# Why is Israel building the world’s tallest solar tower?

 Fig. 1: Something tall in Negev desert (Credit: Inhabitat)
The Ashalim solar project (Figure 1) in the Negev desert of Israel will reportedly power 130,000 homes when it is completed in 2018. This large-scale project boasts the world’s tallest solar tower -- at 250 meters (820 feet), it is regarded by many as a symbol of Israel’s ambition in renewable energy.

Solar thermal power and photovoltaic solar power are two main methods of generating electricity from the sun that are somewhat complementary to each other. Solar tower technology is an implementation of solar thermal power that uses thousands of mirrors to focus sunlight on the top of a tower, producing intense heat that vaporizes water to spin a turbine and generate electricity. The physics principle is the same as a solar cooker that you have probably made back in high school.

Why does the Ashalim solar tower have to be so tall?

Surrounding the tower are approximately 50,000 mirrors that all reflect sun beams to the top of the tower. For this many mirrors to "see" the tower, it has to be tall. This is easy to understand with the following metaphor: If you are speaking to a large, packed crowd in a square, you had better stand high so that the whole audience can see you. If there are children in the audience, you want to stand even higher so that they can see you as well. The adults in this analogy represent the upper parts of mirrors whereas the children the lower parts. If the lower parts cannot reflect sunlight to the tower, the efficiency of the mirrors will be halved.

 Fig. 2: Visualizing the effect of tower height
An alternative solution for the children in the crowd to see the speaker is to have everyone stay further away from the speaker (assuming that they can hear well) -- this is just simple trigonometry. Larger distances among people, however, mean that the square with a fixed area can accommodate less people. In the case of the solar power tower, this means that the use of the land will not be efficient. And land, even in a desert, is precious in countries like Israel. This is why engineers chose to increase the height of tower and ended up constructing the costly tall tower as a trade-off for expensive land.

 Fig. 3: Daily output graphs of towers of different heights
But how tall is tall enough?

 Fig. 4: Energy output vs. tower height
This depends on a lot of things such as the mirror size and field layout. The analysis is complicated and reflects the nature of engineering. With our Energy3D software, however, complicated analyses such as this are made so easy that even high school students can do. Not only does Energy3D provide easy-to-use 3D graphical interfaces never seen in the design of concentrated solar power, but it also provides stunning "eye candy" visualizations that clearly spell out the science and engineering principles in design time. To illustrate my points, I set up a solar power tower, copied and pasted to create an array of mirrors, linked the heliostats with the tower, and copied and pasted again to create another tower and another array of mirrors with identical properties. None of these tasks require complicated scripts or things like that; all they take are just some mouse clicks and typing. Then, I made the height of the second tower twice as tall as the first one and run a simulation. A few seconds later, Energy3D showed me a nice visualization (Figure 2). With only a few more mouse clicks, I generated a graph that compares the daily outputs of towers of different heights (Figure 3) and collected a series of data that shows the relationship between the energy output and the tower height (Figure 4). The graph suggests that the gain from raising the tower slows down after certain height. Engineers will have to decide where to stop by considering other factors, such as cost, stability, etc.

Note that, the results of the solar power tower simulations in the current version of Energy3D, unlike their photovoltaic counterparts, can only be taken qualitatively. We are yet to build a heat transfer model that simulates the thermal storage and discharge accurately. This task is scheduled to be completed in the first half of this year. By that time, you will have a reliable prediction software tool for designing concentrated solar power plants.

# Ten research papers utilizing Energy2D published in the past two years

 Screenshots from recent papers that use Energy2D
 Energy2D simulation of fire
Energy2D is a multiphysics simulation program that was created from scratch and is still under development (though its progress has slowed down significantly because my priority has been given to its Energy3D cousin). The software was originally intended to be a teaching and learning tool for high school students who are interested in studying engineering. Over the past two years, however, we have seen 10 research papers published in various journals and conferences that involved significant applications of Energy2D as a scientific research tool for modeling natural phenomena and engineering systems. The problems that these researchers simulated range from solar energy, industrial processes, geophysics, and building science. The authors come from universities from all over the world, including top-notch institutions in US, Europe, and China.

 Energy2D simulation of thermal bridge
The publication of these papers and very positive user feedback suggest that Energy2D seems to have found itself an interesting niche market. Many scientists and engineers are unable to invest a lot of time and money on its complicated commercial counterparts. But they nonetheless need a handy simulation tool that is much more flexible, intuitive, and capable than formulas in books to deal with realistic geometry -- at least in 2D. This is where Energy2D comes into play.

Reaching this milestone is critically important to the free and open-source Energy2D software, whose future will be reliant on community support. Its modest popularity among scientists is a valid demonstration of the broader impact expected by the National Science Foundation that funded its development. One can only imagine that there are many more users who used the software in their workplace but didn't publish. Now that good words about it have spread, we expect the usage to continue and even accelerate. To better support our users, we have added a community forum recently. We also plan to work with Professor Bob Hanson to port the Java code to JavaScript through his SwingJS translator so that the program can run on more devices.

The list of these papers is as follows:
1. Mahfoud Abderrezek & Mohamed Fathi, Experimental Study of the Dust Effect on Photovoltaic Panels' Energy Yield, Solar Energy, Volume 142, pp 308-320, 2017
2. Dennis de Witte, Marie L. de Klijn-Chevalerias, Roel C.G.M. Loonen, Jan L.M. Hensen, Ulrich Knaack, & Gregor Zimmermann, Convective Concrete: Additive Manufacturing to Facilitate Activation of Thermal Mass, Journal of Facade Design and Engineering, Volume 5, No. 1, 2017
3. Javier G. Monroy & Javier Gonzalez-Jimenez, Gas Classification in Motion: An Experimental Analysis, Sensors and Actuators B: Chemical, Volume 240, pp 1205-1215, 2017
4. Tom Rainforth, Tuan Anh Le, Jan-Willem van de Meent, Michael A. Osborne, & Frank Wood, Bayesian Optimization for Probabilistic Programs, 30th Conference on Neural Information Processing Systems, Barcelona, Spain, 2016
5. E. Rozos, I. Tsoukalas, & C. Makropoulos, Turning Black into Green: Ecosystem Services from Treated Wastewater, 13th IWA Specialized Conference on Small Water and Wastewater Systems, Athens, Greece, 2016
6. W. Taylor Shoulders, Richard Locke, & Romain M. Gaume, Elastic Airtight Container for the Compaction of Air-Sensitive Materials, Review of Scientific Instruments, Volume 87, 063908, 2016
7. Zachary R. Adam, Temperature Oscillations near Natural Nuclear Reactor Cores and the Potential for Prebiotic Oligomer Synthesis, Origins of Life and Evolution of Biospheres, Volume 46, Issue 2, pp 171-187, 2016
8. Jiarui Chen, Shuyu Qin, Xinglong Wu, & Paul K Chu, Morphology and Pattern Control of Diphenylalanine Self-Assembly via Evaporative Dewetting, ACS Nano, Volume 10, No. 1, pp 832-838, 2016
9. Atanas Vasilev, Geothermal Evolution of Gas Hydrate Deposits: Bulgarian Exclusive Economic Zone in the Black Sea, Comptes rendus de l‘Académie bulgare des Sciences, Volume 68, No. 9, pp 1135-1144, 2015
10. Pedro A. Hernández, et al., Magma Emission Rates from Shallow Submarine Eruptions Using Airborne Thermal Imaging, Remote Sensing of Environment, Volume 154, pp 219-225, November 2014

# 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

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.

 Fig. 1 2D view of Concord Consortium building in Energy3D
Solar design depends on accurate geometry. Rooftop solar panel design requires accurate 3D models of buildings, for example the shape of the roof, the height of the building, and the surrounding objects such as trees. Likewise, solar power station design requires accurate information about the field.

 Fig. 2 3D view of Concord Consortium building in Energy3D
The easiest way to obtain these information is through Google Map, from which the dimension of an object can be measured. Although Google Map has not provided elevation data for a point yet, Google Earth does for many towns.

Earlier this year, students who performed solar design with Energy3D in our pilot tests must use Google Earth to retrieve the geometrical data for use in Energy3D design later. Having to master two sophisticated software tools simultaneously in a short time has turned out to be quite a challenge to many students. So an idea came to our mind: Why not just make Google Earth work within Energy3D? (Note: In fact, this is also a common feature among CAD software such as SketchUp.)

 Fig. 3 Solar heat map of Concord Consortium building
It turned out that this integration is fairly simple, because Google has done the hard part of providing an easy-to-use Web API for virtually every platform. So in the latest version of Energy3D (V5.8.2 or higher), users will have an internal Google Map ready to help them with their solar designs.

 Fig. 4 2D view of a solar farm in Concord, MA in Energy3D
Solar designers can specify a target location in Energy3D and then a Google Map image will be downloaded and used to overlay the ground in Energy3D. They can then draw a 3D building on top of this image by tracing the envelope of the building, eliminating the need to set the dimension of each side numerically. Figures 1-3 demonstrate the result of this new feature using the Concord Consortium's office building as an example.

 Fig. 5 3D view of a solar farm in Concord, MA in Energy3D
A remarkable advantage brought by this feature is that it is easy to add model trees on top of the images of surrounding trees. A future version will also allow users to adjust the height and spread of a model tree based on the Google Map image.

Other than assisting designers to acquire site data, the map image also provides a rendering of how a new design may look like in an environment with existing buildings (just pretend for a moment that the building in Figure 2 hadn't existed and were a proposal to build two new houses at the site). Furthermore, with Google Map's elevation API, we will also be able to construct a terrain model of the ground (which is currently flat). Such a terrain model will not only make the energy simulation more accurate by taking all the surrounding objects into account but also make the rendering more realistic by giving the 2D map image a 3D effect (similar to the new 3D view of Google Map).

Based on Energy3D, we have created two solar design challenges for students to make meaningful contributions to the solarization movement. One is to solarize their own houses by designing rooftop solar panels. The other is to solarize their own schools and towns by designing solar farms (Figures 4 and 5). Aligned with the Next Generation Science Standards (NGSS) that require students to think and act like scientists and engineers, our goal is to engage students to practice science and engineering through solving real-world problems. But real-world problems are often complex and difficult (otherwise they are not problems in the real world!). This calls for the development of advanced tools that can empower students to tackle real-world problems. Our Energy3D software provides examples of how technology may knock down the barriers and help students attain the high standards set by the NGSS.

# Modeling horizontal single-axis solar trackers in Energy3D

In the last post, I have blogged about modeling dual-axis solar trackers in Energy3D. To be more precise, the trackers shown in that blog post are altitude-azimuth (Alt/Az), or altazimuth trackers, or AADAT in short. In this post, I will introduce a type of single-axis tracker -- the horizontal single-axis tracker, or HSAT in short.

 Fig. 1 Solar panel arrays rotated by HSATs
Because single-axis trackers do not need to follow the sun exactly, there are many different designs. Most of them differ in the choice of the axis of rotation. If the axis is horizontal to the ground, the tracker is a HSAT. If the axis is vertical to the ground, the tracker is a vertical single-axis tracker, or VSAT in short. All trackers with axes of rotation between horizontal and vertical are considered tilted single-axis trackers, or TSAT in short. None of these single-axis trackers can help the solar panels capture 100% of the solar radiation that reaches the ground. Exactly which design to choose depends on the location of the solar farm, among other consideration such as the cost of the mechanical system.

 Fig. 2 Compare daily outputs of HSAT, AADAT, and fixed in four seasons.
HSAT is the first type of single-axis tracker that has been implemented in Energy3D. HSAT is probably more common than VSAT and TSAT and is probably easier to construct and install. In most cases, the rotation axis of a HSAT aligns with the north-south direction and the solar panels follow the sun in an east-to-west trajectory, as is shown in the YouTube video embedded in this post and in Figure 1.

 Fig. 3 Compare annual outputs of HSAT, AADAT, and fixed.
How much more energy can a HSAT help to generate? Figure 2 shows the comparison of the outputs of a HSAT system, an AADAT system, and an optimally fixed solar panel on March 22, June 22, September 22, and December 22, respectively, in the Boston area. The results suggest that the HSAT system is almost as good as the AADAT system in June but its performance declines in March and September and becomes the worst in December (in which case it can only capture a little more than half of the energy harvested by the AADAT system). Interestingly, also notice that there is a dip at noon in the energy graphs for March, September, and December. Why so? I will leave the question for you to figure out. If you have a hard time imagining this, perhaps the visualizations in Energy3D can help.

 Fig. 4 Compare wide- and narrow-spacing of HSAT arrays
Figure 3 shows the annual result, which suggests that, over the course of a year, the HSAT system -- despite of its relatively unsatisfactory performance in spring, fall, and winter -- still outperforms any fixed solar panel, but it captures about 86% of the energy captured by the AADAT system.

An important factor to consider in solar farm design is the choice of the inter-row spacing to avoid significant energy loss due to shading of adjacent rows in early morning and late afternoon. But you don't want the distance between two rows to be too far as the rows will occupy a large land area that makes no economic sense. With Energy3D, we can easily investigate the change of the energy output with regard to the change of the inter-row spacing. Figure 4 shows the gain from HSAT is greatly reduced when the rows are too close, essentially eliminating the advantages of using solar trackers. Despite of their ability to track the sun, HSATs still require space to achieve the optimal performance.