New Linkage with Linear Actuator for Tracking PV Systems with Large Angular Stroke

Transcription

1 744 CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 24,aNo. 5,a20 DOI: 0.390/CJME , available online at New Linkage with Linear Actuator for Tracking PV Systes with Large Angular Stroke VIŞA Ion, DIACONESCU Dorin, SĂULESCU Radu, VĂTĂŞESCU Monica, and BURDUHOS Bogdan Renewable Energy Systes and Recycling Research Centre, Transilvania University of Braşov, Roania Received Deceber 23, 200; revised May 6, 20; accepted May 20, 20; published electronically May 25, 20 Abstract: This paper focuses on the developent of an optiized photovoltaic tracking syste involving low-cost, relative siple echaniss, with linear actuators able to insure strokes coparable with those resulted when using gear rotary actuators. Starting with a rhobus linkage, with a linear actuator on the diagonal used for the elevation otion till 90, a new perforance solution is generated. This new linkage allows large angular strokes by using an asyetric rhobus and an eccentrically positioned linear actuator. The paper can be divided in three ain parts. Firstly the kineatical odeling of the new linkage is addressed, which perits the establishing of the linkage diensions according to two adjustable paraeters (k 2, k 5 ). Using the resulted correlations, in the second part the linkage synthesis algorith is developed; the steps followed in this algorith are presented in a nuerical application considering a tracked PV platfor, where the aziuthal vertical oveent is obtained with the new proposed rhoboidal linkage. In the last part of the paper an analysis is done with the ai of deterining the PV platfor tracking efficiency (which represents the ratio between the received and the available bea solar energy) using the new linkage, in the eteorological conditions of Braşov, Roania ipleentation site. Key words: solar tracking linkage, linear actuator, angular stroke, transission angle Introduction Increasing the efficiency of the solar energy conversion in solar photovoltaic (PV) odules can be reached by using tracking systes, by adapting the integrated product to the in-field conditions and by novel solar energy aterials [ 2]. Most of the tracking systes are based on echaniss (equatorial, pseudo-equatorial and aziuth type), providing the solar convertor s orientation by using one or two otions: a daily otion (with a relative high angular stroke, up to 80 ) and an elevation (seasonal) otion with an angular stroke usually up to 90 [3 4]. Practical applications are ainly developed considering the following alternatives [5 6] : a) the daily otion using a gear based echanis (wor, cycloid, ixed haronic, etc), with high transission ratio; b) the elevation otion using linkages with a variable length (e.g., a linear actuator with screw). The tracking otion can be continuous but any applications use a step-wise algorith, because the continuous version iplies huge transission ratios. A coparative analysis of the gear rotary actuators with the linear screw ones shows two iportant aspects [5 7] : a) the Corresponding author. E-ail: bogdan.burduhos@unitbv.ro This paper is supported by the Sectoral Operational Prograe Huan Resources Developent (SOP HRD), Post Doctoral School, financed fro the European Social Fund and by the Roanian Governent (Grant No. POSDRU / 89/.5 / S / 59323) rotary actuators can reach large angular strokes but are expensive due to their coplexity and high technological costs; b) the screw linear actuators are significantly cheaper but can insure only liited angular strokes (20 40 ) as a result of possible blocking. Based on this analysis, the paper focuses on the developent of an optiized tracking syste involving low-cost, relative siple echaniss, with linear actuators able to ensure coparable strokes with those resulted when using gear rotary actuators. One solution is obtained by a serial connection of a triangle echanis (with linear actuator) with an aplifier four bar echanis; although this solution can insure a stroke of 80, it has the disadvantage of a relative large volue. Transforing the four bar echanis into a spatial echanis results in a volue reduction, but the transission angles are decreased [8 9]. Starting with a rhobus linkage having a linear actuator on the diagonal used for the elevation otion [5 6, 0], a new perforance solution is generated. This new linkage allows large angular strokes by using an asyetric rhobus and an eccentrically positioned linear actuator. The kineatical odeling of this linkage and the synthesis algorith, developed for a nuerical exaple of an aziuth tracked PV platfor, are presented in the paper. 2 Linkage Kineatical Modeling The structure of the proposed linkage, presented in Fig. and

2 CHINESE JOURNAL OF MECHANICAL ENGINEERING 745 in Fig. 2, is accopanied by the following notations: D, A, E three collinear points of the basis; AB=AD=l ; BC=CD=l 2 ; DE=l 5 ; EC=s; DAB=a; k 2 =l 2 /l ; k 5 =l 5 /l EC = s ax =l d ; EC 2 =s in =l i ; Δs=l d l i ; k d =l d /l ; k i =l i /l ; k s =k d k i ; k g =l g /l ; b =b in iniu transission angle; b in.ad. iniu aditted transission angle; B 2 and B are the orning position and respectively the evening position of the point B; AS is the bisecting line of the angle B 2 AB and shows the South direction; SAB= ψ. L Based on these figures, the expressions for the sizes c, d, a, k d, k i, k s, e, f, and k g are consequently established considering the ratios k 2 (k 2 = l 2 /l ) and k 5 (k 5 = l 5 /l ) as adjustable paraeters, at accepted intervals. The above entioned sizes and their correlations are used in the geoetric synthesis of the new linkage and in the linkage displaceent function deterining (Fig. (b)): a=a(s). Angle c results fro ΔAB 2 C 2 (Fig. (c)):? AC2B2 c- b, () l l2 =, (2) sin( c- b ) sin c 骣 k2 sin b c = arctan. (2 ) 桫 çk cosb - 2 Angle d results fro ΔADC (Fig. (c)):? ACD b - d, (3) l l2 = sin( b - d) sin d, (4) 骣 k2 sin b d = arctan. (4 ) ç 桫 k cosb + 2 Angular stroke Δa has the expression (Fig. (c)): Δ a= 280 [? ( c+ d) ]. (5) Considering Δ DEC and Δ DEC 2 (Fig. (c)) the following equations result: ( EC ) = l = l + l + 2l l cosb, (6) d ld 2 2 kd = = k5 + k2 + 2k5k2cosb, (7) l ( EC ) = l = l + l - 2l l cosb, (8) i li 2 2 ki = = k5 + k2-2k5k2cosb. (8 ) l Fig.. Tracking rhoboid linkage and its afferent notations

3 746 YVIŞA Ion, et al: New Linkage with Linear Actuator for Tracking PV Systes with Large Angular StrokeY 骣 k sin 5 b? e arcsin - 2( c- b ). ( ) 桫 ç k i In the sae way, considering angle f results: Δ DEE and ΔDEC, the EE = l sin[ 2( b - d) - f ] = l sin b, (2) d 5 骣 sin b f b d ç k i. (2 ) = 2( - )- arcsin 5 ç 桫 k d The iniu distance between the pole axis and the actuator axis AA, is odeled according to the geoetric relations in ΔDEC and ΔAEA (Fig. 2(b)), therefore the easures AA and k g result:? DEC b- [ 2( b- d) - f ], (3) AA = AE i sin( DEC ), (4) AA = l = ( l - l )sin(2 d+ f - b ), (5) g 5 lg kg = = ( k5 - )sin(2 d+ f - b). (5 ) l The displaceent transitting function a=a(s), delivered by the linkage presented in Fig. (b), is deterined by replacing the expression b=b(s), resulted fro ΔEDC (by applying cosine theore), in the expression a=a(b), resulted fro ΔADC (after applying sinus theore and before spelling a angle): 骣 l2 + l5 - s b = arccos, (6) 桫 ç 2ll 2 5 Fig. 2. Linkage extree positions and their afferent notations As a consequence, the following correlation is obtained for actuators stroke (Fig. 2(b)): Angle e results fro Δ s = EC- EC2 = ld - li, (9) Δs k = = k - k. (0) l s d i Δ CEE and 2 2 Δ DEE 2 (Fig. 2(a)): EE = l sin[ e + 2( c- b )] = l sin b, () 2 i 5 骣 l sin b a = 2arctanç. (7) ç 2 桫 çl- l2cosb 3 Linkage Synthesis Algorith and Nuerical Application These correlations allow the developent of the linkage synthesis algorith; the steps followed are presented in a nuerical application, for a PV platfor with an aziuth tracking syste, only after the vertical axis. The aziuth oveent is obtained with the new generated rhoboid linkage, presented in Fig.. The input data (Fig. ) are as follows: () The needed aziuth stroke is Δa=200 ; (2) The iniu adissible transission angle is b in.ad. =30 ; (3) Platfors load allows the length of l =350 ;

4 CHINESE JOURNAL OF MECHANICAL ENGINEERING 747 (4) The available linear actuator has a axiu stroke of s= 000 ; (5) The interference between the actuator and the pole is avoided if l g 00. The output data are as follows: The linkage optiu diensions and the step tracking progra are developed considering that the step duration (ove tie of soe seconds + rest tie) is h. Stage : Eqs. (2 ), (4 ) and (5) allow to obtain a faily of curves Δa=Δa(b in, k 2 ), as presented in Fig. 3, where the k 2 ratio has discreet values in the interval:.75,, For the iposed angular stroke Δa=200, allowing to obtain the iniu transission angles (b =b in ) corresponding to each discreet value of the k 2 ratio. Fig. 3. Angular stroke vs. the iniu transission angle (when k 2 =.75, 2, 2.25, 2.5, 2.75) and the values of the iniu transission angle (b in ) corresponding to the angular stroke: Δa=200 Fro the b in discreet values, only the solutions b in b in.ad. =30 are selected (because only these values avoid the echanis blocking): b in =36.4 >30 for (Δa=200 ; k 2 =2.75); b in =35.6 >30 for (Δa=200 ; k 2 =2.5); b in =34.5 >30 for (Δa=200 ; k 2 =2.25); b in =33 >30 for (Δa=200 ; k 2 =2) and b in =30.6 >30 for (Δa=200 ; k 2 =.75); all these solutions are further systeatized (see Table ). Stage 2: The curves failies of type c = c(b in, k 2 ) and d = d(b in, k 2 ) are developed by using Eqs. (2 ) and (4 ), respectively. For each discreet solution (Δa, k 2, b in ), the failies of curves c = c(b in, k 2 ) and d = d(b in, k 2 ) allow to obtain the corresponding values for the angles c and respectively d (Table ): c=53 and d=27 for (Δa=200, k 2 =2.75, b in =36.4 ); c=54 and d=25.5 for (Δa=200, k 2 =2.5, b in =35.6 o ); c=56 and d=24 for (Δa=200, k 2 =2.25, b in =34.5 o ); c=58 and d=22 for (Δa=200, k 2 =2, b in =33 ); c=60 and d=9.3 for (Δa=200, k 2 =.75, b in =30.6 ). Stage 3: Using Eqs. (7), (8 ) and (0), the failies of curves k d = k d (b in, k 2, k 5 ), k i = k i (b in, k 2, k 5 ), and k s = k s (b in, k 2, k 5 ), are obtained, as presented in further (see Fig. 4). The k 2 ratio has the previous values while k 5 has the discreet values: k 5 =.7; 2 and 2.3 (Table ). Fig. 4. Variations of the ratios k d = l d /l, k i = l i /l and k s = (l d l i )/l (Fig. ) as against of the iniu transission angle (when k 2 = l 2 /l =.75, 2, 2.25, 2.5, 2.75 and k 5 = l 5 /l = 2.0) and the values of the previous ratios corresponding to the angular stroke: Δa=200 (Table ) In Fig. 4 there is presented only the case k 2 =2. For each previous selected discreet solution (Δa, k 2, k 5, b in ), the failies of curves k d = k d (b in, k 2, k 5 ), k i = k i (b in, k 2, k 5 ), and k s = k s (b in, k 2, k 5 ) allow to calculate the corresponding values for the ratios k d, k i and k s, respectively.

5 748 YVIŞA Ion, et al: New Linkage with Linear Actuator for Tracking PV Systes with Large Angular StrokeY Table. Exaples of linkage discreet solutions for the considered application k 2 =l 2 /l b in / ( ) c / ( ) d / ( ) k 5 =l 5 /l.7 e / ( ) f / ( ) k d =l d /l k i =l i /l k s =l s /l k g =l g /l l 2 / l 5 / 595 l d / l i / l s / l g / Δa = 200, bin.ad. = 30 l = 350, Δs = 000 lg 00 k 5 =l 5 /l 2 e / ( ) f / ( ) k d =l d /l k i =l i /l k s =l s /l k g =l g /l l 2 / l 5 / 700 l d / l i / l s / l g / k 5 =l 5 /l 2.3 e / ( ) f / ( ) k d =l d /l k i =l i /l k s =l s /l k g =l g /l l 2 / l 5 / 805 l d / l i / l s / l g / Stage 4: Siilarly, the failies of curves of type e = e(b in, k 2, k 5 ), f = f(b in, k 2, k 5 ), and k g = k g (b in, k 2, k 5 ) can be obtained using Eqs. ( ), (2 ) and (5 ) respectively, as presented in Fig. 5. For each solution (Δa, k 2, b in ), the failies of curves allow to calculate the corresponding values for the angles e and f and for the k g ratio. Choosing the optiu solution, fro the values synthesized (see Table ) or fro the other solutions generated through linear interpolation ust consider the practical application (e.g., the overall size of the linkage, the axiu stroke of the linear actuator, avoiding the actuator-pole collision, etc). According to all these restrictions and considering the given input data, the optiu solution is as follows: Δa=200, k 2 = l 2 /l =2.5, b =b in =35.6, c=54, d=25.5, k 5 = l 5 /l =2, e=20, f=2.57, k d = l d /l =4.3, k i = l i /l =.45, k s = l s /l =2.82, k g = l g /l =0.32, l =350, l 2 =875, l 5 =700, l d = 505, l i =507.5, l s =987, l g =2.

6 CHINESE JOURNAL OF MECHANICAL ENGINEERING 749 轾 Δa ψl =? BAD? SAD a() s - 犏 a( sax) + = ψl(). s 犏臌 2 (7 ) For coparison, in Fig. 6(a) there are also presented the variations of the sun-ray angles (altitude α and aziuth ψ) and the variations of the corresponding platfor angles: α =40 (that is constant) and ψ (that approxiates the ψ solar variation with a step of hourly variation). The orientation laws s=s(t) and iplicitly a=a(t), presented in Fig. 7(a), are obtained cobining the curve ψ =ψ (t) fro Fig. 6(a) with the curve ψ L =ψ L (s) fro Fig. 6(b) and using the equality ψ =ψ L. Based on these, in Fig. 7(b) there are presented the variations of the available direct solar radiation B and the direct solar radiation received on the PV platfor B PV during the Suer Solstice in Braşov / Roania. Fig. 5. Variations of the paraeters e, f and k g = l g /l (Fig. ) as against of the iniu transission angle (when k 2 = l 2 /l =.75, 2, 2.25, 2.5, 2.75 and k 5 = l 5 /l = 2.0) and the values of the previous paraeters corresponding to the angular stroke: Δa=200 (Table ) Using these data, Eqs. (6) and (7), the linkage displaceent transission function a=a(s) is traced in Fig. 6(b), together with the displaceent function deterined fro the previous function, but relative to the South direction AS (Fig. 2(b)): Fig. 6. The ain variations fro Fig. 6 and Fig. 7 are detailed in Table 2 nuerically. To evaluate the perforance of the tracking syste according to a synthetic paraeter, the tracking efficiency ratio is calculated as presented in Refs. [5 6]:

7 750 YVIŞA Ion, et al: New Linkage with Linear Actuator for Tracking PV Systes with Large Angular StrokeY E B.PV η tracking = ; (8) EB where E B [Wh/ 2 ] is the energy of the available bea radiation (B): EB = ò Bdt, (9) and E B.PV [Wh/ 2 ] represents the energy of the received bea solar radiation on the PV surface: E d B.PV = ò BPV t. (20) B 0 Extraterrestrial bea solar radiation in [W/ 2 ] (before entering the atosphere) depending on the day nuber in the year (N), and B0 = 367 i[ icos( ? i N 2.72) ]. (22) Also, B PV [W/ 2 ] represents the received bea radiation on the tracked PV surface: BPV = B i cos ν, (23) where ν represents the incidence angle [5 6], odeled by ν = arccos[cos α i cos α i cos( γ - γ ) + sin α i sin α ]. (24) Appling the sequence of Eqs. (8) (24), the tracking efficiency delivered by the proposed aziuth syste is 94.3%. Table 2. PV tracking progra for the day of suer solstice, in Braşov, Roania Solar tie t/h Angle α/( ) Angle ψ /( ) s/ Conclusions Fig. 7. In these correlations, B [W/ 2 ] represents the available direct solar radiation and is described by Eq. (2) as in Ref. [0]: exp 骣 - T B= B R 0, (2) ç 桫 sinα where T R Turbidity factor for Braşov area: T R 3; () The paper proposes a novel solution of linkages with linear actuators, able to reach large angular strokes, optial for tracking of photovoltaic platfors. (2) Starting fro a planar rhobus linkage, with a linear actuator positioned on an its diagonal, a new linkage was generated through the eccentric disposition of the actuator and by giving up the rhobus syetry, on one of its diagonals; through adequate odeling and kineatical synthesis, this solution allows large angular strokes (above 80 ) as well as reasonable transission angles and a reduced over all size. (3) The optiized eccentric positioning of the linear actuator ensures a favorable load of the linkage s eleents, while the rhobus asyetry leads to a significant increase of the angular stroke. (4) A paraeters set, described by angles (Δa, b, c, d, e

8 CHINESE JOURNAL OF MECHANICAL ENGINEERING 75 and f) and the ratios between the eleent lengths (k 2, k 5, k d, k i, k s, k g ), was used to odel the new linkage geoetrical synthesis; soe of these sizes have iposed values or restrictions (Δa, b, Δs, l g, etc), while others (k 2 and k 5 ) are considered adjustable and were set at specific values, in rational nuerical intervals according to the constructive purposes. Based on the correlations between these paraeters, failies of curves were developed, allowing to obtain an algorith, for the linkage geoetrical synthesis; the steps of the algorith are presented considering a nuerical exaple, of an aziuth tracking progra for a vertical axis PV platfor. (5) Using the optiu diensions resulted in the geoetrical synthesis, the linkage transission function a=a(s) was forulated for the nuerical application; based on it, the step aziuth tracking progra, for the PV platfor, was estiated, during the suer solstice day, considering Brasov, Roania as ipleentation site. Considering the specific geo-eteorological conditions, the tracking efficiency (defined as a ratio between the received solar radiation energy on the PV platfor and the available energy of the solar radiation) was estiated (in the ideal preise of a cloudless sky) at the value of 94.3%. References [] GOSWAMI D J, KREITH K, KREIDER J F. Principles of solar engineering[m]. Philadelphia: George H. Buchanan Co., 999. [2] VIŞA I, DIACONESCU D, POPA V, et al. Synthesis of tracking linkages with increased angular stroke[c]//0th IFToMM International Syposiu on Science of Mechaniss and Machines - Syro 2009, Springer Science Business Media B.V., 2009: [3] DIETER G. Engineering design[m]. Boston: Mc Graw Hill, [4] NORTON R L. Design of achinery [M]. 2nd ed. Mc Graw Hill, 200. [5] BURDUHOS B, DIACONESCU D, SĂULESCU R. The synthesis of a planar linkage used to drive the daily otion of a solar tracker[c]//international Conference on Mechaniss and Mechanical Transissions, Tiişoara, Roania, October 8 0, 2008: [6] POPA V, VIŞA I, DIACONESCU D. Tracking progra optiization for a PV aziuthal syste[c]//24th European Photovoltaic Solar Energy Conference and Exhibition, Haburg, Gerany, Septeber 2 25, 2009: [7] MAZEN M, OMAR O B A, SALAH A. Evaluating ulti-axes sun-tracking syste at different odes of operation in Jordan[J]. Renewable and Sustainable Energy Reviews, 2008, 2: [8] CHOJNACKI J A, TENETA J, WIECKOWSKI L. Influence of the accuracy of positioning of the photovoltaic syste on electrical paraeters and on the quantity of produced electric power[c]//23rd European Photovoltaic Solar Energy Conference, Valencia, Spain, Septeber 5, 2008: [9] DUDIŢĂ F, DUDIŢĂ F, DIACONESCU D, et al. Articulated obile couplings[m]. Ed. Orientul Latin, 200. (in Roanian) [0] MELISS M. Renewable energy sources practice[m]. Berlin: Springer Verlag, 997. (in Geran) Biographical notes VIŞA Ion, born 949, is currently a professor and the Rector of Transilvania University of Braşov, Roania. He is also the initiator of two ajor training lines in Roania: Product Design and Renewable Energy Systes and the President of the Roanian branch of the International Association for Prooting the Mechanis Science, IFToMM. Starting with 2009, the ajor university project GENIUS was launched under the coordination of Prof. Visa, aiing to build a new green, energy independent university capus, open to advanced training, research and cooperation with econoic partners on sustainable energy. His current research interests include echanical systes and renewable energy systes. E-ail: visaion@unitbv.ro DIACONESCU Dorin, born in 947, is currently a professor at Transilvania University of Braşov, Roania. He received his PhD degree fro the Transilvania University of Braşov, Roania, in 982. His current research interests include conceptual design of products, echaniss, echanical transissions, obile couplings. E-ail: dvdiaconescu@unitbv.ro SĂULESCU Radu, born in 976, is currently a lecturer at Transilvania University of Braşov, Roania. He received his PhD degree fro the Transilvania University of Braşov, Roania, in His current research interests include conceptual design of products, echaniss, echanical transissions. E-ail: rsaulescu@unitbv.ro VĂTĂŞESCU Monica, born in 984, is currently PhD candidate at Transilvania University of Braşov, Roania. Her thesis will present the optiization of a dual-axis aziuth tracking syste, fitted with one aziuth actuator and a spatial linkage of RRSS type, ipleented in Brasov/Roania geographic area. E-ail: aria.vatasescu@unitbv.ro BURDUHOS Bogdan, born in 982, is currently a postdoctoral researcher at Transilvania University of Braşov, Roania. He received his PhD degree fro the Transilvania University of Braşov, Roania, in His current research interests include renewable energy systes and photovoltaic sun-tracking systes. E-ail: bogdan.burduhos@unitbv.ro