Worked Example: Stationary Battery Sizing for a 30-Minute UPS Backup per IEEE 1185

A commercial building requires a 48 V DC UPS system to provide 30 minutes of backup power for critical IT and communications loads. The battery bank must be sized to deliver the required power for the full backup duration while accounting for aging, temperature effects, and design margins.

This worked example follows the methodology of IEEE 1185:2019 — IEEE Recommended Practice for the Design of DC Auxiliary Power Systems for Generating Stations and general stationary battery sizing principles. The approach applies equally to VRLA (valve-regulated lead-acid) and VLA (vented lead-acid) technologies.

Battery sizing is fundamentally about ensuring sufficient ampere-hour capacity at end-of-life, at worst-case temperature, and at the minimum allowable cell voltage — all three conditions simultaneously.

The duty cycle describes the load profile over the backup period. In this case, the load is constant:

Duty Cycle Profile:
  Period 1: 0 to 30 min — 12 kW continuous

This is a single-period, constant-power duty cycle.
No momentary loads (motor starting, etc.) are present.

Total energy required:
  E = P × t = 12 kW × 0.5 h = 6.0 kWh

For more complex duty cycles (e.g., with momentary loads from motor starting or breaker operations), each period would be analysed separately and the most demanding period would govern the cell size. In this case the single continuous load simplifies the analysis.

The battery must deliver the required power at the minimum system voltage (end-of-discharge voltage), because this is when the current is highest. Using the constant-power discharge model:

At end of discharge, the system voltage is at its minimum:
  Vend = 1.75 V/cell × 24 cells = 42.0 V

The discharge current at end voltage (worst case):
  Idischarge = P / Vend  — (Eq. 1)
  Idischarge = 12,000 / 42.0
  Idischarge = 285.7 A

At the start of discharge (fully charged battery at approximately 2.15 V/cell × 24 = 51.6 V), the current would be lower:

Istart = P / Vstart = 12,000 / 51.6 = 232.6 A

The current increases throughout the discharge as voltage drops. The cell must be sized to handle the worst-case (end-of-discharge) current for the full duration.

Battery manufacturers provide discharge curves or tables showing the available capacity (Ah) at various discharge rates and end voltages. For a typical VRLA front-terminal battery (e.g., 12 V 100 Ah monobloc at C10 rate), the manufacturer data for discharge to 1.75 V/cell looks like:

At the 30-minute rate, a single 100 Ah (C8) cell delivers only 55 Ah before reaching 1.75 V/cell. This is the Peukert effect — higher discharge rates yield less available capacity.

Required Ah capacity at 30-minute rate (before correction factors):
  Crequired = Idischarge × t  — (Eq. 2)
  Crequired = 285.7 A × 0.5 h
  Crequired = 142.9 Ah (at 30-minute rate to 1.75 V/cell)

Per IEEE 1185, the battery must be sized with correction factors for aging, temperature, and design margin:

Cdesign = Crequired × ka × kt × km  — (Eq. 3)

Where:
  ka = 1.25 (aging factor — battery capacity drops to 80% at end of life)
  kt = 1.00 (temperature correction at 25°C reference)
  km = 1.10 (design margin for load growth and uncertainty)

Cdesign = 142.9 × 1.25 × 1.00 × 1.10
Cdesign = 142.9 × 1.375
Cdesign = 196.5 Ah (at 30-minute rate)

Now convert this 30-minute rate requirement back to an equivalent C8 rated capacity (since batteries are specified at C8 or C10 rates):

From the manufacturer data, a cell delivers 55% of its C8 rated capacity
at the 30-minute rate. Therefore:

  Crated(C8) = Cdesign(30min) / 0.55  — (Eq. 4)
  Crated(C8) = 196.5 / 0.55
  Crated(C8) = 357.3 Ah (at C8 rate)

We need 24 cells in series for 48 V nominal. Using 12 V VRLA monoblocs (6 cells per monobloc), we need 4 monoblocs in series. Each monobloc must provide the required C8 capacity.

Configuration options:

Option A: Single string of large-capacity monoblocs
  4 × 12 V 370 Ah (C8) monoblocs in series
  Total: 48 V, 370 Ah (C8)
  Strings: 1

Option B: Two parallel strings of medium-capacity monoblocs
  2 strings × 4 × 12 V 200 Ah (C8) monoblocs
  Total: 48 V, 400 Ah (C8) combined
  Strings: 2

Selected: Option A — 370 Ah (C8) single string
  (Fewer cells = lower failure risk, simpler BMS, easier maintenance)
  (370 Ah is the next standard size above 357.3 Ah)

Verify the selected battery meets the 30-minute requirement:

Available capacity at 30-min rate:
  C30min = 370 × 0.55 = 203.5 Ah

Available capacity at end of life (80%):
  CEOL = 203.5 × 0.80 = 162.8 Ah

Required capacity (before aging):
  Crequired = 142.9 Ah

162.8 Ah > 142.9 Ah  ✓ (14% margin at end of life)

Final verification — confirm the selected battery can deliver the required power for 30 minutes at end-of-life:

At end of life (80% capacity remaining):

Maximum sustained current at 30-min rate:
  Imax = CEOL(30min) / t
  Imax = 162.8 / 0.5
  Imax = 325.6 A

Required discharge current:
  Irequired = 285.7 A

325.6 A > 285.7 A  ✓  (14% margin)

Power delivery check at end voltage:
  Pavailable = Imax × Vend
  Pavailable = 325.6 × 42.0
  Pavailable = 13,675 W = 13.7 kW

  13.7 kW > 12.0 kW  ✓

Actual backup time at rated load (new battery):
  tactual = C30min(new) / Idischarge
  tactual = 203.5 / 285.7
  tactual = 0.712 hours = 42.7 minutes

  42.7 min > 30 min  ✓  (42% time margin when new)

A 370 Ah (C8 rate) VRLA battery bank consisting of four 12 V monoblocs in series provides 30 minutes of 12 kW backup with adequate margins for aging, temperature, and design uncertainty. The battery will still deliver the full 30-minute backup at end-of-life (80% capacity) with a 14% margin.

• IEEE 1185:2019 — IEEE Recommended Practice for the Design of DC Auxiliary Power Systems for Generating Stations
• IEEE 1184:2006 — IEEE Guide for Batteries for Uninterruptible Power Supply Systems (temperature correction tables)
• IEEE 1188:2005 — IEEE Recommended Practice for Maintenance, Testing, and Replacement of VRLA Batteries
• IEEE 485:2020 — IEEE Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications (duty cycle method)
• IEC 60896-21 — Stationary lead-acid batteries, VRLA types, test methods
• AS 2676.1 — Guide to the installation, maintenance, testing and replacement of secondary batteries in buildings

Use the ECalPro Battery/UPS Calculator to size battery banks for your backup power systems. Enter the load power, backup duration, system voltage, and environmental conditions — the calculator determines the required battery capacity with all correction factors, Peukert effect compensation, and end-of-life performance verification.