Monday, 2 June 2014

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?


  1. Here's data from our 3.75kW array in Berkshire, from March 2012 (from my daily data spreadsheet) . You can see that August was the peak month in Olympic year (when it rained a lot in the Summer), while July 2013 was our best month to date. It's interesting to compare and contrast your data with ours, but feel free to edit/delete this post if you don't feel it's relevant. Regards, markv.

    per day Month per month
    11.61 March 360.01
    10.63 April 318.90
    12.63 May 391.56
    11.54 June 346.29
    12.40 July 384.50
    12.85 August 398.43
    12.16 September 364.72
    6.09 October 188.83
    4.75 November 142.49
    3.35 December 103.99
    2.36 January 73.20
    5.03 February 140.97
    5.97 March 185.05
    12.88 April 386.42
    13.03 May 403.97
    13.78 June 413.37
    16.58 July 513.86
    13.84 August 428.97
    9.17 September 275.10
    6.16 October 190.91
    4.87 November 146.06
    2.99 December 92.81
    3.95 January 122.44
    6.83 February 191.29
    10.94 March 339.10
    11.41 April 342.39
    12.66 May 392.51

    1. Thanks for your data, Mark. It looks like we may be fairly close to peak production, then, unless it's a very sunny summer! Even so, I think we are now nett producers.