Levelized Cost Of Electricity For Cpv Paper Nishikawa

Presented : International Conference on Solar Concentrators for the Generation of Electricity (ICSC – 5), November 16‐19, 2008, Palm
Desert, CA USA (www.icsc5.com)

LCOE FOR CONCENTRATING PHOTOVOLTAICS (CPV)
Warren Nishikawa, Steve Horne, Jane Melia
warren_nishikawa@solfocus.com
SolFocus Inc., 510 Logue Ave., Mountain View, CA 94043

ABSTRACT

Concentrating Photovoltaic (CPV) systems, a relatively recent form of solar power, presented in the light of LCOE,
are shown to be very competitive with other forms of solar plants under suitable conditions like high solar resource,
land constraints, and high temperatures. The argument is made that the best cost metric for decision making in
the solar industry is the Levelized Cost of Energy (LCOE), as established by the US Department of Energy (DOE)
and National Renewable Energy Laboratory (NREL). It is expressed as ¢/kWh, at net present value, and takes into
account the cost complexities associated with the entire lifetime of a solar plant, from financing through to end of
life. By comparison, the most common customer metric is Cost per Watt peak ($/Wp) which refers to the capital
equipment price only. The industry is shifting to LCOE as solar project financing are heavily reliant upon internal
rate of returns (IRR) based on energy production and operation and maintenance costs, rather than peak power
and capital costs. CPV technology has key advantages in Energy per Peak Watt and the LCOE for CPV
recognizes this advantage in ¢/kWh when compared with other PV technologies. Finally, the variability in real
discount rate and future value of energy is shown to have a significant effect on LCOE for all solar installations.

The Definition of LCOE (cents/kWh)
THE CASE FOR LCOE
A more accurate assessment of financial
The photovoltaic industry is rapidly maturing, and in
performance, the Levelized Cost of Energy (LCOE) was
many markets has passed the point of early adoption. In
adopted several years ago by the National Renewable
these markets, cost, margin, lifetime and reliability
Energy (NREL) and the United States Department of
dominate over technology when decisions are being
Energy (DOE). Significantly, it was used as one of the
made. Especially in Europe, a photovoltaic plant is
metrics for evaluating and driving the goals for the Solar
considered a financial instrument, and the constituents of
America Initiative, a novel and efficient grant program
the value chain are solely engaged with maximizing
begun by DOE in 2005. In coordination with mounting the
margin and revenue, and minimizing cost.
initiative, NREL produced the Solar Advisor Model (SAM)
[1], which models the cost of any phovoltaic power station
The Definition of $/W
in terms of LCOE.
The LCOE takes into account installation and
The classic definition of cost or price has been
commissioning costs, operations and maintenance,
Dollars per Watt peak ($/Wp). It is relatively easy to
degradation and lifetime, and the output. It calculates the
calculate and understand, and is the quantity most quoted
average value of the total energy produced, revalued at
in the industry. A schematic of the calculation is below.
the time of calculation based on forward assessments of
inflation and costs of financing.
SolFocus has adopted LCOE as its dominant metric,
and has been refining a model to help drive decisions both
with customers and internally. The formal definition of
LCOE [2] is given as:

[ ]⎫
⎧N
Figure 1: Cost definition ($/W)
⎨∑ Cn /(1+ dn )
n
⎬
LCOE = ⎩ nN0 ⎭= TLCC
= (1)
While the above is a significant factor when
[ ] [ ]
⎧ ⎫⎧ ⎫
N

⎨∑ Qn /(1+ dr ) ⎬ ⎨∑ Qn /(1+ d) ⎬
marketing solar plant, as a financial metric it has n n
significant limitations, especially when attempting to
⎩ n=1 ⎭ ⎩ n=1 ⎭
evaluate return on investment or when making cross-
where:
technology decisions. It does not take into account all
LCOE = levelized cost of energy
major parameters involved with installing and operating
TLCC = total life-cycle cost
photovoltaic plant, and it is a “fixed time” calculation.
Qn = Energy output in year n
Under normal circumstances it does not account for the
N = Analysis period
cost of financing over the project lifetime or inflation.
dr = Real discount rate (cost of money + other)
dn =Nominal rate (cost of money + inflation)

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Typical Daily Energy
In simplified terms, it can be thought of as: 120%
Fixed Tilt Rating
100%
CPV Tracked

Power (% Rating)
80%

60%
`

40%

20%
Figure 2: Cost definition, LCOE (cents/kWh)
0%
0 4 8 12 16 20 24
It is, in effect, the average cost of every unit of energy Hour of the Day
produced by a generator across its entire lifetime, brought
back to the value of that unit of energy determined at the
Fig 3: Fixed tilt VS tracked PV, energy harvest
time of the analysis.
LCOE presents energy costs at net present value
ADVANTAGES OF USING LCOE accounts for financing, depreciation, inflation and other
economic realities when considering an investment, and
LCOE takes into account the energy generated by will allow a comparison to be made between different
the plant over its entire lifetime and not the peak power. technologies, for example wind or photovoltaics.
Technologies that have a larger kWh/kWp ratio will supply Significantly, it also allows a comparison to be made
more energy for a given rated power. This is an important between different funding scenarios, which can have a
characteristic when comparing the costs and benefits of sizeable impact on average costs.
different technologies. Finally, given that the operator of a plant is paid
The simple definition of rated power is the power based on the energy produced, LCOE will give the best
produced at a set of standard test conditions (STC). In available estimate at the decision time, of the return on the
comparison, energy (kWh) generated is the power investment for any particular product or design.
produced over time based on the irradiance (the available
solar resource), efficiency, and losses. CPV ADVANTAGES FOR LOWER LCOE
2
Rated Power = Efficiency (%) x Panel Area (m ) x Concentrator systems use optics to efficiently
Irradiance (W/m2) at STC* harness a large area of light onto a small photovoltaic cell.
(2) One of their key ratings is the concentration ratio, usually
2
*Note: Irradiance STC for Flat Plate PV is 1000W/m Global
expressed in “suns”. The SolFocus SF-1000S
2
Irradiance, CPV is 850W/m Direct Normal Irradiance
concentrator uses a high concentration ratio of 500 Suns:
the light energy of 500 square centimeters is entrained
2
Energy = Efficiency (%) x Panel Area (m ) x Irradiation
onto a 1 square centimeter cell.
2
(kWh/m -yr x DC Loss Factor(%) (3)
There are a number of advantages of concentrator
systems over non-concentrating or one sun systems, and
An illustration of difference between rated power and
several added costs as well. Only a good LCOE
energy is shown in a typical daily energy plot (see Figure
calculation will allow the complexities to be seen in an
3). The rated power of a system is the power produced at
overall sense, and allow decisions to be made as to their
peak power when the sun is highest in the day. The rated
use. The SolFocus LCOE model takes into account all of
power is determined by a set of test conditions set by
these tradeoffs, the major ones being described below.
industry associations. The true value for solar energy
users is the kWhs produced, shown by the area under the
Sun Tracking
curves for CPV tracked and PV fixed tilted systems. The
energy is collected from the morning to evening,
The tracked photovoltaic systems will harvest a
compared to the power rating which “may” be achieved
greater number of kWh during the day than fixed systems
during a brief moment - if the conditions match the STC.
because their active surface is presented to the sun at the
The power can exceed the rating if there is more
optimum angle the entire time – they don’t suffer from
irradiation hitting the panel than the STC. For CPV, the
“cosine loss”. Trackers cost more than the fixed tilt
concentrator STC (CSTC) is 850W/m2 direct normal
structures though, so despite harvesting approximately
irradiation (DNI). In high DNI areas where CPV systems
40% more energy, the tracked system LCOE will reflect
are deployed, the power will exceed the CSTC since the
only a portion of that improvement. If a project manager is
2
DNI will be greater than 850W/m , therefore energy
considering a tracked system, the LCOE calculation will
produced is the better representation of system
put an upper bound on the tracker cost.
performance. The metric of energy produced per rated
CPV systems, because of their optics, must be
peak power or kWh/kWp will be discussed in following
tracked. SolFocus’ SF-1000S has a field of view or
sections.
acceptance angle of approximately +/- 1 degrees which,
while very lenient for our concentration ratio, demands a

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high performance tracker. So the ratio between higher
3.50
harvesting capabilities and higher tracker costs described

Energy / Rated Power
3.00
above apply. SolFocus’ model takes this into account, and
2.50
includes the cost and time associated with ground
2.00
preparation, installation and commissioning the trackers.
1.50
Using a tracked solution has the benefit of enabling a
1.00
higher energy to be produced for a given rated power.
0.50
0.00
Energy per Peak Watt
Phoenix Mohave Desert
The ratio of energy produced over rated peak power
CPV PV 2 axis tracked
(kWh/kWp) is a key metric for comparing energy
Fixed PV (30 degrees) Fixed TF (30 degrees)
production of various technology. From equations (2) and
(3) above, kWh/kWp is a function of the site irradiation, the
Figure 5: Energy / Peak power for CPV, PV and Thin Film
rating irradiance, DC-AC loss factors, and losses due to
temperature degradation, shown below:
Temperature Performance
Site Irradation (kWh/m 2 .yr) x DC - AC Loss x Temp Loss
Energy
=
Rating Irradiance (kW/m 2 )
Peak Power The high performance triple junction cells used by
SolFocus have a lower coefficient of temperature
degradation than Silicon, and so can be operated at higher
(4)
ambient temperatures. Many sites appropriate to CPV
have daytime temperatures in excess of 45OC, which will
A particular geography must be chosen, where for a
significantly degrade the output of Silicon systems. Figure
fixed tilt system, the irradiation is typically lower than the
6 presents performance data on the degradation rate of
Direct Normal Irradiation for tracked CPV systems. The
the SF-1000S. The power coefficient for the system is
temperature loss factor is the temperature degradation
approximately -0.17%/OC, while a typical Silicon panel
from peak power rating, where for PV the panels are flash
O
2 O
exhibits -0.48%/ C. SolFocus’ LCOE model takes this
tested at 1000W/m and 25 C cell temperature. When on-
characteristic into account, and the model is run on every
sun, PV panels heat up since only a small percentage is
installation proposal using local weather data.
converted to electricity. Manufactures report this condition
as nominal cell operating temperature (NOCT), typically to
O 2
be 50 C at 1000W/m . Based on the temperature 80
coefficient and the temperature rise from 25OC to 50OC,
75
the temperature loss can be calculated. For CPV
Temperature [C]

systems, the ratings are based on a true on-sun rating of 70
2 O
850W/m and 20 C ambient (not cell) where the system is
in operating conditions. Shown in Figure 4, CPV results in 65
a higher Energy (kWh) / Rated power (kWp) compared to
60
Fixed Tilt PV.
55
y = ‐1.260x + 645.2
Tracked Tracked Fixed Fixed
50
CPV PV TF PV
Irradiation (Phoenix) 45
2
(kWh/m /Day) 6.9 8.9 6.5 6.5
445 450 455 460 465 470
2
(kWh/m /Year) 2519 3249 2373 2373
Array Voc (V)
DC-AC Loss Factor (%) 85% 85% 85% 85%
Temp. Coeff.
Figure 6: Interpolation of power temperature
-0.18 -0.48 -0.25 -0.48
(%/Deg C)
coefficient for the SF-1000 CPV system
Temp. Loss 0% -12% -6% -12%
Rating Irradiance
0.85 1.00 1.00 1.00
2
LCOE FOR CPV
(kW/m )
Energy / Peak Power
2519 2430 1891 1775
With the key advantages of high kWh/kWp, improved
(kWh/kWp)
temperature performance, and high efficiencies, the true
Figure 4: Factors for kWh/kWp Calculations value of CPV systems is best represented by the LCOE in
cents/kWh. When comparing the LCOE of different
For comparison across technologies, the kWh/kWp is technologies it is important to make sure that the
illustrated for different locations in the Southwest US in assumptions behind the LCOE calculation are clear and
Figure 5. CPV is very competitive with tracked and fixed aligned. The translation of $/W costs to LCOE used the
PV and where solar resource is good with DNI to global key factors as described above. Additional areas that
tracked >0.77. require vigilance are the financial parameters of the

3|Page

model, specifically the real discount rate, inflation rate and Phoenix was used (see Figure 4) since the US DOE uses
rate of increase of the cost of energy. this location for the assessment of technologies being
developed under the Solar America Initiative (SAI).
Efficiency Trends The CPV roadmap below shows a break-through
against PV fixed prices beginning in 2009 and reaching
The development of high efficiency cells, typified by leading-edge costs by 2011. The leading-edge LCOE are
the triple junction design, has recently dramatically CPV systems with higher kWh/kWp and lower costs.
accelerated compared with Silicon and Thin Film Especially in high DNI areas, such as the Mohave Desert
technologies. At the panel level, the efficiency trends for in California, the LCOE band for CPV is 2 cents/kWh lower
CPV along with other PV technologies is shown in Figure that in Figure 9 and has the potential to reach leading-
7. Alongside this increase in technical activity, interest edge LCOE in 2010.
has been shown by the high volume manufacturing
community, and as a result, it is expected that over the
next few years the absolute cost of these cells and panels
will decrease.

30%

25%

20%

15%

10%

Figure 9. CPV LCOE roadmap in Phoenix, Arizona
5%
2007 2008 2009 2010 2011
Ave CPV 18.0% 20.0% 23.0% 26.0% 28.0%
SENSITIVITY OF LCOE TO FINANCIAL FACTORS
Avg Mono‐Si 15.3% 16.5% 17.7% 19.0% 20.2%
Avg Poly‐Si 12.0% 12.8% 13.6% 14.5% 15.3%
A study of the sensitivity of LCOE to real discount
Avg CdTe 9.5% 10.0% 10.5% 11.5% 12.0%
rates (without inflation) was conducted, and shows a large
Avg a‐Si 7.8% 8.3% 8.9% 9.5% 10.0%
effect. The discount rate based on the cost of capital is a
critical component that depends on macroeconomic
Figure 7: Projected panel efficiency trends factors such as the stock market, interest rates, and
money exchange rates. With all else being equal for a
Capital Cost nominal 2MW plant design, a 2.5% increase in the real
discount rate drives the LCOE higher by 20% (see Figure
Taking industry published data for Silicon and 11).
Thin Film technologies [4], the CPV capital cost trends are In addition, the impact of a potential increase in
shown in comparison from 2008-2011 in Figure 8. The the value of energy was studied, despite not being
system cost in $/W are for 2MW plants which included included in current industry recognized LCOE calculations.
panel, tracker, inverter, transformer, BOS components, In order to take this into account, the LCOE equation (1) is
and installation. re-written as follows:

System $/W 2008 2009 2010 2011 NPV(TLCC) (4)
LCOE =
CPV $7.1-$9.9 $5.6-%7.1 $4.1-$5.1 $3.0-3.5
[ ]
⎧ n⎫
N

⎨∑ Q n (1 + v) /(1 + d) ⎬
PV Price $6.9 $6.5 $6.1 $5.9 n

⎩ n=1 ⎭
PV Cost $2.9 $2.6 $2.2 $2.0
where:
Figure 8: Projected installed system costs
LCOE = Levelized cost of electricity
TLCC = Total life-cycle cost
LCOE Roadmap
Qn = Energy output in year n
N = Analysis period
A CPV industry cost reduction roadmap has been
d = Real discount rate (cost of capital)
created based on improvements in panel efficiency and
v = Yearly increase of the value of energy
system cost trends in Figures 7 and 8. The LCOE for CPV
cost is shown as a range and is compared with PV
The analysis showed that a projected increase in
industry prices and costs for fixed tilt and systems. The
the value of energy by 1.5%/yr resulted in an LCOE
common factors such as cost of capital, inverter
reduction of 14% less (than discount rate alone) where the
replacement costs, and solar resource are based on the
value of the energy off-sets the lifetime costs with greater
same assumptions. The DNI and Global tilt insolation for
impact. (see Figure 11).

4|Page

LCOE vs. Real Discount Rate
120% Baseline scenario:
Relative LCOE compared to Real
Discount Rate of 7.5% scenario
7.5%, no increase in
100%
energy value
80%
60%
40%
20%
0%
Real Discount Rate %
5.0% 7.5% 10.0%

Real Discount Rate ONLY
1.5%/yr Increase in Energy Value

Figure 11. Impact of real discount rate and increase in
value of energy on the LCOE

Knowing and aligning the assumptions regarding
these parameters of discount rates and value of energy is
essential for any meaningful comparison of technologies.

CONCLUSION

LCOE is the best metric for measuring both the
value of solar technology and the true cost of solar
installations. LCOE is the sum of the yearly cost divided
by energy produced over the project lifetime, then projects
these values to back to present day. The key attributes of
CPV have been shown to be:

• Increased Efficiency
• Sun Tracking for Increased Energy Production
• Low Temperature Degradation
• Highest kWh/kWp in High DNI Locations

In high DNI locations such as Phoenix and South West
US, CPV has an LCOE cost potential to compete with the
PV industry as early as 2009 and provide leading-edge
LCOE in 2011. Finally, innovative financing of solar
projects is becoming increasly important where the LCOE
is extremely sensitive to cost of capital and the future
value of energy.

REFERENCES

[1] https://www.nrel.gov/analysis/sam/
[2] W. Short, D. J. Packey, T. Holt, “A Manual for the
Economic Evaluation of Energy Efficiency and Renewable
Energy Technologies”, NREL/TP-462-5173, March 1995
[3] Paul D Maycock, “The Future of Photovoltaics,” 33rd
IEEE Photovoltaics Specialists Conference, San Diego,
CA, May 2008.
[4] Joel Conklin and Michael Rogol, “True Cost of Solar
Power: 10 cents/kWh by 2010,” Photon Consulting, April
2007.

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