April showers were in May

May is out, and there are some new solar power stats to talk about.  Here is the usual plot of the sunniest day (as determined by total power generation) of each month so far:

The horizontal time axis runs from 3:00am to 9:00pm GMT (no correction for summer time: this is all sun time!). The vertical axis runs from zero to 8kW.  The black line is the generation on the particular day.  The orange regions indicate the minimum, lower quartile, median, upper quartile, and maximum generation at that time, over the respective month.

The total power generated on the sunniest day each month (essentially sunny all day) was 26.5 kWh on 13th January, 41.4 kWh on 16th February, 52.0 kWh on 24th March, 55.9 kWh on 16th April, and 54.5 kWh on 15 May.

The May plot is noticeably broader than the April plot, thanks to the longer days.  Despite this, on the sunniest day in May, we generated less power than on the sunniest day in April: May was a pretty rainy month, and even the sunniest day had a partially cloudy afternoon.

We can visualise the distribution of daily power generation for each month, using a violin plot for each month.  A “violin” has two parts:

First is a notched box and whisker plot: the box shows the inter-quartile range, with the horizontal midline line showing the median, and the notches showing an approximate 95% confidence interval for the true median; the whiskers show all the data that is within 1.5 × IQR above or below the relevant quartile; any outliers are shown as spot markers.  In general:

Secondly, this is combined with a kernel density plot, which is essentially a smoothed probability distribution plot.

These show that our power generation distribution is unimodal for each month: there are some dull days, some sunny days, but mostly intermediate days.  Median and mean generation increase significantly from January until April, but April is not significantly different from May.

This is in contrast to the rainfall data we have been gathering: there several of the monthly figures are bimodal.

Violin plots are excellent for showing a lot of statistical information in one go: specific quartiles, plus overall distribution.  They are also easy to plot in Python: I slightly modified the function posted by Flavio Coelho to draw these plots, making some cosmetic changes, and including the mean.

So now we are in June, with the longest day coming soon.  Will this result in the maximum generation, or will we get the sunniest day in some other month?