# Solar Coop – Update II

Since writing the first update on the solar panels on the chicken coop, we had quite the cold snap.  Along with the persistent cold, there was persistent cloud cover and strong winds.  The combination of cold weather meant the battery for the coop had diminished capacity and the cloud cover meant that there would not be enough solar irradiation to fill that reduced capacity.

Each night, I would disconnect the battery from the system and lug into the garage; connecting it to a battery charger for the night.  We also brought the chicken’s waterer into the house to prevent the need in the morning of having to thaw the water. In addition to the routine changes, I removed two things from the electrical-mix: the electric timer and the ammeter. With the battery’s stored energy being consumed so quickly and the water and battery being brought in at night, it did not seem like the timer was needed at all. The ammeter was removed because it stopped working in the sub-zero cold.  Subsequent tests, while it has been warmer outside, show that the meter still works; it just does not like the cold.

We have since made it through that cold spell, and have been in a pleasant middle ground of nice amounts of sun, above freezing day-time temperatures – several days in a row, and light amounts of wind.

With the warmer stint of weather, the battery has been under lighter duty. Even when the solar charge controller has been indicating that the battery is not strong enough to power the inverter, the next day’s sun will be more than enough to give the battery a good charge.

Being a curious, amateur scientist, I wanted to know a bit more about why a lead-acid battery appears to be quite poor at being able to provide energy when the ambient temperature is very low.  This inability to provide energy is quite noticeable and prevalent in colder regions during the winter.  For those who are familiar with starting a car while in the depths of a cold winter – think of how the car’s starter seems to struggle to turn the engine over.  It’s a battle between cold lubricants with a higher than normal viscosity and a lead acid starter battery with diminished capacity.  But, why does cold cause this diminished capacity.

With my day-job being at a university, and I am surrounded by academics and researchers, my first thought was to look into published research on batteries or modeling batteries.

The first paper I found was A mathematical model for lead-acid batteries co-authored by Dr. Ziyad Salameh – Dept. of Electrical Engineering, UMass Lowell, Margaret A. Casacca (student), and William A. Lynch (student).  The paper was published in the IEEE Transactions on Energy Conversion, Vol. 7, No.I, March 1992.

Aside from equations and a mention of a BASIC program that was developed (but this program is nowhere to be found in the paper), the main take aways from the paper are list of five factors that effect a battery’s ability to store energy; for the most part, the list of things is obvious.  (1) State of charge, (2) battery storage capacity, (3) rate of discharge, (4) environment temperature, and (5) shelf-life or age.

(This list is originally from the Complete Battery Book.)

We can say that our battery is fully charged (state of charge is 100% at the on set), has a capacity of 110 amp-hours, the waterer has a draw of at most 10 amps (this is likely not constant as the waterer will turn on when the water is below 35 degrees, and turn off when it reaches a temperature above this), the shelf-life or age is basically “brand new”.  Temperature is likely the deciding factor.

Looking at how temperature effects capacity, you can see that as the temperature drops, the capacity drops, as well.

Assuming this graph is true (there is no documentation or available analysis), at our coldest, the battery is likely to be running at a bit over 60% capacity; meaning, we’ll only get about 66ah from it.  The inverter will shut off when the voltage drops below about 12.10V; according to another battery university article, this likely means the battery has about 50% capacity remaining.  This could roughly be translated into a capacity of 33ah at our coldest, and about 55ah at optimal temperature (which we won’t have until sometime in late May).

Now that I have some numbers that better explain the observation of why didn’t the battery last more than 8 hours on the coldest day, I still want to know why does this happen.  Why does ambient cold have such an effect on lead-acid batteries?

The short answer is internal resistance.  To understand this, you first need to know a bit about how lead-acid batteries work.

A course offered at the University of Colorado Boulder‘s Electrical, Computer and Energy Engineering department has a great set of lecture slides (or here) explaining how lead-acid batteries work.

The gist of how lead-acid batteries work are electrons drifting or flowing from the negative terminal – most often made of lead ($$\ce{Pb}$$) – to the positive terminal – most often made of lead dioxide ($$\ce{PbO2}$$).  The two terminals are submerged in an electrolyte solution.  This is usually in the form of sulfuric acid ($$\ce{H2SO4}$$, where, in solution, it takes the form of aqueous ions $$\ce{{H^{+}}+{SO4^{-2}}}$$).  As you draw electricity from the battery via the positive terminal, electrons flow from the negative terminal to the positive terminal.  How easily or difficult the electrons can move from negative to positive terminals in the internal resistance.

I think of what happens with the electrolyte solution and effect of cold temperatures on it is sort of like what happens to honey when it is chilled.  It is not quite analogous but I think it gets the point across.  If little droplets of honey are running down a piece of glass and you suddenly cool the glass, the honey will begin to run much slower.

Similarly, as the electrolyte solution cools, the ability for electrons to drift efficiently to the positive terminal decreases.  The decrease in electron flow results in less power to be consumed – in our case, by the inverter and waterer.