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Direct tracking error characterization on a single-axis solar tracker
Energy Conversion and Management 105 (2015) 1281–1290
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Direct tracking error characterization on a single-axis solar tracker Fabienne Sallaberry a,b,⇑, Ramon Pujol-Nadal c, Marco Larcher d, Mercedes Hannelore Rittmann-Frank d a
CENER (National Renewable Energy Center), Solar Thermal Energy Department, C/ Ciudad de la Innovación, 7, 31621 Sarriguren, Navarra, Spain Public University of Navarra (UPNA), Projects and Rural Engineering Department, Campus Arrosadia s/n, 31006 Pamplona, Navarra, Spain c University of Balearic Islands, Physics Department, Ctra. Valldemossa km 7.5, 07122 Palma de Mallorca, Spain d Institut für Solartechnik SPF, Hochschule für Technik HSR, Oberseestrasse 10, CH-8640 Rapperswil, Switzerland b
a r t i c l e
i n f o
Article history: Received 24 April 2015 Accepted 30 August 2015
Keywords: Tracking error Single-axis tracking Acceptance angle
a b s t r a c t The solar trackers are devices used to orientate solar concentrating systems in order to increase the focusing of the solar radiation on a receiver. A solar concentrator with a medium or high concentration ratio needs to be orientated correctly by an accurate solar tracking mechanism to avoid losing the sunrays out from the receiver. Hence, to obtain an appropriate operation, it is important to know the accuracy of a solar tracker in regard to the required precision of the concentrator in order to maximize the collector optical efficiency. A procedure for the characterization of the accuracy of a solar tracker is presented for a single-axis solar tracker. More precisely, this study focuses on the estimation of the positioning angle error of a parabolic trough collector using a direct procedure. A testing procedure, adapted from the International standard IEC 62817 for photovoltaic trackers, was defined. The results show that the angular tracking error was within ±0.4° for this tracker. The optical losses due to the tracking were calculated using the longitudinal incidence angle modifier obtained by ray-tracing simulation. The acceptance angles for various transversal angles were analyzed, and the average optical loss, due to the tracking, was 0.317% during the whole testing campaign. The procedure presented in this work showed that the tracker precision was adequate for the requirements of the analyzed optical system. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The method to determine the precision of a solar tracker used in solar thermal collectors has not yet been standardized. Nowadays, existing testing standards for solar collectors consider a solar tracker as a part of the collector [1]. Thus, the losses of efficiency due to tracking imprecision are not quantified in the global collector efficiency test. The International standard IEC 62817 [2] enables to certify solar trackers for photovoltaic applications considering both accuracy and durability. However, this standard accuracy test is not applicable to solar thermal concentrator tracker, particularly to single-axis solar tracker for linear solar concentrator. The Spanish committee AEN CTN 206/SC 117 [3] redacted a proposal to the international committee IEC 117 [4], for the standard characterization of parabolic-trough collector (PTC) solar trackers which led to the creation of a working group for a new standard draft approved in November 2014 [5]. ⇑ Corresponding author at: CENER (National Renewable Energy Center), Solar Thermal Energy Department, C/ Ciudad de la Innovación, 7, 31621 Sarriguren, Navarra, Spain. Tel.: +34 948 25 28 00. E-mail address: [email protected] (F. Sallaberry). http://dx.doi.org/10.1016/j.enconman.2015.08.081 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.
According to Mousazadeh et al. [6], solar trackers are classified according to their orientation (one or two axes) and their actuation (active or passive, and open or closed loop). Depending on the type of collector, different solar tracking systems rely on different tracking strategies. For example, for the Fixed Mirror [7] the receiver is the only moving component, while for the PTC [8], the whole system (mirror and absorber) tracks the sun direction at the same time. The present paper is focused on a small-sized PTC with active loop. In order to identify the tracking error of a solar tracker, devices similar to the sun-sensor on a closed-loop actuation tracker can be used. However, the characterization of the tracking error requires a highly accurate electronic device. Since 1987, when Bhatnagar et al. [9] experimentally measured the average tracking error of a parabolic concentrator with a single-axis tracker at different solar hours using the sun-sensor of the collector, the tracking error is being studied. In that study, the tracking error was estimated from the design of the sensor and was 0.93° at noon. The tracking error has also been investigated in several recent studies. In the work of Díaz-Félix et al. [10], the absolute tracking error distribution of a heliostat was theoretically evaluated using Monte-Carlo simulations. Assuming several error sources on the heliostat position, the tracking errors were found to be up to 0.7°
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Nomenclature
a a0 ac as
bc /r
cc cs Dgtrack gopt
ha hd hi hL hT htrack
q r
s a C
solar absorptance (°) solar absorptance at normal incidence (°) inclination of the solar tracker (°) solar altitude angle (°) collector tilt (°) rim angle (°) concentrator azimuth angle (respect to south) (°) solar azimuth angle (respect to south) (°) optical losses due to tracking error (%) optical efficiency of the collector () acceptance angle (°) defocus angle (°) incidence angle (°) longitudinal incidence angle (°) transversal incidence angle (°) angular tracking error (°) solar reflectance () specular scattering mirrors (mrad) or standard deviation transmittance () aperture width (m) geometrical concentration ratio defined as the ratio of the aperture area to the absorber area ()
with a circularly symmetric Gaussian distribution. In the study by Sun et al. [11], a beam characterization system was used to evaluate the tracking error of two heliostats from a central tower solar plant with an estimated accuracy of about 2% for the positioning angle measurement. Zheng et al. [12] analyzed the tracking error on an Linear Fresnel Reflectors collector, and the effect of different factors such as the reflectors positioning, the rotation axis position, the driver accuracy, the tracking software algorithm, the coordinates and the structure error. In an earlier study, solar tracking using an inclinometer on a double-axis solar tracker was directly characterized [13]. Additionally, a testing procedure was defined to estimate the long-term tracking error due to the positioning of a small-sized solar tracking collector [14]. The maximum optical loss due to tracking was of 8.5%, but the average long-term optical loss calculated for one year was about 1%. For a PTC, a single angle tracking, namely the elevation angle, must be examined in order to determine the solar tracker precision. Various methods are available to control the solar tracker elevation, such as optical device [15], artisanal shadow device [16], and angular sensor (encoder or inclinometer) [13]. There are different optical devices commercially available to characterize the tracking error. In 2009, Davis et al. designed a commercial device [17] with a high accuracy sensor using image processing to estimate the pointing error of double-axis solar trackers. In 2010, Minor and García also presented a solar tracking system based on image processing acquired by a webcam [15], which was able to measure the tracking error of a double-axis tracker with an accuracy of ±0.1°. In 2012, Missbach et al. [18] presented the results of a sun-sensor by Black Photon company, showing highly accurate measurements (standard deviation of 0.01%) on a double-axis tracking system for concentrating photovoltaic (CPV). But all these devices are applicable only for double-axis trackers and not for single-axis trackers. The acceptance angle is commonly provided by the manufacturer of a solar concentrating system. This value is very useful to identify the requirements of the solar tracker mechanism, but does not provide information on the amount of optical losses in real operating conditions.
CPV dabs dglass EW f GbT Gbn Hb IAM k Kb Kb,sim Kb,theor L LED NS PTC u
concentrating photovoltaic absorber tube diameter (mm) glass tube diameter (mm) East–West focal length (m) direct solar irradiance on the aperture plane (W/m2) direct normal irradiance (W/m2) direct normal solar irradiation (MJ/m2) incidence angle modifier () glass tube extinction coefficient (m1) incidence angle modifier relative to the direct incidence radiation () incidence angle modifier relative to the direct incidence radiation, obtained by simulation () incidence angle modifier relative to the direct incidence radiation, obtained by theoretical calculation () collector length (m) Light Emitting Diode North–South parabolic trough collector wind speed (m/s)
In this study, a single-axis solar tracker, used on a small-size PTC, is characterized. The paper is organized as follows: in Section 2 the components are presented; Section 3.1 describes the methodology to obtain the angular tracking error. In Section 3.2 the incidence angle modifier (IAM) is presented by a ray-tracing simulation. In Section 3.3 the optical losses due to the tracking errors are calculated using the angular errors estimated in Section 3.1 and the IAM curve obtained in Section 3.2. The results, presented in Section 4, show that during the testing period the 95th percentile tracking accuracy was 0.33° and the mean weighted optical losses leading to a reduction of the collector efficiency was 0.317%. Finally, the conclusions are compiled in Section 5.
2. Materials 2.1. Solar collector and solar tracker The solar collector referred to in this study is a small-size PTC with a single-axis solar tracker, model PolyTrough 1800 manufactured by the company NEP Solar AG [19]. It had been tested in the SPF laboratory (Institut für Solartechnik [20]) according to the European standard EN 12975-2 [21], recently replaced by the International standard ISO 9806 [1]. In this solar tracker, the algorithm calculated the sun position at different times; hence it was classified as an active open-loop type actuator. However, no encoder was used, but there was a Hall sensor to detect the motor position. The precision of the tracker was supposed to be 0.025°. This collector, shown in Fig. 1, was tested with an East–West (EW) orientation. The study by Larcher et al. [22] and the testing report from SPF [20] provide more details about the solar collector and the tests performed by SPF laboratory. A similar NEP collector PolyTrough 1200 with smaller aperture was tested by Miller et al. [23] at the Australian laboratory CSIRO according to different testing methodologies (standards [21,24] and Ref. [25]). In these studies, the thermal efficiency curves of different models were compared. However, the angle positioning errors of the tracking systems were not studied.
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Fig. 1. Picture of the solar collector PolyTrough 1800.
Table 1 Characteristics of the concentrator [22]. Parameter
Symbol
Value
Focal length Aperture width Collector length Mirror solar reflectance (anodized aluminum with PVD aluminum layer and protective coating) Specular scattering mirrors Absorber tube diameter Absorber tube wall thickness Solar absorptance at normal incidence on the absorber fin (measured at SPF) Angular absorptance dependence (adopted from [26]) Glass tube diameter Glass tube wall thickness Glass tube refraction coefficient on both sides Cover tube transmittance (measured at SPF) Glass tube extinction coefficient Concentration ratio
f a L
647 mm 1845 mm 10.347 m 0.885
Rim angle
q r
a0
4.4 mrad 34 mm 1.5 mm 0.9427
a a0
1 0:017
dabs
dglass
56 mm 2.5 mm 1.473
s
0.895
k C = (L a)/ (p dabs) /r
15 m1 17.3
1 cos hi
1:8
Fig. 2. Scheme of the rotation angles: tracking angle ac, collector inclination bc, collector azimuth cc, the longitudinal and transversal angles hL and hT.
71°
Table 1 presents the dimensions and the physical properties of the NEP PolyTrough 1800. 2.2. Digital inclinometer A tilt angle sensor, model A-2T manufactured by US Digital [27] with connection RS-232C for communication, was used to measure the tilt angle of the solar tracker. This inclinometer was a digital gravity angle sensor that measures inclination on a single axis. The device accuracy was 12-bits. 3. Proposed testing procedure The tracking error characterization proposed was based on the standard IEC 62817 [2] testing procedure. This standard is applicable mainly to double-axis CPV solar trackers. Thus, the proposed testing methodology needs to be adapted for solar thermal PTC trackers, which are mainly single-axis. 3.1. Tracking error characterization For the testing procedure, in order to define the incidence angles of the solar radiation on the collector, first it was necessary to describe three position angles for the collector, two of which were fixed (the collector inclination bc and the collector azimuth cc) and one was moving in order to track the sun (the tracking
angle ac). The angle ac was by definition 0° when the collector aperture was orientated to the zenith, and it represented the rotation angle on the longitudinal axis; the collector inclination bc was also by definition 0° when the collector aperture was orientated to the zenith, and it represented the rotation angle in the transversal axis; the collector azimuth cc was by definition 0° when the collector was orientated to the South, and it represented the rotation angle respect to the South. Fig. 2 illustrates the rotation angles defining the collector position. At first, the solar tracker was positioned on the testing bench or platform. It was crucial to determine the real position of the solar collector, because some errors on the collector positioning could lead to additional tracking errors. The azimuth of the collector cc was set on the testing bench with a precision of ±0.1°. Before the testing sequences, the inclination of the collector bc was measured by a spirit level with an accuracy of ±0.057° and was found to be 0°. To monitor the rotation angle ac, the digital inclinometer, shown in Section 2.2, was located on an aluminum profile which was fixed to a component used for the reflectors holders avoiding torsional or tolerance effects (see Fig. 3). The digital inclinometer was connected by cable to a computer, whose output was recorded every ten seconds. The direct normal irradiance Gbn was measured by a pyrheliometer (model CHP 1 from Kipp & Zonen [28]) and the wind speed u was measured by an anemometer (model WWA 15A from Vaisala [29]. The testing methodology consisted in monitoring the tracker elevation ac, the direct solar irradiance Gb and the wind speed u
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Fig. 3. Picture of the digital inclinometer mounted on the solar tracker.
over several days. The instantaneous data acquired simultaneously with a data logger (ac, Gb, u) was averaged every minute. The transversal and longitudinal incidence angles were calculated by projecting the solar vector hi on the transversal plane (perpendicular to the tracking axis) and on the longitudinal plane (parallel to the tracking axis) of the collector, respectively. First, for the sun’s position, the solar elevation as and the solar azimuth cs were calculated using the solar algorithm reported by BlancoMuriel et al. [30], with an accuracy of 0.5 min of arc (0.0083°). Then, the incidence angles hT and hL were calculated as reported elsewhere [31]. The proposed testing method, based on the standard IEC 62817 [2], requires data recorded for a minimum of five days with a minimum direct normal irradiation Hb of 2400 W h/m2 per day. In addition, the data should be separated into different data bins: one for a low wind (for wind speed u lower than or equal to 4 m/s) and one for high wind speed (for wind speed u higher than 4 m/s). A minimum of total data points (360), a minimum of data points per day (50), and a minimum of data points before and after noon (50) were required. Finally, the typical accuracy and the 95th percentile accuracy were calculated. 3.2. Transversal IAM curve and acceptance angle characterization The aim of this section was to characterize the transversal IAM curve of the concentrating system along the longitudinal plane. The adequacy of the solar tracking system can be verified knowing the acceptance angle ha from the transversal IAM curve. The acceptance angle ha is a key feature of a solar concentrator and can be defined as the maximum angle at which all rays incident on an optical concentrating system are transmitted to its receiver. As suggested by Valan Arasu and Sornakumar [32], in order to determine whether the concentrator matches with the solar tracker, a quality criteria should be that the acceptance angle ha has to be higher than the angular tracking error htrack. In an ideal concentrating system, the solar radiations entering with an incident angle smaller than the acceptance angle are
directed towards the receiver. In a real component, however, optical losses exist due to non-ideal optical properties of materials, dimension of the sun, scattering of mirrors, and geometric position imperfections. These effects cause variations on the theoretical acceptance angle that is obtained assuming an ideal optical system. The IAM defined in many studies [33–37] and standards [1,21,24] is the ratio between the optical efficiency for an incidence angle and the optical efficiency for a normal incidence angle. For a PTC the transversal IAM decreases when the transversal incidence angle hT increases, in absolute value, due to defocusing. That is the reason because an ideal solar tracking for a PTC implies hT = 0°, whereas for a real system a tracking error htrack could occurs which means a non-null transversal incidence angle hT (=htrack – 0°) which leads to a reduced optical efficiency. The transversal IAM values are generally calculated for the longitudinal angle null (hL = 0°). A more detailed study can verify if the acceptance angle is different for hL – 0°, by calculating IAM Kb values for a wide range of transversal and longitudinal angles. The transversal and longitudinal IAM were estimated by a raytracing simulation using a Fortran program previously presented [38] and validated [36,39]. The dimensions and optical properties of the NEP PTC introduced in the simulation program are listed in Table 1. The optical efficiency of the collector gopt was determined for transversal incidence angles between 0° and 4° every 0.1° and longitudinal angles between 0° and 90° every 5°, by simulation issuing 107 rays and assuming a circumsolar ratio of 0.05 [40]. The simulated IAM, Kb,sim, was calculated with Eq. (1) obtaining a whole 3D surface (hT 2 [0, 4]° and hL 2 [0, 90]°). The cos(hi) factor was used for referencing the optical efficiency to the direct solar irradiance on the aperture plane GbT.
K b;sim ðhT ; hL Þ ¼
gopt ðhT ; hL Þ gopt ð0 ; 0 Þ cosðhi Þ
ð1Þ
The theoretical acceptance angle can also be defined in a parabolic trough collector according to Eq. (2) [41], where /r is the rim angle of the parabola and C is the geometric concentration ratio.
ha ¼
sinð/r Þ pC
ð2Þ
The angular acceptance function [41], here referred to as the theoretical transversal IAM, Kb,theor, was given by Eq. (3), where hT is the transversal incidence angle.
K b;theor ðhT Þ ¼
8 > > > < 1
/ > tan ð 2r Þ > > :
1 jhi j < ha rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi /r 2 tan ð 2 Þ pChT 1 ha < jhi j < hd 0
ð3Þ
hd < jhi j
where hd is the defocus angle that is the angle for which all rays miss the receiver and is given by Eq. (4) [41].
1
hd ¼ sin
! 2 tan /2r pC
ð4Þ
The transversal IAM obtained by ray-tracing Kb,sim(hT) was compared to this theoretical function Kb,theor(hT) in Section 4.4. Finally, the acceptance angle value ha was compared to the tracking error htrack in order to verify whether the concentrator optics was adequate to the solar tracking system. Moreover, the acceptance angle ha(hL) was calculated for longitudinal angles hL between 0° and 90°, calculating the threshold for the transversal IAM Kb = 0.98 [24].
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3.3. Estimation of optical losses due to tracking
4. Results
This section aims to quantify the effect of the solar tracker on the concentrator efficiency by using the instantaneous tracking error htrack measured directly with the inclinometer ac (Section 3.1) and the transversal IAM curve obtained by simulation Kb,sim(htrack) (Section 3.2). The optical losses due to tracking error, Dgtrack, were analyzed according to Eq. (5). Considering that the transversal IAM concentrator was symmetric along the optical axis, the tracking error was expected to be dependent on |htrack|.
4.1. Collector positioning
Dgtrack ¼ ð1 K b ðjhtrack jÞÞ 100
ð5Þ
Finally, in order to take into account the variation of the longitudinal IAM Kb(hL), the optical losses due to tracking error were calculated using weights over the whole testing sequence Dgtrack (every one minute) as described in Eq. (6).
Dgtrack
P weighted
¼
g
i ðD track
GbT K b ðhL ÞÞ Dt ðG K b ðhL ÞÞ Dt bT i
P
ð6Þ
The transversal and longitudinal IAM (Eq. (1)) were derived from the 3D surface obtained by ray-tracing Kb,sim(hT).
After the installation of the PTC on the testing bench at SPF, the deviation to the EW orientation cc was determined experimentally in order to ascertain the real positioning of the solar concentrating system. The concentrating solar light on the holders of the receiver was examined. Fig. 4 shows the peak of the shadow on the holders. Assuming that the collector was mounted correctly, it is clear that the receiver was perfectly on the focal line and that all reflector segments were in the correct position. Hence, the majority of rays hitting the reflector should be reflected to the receiver. Only a small part of the reflector was shadowed by the receiver tube that did not receive solar radiation. Fig. 4 shows the shadowed area of the reflector and the concentrated solar light on the receiver. If the collector was tracking with good accuracy, the solar light would hit the bracket of the receiver symmetrically. This analysis was performed with the maximum incident angle. This shadow technique was repeated after changing by 0.1° step the orientation parameter in the tracking software control of the manufacturer, in order to optimize the orientation. The angle of the collector azimuth cc (respect to the south) was estimated to be +0.5° (positive to the west direction), with a precision of ±0.1°. This value was then applied to the tracker controller as a configuration input for the remaining testing days. 4.2. Tracker accuracy estimation
Fig. 4. Schematic picture indicating the shadow (black stripe).
Calculation of the solar elevation as was carried out for the location of the test bench in SPF facilities (latitude = 47.223°N and longitude = 8.818°E determined by the SUNEARTH tool [42] with a resolution of 0.00001°). The variables and requirements described in Section 3.1 were monitored and checked for all the testing days. A statistical analysis was performed in order to study the mean and the standard deviation of the tracking error. The standard deviation was calculated for the one minute average series. Table 2 shows the data range of solar irradiance Gbn and wind speed u for the seven testing days. Only data with as > 10° were selected in order to avoid obstructions in the horizon. A total of 23,022 instantaneous measurements and 3833 mean series were obtained. The maximum wind speed (umax = 3.96 m/s) was lower than the threshold of 4 m/s, because the test was performed according to the standard EN 12975-2 [21] for the solar collector performance under steady-state conditions. The number of measurement points (3833) and testing days (7) was higher than the minimum required by the testing procedure proposal (360 and 5, respectively). The number of points before noon (1856) and after noon (1984) was also higher than the minimum of the procedure proposal (50 for both).
Table 2 Testing data range. Date
Num of instantaneous data
Num of series of one minute
Num of series before noon
Num of series after noon
Mean Gbn [W/m2]
Max Gbn [W/m2]
Hb [W h/m2]
Min u [m/s]
Max u [m/s]
13/08/2012 15/08/2012 17/08/2012 18/08/2012 19/08/2012 21/08/2012 22/08/2012
2767 3298 3716 3732 3748 2982 2779
461 549 619 621 624 496 463
272 254 278 280 281 275 216
190 296 342 342 344 222 248
663 785 859 870 825 595 542
801 902 932 941 905 709 791
5094 7189 8869 9015 8592 4925 4183
0.03 0.01 0.09 0.01 0.01 0.04 0.04
3.96 3.29 2.98 2.38 0.26 1.96 3.52
Total
23,022
3833
1856
1984
–
–
47,867
–
–
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13/8/2012 1.0 0.5 0.0 −1.0 8
9
10
11
12
13
7
14
8
9
10 11 12 13 14 15 16
Hour UTC [h]
Hour UTC [h]
17/8/2012
18/8/2012
0.5 0.0 −0.5 −1.0
−1.0
−0.5
0.0
Tracking error [º]
0.5
1.0
1.0
7
Tracking error [º]
−0.5
Tracking error [º]
0.5 0.0 −0.5 −1.0
Tracking error [º]
1.0
15/8/2012
6
7
8
9 10 11 12 13 14 15 16 17
6
7
8
9 10 11 12 13 14 15 16 17
Hour UTC [h]
Hour UTC [h] 21/8/2012 1.0 0.5 0.0 −1.0
−0.5
Tracking error [º]
0.5 0.0 −0.5 −1.0
Tracking error [º]
1.0
19/8/2012
6
7
8
9
10 11 12 13 14 15 16 17
7
8
9
Hour UTC [h]
10
11
12
13
14
15
Hour UTC [h]
0.5 0.0 −0.5 −1.0
Tracking error [º]
1.0
22/8/2012
8
9
10
11
12
13
14
15
Hour UTC [h] Fig. 5. Inclination error on the solar tracker htrack vs. hour (UTC).
Fig. 5 illustrates the tracking instantaneous error htrack values for the seven days, calculated according to Section 3.1. The oscilla-
tion of the tracking error showed a similar pattern every day and in particular a different behavior before and after noon.
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0.0
Instantaneous mean -70
-50
-30
-10 0 10
30
50
70
4.4. IAM and acceptance angle
Longitudinal incidence angle [°] Fig. 6. Tracking error from the solar tracker htrack for all the testing days: instantaneous (black dots) and mean value for one minute interval (gray) vs. the longitudinal incidence angle hL.
Fig. 6 shows the instantaneous tracking error htrack versus the longitudinal incidence angle of all the testing data, as well as the mean value of every one minute interval, in order to identify the oscillation pattern of the tracking error. The tracking error htrack was between 0.4° and +0.4°. 4.3. Statistical analysis of the tracking error
tracking error histogram
tracking error histogram
(a)
(b)
30
Frequency
15
10
10 5
0
0
Frequency
20
40
25
30
The mean value of the tracking error over one minute interval was (htrack) = 0.05°, and its standard deviation was r(htrack) = 0.18°. On the other hand, the mean value of the absolute tracking error over one minute interval was (|htrack|) = 0.16°, and its standard deviation was r(|htrack|) = 0.10°. Thus, the absolute value clearly differs from the mean value. A minimal mean error implies that the positive and negative values were compensated. The analysis of the absolute angle |htrack| was therefore crucial in order to avoid compensation effects in the average value, and represented the real value of tracking error. Fig. 7(a) shows the distribution of mean tracking error over one minute interval htrack, and Fig. 7(b) shows the distribution of the absolute value |htrack|. Two different peaks were observed in Fig. 7(a), one for the tracking error values centered on 0.275° ± 0.02° and another centered on 0.075° ± 0.02°. About
In this section, the dependency of the optical efficiency of the concentrator to the incidence angles was determined. The transversal IAM curve of the concentrator was calculated as specified in Section 3.2. Fig. 8 shows the IAM Kb,sim for hT between 0° and 4° and for hL between 0° and 80° obtained by ray-tracing simulation. Fig. 9 shows the transversal IAM Kb,sim(hT) obtained by simulation on the longitudinal plane when hL = 0°. The acceptance angle obtained by simulation, which is the angle threshold for which Kb,sim(hT) > 0.98 [24], was ha,sim = 0.58°. The theoretical value of the acceptance angle calculated according to Eq. (2) was ha,theor = 0.998°, and the theoretical value of the defocus angle calculated according to Eq. (4) was hd,theor = 1.506°. Fig. 9 shows how the simulation transversal IAM Kb,sim decreases for transversal angles hT between 0.58° and 2°, which is a range much larger than the range of decrease of the theoretical transversal IAM Kb,theor (0.998–1.506°) calculated from Eq. (3). Thus, techniques using ray-tracing allow a more detailed characterization of the optical behavior of a solar concentrator taking into account the optical properties of the PTC and the sun shape. Using the ray-tracing results the dependency of the acceptance angle on the longitudinal incidence angle can be determined. Fig. 10 shows that the simulation acceptance angle ha,sim(hL) was not constant while varying longitudinal angles, although this variation was very small (less than ±0.17°, with an average value of 0.42°). A slight increase in the acceptance angle was observed for longitudinal angles >65°. Thus, the solar tracker error should be below the minimum value that occurs for hL = 65° (0.25°), and
20
-1.0
-0.5
tracking error [°]
0.5
1.0
the mean absolute tracking error, in Fig. 7(b) only one peak was observed centered at 0.03° ± 0.02°. The 95th percentile accuracy was calculated, and for |htrack| a value of 0.33° was obtained. The mean tracking errors calculated before noon (hL < 0°) and for the afternoon data (hL > 0°) were found to be 0.223° and 0.095° respectively, which were very close to the two peaks observed in Fig. 7(a). Hence, the two peaks are related to the solar tracking behavior before and after noon. The dependency of the tracking error htrack on the wind speed u was analyzed by calculating the correlation factor between the tracking error htrack on the wind speed u. But the r2 was really low (0.467). So the dependency of the wind speed was concluded to be not significant from the available data.
−0.4
−0.3
−0.2
−0.1
0.0
mean tracking error [º]
0.1
0.2
0.0
0.1
0.2
0.3
0.4
mean absolute tracking error [º]
Fig. 7. Distribution of the tracking errors (a) mean over one minute series and (b) mean absolute over one minute series.
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Fig. 8. IAM obtained by simulation 3D surface.
should not consider exclusively the value of acceptance at normal incidence hL = 0° (0.58°). It is important to point out that the value of 0.25° proposed for the tracking error was lower than 0.998° obtained by theoretical results (Eq. (3)). Hence, the procedure proposed in this study was more restrictive for the required accuracy of the tracking error, and aimed to minimize the optical losses. 4.5. Estimation of optical losses caused by the tracking Using the transversal IAM curve Kb,sim(hT) obtained by optical simulation obtained in Section 4.4 and the tracking error distribution obtained in Section 4.3, the optical losses were calculated according to Eq. (5). Fig. 11 shows the distribution of the optical losses. The majority of optical losses were almost null, except to few that reached 4%. The weighted optical loss using the tracking error Dgtrack calculated according to Eq. (6) and using one minute interval average points was 0.317%.
0.5
1.0
1.5
Sim. acceptance angle theoretical acceptance angle theoretical defocus angle
0.0
Acceptance angle [º]
2.0
Fig. 9. Transversal IAM obtained by simulation Kb,sim(hT) compared to theoretical Kb,theor.
0
20
40
60
80
Longitudinal incidence angle [º] Fig. 10. Acceptance angle dependency on the longitudinal incidence angle by simulation ha,sim(hL) and acceptance angle ha,theor and defocus angle hd,theor by calculation.
Fig. 11. Optical losses distribution calculated from mean tracking error over one minute series.
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The 95th percentile for the optical losses was measured to be 2.51%, which means that at 95% of the time the optical losses were below this value. In term of energy, for the NEP collector having an optical efficiency g0 = 0.69674 and an aperture area of 18.45 m2 as published in Larcher et al. [22], the energy loss due to the solar tracker would be 4.5 MJ, which was negligible compared with the theoretical output energy without tracking optical losses neither heat losses given a value of 1622 MJ. 5. Conclusions The solar tracker of a concentrating collector was tested according to the standard draft methodology redaction in the Spanish committee AEN CTN 206/SC 117 [3] and adapted from the IEC standard [4]. This study focused on the estimation of the optical losses due to tracking errors for a small-size PTC medium-temperature collector, but it could be applied to a general single-axis solar tracker. The main conclusions were the following: The angular tracking error could be accurately characterized using a digital inclinometer. The testing methodology proposed by the Spanish committee to the International standard committee [4] was experimentally verified for one single-axis tracker. The proposed procedure, combining experimental data and ray-tracing simulations, allowed the determination of the optical losses due to solar tracker for a given optical system. A solar tracker of a small-size PTC was characterized. The tracking error measured during the testing process htrack was within ±0.4°, the 95th percentile of the tracking accuracy was ±0.33°, and the weighted optical loss was 0.317%. As the optical losses due to tracking error could be a source of uncertainty on the optical efficiency, a recommended maximum acceptable value for those optical losses could be the optical efficiency uncertainty u(g0). But in this case the value of u(g0) was not provided in the collector characterization published by Larcher et al. [22]. The transversal IAM curve was determined by ray-tracing simulation for all longitudinal incidence angles as well as on the transversal incidence plane. The proposed procedure using ray-tracing to evaluate the acceptance angle gives a better required accuracy for the tracking error than the theoretical acceptance angle. By this way, the acceptance angle ha was determined for longitudinal incidence angles between 0° and 80°, and the minimum acceptance angle should be taken into account for the solar tracker accuracy. The theoretical acceptance angle and the theoretical defocus angle give values that are not related to the real optical behavior. Hence, the use of optical simulation should be allowed in the standards in order to determine the optical behavior of solar concentrating systems. In future works, other type of solar trackers for solar thermal applications will be tested with this methodology in order to validate completely the standard draft proposal. The influence of the wind speed on the tracker accuracy will also be considered in future studies by testing a solar tracker in more windy locations. Acknowledgements The authors would like to thank SPF for the testing data and NEP Solar AG for letting us to use those data. The authors would also like to thank the National Renewable Energy Centre (CENER), the Public University of Navarra (UPNA) and the University of Balearic Islands (UIB) for time dedication.
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[32] Valan Arasu A, Sornakumar T. Performance characteristics of parabolic trough solar collector system for hot water generation. Int Energy 2006;7:137. [33] Ambrosetti P, Keller J. Das neue Bruttowaermeertragsmodell fuer verglaste Sonnenkollektoren. IEA Task III: performance testing of solar collectors, Subtask D: characterization of the thermal performance of the solar collectors. IEA; 1985. [34] Eickhoff M, Zarza E. Incident angle modifier of the LS-3-DISS-collectors. Technical report project DISS. Plataforma Solar de Almería; 2002. [35] McIntire WR. Factored approximations for biaxial incident angle modifiers. Sol Energy 1982;29:315–22. [36] Pujol-Nadal R, Martínez-Moll V. Optical characterization of a fixed mirror solar concentrator prototype by the ray-tracing procedure. J Renew Sustain Energy 2014;6. [37] Sallaberry F, García de Jalón A, Olano X, Mateu E, Erice R, Ramirez L. Bi-axial incidence angle modifier using quasi-dynamic test for asymmetrical solar collector using dummy variables. ESTEC, Marseille; 2011.
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Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Direct tracking error characterization on a single-axis solar tracker Fabienne Sallaberry a,b,⇑, Ramon Pujol-Nadal c, Marco Larcher d, Mercedes Hannelore Rittmann-Frank d a
CENER (National Renewable Energy Center), Solar Thermal Energy Department, C/ Ciudad de la Innovación, 7, 31621 Sarriguren, Navarra, Spain Public University of Navarra (UPNA), Projects and Rural Engineering Department, Campus Arrosadia s/n, 31006 Pamplona, Navarra, Spain c University of Balearic Islands, Physics Department, Ctra. Valldemossa km 7.5, 07122 Palma de Mallorca, Spain d Institut für Solartechnik SPF, Hochschule für Technik HSR, Oberseestrasse 10, CH-8640 Rapperswil, Switzerland b
a r t i c l e
i n f o
Article history: Received 24 April 2015 Accepted 30 August 2015
Keywords: Tracking error Single-axis tracking Acceptance angle
a b s t r a c t The solar trackers are devices used to orientate solar concentrating systems in order to increase the focusing of the solar radiation on a receiver. A solar concentrator with a medium or high concentration ratio needs to be orientated correctly by an accurate solar tracking mechanism to avoid losing the sunrays out from the receiver. Hence, to obtain an appropriate operation, it is important to know the accuracy of a solar tracker in regard to the required precision of the concentrator in order to maximize the collector optical efficiency. A procedure for the characterization of the accuracy of a solar tracker is presented for a single-axis solar tracker. More precisely, this study focuses on the estimation of the positioning angle error of a parabolic trough collector using a direct procedure. A testing procedure, adapted from the International standard IEC 62817 for photovoltaic trackers, was defined. The results show that the angular tracking error was within ±0.4° for this tracker. The optical losses due to the tracking were calculated using the longitudinal incidence angle modifier obtained by ray-tracing simulation. The acceptance angles for various transversal angles were analyzed, and the average optical loss, due to the tracking, was 0.317% during the whole testing campaign. The procedure presented in this work showed that the tracker precision was adequate for the requirements of the analyzed optical system. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction The method to determine the precision of a solar tracker used in solar thermal collectors has not yet been standardized. Nowadays, existing testing standards for solar collectors consider a solar tracker as a part of the collector [1]. Thus, the losses of efficiency due to tracking imprecision are not quantified in the global collector efficiency test. The International standard IEC 62817 [2] enables to certify solar trackers for photovoltaic applications considering both accuracy and durability. However, this standard accuracy test is not applicable to solar thermal concentrator tracker, particularly to single-axis solar tracker for linear solar concentrator. The Spanish committee AEN CTN 206/SC 117 [3] redacted a proposal to the international committee IEC 117 [4], for the standard characterization of parabolic-trough collector (PTC) solar trackers which led to the creation of a working group for a new standard draft approved in November 2014 [5]. ⇑ Corresponding author at: CENER (National Renewable Energy Center), Solar Thermal Energy Department, C/ Ciudad de la Innovación, 7, 31621 Sarriguren, Navarra, Spain. Tel.: +34 948 25 28 00. E-mail address: [email protected] (F. Sallaberry). http://dx.doi.org/10.1016/j.enconman.2015.08.081 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.
According to Mousazadeh et al. [6], solar trackers are classified according to their orientation (one or two axes) and their actuation (active or passive, and open or closed loop). Depending on the type of collector, different solar tracking systems rely on different tracking strategies. For example, for the Fixed Mirror [7] the receiver is the only moving component, while for the PTC [8], the whole system (mirror and absorber) tracks the sun direction at the same time. The present paper is focused on a small-sized PTC with active loop. In order to identify the tracking error of a solar tracker, devices similar to the sun-sensor on a closed-loop actuation tracker can be used. However, the characterization of the tracking error requires a highly accurate electronic device. Since 1987, when Bhatnagar et al. [9] experimentally measured the average tracking error of a parabolic concentrator with a single-axis tracker at different solar hours using the sun-sensor of the collector, the tracking error is being studied. In that study, the tracking error was estimated from the design of the sensor and was 0.93° at noon. The tracking error has also been investigated in several recent studies. In the work of Díaz-Félix et al. [10], the absolute tracking error distribution of a heliostat was theoretically evaluated using Monte-Carlo simulations. Assuming several error sources on the heliostat position, the tracking errors were found to be up to 0.7°
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Nomenclature
a a0 ac as
bc /r
cc cs Dgtrack gopt
ha hd hi hL hT htrack
q r
s a C
solar absorptance (°) solar absorptance at normal incidence (°) inclination of the solar tracker (°) solar altitude angle (°) collector tilt (°) rim angle (°) concentrator azimuth angle (respect to south) (°) solar azimuth angle (respect to south) (°) optical losses due to tracking error (%) optical efficiency of the collector () acceptance angle (°) defocus angle (°) incidence angle (°) longitudinal incidence angle (°) transversal incidence angle (°) angular tracking error (°) solar reflectance () specular scattering mirrors (mrad) or standard deviation transmittance () aperture width (m) geometrical concentration ratio defined as the ratio of the aperture area to the absorber area ()
with a circularly symmetric Gaussian distribution. In the study by Sun et al. [11], a beam characterization system was used to evaluate the tracking error of two heliostats from a central tower solar plant with an estimated accuracy of about 2% for the positioning angle measurement. Zheng et al. [12] analyzed the tracking error on an Linear Fresnel Reflectors collector, and the effect of different factors such as the reflectors positioning, the rotation axis position, the driver accuracy, the tracking software algorithm, the coordinates and the structure error. In an earlier study, solar tracking using an inclinometer on a double-axis solar tracker was directly characterized [13]. Additionally, a testing procedure was defined to estimate the long-term tracking error due to the positioning of a small-sized solar tracking collector [14]. The maximum optical loss due to tracking was of 8.5%, but the average long-term optical loss calculated for one year was about 1%. For a PTC, a single angle tracking, namely the elevation angle, must be examined in order to determine the solar tracker precision. Various methods are available to control the solar tracker elevation, such as optical device [15], artisanal shadow device [16], and angular sensor (encoder or inclinometer) [13]. There are different optical devices commercially available to characterize the tracking error. In 2009, Davis et al. designed a commercial device [17] with a high accuracy sensor using image processing to estimate the pointing error of double-axis solar trackers. In 2010, Minor and García also presented a solar tracking system based on image processing acquired by a webcam [15], which was able to measure the tracking error of a double-axis tracker with an accuracy of ±0.1°. In 2012, Missbach et al. [18] presented the results of a sun-sensor by Black Photon company, showing highly accurate measurements (standard deviation of 0.01%) on a double-axis tracking system for concentrating photovoltaic (CPV). But all these devices are applicable only for double-axis trackers and not for single-axis trackers. The acceptance angle is commonly provided by the manufacturer of a solar concentrating system. This value is very useful to identify the requirements of the solar tracker mechanism, but does not provide information on the amount of optical losses in real operating conditions.
CPV dabs dglass EW f GbT Gbn Hb IAM k Kb Kb,sim Kb,theor L LED NS PTC u
concentrating photovoltaic absorber tube diameter (mm) glass tube diameter (mm) East–West focal length (m) direct solar irradiance on the aperture plane (W/m2) direct normal irradiance (W/m2) direct normal solar irradiation (MJ/m2) incidence angle modifier () glass tube extinction coefficient (m1) incidence angle modifier relative to the direct incidence radiation () incidence angle modifier relative to the direct incidence radiation, obtained by simulation () incidence angle modifier relative to the direct incidence radiation, obtained by theoretical calculation () collector length (m) Light Emitting Diode North–South parabolic trough collector wind speed (m/s)
In this study, a single-axis solar tracker, used on a small-size PTC, is characterized. The paper is organized as follows: in Section 2 the components are presented; Section 3.1 describes the methodology to obtain the angular tracking error. In Section 3.2 the incidence angle modifier (IAM) is presented by a ray-tracing simulation. In Section 3.3 the optical losses due to the tracking errors are calculated using the angular errors estimated in Section 3.1 and the IAM curve obtained in Section 3.2. The results, presented in Section 4, show that during the testing period the 95th percentile tracking accuracy was 0.33° and the mean weighted optical losses leading to a reduction of the collector efficiency was 0.317%. Finally, the conclusions are compiled in Section 5.
2. Materials 2.1. Solar collector and solar tracker The solar collector referred to in this study is a small-size PTC with a single-axis solar tracker, model PolyTrough 1800 manufactured by the company NEP Solar AG [19]. It had been tested in the SPF laboratory (Institut für Solartechnik [20]) according to the European standard EN 12975-2 [21], recently replaced by the International standard ISO 9806 [1]. In this solar tracker, the algorithm calculated the sun position at different times; hence it was classified as an active open-loop type actuator. However, no encoder was used, but there was a Hall sensor to detect the motor position. The precision of the tracker was supposed to be 0.025°. This collector, shown in Fig. 1, was tested with an East–West (EW) orientation. The study by Larcher et al. [22] and the testing report from SPF [20] provide more details about the solar collector and the tests performed by SPF laboratory. A similar NEP collector PolyTrough 1200 with smaller aperture was tested by Miller et al. [23] at the Australian laboratory CSIRO according to different testing methodologies (standards [21,24] and Ref. [25]). In these studies, the thermal efficiency curves of different models were compared. However, the angle positioning errors of the tracking systems were not studied.
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Fig. 1. Picture of the solar collector PolyTrough 1800.
Table 1 Characteristics of the concentrator [22]. Parameter
Symbol
Value
Focal length Aperture width Collector length Mirror solar reflectance (anodized aluminum with PVD aluminum layer and protective coating) Specular scattering mirrors Absorber tube diameter Absorber tube wall thickness Solar absorptance at normal incidence on the absorber fin (measured at SPF) Angular absorptance dependence (adopted from [26]) Glass tube diameter Glass tube wall thickness Glass tube refraction coefficient on both sides Cover tube transmittance (measured at SPF) Glass tube extinction coefficient Concentration ratio
f a L
647 mm 1845 mm 10.347 m 0.885
Rim angle
q r
a0
4.4 mrad 34 mm 1.5 mm 0.9427
a a0
1 0:017
dabs
dglass
56 mm 2.5 mm 1.473
s
0.895
k C = (L a)/ (p dabs) /r
15 m1 17.3
1 cos hi
1:8
Fig. 2. Scheme of the rotation angles: tracking angle ac, collector inclination bc, collector azimuth cc, the longitudinal and transversal angles hL and hT.
71°
Table 1 presents the dimensions and the physical properties of the NEP PolyTrough 1800. 2.2. Digital inclinometer A tilt angle sensor, model A-2T manufactured by US Digital [27] with connection RS-232C for communication, was used to measure the tilt angle of the solar tracker. This inclinometer was a digital gravity angle sensor that measures inclination on a single axis. The device accuracy was 12-bits. 3. Proposed testing procedure The tracking error characterization proposed was based on the standard IEC 62817 [2] testing procedure. This standard is applicable mainly to double-axis CPV solar trackers. Thus, the proposed testing methodology needs to be adapted for solar thermal PTC trackers, which are mainly single-axis. 3.1. Tracking error characterization For the testing procedure, in order to define the incidence angles of the solar radiation on the collector, first it was necessary to describe three position angles for the collector, two of which were fixed (the collector inclination bc and the collector azimuth cc) and one was moving in order to track the sun (the tracking
angle ac). The angle ac was by definition 0° when the collector aperture was orientated to the zenith, and it represented the rotation angle on the longitudinal axis; the collector inclination bc was also by definition 0° when the collector aperture was orientated to the zenith, and it represented the rotation angle in the transversal axis; the collector azimuth cc was by definition 0° when the collector was orientated to the South, and it represented the rotation angle respect to the South. Fig. 2 illustrates the rotation angles defining the collector position. At first, the solar tracker was positioned on the testing bench or platform. It was crucial to determine the real position of the solar collector, because some errors on the collector positioning could lead to additional tracking errors. The azimuth of the collector cc was set on the testing bench with a precision of ±0.1°. Before the testing sequences, the inclination of the collector bc was measured by a spirit level with an accuracy of ±0.057° and was found to be 0°. To monitor the rotation angle ac, the digital inclinometer, shown in Section 2.2, was located on an aluminum profile which was fixed to a component used for the reflectors holders avoiding torsional or tolerance effects (see Fig. 3). The digital inclinometer was connected by cable to a computer, whose output was recorded every ten seconds. The direct normal irradiance Gbn was measured by a pyrheliometer (model CHP 1 from Kipp & Zonen [28]) and the wind speed u was measured by an anemometer (model WWA 15A from Vaisala [29]. The testing methodology consisted in monitoring the tracker elevation ac, the direct solar irradiance Gb and the wind speed u
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Fig. 3. Picture of the digital inclinometer mounted on the solar tracker.
over several days. The instantaneous data acquired simultaneously with a data logger (ac, Gb, u) was averaged every minute. The transversal and longitudinal incidence angles were calculated by projecting the solar vector hi on the transversal plane (perpendicular to the tracking axis) and on the longitudinal plane (parallel to the tracking axis) of the collector, respectively. First, for the sun’s position, the solar elevation as and the solar azimuth cs were calculated using the solar algorithm reported by BlancoMuriel et al. [30], with an accuracy of 0.5 min of arc (0.0083°). Then, the incidence angles hT and hL were calculated as reported elsewhere [31]. The proposed testing method, based on the standard IEC 62817 [2], requires data recorded for a minimum of five days with a minimum direct normal irradiation Hb of 2400 W h/m2 per day. In addition, the data should be separated into different data bins: one for a low wind (for wind speed u lower than or equal to 4 m/s) and one for high wind speed (for wind speed u higher than 4 m/s). A minimum of total data points (360), a minimum of data points per day (50), and a minimum of data points before and after noon (50) were required. Finally, the typical accuracy and the 95th percentile accuracy were calculated. 3.2. Transversal IAM curve and acceptance angle characterization The aim of this section was to characterize the transversal IAM curve of the concentrating system along the longitudinal plane. The adequacy of the solar tracking system can be verified knowing the acceptance angle ha from the transversal IAM curve. The acceptance angle ha is a key feature of a solar concentrator and can be defined as the maximum angle at which all rays incident on an optical concentrating system are transmitted to its receiver. As suggested by Valan Arasu and Sornakumar [32], in order to determine whether the concentrator matches with the solar tracker, a quality criteria should be that the acceptance angle ha has to be higher than the angular tracking error htrack. In an ideal concentrating system, the solar radiations entering with an incident angle smaller than the acceptance angle are
directed towards the receiver. In a real component, however, optical losses exist due to non-ideal optical properties of materials, dimension of the sun, scattering of mirrors, and geometric position imperfections. These effects cause variations on the theoretical acceptance angle that is obtained assuming an ideal optical system. The IAM defined in many studies [33–37] and standards [1,21,24] is the ratio between the optical efficiency for an incidence angle and the optical efficiency for a normal incidence angle. For a PTC the transversal IAM decreases when the transversal incidence angle hT increases, in absolute value, due to defocusing. That is the reason because an ideal solar tracking for a PTC implies hT = 0°, whereas for a real system a tracking error htrack could occurs which means a non-null transversal incidence angle hT (=htrack – 0°) which leads to a reduced optical efficiency. The transversal IAM values are generally calculated for the longitudinal angle null (hL = 0°). A more detailed study can verify if the acceptance angle is different for hL – 0°, by calculating IAM Kb values for a wide range of transversal and longitudinal angles. The transversal and longitudinal IAM were estimated by a raytracing simulation using a Fortran program previously presented [38] and validated [36,39]. The dimensions and optical properties of the NEP PTC introduced in the simulation program are listed in Table 1. The optical efficiency of the collector gopt was determined for transversal incidence angles between 0° and 4° every 0.1° and longitudinal angles between 0° and 90° every 5°, by simulation issuing 107 rays and assuming a circumsolar ratio of 0.05 [40]. The simulated IAM, Kb,sim, was calculated with Eq. (1) obtaining a whole 3D surface (hT 2 [0, 4]° and hL 2 [0, 90]°). The cos(hi) factor was used for referencing the optical efficiency to the direct solar irradiance on the aperture plane GbT.
K b;sim ðhT ; hL Þ ¼
gopt ðhT ; hL Þ gopt ð0 ; 0 Þ cosðhi Þ
ð1Þ
The theoretical acceptance angle can also be defined in a parabolic trough collector according to Eq. (2) [41], where /r is the rim angle of the parabola and C is the geometric concentration ratio.
ha ¼
sinð/r Þ pC
ð2Þ
The angular acceptance function [41], here referred to as the theoretical transversal IAM, Kb,theor, was given by Eq. (3), where hT is the transversal incidence angle.
K b;theor ðhT Þ ¼
8 > > > < 1
/ > tan ð 2r Þ > > :
1 jhi j < ha rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi /r 2 tan ð 2 Þ pChT 1 ha < jhi j < hd 0
ð3Þ
hd < jhi j
where hd is the defocus angle that is the angle for which all rays miss the receiver and is given by Eq. (4) [41].
1
hd ¼ sin
! 2 tan /2r pC
ð4Þ
The transversal IAM obtained by ray-tracing Kb,sim(hT) was compared to this theoretical function Kb,theor(hT) in Section 4.4. Finally, the acceptance angle value ha was compared to the tracking error htrack in order to verify whether the concentrator optics was adequate to the solar tracking system. Moreover, the acceptance angle ha(hL) was calculated for longitudinal angles hL between 0° and 90°, calculating the threshold for the transversal IAM Kb = 0.98 [24].
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3.3. Estimation of optical losses due to tracking
4. Results
This section aims to quantify the effect of the solar tracker on the concentrator efficiency by using the instantaneous tracking error htrack measured directly with the inclinometer ac (Section 3.1) and the transversal IAM curve obtained by simulation Kb,sim(htrack) (Section 3.2). The optical losses due to tracking error, Dgtrack, were analyzed according to Eq. (5). Considering that the transversal IAM concentrator was symmetric along the optical axis, the tracking error was expected to be dependent on |htrack|.
4.1. Collector positioning
Dgtrack ¼ ð1 K b ðjhtrack jÞÞ 100
ð5Þ
Finally, in order to take into account the variation of the longitudinal IAM Kb(hL), the optical losses due to tracking error were calculated using weights over the whole testing sequence Dgtrack (every one minute) as described in Eq. (6).
Dgtrack
P weighted
¼
g
i ðD track
GbT K b ðhL ÞÞ Dt ðG K b ðhL ÞÞ Dt bT i
P
ð6Þ
The transversal and longitudinal IAM (Eq. (1)) were derived from the 3D surface obtained by ray-tracing Kb,sim(hT).
After the installation of the PTC on the testing bench at SPF, the deviation to the EW orientation cc was determined experimentally in order to ascertain the real positioning of the solar concentrating system. The concentrating solar light on the holders of the receiver was examined. Fig. 4 shows the peak of the shadow on the holders. Assuming that the collector was mounted correctly, it is clear that the receiver was perfectly on the focal line and that all reflector segments were in the correct position. Hence, the majority of rays hitting the reflector should be reflected to the receiver. Only a small part of the reflector was shadowed by the receiver tube that did not receive solar radiation. Fig. 4 shows the shadowed area of the reflector and the concentrated solar light on the receiver. If the collector was tracking with good accuracy, the solar light would hit the bracket of the receiver symmetrically. This analysis was performed with the maximum incident angle. This shadow technique was repeated after changing by 0.1° step the orientation parameter in the tracking software control of the manufacturer, in order to optimize the orientation. The angle of the collector azimuth cc (respect to the south) was estimated to be +0.5° (positive to the west direction), with a precision of ±0.1°. This value was then applied to the tracker controller as a configuration input for the remaining testing days. 4.2. Tracker accuracy estimation
Fig. 4. Schematic picture indicating the shadow (black stripe).
Calculation of the solar elevation as was carried out for the location of the test bench in SPF facilities (latitude = 47.223°N and longitude = 8.818°E determined by the SUNEARTH tool [42] with a resolution of 0.00001°). The variables and requirements described in Section 3.1 were monitored and checked for all the testing days. A statistical analysis was performed in order to study the mean and the standard deviation of the tracking error. The standard deviation was calculated for the one minute average series. Table 2 shows the data range of solar irradiance Gbn and wind speed u for the seven testing days. Only data with as > 10° were selected in order to avoid obstructions in the horizon. A total of 23,022 instantaneous measurements and 3833 mean series were obtained. The maximum wind speed (umax = 3.96 m/s) was lower than the threshold of 4 m/s, because the test was performed according to the standard EN 12975-2 [21] for the solar collector performance under steady-state conditions. The number of measurement points (3833) and testing days (7) was higher than the minimum required by the testing procedure proposal (360 and 5, respectively). The number of points before noon (1856) and after noon (1984) was also higher than the minimum of the procedure proposal (50 for both).
Table 2 Testing data range. Date
Num of instantaneous data
Num of series of one minute
Num of series before noon
Num of series after noon
Mean Gbn [W/m2]
Max Gbn [W/m2]
Hb [W h/m2]
Min u [m/s]
Max u [m/s]
13/08/2012 15/08/2012 17/08/2012 18/08/2012 19/08/2012 21/08/2012 22/08/2012
2767 3298 3716 3732 3748 2982 2779
461 549 619 621 624 496 463
272 254 278 280 281 275 216
190 296 342 342 344 222 248
663 785 859 870 825 595 542
801 902 932 941 905 709 791
5094 7189 8869 9015 8592 4925 4183
0.03 0.01 0.09 0.01 0.01 0.04 0.04
3.96 3.29 2.98 2.38 0.26 1.96 3.52
Total
23,022
3833
1856
1984
–
–
47,867
–
–
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13/8/2012 1.0 0.5 0.0 −1.0 8
9
10
11
12
13
7
14
8
9
10 11 12 13 14 15 16
Hour UTC [h]
Hour UTC [h]
17/8/2012
18/8/2012
0.5 0.0 −0.5 −1.0
−1.0
−0.5
0.0
Tracking error [º]
0.5
1.0
1.0
7
Tracking error [º]
−0.5
Tracking error [º]
0.5 0.0 −0.5 −1.0
Tracking error [º]
1.0
15/8/2012
6
7
8
9 10 11 12 13 14 15 16 17
6
7
8
9 10 11 12 13 14 15 16 17
Hour UTC [h]
Hour UTC [h] 21/8/2012 1.0 0.5 0.0 −1.0
−0.5
Tracking error [º]
0.5 0.0 −0.5 −1.0
Tracking error [º]
1.0
19/8/2012
6
7
8
9
10 11 12 13 14 15 16 17
7
8
9
Hour UTC [h]
10
11
12
13
14
15
Hour UTC [h]
0.5 0.0 −0.5 −1.0
Tracking error [º]
1.0
22/8/2012
8
9
10
11
12
13
14
15
Hour UTC [h] Fig. 5. Inclination error on the solar tracker htrack vs. hour (UTC).
Fig. 5 illustrates the tracking instantaneous error htrack values for the seven days, calculated according to Section 3.1. The oscilla-
tion of the tracking error showed a similar pattern every day and in particular a different behavior before and after noon.
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0.0
Instantaneous mean -70
-50
-30
-10 0 10
30
50
70
4.4. IAM and acceptance angle
Longitudinal incidence angle [°] Fig. 6. Tracking error from the solar tracker htrack for all the testing days: instantaneous (black dots) and mean value for one minute interval (gray) vs. the longitudinal incidence angle hL.
Fig. 6 shows the instantaneous tracking error htrack versus the longitudinal incidence angle of all the testing data, as well as the mean value of every one minute interval, in order to identify the oscillation pattern of the tracking error. The tracking error htrack was between 0.4° and +0.4°. 4.3. Statistical analysis of the tracking error
tracking error histogram
tracking error histogram
(a)
(b)
30
Frequency
15
10
10 5
0
0
Frequency
20
40
25
30
The mean value of the tracking error over one minute interval was (htrack) = 0.05°, and its standard deviation was r(htrack) = 0.18°. On the other hand, the mean value of the absolute tracking error over one minute interval was (|htrack|) = 0.16°, and its standard deviation was r(|htrack|) = 0.10°. Thus, the absolute value clearly differs from the mean value. A minimal mean error implies that the positive and negative values were compensated. The analysis of the absolute angle |htrack| was therefore crucial in order to avoid compensation effects in the average value, and represented the real value of tracking error. Fig. 7(a) shows the distribution of mean tracking error over one minute interval htrack, and Fig. 7(b) shows the distribution of the absolute value |htrack|. Two different peaks were observed in Fig. 7(a), one for the tracking error values centered on 0.275° ± 0.02° and another centered on 0.075° ± 0.02°. About
In this section, the dependency of the optical efficiency of the concentrator to the incidence angles was determined. The transversal IAM curve of the concentrator was calculated as specified in Section 3.2. Fig. 8 shows the IAM Kb,sim for hT between 0° and 4° and for hL between 0° and 80° obtained by ray-tracing simulation. Fig. 9 shows the transversal IAM Kb,sim(hT) obtained by simulation on the longitudinal plane when hL = 0°. The acceptance angle obtained by simulation, which is the angle threshold for which Kb,sim(hT) > 0.98 [24], was ha,sim = 0.58°. The theoretical value of the acceptance angle calculated according to Eq. (2) was ha,theor = 0.998°, and the theoretical value of the defocus angle calculated according to Eq. (4) was hd,theor = 1.506°. Fig. 9 shows how the simulation transversal IAM Kb,sim decreases for transversal angles hT between 0.58° and 2°, which is a range much larger than the range of decrease of the theoretical transversal IAM Kb,theor (0.998–1.506°) calculated from Eq. (3). Thus, techniques using ray-tracing allow a more detailed characterization of the optical behavior of a solar concentrator taking into account the optical properties of the PTC and the sun shape. Using the ray-tracing results the dependency of the acceptance angle on the longitudinal incidence angle can be determined. Fig. 10 shows that the simulation acceptance angle ha,sim(hL) was not constant while varying longitudinal angles, although this variation was very small (less than ±0.17°, with an average value of 0.42°). A slight increase in the acceptance angle was observed for longitudinal angles >65°. Thus, the solar tracker error should be below the minimum value that occurs for hL = 65° (0.25°), and
20
-1.0
-0.5
tracking error [°]
0.5
1.0
the mean absolute tracking error, in Fig. 7(b) only one peak was observed centered at 0.03° ± 0.02°. The 95th percentile accuracy was calculated, and for |htrack| a value of 0.33° was obtained. The mean tracking errors calculated before noon (hL < 0°) and for the afternoon data (hL > 0°) were found to be 0.223° and 0.095° respectively, which were very close to the two peaks observed in Fig. 7(a). Hence, the two peaks are related to the solar tracking behavior before and after noon. The dependency of the tracking error htrack on the wind speed u was analyzed by calculating the correlation factor between the tracking error htrack on the wind speed u. But the r2 was really low (0.467). So the dependency of the wind speed was concluded to be not significant from the available data.
−0.4
−0.3
−0.2
−0.1
0.0
mean tracking error [º]
0.1
0.2
0.0
0.1
0.2
0.3
0.4
mean absolute tracking error [º]
Fig. 7. Distribution of the tracking errors (a) mean over one minute series and (b) mean absolute over one minute series.
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Fig. 8. IAM obtained by simulation 3D surface.
should not consider exclusively the value of acceptance at normal incidence hL = 0° (0.58°). It is important to point out that the value of 0.25° proposed for the tracking error was lower than 0.998° obtained by theoretical results (Eq. (3)). Hence, the procedure proposed in this study was more restrictive for the required accuracy of the tracking error, and aimed to minimize the optical losses. 4.5. Estimation of optical losses caused by the tracking Using the transversal IAM curve Kb,sim(hT) obtained by optical simulation obtained in Section 4.4 and the tracking error distribution obtained in Section 4.3, the optical losses were calculated according to Eq. (5). Fig. 11 shows the distribution of the optical losses. The majority of optical losses were almost null, except to few that reached 4%. The weighted optical loss using the tracking error Dgtrack calculated according to Eq. (6) and using one minute interval average points was 0.317%.
0.5
1.0
1.5
Sim. acceptance angle theoretical acceptance angle theoretical defocus angle
0.0
Acceptance angle [º]
2.0
Fig. 9. Transversal IAM obtained by simulation Kb,sim(hT) compared to theoretical Kb,theor.
0
20
40
60
80
Longitudinal incidence angle [º] Fig. 10. Acceptance angle dependency on the longitudinal incidence angle by simulation ha,sim(hL) and acceptance angle ha,theor and defocus angle hd,theor by calculation.
Fig. 11. Optical losses distribution calculated from mean tracking error over one minute series.
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The 95th percentile for the optical losses was measured to be 2.51%, which means that at 95% of the time the optical losses were below this value. In term of energy, for the NEP collector having an optical efficiency g0 = 0.69674 and an aperture area of 18.45 m2 as published in Larcher et al. [22], the energy loss due to the solar tracker would be 4.5 MJ, which was negligible compared with the theoretical output energy without tracking optical losses neither heat losses given a value of 1622 MJ. 5. Conclusions The solar tracker of a concentrating collector was tested according to the standard draft methodology redaction in the Spanish committee AEN CTN 206/SC 117 [3] and adapted from the IEC standard [4]. This study focused on the estimation of the optical losses due to tracking errors for a small-size PTC medium-temperature collector, but it could be applied to a general single-axis solar tracker. The main conclusions were the following: The angular tracking error could be accurately characterized using a digital inclinometer. The testing methodology proposed by the Spanish committee to the International standard committee [4] was experimentally verified for one single-axis tracker. The proposed procedure, combining experimental data and ray-tracing simulations, allowed the determination of the optical losses due to solar tracker for a given optical system. A solar tracker of a small-size PTC was characterized. The tracking error measured during the testing process htrack was within ±0.4°, the 95th percentile of the tracking accuracy was ±0.33°, and the weighted optical loss was 0.317%. As the optical losses due to tracking error could be a source of uncertainty on the optical efficiency, a recommended maximum acceptable value for those optical losses could be the optical efficiency uncertainty u(g0). But in this case the value of u(g0) was not provided in the collector characterization published by Larcher et al. [22]. The transversal IAM curve was determined by ray-tracing simulation for all longitudinal incidence angles as well as on the transversal incidence plane. The proposed procedure using ray-tracing to evaluate the acceptance angle gives a better required accuracy for the tracking error than the theoretical acceptance angle. By this way, the acceptance angle ha was determined for longitudinal incidence angles between 0° and 80°, and the minimum acceptance angle should be taken into account for the solar tracker accuracy. The theoretical acceptance angle and the theoretical defocus angle give values that are not related to the real optical behavior. Hence, the use of optical simulation should be allowed in the standards in order to determine the optical behavior of solar concentrating systems. In future works, other type of solar trackers for solar thermal applications will be tested with this methodology in order to validate completely the standard draft proposal. The influence of the wind speed on the tracker accuracy will also be considered in future studies by testing a solar tracker in more windy locations. Acknowledgements The authors would like to thank SPF for the testing data and NEP Solar AG for letting us to use those data. The authors would also like to thank the National Renewable Energy Centre (CENER), the Public University of Navarra (UPNA) and the University of Balearic Islands (UIB) for time dedication.
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