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Batteries, UPS & solar

Runtime of a 48 V LiFePO4 Battery Bank

Lithium iron phosphate (LiFePO4) batteries are now common in solar and backup systems because they tolerate deeper discharge and more cycles than lead-acid. A "48 V" bank is usually built from cells or modules with a nominal 3.2 V per cell, so four 12.8 V modules in series give 51.2 V nominal.

The calculator below is preset for four 12.8 V 100 Ah modules in series, 80 % usable depth of discharge, a 1000 W AC load and 92 % inverter efficiency. The result shows the bank energy, the battery current and the runtime; adjust the depth of discharge to the limit your battery management system and warranty allow.

Last reviewed

nm−+V = n · Vcell Ah = m · Ahcell
Batteries in series add voltage; strings in parallel add ampere-hours. Stored energy is V × Ah, and only the share allowed by the depth of discharge is usable.

For estimation and education. Not a substitute for a licensed engineer, the applicable codes (IEC 60364, NEC/NFPA 70, BS 7671, local regulations) or manufacturer data. Read the disclaimer.

Inputs

Bank builder

V
Ah

Series adds voltage

Parallel adds Ah

Fraction, e.g. 0.5 = 50 %

Load

Load type
W

Typical 0.85–0.95

Result

Battery runtime — Engineerly. Estimate for education only; verify against applicable codes and manufacturer data.

Runtime
3.77h
Runtime
226min
Bank
51.2 V, 100 Ah
Bank energy (nominal)
5.12kWh
Usable energy at DoD
4.096kWh
Battery current
21.23A
C-rate
0.212C

Working, with your numbers

  1. 1. Bank voltage (series adds volts)
    V = V_unit × N_s
    V = 12.8 V × 4
    = 51.2 V
  2. 2. Bank capacity (parallel adds Ah)
    C = Ah_unit × N_p
    C = 100 Ah × 1
    = 100 Ah
  3. 3. Battery current
    I = P_load / (V × η)
    I = 1,000 W / (51.2 V × 0.92)
    = 21.23 A
  4. 4. Runtime (ideal capacity)
    t = C × V × DoD × η / P
    t = 100 Ah × 51.2 V × 0.8 × 0.92 / 1,000 W
    = 3.768 h

Assumptions

  • Constant power load for the whole discharge; battery voltage taken as the nominal bank voltage.
  • Usable depth of discharge 80 % of rated capacity.
  • Inverter efficiency 92 %, constant over the load range.
  • All units in the bank are identical, healthy and balanced.
Chemistry: LiFePO4 (lithium iron phosphate)
Unit: 12.8 V, 100 Ah
Bank: 4S 1P
DoD: 0.8
Load: 1000 W (AC)
Inverter efficiency: 0.92

Check before you rely on this

  • Capacity also falls at low temperature and with ageing; many designers add an ageing factor (for example 1.25 in IEEE 485 for lead-acid).
  • Estimation and education only. Not a substitute for a licensed engineer, the applicable code (IEC 60364, NEC/NFPA 70, BS 7671 or local regulations) or manufacturer data.

Notes for this case

  • LiFePO4 has a Peukert exponent close to 1, so the simple energy method is usually adequate.
  • The battery management system may cut off before the nominal depth of discharge at low temperature or high current.
  • Usable capacity declines with age; many designers add a margin for end-of-life capacity.

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How these formulas were checked: methodology and testing.