Worked example · UPS / Battery Autonomy · Energy method

The 3000 Wh Trap — One Energy Method, One Covered Bank, One That Falls Short

3000 Wh of output is not 3000 Wh of battery. The same energy method walked both ways: a 60 Ah bank that clears a 30-minute duty at 236% of the need, and a 150 Ah bank that misses a 3-hour duty by 44.8 Ah. A worked demonstration of the method, not a specific site installation.

Published 2026-08-01 · EI Portal

3000 Wh of output is not 3000 Wh of battery. The inverter loses a slice of every watt-hour on the way out, and the depth-of-discharge limit stops you spending the whole bank — so the battery must always be bigger than the load's energy, by exactly those two factors. Here is the trap worked through both ways on the same method: one bank that clears its duty comfortably, and one that looks generous and still falls short.

The method

Every number below comes from one energy balance:

output energy Wh  = load W × runtime hours
      base battery Wh   = output Wh / inverter efficiency / allowable depth of discharge
      recommended Ah    = base battery Wh × (1 + margin) / DC bus voltage
      estimated runtime = selected Ah × DC bus voltage × DOD × efficiency / load W
      

with usable energy = nominal × DOD × efficiency. The verdict compares the selected bank against the requirement and returns "Autonomy covered", "Tight on margin" or "Below autonomy".

Case 1 — the 6 kW critical load (covered)

A small UPS critical load: 6 kW at power factor 0.9 (6.67 kVA), 30 min runtime target, 192 V DC bus, 92% inverter efficiency, 80% allowable DOD, 20% design margin — and a 60 Ah bank selected.

The chain:

• Output energy: 6 kW × 0.5 h = 3000 Wh
• ÷ 0.92 inverter efficiency → 3261 Wh
• ÷ 0.80 depth of discharge → 4076 Wh base battery energy
• • 20% margin → 4891 Wh
• ÷ 192 V → 21.23 Ah base required · 25.48 Ah recommended

Note the trap already sprung: 3000 Wh of output became 4076 Wh of battery before margin was applied. Run the balance backwards for the selected bank — drawing 33.97 A from the DC bus:

Estimated runtime 84.79 min (about 1.41 h) against a 30-minute target. Verdict: "Autonomy covered" — the 60 Ah selection is 236% of the margin-adjusted need, with 34.5 Ah spare.

The knife edge

Hold every input and shrink only the selected bank, and the verdict walks through all three states:

• 25 Ah → "Tight on margin" — it covers the 21.23 Ah base requirement, but not the margin
• 21 Ah → "Below autonomy" — below the base requirement itself

The boundaries are exact: covered at 25.48 Ah and above, below autonomy under 21.23 Ah. The middle state exists so a marginal pass never reads as a confident one.

Case 2 — the extended-runtime review (below autonomy)

Now the same method on a long duty: 4 kW load, 180 min runtime target, 120 V DC bus, 88% inverter efficiency, 70% allowable DOD, 20% design margin — and a 150 Ah bank selected. That bank is two and a half times the size of Case 1's, against a load two-thirds as large. It looks generous.

It isn't:

Base requirement 162 Ah · recommended 195 Ah. Estimated runtime 2.77 h against the 3.00 h target — −44.8 Ah spare, the selection covering only 77% of the margin-adjusted need. Verdict: "Below autonomy".

Three hours of load pulled through an 88% inverter and a 70% DOD limit on a low-voltage bus is a lot of nominal capacity — and the same losses that inflated Case 1's requirement by a third here open a gap a big round number cannot close. Divide the load into the nameplate Ah and this bank passes; run the energy method and it misses the target by about a quarter of an hour.

The lesson

Nameplate Ah is not usable energy. The energy method takes the duty down through efficiency and depth of discharge to the battery you must buy, then back up to the runtime a chosen bank actually delivers — and the two directions catch different failures. A bank can be triple the "obvious" size and still read "Below autonomy". Check both ways before you commit, in the UPS / Battery Autonomy Basic Sizing tool — the method itself is unpacked in the companion article.

This is a preliminary energy-method check, not a full battery design. Discharge-rate (Peukert) effects, temperature, ageing, end-of-discharge voltage, real runtime curves and UPS overload capability are not modelled; full sizing to IEEE 485 (vented lead-acid) / IEEE 1184 (UPS) additionally applies a discharge-rate/temperature (Kt) correction the energy method deliberately omits. Ah is the nominal bank capacity at the entered DC bus voltage — series/parallel arrangement is not modelled — and the final selection is confirmed against manufacturer runtime curves.