Tag Archives: Engineering design

A Mickey Mouse-shaped solar farm

Fig. 1: An aerial view of the Mickey Mouse-shaped solar farm
Fig. 2: An Energy3D model of the Mickey Mouse-shaped solar farm
If I didn't tell you that this is an actual solar farm near the Epcot Theme Park in the Disney World in Orlando, Florida, you probably would think this is some kind of school project done by kids. But no, this 22-acre 5 MW project was designed and installed by Duke Energy and it has been powering Disney World's facilities since 2016 (Figure 1 is an image from Disney.com). So this is some kind of serious business and has drawn a lot of media attention. The solar farm is so new that even the latest version of Google Maps in May 2017 still does not show it (it is available through Google Maps API that we are using, though).

By shaping the beloved Mickey Mouse character with tens of thousands of solar panels, Disney World has delivered a strong message to the world that the company is committed to a sustainable future.

Fig. 3: A solar radiation heat map representation (June 22).
But who says that kids should not do this? Perhaps they couldn't do it because of the lack of appropriate support and tool. Not any more. Thanks to the support from the National Science Foundation, our powerful Energy3D software and our Solarize Your World curriculum can probably turn every wild imagination in solar power into virtual reality, particularly for children who may need more inquiry- and design-based activities that connect so deeply to their world and their future. Figure 2 shows a model of the Mickey Mouse-shaped solar farm in Energy3D and Figure 3 shows a heat map representation of the solar radiation onto the solar panel arrays.

Designing ground-mounted solar panel arrays: Part III

Fig. 1: Rows of solar panels on racks in a solar farm
The most common configuration of solar farms is perhaps arrays consisting of rows of solar panel racks such as shown in Figure 1. But have you ever thought about why? Can we challenge this conventional wisdom?

Fig.2: Cover the field with horizontally-placed solar panels
Obviously, some inter-row spacing allows for easier cleaning and maintenance and, perhaps, even integration with agricultural farming (e.g., growing mushrooms that prefer shaded areas). But let's put those benefits aside for now and just consider the energy part of the problem. Let me point out a fact: If we completely cover the entire field with solar panels with zero tilt angle and zero gap (Figure 2), we are guaranteed to capture almost every single photon that strikes the area regardless of time and location. Such a simple-minded "design" will produce the maximal output of any given field at any location and time and there is absolutely no such problem as inter-row shading. So what solar design?
Fig. 3: Comparing two hypothetical fields.

It turns out that, although the simple-minded design can surely generate maximum electricity, each individual solar panel in it does not necessarily generate a maximum amount of electricity over the course of a year, compared with other designs. In other words, it may just use more solar panels to generate more electricity. As engineering design must consider cost effectiveness and even put it as a top priority, an engineer's job is then to look for a better solution that maximizes the production of each solar panel.

Fig. 4: Compare outputs of single panels in two fields (Boston).
A great advantage of Energy3D is that it allows one to experiment with ideas rapidly. So let's create a field with tilted rows of solar panels and leave some gap between them and then use the Group Analysis Tools to compare the daily and annual outputs of individual solar panels in the two hypothetical fields (Figure 3). And let's assume the fields are in Boston.

Fig. 5: Compare outputs of single panels in two fields (Phoenix).
Figure 4 shows that the total annual output of a single solar panel in the field of tilted rows is nearly 20% higher than that of a single solar panel in the field of flat cover in Boston (42° N). In this simulation, the tilt angle was set to be equal to the latitude. This cost effectiveness is one of the main reasons why we choose tilted rows of solar panels in high-latitude areas (aside from the fact that tilted angles allow rain to wash panels more efficiently and snow to slide from them more quickly).

Caveat for low-latitude locations


Fig. 6: Compare outputs of single panels in two fields (Mexico).
Note that this result applies only to high-latitude areas such as Boston. If we are designing solar farms for tropical areas such as Singapore, the story may be completely different. In low-latitude areas, small or even zero tilt angles make sense. Therefore, the design principle may be to cover the field with as many solar panels as possible or to use trackers to increase individual outputs (whichever is more economic depends on the relative prices of solar panels and solar trackers that change all the time). You can experiment with Energy3D to find out at which latitude this principle starts to become dominant. Figure 5 shows that the results in cities with a lower latitude such as Phoenix (33° N) and Mexico City (19° N) in North America. In the case of Phoenix, AZ, the gain from the tilted rows drops to about 10%. In the case of Mexico City, it drops to 5%. So designing a ground-mounted solar array for Mexico may be very different from designing a ground-mounted solar array for Canada.

A complete 3D model of the PS20 solar power plant

According to Wikipedia, the 20 MW PS20 Solar Power Plant in Seville, Spain consists of a solar field of 1,255 heliostats. Each heliostat, with a surface area of 120 square meters(!), automatically tracks the sun on two axes and reflects the solar radiation it receives onto the central receiver, located at the top of a tower that is as tall as 165 meters. The concentrated heat vaporizes water and produces steam that drives a turbine to generate electricity. The Wikipedia page mentions that PS20 uses a thermal storage system, but it is not clear whether it is a molten salt tank or not.

PS20 generates about 48,000 MWh per year, or roughly 132 MWh per day on average without considering seasonal variations.

The full 3D model of the PS20 plant is now available in Energy3D and can be downloaded from http://energy.concord.org/energy3d/designs/ps20-solar-tower.ng3. While it generally costs hundreds of millions of dollars to design and build such a futuristic power plant, it costs absolutely nothing to do so in the virtual space of Energy3D. In a way, Energy3D gives everyone, especially those in developing nations, a powerful tool to explore the solar potential of their regions. Whether you live in a desert or on the coast, near or far away from the equator, in cities or rural areas, you can imagine all sorts of possibilities with it.

I am working on heat transfer, energy conversion, and thermal storage models that can predict the electricity generation accurately. Right now, Energy3D estimates the raw solar radiation input to the receiver on June 22 to be about 656 MWh, considering all the shadowing and blocking losses. If the system efficiency of heat transfer and energy conversion is in the range of 30-50%, then Energy3D's prediction will fall into a reasonable range.

Artificial intelligence research for engineering design

Have you ever thought about what a pity it is when a senior engineer with 40 years of problem-solving experience retires? Have you ever thought about what a loss it is when a senior teacher with 40 years of teaching experience retires? Imagine what we could do for humanity if we find a way to somehow preserve their experience, expertise, and intelligence automatically before these incredible treasures are taken to the graveyard...

Heat map visualizations of different patterns of design task transition
Funded by the National Science Foundation, I have been working on the research and development of artificial intelligence (AI) for engineering design for a number of years and have been developing the Visual Process Analytics for visualizing and analyzing engineering design process data. This exciting intersection among AI (basically everything about how intelligence can be realized), engineering (basically a generative and creative discipline), and cognitive science (basically everything about how humans acquire intelligence) is full of tremendous challenges, but it also creates unprecedented opportunities that constantly entice and enlighten me.

I have recently written a short article to explain my research to the lay people (mostly educators, but the implications are not limited only to education). Check it out at http://energy.concord.org/~xie/papers/aired.pdf

Designing ground-mounted solar panel arrays: Part II

To design a solar panel array, we need to understand the specifications of the type of solar panel that we are going to use (here is an example of the specs of SunPower's X21-series). Although all solar panels provide nominal maximum power outputs (Pmax or Pnom), those numbers specify the DC power outputs under the Standard Test Conditions (STC) or PVUSA Test Conditions (PTC). Those numbers only provide some standardized values for customers' reference and cannot be used to calculate the electricity generation in the real world. Although each brand of solar panel may be designed in different ways and the specs vary, there are a few scientific principles that govern most of them. The calculation of power generation can therefore be drawn upon these fundamental principles. This article covers some of these principles.

The first parameter for solar power calculation is the solar cell efficiency, which defines the percentage of incident sunlight that can be converted into electricity by a cell of the solar panel. This property is usually determined by the semiconductor materials used to make the cell. Monocrystalline silicon-based materials tend to have a higher efficiency than polycrystalline ones. As of 2017, the solar cell efficiency for most solar panels in the market typically ranges from 15% to 25%. The higher the efficiency, the more expensive the solar panel.

Figure 1: All cells in a series (left) and diode bypasses (right)
The solar cell efficiency generally decreases when the temperature increases. To reflect this relationship, solar panels usually specify the Nominal Operating Cell Temperature (NOCT) and the Temperature Coefficient of Pmax. The former describes how high the temperature of the cell rises to under the sun. The latter describes how much the solar cell efficiency drops as the cell temperature rises. If we know the solar cell efficiency under STC, the NOCT, the Temperature Coefficient of Pmax, the air temperature, and the solar radiation density on the surface of the cell, we can compute the actual efficiency of the solar cell at current time.

Now, in order to compute the actual power output of the cell, we will need to know two more things: the area of the cell and the angle between the surface of the cell and the direction of the sun. The area of the cell is related to the packing density of the cells on a solar panel. Polycrystalline solar cells can have nearly 100% of packing density as they are usually rectangular, whereas monocrystalline ones have less packing density as they usually have round corners (therefore, they can't use up the entire surface area of a solar panel). The angle between the cell and the sun depends on how the solar panel is installed. This usually comes down to its tilt angle and azimuth.

Figure 2: Landscape vs. portrait (diode bypasses, location: Boston)
All these parameters are needed in Energy3D's solar radiation simulation. As a user, what you have to do is to understand the meaning of these parameters while designing your solutions and set the parameters correctly for your simulations. As Energy3D hasn't provided a way to select a solar panel model and then automatically import all of its specs, you still have to define a solar panel brand by setting its properties manually.

The next thing we must consider is a little tricky. A solar panel is made of many cells, arranged in an array of, for example 6 × 10. In order for the cells to produce usable voltage, they are usually connected in a series (the left image in Figure 1). In this case, the electric current flowing through each cell is the same but the voltage adds up. However, the problem with a series circuit is that, if one cell gets shaded by, say, a leaf that falls on it, and as a result generates a weaker current, every other cell of the panel will end up generating a smaller output (worse, all the generated electricity that cannot flow freely will turn into heat and damage the cells). To mitigate this problem, most solar panels today use diode bypasses (the right image in Figure 1) or similar technologies to allow the part of the solar panel that is not shaded to be able to contribute to the overall output. However, if the shade is not as spotty as is in the case of a leaf, even the diode bypasses will not be able to prevent complete loss (this video nicely demonstrates the problem). Therefore, our design of solar arrays must consider the actual wiring of the solar cells on the solar panel that we choose.

Figure 3: Month-by-month outputs of four arrays in Figure 2.
What are the implications of the cell wiring? Figure 2 shows four solar panel arrays with two different inter-row distances but the same number of identical solar panels that connect their cells with diode bypasses. The size of each solar panel is about 1 meter × 2 meters. On the racks of two arrays, the solar panels are placed in the landscape orientation -- each rack has therefore four rows of solar panels. On the racks of the other two arrays, they are placed in the portrait orientation -- each rack has therefore two rows of solar panels. When the inter-row spacing between two adjacent racks is the same, our simulation suggests that the landscape array always generates more electricity than the portrait array. This difference demonstrates the effect of the cell wiring using diode bypasses. In the front part of Figure 2 for arrays with narrower inter-row spacing, the simulation shows that about a quarter of the area on the racks after the first one is shaded during the course of the day (as indicated by their blue coloring). When the solar panels at the bottom of a rack is shaded, a portrait orientation reduces the output of 50% of the solar panels (there are two rows of solar panels on each rack in the portrait array shown in Figure 2), while a landscape orientation reduces the output of 25% of the solar panels (there are four rows of solar panels on each rack in the landscape array shown in Figure 2). The difference becomes less when the inter-row distance is longer. So when you have a limited space to place your solar arrays, you should probably favor the landscape orientation.

Figure 4: Shadow analysis shows inter-row shading in four seasons.
Of course, the output of a solar array depends also on the season. When the sun is high in the sky in the summer, the inter-row shading becomes less a problem. It is during the winter months when the shading loss becomes significant. This is shown in Figure 3. A snapshot of the shadow analysis (Figure 4) illustrates the difference visually.

For sites in the snowy north, another factor in the winter that favors the landscape orientation is the effect of snow accumulation on the panels. As soon as snow slides off the upper third of a solar panel in the landscape arrangement, it will start to generate some electricity. In the case of the portrait arrangement, it has to wait until all the snow comes off the panel.

Note that this article is concerned only with the cell wiring on a solar panel. The wiring of solar panels in an array is another important topic that we will cover later.

Introducing the Virtual Solar Decathlon

Hypothetical solar power near Hancock Tower in Boston
At the ACE Hackathon event on April 28, we introduced the concept of the Virtual Solar Decathlon to students at Phillips Academy who are interested in sustainable development.

Hypothetical solar canopies at Andover High School
The U.S. Department of Energy's Solar Decathlon challenges 20 collegiate teams to design, build, and operate solar-powered houses that are forward-thinking and cost-effective. Such a project, however, may take up to a year to complete and cost up to $250,000.

PS20 solar power tower in Seville, Spain
For a few years, I have been thinking about creating a high school equivalent of the Solar Decathlon that costs nothing, takes a much shorter time, and allows everyone to participate. The result of this thinking process is the Virtual Solar Decathlon that can now be supported by our Energy3D CAD software (and increasingly so as we added new features to allow more clean energy technologies to be simulated and designed). The goal of the Virtual Solar Decathlon is to turn the entire Google Earth into a simulation-based engineering lab of renewable energy and engage students to change their world by tackling energy problems (at least virtually) that matter deeply to their lives.

Here is the link to our presentation at Phillips Academy.

High school students to solarize the city of Lowell — virtually


In April, high school students in Lowell, Massachusetts will start exploring various solarization possibilities in the city of Lowell -- famously known as the Cradle of American Industrial Revolution. Many municipal properties and apartment buildings in Lowell have large roofs that are ideal for rooftop solar installations. Public parking facilities also provide space for installing solar canopies, which serve the dual purpose of generating clean energy and providing shade for parked cars. Students will discover the solar potential of their city and calculate the amount of electricity that can generated based on it.

This project is made possible by our Energy3D software, which supports engineering-grade solar design, simulation, and analysis. The Lowell High School, local business owners, and town officials have been very supportive about this initiative. They provided a number of public and private sites for students to pick and choose. Some of them have even agreed to serve as the "clients" for students to provide specifications, inputs, and feedback to students while they are carrying out this engineering project.

Among the available sites, five public parking garages managed by the municipal authority, which have not installed solar canopies, will be investigated by students through feasibility studies that include 3D modeling, solar energy simulation, and financial planning. Through the project work, students will author reports addressed to the property owners, in which they will recommend appropriate solar solutions and financial options.

Solving real-world problems like these creates a meaningful and compelling context and pathway for students to learn science and engineering knowledge and skills. Hopefully, their work will also help inform the general public about the solar potential of their city and the possibility of transitioning it to 100% renewable energy in the foreseeable future, which is a goal recently set by Massachusetts lawmakers.

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
Among them, researchers from Delft University of Technology, Technical University of Darmstadt, and Eindhoven University of Technology wrote in their recent paper about the validity of Energy2D: "The software program Energy2D is used to solve the dynamic Fourier heat transfer equations for the Convective Concrete case. Energy2D is a relatively new program (Xie, 2012) and is not yet widely used as a building performance simulation tool. To gain more confidence in the predictions with Energy2D, an analytical validation study was therefore carried out first, inspired by the approach described in Hensen and Nakhi (1994). Those analytical solutions and the simulation results of the dynamic response to a 20°C temperature step change on the surface of a concrete construction with the following properties were compared for this research." They concluded that "the simulation results never divert from the exact solution more than 0.45°C and it is therefore considered acceptable to further use this model."

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.