible repository for added detail: some models 

downplay regionality, instead prioritizing temporal detail, modeling of individual generator 

operations, or other characteristics. Single-region models may be sufficient for modeling a small 

or isolated system such as an island, small country, or service territory, or they may be desirable 

if the analytical focus values simplicity or short run times. Short et al. (2006) constructed SEDS 

with a single region covering the United States because of the complexity associated with 

developing and assigning probability distributions to model parameters, the desire for quick runtimes, and the focus of the model on which system characteristics are most likely to lead to 

national market-penetration swings. SEDS is predicated on the hypothesis that marketpenetration swings occur at a national level, with national rather than local factors providing the 

major penetration drivers. 

Table 2 summarizes the spatial extent and resolution for selected models. Many of the models 

encompass the continental United States, and Figure 5 shows regional maps for several of those 

models to allow comparison. Even among aggregated models, certain regional divisions, for 

instance carving out the sunny Southwest from neighboring regions, can improve differentiation 

of solar resource by establishing a region with an excellent resource. Further subdivision within a 

large resource regime—as in IPM, ReEDS and SWITCH-WECC—can allow a model to 

distinguish solar resource further as being near major cities or remote or distinguish among 

subtleties in seasonal performance, daily solar cycles, and so forth. Maps for most of the models 

not shown in Figure 5 are available in the cited publications. 
18

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Table 2. Spatial Extent and Resolution of Selected Models

Model Spatial Extent No. of 

Regions

U.S. Regional 

Models

RREEOM

Budischak et al. (2013) PJM (Eastern United States) 1

RPM

Mai et al. (2013a) Rocky Mountain Power Pool 31

EU (+) Models

THEA

Nicolosi (2012)

Germany – interconnected systems 

with 11 EU zones 11

LIMES-EU

Haller et al. (2012) EU, Middle East, and North Africa 20

PERSEUS-RES-E

Rosen (2007)

EU-15 and 6 neighboring EU 

countries 21

REMix

Scholz (2012) EU and North Africa 36

U.S. Models

(some including 

parts of Canada)

SEDS

Short et al. (2006) Lower 48 United States 1

NEMS

EIA (2013) Lower 48 United States 22

US-REGEN

EPRI (2013) Lower 48 United States 15

SWITCH-WECC

Johnston et al. (2013)

Western Interconnect 

(#U.S. + #Canada + #Baja California 

Norte)

47 + 2 + 1

ENERGY 2020

SSI and ICF (2012)

Lower 48 United States and Canada

(#U.S. + #Canada) 50 + 10

ReEDS

Short et al. (2011)

Martinez et al. (2013)

Lower 48 United States and Canada

(#U.S. + #Canada)

PV regions:

134 + 18

CSP 

regions:

356 + 45

IPM

EPA (2013)

Lower 48 United States and Canada

(#U.S. + #Canada) 54 + 10

GCAM 

Smith et al. (2011)

PNNL (2012)

United States 12

Global Models

Global 14

ReMIND-R

Luderer et al. (2011) Global 11
19

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ReEDS: 134 PV, 356 CSP

Source: Short et al. (2011) NEMS: 22 

Source: EIA (2013)

IPM: 64

Source: EPA (2013)

SWITCH-WECC: 50 

Source: Johnston et al. (2013)

US-REGEN: 15

Source: EPRI (2013)

GCAM-USA: 12

Source: Smith et al. (2011)

Figure 5. Regional maps of selected electricity system models with United States (or similar) 

coverage
20

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6 Incorporating Solar Resource Assessments

The deployment of solar technologies is limited by the availability of solar resource (insolation),

which is defined using a solar resource assessment. This assessment is a geospatial analysis that 

uses solar resource data to estimate the quantity and quality of solar resource that can be used to 

generate electricity over some spatial extent. The following subsections describe solar resource 

data and solar resource assessments.

6.1 Solar Radiation Data

A solar resource assessment begins with quantifying ground-incident solar radiation in a given 

area. Solar radiation can reach the earth’s surface either directly from the sun (direct normal 

irradiance) or indirectly after being scattered by the atmosphere or cloud interference (diffuse 

horizontal irradiance). The sum of the direct and indirect radiation gives the total solar radiation 

reaching the earth’s surface (global horizontal irradiance or GHI). The amount of groundincident radiation that actually reaches a solar array18 is a function of the type of solar system 

(fixed-axis PV, tracking PV, CSP) and the orientation of the solar array relative to the sun’s 

position in the sky. PV systems can use both direct and diffuse radiation as well as groundreflected19 radiation in the case of tilted arrays. Tracking PV arrays and mirrored solar arrays 

(CSP) mainly rely on the DNI component (3TIER 2013; SECO 2008; Yates and Hibbert 2010).

Estimates of direct and diffuse solar radiation are derived either from actual measurements or 

from radiation models. Because ground-based solar radiation measurements are expensive to 

collect (e.g., due to hardware, operation, and maintenance) and inconsistent across sites (e.g., due 

to variable instrument quality and incomplete data), comprehensive, consistent datasets are 

largely sourced from radiation models (Wilcox et al. 2008). Both models and ground 

measurements are used to develop datasets. Commercial solar datasets such as Meteonorm20 and 

3TIER provide detailed global coverage. Meteonorm is a comprehensive source of synthetic 

global meteorological data based on 8,300 meteorological stations and satellite data. The 3TIER

global solar dataset provides satellite-derived estimates of hourly radiation over 15 years (3TIER 

2013). Publically available solar datasets are typically not as detailed or as comprehensive as 

commercial products, but the information is free. For example, the National Oceanic and 

Atmospheric Administration (NOAA) Global Monitoring Division Radiation (G-Rad)

Observation Networks

21 includes measured solar radiation for more than two dozen sites 

worldwide, with half of the sites in the United States. The Satel-Light dataset22 includes solar 

radiation for western and central Europe on multiple times scales. The National Aeronautical and 

Space Administration’s (NASA’s) Surface meteorology and Solar Energy (SSE) dataset23

provides global coverage of modeled solar radiation. The NREL Renewable Resource Data 

Center (RReDC)24 is a clearinghouse for multiple sources of measured solar radiation for 

multiple regions in the United States as well as India and Saudi Arabia. The RReDC also 

 18 Here, solar array refers to either a configuration of PV panels or CSP heliostats. 19 The ground-reflected radiation is usually negligible compared to direct or diffuse radiation. 20 Meteonorm: http://meteonorm.com/products/meteonorm/. 21 NOAA G-Rad: http://www.esrl.noaa.gov/gmd/grad/. 22 Satel-Light: http://www.satel-light.com/. 23 NASA SSE: https://eosweb.larc.nasa.gov/project/sse/sse_table. 24 RReDC: http://www.nrel.gov/rredc/solar_data.html.
21

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includes a modeled dataset25 named the National Solar Radiation Data Base (NSRDB), which 

includes simulated hourly radiation for nearly 1,450 meteorological ground stations and 10-km 

gridded solar radiation sourced from a satellite-based model for the United States (Perez et al. 

2002).

6.2 Assessing the Potential for Solar Power

Raw solar resource represents an upper bound on resource potential: the expected insolation 

levels over the study region. To produce a data assessment useful for an electricity model, that 

raw insolation data needs to be processed, taking into account geographic restrictions and 

engineering and economic considerations. To reflect these aspects of quantifying resource 

potential, producers of resource assessments have organized a hierarchy defining levels of 

assessment types. The resource assessment levels described by De Vries et al. (2007) are the 

following:

• Geographic potential is the theoretical extractable energy flux in areas suitable for 

development. Suitable areas are determined using topographical and land-use constraints. 

Capacity-expansion models using geographic-potential supply curves need a method for 

converting the theoretical extractable energy into an estimate of electricity production.

• Technical potential accounts for considerations of the deployed technology, including 

conversion losses and deployment density (or packing factor),

26 that reduce the amount 

from the geographic potential. The conversion losses can be estimated with a conversion 

efficiency, statistical method, or production-simulation model. Deployment density sets 

the amount of production capacity that can be arrayed in a given area. In exchange for 

harvesting a larger fraction of insolation, tracking PV systems occupy more area than a 

comparable capacity of fixed-tilt PV. Technical potential is a likely input for an 

electricity system capacity-expansion model with internal mechanisms for comparing the 

economics of solar resource options with other non-solar resource options. 

• Economic potential is the technical potential that can be produced at costs competitive 

with alternative energy sources. An assessment of economic potential should incorporate 

factors influencing cost competitiveness non-uniformly across regions: expected 

performance, accessibility of the resource to transmission infrastructure and load, and 

environmental or public concerns that might influence cost.

• Implementation potential is the speed at which the potential for solar resource to 

produce electricity is realized (if at all). The implementation depends on production costs 

of solar resources and non-solar resources, policies, and societal preferences.

Most capacity-expansion models are designed to make economic decisions internally. Models 

that use solar resource assessments usually start from supply curves best characterized as hybrid 

technical/economic potential: the assessment quantifies and orders attractiveness of potential 

sites but does not draw the cost-competitiveness line. That line, and therefore the economic and 

implementation potential, are determined within the model. 

 25 Less than 1% of the dataset is sourced from measured data. 26 Denholm and Margolis (2008a) give suggestions for PV system packing factors.
22

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That supply curves order sites by attractiveness does not necessarily imply that performance is 

fully monetized in the supply curves. A supply-curve step can offer quantity available 

(megawatts of capacity or megawatt-hours of energy generated) with expected performance, at a 

set cost (dollars per megawatt or per megawatt-hour). The model can then factor both cost and 

performance into its decision making. 

Expected performance can be classified in upstream terms of insolation or downstream terms 

like capacity factor27 or expected annual output. Converting from site insolation to an output 

metric can be done roughly by applying a conversion-efficiency figure or more completely by 

using a statistical analysis or by processing a site irradiance time series into expected power 

output using a production-simulation model. A statistical analysis could, for example, quantify 

the expected power output of a solar system by considering the current-voltage diagram for a PV 

system vis-à-vis a distribution of expected solar radiation during a particular period. A 

production-simulation model projects the estimates of ground-incident solar radiation onto a 

solar array and uses detailed engineering calculations for simulating the electrical output of a 

particular solar system based on the design specifications. Yates and Hibbert (2010) compare a 

suite of solar production-simulation models used in North America, including PVWatts, System 

Advisor Model (SAM), PV-DesignPro, PV*SOL, and PVsyst.

28 Both PVWatts and SAM are 

publically available and free of charge. Yates and Hibbert state that PVWatts has been the PV 

industry standard in the United States for estimating solar production in part due to its simplicity. 

SAM has more flexibility in model options and provides detailed financial calculations as well as 

ancillary tools for design optimization, parametric analysis, sensitivity analysis, and statistical 

analysis. PV-DesignPro, PV*SOL, and PVsyst are all commercial models that require user buyin for the full model license. PV-DesignPro is similar to SAM but provides highly detailed 

information to the user during each step of the modeling process. PV*SOL models multiple 

arrays and inverters in a single simulation, which similar models do not. PVsyst’s flexible input 

structure allows users to define system characteristics accurately.

Information about site-specific costs (e.g., for connecting a site to transmission or load) or costs 

relating to permitting and environmental concerns are candidates for inclusion in the cost 

dimension of the constructed supply curve. Some environmental concerns might remove a 

possible site from the potential itself (as part of the geographic potential assessment), but sites 

requiring additional scrutiny or special remediation—rather than those where development is 

simply off the table—can be dealt with via added cost in a techno/economic supply curve.

Many of the models surveyed include transmission connection cost in their resource assumptions 

but at varying levels of detail. Costs can be captured using a simple cost adder per kilowatt-hour, 

applying a cost per line size and estimated distance, or constructing a supply curve from detailed 

geospatial analysis that links individual sites to transmission infrastructure features. Using the 

 27 Capacity factor is the fraction representing the ratio of power generated during a specific period to the power that 

could have been generated had the plant operated at full power throughout the period. 28 PVWatts: http://pvwatts.nrel.gov/

SAM: https://sam.nrel.gov/

PV-DesignPro: http://www.mauisolarsoftware.com/

PV*SOL: http://www.solardesign.co.uk/pv.php

PVSyst: http://www.pvsyst.com/en/
23

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most basic approach, EPPA applies a simple cost adder of $0.01/kWh to account for additional 

transmission requirements to access solar resources (Morris 2008). Both RPM and SWITCHWECC use a flat cost per distance (e.g., dollar per megawatt-mile) of transmission required to 

connect solar resource to the existing grid (Mai et al. 2013a; Johnston et al. 2013). Several 

models— GCAM, NEMS, ReEDS and SEDS—use analyses based on a geographic information 

system (GIS) to apply additional solar resource transmission detail (Zhang et al. 2010; EIA 2013; 

Short et al. 2011; Short et al. 2006). 

Overall, the process of developing a resource potential supply curve with a GIS analysis involves 

a significant effort, but a resource assessment does not necessarily have to be done by the model 

team or be specific to one model. Especially if the assessment’s spatial-reporting resolution can 

be adjusted easily to different models’ regional structures, a high-quality resource assessment or 

set of supply curves can be useful to multiple models. For example, PNNL adopts rooftop PV 

supply curves developed by NREL in Denholm and Margolis (2008b) for use in GCAM (Smith 

et al. 2010). Other recent solar resource assessments include those produced by Lopez et al. 

(2012), for the United States, and Trieb et al. (2009), for global CSP potential.
24

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7 Accounting for Solar Generation Variability and 

Uncertainty

When considering the economic viability of VRRE technologies such as PV and CSP, one 

should consider both the cost and value of the services provided by the technology. For solar 

technologies, this cost-value proposition includes, among other things, the value of produced 

energy (including the likelihood the plant will produce power at valuable times and the lost value 

of production curtailed when supply exceeds demand), the ability to displace the need for 

alternate generation sources (capacity value), and any additional operational costs induced in 

other generating units. Thus, a capacity-expansion model seeking to reproduce realistic 

investment behavior must account for such operational factors and their corresponding costs and 

benefits. Because capacity-expansion models are primarily designed to reproduce reasonable 

investment behavior, they seek not operational fidelity but sufficient information about operation 

to inform investment behavior properly. Solar generation is variable and uncertain. Variability 

means that plant output fluctuates over time, based on predictable and unpredictable external

factors. Uncertainty means that some portion of the output variability is unpredictable. The total 

variability can be mitigated with an increased number of/more dispersed PV systems. Figure 6

illustrates this mitigation effect by comparing the higher total variability for one PV system 

versus 100 systems. In addition, PV and CSP without TES are not dispatchable technologies: an 

operator has limited ability to adjust output based on system needs (especially to generate more 

power; reducing output is significantly easier).

Figure 6. Solar variability: 100 small PV systems throughout Germany, June 1995 

Source: Wiemken et al. (2001)

Because of these characteristics, electricity models generally treat VRRE technologies 

differently from conventional, thermal technologies. The models we discuss do not always 

incorporate all the characteristics, and they account for the characteristics in different ways. In 

the world of simplified operation required for capacity-expansion models, the variety of 

techniques produces a marketplace of ideas from which modelers can learn. The following 

subsections address ways in which capacity-expansion models account for the impact of solar 

energy’s variable and uncertain generation on dispatch, curtailments, and electric-system 

reliability.
25

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7.1 Dispatch (Value of Energy at Time Delivered)

Computational constraints limit the level of system-operation detail in long-term capacityexpansion models compared with unit-commitment or production-cost models. To balance 

accuracy and usability, modelers generally reduce the temporal resolution of the model from the 

hourly or sub-hourly ideal and create simplified dispatch periods, either by selecting a 

representative subset of hours to model or by aggregating hours into time blocks. Surveying 

across models shows the variety of methods for reducing time resolution, some that maintain 

chronology (sequential time series) and some that do not:

• Representative subsets of chronological hours, e.g.,

o Select a representative peak and non-peak period

o Select a weekend and weekday

o Select typical days in each month or season

• Time blocks of non-chronological aggregate hours, e.g.,

o Organize consolidated hours by when they occur (time-slices, e.g., summer 

afternoons)

o Organize consolidated hours by their load characteristics (load-duration-curve 

segments, e.g., base load, intermediate, and peak)

o Focus on extreme hours (e.g., combinations of high/low demand with high/low 

VRRE output).

Table 3 summarizes the simplified dispatch period representations for selected models. The 

number of annual dispatch periods ranges from as few as three (SEDS) to more than 400 (RPM).

Having only three dispatch periods does not necessarily mean a model is less useful than one 

with more than 400; rather, each model is designed with the temporal resolution best suited for 

the model’s scope. Certain models are inter-temporal optimizations and consider multiple 

investment periods simultaneously. These models might choose to have fewer dispatch periods 

for each investment period compared with models that sequentially optimize investment periods. 

Some models consider chronological hours, which allow for more detailed thermal-generation 

modeling (e.g., ramping, minimum up/down times). Figure 7 illustrates the dispatch periods for 

three particular models that use either non-chronological or chorological dispatch periods. 

Nweke et al. (2012) discuss the benefits of chronological optimization in relation to PLEXOS,

29

noting that the demand profile is a significant input. Chronological modeling can capture more 

effects of VRRE on the dispatch of thermal units (e.g., unit commitment, startups, and ramping) 

than non-chronological modeling can. However, the more detailed modeling of dispatch 

constraints also introduces longer computational times.

A primary purpose of having multiple dispatch periods (either representative subsets of 

chronological hours or time blocks of non-chronological aggregated hours) is to capture the 

greater value of providing energy in times of higher load and the lower value when load is low. 

 29 This is the detailed operational model and not the capacity-expansion model PLEXOS LT Plan.
26

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Because solar power is generally correlated with load—higher during the day, lower at night, and

greater in the summer, when many regions in the United States experience their peak loads—

having good temporal differentiation allows models to see that solar power is more valuable than 

a simple cost-of-energy metric would indicate and to incorporate that apparent value into their 

investment decisions.

To capture the relationship between solar power output and load correctly, models need high 

temporal resolution or a correction factor that distills the solar-load correlation. For example,

NEMS (EIA 2013) and ReEDS (Short et al. 2011) both use seasonal and diurnal time-slices (9 in 

NEMS, 17 in ReEDS) and use time-slice capacity factors to approximate the relationship 

between VRRE and load. Similarly, GCAM (Zhang et al. 2010) uses 10 time blocks for a simple 

dispatch algorithm to assess the relationship between solar output and load. The time-block 

results are aggregated to the annual scale for use in a long-term analysis of balancing energy 

supplies and end-use demands across multiple sectors. US-REGEN (EPRI 2013) uses a 

clustering algorithm to select time blocks with similar load-wind-solar as well as extreme 

moments (e.g., the set of high load hours with low output from wind and solar). Certain models 

such as MARKAL, PLEXOS LT Plan and RPM have the benefit of allowing for user-defined 

temporal resolution (Loulou et al. 2004; Energy Exemplar 2013; Mai et al. 2013a).

Some capacity-expansion models consider a full 8,760-hour dispatch (i.e., every hour of every 

day in a year), but doing so tends to limit detail in other areas like spatial coverage, transmission, 

or time horizon (e.g., THEA). REMix uses chronological hourly profiles in its 10-region version, 

but it requires temporal reductions (e.g., every 2 hours of every 5 days) to explore 36 regions

(Scholz 2012). Similarly, PLEXOS LT Plan uses hourly modeling for a short-term planning 

horizon and has the capability to employ either reduced sampled chronology or load-durationcurve time blocks for longer horizons to maintain computational tractability (Energy Exemplar 

2013). Palmintier and Webster (2011) combine long-term planning and real-time dispatch

(hourly), but their model disregards transmission and balances supply and demand for only one 

node. Contemporary hardware and algorithms simply do not enable the model complexity that 

hourly resolution would entail in a model with the technological and geographical detail and time 

horizons desired for relevant analysis. Fortunately, clever choice of subsets or aggregation of 

hours can provide good operational fidelity with manageable complexity.

Models that operate representative subsets of chronological hours rather than time blocks of 

aggregate non-chronological hours can benefit from selecting appropriate subsets and wellpaired solar output data to avoid over-specifying the system. The fewer hours represented, the 

greater the risk of two undesirable conditions: for the system overall, a mismatch between 

performance of modeled hours and actual time; and, for solar specifically, arbitrarily high or low 

values assigned to particular solar resources when output over those hours is well or poorly 

correlated with load. Modelers use a variety of techniques to select subsets that minimize such 

concerns. LIMES-EU uses an algorithm to select 12 characteristic days that are representative of 

temporal and spatial fluctuations (Haller et al. 2012). RPM selects a week for each season that is 

most representative of “typical” seasonal electricity demand, i.e., the week with the lowest root 

mean square error deviation from the demand in each hour of the average week of the season

(Mai et al. 2013a). 
27

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Solar system operation within the modeled time resolution is a strong determinant of how the 

system is valued within the model. For example, models that use time blocks of nonchronological aggregate hours (whether time-slices or load-duration-curve segments) generally 

assume that dispatch (output, prices, etc.) is uniform within a dispatch period. Therefore, if 

seasonal and diurnal solar output differences are represented with high fidelity by time block—

e.g., differentiation between midday and overnight—solar is likely to be valued more accurately 

than if not. To be clear, load-duration-curve segments often do differentiate between day and 

night because that segmentation falls out naturally from the traditional late-afternoon-peaking 

load profile.
28

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IPM: 6 dispatch periods per year; non-chronological LDC

Source: EPA (2013)

ReEDS: 17 dispatch periods per year; non-chronological time-slices

Source: Mai et al. (2012)

SWITCH-WECC: 144 dispatch periods per year; chronological hours

Source: Nelson et al. (2012)

Figure 7. Visualization of dispatch periods for selected electricity system models
29

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Table 3. Description of Simplified Dispatch Periods for Selected Models

Model

Inter-temporal 

or 

Sequential

Detailed Breakdown of 

Dispatch Periods (dp.) per 

Year (yr.), Season (s.), Month

(m.), Day (d.) 

Dispatch 

Periods

(dp.)

per Year 

(yr.)

Chronological

SEDS 

Short et al. (2006)

Sequential

5-year steps through 

2050

3 dp./yr. (peak, intermediate, 

base load) 3 dp./yr. No

IPM 

EPA (2013)

Sequential

Seven model years 

from 2016 – 205030

2 s./yr. (summer, winter)

x 3 dp./s. (peak, intermediate, 

base load)

6 dp./yr. No

NEMS

EIA (2013)

Sequential

1-year steps through 

2040

3 s./yr. (summer, winter, 

fall/spring)

x 3 dp./s. (peak, intermediate, 

base)

9 dp./yr. No

GCAM

PNNL (2012)

Sequential

15-year steps through 

2095

10 dp./yr. (summer-5, winter-3, 

spring/fall-2) 10 dp./yr. No

ReEDS

Short et al. (2011)

Sequential

2-year steps from 

2010–2050

4 s./yr.

x 1 d./s. 

x 4 dp./d. (morning, afternoon, 

evening, night)

+ 1 super peak dp.

17 dp./yr. No

Energy2020

SSI and ICF (2012)

Sequential

1-year steps with a 

variable model horizon

4 s./yr.

x 6 dp./s. (high peak, low peak, 

high, intermediate, low, 

intermediate, high base load, low 

base load)

24 dp./yr. No

PERSEUS-RES-E

Möst and Fichtner 

(2010)

Sequential

5-year steps through 

2030

4 s./yr.

x 2 d./s. (2 weekend days, 1 

weekday)

x 3 dp./d. (weekend)

OR

x 6 dp./d. (weekday)

48 dp./yr. Yes

US-REGEN 

EPRI (2013)

Inter-temporal

5-year steps from 

2010–2050

46 dp./yr. 46 dp./yr. No

LIMES-EU 

Haller et al. (2012)

Sequential

5-year steps from 

2010–2050

4 s./yr.

x 3 d./s.

x 4 dp./d.

+ 1 peak dp.

49 dp./yr. Yes

SWITCH-WECC

Johnston et al. 

(2013)

Inter-temporal

10-year steps from 

2010–2050

12 m./yr.

x 2 d./m. (peak, median)

x 6 dp./d.

144 dp./yr. Yes

RPM

Mai et al. (2013a)

Sequential

5-year steps from 

2010–2030

4 s./yr.

x 4 d./s. (1 weekend, 3

weekdays)

x 24 dp./d.

+ 1 peak day (24 dp.)

408 dp./yr. Yes

 30 The seven model run years in IPM include 2016, 2018, 2020, 2025, 2030, 2040 and 2050.
30

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7.2 Curtailment

Estimating curtailments in capacity-expansion models is important to valuing potential solar 

investment properly, but it is a complex, multifaceted problem involving expectations for load, 

solar output, and thermal-unit commitments. A primary difference between solar generation and 

conventional, thermal generation is that solar output is primarily constrained by external 

(insolation) conditions, rather than being available as the system or plant operator desires. Unlike 

a fossil unit that can choose to operate as load allows, shifting fuel from low demand times to 

high, a solar facility (except for CSP with TES) does not have the luxury of shifting insolation to 

more-valuable hours.

System operators encounter periods when the minimum output of committed units exceeds load

and will often shut down or reduce the output of a renewable generating facility before shutting 

down a fossil unit, because the renewable generators often have much lower startup costs and 

quicker shutdown/startup. This curtailment is a deadweight loss to the solar operator, because 

any unexploited insolation cannot be recovered. A solar facility with high curtailments takes in 

less revenue, meaning that expected curtailment levels are an important component of 

investment decisions. 

Expected curtailment levels are a function of the relationship between plant output and load but 

are also affected by the rest of the generating fleet: other renewable generators and the must-run 

level of committed thermal units. In particular, while solar curtailments are generally low at low 

levels of solar penetration—because loads are high through the middle of the day when solar 

output is maximized—analyses have shown that curtailment levels can increase dramatically 

with increasing solar penetration (Denholm and Margolis 2007a; Denholm and Margolis 2007b;

DOE 2012; NREL 2012); even if solar could provide much of the midday energy, thermal units 

have to remain online to be available to meet evening loads. A corollary to curtailments 

increasing with solar fraction is that increased baseload capacity, e.g., a new nuclear plant, will 

also tend to increase VRRE curtailments. In light of curtailments being a system-wide 

consequence, while the curtailed unit is singled out for reduced operation, the curtailment should 

be considered a system-wide cost (foregone potential energy) rather than a penalty upon that 

generator.

Models have been approaching the curtailment problem in two ways. In models with sufficient 

temporal resolution to model unit commitment and cycling directly, like PLEXOS LT Plan

(MMA 2007),

31 the model will often return a negative price—representing the willingness of 

thermal unit operators to pay to stay online rather than incur the cost of shutting down and 

starting up again later—in curtailment hours to signal renewable generators to turn down. THEA 

(Nicolosi 2012) uses a technology premium as a proxy for market-driven curtailment to define 

the price level (negative) at which to curtail energy. As with value of energy, it is important to 

have sufficient temporal extent as well as resolution to obtain a representative sample of hours. 

Time-block models must approach curtailments indirectly, assigning curtailment levels by time 

block based on system conditions. ReEDS operates a statistical algorithm to estimate the fraction 

of hours within each time-slice in which renewable generation is expected to be curtailed, both 

for existing units and for potential new investments (Short et al. 2011).

 31 Specifically, this discussion relates to the short-term chronological dispatch module of PLEXOS LT Plan.
31

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7.3 Electric System Reliability

In addition to considering the energy provided by solar generators, an effective capacityexpansion model considers how solar deployment interplays with the electricity system’s goals 

of resource adequacy and operating reliability. The North American Electric Reliability 

Corporation defines these characteristics as follows (NERC 2008):

• “Adequacy is the ability of the electric system to supply the aggregate electric power and 

energy requirements of the electricity consumers at all times, taking into account 

scheduled and reasonably expected unscheduled outages of system components.” 

• “Operating reliability is the ability of the electric system to withstand sudden 

disturbances such as electric short circuits or unanticipated loss of system components.”

The following subsections explore how various capacity-expansion models account for resource 

adequacy and operating reliability.

7.3.1 Resource Adequacy: Effective Load-carrying Capacity

Resource adequacy is a requirement to be able to supply enough raw power to serve all expected 

loads. Adequacy metrics are often statistical estimates of the generating capacity that must be 

procured to meet loads given the uncertainty in timing and magnitude of peak-load events and 

incorporating the risk of outages to generators and transmission lines. Brun (2011) cites 1 day in 

10 years (1-in-10) as a common loss of load probability (LOLP) target for adequacy. Effective 

load-carrying capacity (ELCC)—the amount of load that can be added to the system without 

changing the system’s LOLP—gauges how much a generator contributes toward adequacy.

ELCC is often called “capacity value” or “capacity credit.”

Even though solar generators are not fully dispatchable and reliable like thermal generators, they 

do have substantial capacity value, especially at low penetration fractions. The average capacity 

value tends to erode with expansion of solar generation capacity, because increasing solar 

generation eventually causes the residual (load less VRRE) peak load to shift to an hour when no 

or less solar resource is available (Sigrin et al. 2014). Including capacity value—for instance, by 

accounting for the reduced need for additional peaking units—as a component of a prospective 

investment’s net value can measurably improve the economics of solar investments, although 

that value stream erodes as deployment increases and the capacity value declines. 

Although a few models disregard solar’s capacity value—such as PERSEUS-RES-E, which does 

so on the basis that solar will have a small future impact in the German electric power system 

over the modeled time horizon32 (Rosen 2007)—most models reviewed here attempt to account 

for it. Other models, like ENERGY 2020 (SSI and ICF 2012), assume a fixed capacity value for 

VRRE even though a fixed-value estimate can misrepresent solar’s contribution to adequacy.

One common formulation is a requirement that VRRE be accompanied by backup capacity to fill 

the gap between the VRRE’s capacity value and its nameplate capacity. These formulations, as 

with GCAM (Smith et al. 2011), allow erosion of capacity value with increasing VRRE 

penetration: a low level of required backup with little solar increases to higher levels—even 

100% backup—at high solar penetration. There is risk in such a backup-capacity formulation of 

 32 PERSEUS-RES-E uses a statistical analysis of wind feed-in to estimate capacity value for wind power. 
32

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over-penalizing the renewable generator by requiring backup capacity even if the system already 

meets resource adequacy.

To include both capacity value and adequacy needs in the model, many optimizations include a 

constraint to meet adequacy requirements and allow solar generators to contribute some capacity 

value metric toward that constraint. REMix (Scholz 2012) and SWITCH-WECC (Nelson et al. 

2012) assign a capacity value equal to the capacity factor in that hour or time block. RPM (Mai 

et al. 2013a) uses a simplified net-load approach that estimates the capacity value as the ability 

of solar to reduce the peak load. Other models use exogenous estimates of capacity value.

PLEXOS LT Plan (MMA 2007) uses peak contribution factor estimates from Transpower33

multiplied by capacity to determine a generator’s contribution to reserves during peak periods.

Finally, some models use endogenous calculations for determining capacity value. ReEDS (Short 

et al. 2011) dynamically estimates the capacity value of solar using a z-statistic approximation 

for ELCC (Dragoon and Dvortsov 2006) based on solar deployment level, resource 

diversification, transmission, and correlation with load and other renewable generators.

CSP can be modeled with or without TES (Section 4), with strong implications for capacity 

value. GCAM and ReEDS (Zhang et al. 2010; Short et al. 2011) assume CSP with hybrid 

auxiliary backup (GCAM) and CSP with TES (both models) can be relied on for power when 

necessary and therefore contribute full capacity toward adequacy requirements. ReEDS models 

CSP without TES as akin to PV: with a z-statistic approximation for ELCC.

7.3.2 Operating Reliability: Ancillary Service Requirements

The need for ancillary services to maintain operational reliability imposes a cost on electricpower systems by holding some otherwise-economic-to-dispatch capacity in reserve to respond 

to system needs. The variability and uncertainty of VRRE increases the variation in residual load 

and adds to the operating-reliability burden of the system. Various studies (Ela et al. 2010; 

Hummon et al. 2013) have characterized how solar and wind generators affect the operation of 

other units and the need for ancillary services, for instance by increasing the size and frequency 

of 1-hour ramping events. These operational costs induced by VRRE can be significant, so 

whether and how capacity-expansion models account for them can affect the attractiveness of 

potential renewable generator investments.

These additional reliability burdens can vary across solar technologies. By their nature, PV 

systems are highly sensitive to changes in insolation (due to cloud cover), although dedicated 

storage systems for PV plants can cushion the effects of variability and uncertainty. CSP, even 

without TES, has a smoother response to changes in insolation than PV due to thermal inertia, so 

models often consider it to have reduced ancillary-service needs. ReEDS (Short et al. 2011), for 

instance, assumes that CSP generators do not require additional operating reserves. In reality, 

CSP systems may not be quite this robust unless they include TES or a dedicated auxiliary 

backup system (e.g., a natural gas turbine). For some models, the existence of storage is 

justification for ignoring the effects of solar variability and uncertainty on ancillary service 

 33 Transpower owns and operates the National Grid, the high-voltage transmission network connecting areas of 

generation with towns and cities across New Zealand (https://www.transpower.co.nz/about-us).
33

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requirements, including costs. GCAM (Zhang et al. 2010) assumes away the effects of variability 

and uncertainty for CSP with TES and CSP hybrid plants with auxiliary backup. RREEOM 

(Budischak et al. 2013) ignores reserves requirements, intra-hour resource variability, and 

ramping by assuming these will be covered by quick-response storage in a scenario where nearly 

all of the electricity demand is supplied by a portfolio of wind, solar, and electrochemical 

storage.

There are different classes of operating-reserve products, such as regulation reserves and loadfollowing reserves (Ela et al. 2010). Figure 8 illustrates regulation and load-following reserves. 

There are also different classes of operating-reserve contributors—such as automatic generation 

control, spinning, and non-spinning reserves—that can supply these products. Large-scale, longterm planning models are unlikely to include a large number of these services, choosing instead 

to simplify to one or two operating-reserve products and generalizing the contributors that can 

provide them. ReEDS (Short et al. 2011) requires operating reserves based on two standard 

deviations (95% confidence interval) of the distribution of hour-to-hour changes in output, a 

structure adopted from the Minnesota Wind Integration Study (Zavadil et al. 2004). In most 

models that include operating-reserve products, as in real systems, conventional generators and 

electricity-storage systems are allowed to withhold generation in favor of providing spinning or 

non-spinning reserves.

Figure 8. System load following and regulation.

Source: Kirby (2004)
34

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The European convention for operating reserves is to distinguish primary, secondary, and tertiary 

reserves, which correspond to progressively longer response timescales. Primary reserves 

respond immediately to changes in system frequency and stabilize it. Secondary reserves return 

the frequency to its nominal value during contingency and ramping events. Tertiary reserves are 

manually activated during a contingency event to replace supply units that fail or to reroute 

power during a transmission outage. They operate on a timescale above 5 minutes and allow both 

spinning and non-spinning (quick-startup) resources. Both THEA (Nicolosi 2012) and 

PERSEUS-RES-E (Rosen 2007) include positive and negative tertiary reserve products: baseline 

tertiary reserve requirements for contingencies and demand fluctuations, with additional reserves 

required to balance renewable forecast error. PERSEUS-RES-E also applies an efficiency

penalty to conventional units whose operation is changed to accommodate VRRE, increasing 

generation cost and/or emissions due to increased startups, shutdowns, and ramping.
35

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8 Conclusions

The process of designing and developing a capacity-expansion model for making long-term 

electricity system projections includes many tradeoffs. Electricity systems are famously 

complex: comprising hundreds or thousands of generation and transmission components, 

requiring precise balancing of generation and load across wide areas in real time, and involving 

dozens of entities making continual decisions about planning, operation, regulation, and markets. 

Compressing such a complex system into a model that can be populated with real-world data and 

solved in a reasonable interval requires a host of approximations and simplifications. 

This report highlights a set of the decisions modelers must make to represent solar generating 

technologies in capacity-expansion models, and it discusses current practices among a set of 

electricity models used for research or long-term policy and technology analysis. Compared to a 

dispatchable thermal generation technology like a natural gas plant, solar technologies embody 

several subtleties that should be included to represent the behavior of their real-world analogues. 

In particular, solar generation varies substantially—and sometimes unpredictably—over time 

(from inter-annual to seasonal to sub-hourly variations) and across space. The variability and 

uncertainty produce numerous important consequences for electric-system operation and 

capacity investments, which capacity-expansion models must capture as solar becomes a larger 

contributor to electric systems.

No single method of incorporating solar technology characteristics is best for all models, as each 

model has its own structures, circumstances, and priorities that color its decisions. This report,

therefore, shows examples of how specific models address the various challenges and 

compromises associated with incorporating solar technologies. The multiple viewpoints from 

different models create a landscape of solutions from which to understand these issues better.

Taken together, the growing body of advanced models and accompanying literature—enabled by 

improved data, algorithms, and computing power—has been enhancing the representation of 

solar technologies as these technologies have become more widespread.
36

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