Tag Archives: Solar energy

Automatic remeshing in Energy3D for solar analysis

A headache in the practice of simulation-based engineering or computer-aided engineering is the incompatibility of the meshes used to create and render structures (let's call them the drawing meshes) and the meshes needed to simulate and analyze certain functions (let's call them the analysis meshes). This incompatibility stems deeply from the fundamental differences in computer graphics for visual rendering and computer simulation for physics modeling.

When importing a model from a CAD tool into a simulation tool, engineering analysts often have to recreate new analysis meshes for their computation, which requires fine-grained discretization such is in the case of finite element analysis and other methods. It becomes a nightmare when the conversion from the drawing meshes to the analysis meshes can only be done manually. Even if only a few drawing meshes need to be taken care by hand while the majority of the meshes can be converted automatically, the analyst still would have to check all the meshes to make sure that every mesh is good for simulation. So we really need a tool that can deal with all sorts of scenarios. And this kind of tool is by no mean easy to develop.


Mesh incompatibility was (and may remain for a long time) a problem for Energy3D when it imports structure models created by other tools such as SketchUp. For example, in most architectural CAD models, a structural element such as a wall or a roof (or a part of them) is represented by two planar meshes that have exactly opposite normal vectors, representing the interior and exterior surfaces, respectively. These two meshes have identical coordinates for their vertices, though the orders of their definition are different (one goes clockwise and the other anticlockwise in order for their normal vectors to be exactly opposite). Whatever they represent has therefore no thickness, but with the two faces, we can apply two different textures to them so that the viewer can tell if they are looking at its interior or exterior surface.


While this sounds good to people who use such models in 3D games, it spells troubles to Energy3D. The first problem is that it increases the number of vertices that Energy3D has to load and, therefore, the memory footprint of such models. In a physics simulation, a structural element without thickness is meaningless. If we don't really need the two faces in most cases (we do in some other cases, but I will skip that line of discussion in the article), why bother to import them in the first place? Despite spending days on researching on the Internet and checking the Collada specification, I couldn't figure out how to force SketchUp to export only the exterior meshes (SketchUp's Colloda export function does provide the option of exporting two-sided faces or not, but it sometime exports only the interior sides for some meshes, mixed with exterior sides for others). So it occurred to me that I had to deal with them in the Energy3D code.

If we don't treat them and use the meshes as they are, we then have the second problem: which mesh should we pick to be the side that receives solar radiation? While it is self-evident which mesh of the two identical ones faces outside when we look at the 3D model after it is rendered on the computer screen, we absolutely have no way to tell from their coordinates alone in our code. Somehow, we have to invent an algorithm that simulates how people discern it when they look at the 3D view of the model on a computer screen.

Picking and choosing the right meshes, of course, is crucial to the correctness of the simulation results. In order to test the new algorithms in Energy3D, I selected the lower Manhattan island and the US Capitol Building as two test cases. The results of the lower Manhattan island have been reported in an earlier article. But the Capitol Building has turned out to be a harder case as -- with over 15,000 meshes -- it is geometrically more complicated and it has so many details that really put our code to test. After more than a week of my work on solving a myriad of problems, it seems that Energy3D has passed the test (or has it?). The screenshots of the solar irradiance heat maps of the Capitol Building from different angles show that severe anomalies are practically non-existent across the heat maps.


The heat maps occasionally suffer from a flickering effect called "Z-fighting" when two planar surfaces are visually close, especially when being looked at from a distance sufficiently far away. For the Z-fighting between identical meshes, this can be mitigated by increasing the offset of their distance. But, as this doesn't affect the simulation result, it is less a concern for the time being.

Automatic remeshing for solar analysis may also need to include automatic repair of models that contain errors. For example, some models may contain surfaces that have only one mesh with the normal vector pointing inward (this could happen if the original designer accidentally used the "Reverse Faces" feature in SketchUp without realizing that the normal vectors would be flipped). This kind of mesh is tolerated in SketchUp because it does not affect rendering. But they cannot be tolerated in Energy3D because such a single-face mesh with a north-pointing normal vector, which appears to the viewer as south-facing, will show little to zero solar radiation when the sun shines on it. Luckily, due to the visualization in Energy3D, we can quickly spot those incorrect surfaces and fix them by reversing their faces manually. But we will need to find a way to automate this process (not easy, but not impossible).

Solar analysis of metropolitan areas using Energy3D

Fig. 1: Sunshine at the lower Manhattan island
Energy3D can be used to analyze the solar radiation on houses, buildings, and solar power plants to help engineers design strategies for exploiting useful solar energy or mitigating excessive solar heating. This blog post shows that Energy3D may also be used to analyze the solar radiation in large urban areas (e.g., to study the effect of urban heat islands).

Fig. 2: Solar irradiance heat map of Manhattan on 4/25
To demonstrate this application, I chose a 3D model of a section of the lower Manhattan island as a test. The 3D model was downloaded from SketchUp's 3D Warehouse. It was supposedly created after the lower Manhattan island in 2008. I didn't bother to check for accuracy as this was supposed to be a test of Energy3D. Figure 1 shows the model of the Manhattan area.

Fig. 3: More solar irradiance heat maps.
The model has more than 8,000 meshes of various sizes (a mesh is a polygon area for computational analysis and graphical rendering in Energy3D). The entire area is so big that even a low-resolution daily simulation took more than five hours to complete on my Surface Book computer. Figures 2 and 3 show the rendering of the solar irradiance heat map on top of the 3D model after the computation completes.

Our next step is to figure out how to optimize our simulation engine to speed up the calculations. The latest version of Energy3D already includes some optimizations that allow faster re-rendering of the solar irradiance heat map by re-generating the texture images without re-calculating the solar irradiance distribution.

Importing and analyzing models created by other CAD software in Energy3D: Part 2


Fig.1: The Gherkin (London, UK)
In Part I, I showed that Energy3D can import COLLADA models and perform some analyses. This part shows that Energy3D (Version 6.3.5 or higher) can conduct full-scale solar radiation analysis for imported models. This capability officially makes Energy3D a useful daylight and solar simulation tool for sustainable building design and analysis. Its ability to empower anyone to analyze virtually any 3D structure with an intuitive, easy-to-use interface and speedy simulation engines opens many opportunities to engage high school and college students (or even middle school students) in learning science and engineering through solving authentic, interesting real-world problems.
Fig. 2: Beverly Hills Tower (Qatar)

There is an ocean of 3D models of buildings, bridges, and other structures on the Internet (notably from SketchUp's 3D Warehouse, which provides thousands of free 3D models that can be exported to the COLLADA format). These models can be imported into Energy3D for analyses, which greatly enhances Energy3D's applicability in engineering education and practice.

Fig. 3: Solar analysis of various houses
The images in this post show examples of different types of buildings, including 30 St Mary Axe (the Gherkin) in London, UK (Figure 1) and the Beverly Hills Tower in Qatar (Figure 2). Figure 3 shows the analyses of a number of single-family houses. All the solar potential heat maps were calculated and generated based on the total solar radiation that each unit area on the building surfaces receive during the selected day (June 22).

These examples should give you some ideas about what the current version of Energy3D is already capable of doing in terms of solar energy analysis to support, for example, the design of rooftop solar systems and building solar facades.

In the months to come, I will continue to enhance this analytic capacity to provide even more powerful simulation and visualization tools. Optimization, which will automatically identify the boundary meshes (meshes that are on the building envelope), is currently on the way to increase the simulation speed dramatically.

Importing and analyzing models created by other CAD software in Energy3D: Part 1

Fig. 1: Solarize a COLLADA model in Energy3D
Fig.2: A house imported from SketchUp's 3D Warehouse
Energy3D is a relatively simple CAD tool that specializes in building simulation and solar simulation. Its current support for architectural design is fine, but it has limitations. It is never our intent to reinvent the wheel and come up with yet another CAD tool for architecture design. Our primary interest is in physics modeling, artificial intelligence, and computational design. Many users have asked if we can import models created in other CAD software such as SketchUp and then analyze them in Energy3D.

Fig. 3: A house imported from SketchUp's 3D Warehouse
I started this work yesterday and completed the first step today. Energy3D can now import any COLLADA models (*.dae files) on top of a foundation. The first step was the inclusion of the mesh polygons in the calculation of solar radiation. The polygons should be able to cast shadow on any object existing in an Energy3D model. This means that, if you have a 3D model of a neighboring building to the target building, you can import it into Energy3D so that it can be taken into consideration when you design solar solutions for your target. Once you import a structure, you can always translate and rotate it in any way you want by dragging its foundation, like any existing class of object in Energy3D.

Fig. 4: A house at night in Energy3D
Due to some math difficulties, I haven't figured out how to generate a solar radiation heat map overlaid onto the external surfaces of an imported structure that are exposed to the sun. This is going to be a compute-intensive task, I think. But there is a shortcut -- we can add Energy3D's solar panels to the roof of an imported building (Figure 1). In this way, we only have to calculate for these solar panels and all the analytic capabilities of Energy3D apply to them. And we can get pretty good results pretty quickly.

Fig. 5: A 3D tree imported from SketchUp's 3D Warehouse
Figures 2-4 show more examples of how houses designed with SketchUp look like in Energy3D after they are imported. This interoperability makes it possible for architects to export their work to Energy3D to take advantage of its capabilities of energy performance analysis.

Being able to import any structure into Energy3D also allows us to use more accurate models for landscapes. For instance, we can use a real 3D tree model that has detailed leaves and limbs, instead of a rough approximation (Figure 5). Of course, using a more realistic 3D model of a tree that has tens of thousands of polygons slows down the graphic rendering and simulation analysis. But if you can afford to wait for the simulation to complete, Energy3D will eventually get the results for you.

Accelerating solar farm design in Energy3D with a new model of solar panel racks

Fig. 1: A solar farm of 5,672 solar panels on 8/16 in Boston
The solar simulation in Energy3D is based on discretizing a solar panel, a reflector, a solar water heater, a window, or any other surface into many small cells (mesh), calculating the solar radiation to the centers of the cells, and then summing the results up to obtain the total energy output. For example, a photovoltaic solar panel can be divided into 6x10 cells (this is also because many residential versions of solar panels are actually designed to have 6x10 solar cells). The simulation runs speedily when we have only a few dozen solar panels such is in the case of rooftop solar systems.

Fig. 2: Simulation of 5,672 solar panels on 8/16 in Boston
Unlike rooftop solar systems, large-scale solar farms typically involve thousands of solar panels (mega utility-scale solar farms may have hundreds of thousands of solar panels). If we use the same discretization method for each panel, the simulation would run very slowly (e.g., the speed drops to 1% when the number of solar panels are 100 times more). This slowdown basically makes Energy3D impractical to use by those who cannot afford to wait such as students in the classroom who need to get the results quickly.

Fig. 3: The result of the accelerated model
Fig. 4: The result of the original model
Luckily, solar panel arrays are often installed on parallel long racks in many solar farms (Figure 1). For such solar panel arrays, a lot of calculations could be spared without compromising the overall accuracy of the simulation too much. This allows us to develop a more efficient model of numeric simulation to do solar radiation calculation and even explore methods that use non-uniform meshes to better account for areas that are more likely to be shaded, such as the lower parts of the solar panel arrays. By implementing this new model, we have succeeded in speeding up the calculation dramatically. For example, the daily solar simulation of a solar farm consisting of more than 5,000 solar panels took about a second on my Surface Book computer (Figure 2 -- in this scene I deliberately added a couple of trees so that you can see the result of shading). With the previous model I would probably have to wait for hours to see the result and the graphics card of my computer would take a very deep breath to render more than 5,000 dynamic textures. This is a huge improvement.

Figures 3 and 4 show a comparison of the simulation results between the new and old models. Quantitatively, the total output of the new model is 93.63 kWh for the selected day of June 22 in Boston, compared with 93.25 kWh from the original model. Qualitatively, the color shading patterns that represent the distribution of solar radiation in the two cases are also similar.

The new rack model supports everything about solar panels. It has a smart user interface that allows the user to draw racks of any size and in any direction -- it automatically trims off any extra length so that you will never see a partial solar panel on a rack. When tracking systems are used with long, linear racks, there is only one way to do it -- horizontal single-axis tracker (HSAT). The new model can handle HSAT with the same degree of speed-up. For other trackers such as the vertical single-axis tracker (VSAT) or the altazimuth dual-axis trackers (AADAT), the speed-up will not be as significant, however, as the inter-rack shading is more dynamically complex and each rack must be treated independently.

Designing solar farms and solar canopies with Energy3D

Fig. 1: Single rack
Many solar facilities use racking systems to hold and move arrays of solar panels. Support of racks is now available in our Energy3D software. This new feature allows users to design many different kinds of solar farm, solar park, and solar canopy, ranging from small scale (a few dozen) to large scale (a few thousand).

Fig. 2: Multiple racks
Mini solar stations often use a single rack to hold an array of solar panels (Figure 1). This may be the best option when we cannot install solar panels on the building's roof. You probably have seen this kind of setup at some nature centers where the buildings are often shadowed by surrounding trees.

If you have more space, you probably can install multiple racks (Figure 2), especially when you are considering using altazimuth dual-axis solar trackers to drive them. This configuration is also seen in some large photovoltaic power stations.

Fig. 3: Rack arrays
Larger solar farms typically use arrays of long racks (Figure 3). Each rack can be driven by a horizontal single-axis tracker. Using taller racks usually requires larger inter-rack spacing, which may be an advantage as it allows maintenance trucks to drive through. In a recent experiment, SunPower experimented with how to grow crops or raise animals in the inter-rack space with their Oasis 3.0 system. So arrays of taller racks may be desirable if you want to combine green energy with green agriculture.

Fig. 4: Solar canopy above a parking lot
If you raise the height of a rack, it becomes a so-called solar canopy that provides shading for human activities like the green canopies of trees do. The most common type of solar canopy converts parking lots into power stations and provides shelters from the sun for cars in the summer (Figure 4).

Designing solar canopies for schools' parking lots may be a great engineering project for students to undertake. This is being integrated into our Solarize Your School Project. In fact, Figure 4  shows a real project in Natick High School in Massachusetts. The hypothetical design has more than 1,500 solar panels (each of them has the size of 0.99 x 1.96 m) and costs over a million dollars.

Modeling Charlottesville High School’s solar project using Energy3D

Schools have plenty of roof space that can be turned into small power plants to provide electricity to students. Many schools have already taken actions. Some teachers even use the subject matter in their teaching. But in most cases, students are not profoundly involved in solarizing their own schools.

Fig. 1: Google Map 3D vs. Energy3D
Sure, students are not professional engineers and adults may not trust them when making serious investments in solar energy. But there is a safe way to let them try: Computer simulation allows students to model and design solar panel arrays for their schools without incurring any cost, risk, or injury.

Fig. 2: 88-panel arrays on CHS's roof.
There have been scores of software programs for professional solar designers. But they usually cost $1,000 per license or annual subscription as their market is really a small niche. In addition to this cost barrier for schools, most of these tools do not necessarily cover education standards or support student learning. Thanks to the National Science Foundation, there is now a powerful free alternative for all students and teachers -- Energy3D. A one-stop shop for solar power design and simulation, Energy3D is an extremely versatile CAD tool that can be used to design rooftop solar solutions for not only average homes but also large buildings (you probably have also seen that it can be used to design utility-scale concentrated solar power stations as well). Importantly, Energy3D provides excellent 3D graphics, rich visualizations, and powerful analytical tools that support scientific inquiry and engineering design at fundamental levels. These features make Energy3D a perfect tool for engaging students and fostering learning.

Fig. 3: Solar irradiance map (June 22)
We are collaborating with Charlottesville High School (CHS) in Virginia to plan for a pilot test of the Solarize Your School project, in which students will learn science and engineering concepts and principles through designing large-scale solar panel arrays that achieve optimal cost effectiveness. To make sure every student has the same building to solarize, I sketched up an Energy3D model of CHS as shown in Figure 1 to provide to students as the starting point. If you want to do this for your own school, you can import a Google Map image of the school using the Geo-Location Menu in Energy3D. After the map image shows up in the view, you can draw directly on top of it to get the basic shape right. While it may not be possible to get the exact heights in Google Map, you can use the elevation data provided by Google Earth to calculate the heights of the walls and roofs.

CHS currently has six arrays of solar panels installed on their roof. Five arrays have 88 panels each and one has 10. The panels are arranged in three rows, with the portrait orientation and a tilt angle of 10 degrees (Figure 2). All the panels are 240W AP-240 PK from Advanced Solar Photonics (ASP). Their solar cell efficiency is 14.82%. Their temperature coefficient of Pmax (a property that measures the decrease of solar output when the temperature rises) is -0.4%/°C. Their size is 1650 x 992 x 50 mm. Each panel has three internal bypass diodes. The arrays use REFUsol string inverters to convert electricity from DC to AC, meaning that these arrays probably have little to no tolerance to shade and should be placed away as far from any tall structure as possible. I couldn't find the efficiency of the string inverters, so I chose 90% as it seems typical. I also didn't know the dust level in the area and the cleaning schedule, so I applied 5% of dust loss throughout the year (although the dust loss tends to be higher in the spring due to pollen). Since they went into operation on March 1, 2012, these panels have generated a total of 605 megawatt hours (MWh) as of September 8, 2016, amounting to an average of annual yield at 135 MWh.

Fig. 4: Prediction vs. reality.
I added these solar panel arrays to the Energy3D model with their parameters set for simulation. Figure 3 shows a heat map visualization of solar irradiance on June 22, indicating the ranges of major shading areas. Figure 4 shows the comparison of the predicted output and the actual output in the past 12 months. As some of the arrays were in maintenance for some time in the past year, I picked the highest-performing array and multiplied its output by five to obtain a number that would fairly represent the total yield in the ideal situation. Also note that as there is currently no weather data for Charlottesville, I picked the nearby Lynchburg, which is about 68 miles southwest of Charlottesville, as the location.

The prediction of the total output by Energy3D is a bit higher than the actual output in the past year (139 MWh vs. 130 MWh). If we compare the predicted result with the four-year average, the difference is less (139 MWh vs. 135 MWh). In terms of monthly trend, it seems Energy3D underestimates the winter outputs and overestimates the summer outputs. While the result may be satisfactory for educational use, we will continue to improve the fidelity of Energy3D simulations.

Designing heliostat layouts of concentrated solar power stations with Energy3D

Fig. 1: PS20 field output heat map (June, 22)
Fig. 2: PS20 field output heat map (December, 22)
Fig. 3: Fermat spiral layout (6/22, Phoenix, AZ)
In an earlier article, I have discussed the concepts and issues (shadowing, blocking, cosine efficiency, etc.) related to the design of heliostat layouts for concentrated solar power (CSP) tower stations. I also showed that these problems can be nicely visualized in Energy3D so that people can immediately see them. Instant visual feedback in design time may be very useful to a designer (in fact, this is known as concurrent analysis in the CAD/CFD community, meaning that the tasks of structure design and function simulation run immediately after each other to shorten the wait time between ideation and analysis). Figures 1 and 2 are the heat map visualizations of PS20, a CSP station in Spain, that instantly suggest the possibility of minor blocking problems for some heliostats in the summer and winter. The heat map on each reflector is based on the reflected portion of the direct solar radiation onto a 8 x 8 grid on the reflector plane. Hence it already includes shadowing loss, blocking loss, and attenuation loss. And you didn't read the image wrong, each heliostat reflector has a whopping area of 120 square meters (12 x 10 meters), dwarfing the vehicle in the image!

This blog post features several new tools that were just added to Energy3D to support the actual design tasks.

Fig. 4: Variations of layouts
The first tool is a field layout wizard that provides basic steps for customizing three different types of layout: circular, rectangular, and spiral. It allows you to select the width and height of the heliostat reflectors as well as a variety of parameters to automatically generate a layout. Of course, you can also easily copy and paste to create linear arrays of heliostats to create rectangular layouts. But the wizard does the job faster. Rectangular layouts can be seen at the Jülich Solar Tower in Germany and the Delingha Solar Tower in China. The latter just went into operation this August.

Note that, in Energy3D, the heliostat field must be built on top of a foundation. The size of the foundation you draw sets the boundary of the heliostat field. As the field layout must be done on a foundation, the layout wizard can only be accessed through the popup menu of a foundation.

The spiral layout that Energy3D supports (Figure 3) is an interesting addition. It currently provides the Fermat spiral, which is the pattern you see from a sunflower head. It is so amazing that solar science seems to always go back to the sunflower. The solar trackers for photovoltaic arrays mimic the motion of sunflowers to follow the sun. The spiral pattern of a sunflower head may hold a key to optimal heliostat layouts (Noone, Torrilhon, and Mitsos, Solar Energy, Vol. 862, pp. 792–803, 2012). This may not be too surprising considering that the sunflower has probably evolved into that particular pattern to ensure that each seed has enough room to grow and fair access to sunlight.

Fig. 5: Superimposed heliostats on top of map images (PS20)
The layout wizard provides a baseline model that you can always modify manually to get what you want (Figure 4). All heliostats can be easily dragged, dropped, or removed.

If you want to model after an existing CSP station, you can use the Geo-Location menu of Energy3D to import a map image of the station and then superimpose 3D heliostats on top of the map image where the images of the actual heliostats are located. Figure 5 shows that an Energy3D model of the PS20 station can be perfectly created using this method. The shadows on the ground cast by the heliostats in the Energy3D model even aligns very well with those captured in the map image (I must confess that I tried to guess the right date and time from the shadow of the tower and the rest just follows).

Visualizing design issues in heliostat layouts of concentrated solar power stations with Energy3D

Fig. 1: Visualizing shadowing loss
As a one-stop-shop for solar solutions, Energy3D supports the design of concentrated solar power (CSP) stations. Although the main competitor of the CSP technology, the photovoltaic (PV) power stations, have become dominant in recent years due to the plummet of PV panel price, CSP has its own advantages and potential, especially in energy storage. According to the US Department of Energy, the levelized cost of electricity (LCOE) for CSP has dropped to 13 cents per kWh in the US in 2015, comparable to the LCOE for PV (12 cents per kWh). In general, it is always better to have options than having none. A combination of PV and CSP stations may be what is good for the world: CSP can complement PV to generate stable outputs and provide electricity at night. As a developer of solar design and simulation software, we are committed to supporting the research, development, and education of all forms of solar technologies.

Numerical simulation plays an important role on designing optimal CSP stations. Concentrated solar power towers are the first type of CSP stations covered by the modeling engine of Energy3D. This blog post shows some progress towards the goal of eventually building a reliable simulation and visualization kernel for CSP tower technology in Energy3D. The progress is related to the study of heliostat layouts (the heat transfer part is yet to be built).

Numerous studies of heliostat layouts have been reported in literature in the past three decades, resulting in a variety of proposals for minimizing the land use and/or maximizing the energy output (see a recent review: Li, Coventry, Bader, Pye, & Lipiński, Optics Express, Vol. 24, No. 14, pp. A985-A1007, 2016). The latest is an interesting biomimetic pattern suggested by Noone, Torrilhon, and Mitsos (Solar Energy, Vol. 862, pp. 792–803, 2012), which resembles the spiral patterns of a sunflower head (each floret is oriented towards the next by the golden angle of 137.5°, forming a Fermat spiral that is probably Mother Nature's trick to ensure that each seed has enough room to grow and fair access to sunlight).

Fig. 2: Visualizing blocking loss
If you haven't worked in the field of solar engineering, you may be wondering why there has been such a quest for optimal layouts of heliostats. At first glance, the problem seems trivial -- well, a tower-based CSP station is just a gigantic solar cooker, isn't it? But things are not always what they seem.

The design of the heliostat layout is in fact a very complicated mathematical problem. We have some acres of land somewhere to begin with. The sun moves in the sky and its trajectory varies from day to day. But that is OK. The heliostats can be programmed to reflect sunlight to the receiver automatically. These all sound good until we realize that the heliostats' large reflectors can cast shadow to one another if they are too close or the sun is low in the sky (Figure 1). Like the case of PV arrays, shadowing causes productivity loss (but luckily, reflectors -- unlike solar panels based on strings of connected solar cells -- do not completely lose power if only a part of it is in the shadow).
Fig. 3: Annual outputs of the heliostats in Fig. 2

Unlike the case of PV arrays, heliostats have an extra problem -- blocking. A heliostat must reflect the light to the receiver at the top of the tower and that path of light can be blocked by its neighbors. Of course, we rarely see the case of complete blocking. But if a portion of the reflector area is denied optical access to the receiver, the heliostat will lose some productivity. Energy3D can visualize this loss on each heliostat reflector. The upper image of Figure 2 shows the insolation to the reflectors whereas the lower one shows the portion of the insolation that actually reaches the receiver (you can see that the reflectors closer to the tower get more insolation). Figure 3 shows a comparison of the outputs of the heliostats over the course of a year. As you can see, the blue parts of the reflectors can never bounce light to the receiver because the heliostats in front of them block the reflection path for the lower parts of those heliostats. The way to mitigate this issue is to gradually increase the spacing between the heliostats when they are farther away from the tower.
Fig. 4: Visualizing cosine efficiency

Another problem with CSP tower technology is the so-called cosine efficiency. As we know, the insolation onto a surface is maximal when the surface directly faces the sun (this is known as the projection effect). In the northern hemisphere, however, the heliostats to the south of the tower (the south field) cannot face the sun directly as they must be positioned at an angle so that the incident sunlight can be reflected to a northern position (where the receiver is located). Figure 4 shows a visualization of the cosine effect and Figure 5 shows the comparison of the annual outputs of the heliostats. Clearly, the cosine efficiency is the lowest in the winter and the highest in the summer.
Fig. 5: Cosine efficiency is lower in the winter

Does the cosine efficiency mean that we should only deploy heliostats in the north field as is shown in Figure 6? This depends on a number of factors. Yes, the cosine efficiency does reduce the output of a heliostat in the south field in the winter (maybe early spring and late fall, too), but a heliostat far away from the tower in the north field also produces less energy. For a utility-scale CSP station that must use thousands of heliostats, the part of the south field close to the tower may not be such a bad place to put heliostats, compared with the part of the north field far away from the tower. This is more so when the site is closer to the equator. If the site is at a higher latitude to the point that it makes more sense to deploy all heliostats in the north field, dividing the site into multiple areas and constructing a tower for each area may be a desirable solution. The downside is that additional towers will increase the constructional cost.
Fig. 6: Semicircular layout in the north field

We now multiply these three problems (shadowing, blocking, and cosine effect) with thousands of heliostats, confine them within an area of a given shape, and want to spend as less money as possible while producing as much electricity as possible. That is the essence of the mathematical challenge that we are facing in CSP field design. With even more functionalities to be added in the future, Energy3D could become a powerful design tool that anyone can use to search for their own solutions.

Choose solar trackers: HSAT, VSAT, or AADAT?

Fig. 1: HSAT and VSAT.
Energy3D now supports three major types of solar trackers: Horizontal single-axis trackers (HSAT), vertical single-axis trackers (VSAT), and altazimuth dual-axis trackers (AADAT). I have blogged about HSAT and AADAT earlier. Figure 1 shows the difference between HSAT and VSAT.

With all these options, which should we choose? The decision is based on the additional output of the solar panels, the space required to operate the system, and, of course, the cost of the tracking system. For instance, AADAT may be more complex as it rotates around two perpendicular axes. Space is always an important constraint and it is even more so for large solar farms considering the issue of inter-panel shading. Fixed arrays and HSAT systems may be more efficient in space usage if the inter-row shading is not significant.
Fig. 2 Energy3D predictions of annual outputs.

Let's first compare the annual output of a single solar panel under different conditions, as shown in Figure 2 and summarized in Table 1, calculated using Energy3D.

Table 1. Comparison of total annual outputs of a solar panel that has a fixed tilt angle equal to its latitude, a solar panel that is rotated by a HSAT, a solar panel that is rotated by a VSAT, and a solar panel that is rotated by an AADAT, at four different locations in the US. The unit is kWh.


Locations
Fixed (tilt=lat.)
HSAT
VSAT
AADAT
Boston, MA
428
520
559
603
Anchorage, AK
258
310
371
380
Miami, FL
507
654
617
711
San Juan, PR
523
694
617
738
 
These results suggest that the AADAT system, not surprisingly, generates the most electricity throughout the year at all four locations, as it always faces the sun. The second best, for low-latitude locations, is the HSAT system and, for high-latitude locations, is the VSAT system. In the case of HSAT, the lower the latitude, the closer the performance of the HSAT approaches that of the AADAT. In the case of VSAT, the higher the latitude, the closer the performance of the VSAT approaches that of the AADAT. This means that, considering the cost factor, HSAT at a very low latitude such as the equator is a better choice than AADAT and VSAT at a very high latitude such as Alaska is a better choice than AADAT.
Fig. 3 Optimal layout through heat map tessellation. 

The above analysis is based on a single, isolated solar panel. For arrays of panels, we must consider the shading area each panel sweeps when it is driven by a tracker. Energy3D's heat map visualization of solar irradiance may be a useful tool for designing optimal layouts for VSAT or AADAT panels that cannot be seamlessly aligned into rows such is in the case of HSAT arrays. From a mathematical point of view, an optimal layout must minimize land use. Hence, it can be imagined as a tessellation of effective shade area of individual panels (Figure 3). This may be something interesting to think about.