Battery bank size from load and autonomy

Why a bank is sized on the energy it may surrender, not the energy it stores

Autonomy is the design storm of storage: the number of consecutive days the bank alone carries the load, with the array clouded over, the generator down, or the grid simply absent. Multiplying the daily load by the autonomy days gives the energy that must be DRAWN during that window — not the energy the bank must merely contain, which is a larger number for a reason the third term supplies.

The depth of discharge sits in the denominator because a bank is never run to empty by design. Every chemistry pays for deep cycling in service life, so the designer chooses a fraction of the capacity that may be surrendered and holds the rest in reserve. Dividing by that fraction inflates the nameplate until its usable slice, on its own, covers the whole autonomy demand — a deliberate oversizing that plays the same role the performance ratio plays in sizing a solar array.

The answer is a nameplate in kilowatt-hours: the label figure banks are quoted, priced and compared on. It is a usable-basis screening size, not a shopping list — turning it into amp-hours at a system voltage, into series and parallel strings, and into whole modules is the work of this pack’s conversion and string-count siblings, and each of those steps rounds the bank upwards a little more.

Read the structure before the values. The relation is linear in load and in autonomy — a second day of protection costs exactly one more day of energy — but hyperbolic in depth of discharge, so moving to a chemistry cycled only half as deep doubles the bank outright. The pack also declares the reverse workflow: fix a bank already owned or quoted, and the engine returns the days of autonomy it can honestly promise.

When this calculation is used

• Sizing storage for an off-grid dwelling, where the bank must bridge the run of sunless days the site’s climate makes likely.
• Specifying backup for grid outages, where autonomy is set by the longest interruption worth designing against rather than by weather.
• Solving backwards — the declared reverse workflow — for the days a bank already installed or quoted can actually carry the household.
• Comparing chemistries on equal terms: rerun with each candidate’s rated depth of discharge and watch what the same autonomy demands.

Worked example

Take the duty this pack uses as its own anchor: a cabin drawing 10 kWh in a typical day, required to ride through 2 full days with nothing recharging the bank, on a chemistry operated at a 0.8 depth of discharge.

The figure that returns is the nameplate bank size, in kilowatt-hours, whose permitted slice covers the whole two-day demand. It is the number the rest of this cluster follows: the usable-capacity page shows what fraction of it a load may actually touch, the runtime page turns that fraction into hours against a real load, and the cycle-cost page prices every kilowatt-hour that will ever pass through it. Read it as a screening size to set against budget and floor space, not a completed design.

Now halve the depth of discharge, as a conservatively cycled lead-acid duty would demand. The nameplate doubles while the load and the weather stay exactly as they were — autonomy is priced in chemistry as much as in kilowatt-hours.

What each input represents

Assumptions and limits

• The daily load is a flat average across the autonomy window; a storm that darkens the sky also tends to lengthen heating or pumping runtimes, and no such correlation is modelled.
• No charging occurs during the window at all. Any solar contribution on a merely dull day shortens the real requirement, so the sizing is deliberately pessimistic in that direction.
• The depth of discharge is one constant. Temperature derating, ageing fade and rate effects all shrink what a real bank yields, and each has its own sibling calculator in this pack.
• Conversion losses on the discharge path are not deducted here — the runtime page carries the efficiency term — and nothing in an energy sizing speaks to peak power or inverter rating.

What the guards protect against

• A depth of discharge above one is refused — the pack ships that refusal as a declared test vector. A fraction cannot exceed unity, and the ceiling catches the commonest slip of entering a percentage where a decimal belongs, which would otherwise shrink the bank by two orders of magnitude.
• The daily load must be positive and below a utility-scale cap. A zero load has no bank to size, and a figure beyond the cap is far more likely a monthly or annual total entered as a daily one than a real household.
• Autonomy is bounded to a band measured in days, not seasons: a figure entered in hours, or a wish for a whole winter of storage, falls outside the declared range and is refused as a unit or scoping error rather than sized in silence.

Provenance

Usable-basis autonomy sizing, bank kWh = daily load × autonomy days / depth of discharge

The daily energy load is multiplied by the required days of autonomy and divided by the depth-of-discharge fraction, returning the nameplate bank size in kilowatt-hours; the declared reverse workflow solves for the autonomy a fixed bank size supports.

Screening and reference material, to be checked against the governing standard and a qualified engineer; not a design determination. The signed pack carries its own citation, and the page reports the verification state of the release it mounted.