predicting average energy conversion of

Renewable Energy 29 (2004) 403–411www.elsevier.com/locate/renene

Technical note

Predicting average energy conversion ofphotovoltaic system in Malaysia using a

simplified method

T.M.I. Alamsyah∗, K. Sopian, A. ShahrirDepartment of Mechanical and Materials Engineering, Universiti Kebangsaan Malaysia, 43600 Bangi,

Selangor, Malaysia

Received 27 March 2003; accepted 21 April 2003

Abstract

This paper is about predicting the average conventional energy conversion by a photovoltaicsystem in Malaysia. The calculation is based on average number of days in a month. Averagehourly energy flows are estimated based on knowledge of array test parameters, monthly aver-age of hourly ambient temperature and monthly average of daily hemispherical radiation. Themonthly average of diffuse component of radiation can be predicted based on hemisphericalradiation, by using an appropriate empirical correlation related to the monthly average ofdiffuse fraction to monthly average of clearness index. The values of hourly average radiationare estimated based on a statistical model. 2003 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic system; Average hourly radiation; Kuala Lumpur; Malaysia

1. Introduction

For optimum design of photovoltaic system in certain region, the estimation oflong-term system performance is necessary. One of the approaches to obtain thisinformation is by employing a computer simulation that uses special software suchas TRNSYS[1]. The software can compute system performance with a high temporalaccuracy resolution and integrate the result over time. However the extensivemeteorological data required for simulations are usually not available for extended

∗ Corresponding author. Tel.:+603-8925-1000; fax:+603-8929-6145.E-mail address: [email protected] (T.M.I. Alamsyah).

0960-1481/$ - see front matter 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0960-1481(03)00141-1

404 T.M.I. Alamsyah et al. / Renewable Energy 29 (2004) 403–411

Nomenclature

A area of photovoltaic system (m2)C the concentration for flat-plate array (MJ/m2)Iarray the radiation incident hourly on the array per unit area (MJ/m2)Ib indirect irradiance at normal incidence (MJ/m2)Id hourly diffuse irradiationIh hourly global irradiation on a horizontal plane(MJ/m2)H monthly average of daily extraterrestrial irradiation on a horizontal

plane (MJ/m2)Hd monthly average of daily diffuse radiationHh monthly average of daily ground reflected irradiationKT monthly average of daily clearness indexrt factor for converting monthly average of daily diffuse irradiation on

a horizontal planerd factor for converting monthly of average daily global irradiationUL thermal loss coefficient (W/m2C)iarray monthly average of hourly irradiation on the array surface (MJ/m2)Id monthly average of hourly diffuse irradiationit monthly average of hourly global irradiation on a horizontal planen average number of days in a monthw hour angle measured from solar noon: +ve for afternoon (radians)ws sunset hour angle (radians)wr

s sunset angle on an inclined plane (radians)f latitude of location: +ve, north; �ve, south (radians)d the sun’s declination angle (radian)qz angle of incidence of direct irradiance on the horizontal plane

(radians)qarray angle of incidence of direct irradiance on array plane (radians)s array title angle from the horizontal plane (radians)he energetic efficiency of the auxiliary power utilityb temperature coefficient (C�1)g radiation intensity coefficientta transmittance–absorbance product

periods at many meteorological stations in developing countries. An alternativeapproach is to use simplified and easier computational methods that do not requireextensive data and that can be adapted for hand-calculation methods. This methodwould be easier to understand than the one using computer software.

Several studies in the past have described various simplified methods estimatingthe long-term average performance or energy conversion of photovoltaic system.Ref. [2] describes a procedure which combines basic parameters characteristic of the

405T.M.I. Alamsyah et al. / Renewable Energy 29 (2004) 403–411

photovoltaic array with local monthly mean temperature and a monthly mean clear-ness index to yield a monthly average efficiency, which, when multiplied by monthlyarray insulations, gives electrical energy output. On the other hand, Ref. [3] presentsa method for predicting the monthly average of conventional energy displaced byphotovoltaic system based upon a monthly average of meteorological data.

In this paper, another simplified method for predicting the long-term average con-ventional energy conversion by a photovoltaic system is used to predict an averageperformance of photovoltaic system in Malaysia.

2. Prediction of electrical output of the photovoltaic array

The efficiency of a photovoltaic (PV) array is a function of cell temperature andarray irradiation which is represented by the following equation [2]:

h � hr 1�b(Tt�Tr) � glog10Iarray (1)

where hr is the array efficiency measured at reference cell temperature and this isrelatively constant for the range of operating temperatures encountered in flat-platearray [3], where Tc is the cell temperature and Tr is the reference cell temperatureat which hr is determined, g is radiation-intensity coefficient for cell efficiency, andIarray is the radiation incident on the array per unit area. Eq. (1) is written with g= 0 [3].

It is convenient to subtract and add the ambient temperature, Ta, from and to thetwo temperature terms in parentheses in Eq. (1), Tc and Tr respectively, and to giveafter setting g = 0. The equation can be written as follows:

h � hr[1�b(Tc�Ta) � b(Ta�Tr)] (2)

The energy balance of the array equates the solar energy gain in the array to theelectrical output and thermal losses which can be expressed by the following equ-ation:

taIarray � hIarray � UL(Tc�Ta) (3)

where ta is the transmittance–absorbance product of the array and UL is the thermalloss coefficient per unit area between array and ambient temberature. Meanwhile hin Eq. (3), is of the order of 0.1 ta. Therefore, Eq. (3) can be estimated by thefollowing equation:

Tc�Ta � 0.9�taUl�Iarray (4)

The term, ta /UL, can be determined from measurements of cell temperature, ambienttemperature and solar radiation at nominal operating cell temperature (NOCT) con-ditions Iarray = 800 W/m2 = 2.88 MJ/m2 /h, wind speed = 1 m/s and h = 0 in Eq.(3). ta/UL is obtained as:

taUL

�(Tc,NOCT�Ta,NOCT)

Iarray,NOCT(5)


Assuming ta /UL to be constant over the relevant operating temperatire range, Eq.(4) with ta /UL obtained from Eq. (5), can be used in Eq. (2) to obtain:

h � hr�1�0.9bIarray

Iarray,NOCT(Tc,NOCT�Ta,NOCT)�b(Ta�Tr)� (6)

The electrical energy output, Qc, of the array is given by:

Qc � hAIarray (7)

where h is obtained from Eq. (6) and A is the area.The average of hourly radiation incident on the array Iarray can be approximated

by the following equation [1]:

Iarray � Ibcosqarray �1C

Id (8)

where Ib is direct irradiance at normal incidence, qarray is the angle of incidence ofdirect irradiance on the array, C is the concentration (which is equal to 1 for a flat-plate array) and Id is the diffuse irradiance. If all the radiation in an hour is assumedto be concentrated at the middle hours, Eq. (8) also gives the hourly irradiationincident on the array, with qarray measured at the middle of the hour.

Often, hourly radiation data, especially the data that resolved into component beamand diffuse, are not available at many meteorological stations in Malaysia. The rec-ords available at most meteorological stations are those of monthly averages of dailyhemispherical (global) irradiation on a horizontal plane. Hd, which can be predictedfrom one of the several correlations given by Refs. [4–6]. Other factors relating theratio Hd /H with monthly average clearness index, KT, for ws � 81.40° and 0.3�KT�0.8 can be expressed by the following equation:

Hd

H� 1.311�3.022KT � 3.427K2

T�1.821K3T (9)

where Hd can be obtained with KT = H /H0 where H0 is the monthly average ofextraterrestrial radiation.

H and Hd can be resolved into monthly average of hourly values, it and id, respect-ively, by the use of conversion factors. rt, and rd [1,7]. These are presented in thefollowing equation as:

it � rtH (10)

and,

id � rdHd (11)

where rt and rd resolve monthly average of daily irradiation to monthly average ofhourly values.

Ib of Eq. (8) can be expressed in terms of the hemispherical radiation on a horizon-tal plane, Ih, and diffuse radiation, Id, as:


Iba �(Ih�Id)cosθz

(12)

where qz is zenith angle. Eq. (8) can be written, after replacing the instantaneous orhourly irradiation values, I, by the monthly average hourly irradiation, i, obtainedfrom Eqs. (10) and (11), as:

iarray � (it�id)cosqarray

cosqz

� id (13)

The other variable in Eq. (11) that still needs to be evaluated is cosqarray / cosqz. Forfixed-plate surface located at latitude, f with azimuth equal to zero and tilt angle s,cosqarray / cosqz is given by the following equation [9]:

cosθarray

cosθz�

cos(f�s)(cosw�cosws)cosf(cosw�cosws)

(14)

The angle wps in Eq. (14) is given by:

cosws � �tan(f�s)tand (15)

where d is the declination of the sun.For an array with tilt, s, equal latitude, f, as assumed in this paper, Eq. (15) is

evaluated with cosws = 0.Now, Eq. (13) can be evaluated using values of cosqarray / cosqz and calculated at

the middle of each hour for an average number of days in a month, to obtain monthlyaverage values of Iarray, which are entered into the array efficiency and energy asseen in Eqs. (6) and (7) [8].

3. Simulation procedure

This section outlines the simulation procedure which can be adopted to determinethe average performance of the PV system in Kuala Lumpur, Malaysia. As anexample, the average of the month of May is selected. The procedure is suitable forhand calculations and the speed of calculation can be enhanced by using a spread-sheet application, e.g. Microsoft Excel.

For each month, the average number of days, n, is used for the simulation asrecommended by Ref. [6]. Long-term monthly average meteorological data are used.This is assumed for the average number of days. Day time hourly values of theradiation available per unit array area, iarray, are calculated using location, radiationdata as given in the table for the month of May in Kuala Lumpur. In Table 4, w isthe hour angle, n is the average number of days for the month, d is the sun’s decli-nation on the average number of days of the month, f is the latitude of the locationand ws is the sunset hour angle calculated based on f and d. it and id are the averagehourly diffuse and hemispherical radiation calculated from the monthly average radi-ation, H and Hd, using Eqs. (10) and (11) with the appropriate conversion factors,


Table 1Radiation data in May for Kuala Lumpur, Malaysia

Description Value

Monthly average of diffuse Hd 8.76 MJ/m2

Monthly average of daily radiation on horizontal 17.7 MJ/m2

surface HMonthly average of clear index Kt 0.495

Table 2Data ambient temperature (location: latitude Kuala Lumpur, Malaysia)

Time Temperature

6:00;7:00 23.77:00;8:00 24.18:00;9:00 25.69.00;10:00 27.510:00;11:00 27.711:00;12:00 27.812:00:13.00 26.713:00;14:00 31.214.00;15:00 29.615.00;16:00 31.316:00;17:00 28.817:00;18:00 29.9

Table 3System array parameters

Array type Flat plate

Reference efficiency, hr 0.10Reference cell temperature, Tr 25 °CIarray,NOCT 800 W/m2

Temperature coefficient, b 0.004/°CAmbient temperature at NOCT, Ta,NOCT 20 °CCell temperature at NOCT condition, Tc,NOCT 46 °CPower conditioning efficiency, ht 0.90


Tab

le4

Det

erm

inat

ion

ofav

erag

eho

urly

radi

atio

nav

aila

ble

atth

ear

ray

(loc

atio

n:K

uala

Lum

pur;

latit

udef

3.1° ;

mon

thM

ay.

Ave

rage

Hd

=87

6.2

MJ/

m2

Kt

=0.

495.

H=

17.7

0M

J/m

2,

Arr

ayty

pe:

flat

plat

e

Tim

ew

nq

ws

r dr t

i ti d

cosq

arra

y/c

osq z

i arr

ayT

ah

Qc

(MJ)

(rad

iatio

ns)

(rad

ians

)(r

adia

ns)

6.00

�7.

00�

1.43

135

0.05

41.

589

0.01

90.

0137

0.16

60.

2420

0.82

440.

2287

23.7

00.

100.

6722

7.00

�8.

00�

1.17

135

0.05

41.

589

0.08

20.

0430

0.46

40.

7611

0.93

40.

7415

24.0

40.

102.

1800

8.00

�9.

00�

0.92

135

0.05

41.

589

0.10

60.

0750

0.71

81.

3280

0.95

81.

3024

25.6

00.

093.

5164

9.00

�10

.00

�0.

6513

50.

054

1.58

90.

123

0.10

560.

928

1.86

900.

967

1.83

7927

.50

0.09

4.96

2510

.00�

11.0

0�

0.39

135

0.05

41.

589

0.13

20.

1290

1.07

72.

2830

0.97

22.

2492

27.7

00.

096.

1404

11.0

0�12

.00

�0.

1313

50.

054

1.58

90.

132

0.14

241.

156

2.52

000.

974

2.48

4527

.80

0.09

6.63

3712

.00�

13.0

00.

1313

50.

054

1.58

90.

123

0.14

241.

156

2.52

000.

974

2.48

4526

.70

0.09

6.85

7313

.00�

14.0

00.

3913

50.

054

1.58

90.

106

0.12

901.

077

2.28

300.

972

2.24

9231

.20

0.09

6.27

5414

.00�

15.0

00.

6513

50.

054

1.58

90.

106

0.10

560.

928

1.86

900.

967

1.83

7929

.60

0.10

5.29

3315

.00�

16.0

00.

9213

50.

054

1.58

90.

082

0.07

500.

718

1.32

800.

958

1.30

2431

.30

0.10

3.82

9016

.00�

17.0

01.

1713

50.

054

1.58

90.

053

0.04

300.

464

0.76

110.

934

0.74

1528

.80

0.10

2.18

0017

.00�

18.0

01.

4313

50.

054

1.58

90.

019

0.01

370.

166

0.24

200.

8244

0.22

8729

.90

0.10

0.67

22


Fig. 1. The energy output from a photovoltaic system.

rt and rd, respectively, cosqarray / cosqz is obtained for Eq. (13) and iarray is obtainedfrom Eq. (12). Radiation data are given in Table 1. Now the hourly energy flow forthe system parameter is given in Table 3. The values of iarray obtained from Table2 are tabulated in Table 3 and used together with temperature-dependent h of Eq.(6). The efficiency of power conditioning array output, hcQe, is calculated from Eq.(7). Temperature data are also obtained from Table 2. Then, this can be simulatedand the simulation result is tabulated in Table 4. The energy output from a photovol-taic system is presented in Fig. 1.

4. Conclusion

A method predicting energy conversion or performance of photovoltaic system inMalaysia is presented. The approach is suitable for hand calculation. For each month,simulations are examined for only one day. This method can be speeded up by usinga spread sheet application. This method is suitable for primary evaluation of theaverage performance of photovoltaic system in Malaysia as well as in other countries.However, at the final stage, intensive evaluation including technoeconomic analysisis necessary.

Acknowledgements

The authors would like to thank the Ministry of Science, Technology and Environ-ment for the financial support under IRPA Grant No. 02-02-02-0005-PR23/11-10.


References

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[5] Erbs DG, Klien SA, Duffie JA. Estimation of the diffuse radiation fraction for hourly, daily, andmonthly average global radiation. Solar Energy 1982;28:155.

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predicting average energy conversion of

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