Battery runtime under a constant load

How stored kilowatt-hours, a lossy inverter and a steady load become a clock

Energy over power is time: that is the whole relation, and its honesty lives in which energy figure goes on top. The numerator is USABLE capacity — nameplate already discounted by the depth of discharge on the previous page — so a runtime computed from the label instead inherits an optimism of exactly the held-back fraction, which for some chemistries is half the battery.

The efficiency term concedes that stored direct current does not reach an appliance intact. Inversion to alternating current, conversion electronics and cable resistance each take a share, and the factor multiplies the energy DOWN before the load divides it. It is a discharge-path figure, distinct from the round-trip efficiency this pack treats in its own sibling — that one also counts the losses of putting energy in, which no discharge clock should be charged for.

A constant load is the idealisation that makes runtime a division. Real households duty-cycle — compressors start and stop, heaters cut in and out — so the honest entry is the time-AVERAGED power of the circuit over the window, which a meter or an energy audit supplies. Peaks matter to a different budget entirely: the inverter’s continuous and surge ratings, which this pack sizes in two dedicated siblings, decide whether the load can run at all, while this page decides only for how long.

The pack declares the reverse workflow, and here it is the practical direction: fix the hours an outage plan must survive, and the engine returns the steady load the bank can afford to carry for them. That number, set against the household’s appliance list, is load-shedding turned from a vague intention into an explicit power budget.

When this calculation is used

• Outage planning: the hours the essential circuit survives on the bank as actually installed and configured.
• Deciding what stays on — the declared reverse workflow returns the power budget a required runtime imposes, appliance by appliance.
• Screening backup for equipment that must ride through interruptions, where the required duration is known and fixed in advance.
• Checking a vendor’s runtime claim by recomputing it from the same datasheet’s usable capacity and conversion efficiency.

Worked example

Run the pack’s anchor duty: a small backup bank holding 5 kWh of usable energy, a discharge path at 0.8 efficiency, carrying a steady 0.4 kW of essentials — roughly a refrigerator, a router and a room of lights.

The engine returns the runtime in hours. Read it against two horizons: the outages the local grid actually produces, and the recharge that ends the episode — a solar recharge arriving next morning asks far less of the bank than a multi-day storm, which is the autonomy question the first page of this cluster sizes for. If the hours fall short, the reverse workflow says how much load must go; the sizing page says how much bank must come.

Now add one more appliance and watch the clock shrink in inverse proportion — doubling the load halves the hours, with no economy of scale to soften it. Runtime is the budget that makes load-shedding discipline visible.

What each input represents

Assumptions and limits

• The load is constant for the whole window; a duty-cycling circuit is represented only as well as its time-averaged power represents it.
• Efficiency is one fixed fraction, although real inverters convert less efficiently at light load than near their rated point.
• The usable energy is taken as fully deliverable regardless of discharge rate — no rate-dependent capacity effect is modelled here.
• Temperature is not consulted: a cold bank delivers fewer hours than its rating suggests, and this pack carries a temperature-derated runtime sibling for exactly that.

What the guards protect against

• A zero load is refused — the pack ships that refusal as a declared test vector. With nothing drawing power the division has no finite answer, and an infinite runtime is not a result any backup plan can use; the refusal surfaces the modelling gap instead.
• The efficiency must lie strictly between zero and one: a lossless discharge path does not exist, and the same ceiling catches a percentage entered where a decimal fraction belongs before it multiplies the hours a hundredfold.
• The usable capacity must be positive and below a utility-scale cap, so a watt-hour figure entered as kilowatt-hours — a thousandfold slip — is refused as a unit error rather than returned as a runtime measured in weeks.

Provenance

Constant-load runtime relation, hours = usable kWh × efficiency / load kW

The usable battery capacity is multiplied by the discharge-path efficiency and divided by the constant load, returning the runtime in hours; the declared reverse workflow solves for the load a required runtime permits.

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.