Effect of ambient temperature on the demanded energy of solar cells at different inclinations

~

Pergamon

Renewable Energy, Vol. 14, Nos. 1-4, pp. 149-155, 1998 © 1998 Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain P l h S0960-1481 (98) 0 0 0 6 1 - 5 0960-1481/98 $19.00+0.00

E F F E C T O F A M B I E N T T E M P E R A T U R E ON T H E D E M A N D E D ENERGY OF SOLAR CELLS AT DIFFERENT INCLINATIONS

A.M.AL- SABOUNCHI Solar Energy Research center, Jadiriyah , P.O. Box 13026, Baghdad-IRAQ

ABSTRACT With increase of ambient temperatue there is a deficiency in electrical energy that solar cells supply than their values under ideal conditions (25 °c -1000 w/m2), this sitiuation be of a high affection especially in countries of a hot climate. In this work the cell temperature inside a solar panel is calculated depending on values of ambient temperature , solar radiation and multi other parameters related to climate and solar panel manufacturing. The ideal and actual energy that is supplied by a certain area of solar cells under ideal and actual conditions is measured to determine the defficiency between the two cases, then a new formula is applied to determine the exact substitutive area of solar cells that must be added to the initial area so as the energy supplied by the cells under actual conditions is the same as that under ideal conditions. A comparsion and evaluation of the results are made for multi inclinations according to the climatic data of Baghdad city.Constants are derived for Baghdad city which can be applied in designing PV systems to get values of actual energy supplied by solar cells at any temperature are exactly the same as that calculated under ideal conditions at Tc=25 °c. © 1998 Published by Elsevier Science Ltd. All rights reserved. INTRODUCTION Temperature consideration is important when considering the use of solar cells for economical power generation , where it is a key factor in the performance of solar cells for at least two reasons. First, the power (and voltage) output of a solar cells decreases monotonically with increasing temperature at a rate depending on the particular cell, but normally by a factor varying between 4000-6000 ppm/°c at 25 oc(Buresh,1983). Second , for single or poly crystrals, the life expectancy of a solar cell also decreases with increasing temperatue . In areas of high level ambient temperature climate like Iraq the performance of PV system are highly affected by ambient temperature increasing, which it sometimes in extreme summer exceeds 50 °c, that will cause a rise in cell temperature , ( T c ) to about 70 "c or more ,depending on the production specifications of the solar modules. For example, a solar module type A E G P Q S / 4 0 / 0 shows a decreasing in Pmax of about 0.44% in p.u. of ideal Pmax for each l°c above 25 °c ,then at cell temperature ( T c ) equal to 70 °c ,such solar module type lose about 20% of the specified Pmax, which is eventually affecting the energy balance of PV systems. Furthermore, recieved quantity of solar radiation is another parameter that affects the solar cell temperature,because part of the incident radiation i~ transformed into heat within the semiconductor, that heat is proportional to the value of recieved solar radiation, which is also affected by the inclined surfaces 149

150

A . M . AL-SABOUNCHI

Tilt factor 1.8 1.6

._.'%

1./. ~-X,, 1.2 1 0-8 0.6

2

3

4

5

6

7

8

9

10

11

12

Months • B=0

+ 13=10

w B=20

n B=30

x B=40

0 B=50

Fig. 1. Tilt factors at different inclinations during the year Since that recieved quantity of solar radiation varies with variations in surface inclinations, then consequently, consideration of surface inclinations of solar modules is an important parameter in determining cell temperature .In this w o r k , the effect of solar cells temperature rise is considered, where the standard conditions of solar cells performance is assumed to be that at Tc=25 °c. A certain procedure was placed to evaluate the exact areas of solar cells that might be added to the specific area under ideal conditions, to substitute exactly the deficiency in energy due to cell temperature rise above 25 %. TILT FACTOR CONSIDERATION Consideration of surface inclinations of solar modules as one of the affecting parameters on the cell temperature, is taken into account in this work through determining the tilt factors of the inclined surfaces of PV modules. The average daily radiation on a tilted surface ,(IT),is expressed as: Iv=R* H v . . . . . . . . . . . . ( 1) Where ' R-Tilt factor & Hw-Monthly daily average & t o t a l horizontal radiation. According to Liu and Jordan formula, (R) can be determined according to (Lunde, 1980)as • RbHTb R = "--'~'T + Where: R b

(I+cosB) 2

HTd HT

+,,(1-cosB)f 2

. . . . . . . . . . . . . . (2)

-Direct beam elevation factor

HTb & HTa - Monthly daily average total horizontal beam & diffuse radiation. B - Tilt angle in degree. - Ground reflectivity. Note that ,values of HTd/H T are calculated according to (Riahi, 1987) as: HTd/HT = 1.076 - 1282 * K r . . . . . . . . . . . . . . . . . . . . . . . . . . . (3) Where K T is the clearness index. Then, applying equation(2) on different inclination surfaces and for each month yields results as indicated in figure (1).

Effect o f ambient temperature on solar cells

151

SOLAR CELL TEMPERATURE CONSIDERATION In this work the solar cell temperature (Tc) is expressed as a function o f the known ambient temperature ( T a ) , and the various heat transfer parameters (hc,hr,hf, and others) as well as solar flux (I), at the surface o f the panel, the solar absortance(sa) and the infrared emissivity (C) o f the solar cells,the optical transmittance (tg) and infrared transmittance (tg) o f the glass, and the tilt angle (B) o f solar panel with respect to horizontal.Other parameters that would enter the analysis include the wind speed (V); cloud cover,(n); and the air dew point temperature (Tdp),indicative o f the air humidity.The cell temperature is expressed according to the general formula in (Ingersoll, 1986) as:

To: EpI - P +[hc + 0.5 C p ( l + c o s B ) (CsCn)V4hr + h f + F e Fb hr] Ta . . . . . . . . (4)

hc + 0.5 Cp ( l + c o s B ) hr + h f + F e Fb Hr where: Ep - Glass optical efficiency,

hr - Unit radiative heat transfer.

P - Solar cell p o w e r output, in w . h f - Back panel convective heat trasnsfer. hc - Convective coefficient. Fe - Back panel surface emissivety factor. Cp - Infrared efficiency. Fb - Back panel surface config, factor. Cs - Sky emmisivity. Ta - Daylight ambient temperature ,in " c Cn - Sky cloud cover coefficient. I - Solar flux,in w/m' Equation(4) is applied at different inclinations on 1 m 2 o f solar cells with a standard efficiency ,(Em),equal to 10%, and using the climatic data o f Baghdad city. The results are as shown in table(l).

Table 1. Results o f T a & Tc o f solar cells at different inclinations (B) ,in Baghdad city

Jan

Feb

Mar

Ambient Temperature{Ta} in "c Apr May Jun Jul Aug ~

Oct

Nov

Dec

11.9

17.8

21.5

27.2

34.3

24.3

18.5

50.5 52.7 54.3 555 56.2 562

377 401 42.1 436 44 7 453

32.6 35.5 38.1 40l 416 425

B 0 10 20 30 40 5/)

34.2

39.6

42.2

40.3

39.2

Cell Temperature (Tc) in °c 24.2 26.3 28.2 29.5 30.7 31.2

31.4 33.3 34.8 35.8 36.5 36.6

37.3 38.5 39.2 395 39.5 38.9

43.9 44.3 44.4 43.9 43.3 423

52.2 52 51.6 50.7 49.6 48.2

57.3 56.9 56.1 55.1 53.7 52.2

60.4 60.1 59.4 58.4 57.1 55.5

58 58.2 58 57.5 56.6 55.3

56.9 58 58.7 588 586 578

CONSIDERATION OF SOLAR CELL DEFICIENCY In designing photovoltaic systems specially those in hot areas, the rise in solar cells temperature highly affects the values o f Pine x and efficiency o f the solar modules.The effect that related to Pmax is expressed as Pa = Ps - Ps * D f * (Tc - 25) . . . . . . . (5) Where: Pa Ps

- Actual Pnwx o f solar cells at Tc above 25 °c - Standard Pmax o f solar cells at Tc = 25 °c.

D f - Deficiency f a c t o r As an example, assume that a 1 nl 2 solar module o f ( P s ) equals to 100 watt and standard efficiency 0 1 , is operated at Tc = 65 oc, with a (Dr) equals to 0 5 % , (Pa) is determined according to equation (5) ,as: Pa=100'(1-.005"40)=80 watt

152

A.M. AL-SABOUNCHI

That means there is a deficiency o f ( 2 0 ) watt less than the ideal power under standard conditions. Then the actual efficiency, (Ern a )is calculated as: Ema-

Pa/( Sc * A)

. . . . . . . . . (6)

Where ,(Sc) is the solar constant which is equal to 1000 (w/m 2) ,and ( A ) i s solar cells area. Applying equation (6) on the e x a m p l e , yields: Ema = 0.08 . If an additional solar cell o f P m a x equal to the calculated deficit power (20 watt in the example),is added to (Ps) to substitute the deficit, it gives a new Pmax equal to 120 watt. N o w since that new(Ps) is determined under standard conditions,there is a still deficit in the output power at (Tc=65 °c),which is calculated as: Pa = 120 * (1 - 0.005 * 40) = 96 watt A new procedure to determine the additional area that must be added to the initial area to get exactly an actual power equal to (Ps) at any value of ( T c ) , is derived as follows. Assume that the cell temperature (Tc) exceeds 25 °c ; the deficit power (Dp) ,is determined according equation(5) as :

i.e,

Dp = Ps * D f * ( T c - 25) Pa = Ps - Dp

. . . . . . . . . . . (7) . . . . . . . . . . . (8)

To substitute (Dp),a certain value o f solar power must be add to (Ps) under standard conditions, to get an output power at any Tc > 25 °c equal to ( P s ) , that is determined as : Dp = Ap - Ap * D f * (Tc - 25) . . . . . . . (9) Where,(Ap)is the additional solar power that must be added to(Ps) at Tc=25°c that gives an additional power at Tc>25°c equals exactly to(Dp).Then,(Ap) is simply formulated basing on equation(9), as : Ap = D p / [ 1 - D f * (Tc - 25)1 . . . . . . . . . . (10) To determine the area of solar modules corresponding to (Ap), equation (10) is divided by (Sc * Era) Applying equation (10) on the same example after determining (DP) from eq.(7), yields : Ap=20/[1-.005'40] = 25 watt Then,

Pse - Ps + Ap

. . . . . . . . . . . . (11)

Where (Pse) is the exact value o f solar power at Tc=25°c, that gives the same quantity of (Ps) at any ( T c ) Applying equation (11) on the example yields Pse 125 watt .Then determining Pa, by applying equation(5),as: Pa = 125 * (1 - .005 * 40) = 100 watt As it s h o w n , (Pa) at Tc = 65 °c is exactly equal the initial value of(Ps). Then similarly, the area ,(Ase),of solar power corresponding to (Pse), is found as : Ase = P s e / S c * E m . . . . . . . . . . . . (12) Applying equation (12) on the example ,gives (Ase) equal to 1.25 m 2, that means we need a solar cells area equal to 1.25 times the area calculated under ideal conditions to substitute exactly the deficit due to temperature rise o f cells above 25 %. NUMERICAL APPLICATION A computer program was designed in this work ,that includes the considerations o f tilt factors, solar cell temperature and deficiency of solar cell with temperature rise. Depending upon the climatic data of Baghdad city,the program was applied on a solar cell area equals l m2,with a standard efficiency 10% ,mounted at different inclinations from (0 to 50)degrees.

153

Effect of ambient temperature on solar cells

The monthly daily average value of ideal energy, IE(i),that can be generated by the solar cells area at 25 %, is calculated for each month as: IE(i) = Hr(i ) * R(i) * E m (13) .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

To find the monthly daily average of actual energy ,AE(i), equation(13) is applied with Ema substituted instead of Em,where equation (5) is applied to determine Pa(i) with Tc(i) expressed for each month according to equation (4) ,then the new actual efficiencies, Ema(i ) is calculated from equation (6), results ofEma(i ) are as shown in table (2) Table 2. Actual values of efficiencies at different inclinations (B) at actual values of Tc Actual solar cells efficiency during the year B Jan Feb M a r Apr M a y Jun Jul A u g Seo Oct Nov Dec 0 10 9.67 9.38 905 8.63 8.38 8.22 8.35 8.39 8.72 9.35 9.6 10 9.39 9.58 932 9.03 8.64 8.39 824 8 . 3 3 834 86 9.24 947 20 9.83 9.5 928 903 8.66 8.43 8.27 8.34 8 . 3 1 8 . 5 3 9.14 9.34 30 9.76 9.45 9.27 9.04 8 . 7 1 8.49 8.32 8.37 8.3 8.47 9.06 9.2 40 9.71 9.42 9.27 9.08 8.76 8.56 8.39 8.41 8.31 8 . 4 3 9 . 0 1 9.16 50 9.68 9.41 9.3 9.13 8.83 8 . 6 3 8.47 8.48 8 . 3 5 8.43 8.99 9.12 The monthly daily average of ideal and actual energy,(IE and AE), in w.h/m 2 are presented in table(3) for each month at different inclinations ,according to equation (13). Table 3. Results of IE and AE, in w.h/m 2 at different inclinations (B) for each month Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

B IE--AE IE--AE IE--AE IE--AE IE--AE IE--AE IE--AE IE--AE IE--AE IE--AE IE--AE IE--AE 0

285-285

384-372

468-538

538-487

590-509

693-581

720-592

652-544

562-472

464-405

320-300

275-265 332-314

10

335-333

436-418

501-467

551-497

585-506

677-569

708-583

661-551

596-497

524-452

375-347

20

378-372

478-455

522-485

522-498

570-494

649-458

682-565

655-547

616-512

571-487

422-385

380-355

30

412-402

509-481

532-493

541-489

543-473

609-517

643-535

535-532

612-516

604-512

458-415

420-388

40

435-423

527-497

530-491

518-471

50%444

557-477

591-496

601-506

611-508

622-525

483-435

449-411

50

449-434

532-501

515-479

486-443

461-407

496-429

528-448

554-470

587-490

624-526

496-446

466-425

To find Ase(i) for each month i, the set of equations (10 to 12) is applied for each month, then the monthly daily average values of actual energy generated by the new solar cells area (Ase),is expressed as: AEe(i) = HT(i ) * R(i) * Ase(i) * Ema(i ) . . . . . . . . . . (14) Where,AEe(i) is the monthly daily average of energy generated by solar cells for each month ithat corresponds to Ase(i).The results are shown in table (4). Table 4. Results of the monthly daily average of AEe in w.h/m 2 for each month. Values of A E e during a year B Jan Feb M a r Apr M a y Jun Jul Aug ~ Oct Nov Dec 0

285

384

468

10

335

436

501

20

378

478

522

538 551 552

590

693

720

651

562

464

320

585

677

708

661

596

524

375

275 332

570

649

682

655

616

571

422

380 420

30

412

509

532

541

543

609

643

635

621

604

548

40

435

527

530

518

507

557

591

601

611

622

483

449

50

449

532

515

486

461

496

528

554

587

624

496

466

154

A.M. AL-SABOUNCHI

Enerc t(whl~) 5~0

/

I

/*8O

/*200

5

10

15

20

25

30

'",

35

/*0

/*5

50

55 60

~lt angle ( d e g r e e ) • Standard + Actual Fig.2. Annual daily average of electrical energy generated by lm2 solar cells for muttiBaghdad city By considering the results oftables(3&4)it can be noticed clearly that the values of AEe(i) in table (4) ,are exactly equal the values of ideal energy ,IE(i), at Tc=25 °c that presented in table (3). In order to choose the best tilt angle for Baghdad city at which the solar cells modules are mounted, the annual daily average of solar radiation is determined for each tilt angle from (0 to 50) degree as: 12.

Annual daily average radiation = [ ~ E(i)* DA(i) ] / 365 . . . . . . . . . . . . . (15) Equation (15) is solved for the annual daily average values of actual and exact or ideal energy, by substituting for E(i) by(AE(i) and AEe(i)) respectively,notice that DA(i) is the number of days for month i , the results are as shown in figure(2). From the figure it is shown obviously that in Baghdad ,the tilt angle (30) degree is the best angle to be used in mounting solar arrays of PV systems so as to gain best values of solar radiation during the whole year. Table (5) indicates the values of exact areas of solar cells (Ase) that are calculated according to equations(10 to 12) at multi inclinations ,in pu.ofthe standard areas so as to cancel exactly the deficit in the generated energy due to cells temperature rise above 25 °c Notice that such values are considered as the related factors that can be applied for Baghdad city Table 5. The added areas of solar cells in p.u. of standard areas for multi inclinations p.u. added areas B Jan Feb Mar Apr May Jun Jul Aug Sep Oct Non Dec 10 20 30 40 50 60

1.006 1.016 1.024 1.029 1.032 1.032

1.043 1.051 1.057 1.061 1.062 1.06

1.072 1.076 1.078 1.078 1.075 1.069

1.107 1,107 1.105 1.101 1.094 1.086

1.156 1.153 1.148 1.14 1.131 1.121

1.189 1.148 1,177 1.168 1.157 1.145

1.213 1.208 1.201 1.191 1.18 1.167

1.199 1.198 1.194 1.187 1.178 1.167

1.198 1.2/)2 1.204 1.201 1.196 1.187

1.16 1.172 118 1.148 1.185 1.181

1.081 1.093 1.103 1.109 1.113 1.113

1.055 1.07 1081 109 1096 1.098

DISCUSSION AND CONCLUSIONS It can be noticed from table (1) , that mounting the solar cell modules inclined at a certain tilt angles increases the values of tilt factor during Winter months and decreases them during Summer months, which lead to provide an effective benefits.

Effect of ambient temperature on solar cells

155

One of these benefits presented in reducing the expected surplus energy recieved by modules during Summer ,which yields to reduce the cells temperature and cells efficiency deficit. Other benefit is that it provides more recieved energy by solar modules during Winter, resulting in reducing the expected deficit in recieved solar radiation ,notice that the low ambient temperature during Winter months, reduces the effect of cells temperature rise on the cells efficiency during Winter. Also it can be noticed that,due to the increasesd values of (Tc) during Summer ,the solar cells show a high deficit in efficiency on Summer comparing to that on Winter ,then consequently more addition of solar cells area must be added during Summer to match the demand of energy. From other side of view, the increase of tilt angles lead to decrease the additional solar cells area during Summer , that because in Summer the decrease in tilt factor values causes a reduction in the recieved solar radiation,reducing the rise in cells temperature and finaly reducing the deficit in the cells efficiency. It can be concluded that the values of p.u. solar cells area (Ase) shown in table (5) are determined as a factors related to Baghdad city that one can multiply them by the values of calculated areas of solar cells modules under ideal conditions ,at different tilt angles to get a values of actual generated energy equal exactly that calculated under ideal conditions and for any month among the yearNotice that emphasis is placed to use the factors corresponding to (30) degree inclination where it is the optimum value for Baghdad city.A computer program was made for the above purpose which affords the facilities of determining such factors for any area at any inclination. REFFERENCES - Buresh,M.,(1983)Photovoltaic Energy systems,McGraw-Hill, New York, 77-78. - Peter J. Lunde,(1980). Solar Thermal Engineering ,John Wily & Sons, New York, 98-120. -M.Al-Riahi,(1987).Angular Disertation of Global Solar Radiation on Inclined Surfaces at Baghdad, Proceedings of the ISES Solar World Congress, the Tenth Biennial Congress of the International Solar Energy Society, Hamburg,FRG.4, 3779-3783. -J.G Ingersoll, (1986). Simplified Calculation of Solar Cell Temperature in Terrestrial Photovoltaic Arrays, Journal of Solar Energy Engineering, Vol. 108/95,95-101.