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Standard UPS/battery sizing relations9 min read

Worked Example: Sizing a Redundant (N+1) UPS System and Its Battery Runtime

A 200 kW critical load, sized to a standard UPS frame with full N+1 redundancy — plus how much battery energy a 15-minute ride-through actually needs.

Scenario

Critical load200 kW at 0.9 power factor
Design margin20%
Redundancy2 UPS frames, N+1 (either one can carry the full load alone)
UPS rated output PF0.9
Required backup time15 minutes
Battery depth of discharge / inverter efficiency80% / 92%
DC bus voltage480 V

Step-by-step calculation

Step 1: Convert critical load to kVA and apply design margin

designLoadKva = kW / PF marginedLoad = designLoadKva x (1 + margin%)
200 / 0.9 = 222.2 kVA; 222.2 x 1.20
marginedLoad = 266.7 kVA

Step 2: Find per-unit required capacity for N+1 redundancy

With 2 frames installed and N+1 redundancy, either frame alone must carry the full margined load.

perUnitRequired = marginedLoad / (N - 1)
266.7 / 1
perUnitRequired = 266.7 kVA per frame

Step 3: Round up to a standard UPS frame size

Step 4: Compute usable battery energy for the required backup time

usableEnergy = loadKw x (backupMinutes / 60)
200 x (15 / 60)
usableEnergy = 50 kWh

Step 5: Convert to nameplate battery energy and approximate Ah

nameplateEnergy = usableEnergy / (DoD x inverterEff) Ah ≈ (nameplateEnergy x 1000) / DCvoltage
50 / (0.80 x 0.92) = 67.9 kWh; 67,935 / 480
nameplateEnergy = 67.9 kWh, ≈141.5 Ah at 480 V DC

Result summary

CheckRequirementActualStatus
Recommended UPS frame sizen/a (this is the sizing result)300 kVA (270 kW) per frame, 2 frames installed✓ PASS
Battery nameplate energyn/a (this is the sizing result)67.9 kWh (≈141.5 Ah at 480 V)✓ PASS
Full N+1 redundancy for this 200 kW load requires two 300 kVA UPS frames (600 kVA installed to reliably deliver 266.7 kVA), each backed by roughly 68 kWh of nameplate battery energy to bridge 15 minutes.

Key insight: Depth of discharge and inverter efficiency both shrink usable energy relative to nameplate battery capacity — a battery can't be discharged to 0% DoD without damage, and DC-to-AC conversion isn't lossless, so the nameplate battery has to be meaningfully larger (67.9 kWh here) than the 50 kWh the load actually needs, purely to account for those two real-world losses.

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Frequently asked questions

Why does N+1 redundancy here mean each unit carries the full load, not half?

N+1 specifically means N units are needed to carry the load, plus 1 spare — with N=1 required unit and 1 spare (2 total installed), each individual frame has to be sized for the full margined load, since either one must be able to run the entire critical load alone if the other fails or is taken down for maintenance. This is the same underlying principle as the N-1 redundancy convention used in the Transformer Sizer calculator, just phrased from the opposite direction (N+1 installed vs. N-1 surviving).

Is this battery estimate as rigorous as the dedicated Battery & DC System Sizing calculator?

No — this is explicitly a quick sizing estimate (usable energy = load x time, then correcting for DoD and efficiency), not a full IEEE 485 duty-cycle section-by-section design. For a final battery specification, especially one with a varying load profile rather than one constant load for the whole backup period, the dedicated Battery & DC System Sizing calculator's full method should be used instead.

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