Tag Archives: Computer-Aided Engineering

Virtual Solar Grid adds Crescent Dunes Solar Tower

The Crescent Dues Solar Tower as modeled in Energy3D
A light field visualization in Energy3D
A top view
The Crescent Dunes Solar Power Tower is a 110 MW utility-scale concentrated solar power (CSP) plant with 1.1 GWh of molten salt energy storage, located about 190 miles northwest of Las Vegas in the United States (watch a video about it). The plant includes a whopping number of 10,347 large heliostats that collect and focus sunlight onto a central receiver at the top of a 195-meter tall tower to heat 32,000 tons of molten salt. The molten salt circulates from the tower to some storage tanks, where it is then used to produce steam and generate electricity. Excess thermal energy is stored in the molten salt and can be used to generate power for up to ten hours, providing electricity in the evening or during cloudy hours. Unlike other CSP plants, Crescent Dunes' advanced storage technology eliminates the need for any backup fossil fuels to melt the salt and jumpstart the plant in the morning. Each heliostat is made up of 35 6×6 feet (1.8 m) mirror facets, adding up to a total aperture of 115.7 square meters. The total solar field aperture sums to an area of 1,196,778 square meters, or more than one square kilometer, in a land area of 1,670 acres (6.8 square kilometers). That is, the plant is capable of potentially collecting one seventh of all the solar energy that shines onto the field. Costing about $1 billion to construct, it was commissioned in September 2015.

A close-up view of accurate modeling of heliostat tracking
Since its inception in January 2018, our Virtual Solar Grid has included the Energy3D models of nearly all the existing large CSP power plants in the world. That covers more than 80 large CSP plants capable of generating more than 11 TWh per year. The ultimate goal of the Virtual Solar Grid is to mirror every solar energy system in the world in the computing cloud through crowdsourcing involving a large number of students interested in engineering, creating an unprecedentedly detailed computational model for learning how to design a reliable and resilient power grid based completely on renewable energy (solar energy in this phase). The modeling of the Crescent Dunes plant has put our Energy3D software to a stress test. Can it handle such a complex project with so many heliostats in such a large field?
A side view

Near the base of the tower
Over the shoulder of the tower
The solar field
This became my President's Day project. To make this happen, I had to first increase the resolution of Google Maps images supported in Energy3D. A free developer account of Google Maps can only get images of 640 × 640 pixels. When you are looking at an area that is as big as a few square kilometers, that resolution gets you very blurry images. To fetch high-resolution images from Google without paying them, I had to basically make Energy3D download many more images and then knit them together to create a large image that forms an Earth canvas in Energy3D (hence you see a lot of Google logos and copyrights in the ground image that I could not get rid of from each patch). Once I had the Earth canvas, I then drew heliostats on top of it (that is, one by one for more than 10,000 times!) and compared their orientations and shadows rendered by Energy3D with those shown in the Google Maps images. Now, the problem is that Google doesn't tell you when the satellite image was taken. But based on the shadows of the tower and other structures, I could easily figure out an approximate time and date. I then set that time and date in Energy3D and confirmed that the shadow of the tower in the Energy3D model overlaps with that in the satellite image. After this calibration, every single virtual heliostat that I copied and pasted then automatically aligned with those in the satellite image (as long as the original copy specifies the tower that it points to), visually testifying that the tracking algorithm for the virtual heliostats in Energy3D is just as good as the one used by the computers that control the motions of the real-world heliostats. Matching the computer model with the satellite image is essential as the procedure ensures the accuracy of our numerical simulation.

The solar field
After making numerous other improvements for Energy3D, the latest version (V7.8.4) was finally capable of modeling this colossal power plant. This includes the capability of being able to divide the whole project into nine smaller projects and then allow Energy3D to stitch the smaller 3D models together to create the full model using the Import Tool. This divide-and-conquer method makes the user interface a lot faster as neither you nor Energy3D need to deal with 9,000 existing heliostats while you are adding the last 1,000. The predicted annual output of the plant by Energy3D is 462 GWh, as opposed to the official projection of 500 GWh, assuming 90% of mirror reflectance and 25% of thermal-to-electric conversion.

One thing I had to do, though, was to double the memory requirement for the software from the default 256 MB to 512 MB for the Windows version (the Mac version is fine), which would make the software fail on really old computers that have only 256 MB of total memory (but I don't think such old computers would still work properly today anyways). The implication of this change is that, if you are a Windows user and have installed Energy3D before, you will need to re-install it using the latest installer from our website in order to take advantage of this update. If you are not sure, there is a way to know how much memory your Energy3D is allocated by checking the System Information and Preferences under the File Menu. If that number is about 250 MB, then you have to re-install the software -- if you really want to see the spectacular Crescent Dunes model in Energy3D without crashing it.

With basically only the three Ivanpah Solar Towers left to be modeled and uploaded, the Virtual Solar Grid has nearly incorporated all the operational solar thermal power plants in the world. We will continue to add new CSP plants as they come online and show up in Google Maps. In our next phase, we will move to add more photovoltaic (PV) solar power plants to the Virtual Solar Grid. At this point, the proportion of the modeled capacity from PV stands at only 8% in the Virtual Solar Grid, compared with 92% from CSP. Adding PV power plants will really require crowdsourcing as there are many more PV projects in the world -- there are potentially millions of small rooftop systems in existence. On a separate avenue, the National Renewable Energy Laboratory (NREL) has estimated that, if we add solar panels to every square feet of usable roof area in the U.S., we could meet 40% of our total electricity need. Is their statement realistic? Perhaps only time can tell, but by adding more and more virtual solar power systems to the Virtual Solar Grid, we might be able to tell sooner.

Virtual Solar Grid comes online

Fig. 1: Modeled output of the Virtual Solar Grid
Fig. 2: A residential rooftop PV system.
If you care about finding renewable energy solutions to environmental problems, you probably would like to join an international community of Energy3D users to model existing or design new solar power systems in the real world and contribute them to the Virtual Solar Grid — a hypothetical power grid that I am developing from scratch to model and simulate interconnected solar energy systems and storage. My ultimate goal is to crowdsource an unprecedented fine-grained, time-dependent, and multi-scale computational model for anyone, believer or skeptic of renewables, to study how much of humanity's energy need can be met by solar power generation on the global scale — independent of any authority and in the spirit of citizen science. I have blogged about this ambitious plan before and I am finally pleased to announce that an alpha version of the Virtual Solar Grid has come online, of course, with a very humble beginning.

Fig. 3: The Micky Mouse solar farm in Orlando, FL.
Fig. 4: NOOR-1 parabolic troughs in Morocco.
As of the end of January, 2018, the Virtual Solar Grid has included 3D models of only a bit more than 100 solar energy systems, ranging from small rooftop photovoltaic solar panel arrays (10 kW) to large utility-scale concentrated solar power plants (100 MW) in multiple continents. At present, the Virtual Solar Grid has a lot of small systems in Massachusetts because we are working with many schools in the state.

With this initial capacity, the Virtual Solar Grid is capable of generating roughly 4 TWh per year, approximately 0.02% of all the electricity consumed by the entire world population in 2016 (a little more than 2 PWh). Although 0.02% is too minuscule to count, it nonetheless marks the starting point of our journey towards an important goal of engaging and supporting anyone to explore the solar energy potential of our planet with serious engineering design. In a sense, you can think of this work as inventing a "Power Minecraft" that would entice people to participate in a virtual quest for switching humanity's power supply to 100% renewable energy.

Fig. 5: Khi Solar One solar power tower in South Africa.
Fig. 6: PS 10 and PS 20 in Spain.
The critical infrastructure underlying the Virtual Solar Grid is our free, versatile Energy3D software that allows anyone from a middle school student to a graduate school student to model or design any photovoltaic or concentrated solar power systems, down to the exact location and specs of individual solar panels or heliostats. Performance analysis of solar power systems in Energy3D is based on a growing database of solar panel brand models and weather data sets for nearly 700 regions in every habitable continent. To construct a grid, micro or global, an Energy3D model can be geotagged — the geolocation is automatically set when you import a Google Maps image into an Energy3D model. Such a virtual model, when uploaded to the Virtual Solar Grid, will be deployed to a Google Maps application that shows exactly where it is in the world and how much electricity it produces at a given hour on a given day under average weather conditions. This information will be used to investigate how solar power and other renewables, with thermal and electric storage, can be used to provide base loads and meet peak demands for a power grid of an arbitrary size, so to speak.

Finally, it is important to note that the Virtual Solar Grid project is generously funded by the U.S. National Science Foundation through grant number #1721054. Their continuous support of my work is deeply appreciated.

General Motors funds engineering education based on Energy3D

Designing a parking lot solar canopy at Detroit Airport
General Motors (GM), along with other RE100 companies, has committed to powering its worldwide factories and offices with 100% renewable energy by 2050. Last month, the company furthered its commitment by giving the Engineering Computation Team at the Concord Consortium a $200,000 grant to promote engineering education using renewable energy as a learning context and artificial intelligence as a teaching assistant.

Modeling GM's rooftop solar arrays in Baltimore, MD
Modeling GM's solar arrays in Warren, MI
The project will use our signature Energy3D software, which is a one-stop-shop CAD tool for designing and simulating all kinds of solar power systems including photovoltaic (PV) and concentrated solar power (CSP), both of which have reached a very competitive cost of merely 5¢ per kWh or below in the world market. A unique feature of Energy3D is its ability to collect and analyze "atomically" fine-grained process data while users are designing with it. This capability makes it possible for us to develop machine learning algorithms to understand users' design behaviors, based on which we can develop intelligent agents to help users design better products and even unleash their creativity.

The generous grant from GM will allow us to bring this incredible engineering learning tool and the curriculum materials it supports to more science teachers across New England. It will also help extend our fruitful collaboration with the Virtual High School (VHS) to convert our Solarize Your World curriculum into an online course for sustainable engineering. VHS currently offers more than 200 titles to over 600 member schools. Through their large network, we hope to inspire and support more students and teachers to join the crucial mission that GM and other RE100 companies are already undertaking.

By supporting today's students to learn critical engineering design skills needed to meet the energy and environmental challenges, GM is setting an example of preparing tomorrow's workforce to realize its renewable energy vision.

High Frequency Electronics and Thermtest feature Energy2D

Credit: High Frequency Electronics
High Frequency Electronics is a magazine for engineers. In the cover article titled "Substrate Selection Can Simplify Thermal Management" in its November 2017 issue, author John Ranieri included our Energy2D software as one of the modeling tools recommended to the reader, alongside with mainstream commercial products from industry leaders such as Mentor Graphics and ANSYS. The software is also featured by Thermtest, a UK-based company that focuses on thermophysical instruments. Thermtest supplements the software with a database of standard materials, making it easier for engineers to use.

An Energy2D model of a heat source and a heat sink
According to the article, "heat haunts many RF/microwave and power electronics circuits and can limit performance and reliability. The heat generated by a circuit is a function of many factors, including input power, active device efficiencies, and losses through passive devices and transmission lines. It is often not practical to disperse heat from a circuit by convection fan-driven cooling, and heat must be removed from sensitive components and devices, by creating a thermal path to a metal enclosure or heat sink with good thermal conductivity." As a thermal simulation tool, Energy2D can certainly be very useful in helping engineers conceptualize and design such thermal paths.

More importantly, Energy2D can make your engineering experience as fun as playing a sandbox game! As one of our users recently wrote, "I am working as consulting engineer and we often have to make quick estimations where a steady-state node model is too simplified and setting up a complex FEM model is overkill. Energy2D is a very handy tool for something [like] that and I like the click'n'play sandbox feeling in combination with the physical correctness. I never thought FEM could be that fun."

Energy3D allows users to select brand name solar panels

Fig. 1: 20 brand name solar panels in Energy3D
Fig. 2: The daily outputs of 20 types of solar panels
Previous versions of Energy3D were based on a generic model of solar panel, which users can set its properties such as solar cell type, peak efficiency, panel dimension, color, nominal operating cell temperature, temperature coefficient of power, and so on. While it is essential for users to be able to adjust these parameters and learn what they represent and how they affect the output, it is sometimes inconvenient for a designer to manually set the properties of a solar panel to those of a brand name.

Fig. 3: The Micky Mouse solar farm
From Version 7.4.4, I started to add support of brand name solar panels to Energy3D. Twenty brand names were initially added to this version (Figure 1). These models are: ASP-400M (Advanced Solar Photonics), CS6X-330M-FG (Canadian Solar), CS6X-330P-FG (Canadian Solar), FS-4122-3 (First Solar), HiS-M280MI (Hyundai), HiS-S360RI (Hyundai), JAM6(K)-60-300/PR (JA Solar), JKM300M-60 (Jinko), LG300N1C-B3 (LG), LG350Q1K-A5 (LG), PV-UJ235GA6 (Mitsubishi), Q.PRO-G4 265 (Q-cells), SPR-E20-435-COM (SunPower), SPR-P17-350-COM (SunPower), SPR-X21-335-BLK (SunPower), SPR-X21-345 (SunPower), TSM-325PEG14(II) (Trina Solar), TSM-365DD14A(II) (Trina Solar), VBHN330SA16 (Panasonic), and YL305P-35b (Yingli). Figure 2 shows a comparison of their daily outputs in Boston on June 22 when they are laid flat (i.e., with zero tilt angle). Not surprisingly, a smaller solar panel with a lower cell efficiency produces less electricity.

Note that these models are relatively new. There are hundreds of older and other types of solar panels that will take a long time to add. If your type is not currently supported, you can always fall back to defining it using the "Custom" option, which is the default model for a solar panel.

Adding these brand names helped me figure out that the solar panels deployed in the Micky Mouse Solar Farm in Orlando (Figure 3) are probably from First Solar -- only they make solar panels of such a relatively small size (1200 mm × 600 mm).

Deciphering a solar array surprise with Energy3D

Fig. 1: An Energy3D model of the SAS solar farm
Fig. 2: Daily production data (Credit: Xan Gregg)
SAS, a software company based in Cary, NC, is powered by a solar farm consisting of solar panel arrays driven by horizontal single-axis trackers (HSAT) with the axis fixed in the north-south direction and the panels rotating from east to west to follow the sun during the day. Figure 1 shows an Energy3D model of the solar farm. Xan Gregg, JMP Director of Research and Development at SAS, posted some production data from the solar farm that seem so counter-intuitive that he called it a "solar array surprise" (which happens to also acronym to SAS, by the way).

The data are surprising because they show that the outputs of solar panels driven by HSAT actually dip a bit at noon when the intensity of solar radiation reaches the highest of the day, as shown in Figure 2. The dip is much more pronounced in the winter than in the summer, according to Mr. Gregg (he only posted the data for April, though, which shows a mostly flat top with a small dip in the production curve).

Fig. 3: Energy3D results for four seasons.
Anyone can easily confirm this effect with an Energy3D simulation. Figure 3 shows the results predicted by Energy3D for 1/22, 4/22, 7/22, and 10/22, which reveal a small dip in April, significant dips in January and October, and no dip at all in July. How do we make sense of these results?

Fig. 4: Change of incident sunbeam angle on 1/22 (HSAT).
One of the most important factors that affect the output of solar panels, regardless of whether or not they turn to follow the sun, is the angle of incidence of sunlight (the angle between the direction of the incident solar rays and the normal vector of the solar panel surface). The smaller this angle is, the more energy the solar panel receives (if everything else is the same). If we track the change of the angle of incidence over time for a solar panel rotated by HSAT on January 22, we can see that the angle is actually the smallest in early morning and gradually increases to the maximum at noon (Figure 4). This is opposite to the behavior of the change of the angle of incidence on a horizontally-fixed solar panel, which shows that the angle is the largest in early morning and gradually decreases to the minimum at noon (Figure 5). The behavior shown in Figure 5 is exactly the reason why we feel the solar radiation is the most intense at noon.

Fig. 5: Change of incident sunbeam angle on 1/22 (fixed)
If the incident angle of sunlight is the smallest at 7 am in the morning of January 22, as shown in Figure 4, why is the output of the solar panels at 7 am less than that at 9 am, as shown in Figure 3? This has to do with something called air mass, a convenient term used in solar engineering to represent the distance that sunlight has to travel through the Earth's atmosphere before it reaches a solar panel as a ratio relative to the distance when the sun is exactly vertically upwards (i.e. at the zenith). The larger the air mass is, the longer the distance sunlight has to travel and the more it is absorbed or scattered by air molecules. The air mass coefficient is approximately inversely proportional to the cosine of the zenith angle, meaning that it is largest when the sun just rises from the horizon and the smallest when the sun is at the zenith. Because of the effect of air mass, the energy received by a solar panel will not be the highest at dawn. The exact time of the output peak depends on how the contributions from the incidental angle and the air mass -- among other factors -- are, relatively to one another.

So we can conclude that it is largely the motion of the solar panels driven by HSAT that is responsible for this "surprise." The constraint of the north-south alignment of the solar panel arrays makes it more difficult for them to face the sun, which appears to be shining more from the south at noon in the winter.

If you want to experiment further, you can try to track the changes of the incident angle in different seasons. You should find that the change of angle from morning to noon will not change as much as the day moves to the summer.

This dip effect becomes less and less significant if we move closer and closer to the equator. You can confirm that the effect vanishes in Singapore, which has a latitude of one degree. The lesson learned from this study is that the return of investment in HSAT is better at lower latitudes than at higher latitudes. This is probably why we see solar panel arrays in the north are typically fixed and tilted to face the south.

The analysis in this article should be applicable to parabolic troughs, which follow the sun in a similar way to HSAT.

Canadian researchers use Energy3D to design renewable energy systems for mobile hospitals in Libya

Fig. 1: A H-shaped mobile hospital designed using Energy3D
Prof. Tariq Iqbal and his student Emadeddin Hussein from the Department of Electrical and Computer Engineering at the Memorial University of Newfoundland in Canada published a paper in the Journal of Clean Energy Technologies titled with "Design of Renewable Energy System for a Mobile Hospital in Libya."

The researchers recognized that the United Nations' efforts to provide field hospitals have recently decreased in areas that face a high risk in transportation, lack of power, and lack of security for field officers, such as war-torn countries like Libya and Syria. In those unfortunate parts of the world, lack of aids and health resources have a major effect on people's lives. Their paper proposes a photovoltaics (PV) hybrid system for supplying an electric load of a mobile hospital in an area where there is no grid. Such a hybrid system is believed to be a cost-effective solution to power a mobile hospital capable of providing uninterrupted power to support a doctor and two nurses.

Our Energy3D software was used in their research as a simulation tool to study the heat load and optimize the design solution. Figure 1 shows a H-shaped design from their paper (I guess the H-shape was chosen because it is the initial of the word "hospital").

Fig. 2: Energy3D supports 450 regions from 117 countries.
We highly appreciate the researchers' efforts in finding ways to help people living in remote areas and war zones in the world. We are glad to learn that our software may have helped a bit in providing humanitarian aids to those people. Inspired by their work, we will add more weather data to Energy3D to cover areas in the state of unrest (455 regions from 120 countries are currently supported in Energy3D, as shown in Figure 2). In the future, we will also develop curriculum materials and design challenges to engage students all over the world to join these humanitarian efforts through our global drive and outreach.

Polish researchers independently validated Energy3D with Building Energy Simulation Test (BESTEST)

Fig. 1: BESTEST600 test case
Fig. 2: Comparison of Energy3D results with those of other simulation tools
The Building Energy Simulation Test (BESTEST) is a test developed by the International Energy Agency for evaluating various building energy simulation tools, such as EnergyPlus, BLAST, DOE2, COMFIE, ESP-r, SERIRES, S3PAS, TASE, HOT2000, and TRNSYS. The methodology is based on a combination of empirical validation, analytical verification, and comparative analysis techniques. A method was developed to systematically test whole building energy simulation programs. Geometrically simple cases, such as cases BESTEST600 to 650, are used to test the ability of a subject program to model effects such as thermal mass, direct solar gain windows, shading devices, infiltration, internal heat gain, sunspaces, earth coupling, and setback thermostat control. The BESTEST procedure has been used by most building simulation software developers as part of their standard quality control program. More information about BESTEST can be found at the U.S. Department of Energy's website.

Prof. Dr. Robert Gajewski, Head of Division of Computing in Civil Engineering, Faculty of Civil Engineering, Warsaw University of Technology, and his student Paweł Pieniążek recently used BESTEST600-630 test case (Figure 1) to evaluate the quality of Energy3D's predictions of heating and cooling costs of buildings. By comparing Energy3D's results with those from major building energy simulation tools (Figure 2), they concluded that, "[Energy3D] proved to be an excellent tool for qualitative and quantitative analysis of buildings. Such a program can be an excellent part of a computer supported design environment which takes into account also energy considerations."

Their paper was published here.

Modeling parabolic dish Stirling engines in Energy3D

Fig. 1: A parabolic dish Stirling engine
Fig. 2: The Tooele Army Depot solar project in Utah
A parabolic dish Stirling engine is a concentrated solar power (CSP) generating system that consists of a stand-alone parabolic dish reflector focusing sunlight onto a receiver positioned at the parabolic dish's focal point. The dish tracks the sun along two axes to ensure that it always faces the sun for the maximal input (for photovoltaic solar panels, this type of tracker is typically known as dual-axis azimuth-altitude tracker, or AADAT). The working fluid in the receiver is heated to 250–700 °C and then used by a Stirling engine to generate power. A Stirling engine is a heat engine that operates by cyclic compression and expansion of air or other gas (the working fluid) at different temperatures, such that there is a net conversion of thermal energy to mechanical work. The amazing Stirling engine was invented 201 years ago(!). You can see an infrared view of a Stirling engine at work in a blog article I posted early last year.

Although parabolic dish systems have not been deployed at a large scale -- compared with its parabolic trough cousin and possibly due to the same reason that AADAT is not popular in photovoltaic solar farms because of its higher installation and maintenance costs, they nonetheless provide solar-to-electric efficiency above 30%, higher than any photovoltaic solar panel in the market as of 2017.

In Version 7.2.2 of Energy3D, I have added the modeling capabilities for designing and analyzing parabolic dish engines (Figure 1). Figure 2 shows an Energy3D model of the Tooele Army Depot project in Utah. The solar power plant consists of 429 dishes, each having an aperture area of 35 square meters and outputting 3.5 kW of power.

Fig. 3: All four types of real-world CSP projects modeled in Energy3D
With this new addition, all four types of main CSP technologies -- solar towers, linear Fresnel reflectors, parabolic troughs, and parabolic dishes, have been supported in Energy3D (Figure 3). Together with its advancing ability to model photovoltaic solar power, these new features have made Energy3D one of the most comprehensive and powerful solar design and simulation software tools in the world, delivering my promise made about a year ago to model all major solar power engineering solutions in Energy3D.

An afterthought: We can regard a power tower as a large Fresnel version of a parabolic dish and the compact linear Fresnel reflectors as a large Fresnel version of a parabolic trough. Hence, all four concentrated solar power solutions are based on parabolic reflection, but with different nonimaging optical designs that strike the balance between cost and efficiency.

Analyzing the linear Fresnel reflectors of the Sundt solar power plant in Tucson

Fig. 1: The Sundt solar power plant in Tucson, AZ
Fig. 2: Visualization of incident and reflecting light beams
Tucson Electric Power (TEP) and AREVA Solar constructed a 5 MW compact linear Fresnel reflector (CLFR) solar steam generator at TEP’s H. Wilson Sundt Generating Station -- not far from the famous Pima Air and Space Museum. The land-efficient, cost-effective CLFR technology uses rows of flat mirrors to reflect sunlight onto a linear absorber tube, in which water flows through, mounted above the mirror field. The concentrated sunlight boils the water in the tube, generating high-pressure, superheated steam for the Sundt Generating Station. The Sundt CLFR array is relatively small, so I chose it as an example to demonstrate how Energy3D can be used to design, simulate, and analyze this type of solar power plant. This article will show you how various analytic tools built in Energy3D can be used to understand a design principle and evaluate a design choice.

Fig. 3: Snapshots
One of the "strange" things that I noticed from the Google Maps of the power station (the right image in Figure 1) is that the absorber tube stretches out a bit at the northern edge of the reflector assemblies, whereas it doesn't at the southern edge. The reason that the absorber tube was designed in such a way becomes evident when we turn on the light beam visualization in Energy3D (Figure 2). As the sun rays tend to come from the south in the northern hemisphere, the focal point on the absorber tube shifts towards the north. During most days of the year, the shift decreases when the sun rises from the east to the zenith position at noon and increases when the sun lowers as it sets to the west. This shift would have resulted in what I call the edge losses if the absorber tube had not extended to the north to allow for the capture of some of the light energy bounced off the reflectors near the northern edge. This biased shift becomes less necessary for sites closer to the equator.

Energy3D has a way to "run the sun" for the selected day, creating a nice animation that shows exactly how the reflectors turn to bend the sun rays to the absorber pipe above them. Figure 3 shows five snapshots of the reflector array at 6am, 9am, 12pm, 3pm, and 6pm, respectively, on June 22 (the longest day of the year).

As we run the radiation simulation, the shadowing and blocking losses of the reflectors can be vividly visualized with the heat map (Figure 4). Unlike the heat maps for photovoltaic solar panels that show all the solar energy that hits them, the heat maps for reflectors show only the reflected portion (you can choose to show all the incident energy as well, but that is not the default).

There are several design parameters you can explore with Energy3D, such as the inter-row spacing between adjacent rows of reflectors. One of the key questions for CLFR design is: At what height should the absorber tube be installed? We can imagine that a taller absorber is more favorable as it reduces shadowing and blocking losses. The problem, however, is that, the taller the absorber is, the more it costs to build and maintain. It is probably also not very safe if it stands too tall without sufficient reinforcements. So let's do a simulation to get in the ballpark. Figure 5 shows the relationship between the daily output and the absorber height. As you can see, at six meters tall, the performance of the CLFR array is severely limited. As the absorber is elevated, the output increases but the relative gain decreases. Based on the graph, I would probably choose a value around 24 meters if I were the designer.
Fig. 4: Heat map visualization

An interesting pattern to notice from Figure 5 is a plateau (even a slight dip) around noon in the case of 6, 12, and 18 meters, as opposed to the cases of 24 and 30 meters in which the output clearly peaks at noon. The disappearance of the plateau or dip in the middle of the output curve indicates that the output of the array is probably approaching the limit.

Fig. 5: Daily output vs. absorber height
If the height of the absorber is constrained, another way to boost the output is to increase the inter-row distance gradually as the row moves away from the absorber position. But this will require more land. Engineers are always confronted with this kind of trade-offs. Exactly which solution is the optimal depends on comprehensive analysis of the specific case. This level of analysis used to be a professional's job, but with Energy3D, anyone can do it now.