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TOPIC-04 · Engineering guide

UPS Sizing Versus Battery Runtime

UPS sizing and runtime answer different questions. This fixture needs 1080 W and 1200 VA. Usable energy is 3840 Wh, battery-side power is 1000 W, and runtime is 3.84 hours.

Formula, variables and conditions

P = sum(watts × quantity)
S = sum(watts × quantity / pf)
Required watts and volt-amperes apply the margin once.
E = V × Ah × (socStart − socEnd) × soh
Pbattery = P / efficiency + idle
runtime = E / Pbattery

Variables and units

  • Margin: fraction from 0 to 1, applied once to both watts and volt-amperes.
  • V and Ah: nominal battery voltage and ampere-hours.
  • socStart, socEnd, soh: fractions. Ending state of charge cannot exceed the start. State of health is greater than 0 and at most 1.
  • efficiency: greater than 0 and at most 1. Idle power is in watts and may be 0.

Conditions

  • CASE-004 and the UPS runtime teaching case use this same TC-018 input. There is no second measured scenario.
  • Efficiency is not multiplied into E. The battery-runtime calculator does the opposite: it multiplies efficiency into energy and divides by the AC load.
  • SRC-010 is the project model. Its calculation-record URL is null. It is not a manufacturer runtime curve.

Worked example

One load, quantity 1, idle 0 W. Constant voltage and constant load.

Load
900 W at power factor 0.9
Margin
0.2
Required capacity
1080 W and 1200 VA
Battery window
48 V, 100 Ah, state of charge 1 to 0.2, state of health 1
Efficiency
0.9
Energy / battery power / runtime
3840 Wh / 1000 W / 3.84 hours

E = 48 × 100 × 0.8 = 3840 Wh. Battery power = 900 / 0.9 = 1000 W. Runtime = 3840 / 1000 = 3.84 hours. Apparent power before margin is 900 / 0.9 = 1000 VA, then 1000 × 1.2 = 1200 VA.

Boundaries and common mistakes

Boundaries

  • No Peukert effect, chemistry, temperature, BMS limit or voltage cutoff.
  • Redundancy, transfer and protection coordination are not evaluated.
  • If you put these battery numbers into the battery-runtime calculator, efficiency multiplies the 3840 Wh and the load stays 900 W. That is a different estimate and is not this 3.84 hour result.

Common mistakes

  • Sizing only watts and forgetting volt-amperes when the power factor is below 1.
  • Applying the margin twice.
  • Putting UPS efficiency into the energy term and also dividing the load by efficiency.

Sources