Tag Archives: Energy3D

Energy3D uses intelligent agents to create adaptive feedback based on analyzing the "DNA of design"

Fig. 1: A simple case of teaching thermal insulation.
Energy3D is a "smart" CAD tool because it can monitor the designer's behavior in real time, based on which it can generate feedback to the designer to regulate the design behavior. This capacity has tremendous implications to learning and teaching scientific inquiry and engineering design with open-ended nature that requires, ideally, one-to-one tutoring so intense that no teacher can easily provide in real classrooms.

The computational mechanism for generating feedback in Energy3D is based on intelligent agents, which consist of sensors and actuators (in very generic terms). In Energy3D, all the events are logged behind the scenes. The events provide the raw data stream from which various sensors produce signals based on subsets of the raw data. For instance, a sensor can be created to monitor any event related to solar panels of a house. An agent then uses a decision tree model to determine which actuators should be called to provide feedback to the user or direct Energy3D to change its state. For instance, if a solar panel is detected to be placed on the north-facing roof, the agent can remind the designer to rethink about the decision. Just like what a teacher may do, the agent can even suggest a comparative analysis between a solar panel on the north-facing roof and a solar panel on the south-facing or west-facing roof. Although this type of inquiry and design can be also taught using directly scaffolded instruction that guides students to explore step by step, in practice we have found the effect of this approach often diminishes because many students do not read instruction carefully enough and remember them long enough. It is also challenging for teachers to guide the whole class through this kind of long learning process as students often pace differently. Adaptive feedback provides a way to help students only when they need or just when a need is detected, thus providing a better chance to deliver effective instruction.

Let's look at a very simple example. Figure 1 shows a learning activity, the goal of which is to teach how the thermal property of a wall, called the U-value, affects the energy use of a house. Many students may walk away with a shallow understanding that the higher the U-value is, the more energy a house uses. The challenge is to help them deepen their understanding. For example, how can we make sure that students will collect enough data points to discover that the energy a house uses is proportional to the U-value? How can we support them to find out that the relationship is independent of seasonal change, wall orientation, and solar radiation (e.g., a lower U-value is good in both summer and winter, irrespective of whether or not the wall faces the sun). Helping students accomplish this level of understanding through inquiry-based activities is by no means a trivial task, even in this seemingly simple example. Let's explore what we may do in Energy3D now that we have a way to monitor students' interactions with it.

Fig. 2: An event sequence coded like a DNA sequence.
In nearly all software that support learning and teaching, the events during a process can be coded as a string with characters representing the events and ordered by their timestamps, such as Figure 2. In this case, A represents an analysis event in the Energy3D CAD tool, U represents an event of changing the U-value of a wall, C represents an event of changing the date for the energy simulation, a questionmark (?) represents an event of requesting help from the software, an underscore (_) represents an inactive time period longer than a certain threshold, and * is a wildcard that represents any other event "silenced" in this expression in order to reduce the dimensionality of the problem. For those who know a bit about bioinformatics, this resembles a DNA sequence. In the context of Energy3D, we may also call it as the DNA of a design, if that helps your imagination.

Now that we have converted the sequence of events into a string, we can use all sorts of techniques that have been developed to analyze strings to analyze these events, including those developed in bioinformatics such as sequence alignment or those developed in natural language processing. In this article, I am going to show how the widely-supported regular expressions (regex) can be used as a technique to detect whether a certain type of event or a certain combination of events occurred or how many times it occurred. I feel that regex, in our case, may be more accurate than edit distances such as the Levenshtein distance in matching the pattern. For example, a single substitution of event may represent a very different process despite the short edit distance.

Fig. 3: A sequence that shows high usage of feedback
We know that, a fundamental skill of inquiry is to keep everything else fixed but change only one variable at a time and then test how the system's output depends on that variable. Through this process of inquiry, we learn the meaning of that variable, as explained by Bruce Alberts, former president of the National Academy of Sciences and former Editor-in-Chief of the Science Magazine. In the example discussed here, that variable is the U-value of a selected wall of the house and the test is the simulation-based analysis. A pattern that has alternating U and A characters in the event string suggests a high probability of inquiry, which can be captured using a simple regex such as (U[_\\*\\?]*A)+. Between U and A, however, there may be other types of events that may or may not exist to weaken the probability or compromise the rigor. For example, changing the color of the wall between U and A may also result in an additional difference in energy use of the house that originates from the absorption of solar radiation by the external surface of the wall and has nothing to do with its U-value. In this case, changing multiple variables at a time appears to be a violation of the aforementioned inquiry principle that should be called out by the agent using another regex to analyze the substring between U and A.

An interesting feature in Energy3D is that feedback itself is also logged. Figure 3 shows a sequence that has an alternation pattern similar to that of Figure 2, but it records a type of behavior showing that the user may rely overly on feedback from the system to learn (the questionmarks in the string stand for feedback requests made by the user) and avoid deep thinking on their own. This may be a common problem in many intelligent tutors (sometimes this behavior is called "gaming the system").

The development of data mining and intelligent agents in Energy3D is opening interesting opportunities of research that will only grow more important in the era of artificial intelligence (AI). We are excited to be part of this wave of AI innovation.

General Motors funds engineering education based on Energy3D

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

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

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

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

Energy3D allows users to select brand name solar panels

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

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

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

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

The 2017 Energy Innovation Forum

We are invited to present at the Energy Innovation Forum on October 18 organized by the University of Massachusetts Lowell and the Massachusetts Clean Energy Center. The event will connect about 30 companies in Massachusetts with funders, investors, university researchers, and industry leaders to stimulate innovations in energy technologies.

For those who cannot attend the event, I am sharing our two posters here. You can also take a look at the PowerPoint slides for the Infrared Street View Project and the Virtual Solar Grid Project (we will do both oral and poster presentations). Both projects focus on developing a unique crowdsourcing model that integrates STEM education and energy research. The projects provide examples of using citizen science to support and engage a large number of students to learn science and engineering and participate in large-scale energy research.

The Infrared Street View Project will support research and education in the field of energy efficiency whereas the Virtual Solar Grid Project will support research and education in the field of renewable energy (primarily solar energy at present). Both projects are based on cutting-edge technologies being developed in my lab.

Deciphering a solar array surprise with Energy3D

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Their paper was published here.

Introducing summer intern, data science major Maya Haigis

Before interning with senior scientist Charles Xie this summer, Maya Haigis had no idea how many solar panel manufacturers there are—“There’s a ton!”

A data science major at the University of Rochester, Maya put her analytic skills to work at the Concord Consortium collecting data on solar panels (dimensions, weight, maximum wattage, etc.) and designed a panda solar power plant with Energy3D, an engineering design and simulation tool for renewable energy and energy efficiency. She used Energy3D to create a power plant in the shape of a bald eagle, too.

“Charles heard about the giant panda power plant in Datong, China, in the news, and asked me to replicate it in Energy3D.” Maya says, “It was a good introduction to the features of Energy3D. Charles suggested I do something relevant to the U.S.—like our own national symbol! It was fun imagining flying across the country and seeing a giant bald eagle out of the window instead of the generic rectangles or circles of traditional solar farms.”

She also worked with the Energy3D team modeling local schools and other community buildings for the Solarize Your World curriculum they are designing.

“Maya is a real genius in 3D modeling,” said Charles. “I didn’t expect her to come up with sophisticated 3D structures within a couple of hours with a piece of software that she had never used before. But she did it elegantly. It is remarkable that she has created scores of highly accurate 3D models for school buildings with incredible details.”

Bald eagle solar power in Energy3D (left) and close-up of bald eagle (right).

As a sophomore, Maya is currently on the same path as computer science students, but her curriculum path will soon diverge with a focus on data mining and database systems plus more statistics. She’s always been “a math person,“ she says, but credits her high school AP statistics teacher’s enthusiasm for data and statistics for consolidating her interest.

At the University of Rochester she’s already taken courses in Java, data structures and algorithms, discrete math, calculus, and linear algebra with differential equations. “All data is interesting,” she says, but notes sports stats are particularly fascinating. No surprise, since Maya is a student athlete who plays field hockey at the Division III school where her schedule includes practice six days a week.

She notes, “My brother and I used to have a collection of baseball cards and I would try to memorize the stats of my favorite players. It’s a bit ironic because before games, coaches always say that once you step onto the field, the statistics don’t mean anything and what matters is which team plays the hardest, but I still look through other team stats.”

Recently, Maya had a pivotal experience. She spent half a day at Pfizer working with a business analyst, who serves as a connection between scientists and programmers. “The business analyst would explain to the scientists what the data meant,” she explains. “And if the scientists wanted their data displayed in a certain way, she would talk to the programmers.” Maya can imagine filling a similar liaison role working as data scientist, though she also admits, “I’m not exactly sure what I want to do after college, but I’m looking forward to the data science courses at Rochester, and I’m excited to see what opportunities will arise with big data!”

Modeling parabolic dish Stirling engines in Energy3D

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

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

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

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

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

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

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

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

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

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

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

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

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