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SESSI ON 3A

VI SUAL PRESENTATI ONS

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COMPARISON BETWEEN DIFFERENT SOLAR CONCENTRATORS AS REGARDS TOTHE ELECTRIC GENERATION

Franco Rasello, Emanuele Renzetti

INTEGRARE (INTEGRA Renewable Energy)

Abstract

In this article we compare different solar concentratortechnologies available in the market of the powergeneration. There are two main technologies that usesolar energy: solar thermal concentrator (STC);photovoltaic concentrator (CPV).CPV are then dividedinto two classes: low and high concentration (LCPV &HCPV).

The question is: which is the best technology to realise aproject for solar energy conversion in relation to the site,electric generation and application type.

In the first solution, STC, the total cost is dividedbetween thermal collector, tracking, power block andHTF (Heat Transfer Fluid) system. This technology isregulated by economy of scale; for an application of 1MW its not competitive with CPV but we have betterresults with a bigger size.

In the second solution, CPV, the total cost is dividedbetween solar cell, concentrator, tracking and inverter.

The LCPV that uses low concentration factor could be agood compromise. We can reduce the cost of the cells,in relation to the concentrator factor. Its even possible touse Silicon cells that are ready now instead of morecomplex, expensive and not market ready solutions.

The HCPV using high concentration factor needs to usemore efficient cells (like MJ) to be efficient, but thesetechnologies are very expensive and not mass market(at the moment).Another important difference betweenthe two solutions (LCPV vs. HCPV) is that a lowconcentration factor needs a low precision trackingsystem and doesn't reach high temperature (low costs).AHCPV needs a high precision tracking system (highercosts) and reaches high temperature on the cells.

1. Introduction

The objective of this work is to determine the best solartechnology that can be used in relation to the generatedpower and which component can be improved to obtain

better price.The results could be important both for designers and forproducers.To realise a commercial solution the most importantthing is to reduce the cost of the system and not only cellefficiency. [6]To compare the cost of these technologies we areconsidering the cost of energy production (not of theWp); to do so we consider a place with direct solar

radiation like Decimomannu in the south of Sardinia (theirradiation values are based on 5 years of collectiondata).The data in this paper are obtained from severalpublications and some are extrapolated. [1]This is due to the fact that solar concentrators areentering now the market (especially HPVC) and so thereisnt a big installation history to analyse.

2. Solar technologies description

SOLAR TERMAL CONCENTRATION (STC)

Solar thermal electric systems need an intermediatethermodynamic cycle to produce electricity.

The state of the art of this technology is a great powerplant size >300MW, with a molten salt as Heat TransferFluid (HTF) and vapour as working fluid.

Solar thermal power plant could be divided into threedifferent parts:

(a) Solar field (thermal collector)

(b) HTF, that includes the fluid and all aspect relative tothe storage system and heat exchange

(c) Power Block that includes turbine, cooling tower, heatrecuperator and generator.

The analysis of a smaller power plant size (1 MW and 5MW) is only to compare this power plant with PVtechnologies. [2]

For this small size, steam Rankine cycle isn't the bestsolution so we have analysed an Organic Rankine cyclederived from geothermal.

The efficiency of the power block is 32% for an ORCcycle. For a steam Rankine of a 1MW size the efficiencyis lower, as it decreases with dimension.(The efficiencyof an advance steam Rankine cycle for power plant>150 MW is 43%).[3]

Fig. 1 Functional diagram of a STC solution.

4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen

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This is a complex technology, it requires high operation& maintenance cost and a continuous presence ofoperators. [4]The main advantage related to thistechnology is the possibility to store heat to assureavailability even during night hours. The performance ofthis plant is 22, 4 % for a 1MW installed and 24, 1% for5MW.

This is given by product of

field = mirror * htf * power cycleIn table 1 are displayed the components of the totalcost.

Table 1. Cost of the system components in %.Tecnology STC %cost %cost

Nominal power [MW] 1 5

Solar field [/Wp] 0,791 24,3 0,712 35,1

HTF [/Wp] 0,061 1,9 0,055 2,7

Power Block [/Wp] 1,893 58,1 1,097 54,1

auxiliary [/Wp] 0,120 3,7 0,076 3,7

land and preparation [/Wp] 0,396 12,1 0,089 4,4

total investement [/Wp] 3,261 100,0 2,030 100,0

O&M [/Wp-year] 0,100 3,1 0,088 4,3System efficiency 22,50% 24,10%

Energy production[Wh/m2-yr]

300 322

Energy cost [/kWh] 0,18 0,14

The cost of electricity generated is calculated for twodifferent plants; in fig.3 its clear that the dimension of theplant influences the cost of the power block.

PV concentrator technologies

There are two main benefits from the use ofconcentration in PV systems: (a) the increase inefficiency and (b) the decrease in cost. We analyse two

systems based on CPV technology LCPV and HCPV.

The main difference between LCPV and HCPV is theconcentrator factor and the types of solar cells used.Optics is a TIR-R lens that reaches high concentratorfactor, with a good acceptance angle. [5].Anotherimportant aspect is the thickness of the module.

The cost is in relation to the number of lens per m^2 andthis is obtained from real data of optoelectronicsindustry. The formula used is

1600/N^0, 5 + 0,027N

(optics cost + encapsulated cost in /m2). N is thenumber of optical concentrators per m^2. [6]

The cooling system is an important aspect of themodule; we consider a passive cooling (an active coolingis the best solution to increase the efficiency but morecomplex technology adds more cost to the total). [6]

Other costs considered are due to the moduleassemblage, mounting of it upon the structure, trackingsystems (single axis or two axes), inverters, cables etc.

These values are taken from existing power plants.

High PV Concentrator (HCPV)

The second system analysed is a high concentratormodule (500X).

This represents a solution available on the market , witha tandem GaAs solar cell that reaches a 32% efficiency;several studies show that the III-V J solar cell couldhave better performance (more then 40% ).[7]

Chip size of the useful cell is 1 mm^2; the material usedis in reality 60% greater so the total area becomes 1, 69mm^2.

The cost of tandem cell considered is 14, 7 /cm^2 [6];referred to the cost / surface area of concentrator itbecomes 0, 0294 /cm^2.

The module efficiency is given by the product of threeefficiencies:

module = cell * optics * electronic

We reach a value of 24, 8% with GaAs, and 31 % withMJ.

The annual system efficiency of the power plant is 18,

5% for the first configuration and 23, 1 % for MJ solution.Operation and maintenance costs are the ones of thestructure, inverter and tracking,

The system could be completely automatic and could bemonitored by a remote control. No person is necessaryto control this power plant.

Finally we find the energy cost, [/kWh].

For the first solution we have 0,147 /kWh and 0,131/kWh for MJ.

Table 2.Cost of the system components in %.

TechnologyHCPV 500X

[GaAs]%

HCPV 500X[MJ]

%

Nominal power [MW] 1 1

Concentrator solar celll[/Wp]

1,316 51,1 1,369 57,6

Optics andencapsulation [/Wp]

0,184 7,2 0,147 6,2

Cooling [/Wp] 0,134 5,2 0,107 4,5

Structure , tracking ,assembling

and DC wiring [/Wp] 0,626 24,3 0,501 21,1

Land and Preparation[/Wp]

0,089 3,5 0,072 3,0

Inverter , transformer ,electrics [/Wp]

0,224 8,7 0,179 7,5

Total cost [/Wp] 2,574 100 2,375 100

O&M [/Wp-year] 0,045 1,7 0,036 1,5


268 335

Energy cost [/kWh] 0,147 0,131

Low concentrator (LCPV)

The third system considered has a low concentratorfactor. We analyse three different solutions; a very lowconcentrator factor with 20X, 100X and 200X.


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The 20X solution doesn't require a high precision angleof acceptance; so if C < 20X is possible to use a singleaxis tracker (this decreases both the cost of the structureand the tracker). With this LCPV its possible to realizesolutions to be installed on the roof and in buildingintegration (like flat plat module).

The cell type used for low C is a Silicon solar cell with arear contact. Several studies of this cell under a C factorshow that a non linear efficiency improvement is

possible. We optimized the dimension of the chip inrelation to the C factor; for a 20X the best solution its a5mm square cell, for 100X and 200X its 2mm.

The maximum cell efficiency is 27% for 100X and its 26,5% for 200X and 20X. [8]

The cost of silicon cell is more then 150 times lower thanGaAs and MJ. It's about 0, 09 /cm^2, so the impact onthe total cost of the system is low. This is a veryimportant aspect because the cost for Silicon, in aphotovoltaic standard technology is 60 % of the totalcost.

Module efficiency is 21, 3 % for a 20X, 21, 5% for 100Xand 21, 3 for 200X .

Operation & maintenance cost are similar to the previoussystem, but using a single axis tracking system the costdecreases.

Table 3. Cost of the systems components in %.

TecnologyLCPV20X

[5mm]%

LCPV100X[2mm]

%LCPV200X[2mm]

%

Nominal power [MW] 1 1 1

Concentrator solarcell [/Wp]

0,229 13,9 0,045 3,1 0,023 1,56

Optics andencapsulation [/Wp]

0,398 24,3 0,392 27,1 0,446 29,76

Cooling [/Wp] 0,153 9,3 0,152 10,5 0,152 10,12

Structure , tracking ,assemblingand DC wiring

[/Wp]

0,559 34,1 0,556 38,4 0,573 38,25

Land and Preparation[/Wp]

0,102 6,2 0,101 7,0 0,104 6,95

Inverter , transformer ,electrics [/Wp]

0,200 12,2 0,200 13,8 0,200 13,35

Total cost [/Wp] 1,641 100,0 1,445 100,0 1,498 100,00

O&M [/Wp-year] 0,051 3,1 0,051 3,5 0,052 3,48


235 237 230

Energy cost [/kWh] 0,115 0,113 0,114

3. Cost comparison

To compare different solar technologies, we use, as

main parameter, the cost of energy generated (itincludes all capital costs, energy production, O&M cost,and financial aspect). Every item of the total cost isreferred to the energy cost in order to analyse whichcomponent of the system is the most important andcould be improved.

Fig. 2 represents two solar thermal plants (STC) withdifferent size, and same technology

.

Fig.2 Cost of the system components in %

The main cost is given by the solar field and the powerblock (which includes turbine, condenser, and heatexchanger). If we compare a 5 MW and 1 MW plant we

observe that the power block cost decreases and thesolar field increases (Fig.2). The main reason is theimprovement of power block efficiency. In Fig.3 we casee how plant size affects the energy cost of this type oftechnology.

Fig 3 Cost of the system vs. installed power

For HCPV the main cost is the solar cell concentratorand tracking. In Fig. 4 we have the energy cost for twomodules using tandem solar cell and MJ, with 500X and1000X Concentration level.

The C factor has a big influence on the cell cost inrelation to the entire module; this is 33% of the cost of a1000X, and 51% for a 500X solution. The MJ solution isa new technology and so we can expect a goodoptimisation of it in the near future.

STC solar thermal concentrator

0,00

0,02

0,04

0,06

0,08

0,10

0,120,14

0,16

0,18

0,20

1MW 5MW

/kWh

O&M

LAND

OTHER COST

POWER BLOCK

HTF

SOLAR FIELD

STC curve cost

0

0,02

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

0,2

0 50 100 150 200 250 300 350

Power [MW]

/kWh


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Fig. 4 Cost of the systems components in %.

In the LCPV study we consider three differentconcentrator factors and 4 different chip sizes (which aswe see in Fig. 5 are important to optimize the number ofoptics and their costs).

Fig. 5 Cost of the systems components in %.

The most influential components are structure, tracking

and optics and encapsulation which can be reducedusing LED technologies and by moving forward on thelearning curve. Concentrator solar cell cost is 12% of thetotal for a very low C factor (20X) , 2% of a 100X andonly 1% of a 200x. This means that high concentrationlevel is not an optimal solution for silicon cell.

However LCPV can be used with MJ cells as soon astheir cost will decrease; recent studies show that someMJ cells have high efficiency at C equal to 5-10X [7].

The thickness of low LCPV could be very small (similarto the 1 sun PV).This aspect, with the use of a singleaxis tracking system, give to the LCPV technology thepossibility to be adopted in BIPV or roof solutions with acost three times smaller then a 1 sun PV.

4. Conclusion

From this study we can make the followingconsideration.To realize a big power plant (>10-50MW) the mostefficient technology for best ROI is STC (Solar ThermalConcentrator) using different typologies as ParabolicMirrors, Solar Tower or Dish.

This technology is under improvement and has thepossibility to work even in dark condition using storageheat tanks.For a middle size plant ( 100KW to 10-50 Mw) with directsolar radiation the best solution could be HCPVespecially if MJ will decrease in price and increase inefficiency (as its happening right now).

A lot of improvements are under development and weare expecting in 2007 the start of the market.

The LCPV technology could be interesting in the smallpower plant and in the near term. It seems interesting touse, for their production, the same LED technology toreduce the cost. These systems may have similardimension as a 1 sun PV and so they could be usedeven on roof solution or BIPV using a single axistracking. The LCPV solutions that are using currentSilicon production should use in the future new MJ astheir price will decrease.

References

[1] http://re.jrc.ec.europa.eu/pvgis/pv

[2] E. Prabhu,California Solar Trough Organic Rankine

Electricity System (STORES) Stage 1: Power PlantOptimization and Economics November 2000 May2005Reflective Energies Mission Viejo, California NREL/SR-550-39433 March 2006.

[3]M.Falchetta Il programma Enea sull'energia solare aconcentrazione ad alta temperaturaENEA GrandeProgetto Solare Termodinamico Unit Ricerca eSviluppo Centro Ricerche CasacciaVia Anguillarese, 301- S.Maria di Galeria 00060 Roma

[4]D.Kearney , H.Price (2006) Advances in solar powerplant technology an annual review of research anddevelopment pp 204-223

[5] Jose L.Alvarez , Vincente Diaz , Jusus Alonso Opticsdesign key points for high gain photovoltaic solar energyconcentrators ISOFOTON s.a Severo Ochoa ,50,Parque Tecnologico de Andalucia Malaga 29590 Spain

[6]A. Mart, A. Luque Next generation photovoltaics,high efficiency through full spectrum utilization chapter 6pp 108-133

[7]R. McConnell, M. Symko-Davies MultijunctionPhotovoltaic Technologies for High-PerformanceConcentrators Presented at the 2006 IEEE 4 WorldConferences onPhotovoltaic Energy Conversion (WCPEC-4) Waikoloa,

Hawaii May 712, 2006

[8] A.Mohr aus Stegen Silicon Concetrator Cells in Two-stage photovoltaic system with a concentrator factor of300X Dissertation zur Erlangung des Doktorgrades derFakultt fr Angewandte Wissenschaften der Albert-Ludwigs-Universitt Freiburg im Breisgau

[9] ISOFOTON price

LCPV

0,00

0,05

0,10

0,15

0,20

0,25

1 2 3 5 1 2 3 5 1 2 3 5

cell size [mm] concentrator factor [20

100 200]

/kWh

OPERATION &

MANTEINANCE

INVERTER, TRANSFORMER

ELECTRICS

LAND and PREPARATION

STRUCTURE, TRACKING

COOLING

OPTICS and

ENCAPSULATION

CONCENTRATOR SOLAR

CELL

HCPV

0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

1000X 500X 1000X 500X

Concentrar factor [GaAs] [MJ]

/kWh

OPERATION & MANTEINANCE

INVERTER, TRANSFORMER

,ELECTRICS

LAND and PREPARATION

STRUCTURE, TRACKING,ASSEMBLIN

and DC WIRING

COOLING

OPTICS and ENCAPSULATION

CONCENTRATOR SOLAR CELL


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EXPERIMENTAL TEST AND MODELLING OF CONCENTRATOR SOLAR CELLSUNDER MEDIUM AND HIGH FLUXES

A. Vossier1, S. Quoizola

2, S. Grillo

2, G. Flamant

1and A. Dollet

2*

Laboratoire PROMES-CNRS1B.P. 5 Odeillo - 66125 Font Romeu Cedex -FRANCE

2Tecnosud - Rambla de la thermodynamique, 66100 Perpignan France

*Corresponding author: phone +33 4 68682212, e-mail: [email protected]

ABSTRACT

The goal of this work was to study the potential ofsome concentrator solar cells for operating under highflux.

Single junction GaAs cells and InGaP/InGaAs tandemcells (ISE Fraunhofer) were tested in outdoor conditions. 2dish mirror-based systems were developed for performingmeasurements: a medium concentration system workingbelow 800 suns and a high concentration system working

up to 10,000 suns. Simple analytical models were derivedfrom I-V measurements under low flux in order to evaluate

the conversion efficiencies () at various concentrationratios (X) and temperatures (Tcell). By modelling heattransfer in the CPV systems, 2D temperature profiles inthe cells were calculated for various concentration and

cooling conditions. Theoretical values of (X, Tcell) werecompared to values measured under medium fluxconditions. While free convection on a Cu plate issufficient for cooling cells under medium concentration,active cooling becomes necessary at very highconcentration.

INTRODUCTION

Concentration of sunlight is known to be a promisingway of reducing the cost of photovoltaic conversion. To

date, most concentrator solar cells have been studied

under low and medium concentration ratios (below 500 or

1000 suns), but there is little literature available today on

solar cells operating under very high fluxes (between

1,000 and 10,000 suns) [1].

At such high concentration levels, several

technological requirements must be achieved: high

efficiency of the cooling system, good quality optics and

very low series resistance in order to minimise the

electrical losses in the cell [1].

The ultimate goal of this work will be to test selected

concentrator solar cells under very high solar fluxes (up to10,000 suns) in real outdoor conditions. In this paper, as a

starting point, various concentrator solar cells will be

tested under medium flux, then simple simulations of heat

transfer and energy conversion will be performed. From

both series of results, appropriate conditions and solar

cells will be selected for forthcoming ultrahigh flux

experiments.

EXPERIMENTAL PROCEDURE

Experiments were conducted at Odeillo, a place inthe south of France where particularly good direct sunlightconditions can usually be found. Solar facilities from eitherthe DGA-CEP or PROMES laboratory have been used.

The parabolic dish used for medium concentrationexperiments (figure 1) has a diameter of 1 m and a focallength of 2.8 m. The focal spot diameter is about 30 mm.The maximum concentration ratio is approximately 800 atthe center of the spot. The concentration level ismodulated by means of an iris placed in front of the dish.

Fig. 1. Schematic view of the medium concentrationexperiment (heliostat+ dish double reflection system)

The parabolic dish used for very high flux experimentshas a diameter of 1.5 m and a focal length of 0.65 m. Thefocal spot diameter is 16 mm. The maximum concentrationratio is approximately 10,000 at the center of the spot.

Concentrated

beam

Cooled mask

Solar cell

Heat sink

Glass rod

Fig. 2. Schematic view of the cooled mask and opticalguide designed for high concentration experiments


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In both systems, a water-cooled mask with a 2mmhole in its centre is placed above the cell in order to fit thesize of the incoming beam to the 2 mm cell, and avoid anyoverheating of the surrounding parts (e.g. electricalcontacts). In the particular case of the high concentrationsystem, which has a short focal length, the concentratedbeam is transmitted through a silica rod that is fixed to thewater-cooled mask (fig. 2). In both systems, the solar cellis mounted on a copper plate, itself mounted on a water-

cooled support. IV curves were recorded with a Keithley2600 sourcemeter.

EXPERIMENTAL RESULTS

Our very first experimental tests were performedunder medium concentration (1

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several hundreds of suns. However, operating cells withconcentration ratios between 1,000 and 10,000 requiresvery efficient active cooling systems for dissipating thenon-converted fraction of absorbed radiation as well as theheat due to increased ohmic losses at high currentdensities. In order to estimate the temperature increase inthe cell under various concentration ratios, prior toconducting experiments, 2D simulations of heat transferinside the cell and Cu heat sink were performed by using

the COMSOL (FemLab) software. In the case of passivecooling, heat is transferred by conduction in the solid partsand extracted by radiative and convective exchangesbetween the solids and ambient air, while in the case ofactive cooling, an additionnal "forced convection"contribution is added (water-circulation).

The conduction part of the heat transfer writes, in steady-state conditions:

cond2

2

Qx

T

k =

(1)

where k is the thermal conductivity of the solid (cell or heatsink).

Radiative exchanges between the cell and ambient air aredescribed by the following relation:

Qray= (T4-T0

4) (2)

where is the emissivity of the material and the Stefan-

Boltzmann constant. Values of and k can be easily foundin handbooks.

Passive cooling and active cooling require two differenttreatments for convection:

Case 1 : Passive cooling

The heat flux exchanged by natural convection can bewritten as [3] :

Qconv = h(Tcell -Tair) (3)

where his the natural convection coefficient.The natural heat transfer coefficient of the upper (front)surface (cp-1) of the heat sink is given by :

p

fcpcp

D

kNuh

11

= (4)

where

4/111 59.0 = cpcp RauN

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resistances (Rs) of concentrator solar cells are usually

small (typically in the range 1-10 m), but additionalresistances due to undesirable bad electrical contacts inthe circuit, as well as the resistance of the electrical wiresmust be taken into account. For instance, considering thesize of our dish and the fact that the I-V measurementsystem is located approximately 1.5 m away from thefocus plane, a 3 m long electric wire with a non-negligibleresistance is needed to connect the cell to the Keithley

sourcemeter. The resistance Rw associated with thiselectric wire can be estimated by the following relation :

Rw=S

l(11)

where , l and S are respectively the resistivity, the lengthand the cross-sectional area of the wire. Of course, thevalue of the resistance of this electric wire should beminimized by choosing a very low resistivity metal, suchas silver, and by lowering the l/Sratio.

The total resistance of the circuit is equal to the sumof the resistance associated with the electric wires Rwandthe series resistance of the cell Rs.

R = Rw+ Rs (12)

Three values of the circuit resistance have beenconsidered here, in order to evaluate the power losses in

the circuit when the total resistance is low (R=10 m),

moderate (R=100 m) and very high (R=1)..

The ratio of power loss is defined as the powerdissipated by joule effect divided by the power deliveredby the cell at the maximum power point (Pcell) :

rPL=cell

loss

PP (13)

In our case, the power delivered at the maximal powerpoint has been simply calculated from the measured valueat 1 sun, corrected for the theoretical voltage increaseresulting from the concentration, but losses due to series

resistance have been neglected in this calculation, for asimplification purpose only. This means that the valuesreported in this paper for the ratio of power loss are lowerlimits. This ratio has been calculated for three differentsizes of solar cells : 3.14, 16 and 100 mm, and for fourdifferent concentration ratios (1,000; 2,000; 5,000 and10,000 suns).

Table 3 to 5 show that power dissipation by jouleeffect may drastically reduce the power delivered by thelarger cells submitted to very high concentration ratios.The most critical situation corresponds to large cellsand/or large resistances. In this case, all the powerdelivered by the cell is dissipated by joule effect.

Very mall size solar cells may efficiently work, even at

quite high solar fluxes, if the circuit resistance is kept verysmall (less than 10 m).

Ratio of power loss (%)

Concentrationratio

R= 10 m R= 100 m R= 1

1000 0.5% 4.9% 48.6%

2000 0.96% 9.6% 95.5%

5000 2.34% 23.3% 100%

10 000 4.6% 45.9% 100%

Table 3 : Evolution of the ratio of power loss for a 3.14mm GaAs solar cell under high solar fluxes.


Concentrationratio

R= 10 m R= 100 m R= 1

1000 3.6% 35.8% 100%

2000 7.03% 70.3% 100%5000 17.2% 100% 100%

10 000 33.8% 100% 100%

Table 4 : Evolution of the ratio of power loss for a 16 mmGaAs solar cell under high solar fluxes.


Concentrationratio

R= 10 m R= 100 m R= 1

1000 22.3% 100% 100%

2000 43.95% 100% 100%

5000 100% 100% 100%

10 000 100% 100% 100%

Table 5 : Evolution of the ratio of power loss for a 100 mm

GaAs solar cell under high solar fluxes.

Finally, we have performed a 2D simulation with ComSolin order to simulate the temperature increase due to jouleeffect in the small electrical gold connections extractingthe current from the cell core. The temperature of the goldwires may exceed 900C at 10,000 suns in our cells,which have typically only 4 gold wires. It is concluded thatour solar cells could perhaps operate at slightly higherconcentration, but smaller cells with a rather large numberof electrical gold wires must be used in order to limit thetemperature increase in the cell or in electrical contactsunder very high concentrations.

ACKNOWLEDGEMENTS

We would like to thank J. Gordon, from Ben GurionUniversity (Isral) for his encouragements and stimulatingdiscussions. We also thank R. Garcia and J-J. Huc(PROMES) for their assistance in the design of theexperimental set-up, J-J. Serra, JM Sayous and E. Scheer(DGA) for invaluable technical support.

This work was partly conducted in the framework of anagreement between DGA and CNRS (MCTS researchteam).

REFERENCES

[1] C. Algora. The importances of the very high concentration inthird generation solar cells. Next generation photovoltaics: highefficiency through full spectrum utilization2004. pp. 108-136.

[2] J. Sun, T. Israeli, T. Agami Reddy, K. Scoles, J. Gordon andD. Feuermann. Modelling and experimental evaluation of passiveheat sinks for miniature high-flux photovoltaic concentrator.Journal of solar energy engineering 2005. 127, . pp. 138-145.

[3] G. Siefer, P. Abbott, T. Schlegl and A.W. Bett.Determination of the Temperature Coefficients of Various III-VSolar Cells. 20th European Photovoltaic Solar EnergyConference 2005.


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HIGH-FLUX CHARACTERIZATION OF ULTRA-SMALL TRIPLE-JUNCTIONCONCENTRATOR SOLAR CELLS

Omer Korech, Baruch Hirsch, Eugene A. Katz and Jeffrey M. Gordon

Department of Solar Energy and Environmental Physics, Jacob Blaustein Institutes for Desert Research,Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel

ABSTRACT

Ultra-small multi-junction solar cells comprise thelatest generation of commercial concentratorphotovoltaics, with claims of cell efficiency ~40% achievedat several hundred suns. Cell miniaturization ostensiblyallows greater peak efficiency at higher flux, facilitatespassive heat rejection and permits the practical use of all-glass optics. However, few measurements have been

reported, in particular as a function of concentration andflux distribution. We present extensive measurements oncommercial ultra-small triple-junction solar cells with asolar fiber-optic mini-concentrator. Flux maps on the 1.0mm

2active region within the busbars were varied from

strongly inhomogeneous to uniform, at delivered fluxlevels up to ~5000 suns. These results allow assessmentsof (a) optical and internal resistive losses, as well as (b)cell performance at high flux, including (c) sensitivity to thetype of flux inhomogeneities encountered in high-fluxoptical devices.

INTRODUCTION

Multi-junction solar cells have already

demonstrated conversion efficiencies above 40% atseveral hundred suns [1]

(one sun 1 mW/mm2). High

concentration with inexpensive high-flux optics allowsreducing the system share of costly photovoltaic (PV)cells. Practical considerations then motivate cellminiaturization, which can [2-4]: increase cell efficiency,raise the flux value at which efficiency peaks, facilitatepassive heat rejection and permit all-glass compactminiaturized optics [5-6]. The latter was recentlysuggested for realizing net flux values in excess of 10

3

suns at high collection efficiency with completely passiveheat rejection for a cell area of ~1 mm

2. Such ultra-small

triple-junction solar cells lie at the core of the latestgenerations of commercial concentrating PV systems.

However, there are few published data on cellperformance, in particular as a function of concentrationand flux distribution.

Here we present measurements on commercialultra-small triple-junction GaInP2/GaAs/Ge solar cells [7],generated with our ultrahigh flux real-sun fiber-optic mini-dish concentrator [8-11], and elucidate the principal cellparameters essential for appraising concentrating PV

performance for broad ranges of anticipated operatingconditions.

EXPERIMENTAL

All experiments were performed with a dual-axistracking mini-dish solar concentrator [8] whereintransmissive (quartz-core) optical fibers 1.0 and 0.6 mm indiameter channeled concentrated sunlight to an indoor

test bench (Fig 1). The localized irradiation probe (LIP)[10-11] delivered light confined to the circle delimited bythe fiber tip. This procedure can simulate the intensity andtype of non-uniform distributions produced by manypractical high-flux optics [3, 5-6]. Uniform irradiation of thecell's active area was produced with a square glasskaleidoscope coupled between the distal fiber tip and thecell (Fig 1b). Solar irradiation on the cell Pin wasmoderated with an iris (Fig 1a) and measuredpyrometrically. LIP levels were varied continuously. Thehighest localized concentration with the 0.6 and 1.0 mmfibers was 3700 and 5100 suns, respectively.

Fig 1. (a) Solar mini-concentrator (20 cmdiameter) with fiber-optic transmission indoors [8]. Inputpower is moderated by an iris that preserves the angulardistribution of delivered sunlight. (b) Uniform cellirradiation by a kaleidoscope. (c) Fiber-cell contact in theLIP mode.


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Measurements were limited to clear-sky periods,two hours about solar noon, over the course of severalmonths in Sede Boqer, Israel. The light spectrum on thecell was nearly invariant and close to the air mass 1.5direct beam solar spectrum [8].

Cell dimensions are indicated in Fig 2. Current-voltage (I-V) curves were measured with 3 patterns: (a)uniform illumination of the full 1.0 mm

2active area within

the busbars, (b) LIP with the 1.0 mm fiber, and (c) LIP with

the 0.6 mm fiber. Cells were mounted on a 1.6 mm thickgold-coated Kovar ceramic substrate which was thermallybonded to a passive copper heat sink. The maximumtemperature at the heat sink-substrate interface was only3 K above indoor ambient (actual cell junctiontemperatures cannot be measured directly and exceedthat of the interface).

Fig. 2. Photograph of the square GaInP2/GaAs/Ge triple-junction cell with 4 busbars of 0.2 mm width. Net activearea = 1.00 mm

2. Gross area = 2.56 mm

2.

Short-circuit current Isc was found to beproportional to Pin with Isc/Pin = 0.1380.007 A/Windependent of both Pin and flux distribution. In the

analyses that follow, Fill Factor FF and cell efficiency are calculated as

FF= Pm/(IscVoc) (1)

= Pm/Pin = FFIscVoc/Pin (2)

where Vocdenotes open-circuit voltage, and Pm is themaximum electrical power output.

RESULTS AND DISCUSSION

Fig. 3 summarizes all data for Voc, FFand asfunctions ofPin and flux distribution. Several observationsare germane in evaluating such ultra-small cells for high-flux applications.

(A) Under uniform illumination of the active 1.0mm

2area within the busbars, efficiency is maximum at a

flux level of ~1,000 suns (Fig. 3b) - considerably higherthan the ~350 suns at which the efficiency of an earlier100 mm

2of the same nominal cell architecture peaked

[12].

ABSTRACTS

Position the word ABSTRACT (all upper case) 0.5(12 mm) below the last line of the organization, centered inthe left-hand column. A blank line should be insertedbetween the title and text of the abstract. The abstract textis limited to 2.5 (63.5 mm). Begin the main text of themanuscript 0.39 (10 mm) below the end of the abstract.

HEADINGS

This sheet has been generated in accordance withthe style to be followed for the headings. Major headingsare to be in capitals without underlining, centered over onecolumn and bold. Subheadings are to be lower case with

initial capitals and bold. Subheadings should start at theleft-hand margin on separate lines. Sub subheadings aretreated the same as subheadings. A blank line should beplaced both before and after each heading or subheading.

EQUATIONS

Equations are to be numbered consecutivelythroughout the paper. The equation number, inparentheses, should be placed flush with the right-handmargin of the column. When possible, use an equationeditor.

[ ]12

1

2

1121 TT

G

GIII

I

I

sc+

+= (1)

Fig. 3. Dependence of (a) FF, (b) and (c) Voc on Pin forvarious flux distributions. The experimental uncertainties

are 0.5, 2 and 5 % (relative) for Voc, FF and ,respectively. In Fig 3c, the data for uniform illuminationwere obtained with a flash solar simulator.

0.70

0.75

0.80

0.85

0.90

10 100 1000 10000

Pin [mW]

FillFactor

KaleidoscopeLIP: 1.0 mm fiberLIP: 0.6 mm fiber

2 8

2 9

3 0

3 1

3 2

3 3

3 4

3 5

3 6

1 0 1 0 0 1 0 0 0 1 0 0 0 0P in [ m W ]

Efficiency[%]

K a l e i d o s c o p e

L IP : 1 m m f ib e r

L IP : 0 . 6 m m f ib e r

2600

2800

3000

3200

10 100 1000 10000Pin [mW]

VOC

[mV]

KaleidoscopeLIP: 1.0 mm fiberLIP: 0.6 mm fiberFlash simulator

a

b

c


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(B) The degree of flux non-uniformity producedby LIP with the 1.0 mm fiber did not result in significantdifferences in I-V curves or the principal cell parameters(relative to uniform irradiation), independent of Pin, towithin our experimental uncertainty of 0.5% in both IandV.

(C) The cell parameter most sensitive to seriesresistance, and hence to irradiation distribution, FF,remains roughly independent of both Pin and flux

distribution up to an input power of almost 1.0 W (Fig 3a).The impact of highly localized flux distribution (with the 0.6mm fiber) at higher concentration is considerable as seriesresistance effects are expressed more prominently [11].These trends are also reflected in the efficiency (Fig 3b).

(D) By measuring I-Vcurves across the active 1.0mm

2area inside the busbars with the 0.6 mm fiber, the

spatial dependence of cell performance was mapped, and,for each Pin value, found to be independent of position.This reveals the homogeneous spatial distribution of bothoptical and series resistance losses. (The perfectlyhorizontal behavior of the low-voltage regime in the I-Vcurves we measured attested to negligible shunt losses,as in earlier investigations of cells of comparablearchitecture [10-11].)

(E) When series resistance and heating lossesare negligible, plots ofVoc against ln(Pin) are linear with aslope that reveals the diode quality factor n (for an idealtriple-junction cell, n = 3)

Voc (nkT/q) ln(Isc/Io) (nkT/q) ln(Pin) + const, (3)

where k is Boltzmann's constant, q is the magnitude ofelectron charge and Io denotes the reverse saturationcurrent - consistent with our lower-flux measurements,including their insensitivity to flux distribution (Fig 3c).However, the regressed value of n is ~6, indicative ofstrong recombination in the depletion regions of the cell

junctions. Because previous large (100 and 30 mm2)

versions of the same cell architecture exhibited n

3 [11-12], it would appear that the anomalously high n in theseultra-small cells stems from edge recombination, andmandates proper edge passivation in future fabrication[13-14].

(F) When flux level and/or inhomogeneityengender non-negligible series resistance losses, Vocshould deviate from Eq (3) and should asymptote at highflux [11] (if cell temperature is maintained constant).When, in addition, cell temperature increases with flux, Vocmay decrease as Pin is raised. Because our passive heatsinks were intended to simulate actual concentratoroperation and therefore allowed junction temperatures thatare non-negligibly above ambient, we filtered thetemperature effect by performing measurements in a flash

(s) solar simulator where the cell was uniformlyilluminated and actively cooled to within 1 K of ambient(uppermost curve in Fig 3c). With heating mitigated, theeffect of series resistance in lowering Vocbelow that of Eq.(3) becomes evident at concentration values above ~1000suns. The signature of flux non-uniformity here likelyderives from the large busbar area and the substantialdark current it contributes, which enhances the distributedcharacter of series resistance losses [15-17].

CONCLUSIONS

This report constitutes one of the firstcharacterization studies of the new generation of ultra-small and nominally ultra-efficient multi-junctionconcentrator solar cells, with emphasis upon the sensitivityof their performance to concentration and flux distribution.Information of this type is essential in the design andoptimization of new high-flux photovoltaic systems. It also

highlights the value of fiber-optic mini-concentratorlocalized irradiation probes in mapping cell propertieseven within a 1 mm

2area.

Ultra-small cells are motivated in part by theprospect of higher efficiency that is realized at far higherconcentration values than with previous technologies. Theadequacy of the metallization and busbar design remainedto be established.

GaInP2/GaAs/Ge cells with an active area of 1.0mm

2within the busbars, and busbars of essentially the

same area, were probed by continuous concentratednatural sunlight (in contrast to flash simulators) at fluxlevels up to ~5100 suns with flux distributions (within thebusbars) that varied from uniform to markedlyinhomogeneous with all the light being restricted to 28% of

the active area. (Passive cooling sufficed in all instances.)Their efficiency peaked at ~1000 suns for uniformirradiation of the 1.0 mm

2region within the busbars. In

contrast, earlier generations of concentrator cells hadbeen tailored for efficiency to peak at ~200-300 suns[3,4,7,12].

The fact that plots ofVoc against ln(Pin) are sub-linear above ~1,000 suns indicates that an improved frontcontact configuration could both enhance efficiency andincrease the concentration at which efficiency peaks, e.g.,reconfiguring the busbar toward diminishing dark currentlosses.

The measured diode quality factor n 6 isindicative of an excessive recombination at the cell

perimeter, that could be reduced by passivation of the celledges.The irradiation protocols and inhomogeneous flux

maps used for cell interrogation can be similar to thosegenerated in some of the high-flux optics for concentratorphotovoltaics. As such, they shed light on the performancepenalties (or the lack thereof) that can be anticipated innew generations of photovoltaic concentrator systems.

ACNOWLEDGMENTS

We thank Vladimir Melnichak for technicalassistance, Gary Conley and Steve Horne of the SolFocusInc., Palo Alto, CA for providing the solar cells and

Andreas Bett and Gerald Siefer of the Fraunhofer Institute

for Solar Energy Systems for cell testing with a flash solarsimulator. EAK thanks the Israel Ministry of Absorptionand the Deichmann Foundation for financial support.

REFERNCES

1. US Department of Energy, Press release ofDecember 5, 2006. New World Record Achievedin Solar Cell Technology.


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2. C. Algora. "Very high concentration challenges ofIII-V MJCs," in Concentrator Photovoltaics, Eds.

A. Luque and V.M. Andreev, in press (Springer,Heidelberg) 2007.

3. A. Bett and H. Lerchemueller. "The 'Concentrix'system," in Concentrator Photovoltaics, Eds. A.Luque and V.M. Andreev, in press (Springer,Heidelberg) 2007.

4. K. Nishioka, T. Takamoto, T. Agui, M. Kaneiwa,

Y. Uraoka and T. Fuyuki. "Evaluation ofInGaP/InGaAs/Ge triple-junction solar cell andoptimization of solar cell's structure focusing onseries resistance for high-efficiency concentratorphotovoltaic systems," Sol. Energy Mat. Sol.Cells, 90 (2006) pp. 1308-1321.

5. R. Winston and J.M. Gordon. "Planarconcentrators near the tendue limit," Opt. Lett.30 (2005) 2617-2619.

6. www.solfocus.com/technology_gen2.html.7. Technical prospectus and private

communications (G. Glenn), Spectrolab Inc.,12500 Gladstone Ave., Sylmar, CA,www.spectrolab.com.

8. J.M. Gordon, E.A. Katz, D. Feuermann and M.

Huleihil. "Toward ultrahigh-flux photovoltaicconcentration,"Appl. Phys. Lett.84, (2004) 3642-3644.

9. J.M. Gordon, E.A. Katz, W. Tassew and D.Feuermann. "Photovoltaic hysteresis and itsramifications for concentrator solar cell designand diagnostics," Appl. Phys. Lett. 86 (2005)073508.

10. E.A. Katz, J.M. Gordon and D. Feuermann."Effects of ultra-high flux and intensity distributionin multi-junction solar cells," Prog. Photovoltaics14 (2006) 297-303.

11. E. A. Katz, J. M. Gordon, W. Tassew and D.Feuermann. "Photovoltaic characterization ofconcentrator solar cells by localized irradiation,"J. Appl. Phys.100 (2006) 044514.

12. R.R. King, R.A. Sherif, G.S. Kinsey, S. Kurtz,C.M. Fetzer, K.M. Edmonds, D.C. Law, H.L.Cotal, D.D. Krut, J.M. Ermer and N.H. Karam."Bandgap Engineering in High-EfficiencyMultijunction Concentrator Cells," In: Int. SolarConc. Conf. for the Generation of Electricity orHydrogen, Scottsdale, AZ, May 2005, Proc.NREL/CD-520-38172 (2005).

13. M. S. Carpenter, M. R. Melloch, M. S. Lundstrom,and S. P. Tobin. "Effects of Na2S and (NH4)2Sedge passivation treatments on the dark current-voltage characteristics of GaAs pn diodes,"Appl.Phys. Lett.52 (1988)2157-2159.

14. S.R. Kurtz, J.M. Olson, D.J. Friedman, J.F.Geisz, and A.E. Kibbler. "Passivation ofinterfaces in high-efficiency photovoltaic devices,"NREL/CP-520-26494 (1999).

15. G.M. Smirnov and J.E. Mahan. "DistributedSeries Resistance in Photovoltaic Devices:Intensity and Loading Effects," Solid-StateElectronics 23 (1980) 1055-1058.

16. L.D. Nielsen. "Distributed series resistanceeffects in solar cells," IEEE Trans. ElectronDevicesED-29 (1982) 821-827.

17. V.M. Andreev, V.A. Grilikhes and V.D.Rumyantsev. Photovoltaic Conversion ofConcentrated Sunlight(Wiley, Chichester) 1997.


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FLUXMETER FOR PARABOLIC TROUGH SOLAR CONCENTRATORS

A. Parretta*1,2

, M. Stefancich2, A. Antonini

2, G. Flaminio

3, M. Pellegrino

3, L. Gentilin

4, A. Maccari

4, M. Montecchi

4

1ENEA Centro Ricerche E. Clementel, Via Martiri di Monte Sole 4, 40129 Bologna (BO), Italy.

2Physics Department & CNR, University of Ferrara, Via Saragat 1, 44100 Ferrara (FE), Italy.

3ENEA Centro Ricerche Portici, Localit Granatello, 80055 Portici (NA), Italy.

4ENEA Centro Ricerche Casaccia, Via Anguillarese 301, 00123 S. Maria di Galeria (RM), Italy.

*Phone: +39 (0)51 6098617; Fax: +39 (0)51 6098767; E-mail: [email protected]

ABSTRACT

A fluxmeter for parabolic trough solar concentratorsis described. The concentrated solar radiation impingingon the receiver of the collector is detected around the focalline by eleven concentration cells distributed on the outersurface of a cylindrical sensor head, each one protectedby a translucent window. The sensor head is shaped as acollar to be mounted around the glass tube protecting thecylindrical thermal receiver. Photocurrent and temperatureof each cell are measured and the electric signals sent toremote instrumentation. A fan on the back of the sensorbody improves the cell cooling. Test campaigns carriedout at a solar plant of ENEA-Casaccia (Rome) furnishedflux density distributions in good agreement with thosesimulated on the basis of the shape of the collectingmirrors, which was measured by an optical profilometer.

INTRODUCTION

The widespread use of solar concentration for thephotovoltaic or thermal solar energy conversion demandsthe development of new instrumentation for measurementof total flux or flux density distribution of the concentratedbeam near the receiver. Solar radiation on the ground istypically concentrated at 10-500 suns (1-50 W/cm

2) in

photovoltaic applications and at thousands of suns (>100W/cm

2) in thermal applications. Besides to be suitable to

sustain so high flux densities, these fluxmeters are also tobe designed to match well the receiver, whose geometrychanges with dimension of concentration (2D or 3D) andtype of application.

For planar receivers, typical of photovoltaicapplications, the camera-target method [1] allows to

determine in a simple way the flux density profile on abeam section by the image produced on a Lambertiandiffuser and recorded by a nearby CCD camera. Absoluteflux measurements are also possible by using thefluxmeters developed by Ferriere [2] and Parretta [3]. Thematching of a fluxmeter to the cylindrical receiver of alinear concentrator for thermal applications is a morearduous task. Riffelmann [4] has developed a fluxmeter(PARASCAN) whose sensor head is provided with an

array of photodiodes, and is moved along the receiver axisbetween two holders to record a two-dimensional fluxmap. In order to measure the effective absorbed flux fromthe receiver. The fluxmeter has been realized with twosensor heads, one measuring the total flux incident on thereceiver, the other measuring the total flux lost byreflection.

In this paper we present a fluxmeter whosegeometry is similar to the PARASCAN but which operatesin a different way concerning the selection of the fluxeffectively absorbed by the receiver.

BASIC SCHEME OF THE FLUXMETER

Fig. 1 shows the basic scheme of the fluxmetersensor head.

Fig. 1. Orthogonal section of the fluxmeter sensorhead, with seven cells and large view screens.

The sensor head of the fluxmeter, due to itsgeometry and the use of concentrating cells asphotodetectors, is also called photovoltaic collar (CollareFotovoltaico, CFV). A photovoltaic collar provided withonly seven cells for simplicity, is illustrated in Fig. 1. It is

3 2

4

5

6

x

y

7

8

9


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shaped as a polygon (4) on which the concentrating cells(5) are mounted. The sensor head is mounted around theglass tube (3) protecting the cylindrical thermal receiver(2). The cells temperature is measured by thermocouples(8) placed under the cells. The measurement ofphotocurrent (not shown), coupled to that of temperature,allows to derive the flux density on each solar cell. Finally,the total flux flowing through the cylindrical surface of theCFV is achieved by interpolating the measurements and

integrating on 2. From this, the optical efficiency of lightcollection can be estimated.

In practice, the measurement of the effectiveradiation impinging on the receiver is more complex. Fig.2a shows, for example, that radiation (6A) is measured bythe cell without being collected by the receiver (presenceof misalignments), and vice versa that radiation (6B) iscollected by the receiver without being measured by thecell (incomplete coverage by cells of the irradiation arc).The first problem is partially solved by the use of screens(9) which select the incoming radiation (see Fig. 2b, c).They are characterized by aperture (acceptance) angle

, and are of the large view type (Fig. 2b) or narrow viewtype (Fig. 2c). The narrow view type screens assure abetter selection of light, but are longer than the large viewtype screens. In Fig. 2 are evidenced the edges (17) and(18), which define the screen aperture. The screensshould be blackened in order to avoid unwantedreflections interfering with the direct irradiation.

a)

b)

c)

Fig. 2. a) Cell without screen; b) cell with large viewscreen; c) cell with narrow view screen.Fig. 1 shows an example of sensor head equipped withlarge view screens, where each screen is shared betweentwo adjacent cells.

The flux density (W/m2) at a generic point B of the

receiver surface, characterized by coordinate zand angle

(measured around zaxis), and the total flux incident on

a section of the receiver, with thickness zand centeredon coordinate z, can be calculated as follows (see Fig. 3).

Fig. 3. Scheme of a beam incident on the cell (5),intercepted by the receiver (2) at point B.

When the receiver is aligned with both light collector and

the sun, the solar radiation is focused on zaxis. With acalibrated sensor head, the photocurrent density of i-th

cell, phiJ (i=1, N), is a known function of the flux density,

)(c

iE , measured orthogonally to the average direction ()

of incident flux:

)()()(

c

i

ph

i EkJ = (1)

where () is a function defined in [1], equal to cos() fora Lambertian diffuser. The constant k(in A/W) is the ratiobetween measured photocurrent density (in A/cm

2) and

flux density incident orthogonally on the cell (in W/cm2). If

r1 is the receiver radius and r2 the distance from theoptical axis to the center of the cell (see Fig. 3), then the

flux density at the point (I, z) of the receiver is:

)/(])([cos)]([1212

)()( rrtgrrzEzEc

i

r

i = (2)

The concentration ratio (r2/ r1) between flux density on thereceiver (2) and flux density on the cell (5) remains

unchanged with angle , as such is the ratio ABAC /

(see Fig. 3). The average total fluxtot (in W) incident on

the z-thick section of the receiver, centered oncoordinate z, is obtained by integrating the flux density

)(r

iE over the entire arc

tot of the concentrated irradiation:

===

i

r

itot

rtottot

NEzr

zEzrzz

/...

...)(],[)(

1

)(

1

(3)

withtot in radians. The same considerations are valid if

we consider a window instead of a cell. We will see in nextparagraph, in fact, that the fluxmeter can operate also withcells not directly exposed to the concentrated radiation,

6A5

26B

5

2

17

18

9

5

217

18

9

z

O

5

2

r1 r2

C

A

B

D

z

z


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but covered by diffusive windows. This allows to reducecells temperature and to have a more uniform flux on thecells.

THE FLUXMETER

In the following we describe one prototype of CFVrealized at ENEA-Portici and tested on a parabolic troughsolar concentrator (PCS) located in ENEA-Casaccia

(Rome) [5]. The prototype, CFV2, manufactured by CN diClaudio Nappo (NA, Italy), operates with 11 SunPowerHECO252 solar concentration cells placed behindtranslucent targets with quasi-Lambertian transmissionproperties. This first prototype is devoid of screens whichwill be applied in the next future; despite this, the fluxmeterhas shown to be very accurate. The 11 cells aredistributed over an angular extension of ~210 with anangular resolution of ~20. The diffusive input windows areable to intercept around half of the radiation incident on atransversal section of the receiver. An electric fan, placedon the back of the sensor body, improves the cell cooling.Signals of photocurrent and temperature of the singlesolar cells are measured by remote instrumentation. Themonitoring of both temperature and photocurrent of the

cells allowed to calculate the incident flux density, aftercalibration of the sensor at the PASAN mod. 3B pulsedsolar simulator, equipped with Fresnel lens forconcentration measurements [3]. A schematic view of theCFV2 sensor head is shown in Fig. 4. Each cell (5) is 71.5mm far from the z axis and 36.5 mm from the receiver (2)surface.

Fig. 4. CFV2 sensor head mounted on the glasstube (3) (125 mm outer diameter) of the PCSconcentrator.

The arc covered by the set of eleven cells is 216, then the

distance between adjacent cells is 21.6. The single

cells subtend central angles ~ 10. The sensor has beenrealized from a cylindrical body of aluminium (4), divided in

two separable parts, one for mounting the cells, the other(not shown) for accomodate the fan. The sensor is lockedon the glass tube (3) through Teflon feet (16). Fig. 5shows one input window of the sensor head. Theconcentrated light impinges on the diffusive translucentwindow (14), is reflected by the walls of the prismaticoptical guide (15) and is absorbed by the photodetector(5). This arrangement allows to have on the cell (5) ahomogeneous radiation, independent of the impinging

direction on the input window (14). The cell photocurrent isobtained by measuring the voltage drop on a nearby 0.01

shunt resistance. The cooling of cells is performed bycirculating air in the space (16) existing between the topcover (10)+(11) and the base (4) of the sensor head.

Fig. 5. Section of a sensor head window.

The sensor CFV2 is protected by eleven aluminiumscreens (10) coupled to teflon screens (11), to assure agood thermal insulation for the base (4) of the sensorwhere are accommodated the cells (5). The diffusivewindow (14) assures a flux on the cell proportional to thatimpinging on the window, but independent by its spatialand angular distribution. The angle-resolved response ofthe window/cell system is being studied at the PASANpulsed solar simulator. Photos of the sensor head

assembled and mounted on a glass tube simulating thetrue glass lining of the solar receiver are shown in Fig. 6.On the right side the electric fan improving the solar cellscooling is visible.

Fig. 6. Top of the CFV2 sensor head with visible the

diffusive windows (14) (left); back of the sensor headwith visible the electric fan (right).

The test campaigns carried out at the solar plant ofENEA-Casaccia (see Fig. 7) proved the suitability of thesensor to sustain the radiation flux densities (around 80suns) there produced. Tests at high irradiation showedthat the cells temperature ranges from 60 to 80 C, well

10

11

5 48 1213

1415

16

32

4

5

x

y

z

15

14

10

16

10

11

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1415

16


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below the maximum temperature recommended by themanufacturer (100 C).

Fig. 7. Photo of the 11-cells sensor head mounted

on the PCS receiver during a test campaign.

-100 -50 0 50 100

0

10

20

30

40

50

0,0

0,5

1,0

1,510:00 azi = -32.0 deg

CFV2

Signal/Rad_

eff(arb.u.)

(deg)

idealAC01

Flux(1/rad)

Fig. 8. (top) The sensor is viewed from the vertex ofthe parabolic mirror; (bottom) experimental flux(CFV2) compared with simulations for real (AC01)and ideal (parabolic shape) mirrors.The test measurements furnished the flux density near thefocal line of the solar collector. The distributions were ingood agreement with simulations based on experimentaldata of the optical profile of the collecting mirrors, asobtained by indoor laser measurements [6]. Fig. 8 shows

an example of outdoor measurement: on the top is thepicture of the sensor head taken by the vertex of theparabolic collector; on the bottom, the flux measured bythe CFV2 sensor, compared with the simulations for real(AC01) and ideal (parabolic shape) mirrors. Theshadowing due to the receiver is clearly shown in thepicture; the other dark regions are due to the modulation

of flux distribution shaped as a reverse (bottom). Theagreement between measured and simulated flux worsens

at high values, where the response of windows (14)ceases to be Lambertian, then a suitable correction has tobe applied to the measured data.

CONCLUSIONS

A method for high flux density measurements in troughsolar concentrators has been discussed. The concentratedradiation is measured by eleven SunPower HECO252concentration cells distributed over the outer surface of acylindrical sensor head, and protected by diffusivewindows with quasi-Lambertian transmission properties.The device has shown to be a valid instrument for theaccuracy shown with outdoor tests on a solar trough

concentrator operating at around 80x suns.

REFERENCES

[1] A. Parretta, C. Privato, G. Nenna, A. Antonini, M.Stefancich. Monitoring of concentrated radiation beam forphotovoltaic and thermal solar energy conversionapplications. Applied Optics 2006. 45, pp. 7885-7897.

[2] A. Ferriere, and B. Rivoire. An Instrument forMeasuring Concentrated Solar Radiation: A Photo-sensorInterfaced with an Integrating Sphere. Solar Energy 2002.72, 187-193.

[3] A. Parretta, A. Antonini, M. Armani, G. Nenna, G.

Flaminio, M. Pellegrino. Double-Cavity Radiometer forHigh Flux Density Solar Radiation Measurements.Applied Optics, in press (20 April 2007).

[4] K. J. Riffelmann, A. Neumann and M. Wittkowski.Parascan: a new parabolic trough flux scanner. ISESSolar Worl Congress, Gteborg, June 2003, ISBN 91-631-4740-8.

[5] A. Parretta, C. Privato, L. Gentilin, A. Maccari, A.Mittiga, M. Montecchi, M. Tucci, G. Nenna, Radiometroper ricevitori cilindrici, Brevetto It., Application N.BO2006A000880, 27 Dicembre 2006.

[6] A. Maccari, M. Montecchi. An optical profilometer for

the characterisation of parabolic trough solarconcentrators. Solar Energy2007. 81, pp. 185-194.


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Inverters response time with concentration PV systems

S.Chellini, R.PardellSol3g, S.L., Parc Tecnologic del Valls, 08290 Cerdanyola, Barcelona, Spain

ABSTRACT

After our field experience, based on data collected indifferent installed systems, MPP control inverters show along time response after a drop in irradiance. This effect,that may not affect flat panel based systems significantly,have a big impact on concentration PV systems energycollection efficiency during days of intermittent clouds andsun spells, when light losses its direct irradiancycomponent temporally. Concentration modules fall inthese short periods into nearly zero power production thatimplies that the inverters fall into stand-by mode. Whenthe DNI eventually comes back to usable levels, the MPPcontrol restarts calculating the optimal combination ofvoltage and current from scratch, operation that requires anot negligible time. New MPP tracking algorithms whichremember previous MPP voltage levels must beimplemented in inverters in order to improve energycollection efficiency for concentration PV systems.

INTRODUCTION

Sol3g has installed and tested to date three differenttriple junction based PV high concentration pilot systems.The systems range from 760 to 920 W power at the DCside under working conditions, rated at 1.000 W/m2 DNI.

Data used in this paper comes from a systemlocated in Mont-Ras, a locality close to Girona, Spain,positioned in the geographical site: long 41 55N and lat3 13E. Its power is rated at 760 W.

All three pilot systems use 28 HCPV modulesdesigned and manufactured by Sol3g in its PTV facilitiesat Cerdanyola del Valls. The module is constituted by aprimary optic (a ten Fresnel lens parquet 1,20 meterslong), a secondary optic (a Borosilicate prism) and TripleJunction photovoltaic cells of 5.5x5.5 mm size. Itscharacteristics are:

22.7% module efficiency (@ 1000 W/m2 and 25C) [1]

30 V open circuit voltage.

1,2 A short circuit current.

The tracking system used is made by Feina, acompany located in Catalunya, Spain, with whom wecooperate. The tracking system follows the sun followingan hybrid strategy: using an attached external sensor inclosed control loop when the sun is visible, and calculating

the theoretical position in open control loop, by means ofan astronomic algorithm, when the sky is covered.

Fig. 1: An image of the site installation at Mont-Ras

The modules are connected in two grids of 14modules each, containing two series connected groups of7 modules, and then parallel connected. The DC outputpasses through an electronic device, which sends thesignals to the data logging system. We use to acquire theI-V two analogical/digital converters, I-7018 ICP Con, ableto read eight different DC signals in the range -100 mV;

+100 mV. The electronic device modifies voltage PV DCoutput from 0-300 V to the appropriate range; the PV DCcurrent signal has to be modified into a voltage signal, bya shunt resistance. We also connect to the A/D converterdifferent sensors:

Two temperature sensors (K-type thermocouple):one to measure the ambient temperature andanother for the module temperature.

A humidity sensor. Three calibrated silicon (Spektron) cells to

measure: the direct normal irradiance (DNI),adjusting a matt black tube on the top of the cell,to collect only the direct component of the light;the global normal irradiance (GNI), attaching the

cell to the tracking system; and the globalhorizontal irradiance (GHI).

The data passes through a client box able tocommunicate to the PC by means of RS-485 protocol, andthe values are collected every day in a different file, bysoftware created by Sol3gs (SOLMON program).


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Fig. 2: Data logging system scheme

The system is connected to the String Inverter SWR700 (SMA), a device with maximum power point seekingintegrated in its functionalities. One important thing tounderline, is that the operation state is reached when thestring voltage (UPV) at the inverter is minor than 50 V. Thiscan be very important for the concentration photovoltaicsystems, because in days with low light irradiance and inabsence of the direct component of light, voltage coulddrop to a value below 50 V, which permits to enter in thestand-by state.

The tracking system follows moving every 30seconds to the theoretical sun position, so, during a day ofintermittent clouds and sun spells, the concentrationsystem is able in each favourable break to inject power tothe net, but the inverter has to re-calculate the maximumpower point, scanning the entire I-V curve and re-searching the optimal forward bias.

EXPERIMENTAL RESULT

We will show some data collected during the periodSeptember 2006-February 2007, representing the DNI(W/m2), GNI (W/m2), the generated power by the system,P (W) and its conversion efficiency (PV performance [2])

calculated as:

100max

AE

P

tot

= Eq. 1

where Pmax is the instantaneous power given by thesystem, Etot is in this case, the direct component of thelight (DNI) and A represents the input aperture surface ofthe system (in our case 4.032 m

2). The SOLMON program

has showed some incorrect values of DNI and GNI (andindirectly of the efficiency), caused by punctual incorrectreadings of the I-7018 A/D converter (singular points in thegraphic below).

Day 03/12/2006

0,0%

5,0%

10,0%

15,0%

20,0%

08:52 10:04 11:16 12:28 13:40 14:52 16:04 17:16

Time (hh:mm)

(%)

0

100

200

300

400

500

600

700

800

900

DNI-GNI-Power

eta

DNI

GNI

power

shades

singular

point

Fig. 3: Day 03/12/2006, sunny day with a maximum Tmod35 C; transit at 12:36.

The graphic in Fig. 3 represents time dependence ofthe direct normal irradiance (DNI), global normalirradiance (GNI), the generated power of the installationand finally the conversion efficiency (). The generatedpower reaches a maximum only closed to the sun transit,because of shades those partially covers the tracking

system during the morning.

Day 30/01/2007

0,0%

2,0%

4,0%

6,0%

8,0%

10,0%

12,0%

14,0%

16,0%

18,0%

20,0%

08:52 10:04 11:16 12:28 13:40 14:52 16:04 17:16

Time (hh:mm)

(%)

0

200

400

600

800

1000

DNI(W/m2),GNI(W/m2),P(W)

eta

DNI

GNI

power

singular pointsingular point

Fig. 4: Day 30/01/2007, cloudy day with a maximum Tmod32 C; transit at 13:00.

The graphic in Fig. 4 represents the timedependence of DNI, GNI, P and in a cloudy day, with avery variable direct irradiance in the beginning of the dayand after two PM. A detailed analysis of the DNI andpower values (Fig. 5) in the 14:49 14:58 interval showstwo different power response delays: at 14:50 DNI raisesto 500 W/m

2for 1 minute period, but power remain at the

zero level; at 14:56 the DNI reaches 500 W/m2

and raisesup till 700 W/m

2, and the power takes 1.5 minute long to

raise to the normal production (in those ambient condition

was 450 W).


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-2,0%

0,0%

2,0%

4,0%

6,0%

8,0%

10,0%

12,0%

14,0%

16,0%

18,0%

14:49 14:51 14:52 14:53 14:54 14:55 14:56 14:57 14:59

Time (hh:mm)

(%)

-50

50

150

250

350

450

550

650

750

850

DNI(W/m2),GNI(W/m2),P(W)

eta

DNI

GNI

power

response

delay

Fig. 5: Day 30/01/2007, detail of an irradiance drop.

The GNI during this period never falls below 200W/m

2, which permits to a flat panel to generate power

during all the period.

Detailed analysis of many similar episodes and ofthe integrated daily efficiency under different directirradiance conditions show that the slow response of MPPtracking inverter reduces the overall energy collection

efficiency of the system.

DISCUSSION

An I V analysis shows us how voltage and currentbehave during a day: Fig. 6 represents a sunny day(03/12/2007, reported before), with no great temperaturevariability (the ambient temperature flattens at 20C duringthe day, from 10:00 to 17:00, and the module temperaturereaches 34 C at 14:00, but it is steady in the rest of theday at 30 C). The result is that the current follows the DNIshape, but the voltage remains approximately constant to180 V.

Day 03/12/2006

0

30

60

90

120

150

180

210

240

8:24:00 9:50:24 11:16:48 12:43:12 14:09:36 15:36:00 17:02:24

Time (hh:mm:ss)

Voltage(V)

0

0,5

1

1,5

2

2,5

3

Current(A)

voltage

current

shades

Fig. 6: Day 03/12/2006, time dependence of Voltage and

Current for the tracking system.

We can see in Fig. 7 I V values of another cloudyday (04/11/2007), in which the system disconnects to theinverter when the DNI falls nearly to zero. From 12:15 theDNI starts to raise, and the MPP control inverter searchesfor the MPP, and the system works initially at more than200 V, and it finds the maximum power point voltage at160 V, which is close to the last Vmpm found at 12:05.

The inverter expends a lot of time trying to find itsnew optimal voltage level, and we see that instead ofstarting looking at this point from a zero voltage, and thengoing up to an excessive voltage, it would be much moreefficient to start from the last MPP voltage reached beforethe DNI fell near to zero.

In fact we also see that under very unstable

irradiance conditions the MPP tracking algorithm issomewhat unaccurate, as it is making the PV generatorwork at a voltage around 160 V, which is in fact not theaverage MPP voltage of 180V, thus affecting the efficiencyof the system during the very unstable DNI episodes.

As can be seen, the combined effect of bothproblems (high response time and MPP lack of accuracy)on integrated energy collection efficiency can be verysevere during days where the DNI shows a binarybehaviour.

Day 04/11/2006

0

80

160

240

320

400

480

560

12:00 12:02 12:05 12:08 12:11 12:14 12:17 12:20 12:23

Time (hh:mm:ss)

DNI(W/m2)-GNI(W/m2)-Voltage(V)

0

0,5

1

1,5

2

2,5

3

Current(A)

DNI

GNI

voltage

current

response

delay

mpm

search

point

Fig. 7: Day 04/11/2006, detail of variably DNI component(notice the stability of the GNI). The graph shows timedependency of Voltage and current in the selected range.

CONCLUSION

In this paper, different graphics are shown, usingdata collected from a high concentration PV systemworking under different irradiance conditions.

We notice a long response delay between the DNIfluctuations and the MPP inverter control when the systemhas to work under binary variation of direct irradiance,typical of days in which cloudy conditions alternate withsun spells.

The more variable the irradiance conditions the

greater the effect this slow inverter response will have onthe integrated energy collection efficiency of theconcentration PV system.

In the other hand, we propose to add a voltagecontrol to the inverter electronic device, able to rememberthe operative Vmpm voltage of the system in order toreduce its response time.


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As can be gathered from the data, the systemsvoltage is quite stable around 180 V whenever the inverterreaches MPP. Therefore, a very simple modification of theinverter logic, making its software remember the latestMPP reached voltage, would help drastically reduce theresponse time from more than one minute to a fewseconds.

REFERENCES

[2] F.Chenlo, J.P.Silva Informe tecnico modulos Sol3g2006. Ciemat, Madrid.

[2] A.Luque, S.Hegedus Handbook of PhotovoltaicScience and Engineering 2002. 16.1 pp. 702-715.


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PREDICTION OF PV CONCENTRATORS ENERGY PRODUCTION:INFLUENCE OF WIND IN THE COOLING MECHANISMS.

FIRST STEPS

M. Martnez, I. Antn, G. SalaInstituto de Energa Solar, Universidad Politcnica de Madrid (IES-UPM)

E.T.S.I. Telecomunicacin, Ciudad Universitaria s/n, 28040, Madrid, SpainTel:+34915441060, Fax: +34915446341, mail: [email protected]

ABSTRACT

Making a complete model of a PV Concentrator(CPV) is essential to obtain a good prediction of its energyproduction. For that, it is necessary not only to define theelectrical characteristics of the system in standard testconditions (STC), but also to determine the influence ofthe ambient conditions on the electrical performance.

These conditions are related with the cooling of thesystem, moreover, a proper cooling of a CPV is essentialto obtain a good performance in operation.

This work is going to be focused in only one type ofCPVs, the Point Focus CPVs based in lens optics,because they have a particular characteristic: its classichousing and the internal air are going to contribute to thesystem cooling. We have find out that an importantamount of heat is going to be dissipated through thisregion and not through the module back heat-sink.

We have carried out the first steps of this work,obtaining a thermal behaviour model for this type of CPVsin steady state and calm air. We have used anexperimental method, based on temperaturemeasurements and incoming solar power cast on thesystem. So, finally, we are able to of identify allparameters related with the cooling process and findingout their relation with ambient conditions.

INTRODUCTION

An accurate modeling of PV Concentrators (CPV) forthe prediction of its energy production is essential toestablish the economic viability of this kind of systems atdifferent sites. For that, it is necessary not only to definethe electrical performance of the system at standard testconditions (STC) but also to determine the dependence of

its electrical behaviour on the ambient conditions. Theoutput power of this kind of systems depends on the directirradiance level, light spectrum, ambient temperature andwind direction and speed. This last variable, wind, is themost difficult to model and this work focuses on thecorrelation between the power and the wind in a CPV.

In a CPV, the evacuation of heat is an essential andcomplex task [1]. The operating cell temperature could

reach very high values if the cooling is not theappropriated, because, in this kind of systems, theincoming radiation is multiplied by the effectiveconcentration factor (C), so all the light that is notconverted into electrical power has to be efficientlyevacuated of the system. This is why CPVs have a verycomplex cooling and, when passive cooling is used, windis the agent that has more influence in this mechanism.

In this work, we are going to center our efforts incharacterizing only one kind of CPVs: the Point Focus-Lens housing CPVs. This type of concentrators has aspecial characteristic that is related with its cooling, theyare closed volumes with an internal interface of air that isgoing to be involved in the cooling mechanisms of thesystem.

OBJECTIVES

The main objective of this paper is to describe theexisting connection between the operating celltemperature and the ambient conditions. Once we haveobtained this relation, the change of the energy productionrate to other operating conditions will be simply calculated,what will make the CPV energy prediction easier.

To reach this objective, it is necessary first, to studythe thermal behavior of this type of CPVs in steady state,defining all the parameters involved in the coolingmechanisms and identifying which are going to beinfluenced by wind.

APPROACH

In this section, we attempt to enumerate anddescribe the critical points of the CPV energy predictionprocess.

CPV characterizationFor characterizing a CPV in STC we have first to

measure the DC power of the system. From its IV-Curve(I1, V1), in whatever conditions of operation (B

1, Tcel

1) and

making a transfer to the STC (B*, Tcel

*), with equations

defined below (1), (2) (single junction cells), we obtain theIV-Curve (I2, V2) in STC.


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Table 1 collects the definition of certain parametersof the concentrator and constants which will be necessaryfor the calculation.

1

*

12B

BII =

(1)

( )

S

cell

cellcellS

cell

cellS

g

S

RBBI

TTLnm

BBLn

eTkN

T

TRIV

e

ENVV

+

++=

1

1

1

*

11

*

1

**

1

*

1112

(2)

Table 1. Characteristic parameters of a PV concentratorand essential constants

Characteristic parameters of thesystem

Constants

NS Number of cells connectedin series in the system

Index which fluctuatesbetween 2 and 4

Eg Cell band gap k Boltzmann constantRS Series resistance of the

system, cells and wirese Electron charge

m Diode quality factor

Energy production prediction

The performance of the system at any time isdefined also by equations (1) and (2) as a direct functionof irradiance and cell temperature.

The influence of the ambient conditions in the energyproduction its captured in the parameter operating celltemperature (Tcel). This parameter can be calculated withequation (3) taking the ambient temperature, direct beamradiation and power of the system as inputs.

( )systheleclightacel RPPTT ,+=

(3)

It is here in equation (3) where the parameterthermal resistance (Rth,sys) appears. This parameter is

directly related with the thermal behaviour and cooling of aCPV and will be one of the results obtained from this work.

Cooling mechanisms in CPVsFor passive cooling the main mechanisms involved

are [2]:

Conduction: For carrying the heat from the cell to thedissipating surfaces.

x

Tk

A

q

=

(4)

k Thermal conductivity

Natural Convection and Radiation: For removing theheat from the dissipating surfaces to the surroundingatmosphere.

Natural Convection

ThA

qconv =

(5)

h Convection coefficient

Radiation

( )41

4

2 TTA

q=

(6)

Emissivity

Stefan-Boltzmann constant

ThA

qrad =

(7)

( ) ( )212212 TTTThrad ++= (8)

The general radiation equation, (6), can be writtenlike equation (7) via the radiation coefficient defined inequation (8).

THERMAL BEHAVIOUR

Description of the problemAs we said at the beginning of the paper, it is

necessary to make a thermal study of the system, more indetail; we want to know what are the heat flowing waysfrom the cell to the surrounding atmosphere [1]. To reachthis purpose, we present in Fig. 1 a general thermalscheme, useful for this type of CPVs.

BackAl plate

Housingwalls

Lens

Ta

Ta

Tai

Tcel

Tplate

Plight

P2

P1P4

P3

P5

P6P6

Fig. 1 Scheme of a Point Focus-Lens Housing CPV

In this figure, we can see all the possibilities thathave the heat for flowing from the cell to the ambient air.In addition, as we said before, we have to keep in mindthe internal interface of air, taking into account the heatdissipation through the lateral housing walls and the frontlenses.

The thermal behaviour of a CPV can be representedas an equivalent thermal circuit, Fig.2. The heat flow andthe temperature perform in the same way the current and

the voltage do in electric circuits. Thermal resistorssubstitute ohmic resistors.

From equations (4), (5) and (7), we can define thethermal resistances for all mechanisms involved in theCPV cooling.

Akx

P

TR condth

=

=

1,

(9)


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AhP

TR

conv

convth =

=

1,

(10)

AhP

TR

rad

radth

=

=1

,

(11)

Because both, convection and radiation, are the heatremoval mechanisms from the dissipating surfaces, it isuseful to define a combined convection and radiationthermal resistance.

( ) radconvradconv

radconv

combthRR

RR

AhhR

+

=

+=

1,

(12)

Fig. 2 Equivalent thermal circuit for a Point Focus-LensHousing CPV

Fig.2 shows the equivalent thermal circuitcorresponding to the thermal behaviour of this type ofCPVs represented in Fig.1. All the surfaces and interfacesinvolved in the system cooling are represented by theirequivalent thermal resistance; Table 2 explains themeaning of each resistance.

Table 2 Interfaces involved in the cooling of a Point Focus-Lens Housing CPV

THERMAL RESISTANCES

cell-plate Between the cell and the back Al plateplate Through the back Al plate

cell Between the cell and the internal air

plate Between the back plate and the internal air

wall Between the internal air, through the housingwalls and to the ambient air

len Between the internal air, through the lenses and tothe ambient air

h-s Between the heat-sink and the ambient air

Because the main purpose of this work was todescribe the wind influence in the energy production ofthis type of CPVs, then the first task is to identify whichparts of the system are sensitive to wind. It is obvious thatthe surfaces in contact with the surrounding atmosphereare going to be the ones influenced by wind. In thispreliminary work, we are only going to describe itsbehaviour in calm air; the influence of wind on theseparameters will be analyzed in future works.

In the equivalent thermal circuit the action of wind issimulated by variable convection resistances.

Solving the problemSome simplifications in the circuit will help to obtain

conclusions.

As we said before removing heat from any surface ismade by convection and radiation, but for bright metallicsurfaces the convection coefficient (hconv) is much biggerthan the radiation coefficient (hrad), so we do not have totake into account the irradiation mechanisms in the heatflow dissipating from the metallic surfaces of the CPV.

wallradshradplaterad RRR ,,, (13)

Another aspect to take into account is the heatdirectly flowing from the cell to the internal air. It can alsobe rejected, because the available area for dissipatingheat from the cell (Acel) is much smaller than the back Alplate area (Aplate) which uses both sides for heatdissipation, to closed internal and open external air.

cellcombR , (14)

The biggest approximation we made for solving theproblem was to consider an equivalent thermal resistance(Req) that represents the capacity of dissipating heat from

the internal interface of air to the surrounding atmosphere.This approximation opens a future work for studying morein detail all the parts involved in this heat dissipation.

( ) ( )( ) ( )wallcombwallcondwallconvlencomblencondlenconv

wallcombwallcondwallconvlencomblencondlenconv

eqRRRRRR

RRRRRRR

,,,,,,

,,,,,,

+++++

++++=

(15)

Finally, for making easier the tackling of the problemwe suppose isothermal surfaces for all heat exchangingsurfaces.

0, platecondR (16)

Fig.3 shows the simplified circuit we have used tosolve the problem of the thermal behaviour of a PointFocus-Lens Housing CPV in steady state and in calm air.

The general equations associated to this circuit andneeded for solving the problem are:

eleclightheat PPP = (17)

431 PPPPheat +== (18)

1,PRTT platecellcondplatecel =

(19)

Rcond,plateRcond,cell-plate

Rcond,len Rcond,wall

Rcomb, h-s

Rcomb, wallRcomb, len

Rcomb, cell Rcomb, plate

Rconv, len Rconv,wall

P2

P1 P3

P4

P5 P6Pheat

Tcel

Tai

Ta

Tplate


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4, PRTT plateconvaiplate = (20)

3,PRTT shconvaplate =

(21)

4PRTT eqaai = (22)

Fig. 3 Simplified equivalent thermal circuit for a PointFocus-Lens Housing CPV

RESULTS

We solved the problem related with the simplifiedcircuit represented in Fig.3 applying equations (17) to (22)for one type of these CPVs like a case of study. Thepreliminary results obtained are:

First of all, that an important amount of heat isdissipated through the internal interface of air. For thiscase of study, we obtained that 23% heat flow is notdissipated through the system heat-sink back side.

Therefore, this heat flow from the front lenses and sidewalls must be taken into account in future works with thistype of CPVs.

In addition, we have obtained a relation for thetemperature distribution through the parts of the system inthis case of study. For an overall 50C temperature dropbetween the ambient air and the cell, there are 20C ofdifference between the cell and the back Al plate. Also, wecan advance that the internal air, is about 20C hotter thant

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