From load profile to defensible capacity: sizing a cell site battery

The naive calculation is load in amps multiplied by required hours. It produces a number, the number is always too small, and everyone in the industry knows this, which is why the naive answer is usually followed by an arbitrary safety factor.

The arbitrary factor is the problem. It is either too small, in which case the site does not meet its runtime, or too large, in which case you have bought capacity and enclosure you did not need. Neither is defensible in a review because neither can be traced to a reason.

Here is a sequence that can be.

Step 1: establish the real load

Not the radio load. The load.

Every item drawing from the DC plant during an outage belongs in this number: transmission equipment, monitoring, alarms, environmental controls if they stay powered, lighting if it stays powered, and any equipment a different team installed after the original design.

The most common sizing error is not a mathematical one. It is a load inventory that was accurate three years ago.

If the plant meters DC current, use the measured figure rather than the sum of the nameplate ratings — nameplate sums typically overstate real draw significantly, and using them inflates everything downstream.

Step 2: state where the runtime requirement comes from

A runtime requirement should have a stated origin. In practice it is one of:

• The time for a generator to start and take load, plus margin for a failed first start
• A contractual availability or SLA obligation
• The realistic worst-case time to get a technician on site, which is a function of access, weather, and staffing rather than of distance

Write down which one it is. When someone later asks why the site is sized for eight hours rather than four, the answer needs to be a reason and not a habit.

Step 3: convert to amp-hours at the correct discharge rate

This is where lead-acid catches people. Battery capacity is quoted at a specified rate, commonly a 10 or 20 hour rate. The available capacity at a shorter, higher-current discharge is materially lower.

If your requirement is a short high-current backup and you size from a C10 or C20 figure, you will not get the runtime. Use the manufacturer's discharge data at your actual rate — the tables or curves, not the headline number.

LFP is much flatter in this respect and holds a large fraction of its rated capacity at higher rates, but it is not rate-independent either. Use the data at your rate for whichever chemistry you are evaluating.

Step 4: fix the end-of-discharge voltage before you calculate

Usable capacity is defined by where you stop, and where you stop is set by the lowest voltage your load will accept, with the string's voltage drop included.

A 48 volt nominal system that must not drop below a specified equipment cutoff has a different usable capacity than one with more headroom. Decide the cutoff first. It is an input, not a result.

Step 5: apply the derates, and apply them multiplicatively

Four independent effects reduce what you can count on. They compound rather than adding:

1. Temperature. Capacity is reduced at low temperature, and the reduction is significant well before freezing. Size for the coldest temperature at which you require full runtime, not the annual average. Note that this pulls in the opposite direction from the life derate discussed below.
2. End of life. A battery is conventionally considered to have reached the end of its service life at a defined fraction of rated capacity, commonly 80 percent. If the site must still meet its runtime requirement on the day the string is replaced, size against the end-of-life capacity, not the new capacity. Sizing to new capacity guarantees the site is out of specification for most of the battery's life.
3. Depth of discharge. For lead-acid in particular, planning to routinely take the string to full discharge shortens life sharply. The planned depth of discharge is a design decision that consumes nameplate capacity.
4. Aging and manufacturing spread within the string. The string performs as its weakest block, not as the average of its blocks.

Applying these in sequence produces a required nameplate capacity with four traceable reasons attached to it. That is the difference between a sized system and a guessed one.

Step 6: check the charge side, which is routinely forgotten

A correctly sized battery that cannot be recharged in time is not correctly sized.

After an outage the plant has to restore the string before the next event, while still carrying the site load. If outages at the site cluster — as they do during storms — the recharge time is part of the availability calculation, and the rectifier capacity is part of the design.

For lithium there is an additional constraint: charging below freezing causes permanent damage, so a cold site needs either thermal provision or charge management that will refuse to charge. Either way, the recharge window in cold conditions is not the same as the recharge window on the bench.

Where the rules of thumb stop working

The standard approach degrades in four situations, and these are the ones worth a conversation rather than a spreadsheet:

• Short, very high rate backup, where rate effects dominate everything else
• Wide temperature swings, where the cold-capacity derate and the hot-life derate pull in opposite directions and there is no single conservative choice
• Partial state of charge cycling, where the string rarely returns to full and lead-acid in particular accumulates damage that no capacity calculation will show you
• Frequent shallow outages, where cycle count rather than autonomy is the variable that determines replacement interval

What a defensible sizing document contains

If your sizing can be reviewed by a third party without a conversation, it contains: the measured load and how it was measured, the runtime requirement and its origin, the discharge rate used and the source of the capacity data at that rate, the end-of-discharge voltage and what set it, each derate with its value and its justification, and the recharge calculation.

That is about one page. It survives review, it survives a change of personnel, and it survives the site being audited three years later.

If you have a load profile and a runtime requirement and want the arithmetic checked before it goes into a document, that is a fifteen minute call.