PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS Prog. Photovolt: Res. Appl. 2002; 10: (DOI: /pip.442)

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1 PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS Prog. Photovolt: Res. Appl. 2002; 10: (DOI: /pip.442) Applications Design of Tracking Photovoltaic Systems with a Single Vertical Axis E. Lorenzo 1, *,y,m.pérez 2, A. Ezpeleta 3 and J. Acedo 4 1 Instituto de Energía Solar, ETSI Telecomunicación, Ciudad Universitaria, s/n, 28040, Madrid, Spain 2 Alternativas Energéticas Solares, Pol Industrial La Nava, 1, 31300, Tafalla, Naavarrsa, Spain 3 Energía Hidroeléctrica Navarra, C/Yanguas y Miranda, 1, 31002, Pamplona, Spain 4 Ingeteam SA, C/Pintor Maeztu, 2, 31008, Pamplona, Spain Solar tracking is used in large grid-connected photovoltaic plants to maximise solar radiation collection and, hence, to reduce the cost of delivered electricity. In particular, single vertical axis tracking, also called azimuth tracking, allows for energy gains up to 40%, compared with optimally tilted fully static arrays. This paper examines the theoretical aspects associated with the design of azimuth tracking, taking into account shadowing between different trackers and back-tracking features. Then, the practical design of the trackers installed at the 14 MW Tudela PV plant is presented and discussed. Finally, this tracking alternative is compared with the more conventional fully stationary approach. Copyright # 2002 John Wiley & Sons, Ltd. INTRODUCTION Solar tracking remains an interesting option for PV generation, especially when medium/large gridconnected PV plants are concerned. High reliability and low maintenance requirements have been demonstrated in several practical projects. 1 2 The Toledo PV Plant, for example, where a 1000-m 2 tracking system has been in routine operation since July 1994, with 100% availability. This can be interpreted as a mean time between failures below h, which speaks for itself. Single, horizontal, North South-oriented axis structures associated with flat-plate modules represent by far the most extended tracking solution in current PV plants. 2 4 Because of their inherent lack of shadowing in the North South direction, single tracking devices can drive large surfaces and, owing to the horizontal axis position, associated wind loads tend to be relatively low. It involves a particularly simple and robust mechanical construction, which is a major advantage of this type of tracking. Coming back to the Toledo PV plant, its tracker is formed of four 250-m 2 surfaces, each powered by a single 025-HP standard AC motor. North South oriented horizontal single axis tracking also plays a major role in solar thermal electric technology. In particular, it has been selected for the famous LUZ-developed power plants, 5 totalling m 2 aperture area, which began operation in southern California in However, the horizontal axis position limits energy collection by the tracking surface. This depends on the solar climate and latitude site,, and can be quantified by comparison with the energy collected by an ideal twoaxis tracking, which represents the largest solar radiation potential for a particular location. Table I presents * Correspondence to: E. Lorenzo, Instituto de Energía Solar, ETSI Telecomunicación, Ciudad Universitaria, s/n, 28040, Madrid, Spain. y Lorenzo@ies-def.upm.es Contract/grant sponsor: EC; contract/grant number: NNE5/1999/547. Published online 17 September 2002 Received 31 December 2001 Copyright # 2002 John Wiley & Sons, Ltd. Revised 16 March 2002

2 534 E. LORENZO ET AL. Table I. Yearly solar energy collection in several locations Location ( ) Clearness index a G a0 b, (kw h m 2 ) Two-axis/G a0 c Horizontal/G a0 d Azimuth/G a0 e Static/G a0 f Medellin Morelia Cayro El Paso Tudela Freiburg St Petersburg Ice-Island a Ratio (global horizontal/extraterrestrial) irradiation. b Global horizontal irradiation. c Ratio (two axis tracking/horizontal) irradiation. d Ratio (one North South horizontal axis tracking/horizontal) irradiation. e Ratio (one azimuth axis tracking/horizontal) irradiation. f Ratio (optimally tilted static/horizontal) irradiation. some examples calculated on a yearly basis. This table has been compiled from solar radiation data contained in the H-World database, 6 except for the case of Tudela, where radiation data has been provided by the Regional Meteorological Services of Navarra. Although it does not affect the central message of this paper; it is worth mentioning that significant data differences are found for the same location, when consulting different sources of solar radiation data. The major motivation for the development of other one-axis tracking alternatives is to overcome this limitation, while keeping the mechanics fairly simple. This is the case for the 14 MW PV plant installed in Tudela (Spain), which is formed of 400 azimuth trackers. This type of tracker rotates around its vertical axis, in such a way that the azimuth of the receiver surface is always the same as the Sun s azimuth, while its tilt angle remains constant. Calculation of the solar radiation collected by ideal tracking is rather straightforward, the basic rules are well defined in classical books on solar radiation. 7 Some results in Table I show that azimuth tracking represents an energy collection increase, in comparison with horizontal axis tracking, of about 10%. It can also be seen that the advantages of tracking energy increase for both latitude and clearness index. In the case of Tudela, the energy collected by an ideal azimuth tracker is about 40% higher than that corresponding to an optimally tilted static surface. When several trackers are arranged together, mutual shadows give rise to a design optimisation problem. The lower the spacing between adjacent trackers, the lower is the gross land occupation and, therefore, the lower the land-area-related costs (land, civil works, wiring, etc.). On the other hand, the larger the impact of shadowing, the greater is the detrimental effect on the electricity generation of the PV plant. This paper first examines the theoretical aspects of this problem, by relating the collection of energy to the relevant design parameters, namely, the tilt angle and the aspect relation (length/width) b of the single tracked surfaces, and the spacing between adjacent trackers in North South and East West directions, l NS and l EW, respectively. The so-called Back-tracking 8 features are also considered as a mean of reducing shadowing impact. Then, a cost-optimisation exercise is performed for the particular case of the recently installed 14 MW Tudela PV plant, and some general conclusions are outlined. GEOMETRY OF SHADOWING Let us consider a set of azimuth trackers arranged as shown in Figure 1. Note that the ground cover ratio (GCR), defined as the ratio of total PV module area to total gross land area, is given by: GCR ¼ b l NS l EW ð1þ

3 SINGLE-AXIS TRACKING PV SYSTEMS 535 Figure 1. Design parameters of a tracking field: (a) tilt angle ; (b) aspect relation b; (c) spacing between adjacent trackers in North South and East West directions, l NS and l EW Figure 2. (a) Solar coordinates: azimuth S, and elevation S ; (b) incidence angle of the beam radiation S Figure 2 shows the solar angular coordinates: solar azimuth S, and solar altitude S ; and the incidence angle of the beam radiation on the tracking surface S. Straightforward geometrical considerations lead to: S ¼ 2 S ð2þ East West shadowing Depending on the Sun s position, partial shadowing between two adjacent trackers may occur, mainly in the early morning and late afternoon. Figure 3 shows a case of shadowing in the East West direction. The horizontal projections of two adjacent tracked surfaces and their corresponding mutual shadowing are presented in Figure 3(a), and additional geometrical details are given in Figure 3(b). Note that shadowing occurrence requires two simultaneous conditions. First, the shadow should point to the adjacent tracker and, second, its length should be large enough to reach it. This can be described by introducing a parameter FS EW, being 1 when ideal tracking leads to shadowing occurrence and 0 otherwise. Thus: ðl EW cos S Þ < 1 and ðl EW sin S Þ < s ¼ s 1 þ s 2 ) FS EW ¼ 1 ð3þ

4 536 E. LORENZO ET AL. Figure 3. East West shadowing in ideal tracking. Horizontal projection of: (a) trackers and shadows; (b) a meridian plane where s 1 ¼ b cos and s 2 ¼ b sin cot S ð4þ Because of the finite dimensions of the PV field, East West shadowing unavoidably occurs at in some times during the year ( S! =2 and S! 0, close to sunrise at the equinoxes). When shadowing occurs, it can be avoided by moving the surface s azimuth angle away from its ideal value, just enough to get the shadow borderline to pass through the corner of the adjacent surface (Figure 4). The new surface s azimuth, 0, is given by: 0 ¼ S FS EW ^A C ð5þ where ^A C is the azimuth correction angle, which can be found by analysing the triangles SS 1 S 2 and T 1 S 2 T 2. From the first: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ¼ s 2 1 þ s2 2 þ 2s 1s 2 cos ^A C ð6þ Figure 4. Surface azimuth necessary to avoid East West shadowing 0

5 SINGLE-AXIS TRACKING PV SYSTEMS 537 sin ^S 2 ¼ s 2 s sin ^A C ^1 ¼ 2 S þ ^A C ^S 2 ð7þ ð8þ and from the second: bt 2 ¼ 2 þ ^S 2 ð9þ sin bt 2 ¼ l EW sin ^1 ð10þ The solution of the system formed by Equations (6 10) leads to the value of ^A C. It is worth noting that: ¼ 2 ) ^A C ¼ cos 1 ðl EW cos S Þ ð11þ which represents a maximum limit for the ^A C value for the general case. Because such a maximum always avoids shadowing, it can be used as a rough approximation to the general case. This non-ideal tracking mode is called back-tracking, and has sometimes been implemented in horizontal single-axis tracking. 8 9 Figure 5 shows the evolution of the surface s azimuth at an equinox. One can note that the surfaces begin each day facing South, and gradually rotate towards the East, to avoid shadowing, until some time in the morning, when they reverse direction and rotate West to minimise the beam incidence angle. Then, there is no difference between ideal and back-tracking strategies, until the low afternoon Sun s elevation and ideal tracking strategy would produce shadowing again. Once more the back-tracking reverses direction and gradually returns to face the South. North South shadowing Figure 6 shows the horizontal projection and a tracked surface with its corresponding shadow for a general case. North South shadowing requires, first, that the shadow falls behind the front line of the rear trackers row, and, second that shadow points toward some tracker, and not towards the free space among them. A conservative approach (reasonable for low l EW values) consists of assuming that shadowing occurs just when the first Figure 5. Surface azimuth angle plotted against solar time

6 538 E. LORENZO ET AL. Figure 6. North South shadowing; horizontal projection of a tracker and its shadow condition is fulfilled. This can be described by defining a parameter FS NF, being 1 when North South shadowing occurs and 0 otherwise. Thus: l NS < s sin ^1 þ sin 0 ) FS NS ¼ 1 ð12þ ENERGY PRODUCED BY THE PV PLANT For simplicity, let us consider that all the solar cells of a single-tracked surface are associated in series, that the cell size is negligible compared with the surface size, and that the PV field is large enough to neglect border effects. Note that in the hypothetical situation of only beam radiation, the simple shadowing event would annul the output of the whole PVarray. Thus, neglecting the albedo, the electrical power from the PV field is given by: P ¼ A FS NS Bð; 0 ÞþDð; 0 Þ ð13þ where and A are the global efficiency of the PV plant, and Bð; 0 Þ and Dð; 0 Þ are the beam and diffuse irradiances incident on the tracked surfaces. The annual electrical energy produced by the PV plant, E PV,is given by the integral of P over the whole year, and is easily calculated from widely available horizontal solar radiation data, following classical procedures to translate from horizontal to inclined surfaces. 10 In particular, we have developed an hourly-based software application that uses as input the twelve monthly mean values of the horizontal global daily irradiation. It considers the diffuse global correlation proposed by Collares Pereira and Rabl, 11 the Liu and Jordan method 12 to estimate hourly irradiation values from the daily irradiation, and the model proposed by Hay and McKay 13 to estimate the circumsolar and isotropic components of the diffuse solar radiation. Then, the circumsolar radiation has been treated as beam radiation for consideration of shadowing. On the other hand, we have estimated the global efficiency of the PV plant by considering separately each phenomenon that affects its behaviour, as indicated by the following expression: ¼ TC AL INV ð14þ where * is the efficiency of the PV array under standard test conditions (STC), TC takes into account the dependence of the efficiency on the operating temperature of the solar cells, 14 AL takes into account the angular reflection losses at the PV module surface, 15 and INV considers the DC-to-AC conversion losses. 16

7 SINGLE-AXIS TRACKING PV SYSTEMS 539 Figure 7. Relative yearly energy production of ideal one-axis trackers plotted against tilt angle for several locations In this way, a value for annual energy production can be calculated for each PV field configuration, i.e., for each set of, b, l EW and l NS values, given the characteristics of the PV modules and the inverter composing the PV plant. Obviously, the largest possible energy yield corresponds to the case of only one tracked surface, which excludes mutual shadowing and allows for fully ideal tracking. Just for this case, Figure 7 shows the relative variation of the energy yield, as a function of the angle of inclination of the tracked surface, for several locations. It can be seen that, irrespective of the site, a maximum occurs for an inclination close to the latitude plus 10. It is very interesting that the sensitivity of the annual capture of energy for the inclination angle is very low. A value of approximately 04% loss for each degree of deviation from the optimum value is roughly indicative of the situation. A descriptive empirical expression is: E PV ðþ E PV ð opt Þ ¼ a 0 þ a 1 ð opt Þþa 2 ð opt Þ 2 ð15þ l¼1 where is the site latitude, opt ¼ þ 10 ; a 0 ¼ 1; a 1 ¼ , and a 2 ¼ It is interesting to note that, because the product A is scarcely related to the inclination angle, such functions are essentially independent of the PV module and inverter type. Hence, they describe not only the energy produced by the PV field, but also the energy collected by the PV array. OPTIMAL DESIGN A rough approximation to the produced energy unit cost C E can be made by assuming that it is a linear function of the ratio between the total investment cost and the yearly energy yield. Furthermore, the total investment cost can be divided into a term related to the gross land area (wiring, civil works, fencing, land, etc.) and another term independent of it (PV modules, tracking structures, inverters, etc.). Thus: C E ¼ a ð p 1 p þ l EW l NS N T p 2 Þ ð16þ E PV where p 1 is the cost per unit of peak power of the PV system excluding land, p* is the STC power of the PV array, p 2 is the land area related cost per unit area, N T is the number of trackers composing the PV field, and a is a parameter accounting for the evolution of the economy (discount rate, inflation, etc.). The cheapest conceivable energy cost corresponds to the hypothetical case of only an optimally tilted ideal tracker and no land occupation. It is worth using this case as a reference. Thus: C E C REF E ¼ EREF PV E PV 1 p 2 1 þ GCR G STC p 1 ð17þ

8 540 E. LORENZO ET AL. Table II. Input data for the design of the Tudela PV plant Latitude( ) 421 Reference year, m ¼ 1 12 Global horizontal daily irradiation (W h m , 3184, 4637, 5777, 6611, 7183, 7494, 6489, 5000, 3247, 2118, 1582 Maximum daily temperature ( C) 69, 74, 126, 154, 194, 246, 261, 280, 210, 137, 95, 91 Minimum daily temperature ( C) 07, 10, 36, 54, 91, 127, 130, 146, 112, 70, 33, 32 PV module dimensions (mm) PV array STC efficiency (%) 133 Inverter efficiency parameters 16 k 0 ¼ 001, k 1 ¼ 0025, k 2 ¼ 005 Cost parameters p 1 ¼ 66 s/w p ; p 2 ¼ 6 s/m 2 This ratio represents the relative unit energy cost associated with a particular PV field configuration, and is particularly well suited to judge the merit of its design. The Tudela PV plant Table II summarises the required input data for the optimisation design of the Tudela PV plant. The most obvious criterion is to seek to lower the unit energy cost, i.e., to select the configuration leading to the minimum value of the ratio described by Equation (17). A simple approach consists of the successive optimisation of each configuration parameter. In this way, an inclination equal to opt is first selected. Figure 8 shows the cost ratio as a function of b and l EW, for a given l NS. It is noticeable that the lowest b gives the lowest the energy cost. However, there are practical limits to b. On the one hand, values lower than b 05 imply lengthy pedestal structures, which are inherently unstable in strong winds. On the other hand, all the PV modules of a single series string should be installed in the same tracker to avoid mismatching losses. In our case, the pre-established DC nominal voltage of the PV field (450 V) requires each string to be formed by 36 PV modules, for which 8 different arrangements can be imagined: 1 36, 2 18, 3 12, 4 9, 6 6, 9 4, 12 3 and Moreover, each arrangement can adopt two different physical dispositions, depending on the PV module side chosen as the length. Hence, 16 values for b, ranging from 0012 to 817, are possible. We have finally selected a 3 12 arrangement leading to b ¼ 05675, which is shown in Figure 9. Coming back to Figure 8, it can be seen that the optimum value of l EW is about 23. Now, Figure 10 shows the variations of the cost ratio as a function of l NS, for ¼ opt ; b ¼ and l EW ¼ 23. The ratio (E PV /EPV REF)is also shown. Again, an optimum l NS value around 23 is observed. Hence, the strict optimum design corresponds to a GCR 01, which is much larger than usual values in common PV fields, and has adverse aesthetic implications (trackers too sparsely placed), which can not be neglected in highly visible demonstration Figure 8. Relative energy production (dashed lines) and cost ratio (dotted lines) plotted against East West spacing; tracking aspect relation b is used as parameter

9 SINGLE-AXIS TRACKING PV SYSTEMS 541 Figure 9. Selected tracker for the Tudela PV plant: (a) front; (b) back. The driven mechanism can be observed Figure 10. Relative energy production (dashed line) and cost ratio (dotted line) plotted against North South spacing projects, such as the present case. Because of this, we also have analysed other less land-consuming alternatives. Fortunately, they are largely favoured by the low sensitivity of the unit energy cost to the GCR. The same is true for the energy yield. For example, the figures of merit for the optimal case are (C E /CE REF ) ¼ 1166 and (E PV /EPV REF) ¼ 0923, while for l EW ¼ 1547 and l NS ¼ 2012, the values are (C E /CE REF ) ¼ and (E PV /EPV REF ) ¼ 085 and GCR ¼ In other words, selecting this case implies a 67% energy cost increase, but a 41% reduction of the total occupied land. We have finally selected this case because it adapts particularly well to the available terrain. Figure 11 shows a general view of the plant. Table III presents the yearly performance parameters for this case, as estimated by the model. The corresponding performance ratio, 17 defined as the ratio between the final yield and the on-plane irradiation, is 082, which is rather optimistic when comparing it with current experimental values. The reason lies in the different losses not considered by the model: wiring, dirt, mismatching, supplied PV power below nominal values, etc. Together, they will probably amount to an 11% energy production decrease, leading to a performance ratio of about 073. DISCUSSION We fully understand the reader s surprise when realising that, after the two rather tedious tasks of developing a full behaviour model for the PV plant, and performing a cost optimisation exercise, our final design differs from

10 542 E. LORENZO ET AL. Figure 11. General view of the Tudela PV field Table III. Estimated annual energy performance of the Tudela PV plant Model estimates Horizontal irradiation (kw h m 2 ) 1680 On-plane irradiation (kw h m 2 ) 2366 Effective on-plane irradiation (kw h m 2 )* 2235 Array DC energy yield (kw h kw 1 p ) 2100 PV plant AC final yield (kw h kw 1 p ) 1941 Performance ratio 082 More realistic estimates Other losses (%) 11 PV plant final yield (kw h kw 1 p ) 1728 Performance ratio 073 *Considering shadowing and reflection losses. Table IV. Optimal GCR versus different economic scenario p 2 /p 1 * Optimal GCR *In units of (currency/m 2 )/(currency/w p ). the optimal one, and attaches importance to aesthetic considerations. We also understand the tendency to believe that the usefulness of the model presented is restricted to clarifying the geometry of back-tracking for azimuth tracking, and to estimating the energy performance of the PV field. However, the model can be used to study other relevant problems, such as the sensitivity of the design to economic factors, and the comparison of tracking with conventional static alternatives. For the first point, and because PV modules and tracking structures are expected to become cheaper in the future, we have analysed the variation of the optimal GCR with respect to the ratio p 2 /p 1. Table IV shows the corresponding results. Roughly, a five-fold increase in cost ratio is translated into a two-fold decrease of the required area. It is worth mentioning that the particular circumstances of the Tudela PV project have led to very low p 2 and high p 1, i.e., to a rather low p 2 /p 1 ratio. In our opinion, p 2 /p 1 close to 13 is a more representative value for possible commercial PV plants. For the second point, we have performed a similar design optimisation exercise for a hypothetical PV field composed of fully static conventional support structures, and also operating in Tudela. For the same values of p 1 and p 2, the result is an optimal GCR ¼ 038, but the corresponding energy cost ratio (C E =CE REF )is148. Compared with the actual tracking plant, the static PV plant would require only about 60% of the land, but the energy cost would be 28% higher.

11 SINGLE-AXIS TRACKING PV SYSTEMS 543 CONCLUSIONS This paper has discussed the theoretical aspects of azimuth tracking, including shadowing and back-tracking. From them, a model capable of analysing the relation between the configuration of tracking PV plants (tilt angle, aspect relation and spacing) and their energy performance and energy cost have been also presented. This model has been used on the design of the 14 MW PV plant, recently installed in Tudela (Navarra, Spain). The finally selected value of the GCR is 0182, and the expected yearly energy yield is about 1700 kw h kw p 1. The comparison with conventional static arrangements shows that azimuth tracking land requirements are about 40% larger than conventional static arrangements, but the corresponding energy cost can be significantly reduced, providing the tracking structure s cost is kept close to the static structures. Acknowledgements This work has been supported by the European Commission, under contract NNE5/1999/547. The authors would like to acknowledge the helpful collaboration of all the persons involved in this project. The Diputación Foral de Navarra has been kind in providing the radiation data. REFERENCES 1. Jennings C, Farmer B, Townsend T, Hutchinson P, Gough J, Shipman D. PVUSA The first decade of experience. Proceedings of the 25th IEEE PVSC, Washington, DC, 1996; Lorenzo E, Maquedano C. Operational results of the 100 kw p tracking PV plant at Toledo-PV project. Proceedings of the 13th European PV Solar Energy Conference, Nice, 1995; Stern MJ, West RT. Development of a low cost integrated 15 kw A.C. solar tracking sub-array or grid connected PV power system applications. Proceedings of the 25th IEEE PVSC, Washington, DC, 1996; Illiceto A, Previ A, et al. Progress report on ENEL s 33MW p PV plant. Proceedings of the 12th PV Solar Energy Conference, Amsterdam, 1994; De Laquil III P, Kearney D, Geyer M, Diver R. Solar-thermal electric technology. In Renewable Energy: Sources from Fuels and Electricity. Island Press: Washington, 1993; H-World database. Mean Values of Solar Irradiation on Horizontal Surface. Distributed by CENSOLAR, Sevilla, Duffie JA, Beckman WA. Solar Engineering of Thermal Processes, 2nd edn. Wiley: New York, Panico D, Garvison P, Wenger H, Shugar D. Backtracking: a novel strategy for tracking PV systems. Proceedings of the 22nd IEEE Photovoltaic Specialist Conference, Las Vegas, 1991; Lorenzo E, Macagnan M. Considerations in the design of a one-axis tracking photovoltaic system. Progress in Photovoltaics: Research and Applications 1994; 2: Iqbal M. An Introduction to Solar Radiation. Academic: Ontario, Collares Pereira M, Rabl. The average distribution of the solar radiation correlations between diffuse and hemispherical and between daily and hourly insolation values. Solar Energy 1979; 22: Liu BYH, Jordan RC. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Solar Energy 1960; 4: Hay JE, McKay DC. Estimating solar irradiance on inclined surfaces. Solar Energy 1979; 23: Green MA. Solar Cells. Prentice-Hall: Kensington, Martin N, Ruiz JM. Calculation of the PV modules angular losses under field conditions by means of an analytical model. Solar Energy Materials and Solar Cells 2001; 70: Schmid J, Schmidt H. Inverters for photovoltaic systems. Proceedings of the 5th Contractor s Meeting of the Photovoltaic Demonstration Projects, Ispra, Italy, 1991; Guidelines for the assessment of PV plants. Document B: analysis and presentation of monitoring data, JRC of the European Union. Report EUR EN, Ispra, Italy, 1995.