ENERGY LEARNING CURVES OF PV SYSTEMS
Marzella Görig1,2,3 and Christian Breyer1,4 1 Q-Cells SE, Sonnenallee 17 - 21, 06766 Bitterfeld-Wolfen OT Thalheim, Germany,
E-Mail: [email protected], 2 Hochschule Anhalt, Bernburger Str. 55, 06366 Köthen, Germany,
3 now with: Technische Universität Clausthal, Adolph-Roemer-Straße 2A, 38678 Clausthal-Zellerfeld, Germany,
E-Mail: [email protected], 4 now with: Reiner Lemoine Institut gGmbH, Ostendstraße 25, 12459 Berlin, Germany,
E-Mail: [email protected]
ABSTRACT: Energy demand of photovoltaic (PV) systems is an important part of energy sustainability of PV
systems. PV systems are considered sustainable energy systems when the produced energy is higher than needed.
This paper is using financial learning curve concepts to determine energy demand of main PV modules and systems.
General PV module and PV system energy learning curves are calculated by weighting energy demand of different
PV systems according to their share in PV market. Additionally the contribution of module efficiency into energy
reduction is considered. Energy payback time (EPBT) and energy return on investment (EROI) in 2010 and 2020 are
calculated via energy learning rate.
Keywords: Learning curve, LCA, EPBT, EROI, Silicon Solar Cell, Thin Film Solar Cell, System
1 INTRODUCTION
PV is the fastest growing power technology [1]. The
reasons are on the one hand the cost reductions of PV
systems and on the other hand the increasing need for
sustainable power supply. But how sustainable are PV
systems in detail? Sustainability of PV is essential for
justifying both high growth rates of PV in the present and
PV systems as an important part of energy supply in
future. The relation of cumulated energy demand (CED)
for establishing PV systems and generated energy of
these PV systems is essential for the sustainability of PV.
Energy-Pay-Back-Time (EPBT) is one possibility to
show this relation. Determining how EPBT can develop
in future, it is necessary to analyse the development of
CED. In many publications the CED of PV modules or
PV systems are investigated by Life Cycle Analysis
(LCA) for one technology status but not for a longer
period of time.
The purpose of the presented work is to analyse PV
systems development in terms of CED from the 1970s to
2010 by collecting LCA studies of different publications.
2 METHOD
2.1 General Data Handling
CED data of 73 publications published between 1976
and 2010 [2-74] are registered in a database with the aim
to collect only CED data of full considered LCA. This
means that the total energy demand from silica mining up
to system assembly and recycling with all direct and
indirect energy demand like embodied energy must be
considered. Furthermore year of technology status is
taken from the respective publications.
The following six PV technologies are analysed:
single crystalline silicon (sc-Si), multi-crystalline silicon
(mc-Si), ribbon-Si, thin film amorphous silicon (a-Si),
cadmium telluride (CdTe), copper indium (gallium)
diselenide (CI(G)S). The sc-Si group includes also CED
data of sc-Si/a-Si technology and the a-Si group CED
data of a-Si/µc-Si and µm-Si regarding their similarity
and the rareness of qualitative well analysed LCA.
Actually part of real sc-Si and a-Si data is considerable
higher than that of the respectively familiar technology.
All CED data are first returned to primary energy per
module area on a square metre basis (m²) as much as
possible. Additionally, the publications’ information of
module efficiency increase enables the analysis to
calculate suitable annual module efficiencies for every
year and every PV technology. In this way only average
industrial modules are considered and the data of CED
per power are not biased by high performance modules.
2.2 Framed Modules
Primary energy demand from silica mining up to
module assembly is considered thereby crystalline
modules are considered with and thin film modules
without aluminium frame. Using CED data of
publications which consider crystalline modules without
Al-frame and thin film modules with frame, analysis of
the energy demand of Al-frame is made. Figure 1 shows
all CED values of Al-frames from the years 1983 till
2020.
Figure 1: Primary energy demand of Al-frame from 1983 to 2020. Data are presented in thermal GJ per m² module area.
Considering the fact that many LCA analyses do not
include all direct and indirect energy types, this may
explain the fluctuations of the CED values, leads to the
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motivation of developing an annual average value which
considers the high CED values more than the low ones.
In details, firstly an annual arithmetic average was
calculated. CED values which are higher than the
arithmetic average of the respective year are then
weighted twice higher than the remaining CED values.
By this method low CED values, which may had been
generated from an incomplete LCA study, did not lead to
a too low annual CED. An exponential best-fit curve is
calculated via the weighted annual average CED values.
The exponential curve allows calculating an average
CED value for Al-frames to transform CED values for
modules without frame to modules with frame and vice
versa. This method is used when publications considered
crystalline modules without Al-frame or thin film
modules with frame but only when no LCA for Al-frame
was made. The method is also necessary to achieve
enough CED data for further analyses.
2.3 Silica in PV-industry
Two types of silica have been used in the PV -
industry: On one hand before 2000 the off-spec Si was
mostly mentioned in publications and on the other hand
after 2000 the off-spec Si has been displaced by the solar-
grade (sog) Si. Off-spec Si can be considered as a waste
product from the microelectronic industry. Thus many
authors do not consider the total energy demand of silica
production but only a part of it. The aim of this analysis
is to show the development of total energy demand of PV
systems. Considering the share of Si feedstock in total
EPBT it is shown that the energy demand of Si feedstock
for mc-Si modules is more than a third of the total energy
demand of module production (figure 2). That means
specifically for mc-Si an incomplete consideration of Si
production is not justifiable.
Figure 2: EPBT of different PV systems between 2007 and
2009. Diagram is taken from de Wild-Scholten [69].
Using only LCA studies which include total energy
demand of Si feedstock of mc-Si modules leads to the
fact that only LCA studies after 1995 could be used.
Before 1995 no complete LCA studies of mc-Si modules
could be found.
For the two other crystalline Si modules sc-Si and
ribbon-Si the share of Si feedstock in module’s EPBT is
less than that of mc-Si. In this way it is sufficient to
calculate the annual average of energy demand via the
weighted average method (section 2.2).
As a consequence and also to avoid an incomplete
LCA, the annual weighted average method is used for all
six major PV technologies.
3 ENERGY LEARNING CURVE
Actually the learning curve model is widely used for
cost projects of industrial goods. Here it describes the
fact that the cost of an industrial product decreases
constantly with every doubling of its historic cumulative
production [75]. Substituting the cost parameter of the
traditional learning curve concept for CED values results
in an energy learning curve describing how energy
demand decreases with the doubling of the cumulative
capacity (equation 1). This allows the energy demand of
PV modules to be extrapolated for the future.
2log
1log
0
0.
LR
xx
P
PEE
(1)
Equation 1: Law of energy learning curves. Abbreviations stand
for: cumulated energy demand at historically cumulated capacity
of Px (Ex), CED at initial capacity P0 (E0), historically cumulated capacity (Px), initial capacity (P0), learning rate (LR).
By plotting the annual weighted average CED values
per nameplate module power against their cumulative
capacity the energy learning rate can be derived. Figure 3
shows the results of the six major PV technologies on
basis of primary energy per module power.
For all modules except of CI(G)S an energy learning
rate is determined. For CI(G)S modules too less data are
available, partly due to the latest market introduction
among the six PV technologies taken into account. Hence
the first complete LCAs for CI(G)S were made only after
2000 [5].
Sc-Si modules show high fluctuations especially
before the year 2000. That is mainly a consequence of the
uncertainty in differentiation between incomplete and
complete Si feedstock LCA. LCA data of mc-Si are more
detailed. The high energy reduction between 2004 and
2005 is a result of the sog-Si. Otherwise no complete
LCA data for mc-Si can be found before 1995 [19]
although mc-Si has been produced since the late 1970s
[76]. Including also the incomplete Si feedstock LCA of
mc-Si in the analysis leads only to an energy learning rate
of 8% instead of 24%. This shows the high relevance of
Si production for the energy demand and reduction.
Therefore mc-Si and sc-Si modules show the highest
energy learning rates of all PV technologies and ribbon-
Si with less Si demand shows only a learning rate of
12%.
Thin film modules namely a-Si and CdTe have
needed a relatively low energy demand from the
beginning, hence show also a reduced learning rate.
Although PV modules show a decreasing energy
demand over the last decades, it must be stated that the
energy demand in figure 3 deals with the module power
but the problem is that the module power of all PV
technologies has been increased. Therefore, the influence
of the module efficiency on the energy learning rate has
to be investigated.
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Figure 3: Energy learning curves of six main PV technologies dealing with annual weighted average CED per module power. No constant
learning rate (LR) could be estimated for CI(G)S as a consequence of less data available for the latest technology introduced to the market. The other five PV modules technologies show learning rates between 24% (mc-Si) and 7% (CdTe). C-Si modules include Al-frame. Thin
film modules are considered without frame.
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Table 1 shows the difference between two learning
rates. LRp indicates that the CED deals with module
power and LRA deals with CED per module area. The
results demonstrate that mostly the CED reduction of thin
film modules strongly depends on the increase of the
module power whereas the CED per module area of
crystalline module has been reduced significantly in the
last years. This means that the production of crystalline
Si modules shows enough potential in savings of energy
demand.
Table 1: Energy learning rates of PV module technologies. LRp deals with CED per module power and LRA with CED per
module area. Mostly for thin film modules increasing module
efficiency is the major driving force for a decreasing energy demand per module power. High rate of energy reduction of c-Si
modules is significantly less dependent on module efficiency
than thin film modules.
4 GENERAL ENERGY LEARNING CURVE FOR
PV MODULES
The average energy demand for cumulated PV
capacity can now be derived via the determined energy
learning rates of the six major PV module technologies
and equation 1. If the energy demand of every PV
technology is weighted relative to the share of the
respective technology to the total PV market (figure 4),
general energy demand of the PV module market can be
determined. Data for respective market share are taken
from [77, 78].
Figure 4: Share of different module technologies to the total PV
market from 1970 to 2020. Data from 1980 to 2010 are taken from [77, 78]. Other data are own estimations.
A constant energy demand of 17 GJth/kWp is used for
CI(G)S modules considering the missing energy learning
curve (figure 3). Figure 5 shows the result. Each point
indicates one year from 1977 to 2020.
Figure 5 also demonstrates that the calculated energy
demand of sc-Si in the 1970s is too low. This explains the
irregularity before 1977. However, only one CED value
for the period before 1977 is available. This value is
derived from the first recorded LCA analysis by Hunt
[30] and is may comprise an incomplete LCA. The
calculated values in this period are related to this value.
Considering the period from 1974 to 2010, an energy
learning rate of 17% for the total PV module market was
gained. Considering the time period from 1977 to 2010, a
learning rate of 20% was obtained. The following
analysis deals with the 17% learning rate. Therefore a
determination of too high energy reduction in the future
is avoided. It should be mentioned that the financial
learning rate of c-Si PV modules is also 17% [79]. That
indicates a correlation between cost and energy
reduction.
Figure 5: Energy learning curve of total PV module production from 1974 to 2010. Energy demand is calculated by energy
learning curves of the single PV technologies weighted relative
to their share in PV module market. CI(G)S modules are included with a constant energy demand of 17 GJth/kWp. From
1974 to 2010 the energy learning curve is 17% and from 1977 to
2010 20%.
5 CED OF BOS COMPONENTS
For a complete LCA analysis of PV systems it is also
necessary to consider the energy demand of the balance-
of-system (BOS) components. Available LCA studies
allow to differentiate between rooftop and ground-
mounted BOS components. The energy demand of BOS
components does not include the energy demand for
frames or batteries. LCA studies about BOS components
are not available for every year. Hence, lines of best fit
for rooftop and ground-mounted BOS components were
determined. The lines of best fit are calculated from the
annual weighted average LCA values.
For ground-mounted BOS components the values of
the line of best fit are between 1,600 – 1,800 MJth/m² for
the years 1974 – 2010. They are highly dominated by
ground-mounted BOS including concrete foundation.
Only a small amount of LCA studies already consider
pile driving method. In general, ground-mounted BOS
components show an energy learning rate of only 0.3%.
PV-technology LRP [%] LRA [%] relative
difference [%]
sc-Si
(with Al-frame)
18 14 -4
mc-Si
(with Al-frame)
24 22 -2
ribbon-Si
(with Al-frame)
12 10 -2
a-Si
(without frame)
15 9 -6
CdTe
(without frame) 7 3 -4
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For rooftop BOS components the line of best fit
results in CED values which fluctuate slightly around 400
MJth/m² between 1974 and 2010. Thus the energy
learning rate is 0.4%.
The energy demand of BOS components has not been
changed significantly since the 1970s. Only pile driving
method could reduce energy demand of ground-mounted
systems but not enough LCA studies are performed
considering this issue. Therefore they could not be
considered suitable.
Adding the energy demand of PV modules to the
BOS components result in a lower energy learning curve
than that for only PV modules. Therefore the BOS
components slow down the energy reduction of PV
systems.
Table 3 and 4 (section 12) demonstrate the influence
of BOS components on the system energy learning curve.
The tables also include the total energy demand of
ground-mounted and rooftop PV systems relative to the
PV technology share of the PV market (figure 6). Data
for PV application market shares are taken from [80].
That is a simplified method because it does not include
the difference between the share of PV technologies in
the total PV market and the share of PV technologies in
the PV rooftop or PV ground-market. However, such
detailed data have not been available.
Figure 6: PV application market share from 1970 to 2010. Data
from 1992 to 2009 are taken from [80].
6 TOTAL PV ON-GRID SYSTEMS
After considering single PV technologies and PV
systems the energy demand for the total PV systems
market can now be calculated by energy learning rates.
The general energy learning rate of on-grid PV modules
is determined by weighting the energy demand of
different PV technologies and BOS components relative
to their share in the PV market. Figure 7 indicates the
energy learning curve for CED per module power. The
influence of the different PV technologies can be
determined. Between 1980 and 1988 the share of a-Si in
the PV market raised from 0.38% to 32% [77]. Thus the
a-Si technology has a small amount of energy demand.
Therefore the energy reduction in this period was very
high. After 1998 the PV market was mainly determined
by mc-Si and sc-Si. Hence, the energy reduction was
damped. 2008 the solar boom in Spain has lead to a high
installation of ground-mounted systems. That explained
the high peak at that year.
The energy learning rate for CED per module power
of total PV on-grid systems was 14% for the years 1974 -
2010. Also the financial learning rate of PV systems is
14% [79]. This points out again the correlation between
energy and cost reduction.
Figure 7: Energy learning curve of total PV systems from 1974 to 2010. Energy demand is calculated by energy learning curves
of single PV modules and BOS components weighted relative to
their share in PV module and system market. CI(G)S modules are calculated with a constant energy demand of 17 GJth/kWp.
From 1974 to 2010 the energy learning curve is 14%.
7 VERIFICATION
After determining learning curves of PV systems by
using the energy learning rates of modules and BOS
components, it must be verified if the energy learning
rates are defensible or not. That can be easily done by
using energy parameter as EPBT or EROI. The EPBT of
six rooftop PV systems were calculated and compared to
the results of de Wild-Scholten [69] which is indicated in
figure 2. The annual irradiation on optimally tilted
modules of 1700 kWh/m² and the technology status of
the single PV rooftop systems are assumed like those of
de Wild-Scholten. It must be mentioned that de Wild-
Scholten considered only frameless modules. So the
energy demand of Al-frame must be eliminated by using
best-fit curve (section 2). The assumptions for the
Performance Ratio and lifetime are listed in Table 2.
Table 2: Estimation of Performance Ratio and lifetime of rooftop and ground-mounted PV systems in 2010 and 2020.
Performance Ratio
[%]
Lifetime
[y]
rooftop 2010 80 25
rooftop 2020 84 30
ground-mounted
2010 78 25
ground-mounted
2020 82 30
The results are indicated in Figure 8. Only minor
differences are found between the EPBT of de Wild-
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Scholten and the calculated value from the energy
learning curves. This determined energy learning curves
could be used for further analyses.
Figure 8: Calculated EPBT of six PV modules by using determined energy learning curves. Irradiation and technology
status are chosen analogue to figure 2. Performance Ratios are
listed in Table 2.
8 EPBT AND EROI IN 2010 AND 2020
The catenation between EPBT and energy return on
investment (EROI) is the lifetime which is demonstrated
in equation 2.
EPBT
LEROI (2)
Equation 2: Calculating of Energy Return on Investment.
Abbreviations stand for: Energy Return on Investment (EROI),
lifetime of PV system (L) and Energy Pay Back Time (EPBT).
Thus the development of EPBT in time can be well
calculated using energy learning curves. EROI can be
calculated also using energy learning curve.
2010 is chosen as current technology status and
compared to 2020. EPBT and EROI are calculated using
energy learning rate and annual industry growth rates of
new installed PV capacity of 30% p.a. in 2010s. The
assumed growth rate is less than the enormous annual
growth rate of about 45% in the last years [81]. Economic
demand for PV systems is by 2020 in the order of 3,000 –
4,000 GWp [82]. Hence the assumed growth rate of 30%
p.a. should be a realistic expectation.
Parameters of Performance Ratio and lifetime are
listed in Table 2.
Furthermore annual irradiation on module surface of
optimally fixed tilted PV systems is used [83]. Thus
irradiation is given in a coordinate of a 1°x1° mesh
within 65°S and 65°N, EPBT and EROI could be
determined in same resolution.
Using energy learning curve of total PV systems
leads to EPBT of 1 to 2.5 years worldwide for the
technology status of the year 2010. Within the next ten
years it can be reduced on a level of 0.5 to 1.5 years.
These EPBT has lead to an EROI of about 10 to 25 in
2010 and will lead to an EROI of 20 to 60 in 2020. PV
systems will soon be able to produce in average over 50
times more energy during their lifetime than what they
require for their production. Detailed results are indicated
in figures 9-12.
Figure 9: EPBT of total on-grid modules including all system components for the year 2010. EPBT is calculated by energy
learning rate and with annual irradiation on optimally fixed tilted
module surface in a mesh of 1°x1° within 65°S and 65°N. Performance Ratio is listed in Table 2.
Figure 10: EPBT of total on-grid modules including all system
components for the year 2020. EPBT is calculated by energy
learning rate and with annual irradiation on optimally fixed tilted module surface in a mesh of 1°x1° within 65°S and 65°N.
Performance Ratio is listed in Table 2. Annual growth rate of PV
installations is assumed to be 30% p.a.
Figure 11: EROI of total on-grid modules including all system
components for the year 2010. EROI is calculated by energy
learning rate and with annual irradiation on optimally fixed tilted
module surface in a mesh of 1°x1° within 65°S and 65°N.
Performance Ratio is listed in Table 2. Performance Ratio is
listed in table 4. Lifetime is 25 years.
Figure 12: EROI of total on-grid modules including all system components for the year 2020. EROI is calculated by energy
learning rate and with annual irradiation on optimally fixed tilted module surface in a mesh of 1°x1° within 65°S and 65°N.
Performance Ratio is listed in Table 4. Performance Ratio is
listed in Table 2. Lifetime is 30 years. Annual growth rate of PV installations is assumed to be 30% p.a.
rooftop installation
1700 kWh/m²/y irradiation at optimal tilt angle
0.00
0.50
1.00
1.50
2.00
2.50
sc-Si 2008
14.73%
mc-Si 2007
13.9 %
ribbon-Si
2009 12.8%
CI(G)S 2009
10.65%
CdTe 2009
11.85%
a-Si 2008
7.74%
EP
BT
[y]
BOS
module without frame
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EPBT and EROI will show strong development in the
next ten years. Thus PV systems show high energy
production and therefore they will occupy their position
in the energy supply chain.
9 CONCLUSION
To the knowledge of the authors this publication
shows for the first time that the energy consumption in
PV manufacturing follows the log-linear learning curve
law similar to the evolution of production cost. BOS
components soften thereby the energy reduction. This is
mostly important for thin film modules because they
show the lowest energy reduction. Crystalline Si modules
have the highest energy learning rates, which is mainly
driven by improved silicon production.
General PV module and PV system energy learning
rates show correlation between energy and financial
reduction. Additionally, energy learning curves show a
high potential of PV systems in decreasing EPBT and
increasing EROI. The energy learning curve allows
determining these parameters time-dependent for the past
and future.
10 ACKNOWLEDGEMENTS
The authors would like to thank Friederike Kersten,
Chris Werner, Jörg Müller, Dominik Huljić, Ina von
Spieß, Mahmoud Sayed and the Solarvalley Sachsen-
Anhalt e.V. for their great support during different steps
of preparing this paper.
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12 TABLES
Table 3: Energy learning rates of different PV ground-mounted systems. LR are distinguished between CED per power (LRp) and CED per
module area (LRA). “all PV-Technologies” includes all five listed PV-technologies and a constant energy demand for CI(GS) modules of 17
GJth/kWp, whereas the energy demand of all six PV technologies is weighted relatively to its share in the PV market. Additionally the energy demand (Ein) of the respective PV ground-mounted system in 2010 is calculated by the energy learning curve. Thereby the energy demand of
the ground-mounted BOS components is 1.6 GJth/m² in 2010.
PV-Technology LRP [%] LRA [%] time period Ein (2010)
[GJth/kWp]
Ein (2010)
[GJth/m²]
sc-Si (with Al-frame) 11 9 1974 - 2010 30,1
4,8
mc-Si (with Al-frame) 13 12 1995 - 2010 27,1
3,8
ribbon-Si (with Al-frame) 7 5 1983 - 2009 25,4
3,3
a-Si (without frame) 5 1 1989 - 2010 28,6
2,3
CdTe (without frame) 4 1 1991 - 2010 19,6
2,4
all PV-Technologies 11 8 1974 - 2010 26,3
3,8
Table 4: Energy learning rates of different PV rooftop systems. LR are distinguished between CED per power (LRp) and CED per module area (LRA). “all PV-Technologies” includes all five listed PV-technologies and a constant energy demand for CI(GS) modules of 17
GJth/kWp, whereas the energy demand of all six PV technologies is weighted relatively to its share in the PV market. Additionally the energy
demand (Ein) of the respective PV ground-mounted system in 2010 is calculated by the energy learning curve. Thereby the energy demand of the rooftop BOS components is 0.4 GJth/m² in 2010.
PV-Technology LRP [%] LRA [%] time period Ein (2010)
[GJth/kWp]
Ein (2010)
[GJth/m²]
sc-Si (with Al-frame) 14 11 1974 - 2010 21,3
3,4
mc-Si (with Al-frame) 18 16 1995 - 2010 19,6
2,8
ribbon-Si (with Al-frame) 9 7 1983 - 2009 18,2
2,4
a-Si (without frame) 9 5 1989 - 2010 14,7
1,2
CdTe (without frame) 5 2 1991 - 2010 10,2
1,2
all PV-Technologies 14 11 1974 - 2010 18,6
2,7
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