We have had solar panels on our house for almost three years. Our DC to AC inverter (which converts solar electrons to wall plug electrons) is connected to the "Internet" (it's new, you should check it out) and reports energy production information to a "website." Specifically, this one: SolarEdge Monitoring (there are demo links that anyone can look at without an account). The website collects and presents the data in a few ways, showing current and past production with graphs, and various totals that make a customer feel good about themselves:
Customers can download historical data off the website, which I have done and analyzed. The plot below shows how many Watt hours (Wh) the system has produced each of the last three years (check it out, the plot is interactive!). The system was turned on Feb 10, 2014, so it's no surprise that 2014 has the lowest total. Clearly, 2016 was a much better year than 2015, producing over 8% more energy.
As an aside, here is a histogram of the daily totals over the life of the system. The peak at 0 Wh is real - those are days when the panels are completely covered in snow. Such is solar panel life in Colorado!
The high total for 2016 got me thinking - just how good of a year was 2016? There are many ways to explore this, and I went with one that I'm familiar with: simulation. Essentially, what I did was for every day between Jan 1, 2016 and Dec 31, 2016, I randomly chose the Wh generated on that same calendar day from all my historical samples, and added them up. For example, if I am looking at July 9, 2016, I have three data points (2014, 2015, and 2016), and I choose one of them with equal chance, and add it to the total. I do this for every day of the year, and I do many thousands of simulated years. Out of this simulation I get a distribution of yearly totals:
The mean result is just a shade over 4,000 KWh. I've shown the one, two, and three-sigma regions with decreasing shades of grey. The 2016 total, 4,131 KWh, is well past one sigma, and close to the two sigma value. This indicates that 2016 was indeed a fairly good solar year!
How realistic is this simulation method? 2014 is missing all of January and part of February. In 2015 and 2016, January averaged about 220 KWh. If we take the mean value from simulations of 4,000 KWh, and subtract off 220 KWh, we get 3,780 KWh, which is almost exactly what was recorded for 2014. This is a good piece of evidence that the method might have some validity.
The simulations suggest that 2014 was a normal solar year, and that 2015 (at 3,817 KWh) was a particularly poor solar year. In fact, 2015 was a much worse solar year than 2016 was a good year according to the distributions of simulations.
I've put all the code here for your inspection. I didn't present it here, but in the code I explored a modification to the simulation method that added some "stickiness" to the choice of historical weather performance. My thought was that because day to day weather is highly correlated (tomorrow's weather is most likely similar to today's), enforcing some favoritism to stringing together days that actually were sequential might be more realistic. TL;DR: I get almost identical results at the expense of much slower simulations.
Finally, a happy new year to all of you!