math :: finding battery SOC

Knowing how much energy is left in the batteries is the most important bit of day-to-day information needed to run the off-grid system. The first calculation needed is the maximum capacity of the batteries. Because information was limited on the Energizer (Johnson Control) 6V golf cart battery, I used the specifications from a comparable Trojan battery to make my calculations.

Trojan also has a wonderful guide to battery maintenance: http://www.trojanbattery.com/Tech-Support/BatteryMaintenance.aspx. I assembled the information from their battery maintenance section into a pdf titled Batteries Care that is kept at the cabin in a binder. I started a binder originally so the most important parts of the inverter manual could be quickly referenced, and eventually it grew into an all-encompassing reference manual for all the components of the off-grid system, including maintenance.

CALCULATIONS: Total battery bank capacity:

225 Ah (at 20 hr discharge rate) x 14 batteries = 3150 Amphours

3150 Amphours x 6 Volts = 18900 Watts (DC)

18900 Watts x 85% efficiency of inverter (DC to AC conversion) = 16065 useable 120 VAC Watts

Since it is undesirable to drain a battery 100% it was decided that we should recharge at 50% SOC (state of charge) ideally and 30% if needed.

16065 AC Watts x 50% discharge = 8032.5 useable Watts

16065 AC Watts x 70% discharge (30% SOC remaining) = 11245.5 useable Watts

Assumptions: in order for the estimates to be exact (which is impossible) the following would need to be true:

• batteries have exactly 225 AH capacity
• 6V from each battery is constant throughout the entire discharge of the battery
• the inverter always operates at 85% efficiency
• there are no internal changes in resistance under different discharge rates of the batteries (a 1000 watt load would have to use exactly the same amount of energy in 1 hour as a 100 watt load in 10 hours).

All these assumptions will vary. At best, these calculations are a little better than a best guess.

TEMPERATURE AND BATTERIES

Temperature does some funny things to lead acid batteries. At 80°F (the temperature most batteries are rated at) a fully charged battery my read 12.7 V under no load conditions. At 30°F that same battery may read the same, or lower. Not a lot of difference. The real fun begins when we try to estimate the SOC of the battery bank when a load is applied.

Most of the time we use about 300 Watts in the cabin – primarily for lighting, fans, 26″ LCD TV, laptop charger, and any appliances that are plugged in drawing phantom loads. When our system is 95% charged under a 300 Watt load at 80°F the control panel will read 12.5V. Under the same conditions at 30°F it will read 12.1V. Normally we would recharge the bank as soon as we drop to 12V. However, at 12V @ 30°F the bank is actually SOC 90%. Why does this happen?

To understand why the voltage drops disproportionally at different temperatures under the same 300 Watt load I’ll use oil as an analogy. At 80°F oil will flow through a funnel quite quickly, but at 30°F the oil will be much thicker and flow much slower. Pouring one quart of oil will take more time at 30°F. Note that it takes longer for the oil to flow through the funnel but the amount of oil is the same – temperature does not lower the capacity of the batteries, it only slows down the chemical reaction that produces the flow of electricity. This decreased flow shows as a drop in voltage. This can be verified by taking specific gravity readings of the SOC at different temperatures while under a 300 Watt load.

In short – if a system has a voltage readout, it is important to account for the load (Watts used at a given point in time) that is most commonly used by the system. While a no-load voltage readout will almost always be more accurate, it is often not practical to turn off the system for 2 hours (ideal) and then take a voltage reading.