We're taking a break from Point Break to discuss how STK's Solar Panel Tool calculates its numbers. STK's Solar Panel Tool is used to estimate the amount of power that solar panels generate at a given time. If you are unfamiliar with the tool, search for "Solar Panel Tool" in STK's Help to learn how to use it. The tool uses a graphical rather than analytical approach to determine power.
Effective Area
Below are images of a satellite from the direction of the sun. The fig. 1 is from the normal STK 3D window, and fig. 2 is from the Solar Panel Tool. In fig. 2, the red is the background, the darker red is the satellite's solar panels, and the black is the rest of the satellite.
 |
 |
| Figure 1 | Figure 2 |
Though both images are taken from the same direction, the silhouettes of the two satellites are slightly different. This is because fig. 1 is a perspective view, while fig. 2 is an orthographic view. In a perspective view, the object becomes smaller as the distance from the viewer increases. In an orthographic view, the object remains the same size regardless of the viewer's distance; therefore, the size of every pixel is the same, e.g., 1 cm x 1 cm. An orthographic view also mimics the fact that the sun's rays are virtually parallel to each other given the distance between the sun and a satellite orbiting the earth.
 |
 |
| Figure 3a. | Figure 3b |
The effective area is the area of the solar panel as seen from the sun. The area is used to determine how much of the sun's energy is reaching the solar panel.
Fig. 3b shows the pixels of the magnified section outlined in white in fig. 3a. In this image, there are 35 dark red solar panel pixels, 4 red background pixels, and 25 black satellite body pixels. Each pixel is 0.0095 m2, so the effective area for this image is 35 pixels x 0.0095 m2/pixel or 0.3325 m2.
As you can see in fig. 1, the body of the satellite obscures parts of the far solar panels from the sun. Those parts are not included in the area calculation as would be expected.
"Yes! And I will grant you the power to fire lasers from your heads!"
There is an STK report that outputs the power over time. The method that the tool uses to the calculate the power is based on an equation from Space Mission Analysis and Design:
Power = SPE x SI x Effective Area x 1358 W/m2
- SPE is the solar panel efficiency. A solar panel does not convert 100% of the sun's energy and degrades over time. SPE ranges from 0.0, a piece of cardboard, to 1.0, a perfectly efficient solar panel.
- SI is the solar intensity. The value is 0.0 if the solar panel is in the earth's umbra, 1.0 in full sunlight, and between 0.0 and 1.0 in penumbra.
- The value 1358 W/m2 is the amount of W/m2 that the sun provides near the earth.
This equation is normally insufficient. Users know the specifics of their solar panels and can provide a better estimate of the power. A typical user would more likely execute an STK report of the effective area and solar intensity over time and use those values in their own power equation.
Angles
If you compare fig. 4 for the satellite at a different time to fig. 2, you will notice that the solar panels are different shades of red.
 |
| Figure 4 |
The darker the red, the lower the angle of the sunlight with respect to the solar panel. In fig. 2, the far darker reds indicate lower angles. In fig. 4, the solar panels are almost pure red, which indicates that the sunlight is almost directly impacting the solar panels.
Because we are using a 24 bit color buffer that allocates 8 bits to red, there are 256 levels of red and that translates into 256 different angles. The red value is directly related to the cosine of the angle between the sun direction and a vector normal to the solar panel.
Often, solar panel efficiency degrades as the angle between the sunlight and solar panel normal increases. In STK, a user can execute a report for a specific time that will output these angles for use in their own power equation.
The following is the report for fig. 4. Note that the angle is the angle of the light relative to surface of the solar panel, so 90.0 deg is sunlight directly impacting the solar panels.
| Angle (deg) | Effective Area (m2) |
| 28.072 | 0.009537 |
| 30.912 | 0.009537 |
| 34.110 | 0.009537 |
| 36.310 | 0.009537 |
| 36.870 | 0.009537 |
| 41.510 | 0.009537 |
| 45.219 | 0.009537 |
| 49.188 | 0.009537 |
| 52.021 | 0.009537 |
| 52.757 | 0.009537 |
| 60.074 | 0.009537 |
| 65.478 | 0.009537 |
| 73.901 | 0.009537 |
| 82.819 | 27.189256 |
| 84.924 | 55.931643 |
| 90.000 | 27.427675 |
You might expect only one angle since all of the solar panels appear coplanar; but, there are sixteen different angles. Thirteen of the angles hardly contribute to the effective area; the solar panels are model as boxes, and these thirteen angles are from the box sides. The bulk of that sunlight occurs at angles between 82.819 and 90.0 deg.
"Sometimes I'm scared to think of what goes on in that tiny robot brain of yours."
This is a graphical method for determining the solar panel area. The graphical processing unit (GPU) can easily outperform an analytical method executed on the CPU. Many more test cases can be run as compared to the slower method. Later, more promising orbits and attitudes could be tested against the analytical method to obtain more accurate results.
Since the graphical method counts pixels, the accuracy is partly dependent on the size of the window. More pixels means more accuracy. Each pixel represents a discrete area. In the above example, a pixel's area was 0.0095 m2. If the size of the window were doubled, the pixel's area would be 0.0024 m2, and the estimate of the effective area would be more precise. So, the tool should be run with the largest window possible. There are other precision issues to worry about, such how much effective area a pixel at the edge of a solar panel really contributes.
When the original code was written, the color buffer only allowed 255 levels of red. (Previously, I stated 256 as I was including black, the darkest red of all.) This severely limits the angular precision. Additionally, the angles are not distributed linearly as the red level actually represents the cosine of the angle. Modern GPUs support floating point color buffers. If the code were altered to use such a buffer, the number of red levels would increase dramatically.
There is much more to explain, but my candle grows dim. I hope you have a better understanding of the computations and usefulness of the Mighty Solar Panel Tool.
Can you clarify Figure 3? Does it represent the entire far-side solar array? Does the solar array have a hole or gap in it? Can you show exactly where it was extracted from Figure 2?
James,
I split figure 3, where 3b is the section in 3a outlined in white and magnified.
Im working on the power systems for a Cubesat project for school and we’re attempting to use STK to determine the power requirements. Thus far we have read through the tutorials and have some understanding of the solar panel tool. However, the area report from the solar panel tool yields area values higher than the given area of the model (yet the effective area seems possible). We’ve looked all through the tutorials and can’t seem to figure out how STK calculates the AREA and why these values would be so high. We’re also a little unsure what roles the pixel size and the bound radius play in determining the area. Basically, what steps should we take to calculate the most accurate area and should we be concerned about the higher AREA values if the Effective Area looks accurate.
Thanks!
katie,
Generally, the area will be larger than expected. The accuracy of the area calculation is effected by the area of each pixel, the number of pixels that represents the solar panel, and the angle at which the Sun impinges each pixel. The area calculation is most accurate when the Sun direction is perpendicular to the face the panel and least accurate when the Sun direction is nearly parallel.
To improve both area and effective area calculations, you want the area that each pixel represents to be the smallest possible. To do that:
1. Make the window dimensions as large as possible
2. Modify the bound radius such that as much of your panel covers the screen as possible without any part of the panel going outside the window
I hope this helps.
Hey,
We have a problem again. It is concerned with determining the co-odinates of a vector. We want to obtain the sun vector co-ordinates at different time steps and the vectors of the solar panel faces and take the dot product to determine the effective area to make sure it’s accurate. Is there any way to do this? Thank you..
Katie,
To compare the angle of the sun to your solar panel, you need to have both in a common coordinate system.
First, do a report in STK of the sun direction in the body coordinates of your satellite. To do that,
1. Right click on your satellite in the Object Browser; select Satellite Tools->Report.
2. Select “New” under “Style”, not “Styles”
3. Under “Data Providers”, go to “Vector Choose Axes” and select the plus sign to open the list
4. Go to “Sun” and select the plus sign to open the list
5. Select “Time” and press the right arrow button to move that over to the Report Contents column
6. Select “x/Magnitude” and press the right arrow button to move that over to the Report Contents column
7. Select “y/Magnitude” and press the right arrow button to move that over to the Report Contents column
8. Select “z/Magnitude” and press the right arrow button to move that over to the Report Contents column
9. Press OK.
10. You should see your report “NewStyle” in the Styles list. You can rename it by selecting your report; at the bottom enter your new name and press the “Change Name” button.
To create the report from your report style,
1. Select your report.
2. Press “Create…”
3. Another GUI will pop up asking you to select an axes. The sun direction will be reported in that axes. In your case, select Body for your satellite.
4. Press OK.
You should now see a report over time of the sun direction in the body frame of your satellite. If you want to change the time period or use a different time step, press “Time Period…” (it is just below “Create…”). Another GUI will pop up to allow you to make the necessary time changes.
So, now you have the sun direction in your satellite’s body frame. I don’t know much about your cubesat satellite, but I am guessing that you know the direction of each vector perpendicular to the plane of a solar panel in cubesat’s body frame. Using that data along with the geometry of each solar panel, you can compute the effective area.