The Fresnel Köhler (FK) concentrator was first presented in 2008. Since then, various CPV companies have adopted this technology as base for their future commercial product. The key for this rapid penetration is a mixture of simplicity (the FK is essentially a Fresnel lens concentrator, a technology that dominates the market) and excellent performance: high concentration without giving up large manufacturing∕aiming tolerances, enabling high efficiency even at the array level. All these features together have a great potential to lower energy costs. This work shows recent results and progress regarding this device, covering new design features, measurements and tests along with first performance achievements at the array level (pilot 6.5 Kwp plant). The work also discusses the potential impact of the FK enhanced performance on the Levelized Cost Of Electricity (LCOE

Benitez Gimenez, Pablo

Chaves, Julio

Cvetkovic, Aleksandra

Hernández Sanz, Maikel

Miñano Dominguez, Juan Carlos

Mohedano del Pozo, Raúl

Vilaplana, J.

Zamora Herranz, Pablo

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

Progress In FK Concentrators  
Rubén Mohedanoa, Aleksandra Cvetkovića, Pablo Benítezb,c, Julio Chavesa, Juan 
C. Miñanob,c, Pablo Zamorab, Maikel Hernandeza, Juan Vilaplanaa 
a LPI Europe, S.L., Edif. CeDint Campus Montegancedo UPM 28223 Pozuelo, Madrid, Spain 
b Universidad Politécnica de Madrid (UPM) Cedint, Campus Montegancedo UPM 28223 Pozuelo, Madrid, Spain 
c LPI-LLC, 2400 Lincoln Ave., Altadena, CA 91001 
 
Abstract.  The FK concentrator was first presented in 2008. Since then, various CPV companies have adopted this 
technology as base for their future commercial product. The key for this rapid penetration is a mixture of simplicity (the 
FK is essentially a Fresnel lens concentrator, a technology that dominates the market) and excellent performance: high 
concentration without giving up large manufacturing/aiming tolerances, enabling high efficiency even at the array level. 
All these features together have a great potential to lower energy costs. This work shows recent results and progress 
regarding this device, covering new design features, measurements and tests along with first performance achievements 
at the array level (pilot 6.5Kwp plant). The work also discusses the potential impact of the FK enhanced performance on 
the Levelized Cost Of Electricity (LCOE). 
Keywords: Fresnel lens, nonimaging, concentrator, photovoltaic, solar energy, Köhler integration 
PACS: 42.15.Eq, 42.79.Ek, 88.40.F, 88.40.H, 88.40.jj  
INTRODUCTION 
Minimizing concentrated photovoltaic (CPV) 
energy cost (€/kWh) can be achieved by both lowering 
costs (at all levels) and increasing the energy yield. An 
optical design can help meeting these two goals by: 
• Being more efficient: using the fewest elements 
lead to low optical losses, easier assembly and 
alignment. Apart from that, the FK [1][2] produces 
a “white” spot on the solar cell, preventing the 
unwanted effect of chromatic aberration of the 
irradiance, that leads to cell efficiency drops [3].  
• Utilizing optics feasible at large scale/low cost 
• Showing loose manufacturing and aiming 
tolerances, but always maintaining the high 
concentration (>500) to 
- permit the high-efficiency multi-junction solar 
cells work at their best and use less of them 
- assure high energy yield (system performing 
closer to the sum of the power expected from 
the best modules, low series connection 
mismatch)  
- enable additional cost cuts (lighter structures, 
easier installation…) if there is still an excess of 
tolerances 
Apart from low cost, CPV needs to demonstrate long 
term reliability. Also in this case the FK has 
advantages:  
• it’s based on well known durable materials (PMMA 
or Silicone on Glass –SOG- for the primary lenses 
–POE-and glass for the secondary lenses –SOE-) 
• Cell reliability and efficiency is not compromised 
by hot spots: the FK achieves a very uniform 
irradiance on the solar cell 
• The input beam is split into four that are focused 
near the SOE top surface. When the concentrator is 
off-axis, these spots reach the housing back plate 
(where many elements lie, such as CCA and wires) 
divided and un-concentrated, and therefore burning 
of these elements is more unlikely. This might also 
help to avoid the usage (and costs) of additional 
protection parts. 
The CCA is embedded into the SOE and therefore 
is protected from humidity 
DESIGN SOFTWARE LOOKING AT 
ELECTRICITY GENERATION 
The optical design of nonimaging CPV systems 
often start with the description of the wavefronts 
(defining the light entering the optic and the light 
reaching the solar cell) we’d like the optic to connect 
[4]. The same applies to the FK design at its origin, 
where the design recipe combines general nonimaging 
and Köhler integration principles [5]. Aiming at a 
better description of the best achievable performance 
(plant peak power) and to help taking good business 
decisions, the original software has been enhanced by 
the addition of analysis tools and optimization 
algorithms that take into account all the spectral 
characteristics at play, i.e. those of the source -the sun- 
and receiver (cell external quantum efficiencies EQEs) 
and those of the optical materials involved. 
For a given technology (set of materials used in the 
primary optical element POE –typically PMMA or 
Silicone on Glass SOG- and secondary optical element 
SOE, typically glass), concentration ratio Cg, size of 
cell and f-number (here defined as the ratio of the 
optical depth to the POE diagonal), the design 
algorithm produces a family of preliminary designs 
whose features (such as photocurrent characteristic –
expected short circuit current Isc as a function of sun 
beam tilt angle-, actual acceptance angle –measured on 
the latter-, shape and size of SOEs) can be compared. 
This approach has demonstrated the optimal 
assignation of rays varies depending on all the input 
parameters mentioned above, but also on the criterion 
to select the final design: with this tool the designer 
has the choice to look at a set of f-numbers, 
concentration ratios, maximum photocurrents, angular 
characteristics, size of optics so that he can pick up the 
more balanced choice, with more potential to reduce 
energy costs. 
These design tools might even emulate the 
performance of the plant (array level) using a 
stochastic model that takes into account the cell 
binning and  making some assumptions on the effect 
of assembly and manufacturing errors on performance, 
and for a particular electrical layout [6]. 
Summarizing, the design enables a complete 
optimization looking at the final cost of electricity 
produced, minimizing the risks and facilitating each 
CPV manufacturer select the best scenario 
RECENT RESULTS 
Two different FK systems have been prototyped so 
far, one of them reaching the array level: this complete 
HCPV system prototype has been developed by Pirelli 
in collaboration with LPI, other companies and 
Research Institutes. Here we will focus on this system, 
explaining the results achieved both at the module and 
at the pilot plant levels.  
3.5 W module 
The system has a 120×120mm2 entry aperture area 
and geometrical concentration of 576×, the f-number 
being 1.2, and is meant to work with 5×5mm2 3J solar 
cells. The pictures at FIGURE 1 show images of the 
POE and SOE elements of this system, where the 4 
Köhler sectors are evident. This prototype comprises a 
PMMA Fresnel lens (picture-top, made by Evonik and 
10x Technology) and a B270 glass secondary (bottom-
left) in a configuration producing an almost perfect 
uniform square spot onto the 5x5mm2 MJ cell, as the 
picture on the bottom-left shows.  
 
FIGURE 1 On the top, picture of the FK primary optical 
element. Bottom-left, Secondary optics. In both pictures, the 
4- Köhler sectors are recognizable. Bottom-right, irradiance 
on the plane of the cell, showing a uniform white square 
spot. 
 
A full characterization of this module was carried 
out in parallel by LPI and Pirelli, and the results 
achieved are shown in FIGURE 2. 
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.5 1 1.5 2 2.5 3 3.5
C
ur
re
nt
 (A
)
Voltage (V)
η = 32.7% (@Tcell=25ºC)
Tamb = 26ºC 
η (measured) = 30.6%
FF = 85%
Pm = 3.41 W
ISC = 1.34 A
VOC = 3.01 V
Irradiance = 786 W/m2
Entry Aperture = 144 cm2
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
‐1.8 ‐1.4 ‐1 ‐0.6 ‐0.2 0.2 0.6 1 1.4 1.8
Is
c 
(A
)
Sun tracking error (degs)
Measured Isc
Acceptance at 90%
 
FIGURE 2 Measured IV curve, without temperature 
corrections and photocurrent characteristic Isc(θ). 
 
The single cell module achieves a peak efficiency 
of 30.6% (without temperature corrections!), using a 
commercial 3J cell with 38.0% efficiency. Its 
measured acceptance angle matches that of the 
simulations, and is ±1.26deg. The achievement of the 
theoretical value at the first try confirms the accuracy 
in the design software predictions. 
6.5kWp pilot plant 
Upon confirming the good performance of the 
3.5W modules, the parquet prototyping phase was 
launched. The parquet panels are manufactured using 
roll-to-roll techniques in PMMA. In this case, each 
parquet module comprises 48 units of the 
120x120mm2 PMMA Fresnel lens shown above. The 
tracker holds 4 rows with 10 parquet modules. 
FIGURE 3 shows a picture of the first FK 
prototype array, of 6.5kWp, manufactured by Pirelli 
and installed initially in Manresa (Spain). Such system 
was moved to ENEA facilities in Naples, where it is 
currently being monitored. This 6.5KWp system has 
attained electrical efficiencies up to 27% (DC at the 
entry of the inverter, without any temperature 
correction), which is outstanding since this was 
achieved at the first try, when the assembly process 
was not optimized yet. 
 
  
FIGURE 3 6.5kWp Pirelli Pilot Plant in Manresa 
(Spain). The tracker holds 40 panels comprising 48 
Köhler lenses and cells each. Picture courtesy of Pirelli. 
LCOE EXAMPLE 
The goal of a solar power plant is to produce 
electricity at low cost, and in the end what really 
matters is the LCOE, defined as: 
 
producedEnergyTotal
tLifetimeTotalLCOE cos=  (1) 
In this section we mean to establish a comparison 
between two systems based on Fresnel lenses (the FK 
and the F-XTP, whose SOE is a truncated inverted 
pyramidal mirror) looking at the LCOE they can 
achieve and the profits they can potentially generate. 
We can utilize a simple approach for the calculation of 
the Total Lifetime cost: 
 
Total Lifetime cost=CAPEX×crf + OPEX  (2)  
 
Where CAPEX is the investment and capital 
expenditures and the annuity factor crf is linked to 
WACC, the weighted average cost of capital along the 
20 years lifetime. 
Let us consider the OPEX and crf are identical for 
both systems, (although the FK should enable lower 
OPEX if we consider the wider acceptance values) and 
ranging a 3% of the CAPEX and 9% (WACC  = 6.4%), 
respectively. 
We will assume the two systems compared have 
same Cg, f-number and cells, and hence same kind of 
module housing and components. According to this 
assumption, when it comes to CAPEX, the only 
difference would deal with the secondary optics 
(slightly more expensive in the case of the FK) and the 
royalties fee, that applies to the FK optics only, 
resulting in rough CAPEX figures about 900$/m2 for 
the conventional system and 918$/m2 for the FK.  
Finally, owing to the better acceptance 
characteristics the FK with respect to the F-XTP, and 
its impact on lowering cells series connection 
mismatch, we will assume the plant AC efficiencies 
are 29% for the former, and 25% for the latter.  
With all these assumptions, and considering a 20 
years Lifetime, the LCOE for these two systems would 
range 7 $cents/kWh and 8 $cents/kWh for the FK and 
benchmark system, respectively. Additional to this 
difference and the impact on profits produced when 
looking at the electricity fees that apply, there is the 
fact that the FK produces 893.6 MWh a year ahead of 
the F-XTP. The combination of higher selling margins 
and higher energy production implies the FK system 
yields benefits of 124K$ per year over the 25% 
conventional system. This means the original CAPEX 
over cost is paid off in one and a half years only, and 
the remaining 18.5 years the FK plant would be 
yielding important benefits over the conventional 
system.  
ACKNOWLEDGMENTS 
Support for this work partly comes from the EC 
and Spanish Ministry MICINN under projects 
SSL4EU (Grant agreement n º257550, FP7/2007-
2013) and SIGMASOLES (PSE-440000-2009-8), 
respectively.  
 
REFERENCES 
1. Patent in allowance  
2. Benítez P., Juan C. Miñano, Pablo Zamora, Rubén 
Mohedano, Aleksandra Cvetkovic, Marina Buljan, Julio 
Chaves and Maikel Hernández “High performance 
Fresnel-based photovoltaic concentrator”, Energy 
Express, 2010 Optical Society of America 
3. S. Kurtz, M.J. O’Neill, “Estimating and controlling 
chromatic aberration losses for two-junction, two-
terminal devices in refractive concentrator systems”, 
25th PVSC; pp.361-367, (1996) 
4.  Nonimaging Optics, Winston, Miñano and Benitez, 
Academic Press-Elsevier 2004. 
5. W. Cassarly, “Nonimaging Optics: Concentration and 
Illumination”, in the Handbook of Optics, 2nd ed., pp. 
2.23-2.42, (McGraw-Hill, New York, 2001)R. T. Wang, 
“Title of Chapter,” in Classic Physiques, edited by R. B. 
Hamil, Publisher City: Publisher Name, 1999, pp. 212-
213. 
6. Rubén Mohedano, Aleksandra Cvetkovic, Pablo Benítez, 
Julio Chaves, Pablo Zamora, Juan C. Miñano, Maikel 
Hernandez, Marina Buljan, “Compared performance of 
fresnel-based concentrators at array level” Proceedings 
of the 25th EU PVSEC/WCPEC-5, Valencia 2010 
 
 


Progress In FK Concentrators

Benítez Giménez, Pablo

Archivo Digital UPM

http://oa.upm.es/13163/1/INVE_MEM_2011_109799.pdf

Progress In FK Concentrators

Abstract

Similar works

Full text

Available Versions

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

Archivo Digital UPM