The silicon concentrator photovoltaic generator sophocles: Performance and costs based on material characteristics

Solar Cells, 4 (1981) 47 - 59

47

THE SILICON C O N C E N T R A T O R PHOTOVOLTAIC G E N E R A T O R SOPHOCLES: P E R F O R M A N C E AND COSTS BASED ON MATERIAL CHARACTERISTICS

D. ESTEVE, G. V I A L A R E T and F. THEREZ Laboratoire d'Automatique et d'Analyse des Syst~mes, 7 Avenue du Colonel Roche, 31400 Toulouse (France)

(Received September 12, 1980; accepted October 27, 1980)

Summary The purpose of this paper is to show that in the short term a solution can be f o u n d to enable the immediate exploitation of concentrator photovoltaic systems. The technical requirements, tracking system, optical system and thermal dissipation necessary for concentrator generators are described. T h e n a description o f the p r o t o t y p e generator Sophocles built in this laboratory is presented. The results of various experiments are given. Finally, we review the prospects of reductions in cost for a concentrator generator using a higher concentration ratio and more efficient solar cells, which can lead to a price of $4 Wp-1 if all expenses are taken into account.

I. Introduction

After more than 6 years of experience and because of the interest in new sources of energy, photovoltaic conversion using concentrator generators has reached an advanced level which allows its industrial development to be planned with some chance of success. This t y p e of solution is in competition with the use of thin film materials and traditional single-crystal silicon. The present trend mainly emphasizes silicon fiat plate arrays. Certainly, their production is still very expensive, a b o u t $10 Wp-1 , b u t knowledge of purification techniques for silicon and of its crystal growth mechanisms will contribute to cost reductions. One way of reducing costs is through the introduction first of polycrystalline silicon and later of ribbon silicon. The prospects for cost reductions for modules and systems with time are given in Fig. 1. (1) We observe that the probable cost of concentrator generators will be less than $4 Wp-1 b y 1983. (2) The effects of production automation must be added to the present data related to fiat plates (Fig. 1, areas 2, 3 and 4). Module prices would then fall to less than $2 W p 1 (Fig. 1, level 6); this is a reduction of a factor 0379-6787/81/0000-0000/$02.50

© Elsevier Sequoia/Printed in The Netherlands

48

25-

20-

1976

119801

1978 TIME (YEARS)

I 1982 I

Fig. l. Module price (after U.S. Department of Energy) (system effect, from +100% to +200%): 1, present cost of a prototype concentrator generator; 2, present cost of a watt plan generator; 3, present cost of a watt plan module; 4, lowest price of a module (after

U.S. Department of Energy); 5, expected cost for a concentrator generator (1 MW year-1 ); 6, ffrst-level cost for probable industrial production (after U.S. Department of Energy) [1, 2]. of 3 - 4 for the period from 1985. The relatively short-term outlook will attract considerable investment if we reach price levels which are competitive with oil, especially in isolated regions where there are no electrical power plants. The planning of such a programme depends mainly on the success of basic research work which should lead to the production of cheap solar grade silicon. The purpose of this paper is to show t h a t in the very short term a solution can be f o u n d which enables the immediate exploitation of concentrator systems. Thus we can demonstrate (1) that the performance required from the technical system is available with the present technologies, (2) that the prototypes which can be made show sufficiently high efficiencies and (3) that the material costs are compatible with a basic price of $2 Wp-1 . Finally, we shall show t h a t more attractive prospects can be expected from the success of some projects which are being carried out at present. 2. The technical requirements o f t h e c o n c e n t r a t o r photovoltaic systems

2.1. The tracking system The concentrator photovoltaic generators need an oriented support which follows the sun. The optical axis of the concentrator modules is always pointed towards the sun. A study of the performances of control systems manufactured for several types of heliostats (reflectors and photovoltaic generators) shows that an accuracy of 1 - 2 mrad can be achieved without expensive technologies. This kind of system is shown in Fig. 2. Two

49

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Fig. 2. Two-axis electronic control diagram.

electric motors are controlled using analogue feedback and a quadrant solar sensor. The curves in Fig. 3 show that an accuracy to about 1 mrad in the angle o f orientation is acceptable for concentration ratios as high as 400: AG

- - - 2 N C 1/2 ~

(1)

G where G is the optical efficiency, N is the aperture number, C is the concentrator ratio and ~ is the tracking accuracy. Equation (1) was deduced o n the assumption that the apparent angular size o f the sun has no effect. i

100 o

c.

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c:,~.

~-z

i-

a:: o

c~

vn

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10 100 1000 CONCENTRATION RATIO (X SUNS)

Fig. 3. Global tracking error

vs.

concentration ratio at constant optical losses (5%).

50 In practice, several kinds of heliostat have been studied and developed, especially for thermal conversion plants [ 1 ]. We have demonstrated clearly that this technical problem is n o w almost solved and that the heliostat system represents only a financial limitation whose influence will be evaluated later.

2.2. The optical systems The second important problem concerning global feasibility is the realization of the optical concentrator system. It should be noted that its function is not to produce a well-defined picture of the sun but to concentrate the p h o t o n energy. This means that an arrangement of mirrors [ 3] or Fresnel lenses constructed of large or small prisms [2] can be adopted. Among several solutions which have been analysed, two main systems are under development: (1) cylindroparabolic mirrors made with glass or metal; (2) plastic Fresnel lenses. The modern technologies available can produce such systems. A large quantity can be manufactured, and quality and performance are quite good. For example, concentration ratios of about 400 and efficiencies of up to 80% are observed (Table 1). TABLE

1

Performances of optical concentrator systems

Optical concentrator

Manufacturers

Maximum optical efficiency

Concentration ratio (geometric) (suns)

(%) Linear Fresnel lens

Swedlow-E-System

87

25

P o i n t f o c u s Fresnel lens

RCA-OSG

85 - 87

90 - 4 5 0

P o i n t f o c u s Fresnel lens

T o k y o Plastic Lens Soterem

80

56

Metal p a r a b o l i c t r o u g h ( o n e axis)

A c c u r e x Ski

85

36

2.3. Thermal dissipation Concentration of the sun's energy increases the temperature of the cells. We have to treat the problem of the cooling system for a concentrator generator in greater depth than that for a fiat plate. An increase in temperature reduces the efficiency of the cells: ? = 'h3oo K)(I - - •(T - - 300)}

(2)

with

1

A~

7~(300 K) A T

The measurements [4] give a temperature coefficient ranging from 0.04% to 0.05% °C-1. The excess calories can be dissipated by natural convec-

51

tion on a metallic radiator. We have calculated the surface of such a radiator [5] in terms of the concentration ratio. The results for several temperature excesses are given in Fig. 4. The surface of the radiator and its width related to the lateral heat flow fix the weight of the metal. Considering the weights of the respective parts of the system, the use of optical concentrators increases the number of parts and results in a greater mass on the oriented support. However, since t h e y can be made from cheap metal their influence on the cost is small.

30

/

.25

e20-

0oc

g 10-

20 /,0 60 80 CONCENTRATION RATIO (X SUNS)

I00

Fig. 4. Solar cell surface S vs. c o n c e n t r a t i o n ratio C for various t e m p e r a t u r e excesses A T (aluminium sheet thickness, 5 r a m ; irradiance, 100 mW cm - 2 ; h e a t transfer coefficient for natural c o n v e c t i o n , 2 mW cm - 2 °C - 1 ).

3. Description of a feasible solution: the Sophocles generator The design of the Sophocles generator shown in Fig. 5 was based on thermal constraint; this determines the concentrator-cell-cooler structure. For natural air convection an analytical thermal model was set up to represent the thermal behaviour of an infinite flat metallic plate carrying an infinite number of regularly spaced solar cells. The effects of the thickness e of the plate, the air convection coefficient h and the surface area S of the cells on the concentration ratio C were studied in order to find the exact relationship between S and C (Fig. 4). These isothermal curves show t h a t for a given structure (h, e), under the conditions of m a x i m u m cell temperature elevation above the ambient temperature and a given concentration ratio, there is an upper limit for t h e surface area of t h e cells, above which their temperature may be greater than the fixed limit: It must be remembered that, in 1977, 4 cm 2 silicon solar cells working at a concentration ratio of 40 suns were produced industrially. These cells offer a good solution to the problems due to natural air convection cooling.

52

Fig. 5. Sophocles, a concentrator photovoltaic generator.

When S and C had been determined, feasibility studies led to the modular structure which includes (1) six 4 cm 2 silicon solar cells, (2) six 225 cm e plastic Fresnel lenses and (3) an extruded aluminium support I m long with radiating plates. Two-dimensional thermal analysis of this structure allowed the o p t i m u m dimensions to be calculated with respect to both thermal efficiency and low weight [6, 7]. These are a mean thickness of 3 mm, five radiating plates 11.5 m m long, about 0.4 kg of aluminium per cell and a thermal resistance of 0.18 °C W -1 . The solar cells are supplied by two manufacturers: RTC, Caen, France; Solarex Corp., U.S.A. A typical efficiency at 40 °C under 40 suns illumination was initially 11%. At present the efficiencies are 13% or more. For Fresnel lenses the c o m p u t a t i o n of the geometrical dimensions of the grooves from the optical data of the expected lens did not raise any important problems. The main difficulties arise from the manufacture of the metallic matrix when " h o t injection" technology is applied to methacrylate material. The 15 cm × 15 cm plastic lenses are supplied by the Japanese manufacturer T.P.L. Some of them were tested with the experimental test set-up developed for this particular operation. Typical results consist of a distribution of optical energy in the plane of the solar cell. The mean efficiency reaches 75%. Figure 6 shows the different steps of assembling these systems. The solar cells are connected in series and must be insulated electrically from their support: t h e y are cemented with an adhesive which is both an electrical insulator and a thermal conductor. The plastic lenses are fixed hermetically on top of the modules. An air dryer system prevents condensation inside and allows the modules to " b r e a t h e " with variations in pressure and temperature. The modules are screwed on the panel and their position can be adjusted precisely with reference to the normal direction of the frame. The efficiency of these concentrator modules is typically 10%. The various contributions to the efficiency are summarized in Table 2. The

53

Fig. 6. View of parts of the concentrator. TABLE 2 Efficiencies of various parts of the generator

Parameter

Efficiency

System efficiency

Optical concentrator

80

80

Tracking and mounting tolerances

95

76

(%)

(%)

Silicon cell (25 °C)

14

10.6

Cell bonding and radiator (silicon cell at 40 °C)

93

10

measured parameters of the various parts of the Sophocles generator are given in Table 3. The results refer to experiments with our own p r o t o t y p e generator built in this laboratory. The prices of the materials needed to build the silicon concentrator photovoltaic generator Sophocles expressed in terms of cost per peak watt are listed in Table 4. The sum of the various contributions of each part of the system is $1.5 Wp-1 for the cost of the materials supplied. The generator is sold at a price o f $25 - 30 Wp 1 (Fig. 1, area 1). This is because it is a firstgeneration concentrator array which, like a p r o t o t y p e , was n o t produced by industrial methods. The final cost is higher than the flat plate price, and the difference can reach 50%. This material evaluation is in agreement with most data for concentrator photovoltaic generators published to date; these data are in the range from

54 TABLE 3 Main characteristics of the Sophocles system Angular range Azimuth Elevation Maximum angular speed (rev h -1 ) Global tracking accuracy (mrad) Number of 15 c m x 15 cm Fresnel lenses per module Geometric concentration ratio (suns) Number of 4 cm 2 cells per module Overall module efficiency (%) Decrease A~? in the efficiency vs. tracking error AS for AS < 5 mrad for 5 mrad < A~X< 25 mrad Electrical peak power output for one module Number of modules per square metre Operating temperature (°C) Relative humidity (%) Wind speed for emergency position (kin h -1 ) Extreme wind speed before breaking (kin h -1 )

±180 ° --5 ° horizontal to 85 ° vertical 2 3 6 56 6 10 A~7 = 0 &72 = 1 12 W, 3 V 8 --10 - +50 20 - 100 75 160

TABLE 4 Material costs of the present Sophocles generator

Sophocles subparts (for large quantity production)

Cost ($ Wp -1 )

(%)

Heliostat Array and actuators Electronic tracking

0.44 0.04

29 3

Concentrator Housing and passive aluminium radiator Fresnel lenses Bonds Connections Silicon

0.63 0.09 0.04 0.04 0.22

42 6 3 3 14

Total

1.50

100

$ 0 . 8 - $ 2 Wp- 1. T h e v a l u e s s u m m a r i z e d i n T a b l e 5 give t h e p r i c e s o f v a r i o u s parts of several g e n e r a t o r systems. T h e t w o s o l u t i o n s are very close because t h e m a i n m a t e r i a l a n d l a b o u r c o s t is d u e t o t h e m e c h a n i c a l c o n t r i b u t i o n which reaches 80%. T h u s we p i n p o i n t e d t h e area of high e x p e n d i t u r e (the mechanical assembly) and this can be made cheaper by using well-known industrial automation methods. The use of mass production would enable us t o p r o v i d e a f i n i s h e d p r o d u c t f o r less t h a n t w i c e t h e c o s t o f t h e m a t e r i a l s , as s h o w n i n T a b l e 4.

55 TABLE 5 Material costs for various photovoltaic systems Concentrator

Cost o f material ($ Wp --1 ) Heliostat and support

Tracking

Module (metal)

Module (plastic)

Silicon

Total

Flat plate, watt plan

0.04

0

0.07

0.33

4.44

4.9

Linear focus, one axis, active cooling (at 25 suns)

0.33

0.02

0.24

0.33

0.44

1.36

Point focus, two axes, 0.44 passive cooling, Sophocles (at 50 suns)

0.04

0.63

0.17

0.22

1.50

Point focus, two axes, active cooling (at 50 suns)

0.04

0.24

0.33

0.22

1.27

TABLE

0.44

6

Expected material costs for an automated production of 1 M W

year -1

Expected material cost ($ W p -1 )

Investment

People

Material

Total

Building Management Research Heliostat assembling Concentrator assembling Various

0.22 0.02 0.04 0.06 0.33 0.04

0.06 0.13 0.02 0.16 1.07 0.07

0.22 0.02 0.02 0.48 1.02 0.33

0.50 0.17 0.08 0.70 2.42 0.44

Total

0.71

1.51

2.09

4.31

T h e i m p l e m e n t a t i o n o f a p r o d u c t i o n p l a n t was studied o n this basis. T h e s u b s y s t e m s involved are detailed in Table 6. A t o t a l price o f a b o u t $4 Wp 1 is p l a n n e d f o r a p r o d u c t i o n o f 1 0 0 0 kW y e a r -1 . As well as this r e d u c t i o n f r o m a f a c t o r y p r o d u c t i o n p r o g r a m m e t h e r e are o t h e r f a c t o r s w h i c h c o u l d r e d u c e t h e prices, as we shall describe in S e c t i o n 4.

4. P r o s p e c t s f o r c o s t r e d u c t i o n T h e e x a m p l e o f t h e c o s t analysis carried o u t o n t h e S o p h o c l e s g e n e r a t o r reveals t h a t t h e c h o i c e o f c o n c e n t r a t o r p h o t o v o l t a i c g e n e r a t o r s is o f real

56 economic interest, because it indicates the o u t l o o k w i t h o u t using new concepts. The price will decrease as the m a r k e t grows. One question remains: we w o n d e r wh ethe r it would be m or e reasonable to wait for research work to improve silicon processing and then t o focus all our at t ent i on on flat plates. N e x t we review t he prospects o f cost r e d u c t i o n using a c o n c e n t r a t o r generator.

4.1. Increase in concentration ratio An increase in t h e c o n c e n t r a t i o n ratio of up t o 50 suns produces higher efficiencies and at t he same time reduces t h e surface area of the silicon required. It is advantageous to use t he gain in efficiency which can be formulated f o r silicon cells as follows: = Vl(1 + 0.181nC)

(3)

where ~1 is th e efficiency o f the cell at an illumination o f 1 sun and C is the c o n c e n t r a t i o n ratio. This increase in t he p o w e r o u t p u t is partly compensated b y a mo r e expensive solar cell. Also t he thermal effects are m ore difficult t o reduce because of t he small heat exchange surface bet w een t he cell and the cooler. Applying the result in eqn. (3) and assuming a 14% efficient cell at an illumination o f 1 sun we can e x p e c t an efficiency of 20% at an illumination o f 40 suns (this has t o be c o m p a r e d with the present 14% efficient cells at an illumination of 40 suns). On t he assumption o f a factor of 2 on the price o f such a c o n c e n t r a t o r cell with respect to t he cost given in Table 4, the present cost o f $1.5 Wp-1 becomes a b o u t $1.1 Wp-1 . There are silicon cells which work at c o n c e n t r a t i o n levels higher than 90 suns and at an efficiency o f 17% [ 8 ] .

4.2. Material weight impact A r ed u ctio n in t he material volume of the support and the coolers is useful because we d e m o n s t r a t e d t h a t in t he Sophocles generator the material o f th e frame contributes 70% of t he total price. Recent studies [9] have shown th at b y using an active cooler t he t ot a l weight of the m odul e can be reduced b y as mu ch as a f act or o f 4. 4.3. Influence o f the solar cell efficiencies The k ey to reducing cost is t he solar cell efficiency. We showed above t h a t th e higher efficiency favoured by c o n c e n t r a t i o n produces a reduct i on in the cost o f the p ow e r o u t p u t . Even if we pa y m ore for t he c o n c e n t r a t o r cells, t h e increase in p ow er o u t p u t will result in a decrease in the overall price. Starting f r o m o u r own experience described in this paper {Table 4) on the Sophocles generator, we studied t he variation in the p o w e r o u t p u t generator in terms o f solar cell efficiency. T he relationship bet w een solar cell efficiency and cost was assumed to be linear with a slope of 2 f o r cell efficiencies varying f r o m 10% to 20%. T hen t he cost per peak w at t can be expressed as

57

Pr =

100(Pa + Pc)

(4)

P

where Pa ($ Wp-1 ) is the price of the Sophocles array, Pc ($ Wp-1 ) is the price of the cell for the efficiency considered and P is the o u t p u t power produced by the new efficiency with a 1 m 2 generator. The results are plotted in Fig. 7. We observed that, for a concentrator ratio of about 40 suns as in our prototype, more efficient solar cells produced a cost reduction. Typically, the initial cost of about $1.5 Wp-1 is divided by a factor of 1.6 for 20% efficient silicon cells. Such cells are now available and we can expect higher efficiencies if we combine high performance devices and concentration of the sunlight. As shown in Fig. 8, high efficiency silicon and gallium arsenide cells give performances ranging from 15% to 24% [10]. These two kinds of material can be used in tandem if a dichroic mirror is utilized to split the solar spectrum [11]. In the future (see Fig. 7), better efficiencies obtained from the optimal choice of the level of concentration, from an increase in the optical transmission and from the results of mass production will lead to a price of $2 Wp-1 within 4 - 5 years. After this time this solution has further possibilities for cost reduction resulting from the combined effects of lighter mechanical supports and the introduction of highly efficient solar cells such as gallium arsenide and/or tandem cells. Then the new target of $1 Wp-1 will be realized. It should be noted t h a t these price reductions are comparable with those for silicon flat plates and concentrator generators. In spite of this, we do understand w h y the main effort is now concentrated on flat plates because their setting-up, maintenance and reliability are known. However,

L~

1.so

\

a_ 1,25

100

o

1~-

I

I

15

16 SOLAR CELL

I 1"/ EFFICIENCY

I

I

1~

19

(%)

Fig. 7. P e a k w a t t c o s t v s . solar cell e f f i c i e n c y : curve A , a s s u m i n g t h a t t h e 20% e f f i c i e n t cell c o s t s f o u r t i m e s as m u c h as t h e 14% e f f i c i e n t cell; curve B, a s s u m i n g t h a t r e l e v a n t costs are t w i c e as m u c h ; curve C, a s s u m i n g n o increase in costs.

58

C0STI 'W,'t t4.3,

me0fv0r00s0nd ,nves I ' Research

E

3

Trockinq 215

"~

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1

~lbog 7

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~ . . . p e r for manee effects hm130 Sotor celt efficiencg T~ = 30 °

HIGH- EFFICIE NCY SILICON SOLAR CELLS

1983

(14.% ~ 2 0 % I 1985

) I 1987 PERIOD { YEARS )

Fig. 8". Prospects for reductions in cost

vs.

I IgBg

~_

time.

it should be emphasized that the cost reduction for flat plates is a problem of growth technology which is still under research, whilst concentrator generators present only a problem of production quantity.

5. Conclusion The cost analysis that can n o w be carried o u t for a concentrator generator, compared with similar studies for a flat plate, indicates the following features. (1) At present, concentrator generators are more expensive than fiat plate generators producing the same power. This is because concentrator generators have a poor general assembly technology related to a very low production rate which makes an industrial adaptation with competitive production methods impossible. (2) A detailed cost analysis indicates that the supplied material cost of $1.4 is less than the supplied material cost for a flat plate b y a factor of 3 (the flat plate cost is a b o u t $4.4). Furthermore, it appears that the setting-up of a production chain for a b o u t 1000 kW year -1 would be sufficient to reduce the final price o f a concentrator generator, if we take into account all expenses, to $4, resulting in a cost lower than the best short-term predictions for a fiat plate generator. Our analysis shows that technical solutions exist to the problem of developing photovoltaic conversion and combining it with other methods to produce electrical energy, a combination which would be economically

59 competitive over a long period of time. However, the key to the large-scale development of this solar industry still remains man's determination and national financial support.

References 1 Proc. International Solar Energy Society Congr., Atlanta, GA, May 28 -June 1, 1979, McDowell Hall, Delaware. 2 E. Burgess and M. W. Edenburn, One kilowatt photovoltaic subsystem using Fresnel lens concentrators, Proc. 12th Photovoltaic Specialists' Conf., Baton Rouge, LA, November, 1976, IEEE, New York, 1976, pp. 774 - 780. 3 Proc. Soc. Photo-Opt. Instrum. Eng., 68 (1975) 120. 4 D. T. O'Donnell, S. P . R o b b , R. Rule, R. W. Sanderson and C. F. Backus, Performance of silicon and gallium arsenide concentration cells, Proc. 13th Photovoltaic Specialists' Conf., Washington, DC, June 5 - 8, 1978, IEEE, New York, 1978, pp. 8O4 8O9. 5 D. Follea, Conception et r~alisation expdrimentale d ' u n g~n~rateur photovoltaique concentration p r o t o t y p e , Sophocles 1000, Thesis, University Paul Sabatier, Toulouse, 1979. 6 Proc. 1st Eur. Communities Conf. on Photovoltaic Solar Energy, Luxembourg, September 27 - 30, 1977, Reidel, Amsterdam, 1977, pp. 656 - 719. 7 D. Esteve, Analysis of a 1 kW photovoltaic generator with concentration, Proc. 2nd Int. Solar Forum, Hambourg, 1978. 8 C. E. Backus, Photovoltaics III, concentrators, IEEE Spectrum, (1980) 34 - 36. 9 J. P. Berry and D. Esteve, Etude de refroidissement actif par circulation d'eau et d'air pulse, L A A S - C N R S Rep. 2083 ( Laboratoire d 'Automatique et d'Analyse des Systdmes). 10 R. Sahai, D. D. Edwall and J. S. Harris, High efficiency A1GaAs/GaAs concentrator solar cell development, Proc. 13th Photovoltaic Specialists' Conf., Washington, DC, June 5 - 8, 1978, IEEE, New York, 1978, pp. 946 - 952. 11 R. L. Moon, L. W. James, H. A. Van der Plas, T. O. Yep, G. A. Antypas and Y. Chai, Multigap solar cell requirements and the performance of A1GaAs and Si cells in concentrated sunlight, Proc. 13th Photovoltaic Specialists' Conf., Washington, DC, June 5 - 8, 1978, IEEE, New York, 1978, pp. 859 - 867. -