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13th World Congress in Mechanism and Machine Science, Guanajuato, Mxico, 19-25 June, 2011 A29_596

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Energy Comparison of PV Systems with Mono- and Bi-axial Pseudo-equatorialTracking Mechanisms

B.G. Burduhos * M.M. Vtescu R.G. Sulescu I. Tatu Renewable Energy Systems and Recycling Research Centre, Transilvania University of Braov, Romnia

Abstract One way of increasing the solar energyconversion efficiency is the use of mechanical tracking

systems; among them the pseudo-equatorial typerepresents a viable option. This paper aims to formulatethe optimal pseudo-equatorial tracking solution that can

be implemented in a mountain area, for the particularcase Braov-Romania. Modeling and numerical

simulations were developed, in the prerequisite of theclear sky, considering adjustable values for the maintracking parameters; the results give answers to the

following questions: which pseudo-equatorial tracking solution is best suited for the implementation location:mono- or bi-axial tracking? Which is the most suitableorientation program for the tracking solution?

Keywords: photovoltaic tracking system, orientation efficiency,mono-axial tracking, bi-axial tracking, direct solar radiation

I Introduction

An elegant solution for obtaining clean energy fromsolar radiation is represented by the photovoltaicmodules. Because their efficiency is quite low (~15%) [1]and highly affected by the module temperature, different

possibilities of increasing it are intensively studied.One of them is the use of tracking systems in order to

orientate the PV modules towards the sun. This solution, based on mechanical systems with linkages, cams orgears, is widely approached, both in literature [2, 3] andindustry [4, 5, 6]. Still, an obvious problem is that thetracking systems increase the overall cost of the power

produced. This is why choosing an optimal trackingsystem (efficient and with a simple mechanism) isimportant.

For identifying the optimal pseudo-equatorial systemfor a mountain region, particularly for the Braov-Romania location, this paper extends the results

previously reported, [7], and analyses the influence of theaxes number reduction on the tracking efficiency; thetracking efficiency notion is defined, [8], as the ratio

between the solar energy received on the PVmodule/platform and the available solar energy.

To reach this goal, the paper analyzes, using numericalsimulations, the influence of the time interval between two

* [email protected] [email protected] [email protected] [email protected]

consecutive steps, further denominated as step duration(the sum between the working step and the breaking stepduration).

Next, the results obtained are implemented in thesimulations of a bi-axial solution (Fig. 2a, 3a), able to

follow the sun in the conditions of the Braov Romanialocation, in the clear sky prerequisite.

Further, similar simulations are made for a simplifiedsolution of the pseudo-equatorial tracking system: the mono-axial tracking (Fig. 2b, 3b); these results arecompared to those previously obtained.

a)

b)

Fig. 1. a) Sunray equatorial angles relative to Earth; b) Kinematic chainof the pseudo-equatorial bi-axial tracking mechanical structure

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a)

b)Fig. 2. 3D models for pseudo-equatorial systems of type: a) bi-axial

mechanical structure; b) mono-axial mechanical structure.

a)

b)

Fig. 3. Relative positions of the pseudo-equatorial tracking open chains

to Earth: a) bi-axial chain; b) the mono-axial chain

Finally, based on this comparison, the conclusionsresulted are presented along with implementationrecommendations. The results allow to identify answersto the following questions: what solutions of pseudo-equatorial tracking is proper for the considered location:mono- or bi-axial tracking? What type of orientation

program is best suitable for the selected trackingsolution?

In this study the diffuse solar radiation is neglected.The paper structure contains the following chapters: a)

Modeling of the sunray angles, tracked PV angles anddirect solar radiation; b) Duration of the tracking uniformsteps; c) Bi-axial tracking analysis; d) Mono-axialtracking analysis; e) Responses comparison betweenmono- and bi-axial tracking and f) Conclusion.

II Sun-ray Angles, PV Angles and Radiation Modeling

Modeling the sun ray orientation can use two types ofangles (Fig. 1), the equatorial ones when considering therelations between Sun and Earth (-hour angle, -declination) or the pseudo-equatorial ones whenconsidering the local observer (, ). Solar trackingsystems with equatorial angles have a rather difficultconstruction; this is why systems which use pseudo-equatorial angles are preferred.

a)

0

3

6

9

12

15

0 10 20 30 40 50 60 70 80 90

A m p

l i f i c a

t i o n

F a c

t o r

Pressure angle [deg]

b)Fig. 4. a) Scheme of the triangle linkage with linear actuator; b) The

variation of the amplification factor (Fa / F = 1 / cos B) depending onthe B pressure angle

B

Bi Bf

Bi Bf

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( )T = 1215 ; (1)

( )36580360sin45,23 = n ; (2)

)sin(cossin 1 = ; (3)

=

coscossinsincoscos

sin 1 . (4)

The following notations are used: T solar time; n number of the day; latitude of the observer. Formodeling tracking systems angles the same angles areused but noted with star .

For estimating the solar radiation [ W/m2] captured bythe tracking system the following relations are used:

( )[ ]ooo n B 72.29856.0cos0334.011367 += ; (5)

a)

b)Fig. 5. Example of a complex linkage fitted with linear actuator usedto drive the diurnal move * with large angular stroke (180): a)

linkage kinematical scheme; b) 3D linkage scheme

+=

sin4.99.0exp Ro

T B B ; (6)

)coscoscossin(sinsin 1 += ; (7)= cos* B B ; (8)

*sinsin*)cos(coscoscos * += . (9) Bo (5) represents the extraterrestrial available solar

radiation; B (6) represents the radiation that reaches the earths

surface as beam radiation [9], with (7) the altitudeangle of the sun and T R a local size called turbidityfactor, indicating the radiation losses in theatmosphere under clear sky conditions [10];

B* (8) represents the radiation received by thetracked PV module, with (9) the incidence angle

between the sun-ray and the normal-to-the-module[12]: (Fig. 9, 12, 14, 17, 22)

The relations presented in this chapter will be used todetermine the tracking efficiency of the bi- (Fig. 2a, 3a)and mono-axial (Fig. 2b, 3b) systems described inchapter III and IV.

Further, examples of mechanisms are presented usedfor the movement of the pseudo-equatorial tracker.

The elevation movement * (with strokes 90) iseasily made with linear actuators. Unlike them, thediurnal movements * (with strokes >90) are usuallyobtained with rotary actuators , which are usually less

economically efficient than linear actuators (a gear ratioover 5000 is usually needed) . Extending the use of thelinear actuators for the diurnal movement * is limited bythe fact that a triangle linkage with linear actuator (seeFig. 4a) reduces the angular stroke to about 120-130,due to excessive increase of the pressure angle [3](Fig. 4b).

This problem can be partially solved by using acomposed linkage consisting of two simple linkageswhich are serially connected: a triangle linkage withlinear actuator (Fig. 4) and a four-bar planar linkagewhich amplifies the output angle of the first linkage up to180 or more (see Fig. 5).

III Duration of the Tracking Steps

The tracking of PV modules towards the sun can bedeveloped either continuously or stepwise [13]. Ideally, itis obvious that a continuous movement is preferred witha tracking efficiency very close to 100%, due to thecontinuous small incidence angle. Unfortunately such amovement is technically very difficult because of thevery high transmission ratio. This means that orientationis recommended to be made stepwise. Also, two types ofstep-orientations can be considered: with equal and withnon-equal step duration (the sum between the workingand the breaking duration of each step). Because the

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The movement * has 4 different seasonalorientation programs. These are obtained byapproximating in 1h-steps the mean variation of thesun-ray angle (see the blue step-wise * curve inFig. 15).

For both programs types, numerical simulations have been conducted during the extreme days of the summerinterval, to evaluate their influence on the incident directsolar radiation (Fig. 14, 17). From a comparative analysisof the curves presented in Fig. 14b and Fig. 17b it resultsthat a seasonal variation of * has a larger negativeimpact on the tracking efficiency of a bi-axial trackingsystem.

Fig. 13. Bi-axial, pseudo-equatorial tracking, having a seasonal * anda daily * program, exemplified on the summer seasons limiting day

(106) and on the Summer Solstice day (172)

a)

b)

Fig. 14. The available ( B) and the received ( B*) beam solar radiation ona bi-axial, pseudo equatorial tracked PV surface (B_BiAx), according to

the program described in Fig. 13

Fig. 15.a. Variations of the daily sun angle on the summer season limiting days 106 and 237, on the summer solstice day and on theseasonal referential day 125; the optimum summer season hourly

tracking program, set on summer season referential day 125 (*_125)

Fig. 15.b. Variations of the daily sun angles on the winter season limiting days 281 and 60, on the winter solstice day and on the seasonal

referential day 310; the optimum winter season hourly tracking program, set on winter season referential day 310 (*_310)

Fig. 15.c. Variations of the daily sun angles on the spring season limiting days 61 and 105 and on the spring equinox day , which is also

the seasonal referential day; the optimum winter season hourly tracking program, set on spring season referential day ( *_Spr.Eq.)

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Fig. 16. Bi-axial, pseudo-equatorial tracking, having a daily * and a seasonal * program, exemplified on the summer seasons limiting day

(106) and on the Summer Solstice day (172)

a)

b)

Fig. 17. The available ( B) and the received ( B*) beam solar radiation ona bi-axial, pseudo equatorial tracked PV surface (B_BiAx), according to

the program described in Fig. 15

The annual numerical values of the tracking efficiencyobtained using the two previously described programsand their graphical representation are further presented,in chapter VI (Fig. 27 and Fig. 28).

V Mono-axial Tracking Case

In this chapter, based on numerical simulations, theinfluence of 3 orientation programs for a mono-axialtracking system on the tracking efficiency is analyzed.The mono-axial tracking system is obtained bysimplifying the bi-axial construction and maintaining the

Fig. 18. Variations of the sun angles ( and ), the constant PVelevation ( * = 21 , 30, 40, 50, 60) and the PV diurnal angle * onsummer season limit day 106 , when using daily tracking program on *

Fig. 19. Variations of the sun angles ( and ) on summer season limitday 106 and on the summer solstice day, the constant PV elevation ( *

= 21 , 30, 40, 50, 60) and the PV diurnal angle *, when imposing a seasonal tracking program on *

Fig. 20. Variations of the sun angles ( and ) on the spring season limiting days 61 and 105, the constant PV elevation ( * = 21 , 30, 40,

50, 60) and the PV diurnal angle *_Spr.Eq. when imposing a seasonal tracking program on *

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* axis at a fixed position. Fixing the * movement isconsidered to be even less efficient in terms of tracking,as described in [10].

The main differences between the three consideredmono-axial orientation programs are: In the first case a daily tracking program for * is

imposed (see Fig. 18); In the second case a seasonal tracking program for

* is imposed (see Fig. 19 summer season andFig. 20 spring season and Fig. 15a, 15b, 15c)

In the last case an annual tracking program for * isimposed using Fig. 21.

Using the three proposed programs, simulations wereconducted to evaluate the available and received beamsolar radiation. For the case of daily * orientation

programs, during the spring season an example is presented in Fig. 22.

Fig. 21. Variations of the daily angles and * during the Equinoxes,the Summer Solstice, the Winter Solstice and the year referential day

125

Fig. 22. Variations of the available (B) and received (B*) beam solarradiation on a mono-axial, pseudo-equatorial tracked PV surface duringthe spring season limiting days: 61 and 105, using a daily * program

and a constant PV elevation ( * = 21 , 30, 40, 50, 60)

Fig. 23. The tracking efficiency curves of the pseudo-equatorial, mono-axial PV system having a daily * program and a constant PV elevation

(* = 21 - 60) on the spring season referential days: equinox andseason limiting days: 61 and 105

Fig. 24. The seasonal tracking efficiency curves of the pseudo-equatorial, mono-axial PV system having a daily * program and a

constant PV elevation ( * = 21 -60), in Brasov ( = 45.65 N)

In all the three cases the optimal fixed value of theangle * needs to be established. Its value wasdetermined using numerical simulation using diagramslike those presented in Fig. 23, 24, 25.

The Fig. 23 presents the tracking efficiency variationduring extreme and equinox days of the spring seasonwhen using a daily * tracking program . Using the same

program type for the rest of the seasons the diagram fromFig. 24 is obtained, based on which Fig. 25 results. Fromthe analysis of Fig. 25 it results that for every type of *

program the optimal * angle is 42.Another important parameter which needs to be

evaluated is the optimal angular stroke of the *movement. This is being established using Fig. 26, where4 different angular stokes are considered (160 , 140 ,120 and 90 ).

From the analysis of this diagram, at the previouslyfixed elevation angle *=42 , two angular strokes can beconsidered optimal: first the value 140 because there ismerely a difference between the efficiencies in the 140and 160 cases. The 120 stroke can also be consideredoptimal because a simpler mechanism is needed and thedifference between the efficiencies is negligible (~0.6%).

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Fig. 25. The annual tracking efficiency for the mono-axial, pseudo-equatorial PV system with daily * program , with seasonal * program and with annual * program , for constant PV elevation ( * = 21 - 60)

Fig. 26. The annual tracking efficiency for the mono-axial, pseudo-equatorial PV system tracked according to the annual *program, for 4different * strokes : *=160 ; *=140 ; *=120 and *= 90

VI Responses Comparison of Mono- and Bi-axialTracking

The results obtained in the previous chapters made it possible to compare the annual tracking efficienciesobtained with 6 bi-axial and 3 mono-axial trackingsystems.

From the analysis of Fig. 27 the following statementscan be made: The mono-axial systems are with ~3% less efficient

than the bi-axial ones; The systems with seasonal * program are with ~1%

less efficient than the ones with daily * program; The influence of the * program has a very low

influence on the annual tracking efficiency of thecorresponded system.

Fig. 27. The annual tracking efficiencies for 6 types of bi-axial, pseudo-equatorial PV systems (1. with both * and * daily programs; 2. with

daily * program and seasonal * program; 3. with seasonal * programand daily * program; 4. with both * and * seasonal programs; 5. withannual * program and daily * program; 6. with annual * programand seasonal * program) and the annual tracking efficiencies for 3

types of mono-axial , pseudo-equatorial PV s ystems, having theoptimum * = 42 (with: 1. daily * program; 2. seasonal * program;

3. annual * program)

Fig. 28. The annual tracking efficiency variations depending on thediurnal stroke * for three different * programs in the case of: the bi-axial tracking with daily * program, the bi-axial tracking with seasonal

* program and the mono-axial tracking

Further in Fig. 28 the tracking efficiencies are presented, correlated again to the angular stroke of thediurnal movement *.

The results are 3 sets of curves (Fig. 28), every setrepresenting a different program type for the elevationmovement *: the top curves represent the efficiencyresults in the case of a daily * program; the middle set ofcurves and the curves from the bottom of Fig. 28represent the efficiency in the cases of seasonal andannual (fixed at 42) * programs.

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VII. Conclusions

The main conclusions which can be stated afteranalyzing these results are: The small efficiency increase, of ~1%, between bi-

axial systems with seasonal * and daily orientation program makes the seasonal solution more feasibledue to the simplification of the software componentwhich drives the positioning motors;

For the same reason, when comparing biaxialsystems with a daily, seasonal or annual * programwhere the efficiency difference is even lessobservable, the annual * program is preferred;

From the comparison of the bi-axial tracking systemswith different orientation programs it becomes

obvious that a seasonal variation of * has a largernegative impact on the tracking efficiency than theseasonal variation of *;

In the case of mono-axial tracking systems theoptimal fixed elevation angle *=42 wasdetermined;

From the comparison of mono- and bi-axial trackingsystems the following can be stated: the mosteconomic system is the mono-axial one because foronly a ~3% efficiency loss it greatly simplifies themechanical construction of the PV tracking system;

Considering the previous conclusions, in themeteorological and geographical conditions of a

mountain region (particularly Brasov, Romania), a pseudo-equatorial system with an annual * programand a fixed * angle is preferred;

The optimal angular stroke of the diurnal movement*, in the analyzed conditions, is considered to be140. For higher values, the tracking efficiencyincrease is insignificant;

All the results and conclusions presented in this paper are valid in the conditions of a cloudless sky;for real conditions, most statements are valid withone exception: the fixed angle * will have lowervalues. This aspect will be further investigated in thefuture studies.

Acknowledgement

This paper is supported by the Sectoral OperationalProgramme Human Resources Development (SOPHRD), Post Doctoral School, financed from the EuropeanSocial Fund and by the Romanian Government under thecontract number POSDRU 59323.

References[1] Barnett Allen, Kirkpatrick Douglas, Christiana Honsberg, Very

High Efficiency Solar Cell Modules, Progress in PhotoVoltaics ,17(1), ISSN: 1062-7995, 2009, pg. 75-83.

[2] Helwa, N., Bahgat, A., El Shafee, A., El Shennawy, E., MaximumCollectable Solar Energy by Different Solar Tracking Systems,Energy Sources 22 (2000), 23-34.

[3] Mazen, Abu-Khadera, Omar, Badranb, Salah, Abdallah, Evaluatingmulti-axes sun-tracking system at different modes of operation inJordan, Renewable and Sustainable Energy Reviews 12 (2008),864873.

[4] www.solar-trackers.com[5] www.degerenergie.de[6] www.dobontech.com[7] Vtescu, M.., Ion Via, Du, A., Diaconescu, D, Hermenean I.,

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[11] Burduhos B., Via I., Diaconescu D., Saulescu, R.: The Influenceof the Orientation Axis Number on the Efficiency of a Pseudo-Equatorial Tracker in Brasov Romania, 25th EU PVSEC 25 th European Photovoltaic Solar Energy Conference and Exhibition,Valencia Spain, 5-12 September 2010, pg. 4491-4496.

[12] Diaconescu, D., Via, I., Burduhos, B., Dinicu, V., The IncidenceAngles of the Trackers Used for the PV Panels Orientation. Part I:

Equatorial Trackers, ICEEMS - International Conference onEconomic Engineering and Manufacturing Systems, RECENTJournal, Vol. 8 nr. 3a(21a) (2007), 281-286

[13] Diaconescu D., Visa I., Burduhos B., Saulescu R.: On the StepsOptimization of a Pseudo-Equatorially Tracked PV Panel , 23rd EUPVSEC - 23 rd European Photovoltaic Solar Energy Conference andExhibition, Valencia Spain, 1-5 September 2008, ISBN 3936338 24-8, pg. 3160-3164.

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