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

Capacity Value of Concentrating 

Solar Power Plants

Seyed Hossein Madaeni and Ramteen Sioshansi

Ohio State University

Paul Denholm

National Renewable Energy Laboratory

Technical Report

NREL/TP-6A20-51253

June 2011
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

Golden, Colorado 80401

303-275-3000 • www.nrel.gov

Contract No. DE-AC36-08GO28308

Capacity Value of Concentrating 

Solar Power Plants

Seyed Hossein Madaeni and Ramteen

Sioshansi

Ohio State University

Paul Denholm

National Renewable Energy Laboratory

Prepared under Task No. SS10.1410

Technical Report

NREL/TP-6A20-51253

June 2011
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iii

Acknowledgments

The authors would like to thank Adam Green, Michael Milligan, Mark Mehos, Robin Newmark, 

Walter Short, and Craig Turchi for helpful discussions and suggestions. 
iv

List of Acronyms

APS Arizona Public Service

CSP concentrating solar power 

EFOR expected forced outage rate

EIA U.S. Department of Energy’s Energy Information 

Administration

ELCC effective load carrying capability

ERCOT Electric Reliability Council of Texas

FCA forward capacity auction

FCM forward capacity market 

FERC Federal Energy Regulatory Commission 

GADS Generating Availability Data System 

HTF heat transfer fluid

ISO Independent System Operator 

LOLE loss of load expectation 

LOLP loss of load probability 

LSE load-serving entity

MIP mixed-integer program 

MW-e megawatts of electricity

NERC North American Electric Reliability Corporation 

NP Nevada Power

PHS pumped hydroelectric storage 

PV photovoltaic 

SAM Solar Advisor Model 

SM solar multiple

TES thermal energy storage 

WECC Western Electricity Coordinating Council 
v 

Executive Summary

This study estimates the capacity value of a concentrating solar power (CSP) plant at a variety of 

locations within the western United States. This is done by optimizing the operation of the CSP 

plant and by using the effective load carrying capability (ELCC) metric, which is a standard 

reliability-based capacity value estimation technique. Although the ELCC metric is the most 

accurate estimation technique, we show that a simpler capacity-factor-based approximation 

method can closely estimate the ELCC value.

Without storage, the capacity value of CSP plants varies widely depending on the year and solar 

multiple. The average capacity value of plants evaluated ranged from 45%–90% with a solar 

multiple range of 1.0–1.5. When introducing thermal energy storage (TES), the capacity value 

of the CSP plant is more difficult to estimate since one must account for energy in storage. We 

apply a capacity-factor-based technique under two different market settings: an energy-only 

market and an energy and capacity market. Our results show that adding TES to a CSP plant can 

increase its capacity value significantly at all of the locations. Adding a single hour of TES 

significantly increases the capacity value above the no-TES case, and with four hours of storage 

or more, the average capacity value at all locations exceeds 90%.
vi 

Table of Contents

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

List of Tables ............................................................................................................................................ viii

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

2 Methods for Estimating Capacity Value............................................................................................. 2

2.1 Effective Load Carrying Capability .....................................................................................2

2.2 Approximation Methods ......................................................................................................4

2.2.1 Highest-Load Hours Approximation Method .............................................................5

2.2.2 Highest Loss of Load Probability Hours Approximation Method..............................5

2.2.3 Loss-of-Load-Probability-Weighted Highest-Load Hours Approximation Method ..5

3 Concentrating Solar Power Model...................................................................................................... 6

4 Data Requirements............................................................................................................................. 10

5 Capacity Value of a Concentrating Solar Power Plant without Thermal Energy Storage........... 12

5.1 Effect of Expected Forced Outage Rates on Concentrating Solar Power Capacity Value 21

5.2 Effect of Load Errors on Concentrating Solar Power Capacity Value ..............................22

5.3 Effect of Sub-Hourly Variability on Concentrating Solar Power Capacity Value ............23

6 Capacity Value of a Concentrating Solar Power Plant with Thermal Energy Storage ................ 25

6.1 Capacity Value of a Concentrating Solar Power Plant with Thermal Energy Storage in an 

Energy-Only Market ..........................................................................................................26

6.2 Capacity Value of a Concentrating Solar Power Plant with Thermal Energy Storage in a 

Capacity Market .................................................................................................................32

6.2.1 Capacity Market Procedures .....................................................................................32

6.2.2 Optimization Model ..................................................................................................33

6.2.3 Results .......................................................................................................................34

7 Conclusions ........................................................................................................................................ 38

References................................................................................................................................................. 39
vii 

List of Figures

Figure 1. Schematic of a parabolic trough CSP plant with TES ..................................................... 6

Figure 2. Average annual capacity value of a CSP plant with no TES in different locations ...... 13

Figure 3. Annual capacity value of a CSP plant with no TES at the New Mexico location ........ 14

Figure 4. Hourly LOLPs and dispatch of a CSP plant with no TES at the New Mexico location 

with an SM of 1.0 on August 1, 2000 ............................................................................... 15

Figure 5. Hourly loads and solar radiation at the New Mexico location on August 1, 2000........ 15

Figure 6. Hourly LOLPs and dispatch of a CSP plan with no TES at the New Mexico location 

with an SM of 1.0 on August 10, 2004 ............................................................................. 16

Figure 7. Hourly loads and solar radiation at the New Mexico location on August 10, 2004...... 16

Figure 8. Annual average capacity value of a CSP plant with no TES at the Imperial Valley 

location using the ELCC metric and approximation techniques that select the top 10 

hours .................................................................................................................................. 17

Figure 9. Annual average capacity value of a CSP plant with no TES at the Imperial Valley 

location using the ELCC metric and approximation techniques that select the top 100 

hours .................................................................................................................................. 18

Figure 10. Annual average capacity value of a CSP plant with no TES at the Imperial Valley 

location using the ELCC metric and approximation techniques that select the top 10% of 

hours .................................................................................................................................. 18

Figure 11. Annual average capacity value of a CSP plant with no TES at the New Mexico 

location using the ELCC metric and approximation techniques that select the top 10 

hours .................................................................................................................................. 19

Figure 12. Annual average capacity value of a CSP plant with no TES at the Death Valley 

location using the ELCC metric and approximation techniques that select the top 10 

hours .................................................................................................................................. 20

Figure 13. Annual average capacity value of a CSP plant with no TES at the Nevada location 

using the ELCC metric and approximation techniques that select the top 10 hours ........ 20

Figure 14. Annual average capacity value of a CSP plant with no TES at the Arizona location 

using the ELCC metric and approximation techniques that select the top 10 hours ........ 21

Figure 15. Average annual capacity value of a CSP plant with no TES at the Imperial Valley 

location based on ELCC metric with constant and varying conventional generator 

characteristics .................................................................................................................... 22

Figure 16. Average annual capacity value of a CSP plant with no TES at the Imperial Valley 

location based on ELCC metric with loads shifted ........................................................... 23

Figure 17. Capacity value of a CSP plant with no TES at the Boulder City, Nevada, location 

based on ELCC metric while using hourly and one-minute interval solar data ............... 24

Figure 18. Average annual capacity value of a CSP plant with TES at the Imperial Valley 

location under an energy-only market setting ................................................................... 27

Figure 19. Average annual capacity value of a CSP plant with TES at the New Mexico location 

under an energy-only market setting ................................................................................. 27

Figure 20. Average annual capacity value of a CSP plant with TES at the Death Valley location 

under an energy-only market setting ................................................................................. 28

Figure 21. Average annual capacity value of a CSP plant with TES at the Nevada location under 

an energy-only market setting ........................................................................................... 28
viii

Figure 22. Average annual capacity value of a CSP plant with TES at the Arizona location under 

an energy-only market setting ........................................................................................... 29

Figure 23. LOLP, energy from solar field and energy in storage for a CSP plant at the Nevada 

location with four hours of TES and different SM values on July 12, 1999 .................... 30

Figure 24. LOLP versus energy price for the Death Valley location in year 1999 ...................... 31

Figure 25. LOLP, energy from solar field and energy in storage for a CSP plant at the Death 

Valley location with an SM of 2.7 and different TES sizes on July 12, 1999 .................. 31

Figure 26. Average annual capacity value of a CSP plant with TES at the Imperial Valley 

location under an energy and capacity market setting ...................................................... 35

Figure 27. Average annual capacity value of a CSP plant with TES at the New Mexico location 

under an energy and capacity market setting .................................................................... 35

Figure 28. Average annual capacity value of a CSP plant with TES at the Death Valley location 

under an energy and capacity market setting .................................................................... 36

Figure 29. Average annual capacity value of a CSP plant with TES at the Nevada location under 

an energy and capacity market setting .............................................................................. 36

Figure 30. Average annual capacity value of a CSP plant with TES at the Arizona location under 

an energy and capacity market setting .............................................................................. 37

List of Tables

Table 1. Location of CSP Plants ................................................................................................... 10
1 

1 Introduction

Power system planners are tasked with ensuring 

adequate supply of electricity to meet demand. 

In addition, system planners face consumer and 

political demands to increase the share of 

renewable energy such as wind and solar in 

their energy mix. But the variable and uncertain 

nature of these renewable resources poses some 

challenges for utilities and system operators. 

Planners need an accurate estimate of the 

capacity value of such resources in order to 

represent renewable resources in reliability 

models for long-term planning purposes. 

Concentrating solar power (CSP) plants are one 

renewable technology currently being deployed 

both in the United States and internationally. 

For planners, CSP has a potential advantage 

over many other technologies because of its 

ability to use thermal energy storage (TES).

This report details techniques that can be used 

to estimate the capacity value of CSP plants. 

The techniques consist of models, which 

optimize the commitment and dispatch of the 

CSP plant, and statistical methods used to 

estimate the probability of a system outage 

event. These techniques are compared in terms 

of their computational cost and accuracy. The 

report also presents results for case studies 

conducted at locations throughout the western 

United States. We show that adding TES to a 

CSP plant can significantly increase its capacity 

value. 

Defining Capacity-Related Terms

This document focuses on the capacity 

value of CSP plants. There are a number 

of capacity-related terms commonly used 

with substantially different meanings.

Capacity generally refers to the rated 

output of the plant when operating at 

maximum output. Capacity is typically 

measured in terms of a kilowatt (kW), 

megawatt (MW), or gigawatt (GW) rating. 

Rated capacity may also be referred to as 

“nameplate capacity” or “peak capacity.” 

This may be further distinguished as the 

“net capacity” of the plant after plant 

parasitic loads have been considered, 

which are subtracted from the “gross 

capacity.”

Capacity Factor is a measure of how 

much energy is produced by a plant 

compared to its maximum output. It is 

measured as a percentage, generally by 

dividing the total energy produced in a 

year by the amount of energy it would 

have produced if it ran at full output over 

that year. It may also be expressed as the 

ratio of average output to maximum output 

over a year. 

Capacity Value is the focus of this report 

and refers to the contribution of a power 

plant to reliably meeting demand. 

Capacity value is the contribution that a 

plant makes toward the planning reserve 

margin, with a more comprehensive 

technical definition provided in Section 2. 

The capacity value (or capacity credit) is 

measured either in terms of physical 

capacity (kW, MW, GW) or the fraction of 

its nameplate capacity (%). Thus a plant 

with a nameplate capacity of 150 MW 

could have a capacity value of 75 MW or 

50%.

Capacity Payment is a monetary 

payment to a generator based on its 

capacity value. The capacity payment is 

generally in terms of $/MW where the MW 

is the generator’s capacity value. 
2 

2 Methods for Estimating Capacity Value

A number of different methods have been used to calculate the capacity value of renewable and 

conventional generators [1]-[3]. These methods differ in terms of computational time, 

complexity, and data requirements. A majority of the methods utilize power system reliability 

evaluation techniques [4], which are based on two standard reliability indices—loss of load 

probability (LOLP) and loss of load expectation (LOLE). LOLP is defined as the probability of a 

loss of load event, in which the system load is greater than available generating capacity during a 

given time period. LOLP is typically computed in one-hour increments. The LOLE is the sum of 

the LOLPs during a planning period, typically one year. LOLE gives the expected number of 

time periods in which a loss of load event occurs. Power system planners typically aim to 

maintain an LOLE value of 0.1 days/year (based on the target of one outage-day every 10 years) 

[5]. This value is used as the target LOLE value throughout this report. The capacity value of a 

plant represents the ability of the plant to reduce the probability or severity of a loss of load 

event. Thus, a generator’s capacity value is measured based on how adding it to the system 

changes the system’s LOLP and LOLE.

Generator outages may leave the system with insufficient capacity to meet load. Conventional 

generator outages are typically modeled using an expected forced outage rate (EFOR), which is 

the probability that a particular generator can experience a failure at any given time. When 

renewables are added to a system, the LOLP and LOLE must also capture the variability of these 

resources. To do this, renewable generator outages are modeled using an EFOR, and resource 

variability is estimated using historical data or by simulating such data.

The following sections examine common techniques for estimating capacity value of renewable 

and conventional generators. 

2.1 Effective Load Carrying Capability

One of the most robust and widely accepted techniques for estimating capacity value is 

determining the effective load carrying capability (ELCC) of a generator [6]-[10]. The ELCC of 

a generator can be defined in a number of ways, which will yield very similar results [11]. One 

definition is the amount by which the system’s load can increase (when the generator is added to 

the system), while maintaining the same system reliability (as measured by the LOLP and 

LOLE) [12]. An alternative definition is the amount of a different generating technology that can 

be replaced by the new generator without making the system less reliable [5]-[12].1

 

1 Some authors have used the term “Equivalent Conventional Power” instead of ELCC [4].

 In the 

context of a renewable generator, the latter definition is more attractive because it allows the 

capacity value of a renewable generator to be measured in terms of a conventional dispatchable 

generator. The ELCC of a renewable generator equals the power capacity of the conventional 

generator that yields to the same LOLE as the system with the renewable resource. For example, 

a 100 MW wind generator may have a capacity value that is equivalent to a 30 MW natural-gasfired combustion turbine.
3 

The steps used to calculate the ELCC of a CSP generator2

1. For a given set of conventional generators, the LOLE of the system without the CSP plant 

is calculated using the following formula: 

are as follows:

1

 (1)

T

i i

i

LOLE P( G L ) == < ∑

where T is the total number of hours of study, Gi represents the available conventional 

capacity in hour i, and Li is the amount of load. P(Gi < Li) indicates the probability of 

available generating capacity being less than demand, which is the LOLP in each hour. 

Adding these LOLPs together gives the LOLE. 

2. The CSP plant is added to the system and the LOLE is recalculated. This is shown in (2) 

as LOLECSP, where Ci is the output of the CSP plant in hour i. Since the CSP plant has 

been added to the system, LOLECSP will be lower than LOLE (indicating a more reliable 

system with lower LOLPs).

1

 (2)

T

CSP i i i

i

LOLE P( G C L ) == +< ∑

3. The CSP plant is “removed” from the system and a conventional generator is added. The 

LOLE of the new system, which is denoted as LOLEGen is computed as:

1

 (3)

T

Gen i i i

i

LOLE P( G X L ) =

= +< ∑

where Xi is the available generating capacity in hour i from the added conventional 

generator. This added conventional generator is assumed to have a fixed EFOR, but the 

nameplate capacity of the plant is adjusted until the LOLE of the system with the CSP 

plant and the conventional generator are equal; i.e., until LOLECSP = LOLEGen. Once the 

two LOLEs are made equal to one another, we can say that the capacity value of the CSP 

plant is equivalent to the capacity value of the conventional generator. 

An important difference between renewable resources, such as CSP plants, and conventional 

generators is the cause of unavailability. While CSP plants will experience mechanical failures, 

they are unavailable mostly due to a lack of solar resource.

The ELCC method requires detailed system data, including EFORs of all of the generators in the 

system, generator capacities, and loads. Moreover, due to seasonal and annual weather pattern 

changes, one will typically need several years’ worth of data to accurately estimate the capacity 

value of a CSP plant. Finally, the ELCC method can be computationally expensive, due to the 

complexity of computing the hourly LOLPs. 

 

2 This method can be applied to any generating resource, including non-CSP renewables. This is done by 

substituting the candidate generator, for which the ELCC is being calculated, in place of the CSP plant.
4 

2.2 Approximation Methods 

Calculating capacity value using the ELCC can be a cumbersome process since the capacity of 

the added conventional generator must be adjusted iteratively to achieve equality between the 

two LOLEs. These complications have led to the development of simpler approximation 

techniques. These approximation methods reduce the computational burden by focusing on the 

hours in which the system faces a high risk of not meeting load—typically hours with high loads 

or LOLPs.

Several studies have compared the accuracy of approximation methods and reliability-based 

approaches, such as the ELCC method, for calculating capacity value of wind and photovoltaic 

(PV) solar systems. For example, Bernow et al. [14] and El-Sayed [15] estimate the capacity 

value of a wind plant by considering only the peak-load hours. They use the average capacity 

factor of wind during peak-load hours, defined as the actual output of the plant during those

hours divided by its nameplate capacity, as a proxy for the capacity value. Such comparisons 

have not, however, been carried out for CSP. 

Milligan and Parsons [16] calculate the capacity value of wind by considering a set of “risky” 

hours, as opposed to only peak-load hours. They introduce three different approximation 

methods, which differ based on the set of hours examined. One technique uses the average 

capacity factor during the peak-load hours, whereas another uses the capacity factor during the 

peak-LOLP hours. A third technique uses the highest-load hours but normalizes the capacity 

factors by the LOLPs. This technique places higher weight on the capacity factor of the wind 

plant during hours with high LOLPs. Milligan and Parsons have applied these techniques to the 

top 1% to 30% of hours and have shown that the approximation can approach the ELCC metric 

if a suitable number of hours are considered. Their results suggest that using the top 10% of 

hours is typically sufficient.

Milligan and Porter [17] survey capacity valuation methods applied to wind by different utilities 

and regional transmission organizations. They note that many entities use time-based, as opposed 

to reliability-based, approximation techniques for capacity valuations. The PJM 

Interconnection,3

The following sections describe some of these approximation techniques in further detail. 

 for instance, uses the capacity factor of a wind plant between the hours 3 p.m. 

and 7 p.m. from June 1 through August 30 to calculate the plant’s capacity credit. This approach 

does not require any reliability modeling and is therefore very computationally simple. The New 

York Independent System Operator (ISO) calculates the summer and winter capacity value of its 

existing wind plants separately. The capacity factor of a wind plant between 2 p.m. and 6 p.m. in 

June, July, and August of the previous year determines its summer capacity value. The capacity 

factor between 4 p.m. and 8 p.m. in December, January, and February of the previous year 

determines its winter capacity values. Another example is the Electric Reliability Council of 

Texas (ERCOT), which uses the average output of a wind plant between 4 p.m. and 6 p.m. in 

July and August [17]. 

 

3 The PJM Interconnection is a regional transmission organization in the eastern United States.
5 

2.2.1 Highest-Load Hours Approximation Method

The highest-load hours approximation method is the simplest approach that can be used to obtain 

an estimate of a generator’s capacity value. This approach uses the average capacity factor of the 

CSP plant during the highest-load hours as an approximation for the capacity value. The number 

of hours considered is important since the capacity factor can be highly sensitive to this 

parameter. This study compares three cases in which the top 10, top 100, and top 10% (or top 

876) of load hours are used. Our results indicate that considering only the top 10 load hours 

results in an approximation that is closest to the ELCC metric. It is worth contrasting this with 

capacity-factor-based approximations of the capacity value of wind. Milligan and Parsons [16] 

show that the top 10% load hours give an approximation that is closest to the ELCC. 

2.2.2 Highest Loss of Load Probability Hours Approximation Method

The highest-LOLP hours approximation method is similar to that described in Section 2.2.1, 

except that it uses the highest-LOLP as opposed to highest-load hours. Since this technique 

requires the LOLPs of the original system to be computed, this is a more computationally 

expensive technique than an approximation based on the highest-load hours. This approximation 

also requires more system data to compute the LOLPs. This technique is, however, less 

computationally burdensome than an ELCC calculation since the LOLEs do not need to be 

iteratively recomputed in order to equate the LOLEs of the system with the CSP and 

conventional generator added. If the generating capacities and EFORs of the generators are the 

same across all of the hours of the year, then this technique will yield the same capacity value 

estimate as an approximation based on the highest-load hours. This is because, in such a case, the 

highest-LOLP hours will also be the highest-load hours. 

2.2.3 Loss-of-Load-Probability-Weighted Highest-Load Hours Approximation 

Method

The weighted LOLP-based approximation method also uses the capacity factor of the CSP plant 

during the highest-load hours. The capacity factors are weighted, however, based on the hourly 

LOLPs. This weighting is done since the capacity provided by the CSP is especially needed 

during hours with higher LOLPs. The weights are obtained as: 

1

 (4) i

i T

j

j

LOLP

w

LOLP

=

=

∑

where wi is the weight in hour i, LOLPi is the LOLP in hour i, and T is the number of hours in 

the study. These weights are then used to calculate the weighted average capacity factor of the 

CSP plant in the highest-load hours as: 

1

 (5)

T

i i

i

CV w .CF

′

=

= ∑

where CV is the approximated capacity value of the CSP plant, CFi is the capacity factor of the 

CSP plant in hour i, and T′ is the number of hours used in the approximation. Our results show 

that this method yields capacity value approximations that are closest to the ELCC metric.
6 

3 Concentrating Solar Power Model 

Unlike wind or solar PV, a CSP plant with TES is a partially dispatchable generation technology. 

This is because when TES is incorporated into a CSP plant, the plant operator has the option 

(within the capacity limits of the TES system) of using solar energy to either drive the steam 

turbine in the powerblock or to store the thermal energy instead. Since stored energy can 

supplement the output of a CSP plant during a system shortage event, the capacity value of a 

CSP plant will depend on its dispatch. Capacity value estimations involving conventional 

generators assume that the plants will always be operated in an “optimal” fashion. Thus, we must 

model the dispatch decisions made by the CSP operator to capture these effects. We assume that 

the CSP plant will be operated to maximize revenues, based on wholesale market price signals. 

As such, we base our model on that developed by Sioshansi and Denholm [19], which assumes 

that the CSP plant is operated to maximize revenues from energy sales. We also consider a case, 

which we discuss in Section 6.2, in which the CSP plant participates in an energy and capacity 

market, and the plant is operated to maximize the sum of energy and capacity payments. It 

should be noted that these are not the only markets in which a CSP plant could participate. 

Sioshansi and Denholm [19] study CSP participating in energy and ancillary service markets. 

Moreover, in some cases, such as if the CSP plant has sold its energy through a forward contract, 

the plant will not necessarily adjust its output based on spot market price signals. As such, there 

are other operational scenarios that would yield different dispatch decisions and capacity values 

from what we derive based on these models. 

Figure 1 provides a schematic of a parabolic trough CSP plant including the three main 

components (solar field, TES, and power block). The modeling of each of the components and 

the system as a whole is described in more detail in the following paragraphs. 

Figure 1. Schematic of a parabolic trough CSP plant with TES 

Our optimization model consists of two main parts. The first part is based on the Solar Advisor 

Model (SAM), a software program that simulates the dynamics of a CSP plant [20]. SAM takes 

weather data, including solar radiation and ambient temperature, for each of the locations as an 

input and is used to determine how much thermal energy is collected by the solar field of the 

CSP plant in each hour. SAM also accounts for temperature effects on the efficiency of the solar 

field in collecting solar thermal energy. These data are then used as an input to the mixed-integer 

program (MIP), which is the second part of our model. The MIP model takes the solar field 
7 

output as given and determines how much net energy to put into storage and deliver to the 

powerblock in each hour to maximize revenues. 

In order to give the formulation of the general MIP model, which can model both CSP plants 

with and without TES, we first define the following model parameters:

s : Charging power capacity of TES (MW-t)

d : Discharging power capacity of TES (MW-t)

urs of storage

urly TES energy losses (%)

: Ηο

:Ηο

η 

ρ 

+

Roundtrip TES efficiency losses (%)

P HTF pump parasitic function

 Rated thermal capacity of powerblock (MW-t)

τ Minimum and maximum operating level of powerblock, 

 respectively 

:

h

-

(.) :

τ, :

φ : 

τ

(% of capacity)

SU : Powerblock startup energy (% of capacity)

u : Powerblock minimum up time

f(.) : Powerblock heat rate function

P Powerblock parasitic function

c : Variable generation cost ($/MWh-e

b (.) :

)

SF : Energy from solar field in hour (MWh-t)

M Market-clearing price of energy in hour ($/MWh-e)

t

e

t

t

: t

We also define the following decision variables of the model:

: Storage level of TES at the end of hour (MWh-t)

: Energy put into TES in hour (MWh-t)

: Energy taken out of TES in hour (MWh-t)

: Electric energy sold in hour (MWh-e)

: Energy put into

t

t

t

t

t

l t

s t

d t

e t

τ powerblock in hour (MWh-t)

: Binary variable indicating powerblock is up in hour 

 : Binary variable indicating powerblock is started in hour 

t

t

t

u t

r t
8 

The formulation of the model is then as follows: 

 e

t t

t T

max ( M c ).e , ∈

∑ − (6) 

1 s.t. lt t tt ρ.l s d , = +− − ∀ ∈t T (7) 

0 lt ≤ ≤η.s , ∀ ∈t T (8) 

0 t ≤ ≤ s s, ∀ ∈t T (9) 

0 t ≤ ≤ d d, ∀ ∈t T (10) 

s t tt t t − ++ ≤ φ τ τ. .d SU . r SF ∀ ∈t T (11) 

et t ht b t =− − f ( ) P ( d ) P ( f ( )) τ τ ∀ ∈t T (12) 

tt t ττ τ ττ . .u . .u − + ≤ ≤ ∀ ∈t T (13) 

r

t t t1 u u ≥ − − ∀ ∈t T (14) 

 

t

t j

jtu

u r = −≥ ∑ ∀ ∈t T (15) 

0 1 t t u ,r { , } ∈ ∀ ∈t T (16)

The objective function (6) maximizes revenues from energy sales. Constraint (7) is a flowbalance constraint that determines the amount of energy in storage at the end of hour t as a 

function of the amount of energy in storage at the end of hour t-1 and hour t charge and 

discharge decisions. The term ρ, which multiplies the storage level at the end of hour t-1, 

captures heat losses that will naturally occur within the TES system. These losses are assumed to 

be 0.031% based on tests conducted at the Solar Two CSP Plant in California [21]-[22]. 

Constraints (8) – (10) set power and energy restrictions on TES charging and discharging. Note 

that by setting the parameter η, which represents the number of hours of storage in the TES 

system, at zero, this model can simulate a CSP plant without TES. Constraint (11) requires total 

thermal energy used by the CSP plant in any hour to be no greater than the energy collected by 

the solar field. Total thermal energy used by the CSP plant consists of the sum of net energy 

charged into storage and energy delivered to the powerblock. The term φ in this constraint 

captures first-law roundtrip efficiency losses when energy is put through the storage cycle. These 

losses, which we assume to be 1.5% [19], account for energy losses in an indirect TES system 

due to temperature differences of the heat-transfer fluid (HTF) going into and out of TES. 

Constraint (12) defines the amount of electric energy produced by the CSP plant in terms of the 

efficiency of the powerblock and parasitic loads of various CSP plant components. The heat rate 

function f(.

) in constraint (12) represents the powerblock’s efficiency in converting thermal 

energy to electricity. The functions Ph(

.

) and Pb(

.

) represent HTF pump and powerblock 

parasitics, respectively. We assume in this analysis that the powerblock is wet-cooled, which 

implies that temperature will have a negligible effect on the efficiency of the plant. A dry-cooled 

powerblock could be modeled by multiplying f(.) by a temperature-based correction factor [19]. 

All of these functions are approximated as being piecewise-linear, which guarantee the linearity 

of the MIP. Constraint (13) sets power capacity restrictions when the CSP plant is online. 

Constraint (14) defines the powerblock startup variable in terms of the online variables, while 
9 

constraint (15) ensures that the minimum up-time requirement is met. Constraint (16) is imposed 

to ensure the integrality of commitment and startup variables.

Although different CSP technologies, including parabolic troughs, power towers, and Stirling 

dish systems exist, our analysis focuses on parabolic troughs. Nevertheless, this model is 

sufficiently general to simulate other CSP technologies. Parabolic trough CSP systems consist of 

three separate but interrelated parts: the solar field, the powerblock, and the TES system. As 

such, these three components can be sized differently, each of which can affect the operation and 

capacity value of the plant. The size of the solar field is typically measured either based on the 

area that the field covers or by using the concept of the solar multiple (SM). The SM reflects the 

relative size of the solar field. A plant with an SM of 1 is sized to provide sufficient thermal 

energy to operate the powerblock at its rated capacity under reference conditions. We measure 

the size of the solar field using the SM and consider a range of solar field sizes. The size of the 

TES is measured based on its power and energy capacity. We assume that the power capacity of 

the TES system is such that the powerblock can operate at its rated capacity using energy from 

TES only. The energy capacity of TES is typically measured by the number of megawatt-hours 

of thermal energy (MWh-t) that the system can store or by the number of hours of storage. We 

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

charged at its power capacity, which is also reflected in constraint (8) of the model. Defining 

hours of storage in terms of charging or discharging hours will be nearly identical because of the 

high roundtrip efficiency of the TES system. The size of the powerblock is typically measured 

based on its rated output, measured in megawatts of electricity (MW-e). Since the solar field and 

TES are sized relative to the powerblock size, we hold the capacity of the powerblock fixed at 

110 MW-e. Moreover, we base the operating characteristics of the CSP plant on the baseline 

CSP system modeled in SAM version 2.0. This system assumes that the powerblock can be 

operated at up to 115% of its design capacity, which yields a maximum output of about 120 

MW-e net of parasitic loads. We also assume that the powerblock has a 6% EFOR, based on the 

system modeled in SAM.

Although our analysis assumes a parabolic trough CSP plant, our results can provide bounds on 

the capacity value of other CSP technologies. One technology currently under development is a 

salt tower CSP plant with direct TES. Such a plant would put all of the thermal energy collected 

by the solar field into a storage tank first, from which energy can then be fed into the 

powerblock. Such a design completely decouples solar energy collection from electricity 

generation, which makes the technology potentially more flexible than parabolic trough systems. 

The added flexibility from direct storage implies that salt tower plants should have better 

performance and capacity values than our estimates assuming a parabolic trough system with 

indirect TES. Parabolic trough developers are considering salt-HTF systems, which will also 

benefit from the added flexibility and improved performance of direct storage. 

In order to simplify the analysis, we assume that the CSP operator knows future weather and 

price patterns with perfect foresight in optimizing the dispatch of the plant. We further assume 

that the operation of the CSP plant is optimized 24 hours at a time, using a 48-hour optimization 

horizon. This 48-hour horizon is used to ensure that energy is kept in storage at the end of each 

day if it would provide value on the following day. The operation and profits of CSP plants have 

been shown to be relatively insensitive to these two assumptions [19]. 
10 

4 Data Requirements

This study focuses on the sites in the western United States listed in Table 1. Although the sites 

are not “optimized” for particular market conditions, they have relatively good solar resources 

and cover several states in the Southwest.

Table 1. Location of CSP Plants

CSP Site Coordinates

California – Death Valley 36.03o N, 117.45o W

California – Imperial Valley 33.65o N, 116.05o W

Arizona 32.57o N, 112.45o W

Nevada 36.55o N, 116.45o W

New Mexico 34.35o N, 107.35o W

The ELCC metric and approximation techniques described in Section 2.2 are used to estimate the 

capacity value of a CSP plant with and without TES during the years 1998–2005. These capacity 

value estimates will be highly sensitive to the coincidence between loads and solar resource, so 

accurate system data is vital for these calculations. Data requirements and sources used for this 

analysis are listed below.

1. Conventional generator data

This analysis uses the rated capacity and EFOR of each generator in the Western 

Electricity Coordinating Council (WECC) region.4

The conventional generator used as the benchmark unit in the ELCC calculation is a 

natural-gas-fired combustion turbine with an EFOR of 7%, which is based on the EFOR 

reported in GADS.

The rated capacities are obtained from 

Form 860 (Annual Electric Generator Report) data filed with the U.S. Department of 

Energy’s Energy Information Administration (EIA) [24]. The EIA data specifies a winter 

and summer capacity, which capture the effect of ambient temperature on the maximum 

operating point of thermal generators. The EIA data also specify the prime mover and 

generating fuel of each generator. These data are combined with the North American 

Electric Reliability Corporation’s (NERC’s) Generating Availability Data System 

(GADS) to estimate the EFOR of each generator [25]. The GADS data give historical 

average EFORs for generators based on generating capacity and technology.

2. Hourly load data

Hourly historical WECC load data for the years 1998–2005 are obtained from Form 714 

filings with the Federal Energy Regulatory Commission (FERC) [26]. The FERC data 

includes load reports for nearly all of the load-serving entities (LSEs) and utilities in the 

WECC, although some smaller municipalities and cooperatives are not reflected in the 

data. One issue with these load data is that LSEs do not always properly account for 

daylight savings time in their reports. As such, we also conduct a sensitivity analysis, 

which is described in Section 5.2, in which we shift all loads forward and backward one 

hour to bound the potential effect of misreported load data. 

 

4 WECC is one of the three U.S. interconnected grids and is largely isolated from the other two interconnects—

ERCOT and the Eastern Interconnect.
11 

3. CSP generation profile 

In order to provide the most robust capacity value estimates, multiple years of CSP 

generation data is needed. Since no CSP plants are operating at the exact study locations,5

we model the operation of a CSP plant using the optimization model developed by 

Sioshansi and Denholm [19]. Data requirements for the model include hourly weather 

and historical energy price data for each location. Hourly weather data are obtained from 

the National Solar Radiation Data Base.6

 

5 The Nevada Solar One, SEGS, and Saguaro CSP plants are near the study locations; however, we opt to use the 

same modeled data for purposes of comparison.

 For the two CSP plants in California, the 

California ISO market-clearing price of energy for the SP15 zone is used for the energy 

price in the optimization model (both of the plants studied are located in southern 

California, which the SP15 zone covers). For CSP plants in Arizona, Nevada, and New 

Mexico, load lambda data for Arizona Public Service (APS), Nevada Power (NP), and 

PNM (the largest utility in New Mexico) are used, respectively. The load lambda data are 

obtained from Form 714 filing with FERC [26]. Since load lambda data for APS in the 

year 1999 is not available, capacity values for the Arizona site are not calculated for this 

year.

6 These data are available for download at http://rredc.nrel.gov/solar/old_data/nsrdb/.
12 

5 Capacity Value of a Concentrating Solar Power Plant without 

Thermal Energy Storage

We begin by first computing capacity values of CSP plants without TES. These calculations use 

CSP generation patterns, which are optimized using the model described in equations (6) – (16) 

in the ELCC and capacity factor calculations. Since we hold the size of the powerblock fixed, the 

SM is the only size parameter that is adjusted in the plants that we simulate. Figure 2 summarizes 

the average (over the eight years studied) annual capacity values obtained based on the ELCC 

method. The capacity values are all normalized by the maximum net output of the CSP plant, 

which is 120 MW-e.7

Figure 2 shows that the SM has a direct impact on the capacity value of the CSP plant. This is 

because a CSP plant with a small solar field will often operate below its rated capacity, reducing 

its capacity value. As the solar field size increases, more thermal energy will be available during 

such hours, increasing the capacity value. On the other hand, a large solar field will lead to 

greater capital costs and if the CSP plant does not have TES, excess thermal energy that would 

exceed the powerblock rating will be wasted [19]. Sioshansi and Denholm [19] provide estimates 

of the amount of solar thermal energy wasted by a CSP plant without TES, as a function of solar 

field size. While the range of SMs shown is 1.0–3.0, the typical range of SMs for plants with 

storage is closer to 1.3–1.5. The optimal solar field size for a CSP plant without TES will depend 

on the relative capital cost of the components and the incremental value of the added energy and 

capacity value. If the CSP plant is coupled with TES, on the other hand, excess energy that 

would exceed the powerblock rating could be stored and used in later hours. This can make 

investments in larger solar fields reasonable and also increase the capacity and energy value of 

the plant. Selecting an appropriate or optimal solar field size requires an in-depth economic 

analysis. 

 

7 The same normalizing is done for all of the capacity value estimates in this report.
13 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

Arizona Location

Imperial Valley Location

Death Valley Location

Nevada Location

New Mexico Location

Figure 2. Average annual capacity value of a CSP plant with no TES in different locations

Figure 2 also shows that the rank ordering of the locations, in terms of capacity value, can vary 

as a function of solar field size. This is because adjusting the solar field size will change the 

operation of the CSP plants. In some cases, increasing the SM will allow the powerblock to start 

up during a high-LOLP hour when it would otherwise not be able to with a smaller solar field 

due to minimum-load constraints on the powerblock. For instance, with an SM of 1.4 or less, the 

Death Valley location has the highest capacity value, whereas the Arizona location has the 

highest capacity value with an SM of 1.5 or greater. 

Figure 2 represents average annual capacity values over the eight years of study. Capacity values 

can, however, vary significantly from year to year. This is also true for conventional generators, 

since a forced outage during a high-LOLP hour would yield a low capacity value in the year in 

which it occurs. Figure 3 shows capacity values for a CSP plant at the New Mexico location over 

the eight individual years. The differences in annual capacity values reinforce the fact that 

several years of generation data are required to provide a robust capacity value estimate for CSP.
14 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

2003

2000

1999

2005

2002

1998

2001

2004

Figure 3. Annual capacity value of a CSP plant with no TES at the New Mexico location

Figure 3 shows that with an SM of 1.0, the capacity value of the CSP plant in the year 2000 is 

more than four times greater than that in the year 2004. In order to better understand the reason 

behind this, the operations of the CSP plant during the highest-LOLP hours in those two years 

need to be compared. In the year 2000, the highest-LOLP hours occur on August 1. Figure 4 

shows the hourly output of the CSP plant and LOLPs on this day and shows that the plant has an 

average output of about 85 MW-e during the highest-LOLP hours. Since the output of the CSP is 

correlated with the LOLPs, a high capacity value for the plant can be expected. Figure 5 shows 

the amount of thermal solar energy collected by the solar field, which reflects the amount of 

solar irradiance, and load data. As can be seen in Figure 5, load data is strongly correlated with 

solar energy. This correlation is reasonable during a summer day due to the fact that summer 

loads are driven by cooling needs, which will be correlated with solar availability. 
15 

2 4 6 8 10 12 14 16 18 20 22 24

0

10

20

30

40

50

60

70

80

90

100

110

Energy (MW-e)

Hour

2 4 6 8 10 12 14 16 18 20 22 24

0

0.1

0.2

0.3

0.4

0.5

LOLP

LOLP

CSP Generation

Figure 4. Hourly LOLPs and dispatch of a CSP plant with no TES at the New Mexico location with 

an SM of 1.0 on August 1, 2000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0

100

200

300

400

500

600

700

800

900

1,000

Hour

Direct Normal Irradiance (W/m2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

60

70

80

90

100

110

120

Load (GW)

Load

Solar Radiation

Figure 5. Hourly loads and solar radiation at the New Mexico location on August 1, 2000

Figure 6 shows the operations of the CSP plant on August 10, 2004, which is the day with the 

highest LOLPs of that year. The figure shows that CSP generation is not correlated with LOLPs 

in this case. Hence, the capacity value of the CSP plant is relatively lower in 2004 compared to 

2000. Figure 7 shows the amount of thermal solar energy collected by the solar field and load 
16 

data for the day. Unlike the case shown in Figure 5, electricity demand is less correlated with 

solar energy, which causes lower capacity value in 2004.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0

10

20

30

40

50

60

70

80

90

100

Hour

Energy (MWh-e)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0

0.1

0.2

0.3

0.4

0.5

LOLP

LOLP

CSP Generation

Figure 6. Hourly LOLPs and dispatch of a CSP plan with no TES at the New Mexico location with 

an SM of 1.0 on August 10, 2004

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0

100

200

300

400

500

600

700

800

900

1,000

Hour

Direct Normal Irradiance (W/m2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

60

70

80

90

100

110

120

Load (GW)

Load

Solar Radiation

Figure 7. Hourly loads and solar radiation at the New Mexico location on August 10, 2004

Due to computational complexity and data requirements of the ELCC method, using an 

approximation method to estimate the capacity value of a CSP plant may be preferred. Doing so 
17 

can significantly reduce the computational time of the estimation but may affect the accuracy of 

the results. We compare the ELCC calculations to three approximation techniques that are based 

on the capacity factor of the plant. The first two use the highest-load and highest-LOLP hours of 

the year, whereas the third uses the highest-load hours but weighs the capacity factors by the 

hourly LOLPs. These three techniques are referred to as the “Top Loads,” “Top LOLP,” and 

“Top Weighted” techniques, hereafter. Figures 8 through 10 show the average annual capacity 

values of a CSP plant at the Imperial Valley location, based on the three approximation 

techniques. The figures show the capacity value estimates when considering the top 10, top 100, 

and top 10% of hours of each year, respectively. 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

ELCC

Top Weighted

Top LOLP

Top Load

Figure 8. Annual average capacity value of a CSP plant with no TES at the Imperial Valley location 

using the ELCC metric and approximation techniques that select the top 10 hours
18 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

ELCC

Top Weighted

Top LOLP

Top Load

Figure 9. Annual average capacity value of a CSP plant with no TES at the Imperial Valley location 

using the ELCC metric and approximation techniques that select the top 100 hours

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

ELCC

Top Weighted

Top LOLP

Top Load

Figure 10. Annual average capacity value of a CSP plant with no TES at the Imperial Valley 

location using the ELCC metric and approximation techniques that select the top 10% of hours 
19 

Comparing Figures 8 through 10 shows that using an approximation method that considers only 

the top 10 hours of each year yields a capacity value estimate that is closest to the ELCC metric. 

The figures also show that the “Top Weighted” approximation tends to have greater accuracy. 

Similar results are obtained for the other sites. This is demonstrated in Figures 11 through 14, 

which compare the three approximation techniques when considering only the top 10 hours of 

each year to the ELCC calculation for the other locations.

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

ELCC

Top Weighted

Top LOLP

Top Load

Figure 11. Annual average capacity value of a CSP plant with no TES at the New Mexico location 

using the ELCC metric and approximation techniques that select the top 10 hours
20 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

ELCC

Top Weighted

Top LOLP

Top Load

Figure 12. Annual average capacity value of a CSP plant with no TES at the Death Valley location 

using the ELCC metric and approximation techniques that select the top 10 hours

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

ELCC

Top Weighted

Top LOLP

Top Load

Figure 13. Annual average capacity value of a CSP plant with no TES at the Nevada location using 

the ELCC metric and approximation techniques that select the top 10 hours
21 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

ELCC

Top LOLP

Top Load

Top Weighted

Figure 14. Annual average capacity value of a CSP plant with no TES at the Arizona location using 

the ELCC metric and approximation techniques that select the top 10 hours

5.1 Effect of Expected Forced Outage Rates on Concentrating Solar Power 

Capacity Value

Our analysis thus far is based on modeling a system in which the conventional generator set 

varies from year to year. This is because we only model conventional generators that were in 

operation in each year, and this generator set changes from year to year as a result of generator 

construction and retirements. Moreover, the EFORs that are reported in the NERC GADS 

database are annual values, which will also vary from year to year depending on how many 

outages actually occurred. We use these annual EFORs to capture the fact that outage rates can 

vary from year to year. These differences in the conventional generator mix and EFORs can 

contribute to the differences in the annual capacity values of the CSP plants, which are shown in 

Figure 3. Figure 15 compares the average annual ELCC of a CSP plant at the Imperial Valley 

location in cases in which these parameters vary to a case in which these parameters are held 

constant. In the cases in which the parameters are held constant, we use the conventional 

generator mix that was installed in 2005 and EFORs that are averaged over the eight study years. 

Figure 15 shows that the ELCC values are nearly identical, with very little differences for 

smaller-sized CSP plants. The other locations have very similar results. As such, we can 

conclude that variations in the mix and reliability of other generators will have a negligible 

impact on the capacity value of a CSP plant. 
22 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

Different Gen. Set and EFOR

Same Gen. Set and EFOR

Figure 15. Average annual capacity value of a CSP plant with no TES at the Imperial Valley 

location based on ELCC metric with constant and varying conventional generator characteristics

5.2 Effect of Load Errors on Concentrating Solar Power Capacity Value

As noted before, another issue with our capacity value estimates is that some utilities do not 

properly account for daylight savings time in reporting their hourly loads in FERC Form 714 

filings. As such, it is possible that the simulated output of the CSP plant could be offset from the 

system loads and LOLPs. Since the capacity value of CSP is highly dependent on the correlation 

between solar resource availability and load, this potential mismatch in the data can lead to 

different capacity values than what we have estimated thus far. In order to bound the effect of 

misreported load data, we conduct the same ELCC calculations but shift the loads forward and 

backward one hour. Figure 16 shows average annual ELCC values for a CSP plant at the 

Imperial Valley location when the system loads are shifted in this way, and it compares them to 

the base case in which the reported loads are used without shifting. The figure shows that this 

shifting in the loads can reduce the estimated capacity value of a CSP plant by up to 5%; the 

other locations have similar results. The ELCC is reduced regardless of whether the load is 

shifted forward or backward, which suggests that most of the loads reported in the Form 714 data 

are correct. This is because solar resource and CSP generation will have some correlation with 

system loads, and this correlation is maximized when the loads are not shifted. 
23 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

Base Case

Shift Load One Hour Forward

Shift Load One Hour Backward

Figure 16. Average annual capacity value of a CSP plant with no TES at the Imperial Valley 

location based on ELCC metric with loads shifted

5.3 Effect of Sub-Hourly Variability on Concentrating Solar Power Capacity 

Value

Our analysis thus far is based on using hourly solar data and modeled CSP generation to 

calculate ELCCs and capacity factors. Solar radiation can have noticeable sub-hourly variation 

due to passing cloud cover. Sub-hourly variation may impact the capacity value and integration 

costs of many renewable resources, such as wind and solar PV. CSP may not suffer from this 

issue as much, however, since the HTF of a CSP plant will have some thermal inertia, which can 

maintain output during a brief reduction in solar radiation. Indeed, a CSP plant with direct TES 

will not suffer from short-term transients at all since the powerblock is fed by the TES system 

and not directly from the solar field. 

In order to determine the effect of sub-hourly variability on the capacity value of CSP, we 

compare our ELCC calculations when CSP output is modeled using one-minute and hourly data. 

We use one-minute solar data for a CSP plant located around the Nevada One site in Boulder 

City, Nevada. The coordinates of the modeled location are 35.80o

 N, 114.97o W. We use oneminute weather data from the year 2007 and compare a case in which the CSP plant is modeled 

using the one-minute data to a case in which hourly averages of the one-minute data are used 

instead. SAM and the CSP dispatch model are both adapted to model one-minute operations by 

appropriate scaling of the model variables and parameters. The same hourly conventional 

generator and load data are used in both cases; thus, any differences in the ELCC estimates are 

solely due to the one-minute weather data as opposed to hourly averages. Since the loads are 
24 

assumed constant during each hour, these ELCC estimates will not capture sub-hourly load 

variations and potential correlation between these and solar radiation patterns. 

Figure 17 shows the ELCC estimates for the CSP plant as a function of the solar field size, using 

the one-minute and hourly average data. The results show that the hourly average data will 

provide a close approximation of the ELCC if one-minute data is used. The maximum difference 

in the ELCC between the one-minute and hourly average data is 5.8%. For most plant 

configurations, the hourly average data tends to overestimate the ELCC. This is because with 

one-minute data, subhourly variations in solar radiation can keep the powerblock from running 

above its minimum operating point. These variations are not fully captured when the one-minute 

data is averaged. The differences in the estimated ELCCs are maximized for plants with an SM 

between 2.4 and 2.8. This is because plants with this configuration have more time periods in 

which solar radiation variability can prevent the powerblock from starting up, which is not 

captured without hourly data. Despite these issues, the small difference in the ELCC values 

suggest that hourly data can provide relatively good capacity value estimates if sub-hourly data is 

not available or too computationally intensive to work with. 

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

10

20

30

40

50

60

70

80

90

100

SM

Normalized Capacity Value (%)

Hourly Solar Data

One-Minute Solar Data

Figure 17. Capacity value of a CSP plant with no TES at the Boulder City, Nevada, location based 

on ELCC metric while using hourly and one-minute interval solar data
25 

6 Capacity Value of a Concentrating Solar Power Plant with 

Thermal Energy Storage

A major benefit of coupling CSP with TES is that TES will make the CSP plant more 

dispatchable. This is because TES allows the CSP plant to store excess energy collected by the 

solar field when it is not needed and discharge that energy later when solar resources are lower. 

Our results in Section 5 clearly show that the ability of a CSP plant to generate electricity in 

critical peak hours with high loads or LOLPs has a significant impact on capacity value. 

Therefore, adding TES to a CSP plant can increase its capacity value by allowing it to generate 

electricity during critical periods when solar resources are not available. As suggested earlier, 

adding TES to a CSP plant can also make a higher SM more economic since excess thermal solar 

energy collected by the solar field will not be wasted and can be stored and later used. 

Estimating the capacity value of a CSP plant is more complicated when it has a TES system. 

This is because a proper capacity value estimate must not only account for how much energy the 

plant generates each hour but also how much energy it could produce using energy in storage. 

One must account for energy in storage because if a system shortage event occurs, the CSP plant 

would, in principle, use energy in storage to help support the system. Modeling energy in storage 

is difficult because of the energy-limited nature of energy storage. Namely, if energy in TES is 

used in hour t, then it cannot be used in any hour s > t. A previous capacity value estimation 

technique for energy storage technologies was developed by Tuohy and O’Malley [23] and 

applied to pumped hydroelectric storage (PHS). Their technique uses operational data to 

determine the maximum potential output of the PHS device in each hour if the energy in storage 

is discharged at maximum capacity (based on the available energy in storage). The capacity 

value of the PHS device is then estimated from the maximum potential output data using a 

capacity-factor-based approximation technique. 

We apply a similar approach to estimate the capacity value of the CSP plant with TES. As in the 

case without TES, we assume that the operation of the CSP plant and TES is optimized to 

maximize the revenues that the CSP plant receives. Once the operation of the CSP plant is 

established, we can determine the maximum potential output of the CSP plant by first computing 

the maximum amount of thermal energy that can be delivered from the solar field and TES to the 

power block in each hour as: 

t tt t min{ . , .min{ , . } . .(1 )} (17) 1 SF d l SU u μ τ ττ φ ρ τ + = + −− −

Equation (17) defines the maximum thermal energy that can be delivered to the powerblock in 

each hour ( t

μ τ ) as the minimum of the powerblock’s rated capacity ( .

+ τ τ ) and the sum of 

thermal energy collected by the solar field and the amount of energy available in TES 

( 1 .min{ , . } t t + − SF d l φ ρ ). Equation (17) assumes that if the powerblock is offline it can be 

committed within the hour in case of a system shortage event [27]. We can also define how much 

of the t

μ τ MWh-t is taken from TES as:

 (18) tt t d SF μ μ = − τ
26 

Finally, the maximum potential output of the CSP plant, et

μ

, is given by: 

e ( ) ( ) ( ( )) (19) t t ht b t f Pd P f μμ μ μ =− − τ τ

Once we determine the maximum potential output, we estimate the capacity value using the top 

weighted approximation technique considering the 10 highest-load hours of each year since our 

results in Section 5 show this to be the most accurate approximation. 

We model the operations of the CSP plant under two different market settings. The first is an 

energy-only market, in which the CSP plant only receives payments for the electricity that it 

supplies to the market. The operation of the CSP plant in the energy-only market setting is 

optimized using the model given in Section 3 and is represented by objective function (6) and 

constraints (7) through (16). The other market setting that we examine is one in which the CSP 

plant can receive energy and capacity payments. In this case the optimization model must be 

changed to co-optimize the sum of energy and capacity payments. Further details of the capacity 

payment model are given in Section 6.2. 

6.1 Capacity Value of a Concentrating Solar Power Plant with Thermal Energy 

Storage in an Energy-Only Market

Figures 18 through 22 summarize the average annual capacity value of CSP plants at the 

different locations that we study. The figures show that the capacity values are typically 

increasing with the SM and the hours of TES in the CSP plant, although this relationship is not 

perfectly monotonic. At all of the locations, adding some TES increases the capacity value of the 

plant above the no-TES case. For instance, a CSP plant at the New Mexico location with an SM 

of 1.5 and no TES has a capacity value of about 78 MW-e. Adding one hour of TES to this plant 

addresses many of the days on which solar and load are not well correlated and increases its 

capacity value by 47% to 115 MW-e. 
27 

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 18. Average annual capacity value of a CSP plant with TES at the Imperial Valley location 

under an energy-only market setting

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 19. Average annual capacity value of a CSP plant with TES at the New Mexico location 

under an energy-only market setting
28 

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 20. Average annual capacity value of a CSP plant with TES at the Death Valley location 

under an energy-only market setting

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 21. Average annual capacity value of a CSP plant with TES at the Nevada location under an 

energy-only market setting
29 

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 22. Average annual capacity value of a CSP plant with TES at the Arizona location under an 

energy-only market setting

In some cases, however, adding an incremental hour of TES or increasing the solar field size may 

cause a slight reduction in the capacity value of a plant. This is because different CSP plant 

configurations will yield different operational decisions, and in some cases a larger CSP plant 

may have less energy in TES during a high-LOLP hour. For example, a CSP plant at the Nevada 

location with four hours of TES and an SM of 2.2 has a capacity value of 117 MW-e in 1999. 

The same CSP plant with an SM of 2.7 would have a lower capacity value of only 95 MW-e in 

1999. This difference in the capacity value is due to less energy being in the TES of the larger 

CSP plant on July 12, which is the day with 5 of the 10 highest hourly LOLPs of the year. The 

larger CSP plant has less energy in storage because the larger solar field provided sufficient 

energy to operate the powerblock above its minimum operating point in the afternoon of the 

previous day. The smaller solar field of the CSP plant with an SM of 2.2 could not meet this 

minimum-load constraint, and as such the output of the solar field was stored. Thus, the CSP 

plant with an SM of 2.2 can, on average, generate up to 74 MW-e during the five highest-LOLP 

hours on July 12. The larger CSP plant with an SM of 2.7 can only generate up to an average of 

54 MW-e during these hours. Figure 23 shows the amount of energy in storage and energy 

collected by the solar field in each hour on July 12 for these two CSP plant configurations. It is 

important to note that due to weather patterns on this particular day, the solar field only collects 

solar energy during hour 18—the output of the field is zero in the remaining hours. 
30 

Figure 23. LOLP, energy from solar field and energy in storage for a CSP plant at the Nevada 

location with four hours of TES and different SM values on July 12, 1999

Adding TES can also, in some cases, reduce the capacity value of the CSP plant, although this is 

less typical. For example, a CSP plant at the Death Valley location with an SM of 2.7 and one 

hour of TES has a capacity value of 79 MW-e in 1999. Increasing TES by one hour for the same 

CSP plant reduces its capacity value to 75 MW-e. The reduction in capacity value stems from the 

fact that energy prices are not necessarily correlated with hours with highest LOLPs, as 

suggested by Figure 24, which is a scatter plot of California ISO energy prices and LOLPs in the 

year 1999. The operation of both of the CSP plants on July 12, which is the day on which the 

highest LOLPs of the year occur, is shown in Figure 25. 
31 

Figure 24. LOLP versus energy price for the Death Valley location in year 1999

Note: The x-axis used to represent LOLPs has a logarithmic scale.

Figure 25. LOLP, energy from solar field and energy in storage for a CSP plant at the Death Valley 

location with an SM of 2.7 and different TES sizes on July 12, 1999
32 

Figure 25 shows that in hour 16, during which the LOLP is the highest, the larger CSP plant has 

less energy in storage compared to the smaller CSP plant. This reduces the capacity value of the 

larger CSP plant. The reason behind these operations is that in hours 12 through 15 of the day, 

the larger CSP plant will use energy in TES to generate electricity since energy prices are higher 

in these hours than in hours during which the highest LOLPs occur. The smaller CSP cannot do 

so since its smaller TES system does not have sufficient energy in storage to operate above its 

minimum generation point during these hours. These operational differences leave the smaller 

CSP plant with more energy in TES during hour 16, which yield the higher capacity value.

6.2 Capacity Value of a Concentrating Solar Power Plant with Thermal Energy 

Storage in a Capacity Market

In Section 6.1 we estimate the capacity value of a CSP plant with TES in an energy-only market. 

The results there suggest that adding TES to a CSP plant will tend to increase the capacity value 

of the plant, although this relationship is not monotonic. This is because energy prices and 

LOLPs will not always be perfectly correlated, and there can be high-LOLP hours that have 

lower energy prices than other hours with lower LOLPs. An example of this is demonstrated in 

Figure 25. An alternative market design that could help reduce the impact of such price and 

LOLP patterns is an energy and capacity market. Under such a market design, the CSP plant 

receives both payments for electricity that it generates, as well as the capacity that it provides the 

system. Many electricity markets have moved toward adopting capacity markets. Even in 

systems that do not have an explicit capacity market, such as the APS, NP, and PNM service 

territories, a model that maximizes the sum of energy and capacity payments may be more 

appropriate. This is because such integrated utilities would likely operate a CSP plant to 

minimize its overall energy supply costs—which would be akin to our energy revenue 

maximization. However, such utilities would also likely adjust the operation of their plants to 

have more energy available in TES during anticipated system shortage events. 

The introduction of a capacity market tends to increase the capacity value of a CSP plant since 

capacity payments typically have performance requirements that are related to the capacity value 

of a generator. Most capacity markets impose financial penalties on generators that do not meet 

the performance requirements. Although the specific performance requirements differ from 

market to market, they are typically related to how much firm capacity a generator has available 

during system shortage events. Our capacity market model is based on the forward capacity 

market (FCM) used by ISO New England, although the modeling framework is sufficiently 

general that it can be adapted to model other markets as well.

6.2.1 Capacity Market Procedures

The objective of a capacity market is to encourage enough generating capacity to enter the 

system so that reliability requirements are met. This objective is met by a forward capacity 

auction (FCA).8

 

8 These auctions are held three years in advance for ISO New England’s FCM.

Resources that participate and are selected in the FCA are eligible to receive 

capacity payments throughout the capacity commitment period based on their capacity 

commitment obligations. Capacity payments are subject to certain performance requirements, 

however. Performance requirements are set so that the capacity resources contribute to system 

reliability during hours in which shortage events could occur. The definition of shortage events 

will differ between capacity markets. Some markets, such as the FCM, define shortage events as 
33 

periods during which reserves (spinning and non-spinning reserves) fall below certain levels. 

This definition does not necessarily imply that supply is less than demand during the shortage 

event hours. For instance, if the reserve level falls to 1%, generating capacity will still be greater 

than demand, but due to low reserve levels the probability of having a capacity deficiency is 

high. Based on this definition, there is a one-to-one relationship between shortage event hours 

and the hourly LOLPs. In this study, the 10 hours of each year with the highest LOLPs are 

defined as shortage event hours. 

A generator that fails to provide its contracted capacity during a shortage event hour will incur 

financial penalties. The FCM sets penalties based on the cost of replacement capacity. We 

assume that the capacity market uses the cost of a natural-gas-fired combustion turbine, which 

we assume to be $671/kW in 2008 dollars, to set the penalties. This cost is then translated into an 

annualized cost of $73.81/kW-year, using an 11% capital charge rate. We assume that the 

capacity market imposes a penalty that is equal to half of this annualized cost, which is reflective 

of the penalties imposed in the FCM. We use consumer price index data to deflate the cost of the 

combustion turbine to previous-year dollars.

6.2.2 Optimization Model

In order to determine the operations of a CSP plant in an energy- and capacity-market setting, 

our model must be adjusted to maximize the sum of energy and capacity payments and net of 

any capacity penalties. We follow a similar approach to that used in Section 6.1 and add 

variables to our optimization model that determine the maximum potential generation from the 

CSP plant in each hour (based on energy in TES and collected by the solar field). The difference 

between the firm capacity sold and this maximum potential generation is the shortfall from the 

capacity commitment, and these shortfalls are penalized in the objective function to reflect 

capacity penalties. In order to give the formulation of the model, we define the following 

parameters:

: Market clearing price of capacity ($/MW-year)

: Penalty factor for unserved capacity requirements 

: Set of hours during which shortage events occur

c M

PF

H

We also define the following variables:

: Firm capacity sold

e : Maximum potential net electric energy (MWh-e) produced by powerblock in each hour

sold

t

C

μ

: Maximum potential thermal energy taken out of storage (MWh-t) in each hour

: Maximum potential total thermal energy (MWh-t) fed to powerblock in each hour

: Shortfall from capacity commit

t

t

short

t

d

C

μ

μ τ

ment in each hour

The formulation of the model is then given by: 

max 

short

ec c t

t t sold

t T t H sold

C ( M c ).e M .C ( M .PF. ),

∈ ∈ C ∑ ∑ −+ − (20) 
34 

s.t. (7)-(16)

e short C C t sold t

μ ≥ − ∀ ∈t T (21) 

1 t t d .l μ ≤ ρ − ∀ ∈t T (22) 

 tt t t .d SU . r SF μ μ − ++ ≤ φ τ τ. ∀ ∈t T (23) 

 e t t ht b t f ( ) P ( d ) P ( f ( )) μμ μ μ =− − τ τ ∀ ∈t T (24) 

tt t . .u . .u μ ττ τ ττ − + ≤ ≤ ∀ ∈t T (25) 

Objective function (20) maximizes the sum of net energy and capacity revenues. The last term in 

the objective function corresponds to penalties associated with shortfalls from capacity 

commitments. Constraints (7) through (16), which are from the original energy-only model, are 

included since the same underlying constraints on the operation of the CSP plant apply. 

Constraint (21) defines the hourly capacity commitment shortfall as the difference between firm 

capacity sold and the maximum potential net electrical generation of the CSP plant. Constraint 

(22) restricts the potential thermal energy taken out of storage (MWh-t) in each hour, based on 

the ending storage level of the previous hour. Constraint (23) limits the total amount of potential 

thermal energy used in the CSP plant to not be greater than the energy collected by the solar 

field. Constraint (24) defines the maximum potential output of the CSP plant in each hour. 

Finally, constraint (25) imposes restrictions on potential capacity of the CSP plant when the 

powerblock is online.

Because the penalty term in the objective function is non-linear in the variables, we solve this 

model by fixing the value of Csold and solving the model iteratively until finding a maximum. For 

the cases that we consider, selling 120 MW-e of capacity (the maximum net output of the CSP 

plant) maximizes CSP revenues.

6.2.3 Results

The model, given by objective function (20) and constraints (7) through (16) and (21) through 

(25), is used to determine the optimized operation of the CSP plant in each hour. We then apply 

the same capacity-factor-based approximation technique used in Section 6.1 to estimate the 

capacity value of the plant. Figures 26 through 30 summarize the average annual capacity value 

of the CSP plants at the different locations.
35 

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 26. Average annual capacity value of a CSP plant with TES at the Imperial Valley location 

under an energy and capacity market setting

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 27. Average annual capacity value of a CSP plant with TES at the New Mexico location 

under an energy and capacity market setting
36 

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 28. Average annual capacity value of a CSP plant with TES at the Death Valley location 

under an energy and capacity market setting

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 29. Average annual capacity value of a CSP plant with TES at the Nevada location under an 

energy and capacity market setting9

 

9 The unusual result for Nevada (compared to the other locations) is due to a day in 1999 where an SM of less than 

2.7 was insufficient to meet the minimum generation requirement during one 3-hour period of high LOLP. This 

demonstrates the need to examine performance over a large period of time to examine the impact of variability on 

resource adequacy.
37 

0 2 4 6 8 10 12

60

65

70

75

80

85

90

95

100

Hours of TES

Normalized Capacity Value (%)

SM 2.7

SM 2.3

SM 1.9

SM 1.5

Figure 30. Average annual capacity value of a CSP plant with TES at the Arizona location under an 

energy and capacity market setting

Figures 26 through 30 show the benefits of implementing a capacity payment scheme, as 

opposed to an energy-only market. Adding capacity payments tends to slightly increase the 

capacity value of the CSP plant. Moreover, the capacity value is more monotonic in the size of 

the plant. There are still, however, some cases in which increasing the size of a CSP plant can 

result in a slight reduction in the capacity value. Even when the capacity payment is added, there 

may still be high-LOLP hours in which the value of energy (when accounting for the energy 

price and capacity penalty) is lower than other hours with lower LOLPs. However, these cases 

are rare and their magnitude (in terms of capacity value reductions) is relatively small.

More broadly, contrasting these results with the energy-only market design, and Figure 23 in 

particular, demonstrates the benefit of capacity payments (or co-optimizing the energy and 

capacity value of a CSP plant) in improving the system benefits of CSP. Figure 23 shows that the 

larger CSP plant has a lower capacity value because of poor correlation between energy prices 

and LOLPs and the lack of solar resource during high-LOLP hours. If a CSP plant can anticipate 

potential high-LOLP periods or shortage events, the total value of the plant to the system can be 

drastically increased by slightly adjusting plant operations. 
38 

7 Conclusions

This study estimates the capacity value of a CSP plant at a variety of locations within the WECC, 

while accounting for rational dispatch behavior of a CSP operator. This is done by optimizing the 

operation of the CSP plant and by using standard reliability-based capacity value estimation 

techniques. Although the ELCC metric is the most accurate estimation technique, we show that 

capacity-factor-based approximation methods can closely estimate the ELCC value. 

When introducing TES, the capacity value of the CSP plant is more difficult to estimate since 

one must account for energy in storage. We apply the capacity-factor-based technique used by 

Tuohy and O’Malley [23] under two different market settings: an energy-only market and an 

energy and capacity market. Our results show that adding TES to a CSP plant can increase its 

capacity value significantly at all of the locations. Adding a single hour of TES significantly 

increases the capacity value above the no-TES case, in most cases to above 90%. Although 

additional hours of TES increase the capacity value of the plant, their marginal benefit is less 

than the first hour of TES. Nevertheless, Sioshansi and Denholm [19] show that a greater number 

of hours of TES can have incremental energy and ancillary service benefits. Since energy prices, 

LOLPs, and solar resource will not be perfectly correlated, the use of capacity payments (or cooptimization of energy and capacity value) can significantly increase the value of a CSP plant to 

the power system compared to an energy-only market. 

The capacity value estimates we provide examine a single CSP plant, which will have a marginal 

effect on the rest of the system. Clearly, changes in the generation mix or load patterns could 

affect the capacity value of a CSP plant. Adding more CSP (or PV) plants, especially if they are 

concentrated at similar locations in the system, can reduce the marginal capacity value of 

additional CSP capacity. Adding TES to a CSP plant can alleviate this reduction in the marginal 

capacity value, however, since it gives the CSP plant additional flexibility in dispatching its 

generation. 
39 

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