Stationary Battery Sizing

The IEEE 485 period method: the duty cycle is cut into sections, each change in current is weighted by a capacity rating factor, and the largest section sets the size.

1. What this check does

Takes the DC duty cycle as periods of current in order, works out the number of cells and the end-of-discharge voltage per cell, computes the uncorrected capacity each section needs, takes the largest, and applies the temperature, aging and design-margin factors to give the rated capacity at the 8-hour rate.

2. Inputs used

Chemistry (lead-acid 2.0 V or nickel-cadmium 1.2 V nominal per cell), nominal and minimum DC system voltage, optionally the cell count.
Duty cycle: periods in order with duration (minutes) and current (A). Momentary loads (breaker trips, inrush) are entered as 1-minute periods, as IEEE 485 recommends.
Capacity rating factor K: the manufacturer's curve (K in hours against duration, at the end voltage), or an estimate from the 8-hour rate with a Peukert exponent.
Temperature factor (1.0 at 25 °C; IEEE 485 Table 1 or the manufacturer), aging factor (1.25) and design margin (1.10).

3. Formulas and assumptions

Cells and end voltage

Cells

N = \mathrm{round}\!\left(\dfrac{V_{\text{nom}}}{V_{\text{cell}}}\right) \qquad V_{\text{end}} = \dfrac{V_{\min}}{N}

V_cell = 2.0 V lead-acid, 1.2 V nickel-cadmium.

Section method

Section capacity

F_s = \sum_{p=1}^{s} \bigl(A_p - A_{p-1}\bigr)\, K\bigl(T_{p \to s}\bigr)

T = time from the start of period p to the end of section s; A0 = 0.

Rating factor

K(t) = \dfrac{C_8}{I_t} \quad\text{(manufacturer)} \qquad K(t) \approx 8\left(\dfrac{t}{8\ \mathrm{h}}\right)^{1/n} \quad\text{(estimate)}

n = Peukert exponent, default 1.25.

Required

C_{\text{req}} = \max_s F_s \times k_T \times 1.25 \times k_{\text{margin}}

Rated capacity at the 8-hour rate; kT from IEEE 485 Table 1 for the lowest electrolyte temperature.

Symbols

$V_{\text{nom}},\ V_{\min},\ V_{\text{cell}},\ V_{\text{end}}$	Nominal and minimum DC system voltage; nominal and end-of-discharge voltage per cell	V
$N$	Number of cells
$A_p,\ T_{p \to s}$	Current in period p; time from its start to the end of section s	A, h
$K(t),\ C_8,\ I_t$	Capacity rating factor; rated capacity at the 8-hour rate; current the cell delivers for t	h, Ah, A
$n$	Peukert exponent used for the estimate
$F_s,\ C_{\text{req}}$	Uncorrected capacity of section s; required rated capacity	Ah
$k_T,\ k_{\text{margin}}$	Temperature correction; design margin (aging 1.25 is fixed)

Section method: for section s the capacity is the sum over periods 1..s of the change in current entering each period times K for the time from that period's start to the end of section s. Negative changes (load decreasing) reduce the section, as the standard allows.
K(t) = rated capacity at the 8-hour rate ÷ the current the cell can deliver for t at the end voltage. Without manufacturer data it is estimated as 8 × (t / 8 h)^(1/n) with Peukert exponent n (default 1.25), which follows the published curves within roughly 10 % for lead-acid from 15 minutes upward and is least reliable for 1-minute periods.
Cell count = nominal voltage ÷ nominal cell voltage, rounded; end voltage per cell = minimum system voltage ÷ cells. A warning appears outside 1.60–1.95 V (lead-acid) or 0.95–1.14 V (nickel-cadmium).
Defaults are RokBench assumptions in line with IEEE 485: aging 1.25 and a 10 % design margin; temperature 1.0 unless entered.

4. What is NOT checked

Random (non-coincident) loads and the IEEE 485 treatment of them.
Charger sizing, recharge time and float voltage; the voltage window at the load terminals including cable drop.
Rack, spill containment, ventilation and room design; short-circuit current of the battery.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

IEEE Std 485 — sizing lead-acid batteries for stationary applications
IEEE Std 1115 — sizing nickel-cadmium batteries for stationary applications
IEEE Std 1635 / ASHRAE 21 — ventilation of battery installations
NFPA 70 (NEC) Article 480 — storage batteries

6. Validation cases

These worked examples run through the engine on every change; the expected values come from the cited source. All cases: Validation.

125 V switchgear battery, four-period duty cycle with an entered K curve battery/sizing · Hand calculation

Pass

Source: Hand calculation of the IEEE 485 section method with the K curve entered as points (linear between points) — Periods 120 A/1 min, 15 A/59 min, 40 A/120 min, 100 A/1 min. K points (min → h): 1 → 0.9, 15 → 1.6, 60 → 2.8, 180 → 5.0, 480 → 8. S1 = 120·0.9 = 108. S2 (60 min) = 120·2.8 − 105·K(59) = 336 − 291.2 = 44.8. S3 (180) = 120·5.0 − 105·K(179) + 25·K(120) = 600 − 523.1 + 97.5 = 174.4. S4 (181) = 120·K(181) − 105·5.0 + 25·K(121) + 60·0.9 = 601.2 − 525 + 97.96 + 54 = 228.2 → × 1.25 × 1.10 = 313.8 Ah. 125/2 = 62.5 → 63 cells, 105/63 = 1.667 V/cell.

Quantity	Expected	RokBench	Error	Result
cells	63	63	0%	Pass
endVoltagePerCell	1.667	1.667	0%	Pass
uncorrectedAh	228.2	228.2	0%	Pass
governingSection	4	4	0%	Pass
requiredAh	314	314	0%	Pass

7. Known issues and changes

See the Changelog. Try the tool: Stationary Battery Sizing.