This work was performed by the Jet Propulsion Laborato ry, California Institu re of Technology, under National Aeronautics and Space Administration Contract NAS7-100, for the U.S. Department of Energy.

The JPL Low-Cost Silicon Solar Array Project is funded by DOE and forms part o f the Solar Photovoltaic Conversion Program to initiate a major effort toward the development of low-cost sola r arrays.

5101-43

LOW-COST SILICON SOLAR ARRAY PROJECT

MODULE EFFICIENCY DEFINITIONS, CHARACTERISTICS AND EXAMPLES

October 7, 1977

R. Grippi

Approved:

R. G. Ross LSSA Engineering Manqger

JET PROPULSION LABORATORY

CALIFORNIA INSTITUTE Of TECHNOLOGY

PASADENA, CALIFORNIA

5101-43

DISTRIBUTION

M. Alper (2) ---------------------------------------- 169-527 J. Arnett------------------------------------------- 157-507 R. Barlow------------------------------------------- 157-205 D. Bickler------------------------------------------ FHB-201 w. Callaghan---------------------------------------- 169-422 H. Carroll------------------------------------------ 157-507 E. Costogue ------------------------------ .---------- FHB-201 C. Coulbert ----------------------------------------- 67-201 G. Cununing ------------------------------------------ T-1073 K. Dawson------------------------------------------- 198-102 G. Downing------------------------------------------ 198-B9 L. Dumas-------------------------------------------- 157-102 R. Embry (2) ---------------------------------------- 200-119J R. G. Forney---------------------------------------- 169-422 A. Garcia------------------------------------------- 156-316 J. Goldsmith---------------------------------------- 169-422 C. Gonzalez----------------------------------------- 144-218 J. Griffith----------------------------------------- 150 R. Grippi (5) --------------------------------------- 158-224 D. Hess--------------------------------------------- 138-310 A. Hoffman------------------------------------------ 157-507 P. Jaffe-------------------------------------------- 79-6 R. Josephs------------------------------------------ FHB-201 P. Lyman-------------------------------------------- 157-205 H. Maxwell------------------------------------------ 157-507 D. Moore-------------------------------------------- 157-410 R. Ross (3) ----------------------------------------- 157-507 E. Royal-------------------------------------------- 157-507 D. Runkle------------------------------------------- 157-102 J. Schmuecker --------------------------------------- 158-224 J. Sheldon------------------------------------------ 200-119 S. Sollock------------------------------------------ 158-205 J. Spiegel------------------------------------------ 157-102 J. Stultz------------------------------------------- 157-102 P. Sutton------------------------------------------- 157-507 G. Turner------------------------------------------- 198-212 B. Wada--------------------------------------------- 157-507 B. Wagoner------------------------------------------ 158-224 A. Wilson------------------------------------------- 157-410

i j i

5101-43

CONTENTS

I. INTRODUCTION----------------------------------------------- 1-1

II. MODULE EFFICIENCY------------------------------------------- 2-1

A. ENCAPSULATED CELL EFFICIENCY------------------------- 2-1

B. NOMINAL OPERATING CELL 'l'EMPERATURE EFFICIENCY -------- 2- 2

C. MODULE PACKING EFFICIENCY---------------------------- 2-3

III. MODULE EFFICIENCY EXAMPLES--------------------------------- 3-1

REFERENCES------------------------------------------------- 4-1

APPENDIX

A. MODULE EFFICIENCY CALCULATIO~S ----------------------- A-1

V

5101-43

Figures

Tables

2-1. Border and Bus Efficiency------------------------------ 2-4

2-2. Cell Interconnect and Nesting Efficiency--------------- 2-6

3-1. Solar Cell Layout Configurations----------------------- 3-4

3-2. Potential Solar Cell Nesting Efficiency---------------- 3-5

3-3. Nesting Efficiency Relative to Number of Cells per Module--------------------------------------------- 3-7

3-4. Straw-man Ribbon Module Configuration------------------ 3-9

A-1. Straw-man Module Configuration------------------------- A-2

A-2. Factors in Bus Efficiency------------------------------ A-4

A-3. Interconnect Area-------------------------------------- A-6

A-4. Nesting Efficiency Relative to Number of Cells per Module--------------------------------------------- A-8

3-1. Module Efficiency Factors------------------------------ 3-2

3-2. Future Module Efficiency Examples---------------------- 3-8

vii

5101-43

SECTION I

INTRODUCTION

With the current trend toward lower module dollar-per-watt cosL, present system studies are placing greater emphasis on module efficiency since area-related costs become a greater portion of the system costs. The increased emphasis on module efficiency provides the need for esta­blishing a standard method for specifying, comparing and discussing module efficiency. This report presents the definition of module efficiency and discusses the factors that comprise module efficiency. In addition, numerous examples of module efficiency factors are presented and dis-cussed based on existing JPL large-scale procurements and research and development modules. Conclusions are drawn as to the maximum module efficiency possible with current technology.

~1

5101-43

SECTION II

MODULE EFFIC !ENCY

Module efficiency is the module peak power output divided by gross module area and solar insolation at Standard Operating Conditions (SOC). Standard Operating Conditions are 100 mW/cm2 insolation per Reference 1, with the cell temperature equal to the Nominal Operating Cell Temperature (NOCT):

Module Efficiency= Module Peak Power I SOC Gross Module Area x Solar Insolation

This definition has the advantage of providing accurate performance com­parisons at expected field conditions for various module designs with different thermal performance and cell I-V temperature characteristics. It also provides an incentive to optimize the module cell performance and costs for actual field conditions. Clearly, this efficiency is achieved in the field only if the system operates at a voltage corres­ponding to the maximum power.

Module efficiency is considered a product of three major efficiency terms: encapsulated cell efficiency, nominal operating cell temperature efficiency and module packing efficiency.

where:

11 m = 11ec x 11 noct x 11p

11 = Module efficiency m

11 = Encapsulated cell efficiency, STC ec

11 = Nominal operating cell temperature efficiency noct

11P = Module packing efficiency.

2-1

5101-43

A. ENCAPSULATED CELL EFFICIENCY

Encapsulated cell efficiency is the average solar cell efficiency within an encapsulated module at Standard Test Conditions. Standard Test Conditions (STC) is defined as 100 mW/cm2 insolation and zaoc cell temper­ature per Reference 1. By definition, this efficiency is the power per projected cell area divided by the solar insolation, i.e.,

Module Peak Power nee= Number Cells* Projected Cell Area* Solar Insulation STC

Encapsulated cell efficiency consists of several efficiency factors. These items include bare cell, cell electrical mismatch and optical transmission efficiencies, i.e.,

where:

nee = Encapsulated cell efficiency, STC

nc = Bare cell efficiency at STC

nmis = Electrical mismatch efficiency including interconnect I2R losses.

nt = Optical transmission through cell encapsulant efficiency

B. NOMINAL OPERATING CELL TEMPERATURE EFFICIENCY

In the field, cell temperature varies with the ambient thermal environment according to the thermal properties of the module of interest, and is generally different for different module designs. Because module power and efficiency decrease at a rate of approximately 0.5%/0C increase in cell temperature, an accurate comparison of module field performance requires that operating temperature differences be accounted for. This is accomplished by the Nominal Operating Cell Temperature efficiency (nNOCT), which represents the fraction of the power output measured at STC (100 mW/cm2, 280C) which is available at (100 mW/crn2 NOCT), when the solar cells have achieved their NOCT. The NOCT value, typically around 45°c, is the module cell temperature measured under standardized field operatinp, conditions which are representative of the average thermal environmental conditions in the United States during times when solar arrays are producing power. These thermal conditions, referred to as the Nominal Terrestrial Environment. (NTE) are defined as (see Reference 2):

Mounting: Tilted, open back, open circuit

Insolation: 80 mW/crn2

2-2

2ooc Air temperature:

Wind velocity: 1 m/s

5101-43

The 80 rnW/cm2 lnsolation level used to define the thermal environment for NOCT should not be confused with the 100 mW/cm2 insola­tion level used as the electrical reference level.

Because the rate at which power output varies with temperature (~P/~T) is also different for different modules, n is calculated noct using the following expression:

~ noct = Pat NOCT Pat 28°c = 1

Ll.P /Ll.T (NOCT - 28) Pat 28°c

C. MODULE PACKING EFFICIENCY

Module packing efficiency is the fraction of gross module area occupied by projected cell area, i.e.,

1l p = Number of Cells x Projected Cell Area

Gross Module Area

Pdcking efficiency consists of several efficiency factors. These items include border, bus~ interconnect and cell nesting efficiencies, i.e.,

where:

rip = packing efficiency

,,br = border efficiency

ribs = bus efficiency

riic = interconnect efficiency

11n = cell nesting efficiency

2-3

5101-43

Border area efficiency is 1 minus the fraction of gross module area used for module attachment flanges/interfaces, ends and side closures, i.e.,

71 br = 1 _ Border Area

Module Area (Refer to Figure 2-1)

Bus area efficiency is 1 minus the fraction of the module area minus border area used for electrical bus bars in series-parallel arrangements, ter­mination schemes, and the excess space between cells, and the module border and cell layout envelope, i.e.,

Bus Area =

1 - Module Area - Border Area (Refer to Figure 2-1)

Cell interconnect area efficiency is 1 minus the fraction of module area minus border area minus bus area used for cell interconnection schemes. The entire annular space around a cell is allocated to this efficiency factor even though only a portion is used for the physical interconnect.

11. 1.C

= 1 _ Interconnect Area Module Area - Border Area - Bus Area

(Refer to Figure 2-2)

Nesting area efficiency is the last of the efficiency terms and is therefore the fraction of the remaining module area occupied by projected cell area, i.e.,

Projected Cell Area Module Area - Border Area - Bus Area - Interconnect Area

(Refer to Figure 2-2)

More specifically, however, the nesting area efficiency denotes the ability of the solar cells to nest tightly when they, together with their annular interconnect areas, are brought into contact with one another. Square or rectangular cells have an nn=l; a rectangular array of circular cells has an nu= ~/4. The nesting efficiency is determined by the shape of the solar cells and the geometric arrangement of the cells. Excess space between cells not attributed to nesting ability or interconnect needs is generally lumped into the bus area defined earlier. For this reason bus area is often calculated last, after the nesting efficiency has been determined. The following formulas are useful for calculating the bus efficiency when this is done:

= 1 _ Bus Area Module Area - Border Area

2-4

BORDER AREA

5101-43

BORDER ANO BUS EFFICIENCY

11 BR = I _ BORDER AREA MODULE AREA

"es BUS AREA 1 - MOD. AREA - eel DER AREA

ATTACHMENT HOLE

Figure 2-1. Border and Bus Efficiency

2-5

5101-43

Cell Area Bus Area= Module Area - Border Area - Interconnect Area - --------­Nesting Efficiency

therefore:

Cell Area Module Area - Border Area - Interconnect Area - --------­Nesting Efficiency =1----------------------------.=.-----~ Module Area - Borde.r Area

As discussed above, module efficiency is·given by:

n =n xn xn xn xn xn xn xn • 1m ·1c ·1mis ·•t ·1noct ·1br ·1bs ·1ic ·1n

or

The Appendix provides examples for calculating module efficiency factors.

2-6

t'rj .....

OQ ~ ti (1)

N I

N . n (1) I-' I-'

H ::, rt (1) ti n 0 ::s ::s (1)

N n I rt ......

P> ::, p..

z (1) (I)

rt ~-::, OQ

ti:.:I Hl Hl ..... n ..... (1) ::, n '<

SOLAR CELL--------------

A

\...ia J CELL INTERCONNECT SPACE ---..c--------------~

A

CELL NESTING SPACE L\ r.1-;

SECTION A-A

CELL INTERCONNECT EFFICIENCY

ROUND CELL, .,, ,c = 1 - . . - . 7T O t (f H':_SlMR.~YLEt. ... 1 XF 1

CELL NESTING EFFICIENCY

fl _ TOTAL CELL AREA N ... 1..a.An. IKE a hXKKEh IDEI Bl IE XDEX IF XDEX

Ul ....... 0 I-' I

,i::.... w

5101-43

SECTION III

MODULE EFFICIENCY EXAMPLES

A sununary of state-of-the-art module efficiency factors is shown in Table 3-1. This summary consists of modules manufactured for JPL under the 46 kW (Block I), 130 kW (Block II) and research and development pro­curements. Block I modules are 1975 technology, Block II modules are 1976 technology and research and development modules are 1976-1977 technology.

As shown on Table 3-1, encapsulated cell efficiency varies from 10% to 12.5% on the ten different module designs. Major factors which affect the 20% range in encapsulated cell efficiency would be the optical trans­mission and reflection efficiency through the encapsulant and cover mate­rial, and quality and efficiency of bare cells.

Nominal operating cell temperature efficiency varies from 87% to 96%. As discussed previously, module power in the field is strongly coupled to the cell operating temperature. Modules with higher n

• 1noct have certain key thermal characteristics, which are:

1. The presence of good thermal conductance paths from the cell to high-emittance external surfaces is the primary require­ment for low cell operating temperature. Clearly, air gaps between the cell and exterior surfaces create greenhouse effects which are extremely harmful and raise cell tempera­ture by about 15°c. ·

2. The presence of good lateral conduction from the cell to low­absorptance, high-emittance surfaces between cells can reduce cell temperatures by nearly 10°c.

3. The presence of finned rear surfaces to increase convective 0 cooling can reduce cell temperatures nearly 5 C.

Obviously the direct incorporation of all affect other efficiency factors and cost. module for maximum efficiency and minimum through a systems approach.

these thermal features may Therefore, the design of a

cost can best be achieved

Increasing encapsulated cell efficiency or nominal operating cell temperature efficiency is one means of increasing module efficiency; a second approach is to increase the packing efficiency or percent of module which is active cell area. Solar module active cell area is largely affected by three variables: 1) module size, shape and aspect ratio, which influences the ratio of unused border and bus to enclosed module area; 2) solar cell spacing as required to accommodate electrical interconnection of the cells; 3) solar cell shape, which influences solar cell nesting efficiency.

Table 3-1 shows examples of border, bus, interconnect and nesting efficiencies. As shown, border efficiency is typically around 90%; that is, 10% of the module is used for border and attachment flanges not available for solar cells. Border efficiency can be easily raised to

3-1

w I

N

Table 3-1. Module Efficiency Factors

TABLE 3-1

MOUULE 77 EC fl NOCT 17BR 77 BS 77 IC MANUFACTURER

I\ @]ID ~ 0.90 (0.79) 0.93 0.111 0.93 0.91 0.84 0.92

. B 0.105 (0. 87) (0.84) 0.95 0.94

0.108 0.89 ~ (0 (0.90)

C 0.110 0.91 0.91 0.91 0.96 0.107 0.91 0.87 0.86 0.97

I) 0.110 0.95 0.84 0.86 0.93 0.109 0.93 0.91 0.87 0.93

E 0.118* o. 93,~ 0.92 Q.98 0.94

F (0.100*) 0.92* 0.87. Q.92 0.97

C 0.112* 0.93* 0.96 0.94 0.95

H 0.123* 0.91* 0.84 0.97 0.96

I 0.102* 0.89* 0.88 0.94 ~

l)ec Encapsulated cell Efficiency, STC

~noct Nominal Operating Cell Temperature Efficiency

qbr Border Area Efficiency

qbs Bus Area Efficiency

'lie; Cell Interconnect Area Efficiency

'1 N 11 p 11M PROCUREMENT

0.80 0.52 0.062 Block (0.78) 0.55 0.59 Block

0.80 0.60 0.059 Block

~ 0.69 0.071 Block

o.78 0.62 0.064 Block 0.78 0.57 0.054 Block

0.81 0.55 0.056 Block 0.80 0.59 0.061 Block

Q.83 -~ 0.077 R&D

0.82 0.64 (0.059) R&D

0.81 0.69 0.072 R&D

0.82 0.64 (0.072) R&D

0.82 0.67 0.061 R&D

'ln; Cell Nesting Efficiency

~ ; Packing Efficiency p .

I II

I II

I II

I II

'lm = 'lee 11noct • 'lp :a: Module Efficiency

* estimated

( ) Min.

Q Max.

Ul f-' 0 f-' I

.i:--, w

5101-43

95% by optimizing the module configuration through minimum edge features and attachment interfaces. On small modules, the border is more predomi­nant because of minimum hardware requirements; therefore, in this case it may be difficult to achieve 95% efficiency. On a glass module, the frame bite around the perimeter of the glass, which is part of the bor­der efficiency, is approximately 0.5 inch for adequate structural sup­port. Again, it may be difficult to achieve a high border efficiency on a glass module.

Bus efficiency varies from 79% to 99%. Much of the lost space is attributed to excessive space between the cells and the side and end border because smaller-than-optimum cells have been placed in a given envelope. In several cases, this area has been used for bus bars in series-parallel configurations and module electrical termination features.

As shown in Table 3-1, interconnect efficiency typically varies from 90% to 99%. This efficiency is related to the spacing required for the particular cell interconnect design. Each design may require a dif­ferent spacing, depending upon the details of the interconnect and its stress relief scheme. In many cases, the spacing is based upon the manufacturer's experience rather than engineering analysis. With a rigorous design, the e~ficiency can be improved to 98%.

Cell nesting efficiency is a measure of the cell shape to package within a minimum envelope after all other packing factors are removed. As such, square or rectangular cells have a nesting efficiency of 100%, while round cells have a varying nesting efficiency of 78% to 88%, depending upon the number of cells and module aspect ratio. An improve­ment in round cell nesting efficiency is achieved by modifying the round cell toward hexagonal and square shapes. However, this improvement should be reviewed with respect to module cost-benefits. As shown in Figure 3-1, existing module designs have nesting efficiencies from 78% to 83%.

Solar cell nesting efficiency is affected by module shape and aspect ratio, and cell shape. Figure 3-1 identifies the solar cell lay­out configurations for determining cell nesting efficiencies for hexagon and tight staggered round cells. Figure 3-2 shows cell nesting efficiency as affected by cell shapes, round and hexagon, and by module size as related to modules with an identical number of cell columns and rows. It can be seen that a rectangular pack of round cells nests at a constant 78.5% efficiency, while a tight staggered pack nests at a significant increase above this value.

As shown in Figure 3-2, staggered hexagon cells nest 6-8% better than round cells in larger modules. (Hexagon cells are not cost effec­tive at this time.) Another consideration shown in Figure 3-2 is the use of half-cells to fill out the module end spaces which are left when a tight sbaggered pack is used. With larger modules, an approximate 3% gain in packing efficiency can be realized by using half-cells. How­ever, this can only be accomplished in a series-parallel arrangement by using half-cells in each group of parallel cells.

~3

5101-43,

ROUND STAGGERE°D

SROWS

4 COLUMNS

HEXAGON

ROUND NON-STAGGERED

Figure 3-1. Solar Cell Layout Configurations

Figure 3-1.

3-4

100

90

88

#

>-u z w Q "-"-~

c., 84 z ;:: V'I w z :j 82 w u

80

78

76

74

72

70

68 0

5101-43

---r------.-----,----~----r------~---

2

HEXAGON WITH 1/2 CELLS

4 6 8 10

ROUND NON-STAGGERED CELLS

12 14 16

NUMBER COLUMNS AND ROWS

18

Figure 3-2. Potential Solar Cell Nesting Efficiency

3-5

20

5101-43

Modules with an identical number of cell rows and columns in a staggered pattern have a nesting aspect ratio of 1.0. Rectangular mod­ules with higher nesting aspect ratios have nesting efficiency relation­ships shown in Figure 3-3. For a constant number of cells, increasing the nesting aspect ratio provides a slight increase in nesting effi-ciency. A point of diminishing returns in nesting efficiency is reached around 250 cells per module as shown in Figure 3-3.

Table 3-2 shows efficiency examples for future modules. The first row represents estimates of efficiencies to meet a 7% minimum efficiency requirement for future large-scale procurements. The second row shows that a maximum efficiency of 9% may be achieved with current technology by a rigorous systems-type design. Obviously, the cost impact of this design needs to be considered.

Recent improvement in solar cell ribbon technology has made a rib­bon module a potential contender for future large-scale procurements. A straw-man ribbon module configuration is shown in Figure 3-4. This mod­ule consists of 36 cells in series to provide 15 volts in an NTE. Each cell is a ribbon 9.0 inches long and 1.3 inches in width. The third row in Table 3-2 shows an estimated range of efficiencies for this rib­bon module. As shown, the nesting efficiency of 100% provides the major advantage for the ribbon module. It should be noted that a ribbon mod-ule requires an interconnect scheme which allows the cells to be positioned around 0.010 inch apart to achieve the 99% interconnect efficiency. A typical cell spacing of 0.080 reduces the interconnect efficiency to approximately 94%.

~6

100

98

96 -

94

92

90

88

'#

> 86 u z "' Q ... M ... "' C) z ;::: .,, et "' z

80

78

76

7,4

72

70

68 0 2

5101-43

NESTING RATIO

4 6 8 10 12

NUMBER COLUMNS

ROUND CELLS

ROWS COLUMNS

14 16 18 20

Figure 3-3. Nesting Efficiency Relative to Number of Cells per Module

3-7

5101-43

Table 3-2. Future Module Efficiency Examples

11 EC T1NOCT 11 BR 11BS 11 rc 11N Tlp 11M

Future Procurement 0.117 0.90 0.94 0.93 0.95 0.86 o. 71 0.075

Maximum Current Technology 0.125 0.93 0.95 0.99 0.98 0.83 o. 77 0.09

Ribbon Module (minimum) 0.08 0.93 0.88 0.98 0.94 1.00 0.81 0.060

Ribbon Module (maximum) 0.10 0.93 0.88 0.98 0.99 1.00 0.85 0.080

11 =11 xq xri m ec noct p

3-8

5101- 43

36 CELLS J ,J X 9 .Q

Figure 3- 4. Straw- man Ribbon Module Configuration

3- 9

5101-43

REFERENCES

1. 1·Terres trial Photovoltaic tteasurernen t Procedures, 11 NASA TM 7 3702, National Aeronautics and Space Administration, Lewis Research Center, Cleveland, Ohio, June 1977.

2. Stultz, J.W., and Wen, L. C., "Thermal Performance Testing and Analysis of Photovoltaic Modules in Natural Sunlight," Low-cost Silicon Solar Array Project Task Report No. 5101-31, Jet Propulsion Laboratory, Pasadena, California July 29, 197?.

4-1

5101-43

APPENDIX

MODULE EFFICIENCY CALCULATIONS

This appendix provides detail examples for calculating the effi­ciency factors that comprise module efficiency. The module used for this example contains 108 cells, three parallel strings of 36 cells each, each cell 3.60 in. in diameter (Figure A-1).

A. ENCAPSULATED CELL EFFICIENCY

6.0 MODULE 1-V CURVE @ 28°C

------------, MAXIMUM POWER

4.5 I I

a I E C, I ..: z 3.0 I u.,

ai:: al!: I :::::> u

I 1.5 I

I I

0 0 5 10 15 20

VOLTAGE

P =IV= 5.55 amp x 16.4 volts= 91.0 watts

Y)ec = Module Peak Power I STC

Number Cells x Projected Cell Area x Solar Insulation

91.0 watts =-----------------~---------------------x 1000 mW watt 108 cells x 66.7 cm2 x 100 mW/cm2

= 12.6%

B. NOCT EFFICIENCY

AP (NOCT - 28°) P at NOCT AT =-P-a_t_2_8_0_c=l----P-a_t_2_8_o __

A-1

5101-43

30.6" ----------~ j_ --------'' T

.75 II

MODULE AREA =47.9 x 30.6= 1466in.2

END BORDER= 2(30.6 x .75) = 46 in.2

SIDE BORDER = 2(47. 9 - • 75 - .75) .5 = 46 in. 2

Figure A-1. Straw-man Module Configuration

A-2

.5"

BORDER AREA

or

where:

then:

5101-43

0 11NOCT = 1 - pcoeff (NOCT - 28 C)

0

P ff" . = 0.00524 watts/ C (typical) coe 1c1ent watt

NOCT = 43°c (determined per Reference 2)

11NOCT = 1 - 0.00524 (43-28)

= 0.921

C. BORDER EFFICIENCY

Refer to Figure A-1.

11 hr = 1 _ Border Area

Module Area

= l _ 2(30.6 X 0.75) + 2 [(47.9 - 0.75 - 0.75) 0.5] 30.6 X 47.9

= 1 _ 92. 3 in; 1466 in

= 0.937

D. BUS EFFICIENCY

Refer to Figure A-2.

11 bs = 1 _ Bus area

Module Area - Border Area

A-3

J·

46.4

5101-43

29.6 .30

0 0

ENO BUS AREA -= 2(29 .6 x .3) .,, 18 in. 2

SIDE BUS AREA-= 2(46.4-.3-.3).2: 18in.2

CENTER BUS AREA:: (46 .4 - .3 - . 3) .25 = 11 in. 2

Figure A-2. Factors in Bus Efficiency

A-4

·J

5101-43

= l _ 2(29.9 X 0.3) + 2(46.4 - 0.3 - 0.3) 0.2 + (46.4 - 0.3 - 0.3)0.25 1466 - 92.3

47 in2

= 1 - 1374 in2

= 0.966

When bus area is difficult to establish, the following method is useful for calculating buss efficiency:

Determine n from figure A-4 then, n

Bus Area Cell Area = Module Area - Border Area - Interconnect Area - --------­Nesting Efficiency

therefore

Cell Area Module Area - Border Area - Interconnect Area - --------­Nesting Efficiency =1--------------------------~-----~ Module Area - Border Area

1466 - 92 - 37 1099

= l ________ -_._8_5_2 1466 - 92

47 in2

= 1 - 1374 in2

= .966

E. INTERCONNECT EFFICIENCY

Refer to Figure A-3.

Interconnect Area 11 IC =

1 - Mod_ule Area - Border Area - Bus Area

A-5

5101- 43

INTERCONNECT AREA NUMBER CELLS ( 7T X DX t)

]08 (7r X 3 .6] 5 X 0 . 030)

37 ;/

Figure A- 3 . Interc onn e ct Are a

A-6

0.030

where

5101 - 43

Cell Diameter 3 . 60 in.

0 . 060 in. Cell Spacing

Number Cells = 108

1l IC = l _ 108(TI X J.615 X 0 .060/2)

1466 - 92 - 47

1 37 in2

1327 in2

= 0 . 971

F. NESTING EFFICIENCY

Projected Cell Area 11 = ~~~~~~~~~::...::..:::-i..--=-=-=-==---=-=-=-=---=-:-=-==--~~~~~~~~~ n Module Ar ea - Border Area - Bus Area - Interconnect Area

108 X * X J .602

1466 - 92 - 46 - 37

_ 1099 in~ = 1 1291 in

0 . 85 '

Check by referring to Figure A- 4.

Nesting r atio Numbe r rows Number columns

12 - 9

= 1.33

A-7

100

98

96

94

92

90

88

#

> 86 u z ..... u ii: 134 II. w (!) z ~ V,

82 ..... z

80

78

76

74

72

70

68 0 2 4 6 8

5101-43

ROUND CELLS

ROWS NESTING RATIO .; COLUMNS

10 12 14

NUMBER COLUMNS

16 18 20

Figure A-4. Nesting Efficiency Relative to Number of Cells per Module

A-8

therefore

11 = 0. 85 n

5101-43

G. PACKING EFFICIENCY

Check:

H. MODULE EFFICIENCY

T) p = T)b X f}b X 11. X 11 r s ic n

= 0.937 X Q.966 X Q.971 X 881

= o. 748 ~---------.....

= Projected Cell Area 11 p Module Area

TT 2 108 x 4 X 3.60 = 30.6 X 47.9

1099 = 1466

= o. 748 __________ .....

= 0.126 X 0.921 X Q.748

= 8. 7%

NASA-JPL-Coml .. L.A., Cali!.

A-9

~ 5101-43