Diese Arbeit wurde vorgelegt amLehrstuhl fur Aachener Verfahrenstechnik (AVT)

Erkennung von Verschmutzung auf HeliostatspiegelnDetecting Soiling of Heliostat Surfaces

ProjektarbeitComputational Engineering Science

September 2017

Vorgelegt von Jana Sasse, 334312Presented by jana.sasse@rwth-aachen.de

Lennart Schumacher, 345785lennart.schumacher@rwth-aachen.de

Alexander Kristof, 346609alexander.kristof@rwth-aachen.de

Erstprufer Prof. Alexander Mitsos, Ph.D.First examiner AVT - Aachener Verfahrenstechnik (SVT)

RWTH Aachen University

Koreferent Dr. rer. nat. Pascal RichterCo-supervisor Lehrstuhl fur Mathematik (MathCCES)

RWTH Aachen University

Jeff Cumpston, Ph.D.AVT - Aachener Verfahrenstechnik (SVT)RWTH Aachen University

Eigenstandigkeitserklarung

Hiermit versichere ich, dass ich diese Projektarbeit selbstandig verfasst und keine an-deren als die angegebenen Quellen und Hilfsmittel benutzt habe. Die Stellen meinerArbeit, die dem Wortlaut oder dem Sinn nach anderen Werken entnommen sind, habeich in jedem Fall unter Angabe der Quelle als Entlehnung kenntlich gemacht. Dasselbegilt sinngemaß fur Tabellen und Abbildungen. Diese Arbeit hat in dieser oder einerahnlichen Form noch nicht im Rahmen einer anderen Prufung vorgelegen.

Aachen, im September 2017

Jana Sasse, Lennart Schumacher, Alexander Kristof

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Contents

List of Figures IV

List of Tables V

Abstract 1

1. Introduction 11.1. State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2. Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2. Experimental methods 42.1. Lab experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2. Outside experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3. Solar-field experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3. Data and analysis 73.1. Lab experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2. Outside experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3. Solar-field experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4. Discussion 144.1. Discussion of analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2. Discussion of software issues and performance . . . . . . . . . . . . . . 15

5. Conclusions and Outlook 15

A. Appendix 18A.1. Detect Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18A.2. Detect Soiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19A.3. Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

References 22

III

List of Figures

1. (a): Heliostat Field in Julich; (b): Heliostat Mirror with different soilinggrades (top left and top right mirrors are in original state after rain;bottom left mirror is artificially soiled; bottom right one is cleaned) . . 2

2. General idea for the construction: a camera is mounted on the receivertower facing the heliostat field . . . . . . . . . . . . . . . . . . . . . . . 3

3. In the lab experiments a colored paper screens reflection on a partiallysoiled mirror is photographed. The blue screen has a small rectangularhole for the camera. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4. For the setup we placed the mirror at a certain angle outside and tooka picture from a suitable distance. The mirror reflects blue sky and issoiled with cocoa powder. . . . . . . . . . . . . . . . . . . . . . . . . . 6

5. After application of cacao powder on the mirrors at the heliostat field inJulich reflectivity is measured on multiple spots per mirror. The cocoapowder is supposed to act as fine dust transported by the wind. . . . . 7

6. The red and white wallpaper backgrounds showed worse results for ouranalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

7. The blue and the gray backgrounds showed the best results for us, whichis fortunate as these are the colors we expect for our sky in practice. . . 8

8. Pictures from our experiments outside: (a) clean mirror; (b) severelysoiled mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

9. For our area detection routine test we edited this picture to look likemultiple mirrors in one picture . . . . . . . . . . . . . . . . . . . . . . . 9

10. Mirrors and their respective number that were used in the experiment.2, 5 and 10 are polished, 1 and 3 are soiled . . . . . . . . . . . . . . . . 10

11. Correlation of reflectivity measurements and deviation from optimal huevalue (red) as well as correlative function derived from that data (blue) 11

12. Pictures from our experiments at the heliostat field in Julich: (a) firstpicture after some mirrors have been cleaned; (b) picture after somemirrors have been artificially soiled . . . . . . . . . . . . . . . . . . . . 12

13. Edited picture derived from data from Julich in order to test our algo-rithm. The top left is in the basic state we found when arriving at theheliostat field, the top right and bottom left are from different stages ofartificial soiling, the bottom right is polished . . . . . . . . . . . . . . . 13

IV

List of Tables

1. Table of initial measurements . . . . . . . . . . . . . . . . . . . . . . . 102. Second measuring routine after soiling some mirrors . . . . . . . . . . . 11

V

Abstract

While the soiling grade of heliostat mirrors on CSP plants has already been knownfor a while to be an important factor on the power plant performance [3, 5], only fewattempts have been made so far to optimize the cleansing. In this report we presenta new method to detect soiling on the heliostat mirrors and optimize the cleaningroutine for heliostat fields. The method involves imaging of the heliostats that areoriented in such a way that light from a particular part of the sky is directed towardsthe camera lens. In our experiment, the camera is located at ground level, and sixmirrors are photographed with this orientation. In this scenario clean mirrors wouldreflect the blue sky above them and would therefore appear to be homogeneously blueon the picture, while soiled mirrors would have a different shade of blue. We wrote aprogram that identifies the mirror boundaries in the picture and analyzes the imagedata within to determine whether cleaning is required. The hue values of the dataare calibrated by reflectometer measurements at known points on the mirror surface,allowing to estimate the variation in reflectivity across the entire mirror surface. Asa result, we present a method that detects mirrors with a reflectivity below a certainthreshold and gives the user a list of these mirrors in order to optimize their cleaningschedule.

1. Introduction

A CSP plant is comprised of a tower on which a solar receiver sits, that absorbs solarradiation that is reflected from an array of mirrors, known as heliostats, nearby (seefigure 1). One aspect of its optimization is the reflectivity of the heliostat mirrorssurrounding the receiver tower. For optimal reflectivity the mirrors must not only beadjusted to reflect in the right angle, but also be as reflective as possible. Usuallythe reflectivity declines over time as the mirrors get dirty. Dust, sand and occasionalevents of rain soil the mirrors and make them less and less reflective. It therefore seemsunavoidable that the heliostat mirrors have to be cleaned regularly if one wants themto perform well.

1.1. State of the art

Previous research into mirror soiling has already shown that the soiling grade of themirrors is an important parameter to consider for the heliostat performance. Forinstance, a CSP site located in South Africa was found to have an average loss ofreflectivity by 0.5% per day [3] with variation in the results depending on the locationof the specific mirrors with respect to their facing direction as well as occasional pe-riods with higher soiling rates. A similar investigation found average soiling rates of0.47% per day during summer and an average soiling rate of 0.16% per day in winter[5]. It appears that environmental conditions like weather or seasonal events are a bigcontributor when it comes to soiling rates. Therefore the soiling rates differ between

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(a) Source: DLR(b) Heliostat Mirror in Julich

Figure 1: (a): Heliostat Field in Julich; (b): Heliostat Mirror with different soilinggrades (top left and top right mirrors are in original state after rain; bottomleft mirror is artificially soiled; bottom right one is cleaned)

CSP sites [5] based on their location. While a comparison between a site in the NegevDesert and a site in Sicily suggests that a dusty environment contributes to biggersoiling than an environment that is rather humid, data comparing sites in Florida andArizona suggest a different impact. It therefore seems that soiling on mirrors dependson more parameters than these two alone. It is worth pointing out that rain can haveboth cleaning and soiling effects, depending on other conditions. Research done by theFraunhofer ISE [5] indicates that rain can have an accelerating effect on the accumula-tion of soiling, while it is also considered a ”natural washing”and therefore deceleratingfactor during winter. However, sufficient data to determine the exact environmentalinfluences is still yet to be gathered. In conclusion, you can say that loss in reflectivityis dependent on the individual CSP plant, its climate conditions, location and cleaninginterval, since the link between those parameters and soiling appear to be non-linear,especially because climate conditions are commonly known to be complex.While the results above were obtained with reflectometers and much effort has beenput into this method [3, 4], it is impractical to repeatedly measure the exact reflectivityof each heliostat at a plant site to determine a cost efficient cleaning schedule. This iswhere we got our idea to generalize the method of measuring by taking pictures of theheliostat field. A camera that is resistant to the high temperatures at the top of thereceiver (e.g. a visual range camera based on a pinhole camera principle [2]) would besuitable for this purpose. As the developers of this camera type pointed out, it could beused to monitor the heliostats with respect to their cleanliness. Obviously, we cannotexpect the same accuracy in the results compared to reflectometer measurements, butthe purpose here is to derive a quick method for determining which of the heliostatsare in need of cleaning.Most heliostat fields of CSP plants are cleaned according to a schedule. This meansthat about every two weeks [1] a maintenance crew drives to the heliostat field andcleans all mirrors. This is hardly cost-effective as not all mirrors require a cleanse inthis schedule. While some might still be very effective for a much longer period of

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time, others might have to be cleaned every few days, especially those with highergeometric optical efficiency, and those which are subject to greater soiling rates dueto their location within the field, ie. mirrors at the boundary of the field subject tothe greatest winds. Our method would therefore allow to selectively determine from asingle photo the mirrors that need cleaning.The Ivanpah Solar Electric Generating System (ISEGS) in the Mojave Desert com-prises three receiver towers that are surrounded by a huge heliostat field with morethan 100,000 mirrors which are aligned in a seemingly chaotic order. This makes itimpractical to send a maintenance vehicle to the field to clean every one of the mir-rors, so they choose to never clean their mirrors. For these types of heliostat fieldsour method could provide a real option to identify a reduced set of mirrors that areseverely soiled and that are worth cleaning despite those difficulties.

1.2. Problem formulation

Our basic idea is to take pictures of the heliostat field on a regular basis (figure 2).This may be once a week or even once every two weeks, but may also be reasonableafter certain weather events like rain or sand storms. First, the mirrors need to bearranged in a way that they reflect a certain part of the sky which is far enough fromthe sun so we have a uniform color distribution. This arrangement should also be thesame each time. The pictures are taken from a high spot which may be on top of thereceiver or possibly by a drone flying above the heliostat field. The camera has to bein an elevated position so the mirrors do not block each other. It should be apparentin this picture if the mirrors reflect a blue sky (and are therefore clean) or if the coloris different, which may occur due to the soiling of the mirror.

Figure 2: General idea for the construction: a camera is mounted on the receiver towerfacing the heliostat field

Our project focused on the following main aspects:

• Conduct experiments in the lab, outside and at a heliostat field to find the

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necessary parameters for useful pictures and to collect data for our algorithm.These experiments are documented in section 2.

• Write an algorithm for the analysis using Matlab. We focused on three mainaspects:

1. The algorithm has to distinguish the mirrors from the background. This isnecessary not only for images taken by a moving drone but also in the caseof a fixed camera.

2. The algorithm has to detect homogeneous soiling like dust or sand as wellas inhomogeneous soiling like bird droppings or dirt blown up by vehiclesor strong winds. For each mirror it then computes a value representing themirrors soiling grade.

3. The output of the algorithm is a list of mirrors which should be cleaned.This list should be variable e.g. with respect to varying threshold values fordifferent mirrors in order to take into account the soiling grades for mirrorswith higher efficiency.

A detailed documentation for the algorithm is found in section 3.

• Discuss the results of the algorithm with respect to its possible applications. Theresults and our drawn conclusions as well as an outlook to possible future projectscan be found in sections 3, 4 and 5.

2. Experimental methods

For the development of our new method it was necessary to conduct several experimentsbeforehand. First, we experimented in the lab in order to determine the optimalbackground (sky) color, test different soiling methods and to get first pictures for ouralgorithm. Afterwards, we did a series of experiments outside to determine the optimalcamera distance and the angular dependencies as well as test our soiling methods inreal environmental conditions and finally we conducted experiments at the heliostatfield in Julich in order to take reflectometer measurements and gather data from anactual heliostat field to test our algorithm.

During the process of analyzing our first pictures, it occurred to us that the methodwe use for taking the pictures is critical to the algorithm and the outcome itself: Alarge distance between camera and mirrors is essential to make the images comparable.The distance between the camera and the mirror determines the angle of perceptiontowards the sky that is shown. The hue and saturation of the sky is not constantacross it and is affected by distance to the horizon and the sun. To keep this naturalgradient at a negligible level the angle and thereby the field of view has to be small.

Taking the pictures under similar blue sky conditions is preferred, because bluewavelengths of light have been described as most reliable when it comes to measure-ments with small dust particles on the mirror [6]. In addition it should be taken care

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of certain camera settings, such as a low ISO (about 100), the exposure time (about1/800s in our experiments) a proper focus on the mirrors as the auto settings are ofteninsufficient for our purpose.

2.1. Lab experiments

First experiments were conducted under lab conditions (figure 3). These involved cre-ating normalized pictures of mirrors reflecting a uniformly colored screen of cardboard.The mirror was placed orthogonal to the table underneath in an enclosed room. Thescreen simulated the sky and the camera was fixed on a bar and placed behind thescreen. It had a small hole for the lens of the camera. The photos were taken with anartificial light source from above without any light coming from outside. To get enoughmaterial to properly develop an algorithm with it photos were taken for each for thescreen colors: red (to simulate evening sky), white (for reference purposes), light blue(to simulate blue sky) and light gray (to simulate clouds). The different screen typeswere accompanied by different soiling grades of the mirror. Apart from cleaned mirrorsseveral levels of soiling as well as combinations of half clean half soiled were used sothat you can properly emulate degrees of soiling on solar power plants. The artificialsoiling on the mirror was produced with a combination of light sand, bark mulch andwater. The resulting pictures are gathered as RAW data images (DNG) with an 13megapixel camera, cut and retouched with GIMP and saved as PNG Images whichprovide lossless data compression.

Figure 3: In the lab experiments a colored paper screens reflection on a partially soiledmirror is photographed. The blue screen has a small rectangular hole for thecamera.

2.2. Outside experiments

Afterwards we did a second series of experiments outside using our knowledge fromthe lab experiments. In these experiments we used the same mirror as in the lab

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experiments (figure 4), cocoa powder and water spray to simulate different soilingsituations, such as sand or dust soiling due to a storm as well as rain in a combinationwith light soiling. The cocoa powder gave a more adequate result since it was finerand created more diverse soiling, such as clusters of dirt on a mirror and - contrary tothe previous material used as dirt - streaks of soil over the mirrors. The images weretaken on a sunny day with few clouds in the sky.

Figure 4: For the setup we placed the mirror at a certain angle outside and took apicture from a suitable distance. The mirror reflects blue sky and is soiledwith cocoa powder.

2.3. Solar-field experiments

Lastly, we did a series of experiments at the heliostat field in Julich, Germany (figure5). As we were allowed to take pictures from ground level only, we aligned the mirrorsfor our purpose, then in several iterations we prepared the mirrors by cleaning orsoiling them, then took reflectivity measurements and took pictures from a distance.This resulted in pictures of multiple heliostat mirrors along with respective reflectivityvalues where some were clean and others were not.

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(a) Measuring the reflectance of a soiled mirror(b) One of our group members applying cocoa

powder as dust on the mirror

Figure 5: After application of cacao powder on the mirrors at the heliostat field inJulich reflectivity is measured on multiple spots per mirror. The cocoa pow-der is supposed to act as fine dust transported by the wind.

3. Data and analysis

The experiments conducted as in section 2 produced results which we will discuss inthis section. We were able to derive a line fit for the correlation of reflectivity to thehue deviation of the pictures taken. These data were sufficient to develop an algorithmwhich returned a cleaning schedule for a picture edited from data from Julich.

3.1. Lab experiments

(a) Picture of half soiled, half cleaned mirrorwith white background

(b) Picture of half soiled, half cleaned mirrorwith red background

Figure 6: The red and white wallpaper backgrounds showed worse results for our anal-ysis.

For the analysis we had to remove the edges of the images and merge the white boxfor the camera into the picture. As it turns out, the background color does have a

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(a) Picture of half soiled, half cleaned mirrorwith gray background

(b) Picture of half soiled, half cleaned mirrorwith blue background

Figure 7: The blue and the gray backgrounds showed the best results for us, which isfortunate as these are the colors we expect for our sky in practice.

significant effect on the results. The gradients are better on mirrors with blue or graybackground (figure 7), while white or red backgrounds diminish the effect of the gra-dients (figure 6).

In addition our soiling method turned out to be unsatisfying. For this experimentwe collected dirt for soiling, which resulted in single clusters of dirt all over the mirror.We found this to be unrealistic since we expect soiling to be evenly distributed overthe mirror.

3.2. Outside experiments

Our experiments outside conducted as in section 2 gave us more insight in the necessaryconditions for gathering our data. The picture of the clean mirror clearly showed thata big distance from the mirror is necessary if you want a uniform sky, the less influenceyou get from the sun, the better the resulting pictures (figure 8). These were also theexperiments where we tested how to soil the mirrors in Julich ”properly”.

During the testing phase of our algorithm we also edited these pictures to test thearea recognition algorithm as seen in figure 9. Unfortunatly, the noisy boundariesbetween mirrors and frame were a problem for our area detection routine, so it gaveinsufficient results.

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(a) Influence of the sun on the background isclearly visible even when the sun doesn’tappear in the picture directly

(b) The left soiling part on the mirror wascreated by ”rain” as the mirror was firstcleaned on that part and then sprayed onwith water which then floated down on thecleaned part.

Figure 8: Pictures from our experiments outside: (a) clean mirror; (b) severely soiledmirror

Figure 9: For our area detection routine test we edited this picture to look like multiplemirrors in one picture

3.3. Solar-field experiments

For security purposes accessing the top of the receiver tower while it is operational wasnot allowed and the pictures of the heliostats had to be taken from ground level.

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# mirror setting ρ in % measurement H S V

1 89.5 - 90.6 random positions 215.4749 0.3826 0.72272 polished 94.7 on average random positions 213.1022 0.4468 0.71893 90.2 - 90.9 random positions 213,7997 0.3798 0.74754 polished 94.1 - 95.3 random positions 213.3576 0.4268 0.73805 90.4 single measurement 213.8038 0.3820 0.74036 90.0 single measurement 213.8922 0.3870 0.73647 90.6 single measurement 213.7686 0.3750 0.73628 91.2 single measurement 213.6642 0.3784 0.73019 89.7 - 90.9 random positions 213.4453 0.4184 0.696710 polished 95.0 - 95.2 random positions 213.6167 0.4549 0.6740

Table 1: Table of initial measurements

Figure 10: Mirrors and their respective number that were used in the experiment. 2,5 and 10 are polished, 1 and 3 are soiled

The experiments showed that the remaining reflectivity of a mirror and its change inhue do correlate in a roughly linear way. All mirrors in the pictures had a distance fromthe camera of more than 40m and had to be reoriented manually to show the same spotin the sky (figure 10). For 5 heliostats this took more than half an hour and had to beredone halfway through the heliostats due to a security shut down of the facility. Fora predefined camera location this orientation can be saved beforehand. Alignment ofmirrors turned out to be a reliable way of making their hue comparable. In unpolishedcondition the mirrors had reflectivities ranging between 90% and 91% and are visuallydistinguishable from polished mirrors with average reflectivities of about 95% as seenin table 1, while measurements of artificially soiled mirrors showed much lower values(table 2).

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# mirror setting ρ in % measurement H S V

1 casual soiling 76 - 86 random positions 216.7415 0.2812 0.74583 casual soiling 72.4 - 86.9 random positions 212.0883 0.2824 0.78892 baseline 214,5087 0,3546 0,75894 baseline 214.3165 0.3890 0.70283 severely soiled 13 - 71.3 random positions 208.0189 0.1947 0.6741

Table 2: Second measuring routine after soiling some mirrors

The reflectivity measured varied with the position of the reflectometer on the mirror,in particular when the mirror was artificially soiled. In addition, the extracted HSVvalues from the pictures only show a weak correlation to the measured reflectivitywhich may be due to big noise within the data.

Figure 11: Correlation of reflectivity measurements and deviation from optimal huevalue (red) as well as correlative function derived from that data (blue)

For mirrors in regular condition as well as polished ones the deviations are verysmall. The deviation of a mirror is defined as the absolute difference of its hue valueand the average hue of the polished mirrors in the same picture when reflecting thesame spot in the sky. Given the case that measurements are conducted during differenttimes of the day or year or different weather conditions, the optimal hue values shouldbe adjusted accordingly. The uncertainty of this method in determining the exactreflectivity just by hue value is clearly shown in the scattering of the points in thesoiled area as shown in figure 11. However, significant soiling can still be practicallydetected. Some of the resulting pictures can be seen in figure 12.

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(a) Baseline picture taken at the heliostat fieldin Julich. Some mirrors are cleaned, theothers are in their basic state.

(b) Picture taken after several mirrors havebeen artificially soiled.

Figure 12: Pictures from our experiments at the heliostat field in Julich: (a) first pic-ture after some mirrors have been cleaned; (b) picture after some mirrorshave been artificially soiled

The original pictures were not of use for our algorithm as they blocked each other anddid not present distinct mirror surfaces. We therefore edited a picture with multipleareas from the picture above on the right hand side to test our algorithm (figure 13).We used unregular shapes for the mirrors to test our mirror detection routine. Theblack background was chosen for convenience purposes, it works with any non- bluebackground color.

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Figure 13: Edited picture derived from data from Julich in order to test our algorithm.The top left is in the basic state we found when arriving at the heliostatfield, the top right and bottom left are from different stages of artificialsoiling, the bottom right is polished

The first step in the algorithm is to detect the individual mirrors in the photo takenby a tower or drone mounted camera and save their measurements independently.

The determination of the soiling grade is based a hue deviation function. As acompletely homogeneously soiled mirror does not contain any major gradients thequality of the areas are tested by checking the blue pixels deviation from an optimumin terms of hue [see A.2 line 32]. The optimal hue value is taken from a polished mirrorfrom the same image. Those deviations are then summed up and normed according tothe size of the individual mirror [line 43]. We later use these deviations in our outputroutine to estimate the remaining reflectivity.

For the output the algorithm takes the data based on the previous computationsof the soiling and analyzes them in order to give final results to the user (pseudocodeis found in A.3). First, all mirrors are exposed to a density function that representsthe importance of each mirror for the overall CSP plant performance. By default, thisvalue is set to 1. The soiling values are then compared to a threshold value that isbased on reflectometer measurements.For this purpose, we determined a function for the estimation of the reflectivity for anarea using the least squares method for our reflectometer measurements.

ρsoil = 92.9237152 − 4.367586 · σ

A plot for values of this function based on our measurements can be found in figure11. It is important to point out that these are heuristic values originating from noisy

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inputs and which we assume to have a strong correlation to the actual reflectivity.Each mirror whose estimated reflectivity is below 90 % is also flagged as ’to clean’.As a result we obtain a list of all mirrors with a flag for each mirror that has to becleaned.Additional visualization methods to show the user where the mirrors are are optional.As an example, we implemented a short routine which highlights all dirty mirrors inred.

This algorithm gave different results with respect to the required minimal reflectivity.A minimal reflectivity value of 90% for figure 13 resulted in the first three mirrorshaving to be cleaned and only the last one (which was polished right before the picturewas taken) was found clean enough, while a lower threshold of 85% gave the instructionto clean the second and the third mirror.

4. Discussion

Now having experimental and computational results we can evaluate our methodswith respect of usability and performance. Our goal is to determine whether theaproach leads to the desired results or not. Farther we are able to outline issues anddisadvantages of the presented strategy in order to improve and further develop thesoftware tools we provided.

4.1. Discussion of analysis

Prior to our investigations we had to assume that there is a linear dependency betweenthe grade of soiling and the reflectivity loss for the mirror. This is a reasonable approachand has been used previously [3, 5]. Unfortunatly, the dependencies depicted in figure11 show that a linear dependency might be a long shot, however, we lack data toestimate a better model. One reason might be that the measurements taken on severlysoiled mirrors were very inconsistent due to the inhomogeneous spreading of the dirtin our experiment.

A problem for a tower mounted camera might be the usual orientation of the he-liostats towards the sun since it would be impractical to unfocus the mirrors duringdaytime while they are supposed to provide heat. A way to solve this problem wouldbe to take the pictures shortly after sunrise or before sunset, but you would have todeal with different color values than during the day, namely more reddish light insteadof blueish.

Although we did not have the same climatic conditions - such as clouds and differentpositions of the sun during the day - in neither of our experiments compared to acommercial heliostat field, our results are still transferable.

Another practical issue is that the optimal hue value used for the code is dependenton polished mirrors and must be determined for each image anew, especially if lightingconditions vary.

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4.2. Discussion of software issues and performance

For the mirror detection Matlab provides a tool which can be used to separate back-ground and foreground by the user defining a certain number of points as either. Theso-called ’Image Segmenter’ proceeds by turning background color black and therebyhighlighting the foreground. This tool eases the mirror detection although Matlab doesnot automatically save the mirrors in our own data structure (or any other). The dis-advantage of that method is the fact that you would still need the points of backgroundand foreground to properly detect the mirrors. They have to be provided separately bythe user. Still, Matlab gives you the algorithm that detects foreground and backgroundso you can still use it in the detection procedure. As it turns out Matlab only needstwo or few more points to properly distinguish between mirrors and the background(grass, sand, etc.). You can see our usage of the generated code in Appendix A.1 onpage 19 from line 1 to line 13.

Since we are using a simple data structure to save detected mirrors for easier pro-cessing, we have to have an algorithm that detects mirrors on that segmented pictureand puts them into that structure. However, processing that image turned out to bea bottleneck of the overall performance of the program. The naive approach wouldbe to start iterating through the segmented image and start detecting mode when anon-black pixel is encountered. That detecting mode counts every non-black pixel inthe row for each column and saves it in the memory until there is no ’non-black row’,which means the algorithm reached the last row of the mirror (see line 73). It switchesinto iteration mode and starts at the first column of the previous mirror. Anotherway of constructing the data structure would be to detect corner points of the mir-ror and interpolating the missing pixels by assuming straight lines between the cornerpoints as boundary for the mirror. However, the former turns out to be satisfying inperformance.

For the detection of soiling computing gradients turned out to be insufficient. As-sumed the heliostat field is in a desert, soiling will probably effect the mirrors evenlywith low differences among them which is why computing gradients would not resultin detecting these soilings. Instead, we have accomplished detection with comparingthe color values with expected blue values for a perfect reflectance.Other approaches with a high pass filter that used a Fourier transformation to at-tenuate signals below a cut-off and allowing signals above were later dropped as thepractical lack of inhomogeneous soiling and the large number of mirrors in one heliostatfield (and thereby in one image) had such filters generate many flaws and then returnthem falsely as soiling.

5. Conclusions and Outlook

Our results look quite promising so far. Over the course of our work we have studiedthe current methods to deal with the heliostat mirror soiling issue and came up with

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a different approach to tackle this problem. We developed an algorithm that coulddetect mirrors of a heliostat field within a picture and give us reliable information onwhich mirrors should be cleaned and in addition we included options for heuristics tooptimize that process.

However, there are certain limitations to our method: So far, the code only worksafter the user determined certain parameters (foreground and background color etc.).This problem should be solvable by using more data points, e.g. analyzing morepictures from actual heliostat fields and use their results to improve the algorithm.Furthermore, the code relies on the uniform color of the sky which has to be determinedfrom day to day. One method might be to clean several mirrors within the field forbaseline measurements, another would be to determine the color of the sky by a directmeasurement. Another issue we might be facing is that from a certain size on it mightnot be possible to get enough pixels for each mirror to compute meaningful results. Asolution to this problem might be to take several pictures of areas of the heliostat field,respectively, or to use a drone to fly over the field and take pictures of smaller portionsof the field. In conclusion, we really need more data points (e.g. more pictures) to beable to optimize the method for commercial usage.

Our work should be seen as a foundation for others to follow and we envision severalimprovements and further applications for this project. Improvements of our methodwould for example be the use of data on weather events to automate the process onwhen to take a picture of the field, use advanced visualization techniques to show theuser where the dirty mirrors are located, improve the image segmentation process bydetecting background and foreground, etc.Further applications of the method could be to embed a cleaning route optimizationroutine for maintenance cars and/or cleaning robots, methods to determine brokenmirrors from the picture, using the pictures for an optimization of the overall heliostatfield performance, etc.

For the application of our method at a concrete heliostat field several steps of preworkare necessary:

1. Determine how many pictures you need to take in order to be able to analyzethe whole heliostat field properly.

2. Determine the most valuable mirrors within the field and compute a functionthat fits this distribution.

3. Determine the threshold for which you want a mirror to be cleaned as soon asit drops below that threshold value. We recommend to start with a thresholdvalue of about 85% reflectivity for a mirror with average output effectiveness withcorresponding higher (or lower, respectively) reflectivity thresholds for more (less)effective mirrors within the heliostat field.

Based on our results we suggest as a cleaning schedule to take a picture of the heliostatfield on a regular basis to run the analysis algorithm. In the main season this might beas often as daily to prevent the most effective mirrors within the field from losing their

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peak performance. In addition we recommend to take a picture after severe weatherevents like rain or a storm.

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A. Appendix

A.1. Detect Mirrors

Listing 1: Detect Mirrors1 function [ mirrors , masked image , bwimg ] = de t e c tm i r r o r s ( img )2

3 % algor i thm taken from Toolbox4 convert rgb co lo r−space o f image to lab5

6 get p ixe l−i d s7

8 % Convert L∗a∗b∗ range to [0 1 ]9 apply Matlab ’ s lazysnapping a lgor i thm on lab-image

10

11 Create masked image12

13

14 %% process b/w−image to 3− t ensor15 % idea o f the f o l l ow i n g a lgor i thm :16 % walk through the p i x e l s17 % i f a p i x e l i s not b l a c k i t must be a mirror18 % in tha t case count a l l p i x e l s in x−d i r e c t i on tha t are not b l a c k19 % un t i l you encounter a p i x e l t ha t i s b lack , which means t ha t20 % mirror ends there .21 % when you encounter the end o f the mirror in x−d i r e c t i on :22 % increase y−d i r e c t i on fo r one p i x e l and re try , beg in at23 % beginning o f prev ious row and check whether mirror i s leaned24 % towards r i g h t or l e f t s i d e ( which means tha t you have to change25 % the beg inning towards nega t i v e x−d i r e c t i on )26 % do tha t u n t i l you meet a x−row with no non−b l a c k p i x e l27 % (and a l s o check i f p i x e l s below tha t ones are non−b l a c k )28 % in tha t case : proceed from the beg inning u n t i l you have no more29 % p i x e l s l e f t30

31 get p i x e l s in x , y−d i r e c t i o n32

33 %i n i t i a l i z a t i o n needed fo r whi le−l oop s ince Matlab does not i t e r a t e over non− i n i t i a l i z e d o b j e c t s in whi le−l oops34 i n i t i a l i z e mirror−t enso r [ dimensions are #p i x e l s in x and #p i x e l s in y ]35

36 i n i t i a l i z e v a r i a b l e s for i t e r a t i o n37 % maximal l eng t h o f mirror in p i x e l s :38 % i f p i x e l in next row i s b lack , go r i g h t f o r maximal max x p i x e l s39 % to determine whether or not the mirror has more p i x e l s in t h i s row40

41 while a mirror in prev ious i t e r a t i o n has been found42 r e i n i t i a l i z e v a r i a b l e s i and j43 while i <= p i x e l s y44 while j <= p i x e l s x45 % i f a va lue isn ’ t b l a c k => must be mirror46 i f cur rent co lo r−value i s not black47 % i f a mirror has a edge pointed towards top l e f t ( edge l ook s l i k e ’/ ’ )48 i f a mirror−row has been detec ted in prev ious row49

50 i f p i x e l to the l e f t i s a mirror−p i x e l51 % go back one p i x e l i f there ’ s a non−b l a c k p i x e l52 % j ge t s increased by one at the end ,53 % so i t a c t u a l l y says ’ j−1’54 j = j −2;55 else56 % f i n i s h e d ca tch ing up with mirror57 j = j −1;58 end

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59

60 % encounter o f a mirror f o r f i r s t time or reencounter61 e l s e i f f i r s t p i x e l o f mirror in row62 enable de t e c t i on mode for f u r t h e r de t e c t i on63

64 % I am in the mirror and count p i x e l in row65 else in de t e c t i on mode66 count p i x e l and save po s i t i o n67 end68

69 % encounter o f non−mirror p i x e l70 else71

72 % f i r s t non−mirror p i x e l in row73 i f p i x e l i s b lack74 set running va r i ab l e back to beg inning index o f f i r s t p i x e l in row75 and go one column lower76

77 % not in mirror but in re loop => maybe gap in mirror78 e l s e i f we have j u s t went one column lower79

80 % h i gh l y reasonab l e t ha t mirror ends there81 i f j f u r t h e r than any p i x e l b e f o r e82

83 %f i n i s h count ing mirror p i x e l s84 r e i n i t i a l i z e v a r i a b l e s and go to end o f loop85

86 end87 end88 end89 j = j +1;90 end91 i = i +1;92 j = 1 ;93 max x = 0 ;94 end95 end96

97 %% pos tp roce s s ing98 % ne : b l u e c h e c k r e a l l o c a t i n g tensor f o r l e s s memory consumption ; only save the99 % non−zero en t r i e s

100 for i = 1 : p i x e l s y101 i f mirror s ( i , 1 , 1 ) ˜= 0102 for j = 1 : p i x e l s y103 r e s i z e new a r ea t en s o r104 end105 else106 break ;107 end108 end109 mirror s = a r ea t en s o r ;110 end

A.2. Detect Soiling

Listing 2: Detect Soiling1

2 function [ s o i l i n g t e n s o r ] = d e t e c t s o i l i n g ( img , area )3

4 get t o t a l number o f Areas5

6 convert image in to hsv c o l o r space7

8 s c a l e Hue to value between 0 and 300 degree s

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9

10 % from DSC07819 , second p i c t u r e in ”w i s s e n s c h a f t l i c h ” f o l d e r with mediocre11 % so i l i n g , mirror 4 , l i g h t n i n g rod cut o f f12 H opt = 213 .4857 ;13

14 i n i t i a l i z e s o i l i n g t en s o r s15

16 for num area = 1 : s ize ( area , 1)17

18 % count number o f l i n e s in area19 num lines = 0 ;20 for i = 1 : s ize ( area ( num area , : , : ) , 2 )21 i f area ( num area , i ,1)˜=022 num lines = num lines + 1 ;23 end24 end25

26 % count number o f p i x e l s in area27 num a l l p i x e l s = 0 ;28 for l ine = 1 : num lines29 num a l l p i x e l s = num a l l p i x e l s + area ( num area , l ine , 3 ) ;30 end31

32

33 % bluecheck rou t ine34 for l ine = 1 : num lines35 for p i x e l = 1 : area ( num area , l ine , 3)36 determine dev i a t i on from i d e a l shade o f blue and save i t in dev i a t i on tenso r37 end38 end39

40 % compute average dev i a t i on o f area41 dev i a t i on ( num area ) = dev i a t i on ( num area ) / num a l l p i x e l s ;42

43

44 % compute s o i l i n g va lue us ing g rad i en t s45 for l ine = 1 : num lines46 for p i x e l = 1 : area ( num area , l ine , 3)47 tmp ( : ) = tmp ( : ) + ( double ( img ( area ( num area , l ine , 2 ) ,48 area ( num area , l ine , 1) + p i x e l − 1 , : ) ) ) ;49 end50 end51

52 % s o i l conta ins average [ r g b ]53 s o i l ( num area , : ) = tmp ( : ) / num a l l p i x e l s ;54

55 tmp ( : ) = 0 ;56 end57

58 % so i l i n g t e n s o r ( : , 1 ) conta ins average ( gray ) s o i l i n g va lue s f o r each area59 s o i l i n g t e n s o r ( : , 1 ) = ( s o i l ( : , 1 ) + s o i l ( : , 2 ) + s o i l ( : , 3 ) ) / 3 . 0 ;60 s o i l i n g t e n s o r ( : , 2 ) = dev i a t i on ( : ) ;61

62 end

A.3. Output

Listing 3: Output1

2 function [ c l e an i ng s ch edu l e ] = output ( s o i l i n g t e n s o r )3

4 % take boo l va lue s from s o i l i n g t e n s o r5 c l e an i ng s ch edu l e = s o i l i n g t e n s o r ( : , 3 ) ;6

20

7 % dens i t y func t i on fo r importance d i s t r i b u t i o n o f mirrors ;8 % by d e f a u l t == 19 den s i t y func = 1 ;

10

11 m i n r e f l e c t i v i t y = 90 ;12

13 for num area = 1 : s ize ( c l e an i ng s ch edu l e )14

15 % i f the r e f l e c t i v i t y o f a not a l ready f l a g g e d area s ink s16 % below the minimal requ i red r e f l e c t i v i t y17 % ( perhaps a f t e r mod i f i ca t i on with the dens i t y func t i on ) , f l a g as d i r t y18 i f c l e an i ng s ch edu l e ( num area ) == 019 r e f l e c t i v i t y = c a l cR e f l e c t i v i t y ( s o i l i n g t e n s o r ( num area , 2 ) ) ∗ den s i t y func ;20 i f r e f l e c t i v i t y <= m i n r e f l e c t i v i t y21 c l e an i ng s ch edu l e ( num area ) = 1 ;22 end23 end24 end25

26 end

Listing 4: CalcReflectivity1

2 function [ r e f l e c t i v i t y ] = c a l cR e f l e c t i v i t y ( dev i a t i on )3

4 % Returns r e f l e c t i v i t y o f a mirror with input dev i a t i on in Hue from Hopt5 % l i n e a r model i s used . parameters were determined with l e a s t square6 % method on j u e l i c h measurements .7 r e f l e c t i v i t y = 92.9237152 + ( dev i a t i on ) ∗ (−4.367586) ;8

9 end

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References

[1] A Fernandez-Garcıa, L Alvarez-Rodrigo, L Martınez-Arcos, R Aguiar, andJM Marquez-Payes. Study of different cleaning methods for solar reflectors used incsp plants. Energy Procedia, 49:80–89, 2014.

[2] N Goldberg, G Kroyzer, R Hayut, J Schwarzbach, A Eitan, and S Pekarsky. Em-bedding a visual range camera in a solar receiver. Energy Procedia, 69:1877–1884,2015.

[3] DJ Griffith, L Vhengani, and M Maliage. Measurements of mirror soiling at acandidate csp site. Energy Procedia, 49:1371–1378, 2014.

[4] A Heimsath, G Kutscheidt, and P Nitz. Measuring reflectance-overview and influ-ence on optical performance, 2011.

[5] Anna Heimsath, Markus Heck, Gabriel Morin, Wilhelm Kiewitt, and WernerPlatzer. Soiling of aluminum and glass mirrors under different climatic condi-tions and techno-economic optimization of cleaning intervals. In SolarPACES 2010Conference, Perpignan, France, 2010.

[6] RB Pettit and JM Freese. Wavelength dependent scattering caused by dust accu-mulation on solar mirrors. Solar Energy Materials, 3(1-2):1–20, 1980.

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