Experimental investigation of the optimum photovoltaic panels&

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Energy 38 (2012) 305e314

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Energy

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Experimental investigation of the optimum photovoltaic panels’ tilt angle duringthe summer period

John Kaldellis*, Dimitrios ZafirakisLab of Soft Energy Applications & Environmental Protection, TEI of Piraeus, P.O. Box 41046, Athens 12201, Greece

a r t i c l e i n f o

Article history:Received 1 August 2011Received in revised form27 November 2011Accepted 29 November 2011Available online 23 December 2011

Keywords:Solar energyExperimental measurementsGreece

* Corresponding author. Tel.: þ30 210 5381237; faxE-mail address: [email protected] (J. Kaldellis).URL: http://www.sealab.gr/

0360-5442/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.energy.2011.11.058

a b s t r a c t

The photovoltaic (PV) technology has made considerable progress during the recent years in both gridconnected and stand-alone applications, especially in areas of high local solar potential. In this context,the interest recently demonstrated in the Greek region concerning PVs encourages the investigation ofoptimum operation conditions for such systems. At the same time, summer-only applications, beingrather common in Greece, require maximum exploitation of the local solar potential during the specificperiod of the year. For this purpose, an experimental study is currently carried out in the area of Athens,in order to evaluate the performance of different PV panel tilt angles during the summer period.According to the experimental results obtained, the angle of 15� (�2.5�) is designated as optimum foralmost the entire summer period, while conclusions drawn are accordingly theoretically validated bymeans of established solar geometry equations.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Remarkable increase of installed capacity worldwide [1] andconstantly decreasing costs [2] of the photovoltaic (PV) technologyhave turned PV applications into one of the most interesting energyalternatives, especially in areas of high quality solar potential. Inthis context, analogous interest is noted during the recent years inthe Greek region as well [3,4], where the favorable local solarpotential (annual solar energy at horizontal plane even exceeding1650 kWh/m2 [5], Fig. 1) encourages operation of such systems.Installed capacity of PVs in Greece (Fig. 2) exceeds 200 MW (end of2010) [6], i.e. almost four times the respective of the previous year(55 MW), while at the same time a promising local PV industryseems to emerge (Fig. 3).

Furthermore, considerable remuneration of energy produced bygrid connected rooftop PV systems under a feed-in-tariff of 550 V/MWh [7] has attracted numerous applicants in the category of<10 kWp (Fig. 4). At the same time, experience gained in the field[8] (7% of installed capacity corresponds to systems below 10 kWpand 17% to systems below 20 kWp) largely applies to the sector ofsmall scale stand-alone systems as well. Actually, owed to the fact

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that there are numerous remote consumers across the Greek region[9,10] that cannot appreciate connection to a solid electricity grid,PV stand-alone applications gradually gain interest on the basis ofexperience obtained by the operation of small to medium scale gridconnected systems.

What should be noted is that a large share of these remoteconsumers concern summer use only (e.g. summer houses,summer hotel units), while in many of these cases, extreme waterneeds (especially in semi arid areas of the Aegean islands) shouldalso be stressed. As a result, use of PV systems in such summer-onlyapplications (when the local available solar potential maximizes) isthought to be an interesting solution that needs to be examined forthe satisfaction of both electrification and irrigation needs [11e14].

At the same time, efficient operation of PV installations dependson many factors, among which is also the tilt angle of panels.Acknowledging the need to ensure maximization of energyproduction during the summer months of the year for the appli-cations previously discussed, a systematic effort is currentlyundertaken to obtain the optimum summer tilt angle of a PVinstallation located in the area of Athens, central Greece. For thispurpose, conduction of experimental measurements during theentire summer season is carried out in the specific study, so as todesignate the optimum panels’ tilt angle during the specific periodof the year.

At this point, it should be noted that investigation on theoptimum panel installation angle started in the early 80’s. At thattime, Felske [15] investigated the optimum tilt angle in relation to

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Fig. 1. Wind and solar potential in the Greek territory (based on data from [5]).

J. Kaldellis, D. Zafirakis / Energy 38 (2012) 305e314306

the off-south angle, concluding that for a given azimuth angle, theoptimum collector tilt should be expected at an angle between 3�

and 10� less than the given location latitude. Furthermore,according to Tsalides and Thanailakis [16], the year-round optimumtilt angle for the area of Athens (37�580 N) and for north-facingpanels serving constant loads was determined at 57�, which is50% higher than the local latitude. Following, Balouktsis et al. [17]presented a similar calculation algorithm for the case of variableloads, estimating the optimum tilt angle of PV panels for the islandof Kythnos (37�250 N) during the entire year. According to theirresults, the optimum angle per month was found to vary from0� (June, July) to 60� (December), while the optimum PV tilt anglefor the entire year was 26�.

Moreover, based on experimental measurements, Kacira et al.[18] investigated the optimum tilt angle of PV panels in SanliurfaTurkey (37�N), by using two PV panels, with the first one kept ata fixed tilt angle and the second one mounted on a two-axis solar

Time Evolution of PV Installed Capacity in Greece

0

20

40

60

80

100

120

140

160

180

200

220

2006 2007 2008 2009 2010 Year

Inst

alle

d C

apci

ty (M

W p )

Annual Capacity Cumulative Capacity

Fig. 2. Recent progress of PV installations in Greece (based on data from [6]).

tracking system. According to their results, the monthly optimumtilt angle ranges between 13� in June and 61� in December. Basedon experimental measurements as well, Gaglia et al. [19] reportedthat the optimum PV tilt angle for the area of Athens (36� 570 N)ranges between 23� and 33�. Finally, Mehleri et al. [20] presenteda computational methodology for the determination of theoptimum tilt angle and the orientation of PV panels, based on solarradiation measurements recorded at the National TechnicalUniversity of Athens (37�580 N). Their conclusion was that theoptimum tilt angle for the entire year is 30�.

At the same time Koronakis [21] investigated the optimum anglefor PV panels operating in Athens for each month of the year,designating that optimum summer angles range from 5� to 17�.Similar were also the results of Benghanem [22] concerningsomewhat lower latitudes (angle of 12� for a latitude of 24.5� N),while Skeiker [23] estimated optimum angles for the month of

Fig. 3. Characteristics of Greek PV manufacturers (based on data from [6]).

Short-Term Time Evolution of PV Rooftop Applications (<10kW ) - Capacity of Applications & in Operation Systems

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

In operationApplications

Fig. 4. Progress of PV rooftop installations in Greece (based on data from [6]).

J. Kaldellis, D. Zafirakis / Energy 38 (2012) 305e314 307

August in the order of 12.5�e17�, for latitudes between 35�N and40�N.

According to the above research results, the optimum angle ofPV panels varies considerably between different studies, mainlydue to the calculation models used and the atmospheric environ-ment of the location at which the experiment takes place. Besidesthat, what may also be concluded is that emphasis is usually givenon the determination of the year-round optimum tilt angle.Considering the above, an attempt is carried out in the presentstudy so as to determine the summer period optimum angle for PVpanels operating in the area of Athens. For this purpose, experi-mental investigation of the subject examined is currently under-taken for the entire summer period. In this context, emphasis isgiven on examining the effect of varying the panel tilt angle fromthe expected optimum one, while accordingly, an effort is made bythe authors so as to interpret results obtained through theoreticalvalidation on the basis of established solar geometry equations.

2. Experimental setup and procedure of the experiment

2.1. Description of the experimental setup

The PV configuration used for the experimental measurementsis installed on the roof of the S.E.A.&ENVI.PRO. Laboratory, i.e. onthe top of one of the buildings comprising the TEI of PiraeusCampus [11]. The exact location is determined by the geographicalcoordination of 37�580 N and 23�400 E and a high quality local solarpotential (see also Fig. 5). The installation consists of two PV arrays,

Long Term Monthly Average of Solar Potential at the Horizontal Plane (Athens, 1990-2000)

0

50

100

150

200

250

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecMonth of the Year

Sola

r Ene

rgy

at th

e H

oriz

onta

l Pl

ane

(kW

h/m

2 )

Fig. 5. Solar potential of Athens based on long term solar irradiance measurements(based on data from [11]).

six panels each (Fig. 6), with each of the arrays being mounted ona metal frame, properly designed so that the tilt angle can beadjusted from 0� to 90�, at a 5� step.

Furthermore, the twelve panels of the installation are connectedin six parallel strings of two. Six ammeters and voltmeters placedon the control panel of the installation (Fig. 6), are used to providethe necessary measurements of current and voltage from each ofthe strings. The orientation of the PV panels is fixed with the azi-muth angle set equal to zero, while their type is multi-crystalline(LA361-K51S-manufactured by Kyocera) with the respective tech-nical characteristics given in Table 1.

Moreover, for the measurement of solar radiation, two pyran-ometers of Li-Cor type are used. The first pyranometer measuresthe global radiation on the horizontal plane and the second ismounted on the PV base so that it can measure the global radiationupon the PV surface, at the tilt angle each time selected (Fig. 6).Finally, what should also be mentioned is that all measurementstaken are also collected in a data logger (STYLITIS-41) (see alsoFig. 6) that is able to store data for up to 30 days through the use ofa computer.

2.2. Description of the experimental procedure

The basic concept of the experimental procedure is to compare,on a real time basis, the performance of four identical PV panelsduring the summer months of the year. The two of them (PV pair I)are kept at a fixed tilt angle of 15� (which is according to the resultsof previous studies expected to be the optimum tilt angle duringthe summer months for the specific area) and the other two are setto periodically vary their tilt angle (PV pair II).

Measurements were taken every 10 min during daylight, whilethe panel tilt angles examined correspond to 0�, 15�, 30�, 45�, 60�

and 75�. Besides that, as already mentioned, measurements weretaken at the hot period of the year (from mid-May to mid-September) with the above mentioned panel tilt angles beingexamined consecutively, for a 20-day period each (see also Table 2).At the same time, the global solar irradiance at both the horizontaland the tilted plane, as well as the current and voltage output foreach of the PV pairs, were all recorded.

After the collection of measurements for the time period ofstudy (e.g. to�toþDt), performance of the two pairs of PV panelsinvestigated is based on the assessment of their energy yield. Morespecifically, the hourly energy output of each pair is calculated as[24]:

EPV ¼Zt¼ toþDt

t¼ to

IiðtÞ,UiðtÞdt (1)

where “Ii” is the current output and “Ui” is the output voltage ofeach pair of PV panels.

However, to obtain amore straightforward comparison betweenthe performance of different tilt angles, estimation of the meancapacity factor “CFPV” for the respective period of measurements isalso undertaken (see also Eq. (2))

CFPV ¼ EPVNp,Dt

(2)

with “Np” being the peak power of the PV panels (i.e. 51 Wp eachpanel).

Prior to the conduction of measurements however, to increasereliability of results obtained, statistical similarity of both the pyr-anometers and the pairs of PV panels used was examined throughthe application of the h-test method [25,26] (see also Appendix A).

Fig. 6. Aspects of the experimental setup.


Similarity of both pyranometers and PV pairs may be reflected fromthemeasurements presented in Figs. 7 and 8 respectively, as well asfrom the data of Table 3. On top of that, what should also be noted isthat to avoid influence of factors such as dust [27,28], all four PVpanels were kept clean from any external pollutant throughout theexperimental period, thus ensuring similar performance which isvalidated by the h-test.

3. Experimental results

Experimental results obtained appear first in Fig. 9, where onepresents representative daily performance comparisons betweenthe fixed and the variable PV panels’ tilt angles. More precisely, inFig. 9 the 10 min average electrical current production “Ii” of each

Table 1Technical characteristics of the PV panels employed.

Parameter Value

Peak power 51.0 WVoltage at maximum power 16.9 VCurrent at maximum power 3.02 AOpen circuit voltage 21.2 VShort circuit current 3.25 ALength 988 mmWidth 448 mmThickness 36 mmWeight 5.9 kgMaximum efficiency 14%

PV pair along with the respective 10 min distribution of solarradiation at the horizontal plane are included. In this context,current production “Ii” is as expected analogous to the distributionof solar radiation, while the effect of the panels’ tilt angle becomesevident.

In fact, by observing the results obtained, there is a minordifference in the produced electrical current between the 15� (fixedangle PV pair) and the 0� (variable angle PV pair) case, which is thenhowever found to increase considerably, up to the point of 60�. Atthe same time, statistical similarity of the two PV pairs is also re-flected from the results of the 15�e15� case, where difference ofcurrent production is negligible. On the other hand, the increasingtrend of “Ii” difference noted between the fixed and the variableangle PV pair seems to fade out in the case of 15�e75�, withmeasurements concerning the specific case taken in the periodbetween late August and mid-September.

At this point it is important to note that the hour on the x-axis inthe respective set of figures is set at local standard time (LST) and

Table 2Experimental measurements’ plan.

Variable angle PV pair Period of measurements

0� 15/5/10 to 3/6/1015� 4/6/10 to 23/6/1030� 24/6/10 to 13/7/1045� 14/7/10 to 2/8/1060� 3/8/10 to 22/8/1075� 23/8/10 to 11/9/10

Comparison of the Fixed and Variable Angle Pyranometers

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000 1200

Pyranometer at Variable Angle (W/m2)

Pyra

nom

eter

at F

ixed

Ang

le (W

/m2 )

Fig. 7. Statistical comparison of the two pyranometers.

Table 3Parameters’ values of the h-test.

Pyranometers PV pairs (both kept at 15�)

Parameter Value Parameter Value

do (W/m2) 0 do (A) 0x1 (W/m2) 479.01 x1 (A) 1.1x2 (W/m2) 460.80 x2 (A) 1.1s1 (W/m2) 302.9 s1 (A) 0.75s2 (W/m2) 291.64 s2 (A) 0.78N1 1149 N1 847N2 1149 N2 847qo 1.47 qo 0x 2292.71 x 1691.37qc 1.96 qc 1.64


therefore the solar noon is not at 12:00 LST, which may also derivefrom the daily profile of the solar radiation measurements pre-sented in some of the cases of Fig. 9 (e.g. 15�e45� and 15�e60�).

Accordingly, based on the use of Eqs. (1) and (2), typical weeklydistribution of “CFPV ” for all comparison sets examined is given inFig. 10. More precisely, according to the results obtained, betterperformance of the 15� panel tilt angle is illustrated in all casesexamined, with the greatest difference between the fixed and thevariable angle PV pairs appearing in the case of 15�e60� (e.g.difference of the daily “CFPV” even above 6% in absolute values).

On the other hand, the 15� “CFPV” value is found to mostly varybetween 15% and 22%, i.e. an expected result for the area and periodof investigation, while difference between the fixed and the vari-able angle PV pairs is minimum in the case of 15�e0� (e.g. evendropping below 0.15% in absolute values). Overall, the 20-day longterm average relative difference between the fixed and the variableangle PV pairs’ “CFPV ” is given in Table 4, where maximum devia-tion noted in the case of 15�e60� is found to decrease in the case of75�, owed mainly to the time period of experimental measure-ments (see also Table 2).

In this context, what should also be stressed is that given thepeak power of the PV panels (i.e. 102 W for each of the pairs),difference noted in the “CFPV” values may be used to estimate therespective reduction in energy production. For example, in theextreme case of 15�e60�, the 20-day energy output of the fixed PVpair (i.e. 9.75 kWh) drops to 7.08 kWh for the 60� PV pair, which isequal to a relative difference of 27.3% (see also Table 4) thatunderlines the importance of selecting the optimum tilt angle.

Comparison of the Fixed and Variable Angle PV Pairs

0,0

0,5

1,0

1,5

2,0

2,5

3,0

0,0 0,5 1,0 1,5 2,0 2,5 3,0

Current "I" of PV Pair I (A)

Cur

rent

"I" o

f PV

Pair

II (A

)

Fig. 8. Statistical comparison of the two PV pairs.

4. Theoretical investigation of experimental results

After the experimental investigation of the optimum tilt anglefor the summer period, an effort is currently undertaken in order tointerpret the results obtained through the theoretical investigationof the problem examined.

Theoretical determination of the optimum summer tilt angle isbased on the established equations of solar geometry [24,29] andmore precisely on the minimization of the solar radiation incidenceangle. Note that zero incidence angle implies vertical incidence ofthe solar radiation upon the surface under study and thusmaximum absorbance of solar radiation (see also Fig. 11).

In this context, incidence angle “q” is provided by Eq. (3), whereparameters involved also include the panel tilt angle “b”, the lati-tude of the location examined “4”, the azimuth angle “g”, the solarhour angle “u” and the solar declination “d”.

cos q ¼ sin d,sin 4,cos b� sin d,cos 4,sin b,cos g

þ cos d,cos 4,cos b,cos u

þ cos d,sin 4,sin b,cos g,cos u

þ cos d,sin b,sin g,sin u (3)

Next, solar declination “d” is given by Eq. (4), where “D” is theJulian day of the year.

d ¼ 23:45,sin½360,ðDþ 284Þ=365� (4)

Furthermore, solar hour angle “u” is a function of solar time “ST”and is provided by the following equation, where “ST” is used indecimal form.

u ¼ 15�,ðST� 12Þ (5)

Subsequently, in order to estimate the solar time “ST”, localstandard time “LST” along with the standard and the local meridianof the area (“Lst” and “Ll” respectively) are required,

ST ¼ LST� 4,ðLst � LlÞ þ Et � c (6)

with (þ) applying for the west hemisphere and (�) for the east. Ontop of that, “c” corresponds to the 1 h correction (i.e. 60 min)applying only during the period from the last Sunday of March tothe last Sunday of October so as to raise the daylight saving time(otherwise c ¼ 0). Furthermore, “Et” corresponds to the timecorrection function, given by the Watt equation below

Et ¼ 9:87,sinð2BÞ � 7:53,cos B� 1:5,sin B (7)

with “B” being also a function of the Julian day of the year “D”.

B ¼ ½360,ðD� 81Þ=364� (8)

Current Production & Solar Irradiance Daily Variation(PV Pair II at 0

o

)

0,0

0,5

1,0

1,5

2,0

2,5

3,0

8:00

8:30

9:00

9:30

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010

:30

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011

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012

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013

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014

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015

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016

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17:0

017

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018

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019

:30

Hour of the Day

PV C

urre

nt "I

" (A)

0

100

200

300

400

500

600

Hor

izol

tal P

lane

Sol

ar

Rad

iatio

n (W

/m2 )

Fixed Angle: 15 degreesVariable Angle: 0 degreesSolar Radiation


o

)

0,0

0,6

1,2

1,8

2,4

3,0

8:00

8:30

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Hour of the Day

PV C

urre

nt "I

" (A)

0

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Hor

izon

tal P

lane

Sol

ar

Rad

iatio

n (W

/m2 )


Current Production & Solar Irradiance Daily Variation (PV Pair II at 15

o

)

0,0

0,5

1,0

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2,5

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3,5

8:00

8:30

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Hour of the Day

PV C

urre

nt "I

" (A)

0

160

320

480

640

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960

1120

Hor

izon

tal P

lane

Sol

ar

Rad

iatio

n (W

/m2 )



o

)

0,0

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1,0

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8:00

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PV C

urre

nt "I

" (A)

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900

Hor

izon

tal P

lane

Sol

ar

Rad

iatio

n (W

/m2 )



o)

0,0

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8:00

8:30

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PV C

urre

nt "I

" (A)

0

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izol

tal P

lane

Sol

ar

Rad

iatio

n (W

/m2 )



o

)

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3,0

8:00

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PV C

urre

nt "I

" (A)

0

150

300

450

600

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900

Hor

izon

tal P

lane

Sol

ar

Rad

iatio

n (W

/m2 )


Fig. 9. Comparison of performance between the fixed and the variable angle PV panels for representative days of measurements.


In this context, using the information of Table 5 concerningassigned values of input parameters, variation of the incidenceangle “q” in relation to the selected panel tilt angle “b” for the entiresummer period is given in Figs. 12 and 13.

More precisely, in Fig. 12 one may obtain an example for the15th of May, which comprises the typical solar day of the specificmonth [30]. As one may see, there are six different curves ofincidence angle “q”, covering the entire range of tilt anglesexamined, i.e. from 0� to 75�, while distribution of the solar irra-diance at horizontal level is also included. In this context, distri-bution of the incidence angle is found to present minimum valuesfor the mid-day period (i.e. when the available solar radiationmaximizes) in the case of panel tilt angle equal to 15�. On theother hand, the situation is inversed during the early morning and

late afternoon hours, when the panel tilt angle of 0� presents thelower incidence angle value.

Nevertheless, as onemayobtain from thefigure, the 15� tilt angleremains optimum for almost the entire day (from 10:00 to 17:00),which also corresponds to the period of maximum solar irradiancekept above 500 W/m2. As a result, it becomes clear that for thistypical day of May, 15� is the optimum tilt angle since it ensures themost vertical incidence of the solar irradiance upon the surface of PVpanels for the period of the day that solar irradiance maximizes.

Similar to Fig. 12, in Fig. 13 one may obtain the respective resultsfor the entire period investigated, on the basis of a one-month timeinterval, again using the typical solar days of each month investi-gated [30]. As one may obtain from the figure, the angle of 15� ismaintained as optimum until late July-early August, although it

Daily Performance Comparison (PV Pair II at 0o

)

0%

5%

10%

15%

20%

25%Da

y 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Dai

ly C

apac

ity F

acto

r

PV Pair I (15 degrees) PV Pair II (0 degrees)


)

0%

5%

10%

15%

20%

25%

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Dai

ly C

apac

ity F

acto

r



)

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5%

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15%

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25%

Day 1

Day 2

Day 3

Day 4

Day 5

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Dai

ly C

apac

ity F

acto

r



)

0%

5%

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25%

Day 1

Day 2

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Day 4

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Day 6

Day 7

Dai

ly C

apac

ity F

acto

r



)

0%

5%

10%

15%

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25%

Day 1

Day 2

Day 3

Day 4

Day 5

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Day 7

Dai

ly C

apac

ity F

acto

r



)

0%

5%

10%

15%

20%

25%

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Dai

ly C

apac

ity F

acto

r


Fig. 10. The impact of the tilt angle variation on the daily capacity factor of the PV panels set at the tilt angle of 15�


should be noted that the respective period of the day, during which15� produce the lower incidence angle, is found to gradually narrow(in comparisonwith the respective of May, i.e. from 10:00 to 17:00).On the other hand, the 30� panel tilt angle seems to produce the

Table 4Relative deviation of the “CFPV ” between the fixed and the variable angle PVpairs.

Variable angle PV pair Relative deviation of CFPV

0� 2.8%15� �0.3%30� 8.5%45� 17.0%60� 27.3%75� 23.6%

Fig. 11. Incidence angle “q” and tilt angle “b” of a given surface.

Table 5Theoretical model inputs.

Parameter Value

Azimuth angle “g” 0�

Standard Meridian “Lst” 30�

Local Meridian “Ll” 23�400

Latitude “4” 37�580

Hourly Variation of the Solar Incidence Angle "θ" in the Area of Athens (May 15-Azimuth Angle "γ=0ο")

0

12

24

36

48

60

72

84

96

108

120

8:00

8:30

9:00

9:30

10:0

0

10:3

0

11:0

0

11:3

0

12:0

0

12:3

0

13:0

0

13:3

0

14:0

0

14:3

0

15:0

0

15:3

0

16:0

0

16:3

0

17:0

0

17:3

0

18:0

0

18:3

0

19:0

0

19:3

0

20:0

0

Hour of the Day

Inci

denc

e An

gle

"θ"

(deg

rees

)

0

100

200

300

400

500

600

700

800

900

1000

Hor

izon

tal P

lane

Sol

ar

Rad

iatio

n (W

/m2 )

β=0 β=15 β=30 β=45β=60 β=75 Solar Radiation

Fig. 12. Theoretical daily distributions of the incidence angle for various panel tiltangles vs local solar potential (May 15).


minimum incidence angle for the following period between mid-August and mid-September. Acknowledging the results obtainedfor the period of examination, it becomes evident that among thedifferent angles currently examined, 15� comprises the most effi-cient in terms of local solar potential exploitation.

Hourly Variation of the Solar Incidence Angle "θ" in the Area of Athens (June 11-Azimuth Angle "γ=0ο")

0

20

40

60

80

100

120

8:00

8:30

9:00

9:30

10:0

010

:30

11:0

011

:30

12:0

012

:30

13:0

013

:30

14:0

014

:30

15:0

015

:30

16:0

016

:30

17:0

017

:30

18:0

018

:30

19:0

019

:30

20:0

0

Hour of the Day

Inci

denc

e An

gle

"θ" (

degr

ees) β=0 β=15

β=30 β=45β=60 β=75

Hourly Variation of the Solar Incidence Angle "θ" in the Area of Athens (July 17-Azimuth Angle "γ=0ο")

0

20

40

60

80

100

120

8:00

8:30

9:00

9:30

10:0

010

:30

11:0

011

:30

12:0

012

:30

13:0

013

:30

14:0

014

:30

15:0

015

:30

16:0

016

:30

17:0

017

:30

18:0

018

:30

19:0

019

:30

20:0

0

Hour of the Day

Inci

denc

e An

gle

"θ" (

degr

ees)

β=0 β=15β=30 β=45β=60 β=75

Fig. 13. Theoretical daily distributions of the incidence angle for va

Accordingly, if matching the time periods of investigation (seealso Table 2) with the theoretical distributions of the incidenceangle, the “CFPV ” deviations previously obtained from theexperimental results may be explained. More precisely, as onemay see, in the early period of the summer, i.e. when the 0� tiltangle was tested, difference between the “CFPV ” of the fixed andthe variable angle PV pairs should be minimum, validating thetheoretical distributions of the respective angles appearing inFig. 12. Besides, as already mentioned, although 15� appears to bemore efficient during mid-day, the opposite is noted during themorning and afternoon hours, when 0� produce the minimumincidence angle.

Furthermore, not considering the month of June (i.e. when the15�e15� pair was tested) and proceeding to the period of early July,greater difference between the 15�e30� relative deviation of the“CFPV” in comparison with the 15�e0� case, see also Table 4, isjustified on the basis of distributions presented, with the 15�

distribution demonstrating a clear advantage over the respective of30�. Subsequently, similar is also the conclusion for the 15�e45�

case (mid-July to end of July-early August), with the greater relativedeviation of the “CFPV” in comparison with the former- illustratedby the comparison of theoretical distributions.

Furthermore, maximum deviation noted in the case of 15�e60�

(from early August tomid-August) is also depicted in the respectiveset of theoretical distributions for the month of August, whilereduction of the relative “CFPV ” deviation in the case of 15�e75�

may be justified by the patterns of theoretical distributions duringSeptember. Note that during the specific period the 15� angle is nolonger considered as optimum and seems to produce similar inci-dence angle values with the corresponding of 75� for an appre-ciable part of the day (morning and afternoon hours).

Hourly Variation of the Solar Incidence Angle "θ" in the Area of Athens (August 16-Azimuth Angle "γ=0ο")

0

20

40

60

80

100

120

8:00

8:30

9:00

9:30

10:0

010

:30

11:0

011

:30

12:0

012

:30

13:0

013

:30

14:0

014

:30

15:0

015

:30

16:0

016

:30

17:0

017

:30

18:0

018

:30

19:0

019

:30

20:0

0

Hour of the Day

Inci

denc

e An

gle

"θ" (

degr

ees) β=0 β=15

β=30 β=45β=60 β=75

Hourly Variation of the Solar Incidence Angle "θ" in the Area of Athens (September 15-Azimuth Angle "γ=0ο")

0

20

40

60

80

100

120

8:00

8:30

9:00

9:30

10:0

010

:30

11:0

011

:30

12:0

012

:30

13:0

013

:30

14:0

014

:30

15:0

015

:30

16:0

016

:30

17:0

017

:30

18:0

018

:30

19:0

019

:30

20:0

0

Hour of the Day

Inci

denc

e An

gle

"θ" (

degr

ees) β=0 β=15

β=30 β=45β=60 β=75

rious panel tilt angles and representative summer period days.


5. Conclusions

Based on an experimental setup, installed at the area of Athens-Greece (37�580 N and 23�400 E) and comprising of a fixed anda variable angle PV array, systematic series of measurements con-cerning the performance of two PV pairs were carried out duringthe summer period. More specifically, consecutive, 20-day sets ofmeasurements were taken for each different angle of the variableangle PV pair (i.e. 0�, 15�, 30�, 45�, 60� and 75�), while keeping thefixed angle PV pair at 15�. More precisely, extensive, 10 minmeasurements of solar irradiance and PV current and voltageoutput were conducted throughout the summer period, allowingfor the estimation of the respective energy production by each ofthe two PV pairs. In this context, emphasis was given on the eval-uation of performance of the two PV pairs through estimation ofthe relative “CFPV ” deviation (of the variable tilt angle PV pair incomparison with the fixed -optimum angle PV pair) during theconsecutive time periods of measurements. According to the resultsobtained, performance deviation is as expected largely dependingon the selected tilt angle and the period of examination, with thegreatest deviation (i.e. 27.3%) between the fixed and the variable tiltangle PV pairs -for the current set of measurements- noted in thecase of 15�-60�. On the other hand, the respective minimumdifference was noted in the case of 15�e0�, with the correspondingdeviation not exceeding 3%.

Subsequently, through the use of solar geometry equations,experimental results were investigated under the view of diurnalincidence angle distributions, considering that maximum energyproduction is ensured by the minimization of the solar incidenceangle. Diurnal distribution of the solar incidence angle was exam-ined for the typical days of the months under examination,covering the entire range of tilt angles investigated. Furthermore,by also taking into account the respective distribution of solarirradiance, theoretical designation of the optimum tilt angle waspossible. More precisely, by examining the patterns of solar inci-dence angle and solar irradiance distributions, the expectedoptimum tilt angle was decided by considering the extent at whichminimization of the solar incidence angle was obtained during theday. Through this theoretical investigation of the problem, experi-mental results obtained were validated, reflecting at the same timethe clear advantage of the 15� (�2.5�) angle in the area of Athensand central Greece in general, for almost the entire summer season.

Appendix A

According to the h-test method, measurements provided by twodifferent measuring instruments of the same type (e.g. two pyr-anometers) may differ by a predefined value of “do” (currentlytaken equal to zero) eat a reliability level of 95%- only if thefollowing condition is validated,

�jqcj < qo < jqcj (A.1)

with “qo” being calculated on the basis of the Student distribution,using the following equation

qo ¼ ðx1 � x2Þ � doffiffiffiffiffiffis21N1

s�

ffiffiffiffiffiffis22N2

s (A.2)

where “xi”, “si” and “Ni” are the average, standard deviation andnumber of measurements respectively.

Furthermore, by using the necessary input values (e.g. see alsoTable 3) and Eq. (A.3) following, the value of freedom degrees “x”

may be estimated.

x ¼

s21N1

� s22N2

!2

s21N1

!2

N1 � 1þ

s22N2

!2

N2 � 1

(A.3)

Using “x” and the value of “qc” -determined by the Studentdistribution tables for a reliability of 95%- similarity or dissimilarityof the twomeasuring instruments is eventually designated throughvalidation -or not- of Eq. (A.1).

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