Case study showing that the tilt angle of photovoltaic plants is nearly irrelevant

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1 Available online at Solar Energy 85 (2011) Case study showing that the tilt angle of photovoltaic plants is nearly irrelevant S. Beringer, H. Schilke, I. Lohse, G. Seckmeyer Institute of Meteorology and Climatology (IMuK), Gottfried Wilhelm Leibniz University of Hannover, Herrenhäuser Str. 2, Hannover, Germany Received 8 May 2010; received in revised form 13 December 2010; accepted 16 December 2010 Available online 28 January 2011 Communicated by: Associate Editor Nicola Romeo Abstract What is the optimum tilt angle of photovoltaic plants in mid-latitudes? This question is of practical importance for the mounting of photovoltaic systems. The present work states a nearly irrelevant difference of the yearly performance of solar cells at various tilt angles. The measuring system included eight multicrystalline silicium solar cells and was mounted on the roof of the Institute of Meteorology and Climatology (IMuK) in Hannover, Germany, for a 1-year period that started from November 2008 until October Each solar collector was mounted at a different tilt angle between 0 and 70 in steps of 10, in a southward orientation. The measurements covered the short circuit current (I sc ), the open circuit voltage (U oc ) and the cell temperature (T) of each cell. From this the maximum power (P mp ) was calculated and analysed. The data has been assessed for monthly sums. Maximum values of P mp were found to appear in a wide angular range, about in the winter months and 0 30 in the summer months. The yearly optimum tilt angle was found to be nearly the same as for summer months. The largest difference of the plant yield was less than 6% for tilt angles between 0 and 70. This holds for both yearly sum and for the summer months. Theoretical calculations performed with INSEL software, however, showed larger deviations than the experimental findings. This is probably due to temperature effects, which tend to level off differences at different incident angles. Further investigations are necessary to test whether the tilt angle is generally irrelevant or whether other sites or years will show different results. Ó 2010 Elsevier Ltd. All rights reserved. Keywords: Tilt angle; Photovoltaic; Solar cells; Experimental; Maximum power 1. Introduction Energy production by solar power systems has found a ready market in the last decade, and is currently experiencing a boom that is not least due to government aid. These subventions are to be decreased to lower costs for customers. This is why it is important to optimise any aspect of solar power systems, and hence, make them more economic. One way is to install the solar collectors in the correct tilt and orientation angle, in which they would obtain the Corresponding author. addresses: beringer@muk.uni-hannover.de (S. Beringer), (H. Schilke), insa.lohse@t-online.de (I. Lohse), seckmeyer@muk.uni-hannover.de (G. Seckmeyer). maximum insolation over a specific period of time. The tilt angle depends mainly on the position of the sun and, therefore, differs from location to location in the world. The best orientation angle is advised to be directed towards the equator. There are already plenty of investigations dealing with this subject to optimize solar power systems according to the correct tilt angle or orientation. Many authors have provided empirical or analytical models to calculate the optimum tilt angle (b opt ) by searching for the maximum total solar radiation on the collector surface. In reference to a specific period of time and purpose, daily, monthly, seasonal or yearly values have been calculated, e.g. (EL-Kassaby, 1988; Soulayman, 1991; Ibrahim, 1995; Lewis, 1987). Elsayed (1989) also presented an analytical model based on long-term averaging of solar data. He outlined values of X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi: /j.solener

2 S. Beringer et al. / Solar Energy 85 (2011) Nomenclature b opt optimum tilt angle ( ) D difference between angles of minimum and maximum values of P mpmon ( ) U latitude C 1 C 8 numbers of solar cells E tilt calculated irradiances on tilted surfaces and cumulated according to P mp (W h m 2 ) I 0 diode current (A) I il current generated by illumination (A) I mp current at maximum power point on I U-curve (A) I sc short circuit current (A) k Boltzmann constant ( JK 1 ) m diode factor () N meas number of measuring days number of days of each month N mon P mp power at maximum power point on I U-curve (W) P mpmon monthly cumulated values of P mp (W h) q charge ( C) R s inner resistance (X) T cell temperature ( C) U T thermal voltage (V) U mp voltage at maximum power point on I U-curve (V) U oc open circuit voltage (V) IMuK Institute of Meteorology and Climatology INSEL INtegrated Simulation Environment Language ISFH Institute for Solar Energy Research Hameln PVSYST Software for photovoltaic systems TRNSYS TRaNsient SYstems Simulation optimum tilt angles given in different literature and conducted that value of tilt angle that can be recommended. In fact there is a wide range of tilt (±20 ) dependent on the applied model and the location. Some authors noted a correlation between the optimum tilt angle and the latitude. Frequently, it is recommended to apply the rule of thumb, in which the yearly optimum tilt angle is about U ±10 (U: latitude) and a difference of tilt with about 10 would hardly affect the performance. Gunerhan and Hepbasli (2007) determined monthly optimum tilt angles for Izmir, Turkey. They found the optimum tilt angle (b opt ) to be equal to U throughout the year, while for summer b opt = U 15 and for winter b opt = U +15 was suggested. They advised to mount the solar collector at the monthly average tilt angle. During the last decade there have also been investigations by using simulation software. This software, which was developed in order to simulate an entire solar power plant, takes the most influential parameters into account. The software usually possesses a database of monthly mean global radiation data and different empirical models. For example Hussein and Ahmad (2004) applied the simulation software TRNSYS to calculate the optimum tilt angle for Cairo, Egypt. They calculated monthly mean solar radiation data and compared it with the output power of solar cells. They stated the yearly optimum tilt angle to be U U 10. Cheng et al. (2009) used the simulation software PVSYST to investigate the correlation between the tilt angle of a fixed solar collector and the latitude. Their calculations encompassed 20 locations on the northern hemisphere. Hence, a solar power plant yields an average of 98.5% of its full capacity using the latitude angle for the tilted panel. There are just a few experimental studies however that present long-term measurements of the output power of solar cells at different tilt angles. In most cases, irradiances were measured at different tilt angles with pyranometers. Another investigation conducted by Nakamura et al. (2001) refers to temperature dependency and output power of solar cells in Hamamatsu, Japan. They adjusted pyranometers and solar panels at six different orientations and three tilt angles. Their analysis covered only sunny days in a period of 6 months (September February). For this period the optimum tilt angle was found to be 30 facing south, i.e. b opt U. The previous review shows that there is a wide range of stated optimum tilt angles in different literature. Therefore many investigations refer to only certain locations, especially to subtropical areas. Some authors, e.g. (EL-Kassaby, 1988) conducted calculations that includes midlatitudes and high-latitudes as well, but there are just a few results obtained from measurements. With regard to photovoltaics, the optimum electric power for a certain period is of economic interest. The electric power of a solar cell is defined as the product of electric current and voltage (P = I U) that is a function of the irradiance and the temperature P = f(e,t). Although P increases in higher irradiances, it decreases in higher temperatures. In general, higher irradiances lead to higher temperatures of the solar collector and, hence, the performance is reduced. Furthermore, the reflection characteristics of the collector surface should be taken into account. As presented by Balenzategui and Chenlo (2005), diverse surface covers behave differently according to reflection losses. For this reason the objectives of this paper are as follows: (1) To provide experimental measurements to state the monthly optimum tilt angle for Hannover, Germany, whose location aptly represents the cloudy midlatitudes weather conditions. Therefore, the maximum electric power (abbr.: maximum power mp)

3 472 S. Beringer et al. / Solar Energy 85 (2011) is calculated. Additionally, the difference among the tilt angles is evaluated. (2) To assess seasonal and yearly optimum tilt angles and to outline the monthly total amount of electric power. (3) To use a simulation software to provide solar radiation data on tilted surfaces for the purpose of comparison. 2. Experimental setup The developed setup consisted of eight solar collectors, three data loggers, holders for the different tilt angles as well as some electronic devices. The solar cells were manufactured from multicrystalline silicium at the Institute for Solar Energy Research Hameln (ISFH), Germany. See Table 1 for detailed technical specifications. Each collector was mounted at a different tilt angle with the following assignment: C 1 =0, C 2 =10, C 3 =20, C 4 =30, C 5 = 40, C 6 =50, C 7 =60 and C 8 =70. The orientation angle of all collectors was directed towards south. The measuring system was then installed on the roof of the Institute of Meteorology and Climatology (IMuK) for a period of 1 year (see Fig. 1). The measuring system was designed to carry out continuous measurements, starting from the middle of November Data was recorded until the end of October The measurements included the short circuit current (I sc ), the open circuit voltage (U oc ) and the cell temperature Table 1 Specifications of the solar cells as given by the manufacturer. General specifications Material Multicrystalline silicium Surface Anti-reflection coating and glass cover Measures Length: 125 mm, width: 125 mm, depth: 200 lm Electrical specifications at E = 1000 W m 2 and T =25 C Nominal power P 2.4 Watts [W] Nominal current I sc 6.0 Ampere [A] Nominal voltage U oc 0.6 Volt [V] Table 2 Daily available data sets of the measured solar cell parameters (I sc, T and U oc, T). Month Daily available data sets November 17 December 17 January 24 February 17 March 29 April 27 May 25 June 29 July 22 August 18 September 28 October 21 (T) of each cell. The data loggers were adjusted to record the mentioned cell parameters every 20 s. Furthermore, an electric circuit was applied to switch between I sc and U oc, so that every 20 s the data set I sc, T and U oc, T of all solar cells was available alternately. Afterwards the data was stored on a PC card, filtered and reduced to mean values for every minute. In further processing, data with bad quality was sorted out, i.e. measurements that were destroyed by certain weather conditions (snow, ice) or that were interrupted by a system failure. Therefore relevant daily data sets were not taken into account. In Table 2 the daily available data sets are listed. 3. Data analysis and results From the measured solar cell parameters (I sc,u oc,t) the maximum power (P mp ) was then calculated. The maximum power of a solar cell is the point on the I U characteristic curve, at which the product P = I U is at its maximum value. The relation between I and U for an illuminated solar cell is given by the equation (Wagner, 2006): I ¼ I il I 0 e UþIRs U T 1 ð1þ or expressed by U U ¼ U T ln I il I þ I 0 IR s : ð2þ I 0 In the above equation I il denotes the electric current generated by illumination, I 0 is the diode current, R s is the inner resistance and U T is the thermal voltage. In order to employ the above equations, the diode current, the inner resistance, as well as the thermal voltage had to be known. U T was calculated from the measured temperatures (T) by using the formula U T =mkt/q, where m is the diode factor, q the charge, and k is the Boltzmann constant. Values of the diode factor are in the range of 1 and 2. A value of m = 1.6 was chosen in this study. The diode current (I 0 ) was determined from the measured open circuit voltage by employing the expression (Wagner, 2006): Fig. 1. Experimental setup on the roof of the IMuK. I 0 ¼ I il e Uoc U T : ð3þ

4 S. Beringer et al. / Solar Energy 85 (2011) Fig. 2. Monthly ratios of P mpmon versus calculations of E tilt (November 2008 June 2009). The measurements are denoted by the gray shaded lines and the calculations are denoted by the vertical dashed lines in the graphic. (Note: values of Y-axis start from 0.5.) The values of each month are normalised to their maximum value respectively.

5 474 S. Beringer et al. / Solar Energy 85 (2011) R s was assumed to be 0.03 X, which is a commonly used value in literature. Neglecting the resistance and with U = 0 it follows from Eq. (1) (short circuit) that I il I sc. To compute P mp, a computer program was developed by the author using Newton Raphson s method. A detailed description on modeling solar cell parameters by applying Newton Raphson s method is given by Chenni et al. (2007). The present calculations, referred to P mp based on that scheme. In the following the basic methodology of calculation should be briefly outlined. After some rearrangements and substitutions by using Eqs. (1) and (2), the following is obtained: h ði mp I sc I 0 Þ ln I sc I mp I 0 þ 1 I mp þ I mpr s U T 1 þði sc I mp þ I 0 Þ Rs U T ¼ 0: ð4þ I mp denotes the electric current at its maximum point. Applying Newton Raphson s method on the previous expression yields I mp : I mpiþ1 ¼ I mpi f ði mp i Þ f 0 ði mpi Þ : ð5þ Eq. (5) clarifies Newton Raphson s method to calculate I mp in an iterative form. The subscript i denotes the ith iteration and f, f 0 denote Eq. (4) and its derivative respectively. Once I mp is determined, U mp and P mp can be calculated: i U mp ¼ U T ln I sc I mp þ 1 I mp R s ; I 0 P mp ¼ I mp U mp : 3.1. Monthly considered results After having calculated P mp, the data sets were cumulated according to the regarded period of time. First diurnal sums were calculated. Afterwards monthly sums were assessed. Next the missing days of measurement had to be taken into account. This was conducted by the calculation of daily mean values of each month multiplied with the number of days of each month: P mpday ¼ 1 N Xmeas P mp;i P mpmon ¼ P mpday N mon : N meas i¼1 In the equation above N mon denotes the number of days of each month, N meas denotes the number of measuring days and P mpmon denotes the monthly cumulated values. For the purpose of comparison, solar radiation data on tilted surfaces were calculated. For this reason the simulation software INSEL (INtegrated Simulation Environment Language) was applied to compute monthly cumulated irradiances on those tilt angles, according to the mounted solar cells. INSEL possesses a database of monthly mean ð6þ ð7þ Fig. 3. Monthly ratios of P mpmon versus calculations of E tilt (July 2009 October 2009). The measurements are denoted by the gray shaded lines and the calculations are denoted by the vertical dashed lines in the graphic. (Note: values of Y-axis start from 0.5.) The values of each month are normalised to their maximum value respectively.

6 S. Beringer et al. / Solar Energy 85 (2011) meteorological data sets including global radiation data. From the available monthly mean values, total monthly irradiances on tilted surfaces were calculated, using empirical models provided by INSEL. This was carried out in three steps: (1) computation of hourly mean values using a model according to Gordon and Reddy, (2) computation of the diffuse fraction of global radiation according to Orgill and Hollands and (3) determination of the tilted solar radiation data E tilt by using the model according to Temps, Coulson and Klucher. Figs. 2 and 3 show the monthly cumulated values (P mpmon and E tilt ). The values of each month are normalised to their maximum value respectively. That is, for example in November the maximum of P mpmon and E tilt was at a tilt angle of 60 by which all values were normalised. As can be seen, both data sets are in good agreement at their maximum values, i.e. at the tilt angle b opt. But in respect to tilt angles different from b opt, there are deviations that make up to 13% at a tilt of 0 (November) and 16% at a tilt of 70 (June). According to the results mounting the solar cell at a tilt angle of in the winter months (October March) and 0 30 in the summer months (April September) would be best for the location of Hannover. In addition, the difference between maximum and minimum values of P mpmon are less than commonly indicated in diverse literature especially in the summer months. Whereas in the winter months the difference D = max min equals approximately D = 10 20%, in the summer months it equals approximately D = 5 10%. Assuming that 75% of the yearly generated power is produced during the summer months, these months will have a higher impact on the yearly optimum tilt angle Seasonal and yearly considered results Frequently, the seasonal or yearly optimum tilt angle is of interest, e.g. for a stationary mounted solar collector. According to this period of time, the values of P mpmon were cumulated and normalised to their maximum value. Fig. 4a shows normalised values of these periods. As can be seen, there is only a small difference D between maximum and minimum values, especially in respect to the summer season and the year. It can be stated that D = 6% in the summer months and D 5% in the year. The experimental found values are more than 10% less than calculated ones and commonly used values in literature. Fig. 4b illustrates the total amount (P mpmon ) of every month. Thus the major part of the yearly total amount of the output power, around 75%, is produced in the summer months. 4. Data quality An influencing factor has been the series resistance R s of the measuring system. In general this resistance is negligible (R s 0) and it can be assumed that I sc I il (Eq. (1)) at Fig. 4. (a) Seasonal (summer, winter) and yearly ratios of the cumulated values. The values are normalised to their maximum value. The summer months include April September and the winter months include October March. The second graph (b) shows the total amount (P mpmon ) of each month. (Note (a): values of Y-axis start from 0.5.) short circuit. However, due to the cabling, junctions and a shunt there has been existent a small resistance. Since the short circuit current was measured, all eight solar cells were required to have nearly the same small resistance to compare them with one another. For that purpose the electric current was designed to record another voltage from which R s could be calculated. It was found that two of the solar cells (C 3 and C 8 ) had a slightly higher resistance especially at higher values of I sc (summer). This lead to smaller values of I sc and hence lead to a reduction of P mp. This influence can be seen in Fig. 3 by means of the month July where the output of C 3 is reduced by about 2%. 5. Conclusion This investigation states a nearly irrelevant difference of the performance of solar cells at various tilt angles. A difference of just 6% between maximum and minimum values was found for the summer season and the year. For the winter season a difference of just 10% was found. These

7 476 S. Beringer et al. / Solar Energy 85 (2011) values are around 10% less than commonly used in literature and than given by calculations of irradiances. A reason might be the temperature effect that affects the open circuit voltage. A higher temperature leads to a reduction of the output performance and is mostly not considered. Another reason could be inaccuracies at the derivation of diffuse irradiances from global radiation data by using empirical models. The diffuse radiation is highly variable in space and time (Seckmeyer, 1989; Pissulla et al., 2009) and can only approximately described by semi-empirical models. The question whether tilting devices can be abandoned can therefore not yet be finally answered. Other sites might be different and this period may not be representative though there is no indication as not to be typical. With the exception of April, which showed unusually frequent sunshine hours, the comparison of mean sunshine hours between the measuring period are in good agreement. Acknowledgments Special thanks to Prof. Dr. Rolf Brendel from the ISFH, who provided the solar plants. In addition, I would like to express my gratitude to Dr. Pietro P. Altermatt from the ISFH, who shared his knowledge and expertise. Thanks also to members of the radiation group, Dr. Irina Smolskaia, Stefan Riechelmann, Korntip Tohsing, Ludmila Anufrieva, Hauke Huchzermeyer and Riyad Mubarak, for the inspired discussions. References Balenzategui, J., Chenlo, F., Measurement and analysis of angular response of bare and encapsulated silicon solar cells. Solar Energy Materials & Solar Cells 86, Cheng, C.L., Jimenez, C.S.S., Lee, M.-C., Research of BIPV optimal tilted angle, use of latitude concept for south orientated plans. Renewable Energy 34, Chenni, R., Makhlouf, M., Kerbache, T., Bouzid, A., A detailed modeling method for photovoltaic cells. Energy 32, EL-Kassaby, M.M., Monthly and daily optimum tilt angle for south facing solar collectors; theoretical model, experimental and empirical correlations. Solar & Wind Technology 5, Elsayed, M.M., Optimum orientation of absorber plates. Solar Energy 42, Gunerhan, H., Hepbasli, A., Determination of the optimum tilt angle of solar collectors for building applications. Building and Environment 42, Hussein, H.E.-G.H.M.S., Ahmad, G.E., Performance evaluation of photovoltaic modules at different tilt angles and orientations. Energy Conversation and Management 45, Ibrahim, D., Optimum tilt angle for solar collectors used in cyprus. Renewable Energy 6, Lewis, G., Optimum tilt of a solar collector. Solar & Wind Technology 4, Nakamura, H., Yamada, T., Sugiura, T., Sakuta, K., Kurokawa, K., Data analysis on solar irradiance and performance characteristics of solar modules with a test facility of various tilted angles and directions. Solar Energy Materials & Solar Cells 67, Pissulla, D., Seckmeyer, G., Cordero, R.R., Blumthaler, M., Schallhart, B., Webb, A., Kift, R., Smedley, A., Bais, A.F., Kouremeti, N., Herman, A.C.J., Kowalewski, M., Comparison of different calibration methods to derive spectral radiance as a function of incident and azimuth angle. Photochemical Photobiological Sciences 8, Seckmeyer, G., Spectral measurements of the variability of global UV-radiation. Meteorologische Rundschau, Gebrueder Borntraeger Verlagsbuchhandlung Heft 6, Soulayman, S.S., On the optimum tilt of solar absorber plates. Renewable Energy 1, Wagner, A., Photovoltaic Engineering, zweite ed. Springer, Berlin Heidelberg.