Our World Statistics Day conversations have been a great reminder of how much statistics can inform our lives. Do you have an example of how statistics has made a difference in your life? Share your story with the Community!
The SAS Solar Farm data (available in the JMP File Exchange) has proven to be a rich topic for discussion and exploration. Besides the cool factor from green technology, the factors (such as sunlight, wind, temperature) can be understood by anyone, and yet the interactions are complex and not all linear. One issue that came up in the comments to my original post was the effect of ambient temperature on the power output. Rather than try to create an accurate model to account for sun position and solar panel angle, I tried some basic visual exploration to get a feel for the relationship of temperature and power.
A fair starting point is a basic plot of power versus temperature for the whole data set.
Here, I've set the graph transparency to 0.3 to give a point cloud effect. The visual is not too helpful except to get us to think about the other factors that are conditioning the relationship between power and temperature. Factors we have in our data set include time of day, day of year and solar irradiance. Other factors we might derive or get externally include solar angle, panel temperature and weather conditions.
Eschewing complex models, I tried conditioning the data on irradiance (sunlight) and time from solar noon (as a proxy for panel angle and sun position). The idea is that, say, two hours before noon and two hours after noon would have the same panel angle and sun position but likely different temperatures and power output levels. Solar noon, also called local apparent noon (LAN), is where the irradiance peaks on sunny days. We only have data in 15-minute intervals, and solar noon seems to be between 12:15 and 12:30 for the Cary, NC, area, and I chose 12:30 for my calculations. From that I calculated Minutes from LAN. Here's the power versus temperature conditioned on both Irradiance and Minutes from LAN.
Most of the panels show a slight negative relationship, as expected for solar cells. Eyeballing the trends suggests about 3kW per degree Celsius, or about 1% per degree. That seems a little high from what I've read, and I think it's because the panels still contain a bit of mixing of different conditions.
To go a step further, I decided to look at individual pairs of times equidistant from solar noon. With plenty of pairs to look at, I filtered it down to pairs with strong power output, a significant temperature difference (more than 4°C), a similar irradiance value and on a single array.
Each line connects a matched pair of temperature/power readings for a given day and panel angle (assuming the angle is proportional to minutes from local area noon). Now we can see that most pairs exhibit a small negative relationship, though there are a few outlier slopes in both directions. What accounts for those? Using Distribution or Tabulate, we find the median slope to be about -1.2 kW/°C, which is about 0.3% per degree based on an average 350kW base.