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.

Designing ground-mounted solar panel arrays: Part I

Fig. 1: Inter-row shadowing (daily total)

Designing a ground-mounted solar panel array is one of the challenges in our Solarize Your World curriculum, in addition to other challenges such as rooftop solar power systems, solar canopies, building-integrated photovoltaics, and concentrated solar power plants. With the support of our intuitive Energy3D software, designing a solar panel array appears to be a small and simple job as students can easily add, drag, and drop solar panels to cover up a site with many solar panels. But things are not always as simple as they seem.

Fig. 2: Solar radiation on an array in four reasons.

The design of a photovoltaic solar farm is, in fact, a typical engineering problem that requires the designer to find a solution that generates as much electricity as possible with a limited number of solar panels on a given piece of land, among many other constraints and criteria. Such an engineering project mandates iterative design and optimization in a solution space that has scores of variables. And the more the variables we have to deal with, the more complicated the design challenge becomes.

Fig. 3: Annual outputs vs. row spacing and tilt angle

This sequence of articles will walk you through the essential steps for designing photovoltaic solar farms under a variety of conditions. To get you started, let's assume that 1) we have a rectangular area for the solar farm; 2) the edges of the area are perfectly aligned with the north-south and east-west axes; and 3) the area is perfectly flat. This kind of site is probably uncommon in reality (unless the site is in a desert). But let's begin with a very simple scenario like this.

Fig. 4: Surface plot of solar output (ideal)

One of the first things that we have to decide is the number of solar panels. This is usually dictated by the budget. Suppose we have a fixed quantity of solar panels that we can install at a site large enough to space them (i.e., let's assume that we are not constrained by the area of the site for the time being). As people usually put solar panels on racks (a rack of solar panels is often referred to as a row -- but don't confuse it with the rows of solar panels you put on each rack), the next things we have to decide are 1) how many solar panels we want to place on each rack, 2) whether these solar panels are placed in "portrait" or "landscape" orientation on the rack, and 3) how long each rack is. From these information, we know the number of rows for the array. For example, the array in Figure 1 has four rows, each of which has 88 solar panels stacked up in a 4x22 landscape configuration. Since the shorter side of each panel is about one meter long, each rack is about four meters wide.

Fig. 5: Surface plot of solar output (using bypass diodes)

How far should the distance between two adjacent rows be? If the solar panels are tilted towards the sun, the rows cannot be too close to one another as the inter-row shadowing (Figure 1) will reduce the total output (sometimes severely, depending on the wiring of the solar cells on the solar panels -- we will investigate this in the next article), but they cannot be too far away from one another, either, as a longer distance between rows will decrease the efficiency of land use. Determining the optimal inter-row spacing for the solar array under design depends on a number of confounding factors such as the tilt angles, location, solar cell wiring, time of year, use of trackers, type of inverters, and shape of the site that greatly complicate the problem (Figure 2). This is a case in which a thorough understanding of the domain knowledge per se does not suffice to solve the problem. As there is no exact solution, we have to come up with a procedure and a strategy to search for an optimal one in the solution space. And, sometimes, this solution space can be so vast that manual search becomes infeasible.

Fig. 6: Line graph of solar output (using bypass diodes)

To simplify the search for now, let's assume that we only have to decide on the optimal values for the tilt angle and the inter-row spacing. This assumption reduces the solution space to only two dimensions. The most straightforward way to nail them down is to gradually vary the tilt angle and the inter-row spacing and then compute the total annual output of the solar panels at each step (Figure 3), a tedious job that took me a couple of hours to do. Once we have the results, we can use Excel to create a surface plot that shows different zones of outputs as a function of the inter-row spacing and tilt angle (Figures 4 and 5 -- we will discuss their differences in the next article; for now, you just need to know that Figure 5 is a more accurate result). The yellow zones in the surface plots are the reduced solution space where we should zero in to find our solution, taking trade-offs with other criteria such as the efficiency of land use into account. To have a clearer view, Figure 6 shows a 2D line graph of the solar outputs as a function of the tilt angle for six values of inter-row spacing.

The conclusions are that a tilt angle that is approximately equal to the latitude of the site (about 42 degrees in the case of Boston, MA) is the best when the rows are relatively far apart (say, 10 meters away center-to-center or 6 meters way edge to edge when the tilt angle is zero) and when the rows become closer, a smaller tilt angle should be more favorable. For instance, with the center-to-center inter-row spacing reduced to 8 and 7 meters, 35 and 26 degrees are the optimal choices for the tilt angle, respectively. With the optimal tilt angles, we will lose about 2% and 4% of electricity output when we reduce the inter-row spacing from 10 meters to 8 meters and 7 meters, respectively. If we don't change the tilt angles, the losses will increase to 3% and 9%, respectively. These findings apply to fixed solar panel arrays that do not track or "backtrack" the sun.

The analyses we have done so far just barely scratched the surface of the problem. We have many other design topics to cover and design factors to consider. But the volume of work thus far should speak aloud for itself that this is not a simple problem. At the same time Energy3D greatly simplifies an engineering task and empowers anyone to tackle it, it could also create an illusion as if engineering were simple. Yes, a What-You-See-Is-What-You-Get (WYSIWYG) 3D design and construction program like Energy3D may be entertaining in ways similar to playing with Minecraft, but no, engineering is not gaming -- it differs from gaming in many fundamental ways.

A demo of the Infrared Street View

An infrared street view

The award-winning Infrared Street View program is an ambitious project that aims to create something similar to Google's Street View, but in infrared light. The ultimate goal is to develop the world's first thermographic information system (TIS) that allows the positioning of thermal elements and the tracking of thermal processes on a massive scale. The applications include building energy efficiency, real estate inspection, and public security monitoring, to name a few.

An infrared image sphere

The Infrared Street View project is based on infrared cameras that work with now ubiquitous smartphones. It takes advantages of the orientation and location sensors of smartphones to store information necessary to knit an array of infrared thermal images taken at different angles and positions into a 3D image that, when rendered on a dome, creates an illusion of immersive 3D effects for the viewer.

The project was launched in 2016 and later joined by three brilliant computer science undergraduate students, Seth Kahn, Feiyu Lu, and Gabriel Terrell, from Tufts University, who developed a primitive system consisting of 1) an iOS frontend app to collect infrared image spheres, 2) a backend cloud app to process the images, and 3) a Web interface for users to view the stitched infrared images anchored at selected locations on a Google Maps application.

The following YouTube video demonstrates an early concept played out on an iPhone: