Lead-Acid Battery Life & Usage

In designing battery bank systems with lead-acid batteries, the issue of cost comes up frequently.  It is sometimes difficult to convey to users the tradeoffs involved in designing a lead-acid battery bank system.  For that reason, some type of simplified model that is relatively easily understood may be helpful.

 First Some Caveats:

 

1. Efficiency: While batteries usually have a high (abt. 95%) ampere-hour efficiency if not on float or being equalized (During these times their efficiency is effectively zero.), because charging voltage is higher than discharge voltage, their energy efficiency is typically 70% - 80%.
2. Capacity:  The capacity of a battery depends on rate of discharge AND temperature.  Generally a lead-acid battery will have higher capacity at a higher temperature, AND may have a very low capacity at low temperatures.  Nickel-Cadmium batteries have a significantly lower ampere-hour efficiency.
3. Manufacturers’ Test Conditions:  The way a manufacture defines depth of discharge (DOD) and the way cycle life is tested and defined differ between manufacturers and may be different from conditions expected in use.  Generally, a manufacturers’ cycle lifetime should be derated by 20% or so (80% of mfg. rating) to arrive at a reasonable expectation of field service life.  Since low temperatures reduce battery capacity – and hence increase depth of discharge for a given load – they will reduce cycle limited battery lifetime.
4. Float Life:  The ideal condition for a lead-acid battery is to be maintained fully charged and have no discharge cycles.  Even under these conditions, corrosion will take place continuously at a rate determined by construction and temperature.  The “float life” is the longest the battery may reasonably be expected to remain in service at a given temperature.  The rule-of-thumb is that lifetime is cut in half for each 10 deg. C (18 deg. F) above the specification temperature.  Obviously lead-acid batteries should not be kept at higher than necessary temperatures if the float lifetime limit is likely to be a consideration.

 

In what follows, I will assume that the battery lifetime will be determined by cycle lifetime and not float lifetime.  In any given application, it should be determined if cycle lifetime for the battery specified is adequate.

 

The Total Lifetime Ampere-Hour Model:

 

The simplest model of lead-acid lifetime that has any reasonable validity that I know of is the total lifetime ampere-hour model.  This model simply states that a given model of battery will need to be replaced after it has supplied a certain total number of ampere-hours in discharge.

 

Put another way, the lifetime is inversely proportional to the repeated depth of discharge, i.e. a battery cycled at 5% of capacity will last twice as long as one cycled at 10% of capacity and four times as long as one cycled at 20% of capacity.

 

Considering the 25% or so tolerance in manufacturers’ battery specifications, this is not too bad a model if interpreted with a certain amount of intelligence and understanding of its limitations.

 

Cautionary example: A battery fully discharged and left idle, or worse, allowed to freeze – is a goner.  End of story.  Also, expecting infinite life of a battery maintained fully charged is optimistic – although well maintained lead-acid batteries have held capacity more than ten years.

 

So, accepting the limitations, what are the implications of this simplified model?

 

Assume that we use the battery each time for, let us say, “X” ampere-hours.  Assume the battery has total ampere-hour life of “Y,” and each battery costs “$Z.”

 

Then the cost of each use will be “(Z * X/Y).” Note that the depth of discharge and the rated ampere-hour capacity of the battery have apparently disappeared. They often reappear when you consult the manufacturers’ tables and see the ratings in terms of depth of discharge and lifetime in cycles.

 

Also, notice that the capacity of the installed battery bank has really disappeared.  That is, a battery bank costing twice as much, with twice the capacity, will last twice as long and be replaced half as frequently, leading to the approximate same cost per use..

 

Obviously, trying to get more than 100% of capacity from a battery is impractical, so this analysis should be used with caution.

 

Example: A “T-105” battery at about 225 Ampere-Hour capacity has an expected life of 5500 10% discharge cycles or 225 X 5500 = 123,750 AH total lifetime capacity at a cost of about $60. At 6 V nominal, this is 743 kWh lifetime capacity or about 8 cents per kWh used.

 

Sealed batteries: Those trying to minimize maintenance should be warned that sealed lead-acid batteries cost about three times as much as equivalent capacity flooded batteries and last about one-half as long.

Return to Solar Resources

 

Alternative Energy Technologies