ABTRACT
Wind and solar power are currently most promising renewable energy sources especially
in the electricity generation sector over the past decades in the United State. Solar
thermal power stations together with wind farms play important roles in the green energy
industry due to the potential to produce electricity for 24hr per day. Although investing in
both solar and wind may be profitable under particular conditions of price and cost
uncertainty, the theoretically optimal strategy is generally investing in only one technology,
that is, solar or wind. In this study Data Envelopment Analysis (DEA) is implemented to
quantitively evaluate the relative efficiencies of 8 concentrating solar powers and 19 wind
farms in the United States. Input – and output-oriented constant return to scale (CRTS)
and variable return to scale (VRTS) radial models are applied to pre-determined three
input and two output variables. The CRTS and VRTS models yielded different results
when comparing CSP and wind farms in the United States. For the CRTS results, the
wind farms outperform the CSP stations while with the VRTS results, there is no
difference between the wind farms and CSP stations overall efficiencies.
1. Introduction
Both solar thermal power stations and wind farms play vital roles in the green energy
industry because they have the potential to produce electricity for 24hr per day with little
impact on the environment.
The United States is home to one of the largest and fastest-growing wind markets in the
world. According to sources of US electricity generation in 2019, wind energy surpasses
hydro to become the largest renewable electricity generation and accounts for 7.3% of
the total 4.12 TWh.[13]
Concentrating solar power (CSP) is a solar technology besides the photovoltaic that is
cheaper and more popular around the world. In the past decade, integrating thermal
energy storage into the CSP increases the time each day that a solar power plant can
generate energy. The first part of this document discusses the previous efforts that
assessed the efficiency difference between solar energy and wind energy.
To determine whether CSP is more efficient than wind technology or vice versa, this study
will use data envelopment analysis method (DEA). DEA is a nonparametric method that
compares feasible input and output combinations based on the available data only. The
second part of this document discusses some notable research on DEA applied to CSP
and wind energy in the United States.
1.1. Concentrating solar power technology
The US Southwest has huge potential production of solar energy. Figure 1 depicts the
horizontal solar irradiance (kWh/m2/D) of the US with the average value of the Southwest
area larger than kWh/m2/D. So, most of the current CSP power stations are placed in
California, Nevada, and Arizona.
Fig.1. Solar radiation map of the US [16]
CSP is a major utility-scale application of solar thermal energy. Sunlight is focused by
mirrors or lenses to reach a high temperature (around 570oF to be effective and
economically applicable) to either generate steam to propel a turbine that produce an
electric current. This system stores heat energy in a thermal storage unit for later use
during peak hours, in the evening or on a cloudy day (Figure 2). Within current technology,
heat is much cheaper to store than electricity.
Fig.2. Schematic of a parabolic trough power plant with a thermal storage system [17]
This study only examines two type of design: parabolic trough power plant and solar tower
that are implemented in the United States. In parabolic trough collector, long, U-curved
mirrors focus the rays of the sun into an absorber pipe (Figure 3). The mirrors track the
sun on one linear axis from north to south during the day. The pipe is placed above the
mirror in the center along the focal line and has the heat-absorbent medium (mineral oil,
synthetic oil) running in it. The hot fluid is conveyed to a heat engine that uses the heat
energy to generate electricity.
Fig.3. Schematic of a parabolic trough collector [18]
Solar tower has rings of small individual flat mirrors (heliostats) surrounding a central
power tower (up to 100-200m), on top of which sits a receiver that gathers the reflected
radiation (Figure 4). The receiver contains a kind of fluid medium that can achieve an
extremely high temperature. The heat produces high-pressure steam for electricity
generation. Solar tower possesses a higher efficiency than parabolic trough power plants
(approximately 20% vs 15%) resulting from its higher concentrating ratio and higher
temperature [17].
Fig.4. Heliostat power tower station [19]
1.2. Wind energy power in the United States
Figure 5 illustrates the growth of cumulative installed wind capacity and generation of
wind power in the United States from 2000 to the end of 2020 [27]. In 2000, the nameplate
generating capacity for wind energy was only 2.54 GW, it increased to 112.48 GW by the
end of 2020. The electricity generation of wind power increased from 5,593 GWh in 2000
to 337,510 in 2020. There are more than 1000 utility-scale wind farms and 500 windrelated manufacturing facilities spread across the United States.
Wind power provided 7.3% of U.S. electricity generation in 2019 and it surpassed hydro
to become the largest source of renewable electricity generation (Figure 6). Wind power
has significant contribution to the United States environmental benefits, avoided 198
million metric tons of CO2 emissions in 2019 [20]. Besides the environmental benefits,
wind industry created more than 120,000 jobs across all 50 states, delivered $1.6 billion
in state and local tax payments and land-lease payment in 2020. Besides, the wind
industry also delivered more than $143 billion of investment in the last decade [28].
Fig.5. Wind power in the United States from 2000 to 2020 [27]
Fig.6. Sources of U.S. electricity generation in 2019 [21]
2. Literature review
Prior research efforts assessed the efficiency between solar energy and wind energy by
using analytical processes, empirical methods, and economical analysis. However, these
previous studies focused upon the performance of photovoltaic technology power plant
not the CSP sites.
Akash et al. (1999) used an analytical hierarchy process (AHP) methodology to evaluate
the fossil fuel, hydro, nuclear, solar photovoltaic, and wind power system in terms of costs,
benefits, and cost-to-benefit ratios in Jordan. AHP can assist decision makers to evaluate
a problem in the form of a hierarchy of references through a series of pairwise comparison
of relative criteria. Subjective judgments on the relative importance of each part are
represented by assigning numerical values. This study evaluated benefits and costs to
select the optimum system for electricity power generation in Jordan. They found out the
best systems are the systems with the lowest cost-to-benefit ratios. Solar photovoltaic
has the lowest ratio (0.058) and is followed by wind (0.061). They concluded that solar
photovoltaic electrical power plants have the potential to be the best type of system for
electricity production in Jordan. However, wind electrical technology is also another
potential candidate with a very close relative weight.
El-Ali, Moubayed, and Outbib (2007) conducted a laboratory experiment to compare solar
photovoltaic and wind energy in Lebanon. They used a mobile solar panel of a 50W
system and a wind converter of a 400W system for their study and performed the
experiments in the Lebanese University. The generated power by the solar panel and
wind machine is recorded for each month of 2006. Due to the difference of wind and solar
systems in term of rated power (50W vs 400W), they multiplied the measured data given
by the solar panel by eight. The efficiency of the wind energy conversion is more than 2.2
times the one of the solar photovoltaic based on the collected data and the efficiency
calculations. The cost analysis for the capital expenditure showed the price of the solar
panels is 3 times more expensive than one wind turbine. The efficiency calculation
together with the cost analysis proved that the wind energy can deliver more than solar
energy. One of the limitations of this study is the generated solar energy is maximum due
to the cleared sky around the study site and the panel surface is always perpendicular to
the solar rays, but the wind speed around this facility is not optimum for the wind machine.
Chang and Ken (2019) determined the economical investment for wind and solar energy
in Texas with economic parameters including payback periods. They used a 50kW wind
turbine system and a 42kW photovoltaic to collect field data. They calculated yearly
production by analyzing the collected data. The results are similar to El-Ali et al.’s study
with the efficiency of wind energy is more than 2.8 times the solar energy. Hence, the
payback periods were estimated to be around 13 years for wind and 19 years for solar
photovoltaic. The advantage of this study is extending the analysis to different areas in
Texas with the same wind turbine, photovoltaic system, and economic parameters
assumption. While the payback periods for wind maintain around 13 years, the payback
periods for solar photovoltaic are in a range of 11.5 – 15 years and depend on the initial
cost.
Oguz and Senturk (2019) also used the payback periods together with the environmental
impacts to investigate wind energy and solar energy on Bozcaada Island, Turkey. An
existing wind farm and a proposed photovoltaic plant are compared by using life cycle
assessment (LCA) and life cycle cost analysis (LCCA). LCA is an evaluation procedure
for the environmental impacts associated with all the stages of a product’s life that are
from raw material extraction through materials processing, manufacture, distribution, use,
and disposal. LCC can predict the total cost of a product throughout the lifespan and is
becoming popular around the world. Results of this study indicate that wind farm is
cleaner and more economical than the photovoltaic power plant for Bozcaada Island.
Gerlach et al. (2011) investigate the competitive or complementary characteristics of
photovoltaic energy and wind energy. In this study, the global potential wind speed and
global horizontal irradiation are the input to calculate possible hourly power generation of
PV and wind power plants in every region of a 1 ox1o mesh of latitude and longitude
between 65oN and 65oS. In every 1ox1o area, two power plants of 1 GW are simulated,
one of PV and one of wind power. The power generation calculation results suggested
the global energy supply potential of photovoltaic and wind power by far exceeds the
energy demand of human mankind. For solar photovoltaic power, the total amounts
increase from the polar caps toward the equator due to the irradiation conditions. On the
other hand, high wind potential power is observed above areas such as the ocean and
deserts. This study proposes that photovoltaic and wind power are technologies that
complement one another. In other words, using a hybrid solar-wind power station will offer
complimentary power feed-in and further reduces the need for balancing power.
In contrast with Gerlach et al.’s study, Gazheli and Bergh’s (2018) approach showed that
the theoretically optimal strategy, in general, investing in only one technology, solar
photovoltaic or wind. This result led to the most argument that diversifying renewable
energy in most countries is a mistaken strategy. This study used the Real Option
approach as it can handle uncertainty about prices and learning, as well as irreversibility
associated with investment decisions. If all capital is invested in one technology, the
learning rate will reduce the critical threshold for exercising it. So, it is important for the
policymaker and the investors to aware what is the most efficient renewable technology
in their countries and encourage investment in the efficient technologies.
The research from Tian Tang (2018) is the first empirical finding that suggests that a wind
farm’s performance has improved over time as the project operator accumulates more
experience. He evaluated 576 US wind projects between 2001 and 2012 using the
channels in the learning curve methods such as learning by doing, learning by searching,
learning by interacting, knowledge spillovers, and the capacity factor of a wind farm.
Learning rate specifies the quantitative relationship between the cumulative experience
of the technology and its cost. By increasing the market share, the cost of a new
technology will decrease and become a more attractive choice than the incumbent
technologies. This study found the performance improvement in the US wind industry by
the collaboration between turbine manufactures and the transmission system operator.
Pietzcker et al. (2014) investigated the role of solar power in achieving climate mitigation
targets and which solar technology will be dominant in the long term (between
photovoltaic and concentrating solar power). He analyzed the economic potential of both
technologies with the economy model REMIND. The results showed that solar power
becomes the dominant electricity source that supplies from 19% to 48% of total 2010 –
2100 electricity. Photovoltaic is cheaper on a direct technology basis and is thus deployed
earlier. But, at high supply shares, the photovoltaic integration costs become so high that
concentrating solar power gains a competitive advantage and is rapidly developed and
overtaking photovoltaic.
Saglam (20171) developed a two-stage data envelopment analysis to quantitatively
evaluate the relative efficiencies of 39 state’s wind power performances for electrical
generation. The results indicate that more than half of the states operate wind power
efficiently with the West-North and South-Central states operate wind power more
productively than the other states by taking advantage of high average wind speed. He
later expanded his research (20172) to the wind farm scale by evaluating the relative
efficiencies of the 236 large utility-scale wind farms. DEA results indicate two-thirds of the
wind farms are operated efficiently but only 6% of them are operating at the most
productive scale size. Besides, Saglam suggested that old technology wind turbines
should be replaced with more productive current technology to increase wind farm’s
performance and is confirmed later by Tian Tang (2018).
Sueyoshi and Goto (2014) applied the DEA-based performance evaluation to PV power
stations in Germany and the United States. A total of 160 PV power stations (80 in
Germany and 80 in the United States) are used for the computation. The empirical results
of this study exhibit that PV power stations in Germany operate more efficiently than those
of the United States. The United States must utilize its solar and land more efficiently and
emulate some of its structure, incentives, and policies.
Sueyoshi and Goto (2017) extended their previous works and examined the type of
Return to Scale (RTS) on very large PV power stations in the United States and Germany.
The RTS measurement is classified into two categories: input-based RTS and outputbased RTS. This study discussed how to handle an occurrence of multiple intercepts
within the framework of the input-based and output-based RTS classifications.
In their latest study, Sueyoshi and Goto (2019) utilized DEA to evaluate the performance
of solar thermal power stations from three regions (i.e., the United States, Spain, and the
other nations) throughout the world and examine which region most efficiently produced
solar thermal power. Their empirical results showed that the CSP power stations in the
US were the most efficient among three regional groups. On the other hand, there is no
significant efficiency difference between CSP technologies (i.e., parabolic trough,
heliostat power tower, and linear Fresnel reflector). Thus, the location of CSP sites is
more important than their technologies at the current moment.
3. Methodology
3.1. Data Envelopment Analysis (DEA)
Data envelopment analysis (DEA) is a common method to apply for energy and
environmental issues. More than 693 articles using DEA method are published in which
407 were related to energy issues and 270 were associated with environment and
sustainability (Sueyoshi et al., 2017). DEA has both advantages and disadvantages and
should be applied with caution. However, the notable characteristic of DEA is linking the
technology innovation in engineering with political and managerial efforts to solve the
problems due to climate change and environmental pollutions.
This research uses the radial DEA methods that are first proposed by Charnes et al.
(1978) and Banker et al. (1984), respectively, constant returns to scale (CRTS) or variable
returns to scale (VRTS).
There are two approaches for both CRTS and VRTS models. The input-oriented model
minimizes input variables while obtaining the given current level of output, and the outputoriented model maximizes output variables while keeping the given current level of input
fixed.
3.2. Input-oriented model
The input-oriented model’s objective is to minimize input variables while maintaining the
current level of output fixed.
Input-oriented under CRTS:
Minimize
θ
s.t.
− ∑𝑛𝑗=1 𝑥𝑖𝑗 𝜆𝑗 + 𝜃𝑥𝑖𝑘 ≥ 0 (𝑎𝑙𝑙 𝑖)
(1)
∑𝑛𝑗=1 𝑔𝑟𝑗 𝜆𝑗
≥ 𝑔𝑟𝑘 (𝑎𝑙𝑙 𝑟)
𝜆𝑗 ≥ 0 (𝑎𝑙𝑙 𝑗)
𝜃: 𝑈𝑅𝑆
In Model (1), θ is an input-oriented efficiency measure determined by Model (1) with n
number of decision-making units (DMUs), s number of good output and m number input
variables. The variable (λ) is an unknown column vector of intensity variables for
connecting xij and grj on all (DMUs). The k indicates a specific DMU to be examined by
DEA.
The input oriented VRTS model can be formulated by adding a convexity constraint to the
Model (1):
Minimize
θ
s.t.
− ∑𝑛𝑗=1 𝑥𝑖𝑗 𝜆𝑗 + 𝜃𝑥𝑖𝑘 ≥ 0 (𝑎𝑙𝑙 𝑖)
(2)
∑𝑛𝑗=1 𝑔𝑟𝑗 𝜆𝑗
≥ 𝑔𝑟𝑘 (𝑎𝑙𝑙 𝑟)
∑𝑛𝑗=1 𝜆𝑗
=1
𝜆𝑗 ≥ 0 (𝑎𝑙𝑙 𝑗)
𝜃: 𝑈𝑅𝑆
3.3. Output-oriented model
The output-oriented model’s objective is to maximize output variables while keeping the
current level of inputs fixed.
Output-oriented CRTS:
Maximize
𝜏
(3)
∑𝑛𝑗=1 𝑥𝑖𝑗 𝜆𝑗
s.t.
≤ 𝑥𝑖𝑘 (𝑎𝑙𝑙 𝑖)
− ∑𝑛𝑗=1 𝑔𝑟𝑗 𝜆𝑗 + 𝜏𝑔𝑟𝑘 ≤ 0
(𝑎𝑙𝑙 𝑟)
𝜆𝑗 ≥ 0 (𝑎𝑙𝑙 𝑗)
𝜏 ∶ 𝑈𝑅𝑆
The level of operational efficiency is measured by an unrestricted measured as follows:
Efficiency score = 1/ 𝜏 ∗
Output-oriented VRTS:
Maximize
s.t.
𝜏
(4)
∑𝑛𝑗=1 𝑥𝑖𝑗 𝜆𝑗
≤ 𝑥𝑖𝑘 (𝑎𝑙𝑙 𝑖)
− ∑𝑛𝑗=1 𝑔𝑟𝑗 𝜆𝑗 + 𝜏𝑔𝑟𝑘 ≤ 0
∑𝑛𝑗=1 𝜆𝑗
(𝑎𝑙𝑙 𝑟)
=1
𝜆𝑗 ≥ 0 (𝑎𝑙𝑙 𝑗)
𝜏 ∶ 𝑈𝑅𝑆
4. Data Description
This study measures and quantitatively evaluates the relative productive efficiencies of 8
CSP power stations and 19 large wind farms, by using both input- and output-oriented
CRTS and VRTS models with three input and two output variables. Figure 7 depicts the
graphical representation of the DEA models. This section presents the selection of both
input and output variables with the detailed collection and the organizations of the data
set.
Fig.7. Graphical representation of DEA models
4.1. Input variables
The data set includes three input variables: (1) Capital expenditure (CAPEX), (2) the field
aperture area, and (3) the average annual potential energy.
Capital expenditure (CAPEX): is the money an organization or corporate entity spends to
buy, maintain, or improve its fix assets such as buildings, vehicles, equipment, or land.
The data of the CSP power stations are taken from the National Renewable Energy
Laboratory (NREL) Database [23]. The data for every wind farm is collected from the
articles, independent reports, and the website of the companies.
The field aperture area is the total area of land use associated with power station plants.
Development of a power plant results in a variety of temporary and permanent (lasting
the life of the project) disturbances. These disturbances include land occupied by energy
collector equipment (wind turbine pads and sun tracking mirrors), access roads,
substations, service buildings, and other infrastructure which physically occupy land area,
or create impermeable surface. Figure 8 provides a simplified illustration of the field
aperture area of a wind farm. This measurement is taken in square meters. This study
collects the data for land area from several sources. For CSP the data is listed on the
NREL database [23], while the data of wind farms are estimated from the number of wind
turbines of each wind farms [22].
The average annual potential energy is measured by kWh/m2/year and indicates the
kilowatt hours of solar or wind energy that could be harvested per square meter per year.
The data for wind farms is calculated from wind speed and can access from Global Wind
Atlas [24]. For the solar, the data comes from the NREL map [25].
The gross generation capacity indicates the full-load, sustainable output of a power
station. This is a primary measure for any power station and shows the potential power a
station can output. Many power stations do not operate at this capacity for various
reasons, including customer demand, equipment inefficiency and the fluctuation of the
daily potential energy. All gross generation of CSP power station come from the NREL
database [23] while the data of wind farms are taken from the open source [26].
The average annual power generation measures a power station’s generated power in
MWh/year. This is the product that electric companies provide to the consumers. This
output is the end goal of any commercial power station, as it dictates how much revenue
a power station can generate in a year. All data for the average annual power generation
in 2019 is obtained from the U.S. Energy Information Administration [27].
Fig.8. Illustration of direct impact area of a wind plant land use [22]
Fig.9. The average annual potential energy of wind power in the United States [24]
Fig.10. The average annual potential energy of solar power in the United States [25]
Table 1 & 2 exhibit all the data set of 8 CSP power stations and 19 wind farms in 2019 in
the United States. Table 3 summarizes descriptive statistics that contains an average, a
maximum, a minimum and a standard deviation (SD) on each factor.
Table 1. Data on solar thermal power stations
DMU#
Facility
Input
CAPEX
(mil.USD)
Output
Field
Resource
aperture
capacity
area (m2) (kWh/m2/yr)
Gross
output
capacity
(MW)
Annual
power
generation
(MWh) 2019
1
Mojave Solar
Project
1,600
1,500,000
2882
280
514,484
2,000
2,200,000
2698
280
791,642
2
Solana
Generating
Station
3
Genesis Solar
Energy
1,250
1,526,170
2724
280
617,043
4
Nevada Solar
One
266
357,200
2698
75
110,241
5
SEGS (I-IX)
1,000
2,314,978
2733
361
497,325
975
1,197,148
2707
110
195,810
6
Cresent Dunes
Solar Energy
Project
2,200
2,600,000
2532
392
1,544,428
7
Ivanpah Solar
Electric
Generation
System
476
464,908
1935
75
69567
8
Martin Next
Generation Solar
Energy Center
Mean
1,221
1,520,051
2,614
232
542,568
Max
2,200
2,600,000
2,882
392
1,544,428
Min
266
357,200
1,935
75
69,567
SD
641
777,077
271
119
447,915
Table 2. Data on wind farms
DMU#
Facility
CAPEX
(mil.USD)
(1)
Field
aperture
area (m2)
(2)
Resource
capacity
(kWh/m2/yr)
(3)
Gross
output
capacit
y (MW)
(4)
8
Alta Wind Energy
Center I-XI
Meadow Lake
Wind Farm
Roscoe Wind
Project
Javelina Wind
Energy Center
Rush Creek
Wind Project
Cedar Creek
Wind Farm
Highland Wind
Energy Center
Bison Wind
Energy Center
Biglow Canyon
Wind Farm
Cimarron Bend
Wind Farm
Blue Creek Wind
Farm
Spring Valley
Wind Farm
Amazon Wind
Farm Texas
Cedar Point
Wind Farm
Glacier Wind
Farm
Desert Wind
Farm
Rim Rock Wind
Farm
Tatanka Wind
Farm
Shiloh I
2,875
4,644,000
10,424
1548
Annual
power
generation
(MWh) –
2019
(5)
3,049,833
1,400
2,403,000
3,776
801
2,154,955
1,000
2,343,000
4,704
781
2,193,126
1,100
2,247,000
2,865
749
2,689,321
1,000
1,800,000
3,889
600
2,300,000
480
1,653,900
4,687
551.3
1,368,837
1,000
1,504,200
4,862
501.4
1,461,072
800
1,489,800
5,633
496.6
1,571,046
1,000
1,350,000
6,202
450
983,163
610
1,212,000
5,510
404
1,758,423
600
912,000
3,784
304
781,432
225
900,000
2,882
300
329,399
493
759,000
4,844
253
990,097
500
756,000
4,800
252
589,976
500
630,000
5,037
210
519,072
400
624,000
3,162
208
523,139
370
567,000
4,327
189
597,163
381
540,000
7,367
180
602,534
220
787
2,875
220
603
450,000
1,063,913
3,000,822
315,876
784,814
4,319
4,899
10,424
2,865
1,744
150
470
1,548
150
336
381,728
1,307,596
3,049,833
329,399
842,698
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Descri
ptive
Statisti
cs
Mean
Max
Min
SD
Table 3. Descriptive statistics
Variables
Input
Output
CAPEX
(mil.USD)
Field aperture
area (m2)
Resource
capacity
(kWh/m2/yr)
Gross
output
capacity
(MW)
Annual
power
generation
(MWh) 2019
Mean
950.82
1,245,182
4,384
415
1,122,494
Max
2,875
3,000,822
10,424
1,548
3,049,833
Min
220
315,876
1,935
75
69,567
SD
654.41
813,326
1,783
307
815,362
5. Results and Discussions
Table 4 summarizes the operational efficiencies of all CSP power stations, measured by
Models (1), (2), (3), and (4). There are differences between the average values from
CRTS and VRTS model results. The average values of CRTS are around 0.375 while the
values of VRTS are from 0.615 to 0.87.
Table 4. Operational efficiencies of CSP power stations
DMU#
CRTS
VRTS
Input-based
Output-based
Input-based
Output-based
1
0.3851
0.3851
0.7694
0.3991
2
0.3970
0.3970
0.8219
0.4458
3
0.3974
0.3974
0.8140
0.4327
4
0.2496
0.2496
1.0000
1.0000
5
0.5237
0.5237
0.8523
0.5576
6
0.1732
0.1732
0.7325
0.2006
7
0.6499
0.6499
0.9711
0.8821
8
0.2254
0.2254
1.0000
1.0000
Average
0.375
0.375
0.870
0.615
SD
0.159
0.159
0.106
0.305
Table 5 summarizes the operational efficiencies of all wind farms, measured by Models
(1), (2), (3), and (4). The average value results from both CRTS and VRTS are consistent.
Table 5. Operational efficiency of wind farms
DMU#
CRTS
VRTS
Input-based
Output-based
Input-based
Output-based
9
0.7997
0.7997
1.0000
1.0000
10
1.0000
1.0000
1.0000
1.0000
11
0.9547
0.9547
1.0000
1.0000
12
1.0000
1.0000
1.0000
1.0000
13
0.9440
0.9440
0.9488
0.9507
14
1.0000
1.0000
1.0000
1.0000
15
0.7588
0.7588
0.7751
0.7746
16
1.0000
1.0000
1.0000
1.0000
17
0.7515
0.7515
0.7812
0.7649
18
1.0000
1.0000
1.0000
1.0000
19
0.6509
0.6509
0.7680
0.6565
20
1.0000
1.0000
1.0000
1.0000
21
0.9603
0.9603
1.0000
1.0000
22
0.5657
0.5657
0.6555
0.5880
23
0.4840
0.4840
0.6043
0.4998
24
0.6381
0.6381
0.8908
0.7243
25
0.6232
0.6232
0.7973
0.6692
26
0.6794
0.6794
0.8367
0.7612
27
0.7396
0.7396
1.0000
1.0000
Average
0.818
0.818
0.898
0.863
SD
0.176
0.176
0.132
0.172
Hereafter, I conduct statistical tests on input-based and output-based efficiencies for both
CRTS and VRTS models. The null hypotheses to be examined are summarized by the
following cases:
First Ho: There is no difference among two types of power stations using CRTS models.
Second Ho: There is no difference among two types of power stations using VRTS models.
Table 6 lists the p-value of the statistical test using 2 samples t test and one way ANOVA
to examine the null hypotheses. The tests indicate that I can reject the first hypothesis but
being unable to reject the second hypothesis. In other words, the wind farms outperform
the CSP stations based on the Constant RTS models while the Variable RTS results show
no difference between the operation efficiencies of wind farms and CSP stations in the
United States.
Table 6. The p-value of statistical tests
CRTS
VRTS
Input-based Output-based Input-based Output-based
2 samples t test
t score
-6.12
-6.12
-0.52
-2.71
P(T<=t) two-tail
0.000
0.000
0.604
0.012
F value
37.46
37.46
0.28
7.32
P value
0.000
0.000
0.604
0.012
alpha
0.01
0.01
0.01
0.01
Confidential level
99%
99%
99%
99%
Null hypothesis rejected
Yes
Yes
No
No
One way ANOVA
6. Conclusion and Future Extensions
The previous research review showed wind energy technology is a mature and efficient
renewable energy technology in comparison with solar photovoltaic technology. CSP
technology with the integrating thermal storage is a new promising prospect that will gain
competitive and overcome the photovoltaic technology. Given the need for a performance
assessment between current CSP sites and the wind farms. Data envelopment analysis
(DEA) is a promising approach to combat various difficulties regarding energy and
environmental issues and. This study used DEA to assess the performance of 8
concentrating solar powers and 19 wind farms in the United States.
This research was the first effort to discuss the operation efficiencies between the CSP
sites and wind farms in the United States. Input – and output-oriented constant return to
scale (CRTS) and variable return to scale (VRTS) radial models are applied to predetermined three input and two output variables. The CRTS and VRTS models yielded
different results when comparing CSP and wind farms in the United States. For the CRTS
results, the wind farms outperform the CSP stations while the VRTS results showed no
difference between the operation efficiencies of wind farms and CSP stations in the
United States.
I acknowledge that this research has drawbacks, all of which need to be explored in near
future. One of them is that a lot of DMU operation efficiencies are unity and it can be
solved by using an extend DEA approach.
References
1. Akash, Bilal A., Rustom Mamlook, and Mousa S. Mohsen. "Multi-criteria selection
of electric power plants using analytical hierarchy process." Electric power
systems research 52.1 (1999): 29-35.
2. Chang, Byungik, and Ken Starcher. "Evaluation of wind and solar energy
investments in Texas." Renewable Energy 132 (2019): 1348-1359.
3. El-Ali, A., N. Moubayed, and R. Outbib. "Comparison between solar and wind
energy in Lebanon." 2007 9th International Conference on Electrical Power Quality
and Utilisation. IEEE, 2007.
4. Elif Oğuz, Ayşe Eylül Şentürk. Selection of the most sustainable renewable energy
system for bozcaada island: wind vs. photovoltaic. Sustainability. 2019;11(15).
doi:10.3390/su11154098
5. Gazheli, Ardjan, and Jeroen van den Bergh. "Real options analysis of investment
in solar vs. wind energy: Diversification strategies under uncertain prices and
costs." Renewable and Sustainable Energy Reviews 82 (2018): 2693-2704.
6. Gerlach, Ann-Katrin, et al. "PV and wind power-complementary
technologies." Proc. 26th European Photovoltaic Solar Energy Conference. Vol. 2.
2011.
7. Pietzcker, Robert Carl, et al. "Using the sun to decarbonize the power sector: The
economic potential of photovoltaics and concentrating solar power." Applied
Energy 135 (2014): 704-720.
8. Sağlam, Ümit. "A two-stage data envelopment analysis model for efficiency
assessments of 39 state’s wind power in the United States." Energy Conversion
and Management 146 (2017): 52-67.
9. Sağlam, Ümit. "Assessment of the productive efficiency of large wind farms in the
United States: an application of two-stage data envelopment analysis." Energy
Conversion and Management 153 (2017): 188-214.
10. Sueyoshi, Toshiyuki, Yan Yuan, and Mika Goto. "A literature study for DEA applied
to energy and environment." Energy Economics 62 (2017): 104-124.
11. Sueyoshi, Toshiyuki, and Mika Goto. "Comparison among three groups of solar
thermal power stations by data envelopment analysis." Energies 12.13 (2019):
2454.
12. Tang, Tian. "Explaining technological change in the US wind industry: Energy
policies, technological learning, and collaboration." Energy Policy 120 (2018): 197212.
13. https://www.eia.gov/energyexplained/electricity/electricity-in-theus.php#:~:text=The%20three%20major%20categories%20of,geothermal%2C%2
0and%20solar%20thermal%20energy.
14. Sueyoshi, T., & Goto, M. (2014). Photovoltaic power stations in Germany and the
United States: A comparative study by data envelopment analysis. Energy
Economics, 42, 271–288.
15. Sueyoshi, T., & Goto, M. (2017). Measurement of returns to scale on large
photovoltaic power stations in the United States and Germany. Energy Economics,
64, 306–320.
16. https://www.nrel.gov/gis/assets/images/solar-annual-ghi-2018-usa-scale-01.jpg
17. https://www.mtholyoke.edu/~wang30y/csp/PTPP.html#US
18. https://www.alternative-energy-tutorials.com/solar-hot-water/parabolic-trough-reflector.html
19. Kearney, D. "Utility-scale power tower solar systems: performance acceptance test
guidelines." Energy Procedia 49 (2014): 1784-1791.
20. United States Environmental Protection Agency | US EPA
21. https://www.eia.gov/energyexplained/electricity/electricity-in-the-us-generationcapacity-and-sales.php
22. https://www.nrel.gov/docs/fy09osti/45834.pdf
23. https://solarpaces.nrel.gov/by-country/US
24. https://globalwindatlas.info/
25. https://nsrdb.nrel.gov/
26. https://www.thewindpower.net/country_windfarms_en_4_usa.php
27. https://www.eia.gov/
28. https://cleanpower.org/facts/wind-power/