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An appraisal of the geometry and energy efficiency of parabolic trough collectors with laser scanners and image processing
Accepted Manuscript An appraisal of the geometry and energy efficiency of parabolic trough collectors with laser scanners and image processing Santiago Salamanca, Pilar Merchán, Antonio Adán, Emiliano Pérez PII:
S0960-1481(18)31333-8
DOI:
https://doi.org/10.1016/j.renene.2018.11.014
Reference:
RENE 10777
To appear in:
Renewable Energy
Received Date: 5 June 2018 Revised Date:
24 September 2018
Accepted Date: 4 November 2018
Please cite this article as: Salamanca S, Merchán P, Adán A, Pérez E, An appraisal of the geometry and energy efficiency of parabolic trough collectors with laser scanners and image processing, Renewable Energy (2018), doi: https://doi.org/10.1016/j.renene.2018.11.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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An Appraisal of the Geometry and Energy Efficiency of Parabolic Trough Collectors with Laser Scanners and Image Processing
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Santiago Salamanca1), Pilar Merchán2), Antonio Adán3) and Emiliano Pérez2)
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Corresponding Author: Escuela de Ingenierías Industriales. Universidad de Extremadura. Avda. de Elvas s/n. 06006 Badajoz. Spain. Email: [email protected]. Tlf: +34 924289300. Fax: +34 924289601
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Escuela Superior de Informática. Universidad de Castilla la Mancha. Paseo de la Universidad, 4. 13071 Ciudad Real. Spain. Email: [email protected]
Abstract
This paper presents an original method for the analysis of the geometric and optical properties of parabolic solar trough collectors using laser scanners and image processing techniques. The aim of the paper is to propose a methodology with which to automatically analyse geometric errors in the mirror and receiver, in addition to presenting an empirical assessment of one of the most important factors that determines the entire energy efficiency of solar plants, which is optical efficiency. The definition of canonical images has allowed us to characterize a set of parameters that evaluates errors on both the surface of the parabolic reflector and regarding the orientation of the receiver. In this framework, energy efficiency is established in terms of two parameters, denominated as the interception index and the concentration index. The proposed method has been tested on-site on real surfaces of parabolic solar trough collectors in an operating solar thermal plant. The results obtained are sufficiently accurate and reliable to be able to recommend that researchers and plants reproduce this method in this kind of installations.
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Keyword: parabolic solar trough collectors, solar thermal power plants, laser scanners, 3D data processing, 3D surfaces.
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: Escuela de Ingenierías Industriales. Universidad de Extremadura. Avda. de Elvas s/n. 06006 Badajoz. Spain. Email: {pmerchan, emilianoph}@unex.es
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1. Introduction
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Parabolic trough power plants are one of the most important methods by which to convert solar energy into electric energy [1][2]. They consist of solar collectors composed of cylindrical parabolic mirrors and a linear receiver (a tube) located at the focus of the parabola.
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The performance of these power plants is influenced by many factors, the most significant being the optical efficiency of the collectors. As is shown in Section 2.1, the theoretical formulation of optical efficiency takes into account aspects such as shadows between solar collectors, errors when the mirrors attempt to track the sun, or a loss of mirror reflectivity owing to the effects of weather and wind. All of these random disturbances can, of course, be modelled and introduced into the final equation. However, the principal loss of energy originates from optical errors in the solar collector system. Optical errors might appear either as the result of the mirrors being placed
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wrongly or because of failures in the manufacturing process. In the latter case, some solar rays would not reach the tube, located in the focus of the parabola, and the heat transfer fluid would not be heated to the adequate temperature. The geometric quality of the solar collectors, therefore, strongly influences the efficiency of a solar thermal power plant. This makes the identification and analysis of the geometry of the solar collector essential.
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Several sensory systems and methods that analyse the geometry of a parabolic trough have been proposed in the last few decades. An extended classification of the techniques used for the characterization of reflective surfaces of solar concentrators can be found in [3].
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The geometric errors detected in the surface of solar collectors can be classified in random or non-random errors. Random errors are mainly due to external causes (e.g. weather, wind, dirt...), whereas non-random errors come from failures in the manufacturing, installation and maintaining processes. These errors greatly alter the solar receiver performance and are closely related to the geometry of the whole reflector [4]. The most important non-random errors are the contour (or slope) and the canting errors. Contour errors refers to deviations from the shape of the mirror, whereas canting errors concern to deviations of the orientation of the individual mirror facets from the nominal directions [3].
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The family of the Hartmann tests, and their variants, is the most effective method that detects shape errors in receivers. In general, these tests are based on analysing the reflected rays at different points of the receiver. The differences between the various versions are in the way to sample and to record the information. In the classical version, a light source, located near the centre of curvature of the mirror, passes through a mask of holes, projecting an array of individual rays into the mirror. The reflected rays are then registered on a photographic plate, thus producing a Hartmann pattern. The Scanning Hartmann Optical Test (SHOT) [5], is a further version that uses a laser source. In this case, the laser source is automatically pointed to a set of predefined positions of the mirror and a photographic plate sequentially records the reflected rays. With this procedure, only slope errors can be detected. A more advanced system, called The Video Scanning Hartman Optical Test (VSHOT), is developed in [6,7]. The photographic plate is here replaced by a camera and a video system. This system recognizes slope and shape errors. Recently, Wheelwright et al. [8] have proposed a new variant of the Hartmann tests based on the generation of a set of light rays that are parallel to the optical axis. The setup consists of an array of lasers on board a moving bar that sweeps the area of the receiver. This procedure therefore decreases the time of the Hartmann test, but requires a more complex and precise experimental system.
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Deflectometry systems [9][10] project structured light patterns onto the target surface, but they have got similar limitations as regards the rapid inspection of large solar plants. Xiao et al. [11] provide a detailed explanation of these different methods for the shape measurement of solar concentrators. However, although they have proved to be useful in the mirror manufacturing phase and structure design stage, none of them would appear to be appropriate once the parabolic troughs have been installed.
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Photogrammetry is a high precision technique used for inspecting standard collectors [12]. The first works about how to use of photogrammetry in the geometric evaluation of solar receivers are published by Shortis and Johson in [13] and [14]. They show a photogrammetric experimental setup that efficiently carries out the data collection stage and propose several basic tests for the assessment of the surface of the receiver. A more in-depth study about the use of photogrammetric 3D data from mirrors and structures that support mirrors is presented by Pottler et al. in [15].
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Beyond the detection of contour and shape errors, some authors have used photogrammetric data to estimate some characteristic parameters of solar collectors, such as the intercept factor. The intercept factor can be calculated from the directions of the solar rays reflected from the parabolic receiver. With this objective, García et al. ([16]) propose a method that first projects the collected data of the mirror into the XY-plane, and then discretises the projected data in a triangular mesh. The normal vectors of the triangular facets are eventually used to calculate the intercept factor. In [17], a similar triangulation-based approach is obtained from a commercial software. Contrary to these approaches, the intercept factor (in fact, an extension of this concept: the interception indexes) has been estimated avoiding such a triangulation process in this paper (Section 2.4), which greatly simplifies and speeds up its calculation. In addition, another characteristic parameter, called energy concentration index, is defined.
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As a major problem, photogrammetric techniques can be tedious and slow. Depending on the size of the scanning project, the whole process, from the targets placement to the target coordinates extraction, could takes from 12 to 24 hours. Therefore, the use of photogrammetry and deflectometry should be restricted to evaluate the quality of the solar concentrators within the design and manufacture phases. Once the receivers have been installed in the solar thermal power plant, the use of these techniques for quality assessment tasks becomes unfeasible.
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3D measurement using laser systems has become increasingly popular in recent years. The range of measurement, manoeuvrability, ease of use and speed, together with the accuracy and resolution of phase shift or time of flight laser scanners [18], make this kind of sensors highly appropriate for the optimisation of solar collector geometries. This method is, therefore, worth investigating, especially when used under working conditions [19]. F. de Asís López et al. [20] demonstrate that the main advantages when using a TLS (Terrestrial Laser Scanner) to characterize a parabolic trough collector, in comparison with photogrammetry, are that less time is needed for data collection – an important consideration in the case of solar fields with large numbers of collectors – and it is simpler to process the point cloud.
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In this paper, a technique that automatically analyses the vast amount of data that are collected after scanning a solar receiver with a TLS is proposed. The objective is to characterise both the optical errors and the energy efficiency of a parabolic trough collector by using computer vision resources. This methodology could be very useful in working solar plants, releasing the operator from making tedious measurements and assessments in the field.
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Compared to the aforementioned approaches, the main contributions of this work are:
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To the best of our knowledge, this is the first work that presents a complete framework that detects geometric errors in parabolic trough collector using terrestrial laser scanners. The canonical image is an original data structure that provides an easy-to-use as-built model representation of parabolic trough collectors. In addition, the canonical image allows to process the data with computer vision algorithms, which provides precise and visual results. Using the proposed framework, the operator can detect imperfections in the parabolic reflector surface and deviations of the receiver pose on site. The former intercept factor is extended with new parameters related to the the raytracing in the parabolic trough collector. These are the -image, the interception indexes and the energy concentration index. The method has been tested on 3D data collected in operating solar thermal power plants, which demonstrates that this technique can be used, not only in the design and
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manufacturing phases of the solar trough collectors, but also in the phase of power generation.
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A flowchart of the proposal is presented in Figure 1. The method is basically structured in three parts: Data Acquisition, Data Representation and Characterisation of Geometry and Energy. The canonical image concept is defined as the base of the data representation and processing. The figure shows different canonical images used in the geometric and energy characterization process and their associated parameters. All of this will be dealt with in Sections 2.
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Figure 1. Overview of the system: main phases,canonical images defined in each stage and the set of parameters
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The remainder of the paper is organised as follows. In section 2 the materials and methods of this work are presented. Specifically, theoretical formulation of optical efficiency in parabolic trough collectors is briefly explained in Section 2.1. Section 2.2 provides details on how the 3D data are acquired and processed. The canonical image concept is introduced here as the main tool employed to characterise parabolic trough collectors. Section 2.3 shows a definition of the parameters concerning optical errors and how to characterise and analyse the geometry of the collector using processing image techniques. Section 2.4 tackles energy efficiency and defines the interception indexes and the energy concentration index. The tests and results are presented in Section 3, while Section 4 discusses the conclusions and future works.
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2. Material and methods
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2.1. Theoretical formulation of optical efficiency in parabolic trough collectors
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The performance of a parabolic trough collector is based on its geometrical and physical properties. This section provides a brief explanation of the factors that have an influence on energy efficiency and how optical efficiency becomes the main factor to be considered in the entire energy process.
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A cross section of a parabolic trough collector is illustrated in Figure 2. First, with respect to the basic geometric concepts, three essential elements can be indicated in this figure: the focal distance f, the diameter of the receiver D and the aperture Wa. As will be shown below, the theoretical equation of the optical efficiency of a collector includes these three parameters.
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A parabola whose vertex is at the origin and whose axis coincides with the y-axis is represented by equation (1):
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The diameter of the receiver D is an important parameter which is easily obtained as follows:
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where is the half acceptance angle and
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is the angle between the collector axis and a reflected beam at the end of the parabola.
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Figure 2. Cross section of a parabolic trough collector
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Optical efficiency is defined as the ratio of the energy absorbed by the receiver to the energy incident on the collector aperture [2]. It depends on the optical properties of the materials involved, the geometry of the collector and the various imperfections which appear as a result of the construction of the collector [3]. Of all these factors, the principal and most complex to evaluate is the intercept factor. The parameters proposed in Section 2.4 could be considered as a new way in which to evaluate optical efficiency on the basis of ray-tracing strategies. A brief presentation of the theoretical equation of the intercept factor as it is found in literature is presented below, along with a discussion regarding how this expression is not, in practice, suitable for the computation of energy efficiency.
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Theoretically, intercept factor, , is the ratio of the energy intercepted by the receiver to the energy reflected by the parabola. In general, depends on the size of the receiver ( ), the solar beam spread () and the geometric errors in the mirror and the receiver ( ). The intercept factor is formulated as follows:
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(5)
Again, the errors associated with the parabolic surface and the receiver are the most important. Guven et al. [4] classified them as random and non-random errors. Random errors are those that can be modelled by using normal probability distributions. These correspond to changes in the width of the sun and the distortion of the parabola as a result of wind loading and scattering effects. In this case, the statistic model is provided by means of the standard deviation of the total reflected energy distribution. The equation is as follows: 4" " #"$%& ' $( "$)(
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There are two non-random errors. Error * is determined using the misalignment angle between the reflected ray from the centre of the sun and the normal vector to the aperture plane of the reflector, and the error + is the displacement of the receiver from the focus of the parabola.
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According to Guven et al. [4], random and non-random errors can eventually be combined to yield the so called universal parameters " ∗ , * ∗and + ∗ , as follows:
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" ∗ "$%& *∗ * + ∗
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Finally, upon employing the universal error parameters, the formulation of the intercept factor is: ;<
1 cos sin 1 cos 1 − 2+ ∗ sin − -* ∗ 1 cos 3 erf 7 : 2 sin √2-" ∗ 1 cos =
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sin 1 cos 1 − 2+ ∗ sin − -* ∗ 1 cos + : 1 cos √2-" ∗ 1 cos 6
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in which erf is the Gaussian error function. It is evident that this means of computing energy efficiency would be precise and reliable if all the parameters inserted in it were available at the same time, but this is frequently not the case. Note that several parameters are usually unknown or difficult to measure, others may change because of the weather, and some of them obey statistical mathematical models which might cause errors. In conclusion, this is not, in practice, the most advisable method with which to measure the optical efficiency of parabolic trough collectors. Unlike the method shown above, the strategy used in this work is based on the study of 3D ray tracing and modelling the surface of the collector. That is, the paths of the rays of the incident radiation are analysed in order to determine the distribution and intensity of the rays on the surface of the receiver. The paths of the rays are obviously dependent on imperfections in the mirrors and on the location of the receiver, and it is for this reason that new parameters that accurately evaluate the geometry of the collector have been defined. The energy of solar collectors has been characterised from an optical point of view by using the framework, shown in the following section, which consists of three stages: collector modelling, surface and receiver pose analysis and the establishment of energy parameters.
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The 3D data acquired consist of millions of unstructured points that accurately represent the shape of the collector (see Figure 3). In order to define a space with an imposed topology, the point cloud has been organised by using a particular 2D data structure. This structure will be very useful as regards representing, characterising and analysing the regions and properties of the collector surface, in addition to the location of the receiver.
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The first step in the process comprises the acquisition of the 3D data that represent the surface of the parabolic mirrors. Most current 3D acquisition methods cannot be efficiently used to acquire data from the parabolic trough collector once it has been installed in the power plant. However, laser scanner devices are particularly suitable for this. As is known, laser scanners do not work properly on reflective surfaces, as is the case of the surfaces of parabolic trough collectors. F. de Asís López et al. [12] have proved that a good characterisation of the collector can be achieved by scanning its rear face. In this work, the same criterion has been adopted, by assuming that the back of the collector is identical to its interior and, is moreover, not reflective.
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a) b) Figure 3. a) Parabolic solar trough collector b) 3D data obtained from the laser scanner 234
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Let us assume that the theoretical equation of the surface of the planned parabolic reflector and the theoretical position of the receiver are known. From here on, the as-planned whole system will be referred to as the “ground truth collector” (GTC). The GTC is usually available when the system is manufactured and installed in the power plant. Let us also give the real system in the solar plant a name: the “as-built collector”, which is denoted with the acronym ABC.
Consider a parabolic surface, with a real dimension of > ? @ meters, oriented in such a way that the focus line is parallel to axis Y, the axes of symmetry of the parabolas follow axis Z and the vertex line lies in the plane A B (B is really an offset). If the parabolic surface is in this pose, any particular feature of the surface at coordinates C, D, A can be stored in an ? E discrete matrix, in which, FG >, E FH @, and FG and FH are scale factors.
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Bearing this idea in mind, a Canonical Image I from the surface of a parabolic reflector is defined as a step function:
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A pixel , of I therefore stores a certain feature of the surface at the point C, D, A. This definition makes it possible to obtain various images corresponding to both the GTC and the ABC parabolic surfaces, which can store different information. From here on, these images will be denoted with a letter which refers to the feature stored followed by the name “image”. For example, the name Z-image corresponds to an image that stores the Z-coordinate of the points of the parabolic surface. The mathematical expression of the canonical images will include the letter I, the acronyms ABC or GTC, and the letter that identifies the specific feature stored. In the earlier example, this Z Z U U would be I ABC or I GTC . Figure 4b) shows examples of images IRST and IVWT . A pseudo colour is used in these images. The blue lines correspond to the bars that hold the collector at the rear part and will not be considered as data.
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I: K1, … , M ? K1, … , EM → O I, C, D, A C FG , D FH , P , Q E
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Figure 4. a) 3D data representation using Canonical Images. b) Examples of canonical images U U IRST IVWT when coordinate Z is chosen as a feature. The blue lines, corresponding to the structure that holds the collector.
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2.3. Characterising the geometric errors of the collector
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In this section, the errors originating from the geometry of the parabolic trough collector are characterised in two respects. First, deviations on the surface of the parabolic reflector is analysed, and both the local and the global parameters are defined. The pose error of the receiver is then evaluated by analysing one parameter. This analysis would be extremely useful if workers wished to repair imperfections on the solar plant.
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2.3.1. Analysing the parabolic reflector surface
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Thanks to the Canonical Images, errors of the ABC parabolic surface can easily be assessed by U U taking coordinate A as a feature. Images IRST and IVWT , are employed to obtain a deviation map ' image IRST
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For a particular pixel located at , X, the local deviation is, therefore: ' IRST can
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Note that image contain positive or negative values. A positive value of means that there is a small groove or crack at this point on the surface, whereas a negative value means a small bulge on the surface of the collector. The aim of this part is to show that it is possible to identify ' and delimitate (potentially erroneous) concave or convex zones in IRST by using image processing ' resources. Figure 5 shows an example of IRST using a colour code representation. In this image, d is represented such that warm and cool colours show the deformed regions.
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' Figure 5. a) Example of IRST . A colour-bar shows the error in d in millimetres. b) Segmentation of convex (pink) and concave zones (blue).
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' In order to identify the location and properties of erroneous zones, a segmentation of IRST is carried out. First, a specific threshold k is imposed and each pixel is classified as convex +, X Y F, concave +, X Z −F and correct (otherwise). A region growing algorithm is then applied for concave and convex seeds separately. Each kind of seed, concave or convex, leads to a cluster of concave or convex pixels in the image. After running this segmentation algorithm, some deformed zones are therefore detected and bounded.
The geometry of each erroneous zone is characterised by calculating the mean deviation [, the absolute and relative areas \ and , a shape coefficient and the location of the erroneous zone in 9
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' IRST . The shape coefficient is obtained after calculating the bounding box, ]^ ? ] , of the region, _ where ` and ]^ Z ]. The location of the erroneous zone is defined as the centroid bG , H c of _a
the bounding box. A local description of geometric errors of the parabolic reflector can, therefore, ' be provided by means of IRST and parameters [, \, and .
This local analysis provides valuable information for damage repairing tasks. For each trough collector, the plant operators can therefore learn: the number and extension of the erroneous zones (by using parameters \ and ); the seriousness of each fault (by analysing parameters and [), and the approximate location of the defective zone (by employing parameter bG , H c).
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Parameters concerning global errors must describe general defects and deviations of the ABC with regard to the GTC. In our case, five global parameters are defined. The first one is the erroneous area percentage ̅ , which provides an idea of how serious the deformation of the whole panel is. ̅ e
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The global concavity and convexity of the parabolic reflector are evaluated using the means (f and f′) and variances (" and "′) of their respective Gaussian distributions (h and h′ in equations (15) and (16)). This is formally expressed as: h+ h n +
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2.3.2. Analysing the receiver pose
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A cylindrical parabolic surface formed of mirrors has the property of reflecting the beams of sunlight towards the focus line, provided that the surface is properly oriented, that is, the axis of symmetry of the directrix parabola follows the same direction as the incoming solar rays. As mentioned previously, the receiver must be precisely placed on the focus line, and it is, therefore, extremely important to avoid pose errors for the receiver to collect the maximum number of rays. This section shows how to obtain the focus line of an ABC and how to measure the error when compared with that of a GTC.
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In order to characterise the receiver pose error, first a simple linear regression on the focuses in plane DA is carried out. A straight line (the blue line in Figure 6b)) fits the set of m focuses in such a way that it makes the sum of squared residuals as small as possible. In the plane YZ, the translation
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U In order to calculate the line that best approximates the real focus line, IRST (see Figure 6 a) is U used. Note that, as explained in Section 2.1, each column of IRST (x-axis of the image) stores the Zcoordinates of all the points on the surface for a fixed y-coordinate. The representation of the points of each column in the XZ-plane therefore results in a succession of points that follow a parabolic trend. The parabola that best fits this sequence of points and the Z-coordinate of its focus can then be calculated. Figure 6a) shows a real parabola fitted to the set of discrete points that have been extracted from I AZ B C for a particular coordinate y and the resulting focus line. Figure 6 b) illustrates the focuses corresponding to the entire Z-image (in blue) and the corresponding ground truth (in red).
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and rotation of the focus line with regard to that of the GTC can be measured. Translation p is calculated as the distance of both lines at the middle point of the A-axis, whereas rotation is obtained from the slope E tan of the focus line.
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2.4. Characterising the ray-tracing in the parabolic trough collector
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The detection and characterisation of the optical errors presented in the previous section can be very useful as regards repairing or correcting faults in the parabolic reflector and errors in the receiver pose. The issue of how to measure the energy efficiency of the collector by means of a raytracing analysis is tackled below.
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2.4.1. The interception indexes
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The function of the solar collector is to reflect the radiation that reaches its mirror towards the absorber tube (receiver). It is clear that the higher the reflected radiation that reaches the tube, the better the performance of the collector. In section 2.1, the intercept factor, , was defined as the ratio of the energy intercepted by the receiver to the energy reflected by the parabola. The objective of this section is to extend this energetic parameter to others (-image and two interception 11
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indexes). Both parameters take into account not only the number of rays which reach the receiver (as proposed in [16] by García-Cortés et al.), but also the zone of the parabolic collector from which the rays impact on the tube.
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The reflected beam on each point of the surface can easily be calculated using the normal vectors of the surface of the collector. The theoretical intersection of each ray with the absorber tube is then checked. It is assumed that the diameter of the receiver, D, is known. The reflected ray intersects the absorber tube if the distance from the reflected ray to the receiver is less than D/2.
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Again, a canonical image that stores successful and unsuccessful interceptions can be defined. Thus, when an interception from a surface-point p ( X , Y , Z ) takes places, the corresponding pixel t s, of an image IRST is marked , denoting the new feature. Feature is now a Boolean t parameter in which ‘1’ signifies interception and ‘0’ signifies no interception. IRST is consequently defined as a binary image with black and white regions, thus enabling the zones of the collector that correctly reflect the radiation to be obtained. Figure 7 illustrates an example in which a few small regions (painted in red) of the parabolic surface erroneously reflect the rays.
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The inner and outer interception indexes are defined as the ratio of the parabolic surface that achieves a successful reflection for each type. These parameters can be formulated in terms of their respective canonical images as follows: 1 t` e e IRST > v^ uv^
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As is known, the absorber tube consists of two concentric cylinders. Therefore, two canonical t` ta images IRST and IRST can be defined for both the inner and outer tubes, using the respective diameters ^ and . A new parameter related to the energy efficiency in terms of ray-tracing can, therefore, be defined.
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t where N is the useful area of IRST in pixels.
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The graphical results shown in Figure 7 denote a dispersion of the zones whose reflections will not touch the absorber tubes. This leads us to believe that many of these zones are not actually defective areas but are rather deviations caused by noisy data or data near to the metal bars that hold the collector (black lines in Figure 7). Note also that the images do not have the same erroneous ' zones as those in images IRST . Therefore, it can be can stated that the theoretically deformed zones of the collector would, apparently, correctly reflect the beams onto the receiver.
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The point here is in the meaning of the word “correctly”. The fact is that some reflected beams reach the receiver but not at the expected point. This behaviour would be correct, at least from the point of view of energy, but it is necessary to go beyond this. Next section provides a discussion concerning the uniformity of the radiation in the receiver.
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Figure 7. Example of λ-image and calculation of (a) outer and (b) inner interception indexes
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2.4.2. Energy concentration index
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The lack of uniformity with which the radiation reaches different areas of the absorber tube obviously affects the energy efficiency of the collector. This section confronts the problem of how to characterise the deviations of the reflected rays with regard to their ideal orientation.
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As is illustrated in Figure 8, if a ray is reflected onto the point of the surface sC, D, A and, instead of reaching the absorber tube at the correct point wCR , DR , AR , it does so at the incorrect x point wn CRn , DRn , ARn , this event is measured and stored in two new canonical images, IRST and y IRST . x {{{{{ in the pixel , . This is formally expressed as: Image IRST stores the distance z ww′ R R
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y The image on the right, denoted as IRST , stores in R , R the number of beams which reach the receiver in A (feature ). Thus, although w is the expected contact point for the ray marked in Figure 8 (that is, in the case of the GTC), the ray makes contact with the receiver in w′, and the corresponding pixel Ro , Ro adds another vote, while pixel R , R is ignored. It is, therefore, y clear that image IRST provides with a map on which the concentration of the rays from the parabolic y surface can be evaluated. Note that IVWT is an image with one vote per pixel.
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In order to be practical and to define a parameter that measures the degree of concentration of y rays in the receiver, IRST has been reduced to a one-dimensional structure: a vector which adds up y the votes for each particular y-coordinate in IVWT . As explained in section 2.2, and can be seen in Figure 3(b), the Y-axis has the same direction as the longitudinal axis of the receiver. Because, in most cases, the deviations in the reflected solar rays cause them to touch in areas of the receiver different than expected (Figure 8), this new parameter will offer information on the concentration of the sunrays on the longitudinal axis of the receiver.
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This new parameter is the energy concentration index at the y-coordinate, , and is defined as the ratio of the number of rays that reach the receiver at the Y-coordinate versus the true number. This parameter is formally formulated as follows:
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where ̅ is the mean energy concentration index and " is the corresponding energy concentration index standard deviation. The region is hyper-energetic if: − ̅ Y "
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Figure 10. Energy concentration index, (dotted line) and hyper-energetic region detected (red squares) of the -image presented in Figure 9 along the Y-axis. In this case, there are no hypoenergetic regions.
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The identification of hypo-energetic and hyper-energetic regions in the receiver could be very useful as regards carrying out further analyses based on the heat transport that the fluid circulates inside the tube, but this is not within the scope of the present paper. For example, Hachicha et al. [21] present a complex model for the absorber tube that is used for heat transfer analysis and numerical simulation. This model could be used in conjunction with the data provided in our work.
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The method proposed in this paper has been tested on three solar trough collectors, denoted as C1, C2 and C3, at a solar power thermal plant. The parabolic mirrors have a focal length of 1490 mm, a length of 8 m and an aperture of 5.5 m. The absorber tube consists of two concentric cylinders: the outer cylinder is made of glass and has a diameter of 125mm, whereas the inner cylinder is made of steel and has a diameter of 70 mm.
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The laser scanner used in the acquisition process was the FARO LS 880. The range (80 m), density (8000 × 3500 points) and precision of this laser scanner are suitable for obtaining an accurate 3D model of the parabolic collector. The three solar trough collectors were scanned twice with the objective of proving the repeatability of the results.
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' Figure 11 a) shows images IRST for test 1 and test 2. Concave (pink rectangles) and convex zones (blue rectangles) are identified in Figure 11 b). Table 1 shows the quantitative results that characterise the global geometric errors of the parabolic surface of the collectors. The table includes the erroneous area percentage ̅ , means, f and f′, and variances "and "′ (the unit employed for all the parameters is EE).
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The receiver pose errors of the three collectors are presented in Table 2. Parameters p, , f' and "' (f' is the mean error and "' is the deviation of the distances between the theoretical focal and the line that approximates the values of the real focal) are included. f' is the mean error of the distances between the theoretical focal and the line that approximates the values of the real focal, and "' is the deviation. The values of t and θ allow the error between the theoretical and the real focal to be characterised: the greater t and θ, the greater the error. This can be verified in C3, in which the maximum mean error f' corresponds to the highest values of | t | and | θ |. Something similar occurs with cases C1 and C2.
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Figure 12 displays the graphs that represent the position of the real and ideal focal axes in the second and third mirror. The similarities between the results obtained in tests 1 and 2 are noteworthy.
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Figure 12. Focus positions in ABC and GTC models. ABC focuses are in blue and GTC focuses are in red. Superimposed is the corresponding regression line in black The results of the energy efficiency parameters are shown in Table 3. The values ^and , represent the number of pixels whose reflections reach the inner and outer absorber tube, respectively. The values are significantly greater than the ^ values. The results are apparently lower than expected. As can be seen in the energy analysis shown in Figure 14, there are hardly any losses, since only in C3 are hypoenergetic zones found, and the prediction is that this defect is barely perceptible in the installation. The reason for this apparent reckoning is that many of the rays that do not reach the tube (shown in red in Figure 13), are data from nearby non-acquired zones, 18
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which are precisely the zones that have the greatest inaccuracies. The next columns in Table 3 show the mean energy concentration index ̅, and the standard deviation " . As mentioned previously, Figure 13 shows ^ -image and -image, in which the green zones correspond to areas of the surface that reflect the rays to the absorber tube, the red zones represent those that do not correctly reflect the rays and the black areas are the parts of the parabola which are not acquired.
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Figure 14 presents the results concerning the energy concentration index . It will be observed that, at certain Y-coordinates the energy concentration index is higher than one, which means that many unexpected rays reach the receiver at this distance. Hypo-energetic zones are found in only one of the collectors. This could be owing to erroneous 3D data, since they all appear at the ends of the Y-axes.
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4. Conclusions
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In this work, an original framework that makes it possible to analyse the optical efficiency of parabolic trough collectors in terms of geometry and energy, using computer vision and image processing techniques, has been defined. Errors and failures in the collector can be easily detected and located by means of the complete information yielded by the approach proposed. All of the above consequently leads to believe that rapid detections and small in-situ reparations will be possible by following this method. This kind of work could have an impact on the cost and profitability of the solar plant.
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Contrary to theoretical solutions, an empirical method which can be put into practice using 3D sensors has been proposed. Both the approach and the parameters defined in the paper are original, although some parameters, and specifically the inner and outer interception indexes, could be viewed as an extension of the existing intercept factor (equation (10)).
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As is reported in section 3, the method has been tested in-situ on three solar trough collectors, taking two samples per collector. The results have been very satisfactory. It has been shown how the parameters facilitate to carry out an easy and precise quality control of parabolic trough collectors by using canonical images together with the set of characteristics. This system is easily reproducible and can be used by other engineers and researchers.
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The results presented in this paper refer to a specific position of the collectors, but the method is versatile and could identify and evaluate the performance of the collector under different conditions, thus opening up new lines of research. The surface deformation owing to the weight or different tensions supported by the metal structure during daily operation could also be studied by repeating the process for different positions of the collectors. Moreover, if the analysis were to be performed for different environmental conditions, the results could reveal how temperature or movement affect the functionality of the solar collectors.
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The future work is addressed to two research lines. In order to identify better the location and ' properties of erroneous zones, the segmentation of IRST into free-shape zones is a key point that should be dealt with. Our primary idea is that the current algorithm will be reformulated using fuzzy-snake segmentation techniques ([22]). The second research line will focus on testing the approach on an extended database of parabolic trough collectors. In addition, in order to avoid the problems of the laser scanners on reflective surfaces (i.e. the solar mirrors of the collector), we are planning to use structured-light techniques to collect dense 3D data. Particularly, the technique developed in [23] could be adapted to this environment in the future. Other interesting issue is that of the influence of the shape of the receiver and how it affect to the performance of the Parabolic Trough Collector. Unfortunately, there are several causes that prevent acquiring 3D data with long-range scanners: first, the majorty of the surface of the receiver is occluded by the collector itself, but also large amount of noise that the 3D data would present due to reflections in the mirrors of the collector and, finally, the material with which the receiver is manufactured (antireflective-coated glass) that makes extremely difficult the acquisition with laser scanners. In this work, the values of the radius and length of the receiver provided in the data sheet of the manufacturer has been used, and it has been assumed that the receiver is an ideal cylinder. The research in the kind of sensors appropriate to acquire this type of material that is located in zones of difficult access could open a new line of research that could be developed in the future.
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This work was supported by the Extremadura Regional Government and European Social Fund [GR10157 project]; and the Spanish Economy and Competitiveness Ministry [DPI2016-76380-R project AEI/FEDER, UE].
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References
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Framework for the optical analysis of solar trough collectors using 3D data. New data structure that allows to process the data with computer vision algorithms. Determination of the interception index using 3D point clouds. Definition of new parameters related with energy efficiency of solar mirrors. Testing of algorithms on 3D data collected in operating solar thermal power plants.
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DOI:
https://doi.org/10.1016/j.renene.2018.11.014
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RENE 10777
To appear in:
Renewable Energy
Received Date: 5 June 2018 Revised Date:
24 September 2018
Accepted Date: 4 November 2018
Please cite this article as: Salamanca S, Merchán P, Adán A, Pérez E, An appraisal of the geometry and energy efficiency of parabolic trough collectors with laser scanners and image processing, Renewable Energy (2018), doi: https://doi.org/10.1016/j.renene.2018.11.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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An Appraisal of the Geometry and Energy Efficiency of Parabolic Trough Collectors with Laser Scanners and Image Processing
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Santiago Salamanca1), Pilar Merchán2), Antonio Adán3) and Emiliano Pérez2)
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Corresponding Author: Escuela de Ingenierías Industriales. Universidad de Extremadura. Avda. de Elvas s/n. 06006 Badajoz. Spain. Email: [email protected]. Tlf: +34 924289300. Fax: +34 924289601
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Escuela Superior de Informática. Universidad de Castilla la Mancha. Paseo de la Universidad, 4. 13071 Ciudad Real. Spain. Email: [email protected]
Abstract
This paper presents an original method for the analysis of the geometric and optical properties of parabolic solar trough collectors using laser scanners and image processing techniques. The aim of the paper is to propose a methodology with which to automatically analyse geometric errors in the mirror and receiver, in addition to presenting an empirical assessment of one of the most important factors that determines the entire energy efficiency of solar plants, which is optical efficiency. The definition of canonical images has allowed us to characterize a set of parameters that evaluates errors on both the surface of the parabolic reflector and regarding the orientation of the receiver. In this framework, energy efficiency is established in terms of two parameters, denominated as the interception index and the concentration index. The proposed method has been tested on-site on real surfaces of parabolic solar trough collectors in an operating solar thermal plant. The results obtained are sufficiently accurate and reliable to be able to recommend that researchers and plants reproduce this method in this kind of installations.
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Keyword: parabolic solar trough collectors, solar thermal power plants, laser scanners, 3D data processing, 3D surfaces.
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: Escuela de Ingenierías Industriales. Universidad de Extremadura. Avda. de Elvas s/n. 06006 Badajoz. Spain. Email: {pmerchan, emilianoph}@unex.es
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1. Introduction
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Parabolic trough power plants are one of the most important methods by which to convert solar energy into electric energy [1][2]. They consist of solar collectors composed of cylindrical parabolic mirrors and a linear receiver (a tube) located at the focus of the parabola.
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The performance of these power plants is influenced by many factors, the most significant being the optical efficiency of the collectors. As is shown in Section 2.1, the theoretical formulation of optical efficiency takes into account aspects such as shadows between solar collectors, errors when the mirrors attempt to track the sun, or a loss of mirror reflectivity owing to the effects of weather and wind. All of these random disturbances can, of course, be modelled and introduced into the final equation. However, the principal loss of energy originates from optical errors in the solar collector system. Optical errors might appear either as the result of the mirrors being placed
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wrongly or because of failures in the manufacturing process. In the latter case, some solar rays would not reach the tube, located in the focus of the parabola, and the heat transfer fluid would not be heated to the adequate temperature. The geometric quality of the solar collectors, therefore, strongly influences the efficiency of a solar thermal power plant. This makes the identification and analysis of the geometry of the solar collector essential.
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Several sensory systems and methods that analyse the geometry of a parabolic trough have been proposed in the last few decades. An extended classification of the techniques used for the characterization of reflective surfaces of solar concentrators can be found in [3].
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The geometric errors detected in the surface of solar collectors can be classified in random or non-random errors. Random errors are mainly due to external causes (e.g. weather, wind, dirt...), whereas non-random errors come from failures in the manufacturing, installation and maintaining processes. These errors greatly alter the solar receiver performance and are closely related to the geometry of the whole reflector [4]. The most important non-random errors are the contour (or slope) and the canting errors. Contour errors refers to deviations from the shape of the mirror, whereas canting errors concern to deviations of the orientation of the individual mirror facets from the nominal directions [3].
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The family of the Hartmann tests, and their variants, is the most effective method that detects shape errors in receivers. In general, these tests are based on analysing the reflected rays at different points of the receiver. The differences between the various versions are in the way to sample and to record the information. In the classical version, a light source, located near the centre of curvature of the mirror, passes through a mask of holes, projecting an array of individual rays into the mirror. The reflected rays are then registered on a photographic plate, thus producing a Hartmann pattern. The Scanning Hartmann Optical Test (SHOT) [5], is a further version that uses a laser source. In this case, the laser source is automatically pointed to a set of predefined positions of the mirror and a photographic plate sequentially records the reflected rays. With this procedure, only slope errors can be detected. A more advanced system, called The Video Scanning Hartman Optical Test (VSHOT), is developed in [6,7]. The photographic plate is here replaced by a camera and a video system. This system recognizes slope and shape errors. Recently, Wheelwright et al. [8] have proposed a new variant of the Hartmann tests based on the generation of a set of light rays that are parallel to the optical axis. The setup consists of an array of lasers on board a moving bar that sweeps the area of the receiver. This procedure therefore decreases the time of the Hartmann test, but requires a more complex and precise experimental system.
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Deflectometry systems [9][10] project structured light patterns onto the target surface, but they have got similar limitations as regards the rapid inspection of large solar plants. Xiao et al. [11] provide a detailed explanation of these different methods for the shape measurement of solar concentrators. However, although they have proved to be useful in the mirror manufacturing phase and structure design stage, none of them would appear to be appropriate once the parabolic troughs have been installed.
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Photogrammetry is a high precision technique used for inspecting standard collectors [12]. The first works about how to use of photogrammetry in the geometric evaluation of solar receivers are published by Shortis and Johson in [13] and [14]. They show a photogrammetric experimental setup that efficiently carries out the data collection stage and propose several basic tests for the assessment of the surface of the receiver. A more in-depth study about the use of photogrammetric 3D data from mirrors and structures that support mirrors is presented by Pottler et al. in [15].
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Beyond the detection of contour and shape errors, some authors have used photogrammetric data to estimate some characteristic parameters of solar collectors, such as the intercept factor. The intercept factor can be calculated from the directions of the solar rays reflected from the parabolic receiver. With this objective, García et al. ([16]) propose a method that first projects the collected data of the mirror into the XY-plane, and then discretises the projected data in a triangular mesh. The normal vectors of the triangular facets are eventually used to calculate the intercept factor. In [17], a similar triangulation-based approach is obtained from a commercial software. Contrary to these approaches, the intercept factor (in fact, an extension of this concept: the interception indexes) has been estimated avoiding such a triangulation process in this paper (Section 2.4), which greatly simplifies and speeds up its calculation. In addition, another characteristic parameter, called energy concentration index, is defined.
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As a major problem, photogrammetric techniques can be tedious and slow. Depending on the size of the scanning project, the whole process, from the targets placement to the target coordinates extraction, could takes from 12 to 24 hours. Therefore, the use of photogrammetry and deflectometry should be restricted to evaluate the quality of the solar concentrators within the design and manufacture phases. Once the receivers have been installed in the solar thermal power plant, the use of these techniques for quality assessment tasks becomes unfeasible.
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3D measurement using laser systems has become increasingly popular in recent years. The range of measurement, manoeuvrability, ease of use and speed, together with the accuracy and resolution of phase shift or time of flight laser scanners [18], make this kind of sensors highly appropriate for the optimisation of solar collector geometries. This method is, therefore, worth investigating, especially when used under working conditions [19]. F. de Asís López et al. [20] demonstrate that the main advantages when using a TLS (Terrestrial Laser Scanner) to characterize a parabolic trough collector, in comparison with photogrammetry, are that less time is needed for data collection – an important consideration in the case of solar fields with large numbers of collectors – and it is simpler to process the point cloud.
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In this paper, a technique that automatically analyses the vast amount of data that are collected after scanning a solar receiver with a TLS is proposed. The objective is to characterise both the optical errors and the energy efficiency of a parabolic trough collector by using computer vision resources. This methodology could be very useful in working solar plants, releasing the operator from making tedious measurements and assessments in the field.
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Compared to the aforementioned approaches, the main contributions of this work are:
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To the best of our knowledge, this is the first work that presents a complete framework that detects geometric errors in parabolic trough collector using terrestrial laser scanners. The canonical image is an original data structure that provides an easy-to-use as-built model representation of parabolic trough collectors. In addition, the canonical image allows to process the data with computer vision algorithms, which provides precise and visual results. Using the proposed framework, the operator can detect imperfections in the parabolic reflector surface and deviations of the receiver pose on site. The former intercept factor is extended with new parameters related to the the raytracing in the parabolic trough collector. These are the -image, the interception indexes and the energy concentration index. The method has been tested on 3D data collected in operating solar thermal power plants, which demonstrates that this technique can be used, not only in the design and
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manufacturing phases of the solar trough collectors, but also in the phase of power generation.
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A flowchart of the proposal is presented in Figure 1. The method is basically structured in three parts: Data Acquisition, Data Representation and Characterisation of Geometry and Energy. The canonical image concept is defined as the base of the data representation and processing. The figure shows different canonical images used in the geometric and energy characterization process and their associated parameters. All of this will be dealt with in Sections 2.
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Figure 1. Overview of the system: main phases,canonical images defined in each stage and the set of parameters
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The remainder of the paper is organised as follows. In section 2 the materials and methods of this work are presented. Specifically, theoretical formulation of optical efficiency in parabolic trough collectors is briefly explained in Section 2.1. Section 2.2 provides details on how the 3D data are acquired and processed. The canonical image concept is introduced here as the main tool employed to characterise parabolic trough collectors. Section 2.3 shows a definition of the parameters concerning optical errors and how to characterise and analyse the geometry of the collector using processing image techniques. Section 2.4 tackles energy efficiency and defines the interception indexes and the energy concentration index. The tests and results are presented in Section 3, while Section 4 discusses the conclusions and future works.
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2. Material and methods
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2.1. Theoretical formulation of optical efficiency in parabolic trough collectors
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The performance of a parabolic trough collector is based on its geometrical and physical properties. This section provides a brief explanation of the factors that have an influence on energy efficiency and how optical efficiency becomes the main factor to be considered in the entire energy process.
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A cross section of a parabolic trough collector is illustrated in Figure 2. First, with respect to the basic geometric concepts, three essential elements can be indicated in this figure: the focal distance f, the diameter of the receiver D and the aperture Wa. As will be shown below, the theoretical equation of the optical efficiency of a collector includes these three parameters.
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A parabola whose vertex is at the origin and whose axis coincides with the y-axis is represented by equation (1):
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The diameter of the receiver D is an important parameter which is easily obtained as follows:
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where is the half acceptance angle and
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is the angle between the collector axis and a reflected beam at the end of the parabola.
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Figure 2. Cross section of a parabolic trough collector
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Optical efficiency is defined as the ratio of the energy absorbed by the receiver to the energy incident on the collector aperture [2]. It depends on the optical properties of the materials involved, the geometry of the collector and the various imperfections which appear as a result of the construction of the collector [3]. Of all these factors, the principal and most complex to evaluate is the intercept factor. The parameters proposed in Section 2.4 could be considered as a new way in which to evaluate optical efficiency on the basis of ray-tracing strategies. A brief presentation of the theoretical equation of the intercept factor as it is found in literature is presented below, along with a discussion regarding how this expression is not, in practice, suitable for the computation of energy efficiency.
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Theoretically, intercept factor, , is the ratio of the energy intercepted by the receiver to the energy reflected by the parabola. In general, depends on the size of the receiver ( ), the solar beam spread () and the geometric errors in the mirror and the receiver ( ). The intercept factor is formulated as follows:
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(5)
Again, the errors associated with the parabolic surface and the receiver are the most important. Guven et al. [4] classified them as random and non-random errors. Random errors are those that can be modelled by using normal probability distributions. These correspond to changes in the width of the sun and the distortion of the parabola as a result of wind loading and scattering effects. In this case, the statistic model is provided by means of the standard deviation of the total reflected energy distribution. The equation is as follows: 4" " #"$%& ' $( "$)(
(6)
There are two non-random errors. Error * is determined using the misalignment angle between the reflected ray from the centre of the sun and the normal vector to the aperture plane of the reflector, and the error + is the displacement of the receiver from the focus of the parabola.
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According to Guven et al. [4], random and non-random errors can eventually be combined to yield the so called universal parameters " ∗ , * ∗and + ∗ , as follows:
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Finally, upon employing the universal error parameters, the formulation of the intercept factor is: ;<
1 cos sin 1 cos 1 − 2+ ∗ sin − -* ∗ 1 cos 3 erf 7 : 2 sin √2-" ∗ 1 cos =
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sin 1 cos 1 − 2+ ∗ sin − -* ∗ 1 cos + : 1 cos √2-" ∗ 1 cos 6
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in which erf is the Gaussian error function. It is evident that this means of computing energy efficiency would be precise and reliable if all the parameters inserted in it were available at the same time, but this is frequently not the case. Note that several parameters are usually unknown or difficult to measure, others may change because of the weather, and some of them obey statistical mathematical models which might cause errors. In conclusion, this is not, in practice, the most advisable method with which to measure the optical efficiency of parabolic trough collectors. Unlike the method shown above, the strategy used in this work is based on the study of 3D ray tracing and modelling the surface of the collector. That is, the paths of the rays of the incident radiation are analysed in order to determine the distribution and intensity of the rays on the surface of the receiver. The paths of the rays are obviously dependent on imperfections in the mirrors and on the location of the receiver, and it is for this reason that new parameters that accurately evaluate the geometry of the collector have been defined. The energy of solar collectors has been characterised from an optical point of view by using the framework, shown in the following section, which consists of three stages: collector modelling, surface and receiver pose analysis and the establishment of energy parameters.
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The 3D data acquired consist of millions of unstructured points that accurately represent the shape of the collector (see Figure 3). In order to define a space with an imposed topology, the point cloud has been organised by using a particular 2D data structure. This structure will be very useful as regards representing, characterising and analysing the regions and properties of the collector surface, in addition to the location of the receiver.
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The first step in the process comprises the acquisition of the 3D data that represent the surface of the parabolic mirrors. Most current 3D acquisition methods cannot be efficiently used to acquire data from the parabolic trough collector once it has been installed in the power plant. However, laser scanner devices are particularly suitable for this. As is known, laser scanners do not work properly on reflective surfaces, as is the case of the surfaces of parabolic trough collectors. F. de Asís López et al. [12] have proved that a good characterisation of the collector can be achieved by scanning its rear face. In this work, the same criterion has been adopted, by assuming that the back of the collector is identical to its interior and, is moreover, not reflective.
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a) b) Figure 3. a) Parabolic solar trough collector b) 3D data obtained from the laser scanner 234
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Let us assume that the theoretical equation of the surface of the planned parabolic reflector and the theoretical position of the receiver are known. From here on, the as-planned whole system will be referred to as the “ground truth collector” (GTC). The GTC is usually available when the system is manufactured and installed in the power plant. Let us also give the real system in the solar plant a name: the “as-built collector”, which is denoted with the acronym ABC.
Consider a parabolic surface, with a real dimension of > ? @ meters, oriented in such a way that the focus line is parallel to axis Y, the axes of symmetry of the parabolas follow axis Z and the vertex line lies in the plane A B (B is really an offset). If the parabolic surface is in this pose, any particular feature of the surface at coordinates C, D, A can be stored in an ? E discrete matrix, in which, FG >, E FH @, and FG and FH are scale factors.
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Bearing this idea in mind, a Canonical Image I from the surface of a parabolic reflector is defined as a step function:
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A pixel , of I therefore stores a certain feature of the surface at the point C, D, A. This definition makes it possible to obtain various images corresponding to both the GTC and the ABC parabolic surfaces, which can store different information. From here on, these images will be denoted with a letter which refers to the feature stored followed by the name “image”. For example, the name Z-image corresponds to an image that stores the Z-coordinate of the points of the parabolic surface. The mathematical expression of the canonical images will include the letter I, the acronyms ABC or GTC, and the letter that identifies the specific feature stored. In the earlier example, this Z Z U U would be I ABC or I GTC . Figure 4b) shows examples of images IRST and IVWT . A pseudo colour is used in these images. The blue lines correspond to the bars that hold the collector at the rear part and will not be considered as data.
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I: K1, … , M ? K1, … , EM → O I, C, D, A C FG , D FH , P , Q E
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Figure 4. a) 3D data representation using Canonical Images. b) Examples of canonical images U U IRST IVWT when coordinate Z is chosen as a feature. The blue lines, corresponding to the structure that holds the collector.
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2.3. Characterising the geometric errors of the collector
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In this section, the errors originating from the geometry of the parabolic trough collector are characterised in two respects. First, deviations on the surface of the parabolic reflector is analysed, and both the local and the global parameters are defined. The pose error of the receiver is then evaluated by analysing one parameter. This analysis would be extremely useful if workers wished to repair imperfections on the solar plant.
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2.3.1. Analysing the parabolic reflector surface
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Thanks to the Canonical Images, errors of the ABC parabolic surface can easily be assessed by U U taking coordinate A as a feature. Images IRST and IVWT , are employed to obtain a deviation map ' image IRST
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For a particular pixel located at , X, the local deviation is, therefore: ' IRST can
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' IRST
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Note that image contain positive or negative values. A positive value of means that there is a small groove or crack at this point on the surface, whereas a negative value means a small bulge on the surface of the collector. The aim of this part is to show that it is possible to identify ' and delimitate (potentially erroneous) concave or convex zones in IRST by using image processing ' resources. Figure 5 shows an example of IRST using a colour code representation. In this image, d is represented such that warm and cool colours show the deformed regions.
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' Figure 5. a) Example of IRST . A colour-bar shows the error in d in millimetres. b) Segmentation of convex (pink) and concave zones (blue).
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' In order to identify the location and properties of erroneous zones, a segmentation of IRST is carried out. First, a specific threshold k is imposed and each pixel is classified as convex +, X Y F, concave +, X Z −F and correct (otherwise). A region growing algorithm is then applied for concave and convex seeds separately. Each kind of seed, concave or convex, leads to a cluster of concave or convex pixels in the image. After running this segmentation algorithm, some deformed zones are therefore detected and bounded.
The geometry of each erroneous zone is characterised by calculating the mean deviation [, the absolute and relative areas \ and , a shape coefficient and the location of the erroneous zone in 9
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' IRST . The shape coefficient is obtained after calculating the bounding box, ]^ ? ] , of the region, _ where ` and ]^ Z ]. The location of the erroneous zone is defined as the centroid bG , H c of _a
the bounding box. A local description of geometric errors of the parabolic reflector can, therefore, ' be provided by means of IRST and parameters [, \, and .
This local analysis provides valuable information for damage repairing tasks. For each trough collector, the plant operators can therefore learn: the number and extension of the erroneous zones (by using parameters \ and ); the seriousness of each fault (by analysing parameters and [), and the approximate location of the defective zone (by employing parameter bG , H c).
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Parameters concerning global errors must describe general defects and deviations of the ABC with regard to the GTC. In our case, five global parameters are defined. The first one is the erroneous area percentage ̅ , which provides an idea of how serious the deformation of the whole panel is. ̅ e
(14)
The global concavity and convexity of the parabolic reflector are evaluated using the means (f and f′) and variances (" and "′) of their respective Gaussian distributions (h and h′ in equations (15) and (16)). This is formally expressed as: h+ h n +
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2.3.2. Analysing the receiver pose
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A cylindrical parabolic surface formed of mirrors has the property of reflecting the beams of sunlight towards the focus line, provided that the surface is properly oriented, that is, the axis of symmetry of the directrix parabola follows the same direction as the incoming solar rays. As mentioned previously, the receiver must be precisely placed on the focus line, and it is, therefore, extremely important to avoid pose errors for the receiver to collect the maximum number of rays. This section shows how to obtain the focus line of an ABC and how to measure the error when compared with that of a GTC.
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In order to characterise the receiver pose error, first a simple linear regression on the focuses in plane DA is carried out. A straight line (the blue line in Figure 6b)) fits the set of m focuses in such a way that it makes the sum of squared residuals as small as possible. In the plane YZ, the translation
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U In order to calculate the line that best approximates the real focus line, IRST (see Figure 6 a) is U used. Note that, as explained in Section 2.1, each column of IRST (x-axis of the image) stores the Zcoordinates of all the points on the surface for a fixed y-coordinate. The representation of the points of each column in the XZ-plane therefore results in a succession of points that follow a parabolic trend. The parabola that best fits this sequence of points and the Z-coordinate of its focus can then be calculated. Figure 6a) shows a real parabola fitted to the set of discrete points that have been extracted from I AZ B C for a particular coordinate y and the resulting focus line. Figure 6 b) illustrates the focuses corresponding to the entire Z-image (in blue) and the corresponding ground truth (in red).
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and rotation of the focus line with regard to that of the GTC can be measured. Translation p is calculated as the distance of both lines at the middle point of the A-axis, whereas rotation is obtained from the slope E tan of the focus line.
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2.4. Characterising the ray-tracing in the parabolic trough collector
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The detection and characterisation of the optical errors presented in the previous section can be very useful as regards repairing or correcting faults in the parabolic reflector and errors in the receiver pose. The issue of how to measure the energy efficiency of the collector by means of a raytracing analysis is tackled below.
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2.4.1. The interception indexes
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The function of the solar collector is to reflect the radiation that reaches its mirror towards the absorber tube (receiver). It is clear that the higher the reflected radiation that reaches the tube, the better the performance of the collector. In section 2.1, the intercept factor, , was defined as the ratio of the energy intercepted by the receiver to the energy reflected by the parabola. The objective of this section is to extend this energetic parameter to others (-image and two interception 11
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indexes). Both parameters take into account not only the number of rays which reach the receiver (as proposed in [16] by García-Cortés et al.), but also the zone of the parabolic collector from which the rays impact on the tube.
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The reflected beam on each point of the surface can easily be calculated using the normal vectors of the surface of the collector. The theoretical intersection of each ray with the absorber tube is then checked. It is assumed that the diameter of the receiver, D, is known. The reflected ray intersects the absorber tube if the distance from the reflected ray to the receiver is less than D/2.
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Again, a canonical image that stores successful and unsuccessful interceptions can be defined. Thus, when an interception from a surface-point p ( X , Y , Z ) takes places, the corresponding pixel t s, of an image IRST is marked , denoting the new feature. Feature is now a Boolean t parameter in which ‘1’ signifies interception and ‘0’ signifies no interception. IRST is consequently defined as a binary image with black and white regions, thus enabling the zones of the collector that correctly reflect the radiation to be obtained. Figure 7 illustrates an example in which a few small regions (painted in red) of the parabolic surface erroneously reflect the rays.
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The inner and outer interception indexes are defined as the ratio of the parabolic surface that achieves a successful reflection for each type. These parameters can be formulated in terms of their respective canonical images as follows: 1 t` e e IRST > v^ uv^
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As is known, the absorber tube consists of two concentric cylinders. Therefore, two canonical t` ta images IRST and IRST can be defined for both the inner and outer tubes, using the respective diameters ^ and . A new parameter related to the energy efficiency in terms of ray-tracing can, therefore, be defined.
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t where N is the useful area of IRST in pixels.
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The graphical results shown in Figure 7 denote a dispersion of the zones whose reflections will not touch the absorber tubes. This leads us to believe that many of these zones are not actually defective areas but are rather deviations caused by noisy data or data near to the metal bars that hold the collector (black lines in Figure 7). Note also that the images do not have the same erroneous ' zones as those in images IRST . Therefore, it can be can stated that the theoretically deformed zones of the collector would, apparently, correctly reflect the beams onto the receiver.
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The point here is in the meaning of the word “correctly”. The fact is that some reflected beams reach the receiver but not at the expected point. This behaviour would be correct, at least from the point of view of energy, but it is necessary to go beyond this. Next section provides a discussion concerning the uniformity of the radiation in the receiver.
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Figure 7. Example of λ-image and calculation of (a) outer and (b) inner interception indexes
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2.4.2. Energy concentration index
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The lack of uniformity with which the radiation reaches different areas of the absorber tube obviously affects the energy efficiency of the collector. This section confronts the problem of how to characterise the deviations of the reflected rays with regard to their ideal orientation.
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As is illustrated in Figure 8, if a ray is reflected onto the point of the surface sC, D, A and, instead of reaching the absorber tube at the correct point wCR , DR , AR , it does so at the incorrect x point wn CRn , DRn , ARn , this event is measured and stored in two new canonical images, IRST and y IRST . x {{{{{ in the pixel , . This is formally expressed as: Image IRST stores the distance z ww′ R R
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x After calculating distances for the whole surface, image IRST can be better evaluated if a colour code is assigned (see Figure 9). The result is an image in which areas with high z values are represented in red whereas low distances are shown in blue.
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Figure 8. Ideal direction of the reflected rays (blue) and deviation of the real rays owing to surface errors (red). 13
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Figure 9. Example of δ -image (left) and χ image (right). z is in millimetres.
y The image on the right, denoted as IRST , stores in R , R the number of beams which reach the receiver in A (feature ). Thus, although w is the expected contact point for the ray marked in Figure 8 (that is, in the case of the GTC), the ray makes contact with the receiver in w′, and the corresponding pixel Ro , Ro adds another vote, while pixel R , R is ignored. It is, therefore, y clear that image IRST provides with a map on which the concentration of the rays from the parabolic y surface can be evaluated. Note that IVWT is an image with one vote per pixel.
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In order to be practical and to define a parameter that measures the degree of concentration of y rays in the receiver, IRST has been reduced to a one-dimensional structure: a vector which adds up y the votes for each particular y-coordinate in IVWT . As explained in section 2.2, and can be seen in Figure 3(b), the Y-axis has the same direction as the longitudinal axis of the receiver. Because, in most cases, the deviations in the reflected solar rays cause them to touch in areas of the receiver different than expected (Figure 8), this new parameter will offer information on the concentration of the sunrays on the longitudinal axis of the receiver.
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This new parameter is the energy concentration index at the y-coordinate, , and is defined as the ratio of the number of rays that reach the receiver at the Y-coordinate versus the true number. This parameter is formally formulated as follows:
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A region at the y-coordinate is hypo-energetic if − ̅ Z −" ̅
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Note that parameter is not restricted to the interval [0,1] and that it might be greater than one. This index provides us with a measurement of the uniformity with which the solar radiation reaches the absorber tube. If there were frequent and meaningful energetic gradients in the tube, a turbulence analysis would be advisable. Hypo-energetic and hyper-energetic regions can, therefore, be detected in the receiver at certain Y-coordinates.
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where ̅ is the mean energy concentration index and " is the corresponding energy concentration index standard deviation. The region is hyper-energetic if: − ̅ Y "
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Figure 10. Energy concentration index, (dotted line) and hyper-energetic region detected (red squares) of the -image presented in Figure 9 along the Y-axis. In this case, there are no hypoenergetic regions.
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The identification of hypo-energetic and hyper-energetic regions in the receiver could be very useful as regards carrying out further analyses based on the heat transport that the fluid circulates inside the tube, but this is not within the scope of the present paper. For example, Hachicha et al. [21] present a complex model for the absorber tube that is used for heat transfer analysis and numerical simulation. This model could be used in conjunction with the data provided in our work.
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3. Results and discussion
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The method proposed in this paper has been tested on three solar trough collectors, denoted as C1, C2 and C3, at a solar power thermal plant. The parabolic mirrors have a focal length of 1490 mm, a length of 8 m and an aperture of 5.5 m. The absorber tube consists of two concentric cylinders: the outer cylinder is made of glass and has a diameter of 125mm, whereas the inner cylinder is made of steel and has a diameter of 70 mm.
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The laser scanner used in the acquisition process was the FARO LS 880. The range (80 m), density (8000 × 3500 points) and precision of this laser scanner are suitable for obtaining an accurate 3D model of the parabolic collector. The three solar trough collectors were scanned twice with the objective of proving the repeatability of the results.
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' Figure 11 a) shows images IRST for test 1 and test 2. Concave (pink rectangles) and convex zones (blue rectangles) are identified in Figure 11 b). Table 1 shows the quantitative results that characterise the global geometric errors of the parabolic surface of the collectors. The table includes the erroneous area percentage ̅ , means, f and f′, and variances "and "′ (the unit employed for all the parameters is EE).
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' Figure 11. a) Representation of images IRST for collectors C1, C2 and C3. b) concave and convex zones
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Table 1: Quantitative results that characterise the global geometric errors of the parabolic surface of the collectors.
C1 C2 C3
̅ 0.22 0.35 0.20
f 5.54 6.15 5.18
Test 1 fn -5.31 -6.31 -6.07
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"′ 2.04 2.49 2.60
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Test 2 fn -5.60 -5.82 -5.93
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"′ 2.26 2.36 2.44
The receiver pose errors of the three collectors are presented in Table 2. Parameters p, , f' and "' (f' is the mean error and "' is the deviation of the distances between the theoretical focal and the line that approximates the values of the real focal) are included. f' is the mean error of the distances between the theoretical focal and the line that approximates the values of the real focal, and "' is the deviation. The values of t and θ allow the error between the theoretical and the real focal to be characterised: the greater t and θ, the greater the error. This can be verified in C3, in which the maximum mean error f' corresponds to the highest values of | t | and | θ |. Something similar occurs with cases C1 and C2.
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Figure 12 displays the graphs that represent the position of the real and ideal focal axes in the second and third mirror. The similarities between the results obtained in tests 1 and 2 are noteworthy.
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Table 2: Receiver pose errors.
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C1 C2
pEE 2.82 1.95
° -0.45 0.39
Test 1 f' EE "' EE 2.82 1.28 1.95 1.10 17
pEE 4.67 1.18
° -0.45 0.43
Test 2 f' EE "' EE 4.67 1.28 1.39 0,98
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Figure 12. Focus positions in ABC and GTC models. ABC focuses are in blue and GTC focuses are in red. Superimposed is the corresponding regression line in black The results of the energy efficiency parameters are shown in Table 3. The values ^and , represent the number of pixels whose reflections reach the inner and outer absorber tube, respectively. The values are significantly greater than the ^ values. The results are apparently lower than expected. As can be seen in the energy analysis shown in Figure 14, there are hardly any losses, since only in C3 are hypoenergetic zones found, and the prediction is that this defect is barely perceptible in the installation. The reason for this apparent reckoning is that many of the rays that do not reach the tube (shown in red in Figure 13), are data from nearby non-acquired zones, 18
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which are precisely the zones that have the greatest inaccuracies. The next columns in Table 3 show the mean energy concentration index ̅, and the standard deviation " . As mentioned previously, Figure 13 shows ^ -image and -image, in which the green zones correspond to areas of the surface that reflect the rays to the absorber tube, the red zones represent those that do not correctly reflect the rays and the black areas are the parts of the parabola which are not acquired.
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Figure 14 presents the results concerning the energy concentration index . It will be observed that, at certain Y-coordinates the energy concentration index is higher than one, which means that many unexpected rays reach the receiver at this distance. Hypo-energetic zones are found in only one of the collectors. This could be owing to erroneous 3D data, since they all appear at the ends of the Y-axes.
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Table 3: Energy efficiency parameters.
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^ ̅ " ^ ̅ " C1 Test 1 0.54 0.75 0.74 0.25 Test 2 0.54 0.75 0.74 0.25 C2 0.53 0.74 0.72 0.21 0.47 0.68 0.68 0.18 C1 0.57 0.78 0.77 0.18 0.57 0.78 0.77 0.1 496
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Figure 14. Concentration indexes and hyper and hypo-energetic positions detected in the receiver.
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4. Conclusions
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In this work, an original framework that makes it possible to analyse the optical efficiency of parabolic trough collectors in terms of geometry and energy, using computer vision and image processing techniques, has been defined. Errors and failures in the collector can be easily detected and located by means of the complete information yielded by the approach proposed. All of the above consequently leads to believe that rapid detections and small in-situ reparations will be possible by following this method. This kind of work could have an impact on the cost and profitability of the solar plant.
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Contrary to theoretical solutions, an empirical method which can be put into practice using 3D sensors has been proposed. Both the approach and the parameters defined in the paper are original, although some parameters, and specifically the inner and outer interception indexes, could be viewed as an extension of the existing intercept factor (equation (10)).
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As is reported in section 3, the method has been tested in-situ on three solar trough collectors, taking two samples per collector. The results have been very satisfactory. It has been shown how the parameters facilitate to carry out an easy and precise quality control of parabolic trough collectors by using canonical images together with the set of characteristics. This system is easily reproducible and can be used by other engineers and researchers.
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The results presented in this paper refer to a specific position of the collectors, but the method is versatile and could identify and evaluate the performance of the collector under different conditions, thus opening up new lines of research. The surface deformation owing to the weight or different tensions supported by the metal structure during daily operation could also be studied by repeating the process for different positions of the collectors. Moreover, if the analysis were to be performed for different environmental conditions, the results could reveal how temperature or movement affect the functionality of the solar collectors.
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The future work is addressed to two research lines. In order to identify better the location and ' properties of erroneous zones, the segmentation of IRST into free-shape zones is a key point that should be dealt with. Our primary idea is that the current algorithm will be reformulated using fuzzy-snake segmentation techniques ([22]). The second research line will focus on testing the approach on an extended database of parabolic trough collectors. In addition, in order to avoid the problems of the laser scanners on reflective surfaces (i.e. the solar mirrors of the collector), we are planning to use structured-light techniques to collect dense 3D data. Particularly, the technique developed in [23] could be adapted to this environment in the future. Other interesting issue is that of the influence of the shape of the receiver and how it affect to the performance of the Parabolic Trough Collector. Unfortunately, there are several causes that prevent acquiring 3D data with long-range scanners: first, the majorty of the surface of the receiver is occluded by the collector itself, but also large amount of noise that the 3D data would present due to reflections in the mirrors of the collector and, finally, the material with which the receiver is manufactured (antireflective-coated glass) that makes extremely difficult the acquisition with laser scanners. In this work, the values of the radius and length of the receiver provided in the data sheet of the manufacturer has been used, and it has been assumed that the receiver is an ideal cylinder. The research in the kind of sensors appropriate to acquire this type of material that is located in zones of difficult access could open a new line of research that could be developed in the future.
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This work was supported by the Extremadura Regional Government and European Social Fund [GR10157 project]; and the Spanish Economy and Competitiveness Ministry [DPI2016-76380-R project AEI/FEDER, UE].
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References
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Framework for the optical analysis of solar trough collectors using 3D data. New data structure that allows to process the data with computer vision algorithms. Determination of the interception index using 3D point clouds. Definition of new parameters related with energy efficiency of solar mirrors. Testing of algorithms on 3D data collected in operating solar thermal power plants.
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