Research Article Solar Tracking Error Analysis of Fresnel...

Research ArticleSolar Tracking Error Analysis of Fresnel Reflector

Jiantao Zheng12 Junjie Yan1 Jie Pei2 and Guanjie Liu2

1 School of Energy and Power Engineering Xirsquoan Jiaotong University Xirsquoan 710049 China2Huaneng Clean Energy Research Institute Beijing 100098 China

Correspondence should be addressed to Jiantao Zheng zhengjiantaohncericom

Received 18 February 2014 Accepted 17 March 2014 Published 6 May 2014

Academic Editors D Jing P Meyrueis J Shi and H Zhou

Copyright copy 2014 Jiantao Zheng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Depending on the rotational structure of Fresnel reflector the rotation angle of the mirror was deduced under the eccentriccondition By analyzing the influence of the sun tracking rotation angle error caused by main factors the change rule and extent ofthe influence were revealed It is concluded that the tracking errors caused by the difference between the rotation axis and true northmeridian at noon were maximum under certain conditions and reduced at morning and afternoon gradually The tracking errorcaused by other deviations such as rotating eccentric latitude and solar altitude was positive at morning negative at afternoonand zero at a certain moment of noon

1 Introduction

Solar energy is plentiful and unlimited Solar-photovoltaicpower generation and solar thermal power generation aretwo basic solar-energy-utilization ways [1] Owing to solarthermal power generation performing good stability highreliability long working time and middlehigh temperaturesteam provision solar thermal power generation is widelyfocused in the energy field

In 1960s Giovanni Francica (Italy) firstly applied linearFresnel reflector (LFR) for development of linear and two-axis tracking Fresnel steam generating system [2 3] Fromthen on lots of research was gradually carried out In orderto enhance the utilization of land area and reduce the shadingcreated by adjacent reflectors Mills and Morrison inventedthe multiabsorption towers technology based on compactlinear Fresnel reflector which was suitable for large-scalesolar thermal power plants [4 5] Mathur et al proposed anoptimal design of thewidth of primarymirror [6] Sootha andNegi made optical design and focused characteristic researchabout linear concentrating technology without secondaryreflectors [7] Du et al estimated the tracking and radiationfor LFR system by increasing the spacing between theadjacent reflectors and got the best method for estimatingheight [8] Pu and Xia designed a small linear concentratingtest device conducting the light tracing simulation andconcentration research [9]

The above research is carried out to optimize the keycomponents and eventually achieve the real-time sun track-ing by the tracking program so the concentrating systemand tracking accuracy are key components to realize thehigh efficiency high performance parameters in Fresnel solarthermal power generation system There are many ways torealize the solar tracking In the condition of low trackingaccuracy requirement or reducing complexity and costs openloop single axis tracking method can be used [10] Du etal resolved sun vector properly by using vector methodand then the tracking rotation angle was got after simplegeometric derivation which was applicable to linear Fresnelreflector without the eccentric structure [11]

This paper analyzes the main impact factors of thetracking accuracy of Fresnel solar reflectors and calculatedthe tracking error and its influence

2 Fresnel Tracking System Error and Analysis

21 Fresnel Lens System Introduction The LFR field whichare comprise of 11 rows of flat mirrors can be imaginedas a broken-up parabolic trough reflector by using linearsegments to focus the radiation as Figure 1 shows Theparabolic trough shape is simulated by several flat reflectors atdifferent positions in order tomake the sunlight reflect to thereceiver tubes fixed on the top of mirrors Each mirror must

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 834392 6 pageshttpdxdoiorg1011552014834392

2 The Scientific World Journal

Absorber

ReflectionIncident

H

120573120579112057921205793

e

Reflector 7RotaryReflector 11

Refle

ctor

4

Refle

ctor

3

Refle

ctor

2

Refle

ctor

1

Refle

ctor

5

Figure 1 Diagram of the Fresnel solar reflection technology

tracks accurately to ensure the virtual parabolic shape andkeep the reflected solar radiation on the absorber all the timeTherefore improving tracking accuracy plays an importantrole in promoting the collection efficiency [12]

The tracking error of Fresnel reflectors could be affectedby time mirror exocentric structure collector orientationheight of absorbers axis position solar altitude angle and soon This paper analyzed the influence of these factors on thetracking error

22 The Analysis of Tracking System Rotation Angle It is wellknown that in order to track the sun the exact position of sunis necessary The main parameters of sun position are shownin Figure 2 which are sun declination angle 120575 hour angle 120596elevation angle 120579 geographic latitude 120593 and longitude 120576 Thesunlight irradiates to point 119875 on the surface of earth whichis determined by elevation angle ℎ

119904and azimuth angle 120582 of

the tangent plane The sun position in the tracking system iscalculated by international SPA algorithm whose accuracy is00003∘ [13 14]

In Figure 2 the sunlight irradiates to the center of mirror(119871 0 0) at space vector of elevation angle ℎ

119904and azimuth

angle 120582 reflection light is vector 997888119903 and the normal vectorof central point of mirror is 997888119899 The angle betweenmirror andhorizontal 119883-axis direction is 120579 and the location position ofreflected rays on collector tubes is (0 119890119867)

If the mirror rotation center is located on the center ofmirror one has the following

997888119903 = (

minus119871

119877119890

119877119867

119877) 119877 = radic1198712 + 1198902 + 1198672

997888119899 = (minus sin 120579 0 cos 120579)

997888119904 = (119904

119909 119904119910 119904119911)

Reflector

North

Eastx

y

eL

120582

z

H

120579

(Sx Sy Sz)

hs

(L 0 0)

(0 e H)

Absorber

Figure 2 Diagram of ray reflection of Fresnel technology

997888119904 times

997888119899 =

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

997888119894

997888119895

997888119896

119904119909

119904119910

119904119911

minus sin 120579 0 cos 120579

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

= 119904119910cos 120579997888119894

minus (119904119909cos 120579 + 119904

119911sin 120579) 997888119895

+ 119904119910sin 120579

997888119896

997888119899 times 119903 =

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

997888119894

997888119895

997888119896

minus sin 120579 0 cos 120579minus119871

119877

119890

119877

119867

119877

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

= minus119890

119877cos 120579997888119894

minus (119871

119877cos 120579 minus 119867

119877sin 120579)997888119895

minus119890

119877sin 120579

997888119896

(1)

The Scientific World Journal 3

According to the law of light reflection it is known that

119904119910cos 120579 = minus 119890

119877cos 120579

119904119909cos 120579 + 119904

119911sin 120579 = 119871

119877cos 120579 minus 119867

119877sin 120579

119904119910sin 120579 = minus 119890

119877sin 120579

(2)

Then

tan 120579 =119871119877 minus 119904

119909

119867119877 + 119904119911

119890 =minus119904119910

radic1 minus 1199042

119910

radic1198712 + 1198672

(3)

In the equation 119904119909 119904119910 119904119911are the vector components of sun

position along the 119883 119884 119885 axis The rotation angle of mirror120579 and deviation distance e of reflected solar radiation in thedirection of absorber can be calculated at a certain moment

There are two rotation methods for mirror rotation oneis rotating around the geometric center of the mirror andthe other is using the reflector supporting shaft as rotationcenter This paper mainly analyzes the tracking error underthe second condition

When the rotation axis is not located in the centerof mirror 119871 and 119867 in formula (3) need to be replacedby 119871-119877 sin 120579 and 119867-119877 cos 120579 Assuming that mirror widthis 800mm spacing between adjacent reflectors is 200mmand focal length is 7m the tracking error under differentdeviation factors was obtained by computer program

3 The Influence of Main ParametersDeviation on Tracking Accuracy

31 The Influence of Frame Eccentric Error on Tracking Accu-racy Because the rotation axis of reflectors is not located atthe geometry center of the mirror the orbit of incident pointon the mirror usually is an ellipse Meanwhile reflectors indifferent columns rotate at different speeds at the same timewhich results in different tracking errors Figure 3 shows thatat winter solstice when reflection mirror 1 and reflectionmirror inmiddle columnperformed 10 cmeccentric distanceat 800 the tracking error is 026∘ and the tracking error ofreflection mirror 11 is 01∘ At 1800 the tracking errors ofreflection mirrors 1 6 and 11 are minus012∘ minus028∘ and minus027∘and the minimum error happens at 1500 1240 and 1025respectively

Eccentric deviation value has significant effect on thetracking error It is shown in Figure 4 that the maximumtracking error at winter solstice caused by different eccentricdistances (5 10 15 and 20 cm)mainly occurs at 800 or 1800Nevertheless the tracking error at around 1240 is zero andthe ratio of eccentric distance is consistent with the ratio oftracking error

In different dates throughout the year the tracking errorcaused by reflector eccentric also changes As shown in

03

02

01

0

minus01

minus02

minus03

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Center 0mWest 6m

Hours of winter solstice day

East 6m

Erro

r (∘ )

Figure 3 The tracking error caused by eccentric deviation ofdifferent column

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

06

04

02

0

minus02

minus04

minus06

5 cm10 cm

15 cm20 cm

Erro

r (∘ )


Figure 4 The tracking error caused by eccentric deviation of themiddle columns

Figure 5 the maximum tracking error of middle column(column 6) with a 10 cm eccentric deviation at the typicaldates of vernal equinox summer solstice autumnal equinoxandwinter solstice happens at 800 and 1800with about 023∘Especially the maximum tracking error happens at wintersolstice

Because of eccentric influence different columns anddifferent time lead to different tracking error On the sameday there is a big error at morning and afternoon but almostno error at a certain moment at noon

32 The Influence of North-South Orientation Deviationon Tracking Accuracy Because geographic northsouth isdifferent from geomagnetic northsouth there exists mag-netic declination The sun location algorithm is based ongeographic north and south thus the truly geographical


The spring equinox The summer solstice

The autumnal equinox The winter solstice

03

02

01

0

minus01

minus02

minus03

800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Hours of the day

Erro

r (∘ )

Figure 5 The tracking error on four typical days

The spring equinox The summer solstice The autumnal equinox The winter solstice

The spring equinox 1 The summer solstice 1 The autumnal equinox 1 The winter solstice 1

1

0

minus1

minus2

minus3

minus4

minus5

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Hours of the day

Erro

r (∘ )

Figure 6 The tracking error caused by north and south directionnegative deviation on four typical days

northsouth of solar field is very important for the trackingsystem Assuming that southwest is negative deviation forsolar field orientation the influence of north-south orien-tation deviation on tracking error can be simulated Thevariation trend of tracking error for different orientationdeviation (5∘ and 10∘) at vernal equinox summer solsticeautumnal equinox and winter solstice is shown in Figure 6

When the orientation axis lays west of 10∘ the trackingerror curves at winter solstice has the biggest slope Thetracking error increases from 066∘ (800) to 45∘ (1200) thenit decreases gradually At 1800 the value is around 008∘

The tracking errors at vernal equinox and autumnalequinox are much smaller than that at winter solstice Theerror value is positive which means the mirror rotation



015

01

005

0

minus005

minus01

minus015

800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Hours of the day

Erro

rs (∘)

Figure 7 The tracking error of solar altitude 02∘ deviation

angle is bigger relative to theoretical tracking angle andthe tracking system runs too fast Nevertheless at summersolstice tracking error presents a negative value whichimplies that the tracking system is too slow

The tracking error with an orientation axis deviation of5∘ westward comparing with an orientation axis deviation of10∘ deviation has a similar changing trend but the value ofthe former is about half of the latter

33 The Influence of Center Height and Center Distance Devi-ation on Tracking Accuracy The height of middle column(column 6) and center distance deviation performs no effecton tracking error in each typical day

When the height of reflectors shows minus10 cm and minus5 cmdeviation its tracking error is 02∘ and 01∘ respectivelyWhen the center distance shows minus10 cm deviation its track-ing error is 04∘ In the case of minus5 cm deviation its trackingerror is 02∘

34 The Influence of Solar Altitude Angle Deviation on Track-ing Accuracy In the Fresnel solar concentrating system solaraltitude angle is one of the key factors for calculating the sunposition It is shown in Figure 7 when the deviation of solaraltitude angle is 02∘ that the tracking error from 800 to 1100and from 1400 to 1800 is about 01∘ The error is positivein the morning (rotating too fast) while it is negative in theafternoon (rotating too slow) In the three hours from 1100 to1400 the error changes gradually from01∘ tominus01∘ Howeverat summer solstice this change mainly occurs from 1230 to1330

35 The Influence of Geographical Latitude-Longitude Devia-tion on Tracking Accuracy Owing to the low energy densityof solar energy it usually requires large area for solar powergeneration thus the geographical latitude longitudes aredifferent in different area of solar field As shown in Figure 8when the longitude has 01∘ deviation at winter solstice thetracking error increases from 0047∘ (at 800) to 0062∘ (at1245) then decreases to 0045∘ (at 1800) The error value and


Table 1 Effect of the tracing error for the middle mirror

Influence factor Eccentric distance Eccentric distance Eccentric distance Eccentric distanceValue 10 cm 10 cm 10 cm 10 cmTypical data Winter solstice Autumnal equinox Summer solstice Spring equinoxMaximum error 027∘ 023∘ 022∘ 024Influence factor Eccentric distance Eccentric distance North and south deviation North and south deviationValue 5 cm 15 cm minus10∘ minus10∘

Typical data Winter solstice Winter solstice Winter solstice Spring equinoxMaximum error 017∘ 04∘ 45∘ 16∘

Influence factor North and south deviation Autumnal equinox Center distance deviation Height deviationValue minus10∘ minus10∘ minus10 cm minus10 cmTypical data Autumnal equinox Summer solstice Typical day Typical dayMaximum error 16∘ minus094∘ 0∘ 0∘

Influence factor Longitude deviation Longitude deviation Longitude deviation Angle deviationValue 01∘ 01∘ 01∘ 005∘

Typical data Winter solstice Equinoxes Summer solstice Typical dayMaximum error 0065∘ 0053∘ 0045∘ 0025∘

Influence factor Latitude deviation Latitude deviation Latitude deviation Angle deviationValue 01∘ 01∘ 01∘ 02∘


Hours of the day



0065

006

0055

005

0045

004800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Erro

r (∘ )

Figure 8 The tracking error of longitude 01∘ deviation

trend at vernal equinox and autumnal equinox are consistentAt summer solstice the tracking error is almost invariable inthe whole day

Figure 9 shows that when latitude has 01∘ deviation atwinter solstice vernal equinox and autumnal equinox thetrends of the tracking errors curves are similar However theerror value at winter solstice is much higher than the othertwo typical days Different from other typical day the errorvalue at summer solstice gradually decreases from +0013∘ (at800) to zero then increases to a maximum value of 0016∘ at1800

Hours of the day



800 900 1000 1100 1200 1300 1400 1500 1600 17001800

003

002

001

0

minus001

minus002

minus003

Erro

rs (∘)

Figure 9 The tracking error of latitude 01∘ deviation

36 Comparison of All Factors By calculating the trackingerror of middle reflector (column 6) due to the variousfactors the comparison results are shown in Table 1

From Table 1 the order of influence on tracking error isnorth-south orientation deviation eccentric deviation alti-tude angle deviation longitude deviation latitude deviationcenter distance and height deviation successively

Height deviation almost has no effect on the trackingprecision ofmiddlemirror However if the height deviation is10 cm the tracking error formirror 1 is 02∘ in typical day andif the center distance deviation is 10 cm the error can reach04∘


4 Conclusion

There are many influence factors for Fresnel solar trackingerror such as reflector supporting structure rotation axisposition driver accuracy tracking software algorithm devi-ation of geographic latitude-longitude and related structureerror When north-south orientation and geographic longi-tude have deviation the tracking error is biggest at noon andit is smaller atmorning and afternoon on the same dayWhenthe mirror rotating center solar altitude and geographiclatitude have deviation the error value changes from positiveto negative and at a certain moment in the midday the erroris zero

Tracking error has a great influence on the solar collectionefficiency For Fresnel solar concentrating system if the errorof tracking is 01∘ the light energy collected by the receivertubes decreases by 10 Therefore improving efficiency andaccuracy of automatic tracking system plays an importantrole in increasing solar collection efficiency and energygeneration and decreasing the cost of solar power

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors gratefully acknowledge the financial supportof the National Energy Applied Technology Research andEngineering Demonstration Project (no NY20130101)

References

[1] J Song and S Ding Solar Thermal Power Plant MechanicalIndustry Press Beijing China 2013

[2] X Li ldquoThe current situation and development of linear concen-trated solar thermal power generation technologyrdquo East ChinaElectric Power vol 39 no 12 pp 2071ndash2075 2011

[3] G Francia ldquoPilot plants of solar steam generating stationsrdquoSolar Energy vol 12 no 1 pp 51ndash64 1968

[4] D R Mills and G L Morrison ldquoCompact linear Fresnelreflector solar thermal powerplantsrdquo Solar Energy vol 68 no3 pp 263ndash283 2000

[5] D R Mills G Morrison J Pye and P Le Lievre ldquoMulti-tower line focus Fresnel array projectrdquo Journal of Solar EnergyEngineering vol 128 no 1 pp 118ndash120 2006

[6] S S Mathur T C Kandpal and B S Negi ldquoOptical design andconcentration characteristics of linear Fresnel reflector solarconcentrators-I Mirror elements of varying widthrdquo EnergyConversion and Management vol 31 no 3 pp 205ndash219 1991

[7] G D Sootha and B S Negi ldquoA comparative study of opticaldesigns and solar flux concentrating characteristics of a linearFresnel reflector solar concentratorwith tubular absorberrdquo SolarEnergyMaterials and Solar Cells vol 32 no 2 pp 169ndash186 1994

[8] C Du P Wang Y Wu and C Ma ldquoLinear Fresnel collectinglens radiation quantity calculationmethodrdquo Journal of ChemicalEngineering vol 62 no 1 pp 179ndash184 2011

[9] S Pu and C Xia ldquoOptical design of a linear reflecting solarconcentrator with all-flat mirrorsrdquo Transactions of the Chinese

Society of Agricultural Engineering vol 27 no 12 pp 282ndash2852011

[10] X Zheng and Q Huang ldquoStudy on sun tracking methods andapplicationrdquo Energy Technology vol 24 no 4 pp 149ndash151 2003

[11] C Du PWang CMa andYWu ldquoVector algorithmof trackingtilted angle of Fresnel concentrated solar power systemsrdquo ActaEnergiae Solaris Sinica vol 32 no 6 pp 831ndash835 2011

[12] R Grena ldquoFive new algorithms for the computation of sunposition from 2010 to 2110rdquo Solar Energy vol 86 no 5 pp 1323ndash1337 2012

[13] X Huang Z Wang Y Li H Qiu and W Huang SolarThermal Power Generation Technology China Electric PowerPress Beijing China 2013

[14] Q Li J Zheng H Xu M Liu and J Pei ldquoThe development oflinear Fresnel solar thermal power generation technologyrdquo SolarEnergy no 7 pp 41ndash45 2012

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Absorber

ReflectionIncident

H

120573120579112057921205793

e

Reflector 7RotaryReflector 11

Refle

ctor

4

Refle

ctor

3

Refle

ctor

2

Refle

ctor

1

Refle

ctor

5

Figure 1 Diagram of the Fresnel solar reflection technology

tracks accurately to ensure the virtual parabolic shape andkeep the reflected solar radiation on the absorber all the timeTherefore improving tracking accuracy plays an importantrole in promoting the collection efficiency [12]

The tracking error of Fresnel reflectors could be affectedby time mirror exocentric structure collector orientationheight of absorbers axis position solar altitude angle and soon This paper analyzed the influence of these factors on thetracking error

22 The Analysis of Tracking System Rotation Angle It is wellknown that in order to track the sun the exact position of sunis necessary The main parameters of sun position are shownin Figure 2 which are sun declination angle 120575 hour angle 120596elevation angle 120579 geographic latitude 120593 and longitude 120576 Thesunlight irradiates to point 119875 on the surface of earth whichis determined by elevation angle ℎ

119904and azimuth angle 120582 of

the tangent plane The sun position in the tracking system iscalculated by international SPA algorithm whose accuracy is00003∘ [13 14]

In Figure 2 the sunlight irradiates to the center of mirror(119871 0 0) at space vector of elevation angle ℎ

119904and azimuth

angle 120582 reflection light is vector 997888119903 and the normal vectorof central point of mirror is 997888119899 The angle betweenmirror andhorizontal 119883-axis direction is 120579 and the location position ofreflected rays on collector tubes is (0 119890119867)

If the mirror rotation center is located on the center ofmirror one has the following

997888119903 = (

minus119871

119877119890

119877119867

119877) 119877 = radic1198712 + 1198902 + 1198672

997888119899 = (minus sin 120579 0 cos 120579)

997888119904 = (119904

119909 119904119910 119904119911)

Reflector

North

Eastx

y

eL

120582

z

H

120579

(Sx Sy Sz)

hs

(L 0 0)

(0 e H)

Absorber

Figure 2 Diagram of ray reflection of Fresnel technology

997888119904 times

997888119899 =

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

997888119894

997888119895

997888119896

119904119909

119904119910

119904119911

minus sin 120579 0 cos 120579

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

= 119904119910cos 120579997888119894

minus (119904119909cos 120579 + 119904

119911sin 120579) 997888119895

+ 119904119910sin 120579

997888119896

997888119899 times 119903 =

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

997888119894

997888119895

997888119896

minus sin 120579 0 cos 120579minus119871

119877

119890

119877

119867

119877

1003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

= minus119890

119877cos 120579997888119894

minus (119871

119877cos 120579 minus 119867

119877sin 120579)997888119895

minus119890

119877sin 120579

997888119896

(1)



119904119910cos 120579 = minus 119890

119877cos 120579

119904119909cos 120579 + 119904

119911sin 120579 = 119871

119877cos 120579 minus 119867

119877sin 120579

119904119910sin 120579 = minus 119890

119877sin 120579

(2)

Then

tan 120579 =119871119877 minus 119904

119909

119867119877 + 119904119911

119890 =minus119904119910


119910

radic1198712 + 1198672

(3)









03

02

01

0

minus01

minus02

minus03

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Center 0mWest 6m


East 6m

Erro

r (∘ )


800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

06

04

02

0

minus02

minus04

minus06

5 cm10 cm

15 cm20 cm

Erro

r (∘ )









03

02

01

0

minus01

minus02

minus03

800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Hours of the day

Erro

r (∘ )




1

0

minus1

minus2

minus3

minus4

minus5

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Hours of the day

Erro

r (∘ )







015

01

005

0

minus005

minus01

minus015

800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Hours of the day

Erro

rs (∘)

















Hours of the day



0065

006

0055

005

0045

004800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Erro

r (∘ )




Hours of the day



800 900 1000 1100 1200 1300 1400 1500 1600 17001800

003

002

001

0

minus001

minus002

minus003

Erro

rs (∘)






4 Conclusion





Acknowledgment


References




















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



















119904119910cos 120579 = minus 119890

119877cos 120579

119904119909cos 120579 + 119904

119911sin 120579 = 119871

119877cos 120579 minus 119867

119877sin 120579

119904119910sin 120579 = minus 119890

119877sin 120579

(2)

Then

tan 120579 =119871119877 minus 119904

119909

119867119877 + 119904119911

119890 =minus119904119910


119910

radic1198712 + 1198672

(3)









03

02

01

0

minus01

minus02

minus03

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Center 0mWest 6m


East 6m

Erro

r (∘ )


800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

06

04

02

0

minus02

minus04

minus06

5 cm10 cm

15 cm20 cm

Erro

r (∘ )









03

02

01

0

minus01

minus02

minus03

800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Hours of the day

Erro

r (∘ )




1

0

minus1

minus2

minus3

minus4

minus5

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Hours of the day

Erro

r (∘ )







015

01

005

0

minus005

minus01

minus015

800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Hours of the day

Erro

rs (∘)

















Hours of the day



0065

006

0055

005

0045

004800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Erro

r (∘ )




Hours of the day



800 900 1000 1100 1200 1300 1400 1500 1600 17001800

003

002

001

0

minus001

minus002

minus003

Erro

rs (∘)






4 Conclusion





Acknowledgment


References




















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of




















03

02

01

0

minus01

minus02

minus03

800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Hours of the day

Erro

r (∘ )




1

0

minus1

minus2

minus3

minus4

minus5

800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800

Hours of the day

Erro

r (∘ )







015

01

005

0

minus005

minus01

minus015

800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Hours of the day

Erro

rs (∘)

















Hours of the day



0065

006

0055

005

0045

004800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Erro

r (∘ )




Hours of the day



800 900 1000 1100 1200 1300 1400 1500 1600 17001800

003

002

001

0

minus001

minus002

minus003

Erro

rs (∘)






4 Conclusion





Acknowledgment


References




















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


























Hours of the day



0065

006

0055

005

0045

004800 900 1000 1100 1200 1300 1400 1500 1600 17001800

Erro

r (∘ )




Hours of the day



800 900 1000 1100 1200 1300 1400 1500 1600 17001800

003

002

001

0

minus001

minus002

minus003

Erro

rs (∘)






4 Conclusion





Acknowledgment


References




















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















4 Conclusion





Acknowledgment


References




















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















Research Article Solar Tracking Error Analysis of Fresnel...

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