Estimation of a

Manufacturers normally advertise solar batteries by their so-called

- Capacity is not constant-- it varies with the load and temperature;
- Batteries are practically never discharged at a constant current.

Most often, the capacity is specified for 20-hour discharge (denoted by C/20). The consumers often do not realize that this quantity is not constant. For example, if a model is rated (say) for 100 Ah at C/20, this means it can supply 100/20=5 amps current for 20 hours. However, if you draw (say) 50 A, this battery may provide a backup only for a little more than one hour. The rule is, the faster the discharge the less actual amp-hours. Some lead acid batteries discharged in one hour provide only about 50% of their listed C/20 Ah ratings. Similarly, the runtime of uninterruptible power supplies (UPS) is usually given at half-load. At full load, they would typically run only 1/3 of their published time rather than ½.

A relationship between the amp-hours and discharge current is given by an empirical Peukert law. It states that:

Some guides mistakenly say that the constant in the above equation is a capacity. It is not. We define the capacity as I×t. Only when I=1 amp, Peukert constant numerically equals to capacity. Since the manufacturers rarely specify it, how do we find battery life

t= I

If we denote known capacity at a rated time t

This formula lets you calculate a battery life

For example, Deka gel model 8G4D lists 169 Ah at 10 hr and 183 Ah at 20 hr. Then:

K=1 + [Log (183/169)] / [Log (169×20/183×10)]=1.13.

At 100 A load this model will run for (169/10)

So far we were considering discharge at a fixed current. In reality, there are three main reasons why a load always varies:

- Inverter produces AC output. Although its internal capacitors deliver a portion of AC current, the remaining portion is drawn from the input source.
- Motor-driven appliances (refrigerators, air conditioners) are periodically cycling on and off.
- Inverter regulates its output voltage. For a given load it supplies constant power. As battery is discharging its voltage gradually drops. As the result, inverter draws more current to meet the power demand.

So, what value of the current should we use in Peukert equation? The best thing you can do is use in the calculations average current based on average power. Let the loads in your home which you want to backup consume in average P watts, the battery initial terminal voltage is Vo and the cutoff voltage is Voff. Then use average current

The calculator to the right lets you estimate the run time of a fully charged battery. If you don’t know its cutoff voltage, assume it is 0.9 of nominal. Normally, 12V models are fully discharged at 10.5V. If you don’t know K, use the following typical values for different technologies: flooded lead-acid: 1.2-1.4; absorbed glass mat (AGM): 1.05-1.2; gel: 1.1-1.25. Note that these numbers may increase with the device age.

Let's now solve a reverse task. Suppose you know your load wattage

Of course, to prolong the battery life cycle you don't want to discharge it more than 50-80%. So, ideally, when you are sizing your battery bank, you should double the result obtained from the above formula.