Spatial irradiance estimation in a thermosolar power plant by a mobile robot sensor network

This is a repository copy of Spatial irradiance estimation in a thermosolar power plant by a mobile robot sensor network in the Depósito de Investigación de la Universidad de Sevilla Version: Author Accepted Version Citation: García Martín, J., Maestre Torreblanca, J.M. y Fernández Camacho, E. (2021). Spatial irradiance estimation in a thermosolar power plant by a mobile robot sensor network. Solar Energy, 15, 735-744. 10.1016/j.solener.2021.03.038 To cite this publication, please use the final published version (if applicable). Please check the document version above. Copyright: Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policy: Please contact us ([email protected]) and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim Spatial Irradiance Estimation in a Thermosolar Power Plant by a Mobile Robot Sensor Network J. G. Martina,∗, J.M. Maestrea, E.F. Camachoa aDepartment of Systems Engineering and Automation, University of Seville, Seville, Spain Abstract An algorithm for mapping Direct Normal Irradiance (DNI) in thermosolar power plants using a Mobile Robotic Sensor Network (RSN) is presented. The algorithm selects measurements spots and allocates the RSN accordingly to carry out the dynamic estimation of DNI. A generic thermosolar power plant with a fleet of vehicles is used as a simulated case study to assess the performance of the algorithm. The results show that the proposed method allows us to obtain a spatial estimation of the DNI that improves the flow control in the loops of the plant, outperforming estimations based on a single pyrheliometer. Keywords: Multi-Robot System, Task planning, Sensor Networks, Direct Normal Irradiance, Distributed Estimation, Thermosolar plant. 1. Introduction1 Thermosolar power plants are large-scale systems where solar collectors gather solar energy to2 generate electric power. In the case of Parabolic Trough Collector (PTC) solar plants, collectors3 are composed of parabolic mirrors and a tube located in the focal point of the parabola where a4 heat transfer fluid (HTF), usually thermic oil, is heated up to generate steam for a turbine (Ca-5 macho et al.,1997,Camacho and Berenguel,2012). In these plants, there is typically a single6 pyrheliometer measuring Direct Normal Irradiance (DNI) to control the HTF flow, which is not7 efficient whenever the DNI received is not homogeneous across the solar field, e.g., due to clouds.8 In these circumstances, it is important to know the direct solar irradiance over the plant in order9 to increase or reduce the HTF flows accordingly to avoid avoid overheating in some parts of the10 ∗Corresponding author Email address: [email protected] (J. G. Martin) Preprint submitted to Journal of L A T EX Templates January 15, 2021 Nomenclature Acronyms HTF Heat Transfer Fluid. TES Thermic Energy Storage. UAV Unmanned Aerial Vehicle. UGV Unmanned Ground Vehicle. DNI Direct Normal Irradiance. MRS Multi-Robot System. MRTA Multi-Robot Task Allocation. WSN Wireless Sensor Network. RSN Robotic Sensor Network. GIS Geographic Information System. PTC Parabolic Though Collector. Sets T(k) Set of tasks in instant k. VSet of unmanned vehicles. GSet of UGVs. ASet of UAVs. CSet of values that sensors can measure. Algorithm variables CFR ij Real cloud factor in cell ij. CFE ij Expected cloud factor in cell ij. CFest ij Estimated cloud factor in cell ij. Hij Information entropy in cell ij. CFEij Cloud factor effect in cell ij. HEij Information entropy effect in cell ij. WEij Wind effect in cell ij. Jij Cost function in cell ij. Algorithm parameters taTime in which algorithm erase unfinished tasks and generate new ones. λ1,2,3,4Weights for CFE HE and WE respectively. a1,2Parameters for CFest. No TNumber of tasks generated each time the algorithm generates new tasks. FForgetting factor. MRTA parameters δMRTA jRepresents the urgency of the tasks, i.e., the penalization for the time taken in performing a certain task j. γiMRTA Represents the penalization for moving a certain robot i. Other parameters Vmean xy mean velocity of vehicles. VZmean vertical mean velocity of vehicles. σoStandard deviation of a measurement taken in the same cell. σmax Standard deviation of a measurement taken in the farthest cell within the range. RDRange of cells where a measurement affects other measurements. 2 plant and not hot enough HTF in other parts of the plant. HTF may reach temperatures over the11 maximum limits. and as a consequence, collectors may need to be defocused, with the undesirable12 waste of solar energy.13 To deal with this issue, some works such as (S´anchez et al.,2018,Masero et al.) propose14 using local valves for controlling the flows in different collectors, requiring a spatial estimation15 of the irradiance throughout the plant. To this end, clouds movement can be forecasted using16 images (Radovan and Ban,2014) and weather information (Zhang et al.,2018). Here, we consider17 DNI sensors mounted on unmanned vehicles as an integral part of the control system. Particularly18 this work presents a first assessment based on simulations for the use of mobile Robotic Sensor19 Network (RSN) to estimate solar irradiance on a thermosolar power plant. Even though unmanned20 vehicles are still expensive, their price is expected to continue decreasing at the same or even at21 a faster pace in the next years. Likewise, the performance increase of the power plant can easily22 outweigh the investment required.23 Multi-Robot Systems (MRS) are formed by more than one robot and have the objective of24 performing a set of tasks in an efficient manner. These systems have been used in the last decades25 for purposes such as logistics (Farinelli et al.,2017), surveillance (Gohari et al.,2019), filming (Zema26 et al.,2017), agriculture (agr), inspection (Brusell et al.,2016), and mapping (Yang et al.,2017).27 Another relevant application of MRS is the generation of RSN, i.e., a Wireless Sensor Network28 (WSN) where sensors can move around the field (Akyildiz et al.,2002,Aydin et al.,2019). In29 particular, RSN have often been proposed for mapping and moniroting environmental variables and30 gathering information for Geographic Information System (GIS) (Bolstad,2016). Some works using31 RSNs for spatial estimation are mentioned in (Rold´an et al.,2016), where one Unmanned Ground32 Vehicles (UGV) and one Unmaneed Aerial Vehicles (UAV) are used to monitor temperature and33 humidity in a greenhouse, and in (Conesa-Mu˜noz et al.,2016), where aerial and ground vehicles are34 respectively used to gather environmental information and perform interventions. Also, in (Zhang35 and Leonard,2010), a cooperative Kalman filter is used for both managing a RSN and estimating36 the state of a static planar scalar field.37 Integration of the collected information is also a relevant topic in this context. For example,38 mapping environmental variables such as temperature, pressure and other geographic data has39 been largely approached using Kriging (Williams,1998), which has became a de facto standard for40 3 many GIS, such as ArcGIS. Kriging is a technique that was first developed in (Matheron,1963) and41 then generalized for all sort of spatial applications in (Cressie and Wikle,2015). In particular, the42 spatio-temporal generalization is specially suitable for events with dynamic variables and shifting43 concentration over a certain area, e.g., fire, contaminating fluids in water, and DNI changes due to44 cloud coverage. Indeed, this technique has been proposed in the literature to estimate and forecast45 solar irradiance, e.g., see (Yang et al.,2013) and (Aryaputera et al.,2015). Also, spatio-temporal46 kriging has been proposed for simultaneous environmental mapping of dynamic variables and sensor47 placement in works such as (Roy et al.,2016), (Roy et al.,2018) and (Graham and Cort´es,2011).48 In this work, we study how the RSN can be managed to collect information for the control sys-49 tem in the most efficient manner. In particular, we integrate several information layers comprising50 data measured by ground and air robots, and fixed sensors such as pyrheliometers. Then, we use a51 Bayesian approach to update the probability that a certain area of the solar field is covered. In this52 way, robots are moved to positions where the information gathered is maximized. This approach is53 aligned with other works in the literature that use Bayesian Inference (BI) and information theory54 to manage RSN such as (inf). Other works that follow this approach are (Julian et al.,2012),55 (Julian et al.,2013), and (Cui et al.,2015), where mutual information is used in lockstep with56 consensus based strategies for the control of a distributed fleet of vehicles acting as a RSN and57 then BI is applied to update the state of the environment.58 The rest of this work is organized as it follows: In Section 2, the problem statement and59 assumptions regarding the thermosolar plant, the vehicle fleet, and the clouds are presented; in60 Section 3, the proposed algorithm for the spatial estimation is detailed; in Section 4, the case study61 where the algorithm is tested is described; in Section 5, the results of the simulations are shown62 and discussed. Conclusions and future investigation lines are given in Section 6.63 2. Problem Statement64 PTC plants have an structured layout where the following elements can be found (see Fig. ??):65 •Collectors that gather solar energy and warm up the thermic oil.66 •Buildings containing:67 –Steam generation plant.68 4 –Turbines.69 –Control rooms.70 –Workshops and storage buildings.71 –Offices.72 •Cooling towers.73 •HTF tanks.74 •Thermic Energy Storage (TES) tanks (in some cases).75 •Manifolds, which distribute (receive) the HTF to (from) the collectors.76 •Parking lots.77 In most cases, the buildings, the parking lots and the TES tanks are located in a central area78 for human operators. All the manifolds that distribute and collect oil come in and out of this area79 and the collectors are placed in rows to maximize the use of available area.80 A grid of DNI measurement spots or cells located in the space between collectors is considered.81 We assume that information from previous measurements and wind vectors in cells is available (e.g.,82 obtained from a numeric model like Harmonie Arome in Spain (Kalnay,2003,AEMET)). Moreover,83 it could be considered that there are other sources of wind information such as anemometers in84 the plant and sensors in the UAVs.85 Clouds are assumed to be composed of a cluster of ellipsoids contained in a larger ellipsoid with86 random dimensions following a Gaussian distribution according to (Kulemin,2003), with velocity87 interpolated from the wind field in each time iteration. An example of the clouds considered can88 be seen in Fig. 1. Note that Spencer equations (Spencer,1971) can be used to obtain solar rays at89 each measurement spot and calculate their interference with clouds.90 5 Figure 1: Example of clouds above the power plant. Since nominal clear-sky irradiance can be computed with clear sky models, irradiance losses91 can be modelled by a cloud factor (CF) in the range 0 −1 in each measurement spot, creating92 the CF grid of Fig. 2a. If CFij = 0, spot ij receives nominal DNI, whereas CFij = 1 implies that93 spot ij receives 0 DNI. Our aim is to estimate the CF grid as precisely as possible. Discretized94 real values are denoted as CF R ij and are approached via a discrete probability distribution for each95 cell, forming the so-called PC field, which is depicted in Fig. 2b. When there is no information96 regarding the field, a uniform distribution for each cell is assumed.97 6 (a) CFRgrid. (b) PC grid. Figure 2: Grids To perform the estimation, an heterogeneous set of unmanned vehicles, V, is considered, which98 is composed of a set Gof UGVs and a set Aof UAVs, i.e., V=G ∪ A. Each vehicle has a DNI99 sensor integrated and can perform measurements at the cell where it is located by using sensors100 such as that in Fig. 3. Task consist of moving a sensing vehicle to a different cell and our aim is101 to generate at each time instant a set of tasks Tto improve DNI estimations, i.e., T=T(k).102 Figure 3: ISS Solar-MEMS sun sensor (Solar MEMS Webpage). Vehicles are assumed to have low level controllers and move always at cruise velocity with some103 7 constraints:104 •Unmanned vehicles must not enter the buildings area. Consequently, there are no measure-105 ment spots inside this area.106 •Manifolds can only be crossed by UGVs using the bridges designed for this purpose.107 •Flying over collectors is not allowed for security.108 Furthermore, each vehicle is assumed to consume and charge its battery in a linear way, with109 rates depending on its features. Likewise, there are different charging stations available for UGVs110 and UAVs.111 Also, some considerations have been assumed regarding the sensors:112 •Sensors have a predefined resolution and range, i.e., they can only take values from an alphabet113 C, and not intermediate values.114 •The probability function of the sensor p(z|c) is known and modelled using truncated normal115 distributions, where zis the value of the measurement and cdenotes the discretized value116 of the field. A subscript ij can be used to denote the value at a given cell (see Table 1).117 Hence, given the prior probability contained in PC field and the conditional sensor probability118 contained in PZ, the posterior probability (probability after a measure is taken) can be easily119 calculated using BI as120 P(cr ij|zij) = P(cr ij )·P(zij |cr ij ) X cr ij ∈C P(ck ij)·P(zij|ck ij)cr ij ∈ C.(1) •Measurements taken while vehicles are moving are less reliable than when they are still for a121 certain time, tcm. Also, measurements taken by UAVs are less reliable than those taken by122 UGVs.123 •Measurements taken by fixed pyrheliometers are the most reliable ones.124 •Measurements in a certain location will affect the beliefs of nearby locations and during a time125 window, i.e., it is assumed that there is a spatio-temporal correlation in the DNI. Therefore,126 8 4. Case-Study213 In this section, we first present the simulated thermosolar plant layout and vehicles considered.214 Then, the proposed algorithm is tested.215 4.1. Thermosolar Plant Layout216 The thermosolar power plant is based on a section of the plant Solacor I in El Carpio,217 Spain (Abengoa) and can be seen in Fig. 6.218 15 100 200 300 400 500 600 700 800 900 1000 1100 X Coordinate (m) 0 100 200 300 400 500 Y Coordinate (m) R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 R 9 R 10 Forbidden area for vehicles Forbidden area for UGVs Forbidden area for UAVs Charge Station UAV UGV Measurement spot Figure 6: Section of the real Thermosolar power plant of El Carpio (Spain) and layout considered in this Case-Study This 30 MW thermosolar plant covers 63 ha (1180 ×540 m), containing its operation zone,219 where the buildings, parking lots, TES and electric station are placed, in the upper centre of the220 plant. Likewise, cold and warm HTF manifolds run paralell from the southern part of the operation221 zone to the extremes of the plant, dividing the plant into three sectors. There are 18 loops in the222 16 south sector of the plant and 8 loops in each one of the north sectors and a bridge for the ground223 vehicles to go from the south to the north at each side of the operation zone. Each loop has 4224 collectors in “U” shape, because loops start and end at the manifolds.225 4.2. Unmanned vehicles parameters226 The parameters of ground and aerial vehicles are given in Table 2and are based on commercial227 models 1, with Vmean being the velocity in the horizontal plane, VZmean the vertical velocity, and228 λithe weight that each agent has in the MRTA step.229 Table 2: Value of the vehicle parameters based on commercial models. Parameter UGV UAV Vmean 1.5 m/s 10 m/s VZmean 0 m/s 3 m/s Discharge rate 0.005 0.1 Charge rate 0.0025 0.03 γMRTA i1.5 1 The initial positions of the vehicles can be seen in Fig. 6and have been randomly generated.230 As for the pyrheliometer, it is fixed and located next to the plant.231 4.3. Bayesian estimation parameters232 It has been considered that the precision of the DNI sensors equipped in the vehicles is 10% so233 that crcan take 11 values from 0 to 1. The measurements follow normal distributions depending234 on the equipment and on how they are takenwith relevant features are presented in Table 3. The235 standard deviation σis assumed to vary for adjacent cells as236 σ=σmax−σo R3 D ·D3+σo,(7) 1UAVs are based on DJI Matrice 200 and UGVs on Summit-XL. 17 where σois the standard deviation in the cell where the measurement has been taken, RDis the237 maximum distance from which a cell is affected by a measurement in another cell, and σmax is the238 value of σat the farthest affected cell.239 Table 3: Measurement parameters σoσmax tm(s) RD(cells) Ground Vehicle 0.05 3 1 4 Moving Ground Vehicle in march 1 5 0.5 4 Aerial Vehicle 0.05 3 1 4 Moving Aerial Vehicle 1.5 6.5 0.5 4 Pyrheliometer 0 3 0.3 2 The algorithm is run every 60 s (ta) and the weights used are λ1= 0.2, λ2= 0.7 and λ3= 0.1.240 4.4. Wind and clouds241 For the case study, wind velocity has been introduced as a vectorial field extracted from a242 numerical model, as stated in Section 2. In particular, the field is defined for a square area243 encompassing the plant and its surrounding area with different values at different heights. The244 mean value of this field is given by the vector h0.554 0.318 0iTm/s.245 In order to simulate dynamically a shadow field in the power plant, cumulus clouds have been246 randomly simulated above the thermosolar plant field between 500 m and 2000 m, which is the247 altitude where this type of clouds usually appear.248 5. Results249 In this section, the results of applying the algorithm proposed for task generation and spatial250 estimation to the case study are presented.251 A set of 30 minute simulations have been run with 3 different CF inputs chosen to test the252 algorithm (multiple cloud shadows with different intensities). Since the proposed algorithm solves253 the MRTA problem heuristically, simulations has been run multiple times. Also, results have been254 compared with the same estimation method but with random generation of the tasks.255 18 Measures of the pyrheliometers CFR Anemometers H CF WE HE CFE J CF est Measures of the robots Figure 7: The real cloud factor value, CFR, appears on the upper left corner. We can see that a cloud is covering a big area of the field and the expected CF is extracted from the real map through the sensors (here we can see that there is a strong belief of a big cloud shadowing the southwest of the plant). The Hfield shows the areas of the field with greater uncertainty in yellow. Even though there is a strong certainty of the presence of a cloud, there are other places where more clouds could be discovered. In addition, anemometers measure wind direction and intensity, which will be used to process the expected CF field (using the kernel hCF ) and to update field W E. In this case, since wind is coming from the lower left corner, this area has higher priority, which decreases linearly with distance. The HE layer is obtained from correcting Husing kernel hH. By adding the weighed CF E,HF E and W E layers we can obtain J(cells with red crosses represent active tasks). Finally, the current estimation can be seen in the lower right corner. An example of the simulations, extracted from the video that can be checked here, can be seen256 in the following figure: In Fig. 9, the real value of the cloud factor in each cell is represented. The257 information gathered until that moment in the PC grid can be seen seen in the two fields obtained258 directly from it, namely, the expected CF field and the H field. From the information contained259 in these fields, the CF E and HE layers are obtained. Likewise, the W E layer is obtained from260 the wind direction and intensity. Then, using the previous layers, Jis obtained. Besides, the261 estimation for the time instant is extracted from CF by means of (5). These active tasks and the262 locations of the vehicles in the plant can be seen in Fig. 8.263 Considering the heuristic nature of the algorithm proposed for solving the MRTA step, the264 same simulations have been run again for the same and different CF inputs. The complete set of265 simulations can be consulted here.266 In case a camera is available as an information source to detect cloud shadows, the algorithm267 can improve its performance. This information provides an extra layer that assigns 1 to shadowed268 cells and 0 to cloudless cells. This way, cloudy areas receive higher priority. The results can be269 19 0 200 400 600 800 1000 0 100 200 300 400 500 1620 seconds R 1 R 2R 3 R 4 R 5 R 6 R 7 R 8 R 9 R 10 Real CF 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Estimated CF CFest=CFe/(1+e(a1.(H-0.5))) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Difference Between Real and Estimated CF real 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Entropy effect 1 =0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 CF effect 2 =0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Wind Effect 3 =0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 J field 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ErrorPA vs Error0 0 10 20 30 40 50 error of proposed algorithm error0 Batteries (Robots 1 to 10) 0 20 40 60 80 100 Expected CF (CFe) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Entropy (H) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 8: Location of the vehicles and the active tasks (second 1620) verified here.270 For the sake of assessment, the error has been computed as the sum of the absolute difference271 between the estimated and the real cloud factor in every cell during the simulation. Fig. 10272 compares the proposed method with and without cameras to the random tasks generation approach273 and to the case where it is assumed that there are no clouds. Although the error made with the274 proposed approach without cameras can be greater at some points, when there is a cloud it improves275 its performance. Also, the proposed method with cameras outperforms all other methods during all276 the simulation length. Likewise, the random tasks approach can be worse than simply considering277 zeros in all cells.278 On the other hand, in Fig. 11, the proposed method (without cameras) is compared to using279 a single pyrheliometer to estimate the irradiance in the whole plant. Notice that whenever the280 pyrheliometer is shadowed, its error explodes. Likewise, the error using only the pyrheliometer and281 the error considering the complete grid zero are the same except for the cases previously mentioned.282 As can be seen, in most cases, once a cloud is detected, vehicles make a good estimation and283 follow it correctly. However, in some cases, particularly when a shadow is too light or the size of284 the cloud is not big enough, they may lose its track. Also, in other cases, clouds are only detected285 when they are already over the plant and not as they start covering it. Likewise, it may occur that286 the allocation finally performed by the MRTA algorithm was unable to fulfill nor regenerate some287 tasks due to the forgetting factor.288 20 Measures of the pyrheliometers CFR H CF WE HE CFE J CF est Measures of the robots Anemometers Cameras Figure 9: Information processing at second 1620 (CF Input No 1) using cameras. Weighing parameters are λ1= 0.09, λ1= 0.6, λ1= 0.01 and λ4= 0.6. The main difference with the case with no cameras is that, in this case, there is an extra layer that give us information about the places where there can be a shadow. Finally, a relatively good estimation can be performed without cameras. Even when some noise289 is introduced, it can be eliminated using a filter. Also, a heuristic considering zero all measurements290 below a certain threshold has been included. The results of this approach can be verified here.291 6. Conclusions292 In this work, an algorithm that solves both the generation of new tasks and the spatial es-293 timation of the DNI has been developed. This algorithm deals with areas where there is little294 information and with those where there is bigger probability of finding shadows according to the295 accumulated knowledge and considering the effect of the wind. The proposed framework is mod-296 ular an can also include additional information sources as cameras capable of detecting shadows297 due to clouds. Likewise, note that this MSN is not designed to be operating at all times, but only298 during cloudy periods. It is in these moments when the control system can make the most from299 the information provided by the proposed system.300 As future development, parametric continuous probability distributions will be considered for301 sensors and for the field probability. Likewise, taking into account another measurements sources302 as the temperature sensors located in the collectors, will be considered. Another future line is303 performing nowcasting using the information gathered and processed by our algorithm. This304 21 0 200 400 600 800 1000 1200 1400 1600 1800 Time (seconds) 0 5 10 15 20 25 30 35 40 45 50 error considering zero in all map error using proposed method without cameras error with random tasks error using proposed method with cameras Figure 10: Comparison of errors. nowcast will not only be useful for controlling the thermosolar power plant but will also be able to305 refine the algorithm proposed in this work, particularly the task generation.306 Acknowledgment307 This project has received funding from the European Research Council (ERC) project OCON-308 TSOLAR (grant agreement No 789051) under the European Union Horizon 2020 Research and309 Innovation Programme.310 References311 M.312 Robots in Agriculture: State of Art and Practical Experiences, author=Rold´an, Juan Jes´us and del Cerro, Jaime and313 Garz´on-Ramos, David and Garcia-Aunon, Pablo and Garz´on, Mario and de Le´on, Jorge and Barrientos, Antonio,314 journal=Service Robots, year=2018, publisher=InTech.315 E.316 Abengoa. 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