Solar energy is considered one of the promisingenergy resources available as a solution to the globalproblems associated with the continuing demand forenergy, caused by the global industrialization andworldwide population increases [1]. Being clean andwidely available for free, the resource can positivelycontribute to the reduction of environmental pollu�tion and to help damp out unstable oil prices, which inturn affects the complex and inter�related issues con�cerning the international community [2]. Solar energyis projected to supply 30% of the world’s energydemand by 2050 and to supply about 64% of the elec�tricity in 2100 [3]. Currently, photovoltaic (PV) systemcomprising the PV modules and related control systemis the sole mean through which the solar energy is con�verted directly into electricity.
The PV module is generally rated according to themaximum DC power output (watts) of the PV modulewhich can only be obtained under Standard Test Con�dition (STC). STC is defined as a module operatingcell temperature (Tc) of 25°C, and incident solar irra�diance (G) level of 1000 W/m2 and under Air Mass AM1.5 spectral distribution [4]. However, since STC is sel�dom encountered, the I–V (current–voltage) curve ofa PV cell describes its energy conversion capability atany existing conditions of light level (irradiance) andtemperature.
1 The article is published in the original.
Solar irradiance and module temperature are themost important factors affecting the energy yield of PVmodule [5, 6]. Most of the radiations emitted are inthe visible spectrum, and its characteristics at theearth’s surface are dependent upon the location.Meanwhile, regarding the sky conditions, there arethree types, which are clear, cloudy and overcast. On aclear sunny day, the power density of irradiance isapproximately 1 kW/m2 [7] and, of course, this num�ber is lower in cloudy and overcast days [8].
Solar radiation modelization should take intoaccount the climatic characteristics of the study area,as these characteristics strongly influence the solarradiation values and the associated statistics [9]. Thesunshine duration is one of the parameters often usedto correlate the global solar radiation [4, 10, 11]. In[12], based on the meteorological data collected from25 stations throughout Thailand, a prediction modelfor solar radiation was proposed. Clearness index (Kt)is another important parameter that is mostly used inthe calculation and analysis of the distribution of solarradiation components onto the earth’s surface. Theauthor in [9] proposed a model for representing distri�butions of data collected in a wide range of climaticconditions. Recently, many studies have been pro�posed for predicting the global solar radiation, utiliz�ing the Artificial Neural Network (ANN), where itconsiders various related climatological and meteoro�logical parameters as input variables [13–15].
Climate�Based Empirical Model for PV Module Temperature Estimation in Tropical Environment1
Mohamed Almaktara, Hasimah Abdul Rahmana, Mohammad Yusri Hassana, and Saidur Rahmanb
aUniversiti Teknologi Malaysia, Johor, MalaysiabUniversity of Malaya, Kuala Lumpur, Malaysia
Received March 01, 2013
Abstract—The paper proposes new mathematical models to estimating PV module temperature for poly andmono crystalline technologies in tropical climate such as in Malaysia. The developed models are based onmeasured hourly global solar radiation, ambient temperature, relative humidity, wind speed and module tem�perature. All data were collected over the year 2009 at GreenTech 92 kWp installed PV system in Selangor,Malaysia. The models were compared using r, MBE, RMSE, and MPE. The results showed that the proposedmodels give the highest value of correlation coefficient r, and good result when considering statistical indica�tors i.e. low RMSE, low MBE, and low MPE values. The results show that the proposed regression modelshave advantages over the conventional approaches for calculating the hourly and day�average PV moduletemperature, and give the closest results comparing to the actual measurements. The proposed approachescan be used as effective tools for predicting the PV module temperature, whether a simple PV module, openrack system, BIPV installations, or even PV/Thermal collector, in remote and rural locations with no directmeasurement equipment. The proposed models can be very useful in studying PV system performance andestimating its energy output.
DOI: 10.3103/S0003701X13040026
DIRECT CONVERSION OF SOLAR ENERGY TO ELECTRIC ENERGY
APPLIED SOLAR ENERGY Vol. 49 No. 4 2013
CLIMATE�BASED EMPIRICAL MODEL 193
2. ESTIMATION OF PV MODULE TEMPERATURE
Since Malaysia has a hot and humid climate, anaccurate estimation of PV module temperature (Tm) isessential because the operating temperature of the PVmodules has a direct effect on the energy producedand intuitively the sizing, designing of the PV systemas well as its performance analysis [16]. It has beendemonstrated in the literature that for each 1°Cincrease in PV module temperature, it causes approx�imately 0.3–0.5% decrease in its efficiency [17, 18].Therefore, for the optimum design of PV power sys�tems, it is desirable to measure their long term perfor�mances at the site of installation.
The short�circuit current Isc and the open�circuitvoltage Voc are the two important parameters of the I–Vcurve of a PV module. Isc and Voc which their productsare the power produced from the PV module, stronglyinfluence the Tm. It has been proven experimentally thatVoc decreases with the increase of the module tempera�ture, which leads to a noticeable decrease in the avail�able maximum electrical power, in spite of a smallincrease of the Isc, as illustrated in Fig. 1.
Currently, the existing model adopted by MalaysiaEnergy Centre (GreenTech Malaysia) relates themodule temperature with ambient temperature (Ta),given as [19], [20]:
(1)
In [21], a new mathematical model has been pro�posed to estimate the module temperature for a tropi�cal climate like in Malaysia. Utilizing historical mea�sured data of hourly global solar radiation, ambientand module temperature over a specific year and byusing regression analysis, a mathematical equationwhich correlates the ambient and module temperaturehad been obtained, equation (2):
(2)
Tm Ta 25.+=
Tm –6.414 1.411Ta.+=
In [22] and [23], the module temperature is calcu�lated from Nominal Operating Cell Temperature(NOCT). NOCT is usually between 42 and 46°C andit is measured when the module is operated under0.8 kW/m2 of irradiance, 1.5AM of spectral distribu�tion, 20°C ambient temperature, and 1 m/s windspeed.
NOCT is then used to determine the Tc duringmodule operation. It was assumed that the differencebetween Tc and Ta depends linearly on G in the follow�ing manner:
(3)
Similar to the linear equation (1), the module tem�perature in (2) also depends only on the ambient tem�perature, thus the authors did not consider other cli�matological factors such as wind velocity and humid�ity, which are very significant in tropical climate likeMalaysia. This can also be observed in equation (3)that is only valid for open rack systems. The module’sNOCT which depends on the mounting scheme for agiven irradiation level must be measured in a properlydesigned and well controlled outdoor test bed, andtherefore, the equation does not apply for BuildingIntegrated Photovoltaic (BIPV) systems [24]. Fur�thermore, the module temperature obtained from (1)and (2) is the average daily module temperature whichmakes it far from the real measured value at specifichour. This eventually affects the calculation of the esti�mation of energy output of the module because of thevariation of ambient temperature over the day. In [25]and [26], the module temperature is calculated explic�itly depending on the ambient temperature and totaltilt irradiation as formulated in the following equation:
(4)
where the constant k, known as the Ross coefficient,expresses the temperature rise above ambient withincreasing solar flux. The main difficulty with this lin�
Tc Ta– NOCT 20–0.8
������������������������G (kW/m2 ).=
Tm Ta kG,+=
0 200 400 600 800 1000
20
40
60
80
0 200 400 600 800 1000
2
4
6
P,
W
I, A 75°C
50°C
25°C
75°C
50°C
25°C
×104
V, V V, V
Fig. 1. I–V and P–V curves of a PV system at G = 1000 W/m2, T = 0, 25, 50, 75°C.
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ear model lies in the estimation of k, which can bemeasured for an installed array but not easily esti�mated beforehand [27]. The reported values for k werein the range 0.02–0.04°C m2/W [28].
The temperature of each individual PV cell definesthe function of its materials, configuration, time ofday, rotation of the earth and environmental factorssuch as wind, temperature, and cloud cover [29]. Thispaper proposes empirical models for estimating PVmodule temperature for two different technologies,using data sets known as Typical Meteorological Year(TMY) or Test Reference Year. These statistically validdata sets are constructed from real monitored datawhich contains a year of hourly meteorological param�eters, including ambient temperature Ta, wind velocityWs, relative humidity RH, and solar radiation G.
3. PROPOSED REGRESSION MODEL (REG.) FOR ESTIMATING Tm
Obviously, the best way to discover the meteorolog�ical parameters at a specific site is by installing mea�suring equipment at many locations which is a verycostly practice. The alternative approach is to corre�late the meteorological parameters at a place wherethe data are already being measured, and the resultantcorrelation may then be used for other locations withsimilar meteorological characteristics. In this researchpaper the models were developed based on the statisti�cal indicators. The statistical analysis was performedusing SPSS [30].
3.1. Bivariate Correlation
Correlation gives a single value, rather than amodel, that measures the relationship between vari�ables. Data are analyzed by using correlation to inves�tigate whether there is a relationship between themodule temperature and various meteorological fac�tors. Bivariate correlation is used to evaluate thedegree of relationship between two or more quantita�tive variables. Correlation coefficient is commonlyused in bivariate correlation technique to measure thestrength of relationship between variables without dis�tinction between the independent and dependent vari�ables [31], represented by:
(5)
(6)
(7)
(8)
rSxy
SxxSyy
���������������,=
Sxy xiyi
i 1=
n
∑1n�� xi yi,
i 1=
n
∑i 1=
n
∑–=
Sxx xi2
i 1=
n
∑1n�� xi
i 1=
n
∑⎝ ⎠⎜ ⎟⎛ ⎞
2
,–=
Syy yi2
i 1=
n
∑1n�� yi
i 1=
n
∑⎝ ⎠⎜ ⎟⎛ ⎞
2
,–=
where Sxx is the total sum of squared for x, Sxy is thesum of product of variables x and y, Syy is the total sumof squared for y.
3.2. Linear Regression
Regression analysis generally models the relation�ship between one or more responses, or dependentvariables and one or more predictors or independentvariables. Linear regression is used to estimate thecoefficients of linear equation, involving one or moreindependent variables, X (predictors) that best predictthe value of the dependent variable, Y. However, whendealing with data sets, the regression line is estimatedfrom the collected data; hence it involves fitting thestraight line to the data set prior to obtaining the equa�tion of the straight line [32]:
(9)
where α and β is unknown regression coefficients rep�resenting the intercept and the slope, i is the randomerror for the i�th pair.
3.3. Statistical Indicators
The performance and accuracy of the modelsdeveloped were evaluated by calculating the MeanBias Error (MBE), the Root Mean Square Error(RMSE), the Mean Percentage Error (MPE). On theother hand, the significance level of a model is nor�mally selected at 95% confidence level. The expres�sions for MBE, RMSE and MPE (%) are given as:
(10)
(11)
(12)
where Tm Estimated (i) is the ith estimated moduletemperature, Tm Actual (i) is the ith measured moduletemperature, N is the number of observations.
The proposed regression model can be used as anestimation tool as it exploits the hourly data measuredon site, over a long period of time rather than the aver�aged data, and this the best way to acquire statisticallyvalid data set for design purpose. The robustness of theproposed tool involves the consideration of multipleclimatological factors that affect the module tempera�ture i.e., Tm = f(hr, G, Ta, Ws, RH). Unlike the explicit
yi α βxi �i,+ +=
MBE 1N��� Tm Estimated i( ) Tm Actual i( )–( ),
i 1=
N
∑=
RMSE
= 1N��� Tm Estimated i( ) Tm Actual i( )–( ),2
i 1=
N
∑
MBE 1N���=
×Tm Estimated i( ) Tm Actual i( )–
Tm Actual i( )������������������������������������������������������������������⎝ ⎠⎛ ⎞ 100× ,
i 1=
N
∑
APPLIED SOLAR ENERGY Vol. 49 No. 4 2013
CLIMATE�BASED EMPIRICAL MODEL 195
and implicit models found in the literature where eachmodel is suitable for a specific type of installation, theestimation of PV module temperature using regressionmodel is suitable for all conditions in which the mod�ules can be mounted in a free�standing manner or byusing BIPV installations, or even PV/Thermal collector.This is mainly because the calculations are based onmeteorological data, and the NOCT is not involved.
4. RESULTS AND DISCUSSION
The solar energy using in proposed locationsnecessitates an exact estimation of the module tem�perature, which has a direct effect on energy outputestimation of PV module. This subject is usually possi�ble through the use of measurement equipment; how�ever, these devices are not always available, especiallyin remote or rural locations that have a potential ofsolar energy installations.
In this paper, five most important effective climato�logical measured parameters have been collected andintroduced for predicting the PV module temperatureusing statistical analysis. The acquired results werecompared with the model adopted by GreenTech (1)to show a considerable improvement in accuracy ofprediction. Also, the proposed models have shownhigher accuracy compared to another similar studywhich was based on regression correlation (2).
4.1. Actual Data
The proposed model was applied for estimatingthe module temperature and the energy yield of sys�tem A (47.28 kWp polycrystalline) of the 92 kWp total
installation at GreenTech Zero Energy Office (ZEO)building in Selangor, Malaysia. All climatologicaldata were obtained from actual measurements byGreen Tech Malaysia. The data were collected fromApril to December 2009 to form a total of6600 hourly data set for each meteorological param�eter. However, since the solar irradiation and thus theenergy output of the system are zero during the nighttime, only the data for 11 hours of daytime were con�sidered. Therefore, a total of 1922 of hourly data forsolar irradiation, ambient temperature, relativehumidity, wind speed, and module temperature werefinally considered.
This reduction in data is very helpful for regressionmodeling in better understanding the data, as themodule temperature at night is unnecessary to be esti�mated where there are no radiation and energy pro�duced from the system.
Table 1 represents a sample of measured data ofsystem A of the 92 kWp BIPV system at GreenTechbuilding. Figures 2–5 show the actual historical mete�orological data measured for system A over the periodbetween 1/4/2009 to 31/12/2009. Figure 2 illustratesthe hourly ambient temperature during the daytimebetween 8:00 am and 18:00 p.m. Clearly, the day’sambient temperature at the site ranges from 24°C and36°C while the average daily ambient temperature is30°C. As Fig. 3 shows, the hourly solar radiation at thesite ranges from 0 W/m2 in overcast time to as high as770 W/m2 in sunny time. From Fig. 4, it is obvious thatthe relative humidity in Malaysia could reach 100%during the daytime. That is sensible since Malaysia is ahot and humid tropical country. This makes the rela�
Table 1. Actual 1–day hourly data at GreenTech building (3/4/2009)
Meteorological parameters, input Output
Hour Ta (°C) G, W/m2 RH, % Ws, m/s Tm, °C
8:00 27.68 67.2 84 0.0 31.55
9:00 28.27 201.08 76 0.3 36.25
10:00 29.51 370.13 68 1.0 40.14
11:00 30.25 396.02 64 2.2 44.68
12:00 32.01 540.22 65 1.1 50.39
13:00 33.02 389.38 65 2.1 53.92
14:00 34.28 453.25 68 1.7 54.95
15:00 34.54 652.05 77 1.3 48.36
16:00 34.72 551.6 79 1.3 43.55
17:00 33.56 148.05 76 2.8 39.79
18:00 32.7 34.3 85 1.5 35.25
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tive humidity an essential factor in estimating themodule temperature, as it affects the energy output ofthe system. Historical hourly wind velocity for thesimilar time period is depicted in Fig. 5. The windspeed in Malaysia ranges from 0 m/s and could reachup to 7 m/s. The latter two factors are introduced here
for estimating the module temperature which had notbeen considered.
The collected data were grouped into three catego�ries: (i) one year available hourly data with 1922 sam�ples, (ii) daily mean hourly data with available175 samples (iii) daily data for each month separately.
240 200
26
28
30
32
34
36
400 600 800 1000 1200 1400 1600 1800 2000Daytime, h
Am
bien
t te
mpe
ratu
re, °
C
Fig. 2. Hourly ambient temperature at the GreenTech site measured between Apr–Dec 2009.
0 200 400 600 800 1000 1200 1400 1600 1800 2000
100
200
300
400
500
600
700
800
Sol
ar ir
radi
atio
n,
W/m
2
Daytime, h
Fig. 3. Hourly solar radiation at the selected site measured between Apr–Dec 2009.
400 200 400 600 800 1000 1200 1400 1600 1800 2000
50
60
70
80
90
100
Daytime, h
Rel
ativ
e h
umid
ity,
%
Fig. 4. Hourly relative humidity measured at the site between Apr–Dec 2009.
APPLIED SOLAR ENERGY Vol. 49 No. 4 2013
CLIMATE�BASED EMPIRICAL MODEL 197
Table 2 summarizes the correlation and the regressionequation obtained for each sample.
4.2. Testing the Regression Models
4.2.1. Estimation of hourly Tm. Figure 6 comparesthe results of hourly estimated Tm from the proposedreg. model (first row of Table 2) and other approaches
in 18/6/2009. It is clear that the proposed Reg. modelhas an observable advantage over the other approachesin terms of accuracy. This is because the proposedapproach considers multiple climatological factorswhich are unconsidered by other approaches. Thecomparison between the actual hourly Tm and the esti�mated Tm for the whole year based on the proposed1922 regression equation is shown in Fig. 7.
0 200 400 600 800 1000 1200 1400 1600 1800 2000
1
2
3
4
5
6
7
Win
d sp
eed,
m/s
Daytime hour
Fig. 5. Hourly wind speed measured at the site between Apr_dec 2009.
Table 2. Summary of correlation and regression model for each category of data
Fig. 6. 1–Day results of estimated hourly Tm between the proposed Reg. model and other conventional approaches.
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4.2.2. Estimation of average daily Tm. This subsec�tion provides the estimation of the average daily PVmodule temperature based on data categorization.Firstly, the regression equation is obtained based onthe whole available days of the year, i.e., 175 days (sec�ond row of Table 2). Secondly, the regression equationis obtained by accounting the data of each month sep�arately. The best model would then be adopted uponcalculating the accuracy indicators, the MBE, RMSE,and the MPE.
Based on the proposed regression models devel�oped from day�based data presented in Table 2, it wasfound that the 175 based model provided the closestresults with actual measurements. The estimated Tmby the proposed 175 model and conventional modelswith reference to the actual measurement, for arbi�trarily selected days, are provided in Table 3. As theresults for the selected days show, the proposed regres�sion model has a merit over the others conventional
two since it gives the closest results to the actualrecords.
The comparison between the results of the pro�posed 175 regression model, with the actual averagedaily module temperature of the whole available daysin the year 2009, is depicted in Fig. 8. As the figureclearly indicates, the results for the whole available testdata comply with results of the arbitrarily selected daysin Table 3. The regression coefficient for the proposedday�average estimation model is 90.7%.
From the results shown in the table and figuresabove, it can be concluded that the estimation ofhourly PV module temperature from the proposed reg.model compared with the actual measurementsattained satisfactory results. However, a remarkableimprovement in terms of accuracy has been attainedwhen Tm was estimated in average daily basis. Fromthe results obtained, it is clear that all proposed reg.models for estimating average daily Tm had an accept�
able degree of accuracy except for September andDecember. This indicates that a full month data isrequired for obtaining a good regression model withminimum error.
Further investigation on the accuracy and applica�bility of the proposed regression models has been con�ducted by calculating the MBE, RMSE and MPE. Itshould be reminded that minimum values of the accu�racy indicators are desirable. Table 4 summarizes theaccuracy indicators of the proposed reg. models. Fromthe table, it is clear that for the estimation of hourlyTm, Tm = 26.97 + 0.77Ta + 0.023G – 0.206RH –0.137Ws ± 2.656 can be adopted. The added termcame from the MBE of the proposed equation, whichovercomes the difference between the estimated valueand the actual value. For the daily average Tm, Tm =20.72 + 0.88Ta + 0.022G – 0.14RH – 0.937Ws ± 1 canbe adopted which is the proposed reg. model from175 days data. The model has the least errors than theregression from the data of each month. This indicatesthat, with more data correlated, more accurate regres�sion model is acquired.
The preceding results were mainly for polycrystal�line technology. Figure 9 shows the actual averagemonthly mean Tm for poly and mono for systems Aand D (27 kWp monocrystalline) of GreenTech ZEObuilding. We here test whether the reg. model obtainedfrom polycrystalline data could be applicable for monotechnology. The results of applying the 1922 reg.model of poly with the actual records for mono�basedPV system indicates that the MBE was found to be6.33, RMSE is 7.37, and MPE is 17.94%. From the175 data results, it was found that the MBE is 6.12,RMSE is 6.32, and MPE is 17.4%. This indicates thatthere is a significant difference between the behaviorof PV module temperature for the two technologies,although both are installed at the same site (same Ta,G, RH, Ws); however, the regression model obtainedfrom system A (poly) is inapplicable for other technol�
ogies like mono. Since the data for mono were alsoobtained from the GreenTech building, the regressionanalysis for mono was also performed so that each
250 20
30
35
40
45
50
40 60 80 100 120 140 160 180
PV
mod
ule
tem
pera
ture
, °C
Daytime hour
Tm ActualTm Estimated
Fig. 8. Estimated average daily Tm by the proposed model (175 data based) and the actual measurement.
Table 4. Summary of the accuracy indicators of the pro�posed reg. equations
Sample MBE RMSE MPE (%)
Hourly 1922 2.656 3.426 6.308
Daily 175 days 1.008 1.337 2.443
28 days of April 1.113 1.445 2.749
29 days of May 1.089 1.405 2.686
29 days of June 1.323 1.722 3.165
31 days of July 1.074 1.428 2.572
30 days of Aug. 1.072 1.433 2.589
6 days of Sep. 2.052 2.588 4.856
22 days of Dec. 2.029 2.562 4.94
10
0
20
30
40
50Polycrystalline Monocrystalline
Mon
thly
mea
n T
m,
°C
April May June July AugustMonth
Fig. 9. Average monthly mean Tm for poly and mono forsystems A and D of PTM ZEO building.
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technology would have its own estimation for PVmodule temperature.
By performing a new regression analysis from themono data, new models for mono technology wereobtained, as indicated in Table 5. With the new reg.models, the accuracy of calculations has greatlyimproved. From the 1922 model which estimates thehourly PV module temperature, MBE was found to be2.23, RMSE is 2.88, and MPE is 6.26%. From the175 reg. model which estimates the average daily mod�ule temperature, MBE was found to be 0.88, RMSE is1.17, and MPE is 2.51%.
CONCLUSIONS
New approaches to estimate the PV module tem�perature for poly and mono crystalline technologies intropical climate have been proposed in this paper. Theproposed models are based on regression analysiswhich correlates the historical actual measurements ofPV module temperature with various meteorologicalparameters. The results show that the proposed regres�sion models have advantages over the conventionalapproaches for calculating the hourly and day averagePV module temperature. The results also show that theregression model for one type of technology is inappli�cable for other technologies, in the sense that eachtechnology has its own physical characteristics. Thestatistical test indicators obtained from the proposedregression model for estimating hourly temperaturefor poly– crystalline–based PV module were 2.65,3.42, and 6.3% for MBE, and RMSE, and MPErespectively. The statistical error test for the best modelfor estimating day�average PV module were found tobe 1, 1.33, and 2.44% for MBE, and RMSE, and MPErespectively. On the other hand, for mono technologybased PV system, test error indicators from the pro�posed regression model which estimates the hourly PVmodule temperature, the MBE was 2.23, RMSE was2.88, and MPE was 6.26%. For estimating the day�average mono�based PV module temperature, theMBE, RMSE, and MPE were 0.88, 1.17, and 2.51%respectively.
The proposed approaches can be used as an effec�tive tool for predicting the PV module temperature;whether a simple PV module, open rack system, BIPVinstallations, or even PV/Thermal collector, in remoteor rural locations with no direct measurement equip�ments. The proposed models also can be very useful in
studying the PV system performance and estimatingits energy output.
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