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.

Contract No. DE-AC36-08GO28308

Transmission Benefits of 

Co-Locating Concentrating 

Solar Power and Wind

Ramteen Sioshansi

The Ohio State University

Paul Denholm

National Renewable Energy Laboratory

Technical Report

NREL/TP-6A20-53291

March 2012
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.

National Renewable Energy Laboratory

1617 Cole Boulevard

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303-275-3000 • www.nrel.gov

Contract No. DE-AC36-08GO28308

Transmission Benefits of 

Co-Locating Concentrating 

Solar Power and Wind

Ramteen Sioshansi 

The Ohio State University

Paul Denholm 

National Renewable Energy Laboratory

Prepared under Task No. SS12.2721

Technical Report

NREL/TP-6A20-53291

March 2012
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iii

Acknowledgment

The authors thank Mark Mehos and Craig Turchi for providing valuable insights on modeling 

CSP systems. Robin Newmark, Samir Succar, Walter Short, and Trieu Mai provided helpful 

comments and suggestions. 
iv

List of Acronyms 

CSP concentrating solar power 

DNI direct normal irradiance

DOE U.S. Department of Energy 

EIA Energy Information Administration 

ERCOT Electric Reliability Council of Texas 

FERC Federal Energy Regulatory Commission 

GE General Electric Corporation 

GW gigawatt 

HTF heat transfer fluid

ITC investment tax credit 

kW kilowatt 

kWh kilowatt-hour 

MIP mixed-integer program 

MW megawatt 

MW-e megawatts electric capacity

MW-t megawatts thermal capacity

MWh-e megawatt-hours of electric energy

MWh-t megawatt-hours of thermal energy

NERC North American Electric Reliability Corporation 

NREL National Renewable Energy Laboratory 

SAM Solar Advisor Model 

SM solar multiple

TES thermal energy storage 
v 

Executive Summary

This report discusses and analyzes the potential benefits of co-locating wind and concentrating 

solar power (CSP) plants in the southwestern United States. Using a location in western Texas as 

a case study, we demonstrate that such a deployment strategy can improve the capacity factor of 

the combined plant and the associated transmission investment. This is because of two synergies 

between wind and CSP. One is that real-time wind and solar resource availability tend to be 

slightly negatively correlated. The other is that low-cost and highly efficient thermal energy 

storage (TES) can be incorporated into CSP. TES allows solar generation to be shifted and used 

to fill-in excess transmission capacity not being used by wind. Adding TES in a transmission 

constrained system can reduce, but not eliminate curtailment, especially during periods of 

extended high wind output and high solar output. Adding transmission constraints associated 

with co-location also reduces performance, including the inability of CSP to provide maximum 

output during periods of both high demand and significant wind output. Overall the economic 

tradeoff between transmission costs and system performance is highly sensitive to assumptions 

regarding transmission and CSP costs. Using data from the years 2004 and 2005, we demonstrate 

that a number of deployment configurations, which include up to 56% CSP (on a capacity and 

energy basis) yield a positive net return on investment. 
vi 

Table of Contents

Acknowledgment ....................................................................................................................................... iii

List of Acronyms........................................................................................................................................ iv

Executive Summary.................................................................................................................................... v

Table of Contents....................................................................................................................................... vi

List of Figures ........................................................................................................................................... vii

List of Tables ............................................................................................................................................. vii

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

2 Background........................................................................................................................................... 2

3 Methods................................................................................................................................................. 6

4 Results................................................................................................................................................. 10

4.1 Dispatch of Wind and CSP Deployments......................................................................................................10

4.2 Transmission Downsizing in Wind and CSP Deployments ..........................................................................13

4.3 Long-Term Economics of Co-Located Wind and CSP Deployments...........................................................20

5 Conclusions ........................................................................................................................................ 27

Appendix A. MIP Model Formulation ...................................................................................................... 28

Appendix B. Capacity Factor Estimation Technique ............................................................................ 31

References................................................................................................................................................. 33
vii 

List of Figures 

Figure 1. Average daily DNI of locations in Texas with at least class-4 wind................................2

Figure 2. Average wind generation duration curve during the years 2004 and 2005 at the location 

modeled in this analysis. .................................................................................................3

Figure 3. Example simulated wind output during a two-day period beginning on January 9, 2005 

and opportunities to fill underutilized transmission capacity with other generation 

sources. ............................................................................................................................4

Figure 4. Average daily DNI of locations in the southwestern United States with at least class-4 

wind. ................................................................................................................................5

Figure 5. Histogram of wholesale energy prices over study period. ...............................................7

Figure 6. Example wind and CSP dispatch beginning May 16, 2004. ..........................................11

Figure 7. Example wind and CSP dispatch beginning April 22, 2004. .........................................12

Figure 8. Example wind and CSP dispatch on October 17, 2004. .................................................13

Figure 9. Capacity factor of the transmission line as a function of transmission capacity and 

generation capacity breakdown. ....................................................................................14

Figure 10. Total generation curtailed (both wind and CSP) as a function of transmission capacity 

and generation capacity breakdown. .............................................................................15

Figure 11. CSP Generation curtailed as a function of transmission capacity and generation 

capacity breakdown. ......................................................................................................16

Figure 12. Average selling price of energy (both wind and CSP), excluding the wind PTC, as a 

function of transmission capacity and generation capacity breakdown. .......................17

Figure 13. Average selling price of CSP generation as a function of transmission capacity and 

generation capacity breakdown. ....................................................................................17

Figure 14. Average annual energy revenues (both wind and CSP), excluding the wind PTC, as a 

function of transmission capacity and generation capacity breakdown. .......................19

Figure 15. Average CSP annual energy revenues, as a function of transmission capacity and 

generation capacity breakdown. ....................................................................................19

Figure 16. Capacity value of deployments as a function of transmission capacity and generation 

capacity breakdown. ......................................................................................................21

Figure 17. Historical transmission construction costs ...................................................................23

Figure 18. Deployment breakeven cost as a function of transmission capacity and generation 

capacity breakdown. ......................................................................................................24

Figure 19: Deployment ROI as a function of transmission capacity and generation capacity 

breakdown. ....................................................................................................................25

List of Tables 

Table 1. Location Studied ................................................................................................................6

Table 2. Per-Plant CSP Construction Costs in 2005 Dollars .........................................................22

 
1 

1 Introduction

One of the challenges in deploying renewable electricity generation is the often remote location 

of high-quality wind and solar resources, requiring new transmission. The state of Texas was one 

of the first regions of the United States to contend with this issue. The highest quality wind 

resources are located in the western part of the state, while the major population centers are in 

the east. About 1.4 GW of wind was added in the McCamey region of Texas in 2001 and 2002, 

despite there only being about 400 MW-e of transmission capacity [1]. This resulted in about 380 

GWh of wind generation being curtailed at an estimated cost of more than $21.4 million in 2002. 

Although substantial transmission capacity has been added, this construction has not kept pace 

with wind development, and nearly 8% of potential wind generation in the Electric Reliability

Council of Texas (ERCOT) was curtailed in 2010 [2].

New transmission is often difficult to construct, and, if it is only carrying wind, these lines will 

tend to be lightly loaded due to the low capacity factor of the generator. For instance, a typical 

wind plant will have a capacity factor of less than 40%. One option to enhance utilization of new 

transmission is to co-locate wind with other resources that can complement their generation. This 

can include conventional generation, energy storage, or other renewables. Denholm and 

Sioshansi [3] demonstrate that energy storage is one viable option, since transmission can be 

downsized (relative to the capacity of the wind generator) and generation that would be curtailed 

can be stored for later use.

Another option is to deploy concentrating solar power (CSP) in areas with good wind resources. 

West Texas has good wind resources (at least class 4, which is defined as having average wind 

speeds of 7 m/s at a 50 m height) that are in close proximity to locations with sufficient direct 

normal irradiance (DNI) for economic siting of CSP plants (average daily DNI of at least 6 

kWh/m2 is typically viewed as the minimum solar resource requirement). CSP plants have an 

additional advantage of being able to incorporate low-cost and high-efficiency thermal energy 

storage (TES), enabling them to become a dispatchable resource.1

In this paper we examine the basic feasibility and performance of wind and CSP plants in 

western Texas that feed into the grid on a radial transmission line. We examine cases in which 

various combinations of wind and CSP are deployed with different amounts of transmission 

capacity. Using historical market price and weather data we model the operation of such a 

deployment and demonstrate how the dispatch, the capacity factor, energy curtailment, and the 

cost of energy are influenced by the combination of wind and CSP. The remainder of this paper 

is organized as follows: Section 2 provides further background on wind and CSP development, 

Section 3 discusses the methods and data used in the analysis, Section 4 summarizes our results, 

and Section 5 concludes. 

 

1 Although it is beyond the scope of this paper, there is a large literature detailing CSP and TES technologies, 

including performance and cost analyses [4-8].
2 

2 Background

The Electric Reliability Council of Texas (ERCOT) is one of three North American 

interconnects, and had a peak system load of about 61 GW in 2005. The interconnects are 

electrically isolated alternating current networks. Although there are some tie lines between the 

interconnects, they largely operate in isolation of one another. The ERCOT region has sufficient 

wind and solar resources to meet the system’s entire current electricity demand, however, its best 

wind and solar resources are in the western part of the state. This is illustrated in Figure 1, which 

overlays areas of Texas that have at least class-4 wind and a daily average DNI of at least 5 

kWh/m2

. Figure 1 excludes areas that would be unsuitable for CSP and wind development, by 

filtering out environmentally sensitive lands, urban areas, water features, terrain with more than a 

3% average land slope, and areas with less than 1 km2 of contiguous land space. Figure 1 shows 

that not all of Texas is within the ERCOT system, however ERCOT accounts for about 85% of 

Texas’s electricity demand. Figure 1 also shows the location studied in this analysis, which is 

discussed further in Section 3. 

Figure 1. Average daily DNI of locations in Texas with at least class-4 wind.

At the end of 2010, ERCOT had installed 10 GW of wind, with the vast majority located in 

western Texas. Substantial transmission capacity has been added to access these resources and 

further transmission expansion is in the planning stages. However, the capacity of wind exceeds 

the transmission capacity, resulting in some wind curtailment. Given the variability of the wind 
3 

resource, and relatively low capacity factor, transmission built for wind will often be 

underutilized. This is illustrated in Figure 2, which is the average generation duration curve for 

the simulated wind plant in west Texas that we study in this analysis over the years 2004 and 

2005. The modeled wind plant has a capacity factor of about 33.9%. 

Figure 2. Average wind generation duration curve during the years 2004 and 2005 at the location 

modeled in this analysis.

CSP has yet to be developed in Texas, largely due to its substantially higher cost compared to 

wind. However the prospect of decreasing CSP costs [10], along with its ability to provide 

dispatchable energy, could result in CSP deployments in the future. CSP in ERCOT faces the 

same challenges as wind in requiring new transmission from western to eastern Texas. This 

increases the cost of a deployment and makes development more challenging. However, CSP has 

the opportunity to use transmission built primarily for wind. Due to the relatively low capacity 

factor of wind and the dispatchability of CSP with TES, CSP generation could “fill in” during 

periods of low wind output. This opportunity is represented by the large area above the wind 

duration curve where transmission capacity is available. Figure 3 illustrates two days of 

simulated wind data, beginning on January 9, 2005, on a transmission line sized at the peak 

output of the wind plant (the data are explained in more detail in Section 3). This shows the 

opportunity to dispatch CSP during periods of low wind output. 
4 

Figure 3. Example simulated wind output during a two-day period beginning on January 9, 2005 

and opportunities to fill underutilized transmission capacity with other generation sources.

However, sharing transmission between resources does present several limitations. To maximize 

transmission utilization, the overall capacity of the transmission will be less than the combined 

maximum output of the CSP and wind plants. Ideally, CSP is dispatched to provide maximum 

output during periods of highest demand. Still, there may be periods during which CSP is forced 

to shift output to periods of lower demand (and correspondingly lower value) due to binding 

transmission constraints. In addition, there will likely be extended periods of time of both high 

wind and solar output, resulting in curtailed generation. Thus co-location of wind and CSP 

represents a tradeoff between maximizing the value of energy production and the cost of 

transmission development. The goal of this analysis is to examine this tradeoff and identify 

opportunities where it may be beneficial to co-locate wind and CSP and share transmission 

resources.

Although we examine a location in Texas, there are other locations in the southwestern United 

States that could support co-location of wind and CSP generation. Figure 4 illustrates this by 

overlaying areas of the southwestern United States that have at least class-4 wind with average 

daily DNI. This figure also filters out areas that are unsuitable for CSP and wind development. 

Thus this analysis could be applied to other potential sites where new, long-distance transmission 

is needed to access both wind and solar resources. 
5 

Figure 4. Average daily DNI of locations in the southwestern United States with at least class-4 

wind.
6 

3 Methods

We base our analysis on the CSP optimization model developed by Sioshansi and Denholm [9, 

10]. The model takes the characteristics of the combined plant (e.g., number and size of CSP 

plants, installed wind capacity, transmission capacity), weather, and market price data as fixed, 

and optimizes the operation of the CSP and wind plants to maximize total revenues. We model 

CSP and wind plants at the location in western Texas that is shown in Figure 1. The details of 

this location are provided in Table 1 and Figure 5 shows a histogram of wholesale energy prices 

over the two-year period studied. The location is not optimized, but is a site with good wind and 

CSP resources. The site is located in a relatively unpopulated area, and would thus require major 

transmission investments to deliver energy to customers. We examine generator dispatch and 

resulting revenues during the years 2004 and 2005, for which high-resolution wind and solar 

resource data are available.

Table 1. Location Studied

Location: 31.49° N, 104.56° W

Interconnection Point: Dallas

Linear Distance: 931 km

Market Pricing Location: ERCOT North Zone

Transmission Distance: 1043 km

Transmission Losses: 4.9%
7 

Figure 5. Histogram of wholesale energy prices over study period.2

As Denholm and Sioshansi [9, 10] note, a CSP plant consists of three interrelated components 

that can be sized differently. The first is the solar field, which is a field of mirrors that 

concentrates solar radiation onto a heat transfer fluid (HTF). The second is the powerblock, 

which is a heat engine that converts thermal energy into electricity. The third is the TES system, 

which can store thermal energy collected by the solar field for later use in the powerblock. The 

size of the powerblock is typically measured by its rated input or output capacities, which are 

measured in MW-t or MW-e, respectively. The size of the solar field can either be measured by 

the area that the mirrors cover or by using the concept of the solar multiple (SM). The SM scales 

the size of the solar field based on the size of the powerblock. A solar field with an SM of 1.0 is 

sized to provide sufficient thermal energy to operate the powerblock at its rated capacity with 

DNI of 950 W/m2

, a wind speed of 5 m/s, and an ambient temperature of 25° C. The size of the 

solar field scales relative to a field with an SM of 1.0 (e.g., a field with an SM of 1.7 is 70% 

larger than one with an SM of 1.0). The TES system has power and energy capacities. The power 

capacity, which is measured in MW-t, determines the maximum rate at which thermal energy can 

be charged or discharged from TES. We assume that the charging capacity of the TES system is 

scaled in proportion to the SM, so that the full output of the solar field can be stored if necessary. 

This is different from designs using indirect thermal energy storage, in which the heat exchanger 

used to transfer energy between the solar field heat transfer fluid and the thermal energy storage 

fluid is economically sized to only exchange energy that exceeds the thermal capacity of the 

powerblock. The energy capacity determines the maximum amount of energy that can be stored 

 

2 In addition there were 18 hours with prices negative prices and 24 hours with prices greater than $400/MWh.
8 

in TES and is typically measured in MWh-t or by the number of hours of storage. We use the 

latter convention and define hours of storage as the number of hours that TES can be discharged 

at its maximum rated power capacity. TES systems in demonstration CSP plants have shown 

extremely high roundtrip efficiencies [5, 11-13].

CSP plants typically have solar fields that are oversized relative to the powerblock (i.e., SMs 

greater than 1.0). This is because a CSP plant with an SM of 1.0 will only allow the powerblock 

to operate at its nameplate capacity for a handful of hours during which DNI falling on the 

effective aperture of the solar field is at or near its annual maximum.

3 Increasing the SM will 

increase the capacity factor of the powerblock. However, if no TES is available, solar energy will 

be wasted during peak-solar hours since the solar field will collect more energy than the 

powerblock can feasibly use. This points to an added benefit of incorporating TES into a CSP 

plant, because it improves the economics of a larger field by increasing utilization of the 

powerblock. 

Our optimization model consists of two parts. The first uses the Solar Advisor Model (SAM) 

[14]. SAM is a software package, based on the TRNSYS time-series simulation program [15], 

that simulates the dynamics of a CSP plant. SAM has been validated against empirical CSP 

operational data from the Solar Energy Generating Systems [16]. Weather data and CSP plant 

characteristics are input to SAM to determine how much thermal energy is collected by the solar 

field in each hour.4

The second part of our model is a mixed-integer program (MIP) that optimizes the operation of 

the CSP and wind plants to maximize revenues. This model takes hourly thermal energy 

collected by the solar field, as determined by SAM, potential generation from the wind plants, 

and energy prices as inputs. Wind data are obtained from the National Renewable Energy 

Laboratory’s (NREL’s) Western Wind Resource Dataset.5 This dataset uses simulated hourly 

wind speed data to estimate the generation from a wind plant installed at a particular location. In 

order to account for the effects of geographic dispersion of wind plants, we use data for 56 

locations around the study site, which can each accommodate up to 30 MW-e of wind. Price data 

are obtained from the ERCOT market operator and the ERCOT North zone price is used in the 

optimization, since we assume that the CSP and wind plant are connected by a radial 

transmission line going to this region [3]. The formulation of this MIP model is given in 

appendix A. 

We assume that the CSP plants that we model have the same characteristics as the default 

parabolic trough system in SAM. This plant has a powerblock with a gross rated capacity of 110 

MW-e, but can be run at 115% of this rated capacity. When the parasitic cooling and HTF pump 

loads are taken into the account, the maximum net capacity of the plant is about 120 MW-e. This 

plant includes a two-tank TES system, which we assume to have a roundtrip efficiency of 98.5% 

[9] and hourly heat losses of 0.031% of the energy in storage [4, 17]. We assume that the CSP 

plants have a SM of 2.0 and four hours of TES which is based on baseline plant designs in the 

 

3 The effective aperture considers cosine losses that occur due to non-normal incidence between the sun and the 

collectors

4 Weather data used for this simulation are obtained from the National Solar Radiation Data Base, available for 

download at http://rredc.nrel.gov/solar/old data/nsrdb/.

5 The Western Wind Resource Dataset is available for download at http://wind.nrel.gov/Web_nrel/.
9 

CSP literature [8]. We also show selected results from cases where the plant has eight hours of 

TES. 

We assume that the total nameplate capacity of the wind and CSP plants is 1,080 MW-e and 

consider cases in which there are between zero and nine CSP plants. Wind generators are then 

added to bring the nameplate capacity of the deployment to 1,080 MW-e. For instance, a 

deployment with four CSP plants would have a maximum CSP capacity of 480 MW-e and 600 

MW-e of wind. We model cases in which the transmission lines connecting the deployment to 

the load center have a capacity of between 600 MW-e and 1,080 MW, meaning that we examine 

cases in which the transmission capacity of the deployment is as low as 56% of its generating 

capacity.

Although our analysis is based on a two-year period, we optimize the operation of the wind and 

CSP plants using a rolling 24-hour planning horizon. This process works by starting at the 

beginning of the study period and optimizing plant operations over a 48-hour period. The 

optimized dispatch for the first 24 hours is fixed and the algorithm rolls forward to the second 

day of the study period. We use the 48-hour optimization horizon to ensure that energy is kept in 

the TES system of the CSP plants if it would have carryover value on the following day [18]. 

Using a longer optimization horizon has little effect on revenues of a CSP plant [9]. Our 

optimization model further assumes that the generator has perfect foresight of weather and price 

data during each 48-hour optimization period. Relaxing this perfect foresight assumption has a 

limited effect on the profit and operation of a standalone CSP plant [9]. Because our analysis 

considers co-located wind and CSP that must share a limited transmission resource and wind 

generation patterns are less predictable than solar, it is likely that deployment profits are more 

sensitive to the perfect foresight assumption than would be for a standalone CSP plant. 
10 

4 Results

4.1 Dispatch of Wind and CSP Deployments

Wind and CSP have two basic complementarities that potentially enable them to share 

transmission. One is that real-time wind and solar resource are often negatively correlated. The 

other is that CSP with TES is partially dispatchable, which allows solar generation to be shifted 

and to fill-in excess transmission capacity during subsequent hours with lower wind and solar 

resource. This allows for increased transmission utilization. 

Figure 6 illustrates these complementarities by showing the dispatch of a deployment consisting 

of 480 MW-e of CSP with an SM of 2.0, 600 MW-e of wind, and 600 MW-e of transmission 

capacity over a two-day-long period beginning on May 16, 2004. Because the transmission line 

is sized at the maximum output of the wind plant, the maximum output of the combined wind 

and CSP system is 180% of the transmission capacity of the deployment. These days show some 

negative correlation between wind and solar resource—wind generation is relatively high 

overnight when there is zero solar resource and the solar peak lags the midday wind peak by at 

least two hours on both days. Thus, adding CSP allows for significantly greater transmission 

usage than if only wind is installed at this site. Figure 6 also demonstrates the other 

complementarity between wind and CSP, namely the ability of TES to store solar energy that 

would otherwise be curtailed. In the four-hour case roughly 32% of the energy collected by the 

solar fields is stored and used to produce energy later in the day when both solar and wind 

resources are near-zero and excess transmission capacity is available. Figure 6a also shows that 

despite this use of TES, about 21% of the thermal energy collected by the solar field is wasted 

due to the limited energy capacity of the system. The figure shows these curtailments in MWh-e 

by applying the average net efficiency (taking into account average parasitic loads) of the CSP 

plant. Despite this limitation, the four-hour TES system is able to reduce CSP curtailment by 

roughly 62% compared to a CSP plant without TES.6

 Adding eight hours of TES almost 

completely eliminates curtailment in this 48-hour period. 

 

6 Figure 6 shows that some of the thermal energy collected by the CSP plants is curtailed in hours 10 through 13, 

whereas there is no curtailment in hours 14 through 17 when all of the thermal energy is stored. This result is due to 

the fact that there are multiple optimal solutions of the dispatch model. For example more energy could be stored in 

hour 10 and energy in hour 14 curtailed while still satisfying the operating constraints of the TES system. Both 

solutions would yield the same profit-maximizing outcome. These multiple optima are also, in part, due to the 

perfect foresight assumption.
11 

(a) Four Hours of TES (b) Eight Hours of TES 

Figure 6. Example wind and CSP dispatch beginning May 16, 2004.

Note: Deployment includes 480 MW-e of CSP, 600 MW-e of wind, and 600 MW-e of 

transmission capacity. Figure 6a assumes CSP with four hours of TES, while Figure 6b assumes 

eight hours. 

There are, however, limitations to these complementarities between CSP and wind. Some 

periods, which tend to occur in the spring, will have extended high wind generation, during 

which the TES system of the CSP plants will be filled and solar thermal energy will have to be 

curtailed due to the limited transmission. Figure 7 demonstrates this for the same deployment 

during a two-day period beginning on April 22, 2005. Figure 7a assumes the base case of four 

hours of TES and in this two-day period about 71% of the energy collected by the CSP plants’ 

solar fields is curtailed. Overall, about 15% of the energy collected by the solar fields is curtailed 

annually, indicating that additional transmission or TES capacity may be desirable. Figure 7b 

shows the benefits of incorporating eight hours of TES, which somewhat reduces curtailment, 

and allows a more continuous output, for example largely filling the gap in hours 0 through 8 and 

44 through 48. Figure 7a also shows that the model prioritizes wind over CSP. This is due both 

to the wind PTC, which makes wind $19/MWh-e more valuable than CSP from a marginal 

revenue perspective, and the higher variable operating and maintenance cost of CSP.7

 

7

Our model only includes the $19/MWh-e Federal wind PTC. Other state and local incentives could provide wind 

with a further revenue advantage over CSP. Conversely, state and local PTCs for CSP could reduce the relative 

revenue advantage of wind. However, this prioritization will occur unless any such incentives are equal for the two 

technologies.
12 

 (a) Four Hours of TES (b) Eight Hours of TES 

Figure 7. Example wind and CSP dispatch beginning April 22, 2004.

Note: Deployment includes 480 MW-e of CSP, 600 MW-e of wind, and 600 MW-e of 

transmission capacity. Figure 7a assumes CSP with four hours of TES, while Figure 7b assumes 

eight hours. 

Another limitation of having a downsized transmission link is that the CSP plant must be 

dispatched around wind generation and is operated in a suboptimal manner compared to a 

transmission-unconstrained deployment. This is illustrated in Figure 8, which shows the 

optimized dispatch of a deployment with 480 MW-e of CSP and 600 MW-e of wind during a 

three-day period beginning on October 17, 2004. For clarity, the dispatch of CSP is shown at the 

bottom of the figure. Figure 8a shows the operation of the deployment if there is no transmission 

constraint (i.e., there is 1,080 MW-e of transmission capacity). The figure shows that 

incorporating TES into the CSP plants allows the plant to sell energy during the highest-priced 

hours. For instance, stored thermal energy is discharged in hours 18, 30, and 62 when prices are 

relatively high.
13 

(a) Transmission-Unconstrained (b) Transmission-Constrained 

Figure 8. Example wind and CSP dispatch on October 17, 2004.

Note: Deployment includes 480 MW-e of CSP and 600 MW-e of wind capacity. Figure 8a is 

transmission-unconstrained and figure 8b has a 700 MW-e transmission capacity. 

Figure 8b shows the operation of the same deployment on the same days with a 700 MW-e 

transmission line. The figure again demonstrates the benefit of TES in allowing CSP generation 

to be shifted to lower-resource hours. For instance, excess energy that would overload the 

transmission line in hours 9 through 15 is stored and discharged in hours 16 through 21 and 28 

through 33, with similar behavior on the following days. However, this dispatch of the CSP plant 

is suboptimal from a market value standpoint. This is because the transmission constraint does 

not allow the CSP plant to sell as much energy during hours 30 through 33, when prices are 

relatively high. It must, instead, sell this energy in hours 42 through 49 when prices are lower. 

On the day shown in Figure 8, the average selling price of CSP energy is $89.10/MWh-e in the 

transmission-unconstrained case, as opposed to only $71.05/MWh-e with the constraint. 

Denholm and Sioshansi [3] demonstrate the same phenomenon when storage is co-located with a 

transmission-constrained wind generator. The operational policies shown in figure 8 and the 

resulting revenue differences represent a tradeoff between the cost and challenges of 

transmission development versus the optimal dispatch of CSP and TES. 

4.2 Transmission Downsizing in Wind and CSP Deployments

Figures 6 and 7 point to the fundamental tradeoffs in deploying wind, CSP, and transmission. 

Reducing transmission capacity will increase the capacity factor of the transmission investment, 

but will also increase generator curtailment and decrease the value of the energy produced by the 

plant. Figures 8 through 12 explore these tradeoffs in greater depth. In addition to the base case 

with four hours of TES, the figures also include cases in which the CSP plants have eight hours 
14 

of TES. Figure 9 shows the capacity factor of the transmission line as a function of the 

transmission capacity and generation mix of the deployment. The transmission and CSP 

capacities are given as a percentage of the 1,080 MW-e generating capacity of the deployment. 

The wind generators that we model have capacity factors over the two years studied of about 

33.9%, whereas the CSP plants with an SM of 2.0 and four hours of TES have a capacity factor 

of roughly 34.5%. Thus if the deployment is transmission-unconstrained, a CSP-only generation 

mix maximizes the capacity factor of the transmission link. For a smaller transmission link, 

however, it is beneficial to build a mix of wind and CSP, in order to exploit the negative 

correlation between wind and solar resource. The mix that maximizes transmission capacity 

factor ranges between 44% (480 MW-e) CSP with a 600 MW-e transmission link up to 89% 

(960 MW-e) CSP with 1,000 MW-e of transmission capacity.

(a) Four Hours of TES (b) Eight Hours of TES

Figure 9. Capacity factor of the transmission line as a function of transmission capacity and 

generation capacity breakdown. 

Note: Transmission and CSP capacities are given as a percentage of the 1,080 MW-e generating 

capacity of the deployment. 
15 

Figures 9 and 10 shows total energy curtailment as a function of the transmission capacity and 

generation mix of the deployment. Figure 10 shows total energy curtailments, while figure 11 

shows CSP curtailments. Figure 11 shows that even in the transmission-unconstrained case there 

will be some CSP curtailment. This is because the solar field, which has an SM of 2.0, is 

oversized relative to the powerblock. Thus, in many hours, the solar field collects more thermal 

energy than can be used directly by the powerblock; while some of this energy can be stored, the 

energy capacity of the TES system limits the amount of such storage. Nevertheless, in the fourhour case, this curtailment is less than 2% of the 1,115 GWh-e of thermal energy collected by 

each CSP plant’s solar field annually. For this reason, a wind-only deployment minimizes 

curtailment (since 100% of the potential wind generation is used) if the deployment is 

transmission-unconstrained. However, with a binding transmission constraint, a mix of wind and 

CSP minimizes curtailment. This is again because the negative correlation between real-time 

wind and solar availability yields a resource profile that results in fewer transmission constraint 

violations. 

(a) Four Hours of TES (b) Eight Hours of TES 

Figure 10. Total generation curtailed (both wind and CSP) as a function of transmission capacity 

and generation capacity breakdown. 

Note: Transmission and CSP capacities are given as a percentage of the 1,080 MW-e generating 

capacity of the deployment. 
16 

(a) Four Hours of TES (b) Eight Hours of TES 

Figure 11. CSP Generation curtailed as a function of transmission capacity and generation 

capacity breakdown. 

Note: Transmission and CSP capacities are given as a percentage of the 1,080 MW-e generating 

capacity of the deployment. 

Figures 11 and 12 show the average selling price of energy from the deployment, excluding the 

wind PTC, as a function of the deployment configuration. Figure 12 shows the overall average 

selling price of wind and CSP generation, while figure 13 shows the average selling price of CSP 

generation only. Figure 12 shows that the overall average selling price of energy is increasing in 

the amount of CSP, which reflects two properties of CSP. One is that real-time solar availability 

tends to be highly correlated with system loads and prices. This correlation is because peak loads 

in the ERCOT system, which tend to be correlated with peak prices, are driven primarily by 

cooling needs, which is highly coincident with DNI. Wind, on the other hand, tends to be slightly 

negatively correlated with energy prices. This negative correlation is shown in Figure 12 since 

the average selling price of energy from a wind-only deployment is very slightly decreasing in 

the transmission capacity. As the transmission capacity of the deployment is decreased, wind 

generation is curtailed in high-wind hours, which tend to be low-price hours. The other property 

of CSP is its dispatchability. This dispatchability allows CSP generation to be shifted, within the 

constraints of the TES system and transmission link, to higher-priced hours. This generation 

shifting is advantageous because, while prices and solar resource tend to be correlated, they are 

not perfectly coincident. This is because cooling loads can often lag the peak in DNI by a few 

hours due to thermal inertia. Thus, adding TES to a CSP plant allows for further energy revenue 

increases. 
17 

(a) Four Hours of TES (b) Eight Hours of TES 

Figure 12. Average selling price of energy (both wind and CSP), excluding the wind PTC, as a 

function of transmission capacity and generation capacity breakdown. 

Note: Transmission and CSP capacities are given as a percentage of the 1,080 MW-e generating 

capacity of the deployment. 

(a) Four Hours of TES (b) Eight Hours of TES 

Figure 13. Average selling price of CSP generation as a function of transmission capacity and 

generation capacity breakdown. 

Note: Transmission and CSP capacities are given as a percentage of the 1,080 MW-e generating 

capacity of the deployment. 
18 

Both Figures 11 and 12 show the effect of downsizing the transmission capacity, which is to 

diminish the value of TES. This is because CSP must share the scarce transmission with wind, as 

illustrated by the example in Figure 6. Thus, as the transmission capacity of the deployment is 

reduced, TES is decreasingly used to shift solar energy to high-price hours and is used instead to 

shift stored energy to low-wind and low-solar hours. Figure 13 also shows that increasing the 

amount of CSP in a deployment reduces the average selling price of CSP. This is, again, because 

the limited transmission capacity forces TES to be increasingly used to shift CSP generation to 

lower-price hours. As transmission constraints increase, the reduction in average price in the 

eight-hour TES case is due to the fact that while additional TES allows more energy to be sold, it 

tends to dispatch in lower-price hours. This means that the benefits of reduced curtailment 

associated with larger amounts of TES are somewhat offset by the lower value of this additional 

energy.

Figures 13 and 14 illustrate how this interaction between transmission and TES impacts 

deployment revenues. The figure shows average annual revenues as a function of the deployment 

configuration. Figure 14 shows total energy revenues from wind and CSP, excluding the wind 

PTC, and Figure 15 shows CSP energy revenues only. The figure shows that CSP earns 

considerably higher energy revenues than wind. This is both due to CSP having a slightly higher 

capacity factor (i.e., producing more energy) and because CSP produces higher-value energy due 

to the coincidence between DNI and prices and the use of TES. The figure also shows that 

downsizing transmission can significantly reduce deployment revenues. This has a greater effect 

on CSP—in the four-hour TES case, reducing the transmission capacity from 1,080 MW-e to 

600 MW-e reduces annual CSP revenues by 26% (which amounts to $61 million for an all-CSP 

deployment), whereas it reduces wind revenues by 22% (which is $36 million for an all-wind 

deployment). The greater effect on CSP reflects the fact that much of the added value of CSP 

derives from its ability to use TES to deliver energy during high-price hours, which is limited 

when the transmission constraint is imposed. Figure 14 also shows the small total revenue 

difference between 4 and 8 hours of storage in CSP-only systems without transmission 

constraints. 
19 

(a) Four Hours of TES (b) Eight Hours of TES 

Figure 14. Average annual energy revenues (both wind and CSP), excluding the wind PTC, as a 

function of transmission capacity and generation capacity breakdown. 

Note: Transmission and CSP capacities are given as a percentage of the 1,080 MW-e generating 

capacity of the deployment. 

(a) Four Hours of TES (b) Eight Hours of TES 

Figure 15. Average CSP annual energy revenues, as a function of transmission capacity and 

generation capacity breakdown. 

Note: Transmission and CSP capacities are given as a percentage of the 1080 MW-e generating 

capacity of the deployment. 
20 

4.3 Long-Term Economics of Co-Located Wind and CSP Deployments

The analysis done thus far assumes the configuration of a deployment and analyzes short-term 

operational decisions. A related question is what deployment configuration would maximize 

long-term economic value. Such an analysis would require comparing upfront capital costs 

against discounted revenue streams over the lifetime of the different deployments. This type of 

an analysis presents four challenges. One is that we only have two years of time-coincident wind 

and solar resource data, which limits our ability to estimate revenues over the full lifetime of a 

deployment. A second is that the cost of utility-scale CSP is rather uncertain due to fluctuations 

in commodity prices and the potential for substantial manufacturing improvements. A third is 

that the cost competitiveness of wind and CSP relative to conventional generating technologies 

will depend on future policy decisions, such as carbon regulation and fuel prices and subsidies. 

Finally, this analysis does not consider the impact of the increased use of renewables on the 

ERCOT market, mix of generators and the value of dispatchable resources, such as CSP with 

TES.

In light of these and other factors that can affect long-term investment decisions, we opt to use 

revenue estimates over the two years modeled to derive breakeven costs for the different 

deployments. The breakeven cost in this analysis is defined as the highest capital cost for the 

deployment that will make an investment economic on the basis of the revenue stream that we 

estimate. We also combine our revenue estimates with wind, CSP, and transmission cost 

forecasts to estimate a year-1 return on investment (ROI), which is the fraction of the investment 

cost of different deployments that is recovered through annual revenues. This analysis focuses on 

the more conservative case with only four hours of TES in the CSP plants. We first discuss the 

revenue, cost, and subsidy assumptions used in our analysis. 

4.3.1 Revenue Estimates

We assume that the wind and CSP deployments receive two revenue streams—energy and 

capacity payments. Energy revenues are estimated based on the optimized value of the objective 

function used in the optimization model. Capacity payments are supplemental payments made to 

a generator for the capacity that it provides the system. Generators that are added to a system 

increase system reliability by reducing the probability that there will be insufficient generating 

capacity in real-time to meet system loads. Capacity payments are intended to monetize this 

benefit. The capacity payment of a deployment is given by the price of system capacity times the 

capacity value of the deployment. We assume that the price of capacity is based on the capital 

cost of a natural gas-fired combustion turbine, which is estimated at $625/kW-e in 2005 dollars 

[19]. We use the cost of a combustion turbine since this is a generation technology that is often 

used for peak-capacity purposes. 

We use the operational performance of the deployments to estimate their capacity value. A 

number of different capacity value estimation techniques have been applied to wind [20-36] and 

CSP [37]. These include reliability theory-based methods and capacity factor-based 

approximations. One of the challenges raised in estimating the capacity value of CSP plants with 

TES is that one must account for both how much energy the generator plans to produce in each 

hour and how much energy is in the TES system. This is because even though the CSP generator 

may plan to produce relatively little energy, the thermal energy in the TES system could be used 

in real-time to help avert a system capacity shortage. This could happen, for example, if energy 
21 

prices during an hour are relatively low and it is optimal (from an energy revenue-maximization 

perspective) to keep energy stored as opposed to generate. 

One proposed method that accounts for this capability of TES is to use the optimized dispatch of 

the CSP plant, as determined by the optimization model, to determine the maximum amount of 

energy that could be produced in each hour using the energy stored in TES [37, 38]. This 

maximum potential generation in each hour is then used to estimate the capacity value using a 

capacity factor-based approximation. We use such a technique, the details of which are given in 

appendix B. 

Figure 16 shows the capacity value of the deployments as a function of the deployment 

configuration. The capacity values are given as a percentage of the 1,080 MW-e nameplate 

generating capacity of the deployments. The figure shows that CSP plants tend to have higher 

capacity values than wind generators, which is consistent with previous findings [20-37]. This is 

both because of the coincidence between solar resource availability and peak loads, as well as the 

dispatchability of CSP with TES. Since TES is used to shift solar energy to the highest-price 

hours, and because energy prices are strongly correlated with system loads and the likelihood of 

a system outage, optimizing TES to maximize energy revenues will also tend to increase the 

capacity value of CSP.

Figure 16. Capacity value of deployments as a function of transmission capacity and generation 

capacity breakdown. 

Note: Capacity value and transmission and CSP capacities are given as a percentage of the 

1,080 MW-e generating capacity of the deployment. 
22 

4.3.2 Cost Estimates

Our ROI calculations take into consideration capital costs associated with wind, CSP, and 

transmission construction, as well as CSP variable generation costs. A recent estimate places the 

capital cost of wind at about $1,650/kW in 2006 dollars [19]. We deflate this to $1,598/kW in 

2005 dollars using consumer price index (CPI) data provided by the U.S. Department of Labor’s 

Bureau of Labor Statistics.8

 CSP is assumed to have a variable cost of $0.70/MWh-e, which is 

included in the optimization model and in our cost calculations. Turchi et al. [8] provide 

forecasts of 2020 CSP construction costs in 2010 dollars. We break these costs into three 

components—a solar field cost that is proportional to the SM of a plant, a TES cost that is 

proportional to hours of storage in the TES system, and a fixed balance of plant cost, which 

includes the powerblock. The TES costs assume that the charging capacity of the TES system is 

equal to the nameplate power capacity of the powerblock, and do not account for the larger 

charging capacity that we assume. If this larger charging capacity is used in the default trough 

system modeled in SAM, the cost of TES increases by about 20% relative to the smaller 

charging capacity. Thus we inflate the TES costs reported by Turchi et al. [8] by this amount to 

arrive at the cost of the TES system that we model. Because of fluctuations in component costs, 

we deflate the costs reported in 2010 dollars to 2005 dollars using the Chemical Engineering 

Plant Cost Indices.9

 Table 2 summarizes the costs used in our analysis. 

Table 2. Per-Plant CSP Construction Costs in 2005 Dollars

Component Cost

Fixed ($ million) 129.69

Solar Field ($ million/SM) 133.00

TES ($ million/hour) 10.59

Figure 17 shows historical transmission construction cost data from a variety of ac and highvoltage dc (HVDC) projects built between 1995 and 2008 [3]. The data shown are for projects 

rated at 500 MW-e or greater and the costs are adjusted to 2005 dollars using CPI data. The 

figure shows that the costs vary significantly among the projects, and could possibly reflect sitespecific differences. Nevertheless, most projects have costs between $200/km-MW-e and 

$800/km-MW-e, and we use these as potential bounding values on the cost of transmission for 

our deployments. The length of the transmission line is assumed to be 12% greater than the 

linear distance between the deployment and the interconnection point, based on the 

characteristics of the Intermountain Power Project from Utah to southern California [39]. 

 

8

These data are available at http://www.bls.gov/data/inflation_calculator.htm.

9

These indices are available at http://www.che.com/pci/.
23 

Figure 17. Historical transmission construction costs

4.3.3 Deployment Subsidies

Wind and solar generators are currently offered a variety of subsidies under Federal, state, and 

local law. Our analysis focuses on Federal subsidies. These include a $19/MWh-e PTC for wind

(based on its value in our analysis year of 2005), and a 30% investment tax credit (ITC) on the 

upfront capital cost of solar. We assume that this ITC applies only to the CSP plants themselves, 

and excludes supplemental costs such as transmission. We include both of these subsidies in 

computing ROIs but exclude them in deriving breakeven costs. We exclude them from 

breakeven cost calculations because doing so would require an assumption about the capital cost 

of CSP relative to wind and transmission (in order to determine what fraction of the cost to apply 

the ITC to). 

4.3.4 Deployment Breakeven Costs 

In order to compare the annual revenues of the deployments that we estimate to a long-term 

capital investment, we use a capital charge rate (CCR). The CCR captures all of the financing 

parameters and translates the total cost of the investment (including principal and financing) into 

an annual cost [3]. We assume an 11% CCR. The breakeven cost is defined as the net annual 

profit of the deployment from energy and capacity payments, less variable CSP generation costs, 

divided by the CCR. We can express the breakeven cost of a deployment as:

CCR

vce

ψ

−+ φφφ , 

where e φ and c φ denote annual energy and capacity revenues, respectively, of the deployment, v φ denotes the associated annual variable cost of CSP generation, and CCR ψ denotes the CCR. 
24 

Figure 18 shows breakeven costs for different deployment configurations. The breakeven costs 

are divided by the 1,080 MW-e nameplate generating capacity of the deployments to give a 

$/MW-e value. As shown previously, CSP plants tend to earn significantly higher revenues than 

wind generators. Thus when the deployment is transmission-unconstrained, a CSP-only 

deployment yields the highest breakeven cost. As the transmission capacity is reduced, however, 

a mix of wind and CSP maximizes revenues and the breakeven cost. This is because shifting the 

generation mix toward wind reduces solar generation that would be curtailed due to the 

transmission constraint, while increasing deployment generation overnight when wind resources 

are higher. Thus the breakeven cost-maximizing deployment configuration ranges between 78% 

(840 MW-e) CSP with 600 MW-e of transmission capacity and 67% (720 MW-e) CSP with 800 

MW-e of transmission. 

Figure 18. Deployment breakeven cost as a function of transmission capacity and generation 

capacity breakdown. 

Note: Breakeven cost and transmission and CSP capacities are given as a percentage of the 

1,080 MW-e generating capacity of the deployment. CSP plants are assumed to have an SM of 

2.0 and four hours of TES. 
25 

4.3.5 Deployment Investment Cost Recovery

Our ROI calculations compare the annual revenues that a deployment earns from energy and 

capacity sales and the wind PTC to the total capital cost of the deployment. Deployments with an 

ROI that is at least as great as the CCR are said to be economic, since the annual revenues earned 

are greater than the annualized cost of the investment. If we define p φ as the wind PTC earned 

by a deployment and w χ , s χ , and t χ as the capital cost of the wind, CSP, and transmission 

components of the deployment, and ITC ψ as the solar ITC rate, then the ROI of the deployment 

is given by: 

. 

Figure 19 shows the ROI of deployments, as a function of their transmission capacity and 

generation capacity breakdown. Figure 19a assumes a transmission cost of $200/km-MW-e, 

while figure 19b uses a cost of $800/km-MW-e. Deployments that have an ROI of at least 11% 

(which is our assumed CCR) are denoted with magenta circles and the deployment with the 

highest ROI is denoted with a black cross. 

(a) (b)

Figure 19: Deployment ROI as a function of transmission capacity and generation capacity 

breakdown.

Note: Transmission and CSP capacities are given as a percentage of the 1,080 MW-e generating 

capacity of the deployment. Deployments with an ROI of at least 11% are denoted by a magenta 

circle. Deployments that maximize ROI are denoted by a black cross. Figure 19a assumes a 

transmission cost of $200/km-MW-e and figure 19b assumes a transmission cost of $800/kmMW-e.
26 

Comparing figures 18a and 18b shows deployment economics are highly sensitive to the cost of 

transmission. There are no economic deployments if the cost of transmission is greater than 

about $485/km-MW-e. However there are a number of deployment configurations with 

transmission capacities as low as 700 MW-e and up to 56% CSP on a capacity and energy basis 

that are economic. Figure 19b shows that the ROI-maximizing deployment with the higher 

transmission cost has a transmission link that is downsized relative to its generating capacity. 

Moreover, when four hours of TES is incorporated into the CSP plants, a deployment with 22% 

CSP, on a capacity and energy basis, is ROI-maximizing, yielding an ROI of about 9.7%. 

It should be noted that these results represent a snapshot of deployments in historic market 

conditions. Escalation in costs of conventional generation, restrictions on carbon emissions, and 

other factors could increase the value of the systems studied here. Furthermore, while some of 

the value of dispatchable CSP is captured by the assumed capacity payment, additional values of 

dispatchable energy, such as the provision of ancillary services could add further revenues [9]. 

Finally the value of dispatchable energy could change as a function of increased penetration of 

variable wind (and solar PV), and this could also change the likely configuration of CSP plants, 

including differing amounts of TES. 
27 

5 Conclusions

This report discusses and analyzes the potential benefits of co-locating wind and solar generation 

in the southwestern United States. Such a deployment strategy can improve the capacity factor of 

the combined plant and the associated transmission investment, with dispatchable CSP shifting 

energy to periods during reduced wind output. However, adding transmission constraints 

associated with co-location reduces performance, including the inability of CSP to provide 

maximum output during periods of both high demand and significant wind output. Furthermore, 

even with the use of TES, there are periods of extended high wind output and high solar output, 

which can result in curtailed energy. Despite these limitations, we do find cases in which a mix 

of CSP and wind can be justified by market revenues, and that in some cases deployments with 

up to 56% CSP capacity yield a positive net ROI. This will depend on a substantial reduction in 

CSP costs. Deployment economics are highly sensitive to transmission development costs, which 

have varied significantly in past projects, as well as future prices of conventional energy and 

potential restrictions on carbon emissions. 
28 

Appendix A. MIP Model Formulation

To give the formulation of the MIP model, we first define the following problem parameters and 

sets: 

T set of hours in optimization horizon, 

C set of CSP plants, 

κ transmission capacity (MW-e),

λ transmission losses,

s pc charging capacity of TES system of CSP plant c (MW-t),

d pc discharge capacity of TES system of CSP plant c (MW-t),

c h hours of charging capacity of TES system of CSP plant c , 

ηc hourly heat losses of TES system of CSP plant c , 

ρ c roundtrip efficiency losses of CSP plant c , 

−

c e minimum power capacity of powerblock of CSP plant c (MW-t),

+

c e maximum power capacity of powerblock of CSP plant c (MW-t),

⋅)( c f heat rate function of powerblock of CSP plant c , 

⋅)( HTFgc HTF pump parasitics function of CSP plant c , 

⋅)( BOP gc balance of plant parasitics function of CSP plant c , 

SU

c e startup energy requirement of powerblock of CSP plant c (MWh-t),

α c variable cost of CSP plant c ($/MWh-e),

π t price of energy in hour t ($/MWh-e),

SF

tc e , thermal energy collected by solar field of CSP plant c in hour t , 

wt total wind energy available in hour t , and 

γ wind production tax credit ($/MWh-e).
29 

We also define the following decision variables:

tcl , storage level of TES of CSP plant c at the end of hour t , 

tc s , energy storage by TES of CSP plant c in hour t , 

d ,tc energy discharged from TES of CSP plant c in hour t , 

σ ,tc binary variable that equals 1 if TES of CSP plant c is being charged in hour t , 

PB

tc e , energy put into powerblock of CSP plant c in hour t , 

net

tc e , net generation from CSP plant c in hour t , 

u ,tc binary variable that equals 1 if powerblock of CSP plant c is online in hour t , 

tc r , binary variable that equals 1 if powerblock of CSP plant c is started up in hour t

, 

wt wind generated in hour t , 

s

t n gross electricity energy sold in hour t , 

p nt gross electricity energy purchased in hour t , and 

t n binary variable that equals 1 if energy is being sold in hour t . 

The formulation of the model is then given by: 

(1)

s.t. (2)

(3)

(4)

(5)

(6)

(7)

(8)

∑ ∑ ∈ ∈





 





−⋅+−⋅

Tt Cc

n

t tcc

p

t

s

tt ewnn , m ax π )( αγ

)1( , 1 ∑ ,

∈

+=−− − Cc

n e

t tc

p

t

s

t ewn

n λ

λ

∈∀ Tt ; 

,)1( 1

κλ

λ

κ ≤−− − ≤− p

t

s

t n

n ∈∀ Tt ; 

0 ,t

s

t κ ⋅≤≤ nn ∈∀ Tt ; 

0 )1( t

p nt κ −⋅≤≤ n ∈∀ Tt ; 

, , η − −+⋅= dsll ,,1, tctctcctc c C ,∈∈∀ Tt ; 

0 , ,

s

cctc ⋅≤≤ phl c C ,∈∈∀ Tt ; 

0 m in }, ,, ,

s

c

S F

tctc tc s σ ⋅≤≤ pe c C ,∈∈∀ Tt ; 
30 

(9)

 (10) 

 (11) 

 (12) 

 (13) 

 (14) 

and (15) 

. (16) 

Objective function (1) maximizes revenues from net energy sales and the wind production tax 

credit (PTC), net of CSP generation costs. We assume a variable operations and maintenance 

cost of $0.70/MWh-e. Constraint set (2) defines gross energy sales and purchases in terms of 

wind and CSP generation by ensuring that all net energy generated is bought or sold. 

Constraint set (3) imposes the transmission limit on net sales (the sum of wind and CSP 

generation must be less than or equal to the transmission capacity). Constraint sets (4) and (5) 

force the generator to only sell or purchase energy at a given time. Constraint set (6) defines the 

amount of energy in each CSP plant’s TES as a function of the previous storage level, plus any 

net energy charged into TES. Constraint set (7) limits the amount of energy in storage to be 

within the size of the TES reservoir. Constraint sets (8) and (9) impose power limits on TES 

charging and discharging. They also prevent the TES system from charging and discharging 

energy simultaneously. Constraint set (10) forces the CSP plant to discharge TES only when the 

powerblock is online. A CSP plant without TES can be modeled using this same framework, by 

setting s pc , d pc , and c h equal to zero. 

Constraint set (11) limits the net amount of thermal energy used by each CSP plant to be no more 

than the amount of energy collected by its solar field. Constraint set (12) defines net generation 

of the CSP plants based on the heat rate function and the parasitic loads of the HTF pumps and 

balance of plant. The HTF pumps must be operated whenever TES is discharged, while the 

balance of plant parasitics account for cooling tower and other component loads. Constraint set 

(13) imposes the upper and lower bounds when the powerblock is online. It also assumes that the 

powerblock takes an hour to startup, during which time it does not produce energy. Constraint 

set (14) defines powerblock startups in terms of transitions in the ‘online’ state variables. 

Constraint set (15) imposes integrality constraints on the state variables. Constraint set (16) 

restricts wind generation to be less than available wind. 

,)1(0 , ,

d

tc ctc d σ ⋅−≤≤ p c C ,∈∈∀ Tt ; 

1 , u ≤− σ ,, tctc c C ,∈∈∀ Tt ; 

, , ,, ,,

S

tctc

S U

c

P B

tctcctc ρ ≤⋅++⋅− ereeds c C ,∈∈∀ Tt ; 

)()()( , , , ,

P

tc

B O

ctc

H TF

c

P B

tcc

n et

tc −= − egdgefe c C ,∈∈∀ Tt ; 

)( )( ,,,,,, tctctc

P B

tctctcc −⋅≤≤−⋅ rueerue− + c C ,∈∈∀ Tt ; 

, ,1,, tctctc − ≤− ruu c C ,∈∈∀ Tt ; 

}1,0{,,, σ nru ,,,, tctctctc ∈ c C ,∈∈∀ Tt ; 

≤≤ ww tt ,0 c C ,∈∈∀ Tt . 
31 

Appendix B. Capacity Factor Estimation Technique

We estimate the capacity factor of the deployments based on the optimized operation of each 

deployment given by maximizing objective function (1) subject to constraints (2) through (16). 

This optimized dispatch is used to compute the maximum amount of energy that the deployment 

could produce in each hour. To define this maximum generation we first define the maximum 

potential thermal energy that can be delivered to the powerblock of each CSP plant in each hour 

as:

m ax { ,0 m in { , m in {)1(}, ~ , , 1, ,tc

S U

ctcc

d

c c

S F

tcc

P B

e tc = ee + − −⋅−⋅ uelp + ρ η . (17) 

Equation (17) defines the maximum thermal energy as the minimum of the rated capacity of the 

powerblock and the sum of energy collected by the solar field and energy in TES (with 

associated energy losses taken into account). Equation (17) further assumes that the powerblock 

can be started up immediately (using the required thermal energy) in the event of a system 

shortage event. We next define the amount of this energy that is taken from TES as: 

S F

tc

P B

tctc eed ,,,

~ ~ −= . 

The maximum potential outputs of the CSP plants are then given by: 

) ~() ~() ~( ~ , , , ,

P

tc

B O

ctc

H TF

c

P B

tcc

n et

tc −= − egdgefe . 

We finally compute the maximum amount of energy that the deployment can provide as: 

} ~ )1( m in { , ~ ∑ ,

∈

⋅−= +

Cc

n e

t tc

s

t n κλ ew . 

We use the quantities, s nt

~ , to estimate the capacity value of the deployment using a capacity 

factor-based approximation. A number of different capacity factor-based approximations have 

been applied to wind and CSP. These methods approximate the capacity value of the plant as its 

average capacity factor during the hours with the highest loads or loss of load probabilities 

(LOLPs). A third method uses the average capacity factor during the hours with the highest 

LOLPs, but also weights the capacity factor in each hour by the corresponding system LOLP. 

Studies show that the LOLP-weighted method provides the most robust capacity value estimates 

[21, 37]. In the case of wind, using the 10% of the hours of the year with the highest LOLPs 

provides the most robust capacity value estimate, whereas using the top-10 hours provides the 

most robust estimate for a CSP plant. Because our analysis considers a mix of wind and CSP 

plants, we opt to use the top-10% LOLP hours of the year, since the capacity value estimate of a 

CSP plant is less sensitive to this parameter.
32 

To estimate the capacity value of the deployment we first define the weight used in each hour as:

∑∈

=

T

t

t

ˆ τ

ζ τ

ζ ω , 

where Tˆ is the set of hours used in the approximation and t ζ is the LOLP in hour t . In our case, 

Tˆ denotes the 10% of the hours in each year that have the highest LOLPs. The capacity value 

estimate is then given by:

∑∈

⋅= Tt

s

tt nv ˆ

~ ω . 

We compute the LOLPs of the system using load data from the ERCOT system operator and 

generator data from Form 860 data collected by the U.S. Department of Energy’s Energy 

Information Administration. These data specify the nameplate capacity and generating 

technology of each conventional plant in the ERCOT system. These are combined with historical 

effective forced outage rate data from the North American Electric Reliability Corporation’s 

Generating Availability Data System.
33 

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