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ScienceDirect Energy Procedia 00 (2015) 000–000 www.elsevier.com/locate/procedia
International Conference on Concentrating Solar Power and Chemical Energy Systems, SolarPACES 2014
Sunshape measurement using a sky imager R. Chauvin1, J. Nou1, E.Guillot1, S. Thil1,2 and S. Grieu1,2,* 1
PROMES-CNRS, Rambla de la thermodynamique, Tecnosud, 66100 Perpignan, France University of Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860 Perpignan, France
2
Abstract Atmospheric properties play a key role in the evaluation of the solar power plant output. Indeed, properties such as the cloud cover and distribution or the aerosol optical depth strongly influence the solar resource availability and variability. Consequently, it is recommended to integrate such information into the plant control strategy in order to avoid over- or underestimation of the electricity generation. Among the different properties to be considered for solar concentrating systems, the radial distribution (sunshape) of the incident solar energy is known to be a driving factor of the concentrator optical efficiency. This sunshape is created by scattering effects of the sunlight produced by aerosols and cloud particles. Measuring the sunshape would provide valuable information about the beam attenuation produced by the atmosphere and would help the plant operator to reduce losses through a more accurate evaluation of the solar resource and its impact on the power plant efficiency. This paper deals with an image processing methodology using a sky imager in order to measure the sunshape and correlate it to the solar resource availability under clear sky conditions. © 2015 The Authors. Published by Elsevier Ltd. Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG. Keywords: Sky imager; sunshape; atmospheric scattering; DNI.
1. Introduction It is widely acknowledged by solar companies and plant operators that cost remains the main drawback of Concentrating Solar Power (CSP) systems. In that context, the CSPIMP (Concentrated Solar Power efficiency IMProvement) project has been initiated in 2013 in order to make CSP plants more competitive. The main target of
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[email protected] 1876-6102 © 2015 The Authors. Published by Elsevier Ltd. Peer review by the scientific conference committee of SolarPACES 2014 under responsibility of PSE AG.
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the project is to improve plant efficiency by developing better procedures for steam turbine start up cycles, maintenance activities and plant control. Regarding the plant control procedures, solar resource assessment and forecasting allow the plant operators to better manage the solar field and the heat transfer fluid flow in real-time. Currently, most of the CSP plants operators only use the Direct Normal Irradiance (DNI) and some basic climatic information, such as the ambient temperature and the wind speed and direction, to operate their plants. However, such measures are not enough to fully understand and anticipate the plant behavior during cloudy days, hazy days or when the concentration in atmospheric particles fluctuates. To overcome these limitations, other devices can be installed on-site to measure the cloud cover, its distribution, its motion, the aerosol content in the atmosphere and its impact on the angular distribution of the DNI. From this point of view, a sky imager is well adapted for the plant operators. Indeed, this device provides a hemispherical view of the whole sky, allowing the cloud cover and the cloud motion to be measured. Both are essential in order to estimate and forecast the direct beam attenuation produced by clouds. In addition, the camera also measures the sky intensity distribution from zenith to horizon. It results that the intensity distribution near the sun (i.e. the sunshape) can be computed for any sky images. On top of that, the camera involves low-cost components, has a robust build (no sun tracker) and does not require much maintenance. As a consequence, due to its abilities and specificities, the sky imager might become an essential tool in the coming years to operate solar plants efficiently. This paper deals with an image processing methodology using a sky imager in order to measure the sunshape and correlate it to the solar resource availability under clear sky conditions. It is organized as follows. Section 2 provides a review of the sunshape measurement, its application to the CSP technology and some details concerning the existing sky imager. Section 3 introduces the experimental setup. Section 4 presents the methodology used to generate the sunshape. Section 5 ends with some results concerning the sunshape fluctuations and the relationship between sunshape and atmospheric turbidity. 2. Context 2.1. Considerations about sunshape
Fig. 1. Overview of the Mie and Rayleigh scattering effects.
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Under clear sky conditions, the direct sunlight is scattered and absorbed by particles during its path through the atmosphere. Depending on the size of the particles, two effects can be found: the Rayleigh scattering and the Mie scattering. The former is produced by particles up to about a tenth of the wavelength of the incident light, while the latter is produced by larger particles and is much more intense in the forward direction (Fig. 1.). It results that Rayleigh scattering effects are visible far from the sun, when sunlight is highly scattered, whereas Mie scattering outshines Rayleigh scattering in the circumsolar area, when sunlight in the forward direction predominates. Unlike the Rayleigh scattering, the Mie scattering is not strongly dependent on the wavelength; it produces a white glare around the sun. In addition, the forward intensity of the Mie scattering depends on the size of the atmospheric particles. Large particles produce a more intense forward lobe than small particles. Therefore, the shape of the aureole surrounding the sun, hereafter named the sunshape, fluctuates depending on the distribution of the particles' size. Conversely, measuring this shape can give an idea about the size distribution of the aerosols and cloud particles, which is useful information for climatic studies. Because of its dependency on particles' size, the Mie scattering is responsible for the spatial and temporal fluctuations of the sunshape. This sunshape can be related to the energy distribution of the sun, defined by the radiance emanating from both the circumsolar region and the solar disk [7–9]. In the performance analysis of concentrating collectors, it is important to consider the circumsolar radiation because of the angular sensitivity of the CSP technologies [10–12]. Indeed, CSP collectors receive only a small part of the circumsolar region (< 1°, typically), whereas it is nearly completely detected by pyrheliometers (~ 2.5°). This causes an overestimation of the DNI and, as a result, of the power plant output. Consequently, many attempts have been made in the past to measure the solar aureole profiles with various measuring systems involving digital cameras, scanning photometers, and telescopes. The first significant attempt was conducted by the Lawrence Berkley Laboratory which recorded nearly 180,000 sunshapes from 11 different U.S. sites between 1976 and 1981 [7]. They have used a telescope, mounted on a solar tracker, equipped with a narrow circular aperture allowing solar intensity up to 3.2° from the sun centre to be measured. A reduced and cleaned database was extracted from these measures and used as a starting point to evaluate the fluctuations of the circumsolar radiation as a function of time and location. Later, the German Aerospace Centre (DLR) acquired about 2,300 solar profiles from three different sites across Europe using a cooled CCD camera [8]. A pyrheliometer and a pyranometer were added to the measurement set up in order to correlate the estimated circumsolar radiation with DNI and GHI. The camera was mounted on a sun tracker, making this system well-designed for sunshape measurement purpose, but less robust and less versatile than a sky imager. Based on these preliminary studies, a sunshape measurement system using a Sun & Aureole Measurement (SAM) instrument, a sun photometer and a post-processing software have been developed. This system seems to be the most successful with its ability to estimate the broadband sunshape and get information on aerosols and solar spectrum, based on radiative transfer models [9]. The SAM uses two spectrally-filtered and calibrated CMOS cameras mounted on a solar tracker and delivered with a processing algorithm to analyze image data (Fig. 2.a). This system has been shown to greatly outperform the previous one from DLR (30% less uncertainty). Three SAM are currently operational, one master system running at PSA, and two replica respectively installed in the Masdar Institute and in the PROMES-CNRS laboratory located in Odeillo. The main drawback of this instrument is its cost. In order to overcome the price limitation, an alternative method for determining the sunshape was elaborated and verified using the SAM as a reference. In this method, a pair of pyrheliometers with different angular acceptance functions is used (Fig. 2.b). By comparing the measurements of the two pyrheliometers, the amount of circumsolar irradiance can be determined [10]. Finally, a low cost, field-deployable instrument has also been developed at the Masdar Institute of Science & Technology. It is based on a Rotating Shadowband Irradiometer specifically modified to measure the circumsolar radiation (Fig. 2.c). It uses a slit receiver which is gradually occulted by the shadowband in order to measure the irradiance profile. The system, named the Sunshape Profiling Irradiometer (SPI), only needs one axis tracker and is more resilient to soiling than the other instruments. The measured sunshapes have been compared to those estimated by the SAM installed in the Masdar institute. First results were encouraging. Nonetheless, further work must be achieved in order to improve the SPI accuracy [11]. To conclude, the sunshape can be used for optimizing the acceptance angle of the collector, based on local measurements of the circumsolar irradiance distribution, computing the real-time optical efficiency of the collectors and/or inferring the aerosol distributions for climate studies.
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(a) Sun & Aureole Measurments system Visidyne
(b) BPI CSR 460 sensor Black Photon Instruments
(c) Sunshape Profiling Irradiometer Masdar Institute
Fig. 2. View of different instruments designed for measuring the radial distribution of the incident solar energy.
The following table summarizes the qualities and drawbacks of each instrument detailed above: Table 1. Overview of the pros and cons of the different sunshape instruments.
Instrument SAM + Sun photometer BPI CSR 460 SPI
Axis 2 axes
Price
2 axes 1 axis
X
Sky camera
No axis
Pros Very high accuracy Broadband and spectral sunshapes High accuracy Cheap & robust Low needs of maintenance Cheap & robust Extended abilities to measure and forecast the solar resource
Cons Expensive High needs of maintenance High needs of maintenance Low accuracy Not fully operational yet
2.2. Sky imagers From subsection 2.1, it is clear that sky imagers can compete with others systems using a camera. Among the existing commercial sky-imaging systems, the most known is the Total Sky Imager developed by Yankee Environmental Systems. It uses a hemispherical mirror to reflect the sky hemisphere into a downward-pointing camera. Other industrial sky imagers exist, such as the SRF-02 and the VISJ1006 cameras, respectively developed by EKO Instruments and Schreder CMS. However, these commercial solutions suffer from a low camera resolution and limited possibilities of customization, preventing any improvement specific to the power plant needs. On the other hand, many customized solutions have been used for research applications, using a non commercial sky imager. One of the first major systems is the Whole Sky Imager developed since the 1980s [12] for military applications by the Atmospheric Radiation Measurement Climate Research Facility. The system is able to detect clouds during daytime and nighttime thanks to very sophisticated algorithms with accurate detection of haze, thin clouds and opaque clouds. Nevertheless, it is not inexpensive to build a system with such qualities. As a consequence, other laboratories have developed cost-effective alternative systems based on a camera equipped with a fisheye lens and protected by a weatherproof enclosure [2, 3]. Among them, we find the Whole Sky Camera, developed by the University of Girona [15], the All-Sky Imager developed at the University of Granada [16] or the sky imager developed by the University of California, San Diego (UCSD) [17]. The UCSD Sky Imager (USI) seems to be the most advanced system. It is specifically designed for the short-term forecasting of solar irradiance. It involves high quality components associated with sophisticated algorithms. The USI is able to provide a cloud map of the studied location, allowing the forecast of ramp events for large solar plants. However, according to their authors, a large part of improvement is still possible, both in technical and scientific terms [17]. Nevertheless, the first works published by these laboratories are encouraging and motivated PROMES-CNRS to get involved in this challenging topic. Consequently, an experimental unit has been installed on the laboratory roof in 2013 in order to develop a customized tool for solar resource assessment and forecast.
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3. Experimental setup PROMES-CNRS decided to build its own system, fully customizable both from a hardware and software point of view. This decision is motivated by the fact that all the existing sky imagers suffer from drawbacks and PROMES-CNRS believes that a custom solution would make such systems more attractive. After a detailed review of the different cameras proposed by manufacturers, a 5 megapixels camera with a color CMOS sensor has been selected. The camera, named 5481VSE-C and provided by IDS-imaging, is equipped with a Fujinon fisheye lens and protected by a waterproof enclosure manufactured by autoVimation (Fig. 3). A CMOS sensor has been preferred to a CCD sensor because in the CCD structure charge flows in the direction where pixels are read, whereas in CMOS sensors the readout is performed locally at each pixel. It results that CMOS sensors are inherently more resilient to smear effect and blooming than CCD sensors near the sun area. Moreover, the camera is simple and easy to setup and operate thanks to its on-board video server offering an intuitive browser-based interface. It is also easy to integrate thanks to the power supplied via Ethernet and the minimal memory requirements because of the MJPEG data compression format. Images are collected every 20 seconds at a resolution of 1920 x 2560 pixels with 8 bits per channel. Finally, the PROMES sky imager is not equipped with a solar occulting device which is frequently used to reduce the light intensity reaching the sensor. Indeed, although this device improves the sky visibility by reducing pixels saturation, it occults the circumsolar area which provides vital information concerning the sunshape measurement. To sum up, the advantages of our system over standard sky imagers include high quality components, a high sensor resolution, a robust build, a small form factor and a full programmability.
Fig. 3. PROMES-CNRS sky imager and a few snapshots.
4. Sunshape measurement In this section, the methodology to estimate the sunshape is detailed. First, the calibration step, which is essential in the sunshape measurement process, is described. Then, the generation of the sky intensity map is briefly presented. This map allows computing the radial distribution of the pixel intensity from the sun to the horizon. 4.1. Camera calibration A geometric angular calibration of the camera has been performed in order to get the relationship between a given pixel on the image and its projection onto the unit sphere. The OcamCalib toolbox [18] has been used to calibrate the camera. It allows an easy calibration of the camera through two steps. First, pictures of a checkerboard in different positions and orientations are taken (Fig. 4). Then, an automatic corner extraction is performed and a least square linear minimization method is used to fit these points with a four-order polynomial. Once the camera is calibrated, it is possible to calculate the Pixel/Zenith Angle ( ) and the Pixel/Azimuth Angle ( ) for every
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pixel on the image, assuming that the camera is pointing the zenith. However, this last assumption is generally not met: the camera is not perfectly aligned with the zenith in reality. Thus, during operating time, a second calibration is automatically performed daily, using the sun position: since the misalignment with the zenith produces a wrong detection of the sun on the image, the camera orientation can be corrected by comparing the real position of the sun with its position on the image. The real position of the sun is calculated using the SG2 algorithm [19], whereas the position of the sun on the image is computed using the circular Hough transform. Finally, from a set of theoretical and real points acquired through the day, a rotation matrix is computed to correct and . In the end, it is possible to get the sun position on the image at any moment, even during cloudy days. This calibration also enables the computation of the Sun/Pixel Angle ( ) for every pixel on the image.
Fig. 4. PROMES sky imager calibration and the resulting sun path.
4.2. Sky intensity map Once the camera is calibrated, the zenith and azimuth angles for every pixel on the image are known ( and ), as well as the angle between the pixel and the sun center ( ). Studies about the relative irradiance and luminance distributions of the sky have exhibited that these distributions can be modeled as a function of and [20–22]. For that reason, it has been decided to transform the sky images provided by our camera into a sky ) coordinate system (Fig. 5). For the sake of computational time, the sky maps are intensity map in the ( generated with a mesh of 1° for both and coordinates.
Fig. 5. Transformation of the sky image into the sky map.
4.3. Sunshape The sunshape can be extracted from the sky intensity map by collecting pixels for which Solar/Zenith Angle ( ): (
)
(
)
is equal to the
(1)
where is the sky intensity map and is the intensity profile of the sunshape measured on the image. For instance, in Fig., . This means that the sunshape corresponds to the rows in the sky intensity map displayed in Fig. 5.
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5. Results and discussion This last section provides some results and discussion about the sunshape and its correlation with atmospheric turbidity. First, the intensity profile from sun to horizon is examined and compared with previous studies. An improved measurement methodology is then detailed. Finally, the measured sunshapes are confronted with the estimated turbidity. 5.1. Considerations about the sunshape profile As mentioned in subsection 4.3, the sunshape corresponds to the row of the sky intensity map where is equal to . Nevertheless, in previous works [13–15], the sunshape is calculated in the circumsolar area without considering . This approach was motivated by the good radial symmetry of the intensity at low . Indeed, we observe in Fig. 5 that the sky intensity map is weakly dependent on for low values, whereas the radial symmetry is lost when increases. For low values, Grether [7] observed that the sunshape profile is almost linear in log-log space in the circumsolar region of the sky: ̃ Consequently, we evaluated the linearity of sunshape without considering the (i.e.
(
)
(2)
, in log-log space, and compared this measure with the estimated 〈 ( )〉). Results are shown in Fig. 6:
Image 1
Image 2 Fig. 6. Pixel intensity profile as a function of SPA using the previous method and the proposed method.
First, we observe that for a low (typically ), both methods yield an almost linear profile in loglog space. The slopes and origins of the lines are similar. However, for higher values, the previous method gives a sunshape that is not linear anymore, whereas it is still the case using the proposed method. This extended linear range allows the sunshade profile to be fitted using a bigger range of values. This is interesting because it increases the robustness of the sunshape intensity profile calculation, especially when there are clouds located in the circumsolar area, which prevents the sky intensity map to be computed for a low . We also notice that no information is available for , due to the saturation of the sensor in this region. This saturation might produce a wrong detection of the circumsolar intensity because of the large gap between the real sun disk diameter ( ) and the one observed in the image. Consequently, the sunshape has been also estimated from the same scene, using a shorter exposure time (Fig. 6). Let's note that the sunshape from Image 2 has been resized in order to match with the sunshape computed from Image 1. First, we observe that the two sunshapes have the same linearity when is higher than 8°. The linearity of the sunshape from Image 2 is less obvious when is higher than 40° due to the low signal-to-noise ratio in that region. On the other hand, the linearity is
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slightly changed when is lower than 8°. To understand this effect, we computed the normalized standard deviation of the sunshapes generated from the two images. The result is shown below:
Fig. 7. Normalized standard deviation of the sunshapes computed from Image 1 and Image 2.
As seen on Fig. 7, the standard deviation of the sunshape generated from Image 2 is significant when is low (up to 12% for ). Therefore, the slope breaks happening for lower than 8° can be due to the radial asymmetry of the pixels intensity in this region. In addition to the calibration errors, strongly emphasized when getting closer to the sun, this asymmetry can be explained by the artifacts on the image (dome soiling, lens flare and blooming effects) and the pixels non-linearity response when pixels are close to their saturation level. However, the respective contributions of these errors are difficult to evaluate. Because the standard deviation of the sunshape generated from Image 1 is twice lower than the other one, we can expect that a significant part of the asymmetry is due to the calibration errors. Indeed, both images have artifacts whereas the calibration error is less apparent as we move away from the sun center. It is deduced that a recalibration of the sky imager has to be done. Regarding the artifacts, work is ongoing in order to remove them from the sky intensity map. However, the relationship between the pixels intensity in the circumsolar area and has been verified and the proposed measuring methodology proves to be more robust for high than the one used by DLR. 5.2. Improvement of the intensity profile measurement Fig. 8 shows the intensity profiles, extracted from the sky intensity map in Fig. 5, as a function of different values:
and for
Fig. 8. Pixel intensity profile as a function of SPA, for different PZA.
We note that the slope of the sunshape is independent of , whereas it is not the case for the origin of the line. It means that can be computed using any of these intensity profiles or a combination of these profiles. Again, the extended linear range obtained as a result of the proposed method allows computing even during highly cloudy days, as long as enough clear sky points are detected on the image. For very large ( ), the intensity profiles seem to increase again. It is especially noticeable when is also large, meaning that the pixel is close to
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the horizon. An explanation is as follows. According to subsection 2.1, for large and/or , Rayleigh scattering becomes predominant. It can be expressed as a function of according to the following equation: (
)
(
As a consequence, the intensity profile ̃ along a specific (2) (i.e. Mie scattering) and equation (3) (i.e. Rayleigh scattering): ̃
(
̃
)
(
)
̃
(
)
(3)
can be formulated as a combination of equation
)
(
From Fig., it is clear that and are also dependent on . Supposing that dependency on , the sky intensity map can be written as follows: ̃
(
)
(
)(
(
) ,
(4) and
have the same
) )
(5)
) is named the gradation function and can be found in [20–22]. { } ⟦ ⟧ are coefficients independent where ( of . The following figure (Fig. 9) corresponds to the fit of the sky intensity map corrected by the gradation ). This very good result validates the previous assumptions. function (
Coefficients values:
{
Mie scattering
Rayleigh scattering
Coefficient of determination:
Fig. 9. Pixel intensity as a function of SPA for the sky intensity map corrected by the gradation function.
5.3. Sunshape versus atmospheric turbidity The sunshapes of eighteen clear-sky images have been generated using the previously described method. The corresponding turbidity has been derived from a broadband measurement of the DNI. Results are summarized in the following figure (Fig. 10):
Fig. 10. Correlation between the sunshape slope and atmospheric turbidity.
As seen on Fig. 10, the sunshape fluctuates from day to day. The images used to perform this analysis were taken with different exposure times. Consequently, only the slope can be compared from one image to another.
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Concerning the correlation between atmospheric turbidity and the sunshape slope, it is hard to bring out a clear relationship. However, it seems that a high slope value, which means a spread sunshape, comes with a high turbidity value. It makes sense because a large turbidity means a polluted atmosphere and thus more Mie scattering. 6. Conclusion A new methodology for measuring the sunshape, using a sky imager, has been presented in this paper. The sky imager has been chosen for its potential ability to measure a wide range of climatic information as the cloud cover, the cloud distribution or the sunshape. Regarding sunshape measurement, a calibration of the camera using a checkboard and the sun position is firstly required in order to compute the subtended angle between pixels, zenith, ) coordinate system azimuth and sun. Once the camera is calibrated, the sky images are mapped into the ( in order to emphasize the correlation of the pixels with both and . The sunshape simply corresponds to the row where . A detailed analysis of the sunshape has shown that this method is more reliable than the method used by DLR and allows the sunshape for an extended range of values to be computed. In addition, the influence of both Rayleigh scattering and has been assessed and a general model of the sky intensity distribution has been established. To conclude, the sunshape slope has been compared with atmospheric turbidity. The two parameters are clearly connected and work is ongoing to highlight their correlation. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
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