How Much Battery Storage is Enough for Roof-Top Solar Panels?

Anyone that has read some of my blog postings is probably sick and tired of me beating the drum for energy storage.  To paraphrase John Lennon's aunt Mimi as quoted in Philip Norman's book "Shout" - "Energy Storage is all very well but I don't want it for breakfast, dinner and tea".  Just to make things clear I do realize that there are more important things in my life than energy storage.  The well-being of my family, the health of planet earth and, of course, world peace.  Having said that I am convinced that energy storage is at least as important as the latest Hollywood wardrobe malfunction - and look at how much exposure those things get!

But I digress.

What I thought would be very useful is an on-line tool that can calculate the amount of solar panels and associated battery storage that would be required to get partially or completely off the grid.  I wanted this to account for the expected solar insolation received at any point on earth for any given day.  Such a tool would allow someone contemplating installation of solar panels to try different scenarios and see which one produced the optimal energy management solution for their particular situation.

I looked around on the web and found a few tools but none that really did what I wanted (if someone knows of a tool please send me the URL).  So I decided to build one.  I didn't think it would be easy but I didn't quite understand the complexities involved.

The first thing I wanted to do was calculate the amount of insolation being received at an arbitrary location.  I graduated with a degree in Geophysics and early in my career I published a number of scientific papers.  For the most part big, hairy equations do not scare me ... much.  But when I looked at the spherical geometry equations used to accurately calculate solar insolation I was quickly ready to pack up my marbles and go home.  This game didn't look like it was going to be that much fun.

Luckily I found an extraordinary site sponsored by two professors from the Arizona State University (Stuart Bowden and Christiana Honsberg). This site is one of the true gems of the Internet and provides comprehensive information including some very effective graphical presentations that describe how solar energy is received and filtered on its journey from the sun to a solar panel. The "Silver Bullet" for me was the on-line solar insolation calculator which accounts for geographic location, time of day and time of year and orientation of a solar panel. I was able to use the Javascript function that is the work-horse of that calculator (based in part on work done at Plataforma Solar de Almerýa (PSA)) in both a modified version of the Insolation Calculator and also in my Residential Microgrid Calculator.   There are a few assumptions underlying these calculators that users should be aware of.

  1. The solar panel is assumed to be installed at the optimal tilt to provide the maximum solar power output averaged over a year. See Charles Landau's site for a complete discussion of this topic which is not as straightforward as you might expect.  It is easy to change the tilt angle in order to investigate the impacts on a particular day.
  2. The calculations assume a clear, perfectly sunny day with no passing clouds.
  3. The calculations assume continuous clear line of sight to the solar panels from sunrise to sunset.  In most urban settings this is unrealistic because of nearby trees, utility poles, buildings, or hills.


I decided that the best way to confirm that the calculations were working reasonably well was to determine sunrise and sunset by the first and last minutes when the equations generated insolation.  I chose March 21 as my test date which I assumed would have 12 hour days and nights and peak insolation at 12:00 noon.  That's when I found out how little I know about the basic interractions of this planet and the sun.

It turns out that our days are always a bit longer than a theoretical calculation would determine because of refraction of sunlight and the fact the sun is not a point but a disc.  As a result daylight lasts about 6 minutes longer at the equator and upwards of 20 minutes longer near the poles.  As a result my first light/last light approach matches the theoretical calculations on the PVEducation site but does not quite match the "actual" sunrise and sunset times available from sites such as the NOAA Sunrise/Sunset calculator. I plan on including a correction based upon a simple curve fitting exercise which does a pretty good job of estimating the extended daylight with the only input variable being lattitude.

It also turns out that days are not exactly 24 hours in length but vary slightly in length throughout the year according to the "Equation of Time". Luckily for me the PSA function handles that.

Once I was able to generate reasonable hourly insolation values for any place on earth the next step was to set up a mathematical "smart microgrid".  As depicted in the graphic above there are some decisions that have to be made and these have been coded into my on-line tool.

  1. If there is spare power available from the solar panels after satisfying the current load in the house then it can be used to charge the battery.  If the battery is fully charged (or if there is no battery) then the power can be sold into the grid.
  2. If there is not enough power available from the solar panels to satisfy the current load in the house then power can be drawn from the battery and failing that (or if there is no battery) power can be purchased from the grid.


The ebbs and flows of electricity between the household load, battery, and grid will depend upon the solar power available, the load pattern, and the capacity of the battery (if one has been installed).  The load pattern can be set in the tool by choosing a peak demand value and a load profile which will implement a predefined residential usage pattern.  However, most people will feel that the predefined usage pattern is not really applicable to them.  In order to handle that it is possible to enter an hourly load pattern either taken from smart meter readings or estimated in some other way.  Note that load patterns will probably vary a great deal between winter and summer.  I plan to add additional load profiles and allow for the storage of user-defined load profiles in a future release of the calculator.

The tool presents two sets of hourly calculations side by side with the default values being for June 21 and December 21 which will represent the best/worst cases for solar power production.  This also allows for easy comparison of two tilt angles or azimuth angles.

So that's it.  Hopefully these tools, like the many other excellent tools already available from PVEducation.org will be valuable as people try and learn more about how roof-top solar panels and a residential smart microgrid can used in combination to achieve a measure of energy independence.

At the end of the day these calculators are no better than the theoretical assumptions and mathematical equations they are based upon. So I would encourage you to give them a try and see if they match any real-world results you might have access to. I would be keen to hear from you - send email to toolsfeedback@debarel.com.


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