Tag Archives: Computer-aided design

Simulation-based analysis of parabolic trough solar power plants around the world

Fig. 1: 3D heat map of the Keahole Plant in Hawaii
Fig. 2: SEGS-8 in California and NOOR-1 in Morocco
In Version 7.1.7 of Energy3D, I have added the basic functionality needed to perform simulation-based analysis of solar power plants using parabolic trough arrays. These tools include 24-hour yield analysis for any selected day, 12-month annual yield analysis, and the 3D heat map visualization of the solar field for daily shading analysis (Figure 1). The heat map representation makes it easy to examine where and how the design can be optimized at a fine-grained level. For instance, the heat map in Figure 1 illustrates some degree of inter-row shadowing in the densely-packed Keahole Solar Power Plant in Hawaii (also known as Holaniku). If you are curious, you can also add a tree in the middle of the array to check out its effect (most solar power plants are in open space with no external obstruction to sunlight, so this is just for pure experimental fun).
Fig. 3: Hourly outputs near Tuscon in four seasons

Fig. 4: Hourly outputs near Calgary in four seasons
As of July 12, I have constructed the Energy3D models for nine such solar power plants in Canada, India, Italy, Morocco, and the United States (Arizona, California, Florida, Hawaii, and Nevada) using the newly-built user interface for creating and editing large-scale parabolic trough arrays (Figure 2). This interface aims to support anyone, be she a high school student or a professional engineer or a layperson interested in solar energy, to design this kind of solar power plant very quickly. The nine examples should sufficiently demonstrate Energy3D's capability of and relevance in designing realistic solar power plants of this type. More plants will be added in the future as we make progress in our Solarize Your World Initiative that aims to engage everyone to explore, model, and design renewable energy solutions for a sustainable world.
Fig. 5: Hourly outputs near Honolulu in four seasons

An interesting result is that the output of parabolic troughs actually dips a bit at noon in some months of the year (Figure 3), especially at high altitudes and in the winter, such as Medicine Hat in Canada at a latitude of about 51 degrees (Figure 4). This is surprising as we perceive noon as the warmest time of the day. But this effect has been observed in a real solar farm in Cary, North Carolina that uses horizontal single-axis trackers (HSATs) to turn photovoltaic solar panels. Although I don't currently have operation data from solar farms using parabolic troughs, HSAT-driven photovoltaic solar arrays that align in the north-south axis work in a way similar to parabolic troughs. So it is reasonable to expect that the outputs from parabolic troughs should exhibit similar patterns. This also seems to agree with the graphs in Figure 6 of a research paper by Italian scientists that compares parabolic troughs and Fresnel reflectors.

The effect is so counter-intuitive that folks call it "Solar Array Surprises." It occurs only in solar farms driven by HSATs (fixed arrays do not show this effect). As both the sun and the solar collectors move in HSAT solar arrays, exactly how this happens may not be easy to imagine at once. Some people suggested that the temperature effect on solar cell efficiency might be a possible cause. Although it is true that the decrease of solar cell efficiency at noon when temperature rises to unfavorable levels in the summer of North Carolina can contribute to the dip, the theory cannot explain why the effect is also pronounced in other seasons. But Energy3D accurately predicts these surprises, as I have written in an article about a year before when I added supports for solar trackers to Energy3D. I will think about this more carefully and provide the explanation later in an article dedicated to this particular topic. For now, I would like to point out that Energy3D shows that the effect diminishes for sites closer to the equator (Figure 5).

Designing panda solar power plants with Energy3D

Fig. 1: Panda power in Energy3D
Fig. 2: Panda power in Energy3D
A Panda-shaped photovoltaic (PV) solar power plant in Datong, China recently came online and quickly went viral in the news. While solar power plants in cute shapes are not a new thing (I blogged about the Mickey Mouse-shaped solar farm in Orlando, FL about six weeks ago), this one drew a lot of attentions because the company that built it, Panda Green Energy Group, is reportedly planning to build 100 more such plants around the world to advertise for renewable energy. According to the company's website, the idea of building Panda-shaped solar power plants originated from Ada Li, a student from Oregon Episcopal School. Li proposed her idea at the COP21 Conference in Paris.

The construction of the 100 MW Datong Panda Solar Power Plant began on November 20, 2016. It is expected to generate 3.2 billion KWh in a life span of 25 years. The plant consists of two types of solar panels of different colors: black monocrystalline solar panels and white thin-film solar panels. The two types form the characteristic shape and pattern of a giant panda, the national treasure of China and the logo of the World Wildlife Fund. Considering the number of people who complain about solar power plants being eyesores in their neighborhoods, these attempts by the Panda and Micky Mouse solar farms and their future cousins may provide examples to mitigate these negative perceptions.

Fig. 3: A close-up view of Panda power.
Fig. 4: A close-up view of Panda power.
One of our summer interns, Maya Haigis, who is a student from the University of Rochester, spent a couple of hours to create an Energy3D model of the Datong Panda Solar Power Plant after I shared the news with her today. The power plant is so new that Google Maps currently show only a picture of it under construction. So Maya went ahead to draw the power plant based on an artist's imagination taken from the news. Her design ended up using about 34,000 solar panels. To make it look like a real giant panda with its trademark black and white fur, I had to quickly add a light gray color option for solar panels in Energy3D. Maya's work came out to be amazingly realistic (Figures 1 and 2). This is even more remarkable considering that Maya had no prior experience with Energy3D.

Panda Green Energy said in the press release that they designed the power plant also for the purpose of engaging youth to join the renewable energy revolution. They are planning to reach out to schools for student site visits. There is also a plan to make the power plant a tourist attraction. I am not sure people would pay to go there to see it. But with Energy3D, we can imagine the experience by taking a virtual tour with the 3D model (Figures 3 and 4). The engineers among us can run Energy3D simulations to analyze its performance and investigate whether such an effort makes scientific sense.

So what about inviting children all over the world to "paint" the brownfields that have scarred our planet with this kind of good-looking solar power plants using Energy3D as a "solar brush?" Welcome to our Solarize Your World Initiative!

Energy3D turns the globe into a powerful engineering design lab for everyone

Fig. 1: Dots represent regions supported in Energy3D.
Many of the readers of my blog may not know Energy3D is, in fact, also a Google Maps application. Energy3D allows users to import a satellite image of a site through the Google Maps API as the "ground image" in its 3D coordinate system, on top of which users can draw 3D structures such as buildings or power plants. Built-in simulation engines can then be used to test and analyze these structures without having to switch to another tool and leave the scene (something known as "concurrent analysis" in the CAD industry). These engines use large geographical and weather datasets for the site as inputs for simulations to accurately take environmental factors such as air temperature and solar radiation into account. As the climate is probably the single most important factor that drives the energy usage in buildings where we live and work, it is important to use weather data from a typical meteorological year (TMY) in a simulation. If no weather data is available for the site, Energy3D will automatically select the nearest location from a network of more than 525 supported worldwide regions (Figure 1) when you import the satellite image from Google Maps. The following table lists the numbers of regions in 176 countries that are currently supported in Energy3D. The United States is covered by a network of 164 nodes. So if you are in the United States, you will have a better chance to find a location that may represent the climate of your area.

Afghanistan 1 Albania 1 Algeria 6
Angola 1 Argentina 3 Armenia 1
Australia 11 Austria 1 Azerbaijan 1
Bahamas 1 Bahrain 1 Bangladesh 1
Belarus 1 Belgium 1 Belize 1
Bolivia 1 Bosnia & Herzegovina 1 Botswana 1
Brazil 8 Brunei 1 Bulgaria 1
Burkina Faso 1 Burundi 1 Cambodia 1
Cameroon 1 Canada 10 Cape Verde 1
Central African Republic 1 Chad 1 Chile 12
China 42 Colombia 2 Comoros 1
Congo 1 Costa Rica 1 Croatia 1
Cuba 1 Cyprus 2 Czech 1
DR Congo 1 Denmark 1 Djibouti 1
Dominica 1 Dominican Republic 1 East Timor 1
Ecuador 1 Egypt 1 El Salvador 1
Equatorial Guinea 1 Eritrea 1 Estonia 1
Ethiopia 1 Fiji 2 Finland 1
France 8 Gabon 1 Gambia 1
Georgia 1 Germany 12 Ghana 1
Greece 2 Guatemala 1 Guinea 1
Guinea-Bissau 1 Guyana 1 Haiti 1
Honduras 1 Hungary 1 Iceland 1
India 11 Indonesia 4 Iran 3
Iraq 1 Ireland 1 Israel 1
Italy 5 Ivory Coast 1 Jamaica 1
Japan 6 Jerusalem 1 Jordan 1
Kazakhstan 1 Kenya 1 Kosovo 1
Kuwait 1 Kyrgyzstan 1 Laos 1
Latvia 1 Lebanon 1 Lesotho 1
Liberia 1 Libya 2 Liechtenstein 1
Lithuania 1 Luxembourg 1 Macedonia 1
Madagascar 1 Malawi 1 Malaysia 2
Maldives 1 Mali 1 Malta 1
Marshall Islands 1 Mauritania 1 Mauritius 1
Mexico 4 Moldova 1 Monaco 1
Mongolia 1 Montenegro 1 Morocco 3
Mozambique 1 Myanmar 2 Namibia 1
Nepal 1 Netherlands 1 New Zealand 2
Nicaragua 1 Niger 1 Nigeria 1
North Korea 1 Norway 1 Oman 1
Pakistan 4 Panama 1 Papua New Guinea 1
Paraguay 1 Peru 2 Philippines 1
Poland 7 Portugal 2 Qatar 1
Republic of China 2 Romania 1 Russia 7
Rwanda 1 Saudi Arabia 2 Senegal 1
Serbia 2 Sierra Leone 1 Singapore 1
Slovakia 1 Slovenia 1 Solomon Islands 1
Somalia 1 South Africa 8 South Korea 2
South Pole 1 South Sudan 1 Spain 8
Sri Lanka 1 Sudan 1 Sweden 1
Switzerland 3 Syria 2 Tajikistan 1
Tanzania 2 Thailand 2 Togo 1
Trinidad & Tobago 1 Tunisia 1 Turkey 3
Turkmenistan 1 Uganda 1 Ukraine 2
United Arab Emirates 2 United Kingdom 6 United States 164
Uruguay 1 Uzbekistan 1 Venezuela 1
Vietnam 2 Western Sahara 1 Yemen 1
Zambia 1 Zimbabwe 1

Fig. 2: Solar sites in Fitchburg, MA.
Energy3D's capability of turning Google Maps into a gigantic virtual engineering design lab has tremendous potential in STEM education and energy revolution. It allows students to pick and choose sites for designing renewable energy and energy efficiency solutions that are most relevant to their lives, such as their home and school buildings (Figure 2). It gives students an authentic tool that supports them to scientifically investigate all sorts of possibilities to design a more sustainable world and effectively communicate their ideas to the public. And, most importantly, with Energy3D being a free tool that anyone can use at zero cost, this can happen at the global scale to engage every student in the world to act now and make a difference!

This global vision is not new. Back in 1995, the National Science Foundation funded my colleagues Boris Berenfeld, Bob Tinker, and Dan Barstow, who were at TERC at that time, a grant to develop a curriculum that they touted as the Globe Lab. The Global Lab Curriculum meant to provide an interdisciplinary, one-year course at the secondary level that supports science standards and school reform through intercultural, scientifically meaningful, and collaborative student investigations in environmental studies. Students were given the opportunity to experience all aspects of genuine scientific research: problem identification, background study, project design, collaboration, data analysis, and communication.

Fig. 3: Solar power plants around the world.
More than 20 years later, technology has advanced so much that we now have many more resources and tools to rethink about this idea. With Google Maps and weather data for countless regions in the world, Energy3D is poised to become a true example of Globe Lab for science and engineering. The integration of the software and our Solarize Your World Curriculum with the current, unstoppable waves of renewable energy innovation and movement worldwide will create numerous exciting possibilities for youth to become truly involved and engaged in shaping their world and their future (Figure 3). While we undertake this grand challenge, it is utterly important to keep in mind that renewable energy does not just stand for some kind of green ideology related only to potential tax hikes -- it also represents trillions of dollars worth of business opportunities and investment in the coming decades committed by almost all governments on the planet to revamp the world's energy infrastructure to provide cleaner air and healthier environment for their citizens. Given this level of global significance, our work will only become more essential and the implications will only become more profound.

As we are mourning the loss of Bob Tinker, one of the architects of the Global Lab Curriculum, carrying on this line of work will be the best way to remember his visions, honor his contributions, and celebrate his life.

Modeling parabolic troughs in Energy3D

Fig. 1. The absorber tube of a parabolic trough
A parabolic trough is a type of concentrated solar collector that is straight in one dimension and curved as a parabola in the other two, lined with mirrors. Sunlight that enters the trough is focused on an absorber tube aligned along the focal line of the parabola, heating up the fluid in the tube (Figures 1 and 2). If the parabolic trough is for generating electricity, the heated fluid is then used to vaporize water and drive a turbine engine. A power plant usually consists of many rows of parabolic troughs.

Fig. 2. A view from the absorber tube.
Parabolic troughs are another common form of concentrated solar power (CSP), in addition to solar power towers that Energy3D has already supported (there are two other types of CSP technologies: Dish Stirling and Fresnel reflectors, but they are not very common). According to Wikipedia, there are currently more parabolic trough-based CSP plants than tower-based ones.

In the latest version of Energy3D (V7.0.6), users can now add any number of parabolic troughs of any shape and size to design a solar thermal power plant.

Fig. 3: Parabolic troughs at different times of the day

Parabolic troughs are most commonly aligned in the north-south axis so that they can rotate to track the sun from east to west during the day. This kind of trackers for parabolic troughs works in a way similar to the horizontal single-axis tracker (HSAT) for driving photovoltaic solar panel arrays. You can observe their motions when you change the time or date or animate the movement of the sun in Energy3D. Figure 3 illustrates this.

Like photovoltaic solar panel arrays, parabolic troughs have the inter-row shadowing problem as well. So the distance between adjacent rows of parabolic troughs cannot be too small, either. But unlike solar power towers, parabolic troughs do not have reflection blocking issues among mirrors. Figure 4 shows this.

This new addition greatly enhances Energy3D's capability of modeling CSP plants, moving the software closer to the goal of being a one-stop shop for exploring all sorts of solar solutions. In the coming weeks, we will start to build 3D models for parabolic troughs in the real world.
Fig. 4: Inter-row shadowing in parabolic trough arrays

Khi Solar One

Khi Solar One (KSO) is a 50 MW solar power tower plant located in Upington, South Africa, which was commissioned in February, 2016. KSO has 4,120 heliostats on 346 acres of land. Each heliostat is as large as 140 square meters, reflecting sunlight to a tower as tall as 205 meters. KSO has two hours of thermal storage. The power plant is expected to generate a total of 180 GWh per year.

A low-resolution simulation of Energy3D predicts that on February 28 (close to when the Google Maps image was most likely taken) and June 28 (a winter day in the southern hemisphere), the total daily input to the solar tower (not the output of electricity generated by the turbines) is about 2.6 MWh and 1.9 MWh, respectively, as is shown in the graphs below.

The Energy3D model of the KSO can be downloaded from this web page, along with other solar power plants.



Creating computer models for all solar thermal power plants in the world

Fig. 1: Energy3D models for six solar power towers
Fig. 2: The Gemasolar Plant
One of the unique features of Energy3D is its ability to model, design, and simulate solar power towers. Figure 1 shows the Energy3D models for six solar power towers: Gemosolar (Spain), PS10 (Spain), PS20 (Spain), Greenway (Turkey), Themis (France), and Badaling (China). To support the research and development on concentrated solar power (CSP) -- a solar power solution alternative to photovoltaic (PV) arrays that may be able to provide some baseload capacity, I have been working on creating a library of 3D models for all the existing and planned solar thermal power plants in the world. The ultimate goal is to develop Energy3D into a versatile CAD tool for all forms of CSP (and PV), based on accurate simulation of existing plants first. The acquisition of the capability of reliably modeling both CSP and PV will enable Energy3D to truly support our Solarize Your World Initiative.

Fig. 3: The Gemasolar Plant
Fig. 4: The Gemasolar plant (June 30)
This article shows a bit of progress towards that goal. I have recently added in Energy3D weather data for scores of sites that already have CSP plants or are planning to build CSP plants. Many of these new sites are in Africa, China, Europe, and South America (some of them were requested by our users in Algeria and Chile). These newly added locations bring the total number of sites supported in Energy3D to more than 250. This growing network should provide you weather data that are approximately applicable to your site (but let me know if your site is not currently covered by Energy3D to your satisfaction). When you import your Earth view in Energy3D, the software will automatically choose the supported location that is closest to your site. If there is already a power tower, you can use the length and direction of its shadow in the picture to estimate the date and time when the picture was taken -- this can be done by turning on the shadow and adjusting the date and time spinner of Energy3D until the calculated shadow approximately aligns with the real shadow. After this is done, the heliostats that you add to the scene will approximately point to the same direction as in the image.

In this article, I picked the impressive Gemosolar Thermosolar Plant near the city of Seville, Spain as a showcase. The plant has 2,650 heliostats on 520 acres of land, each of which is as large as 120 square meters. The tower is 140 meters tall. The annual output is approximately 110 GWh. With molten salt tanks, it can store up to 15 hours of energy. Using a low-resolution setting, it takes Energy3D 5-10 minutes to complete a daily simulation and up to a couple of hours to complete an annual simulation. If you can afford to wait longer, you can always increase the simulation resolution and improve the accuracy of results (e.g., more points on the reflectors better account for blocking and shadowing losses).

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.

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.