Stationary battery calculator: sizing, autonomy and capacity test

What this calculator does

Three calculations on the same bank, in three tabs:

1. Sizing. From the load profile, the minimum capacity that has to be installed.
2. Autonomy. How long an installed bank will last against a constant current.
3. Capacity test. What percentage of rated capacity a real discharge delivered, corrected for temperature.

Sizing to IEEE 485

The full IEEE 485 method splits the load profile into sections and finds, for each one, the cell size that covers it using the manufacturer’s capacity curves. This calculator applies the simplified version used for a first pass:

1. The ampere-hours the profile demands are added up: Σ (current × duration).
2. The temperature factor for the lowest room temperature is applied. It interpolates between the IEEE 485 table points — 1.00 at 25 °C; 1.04 at 21.1 °C; 1.11 at 15.6 °C; 1.19 at 10 °C; 1.30 at 4.4 °C; 1.59 at −6.7 °C — and above 25 °C no credit is taken, which is the conservative choice.
3. The ageing factor is applied, 1.25 by convention.
4. The design margin is added, typically 10% to 15%.

The result is the minimum capacity in ampere-hours. It is not the final cell size: for that you have to enter the manufacturer’s curves with the real discharge rate, because a battery does not deliver the same capacity in 1 hour as in 8.

Estimated autonomy

The second tab uses the Peukert equation,

t = H × (C / (H × I))^n

where C is rated capacity, H the rate it is quoted at (8 or 10 hours on most stationary cells), I the discharge current and n the Peukert exponent, between 1.1 and 1.3 for lead-acid.

It is a familiar and convenient approximation, but an approximation: it drifts from reality on very fast discharges and at very small currents, and it takes no account of the end-of-discharge voltage or the initial state of charge. Use it to decide whether a bank is comfortable or tight; not to certify an autonomy.

Capacity test to IEEE 450

The only way to know a battery’s capacity is to discharge it. The third tab calculates

Capacity (%) = (time achieved / expected time) × 100

corrected for the mean cell temperature during the test with the IEEE 450 factor, 1 + 0.008 × (T − 25 °C). With cells at 30 °C the battery over-performs, and without correcting you would record a result about 4% better than the truth.

Reading: 90% or above, normal service; between 80% and 90%, shorten the test interval; below 80%, replace.

Worked example

125 V DC system in a substation whose room drops to 10 °C in winter. Profile: 120 A for the first minute, 25 A for 179 minutes and 80 A in the final minute.

• Profile demand: 120×(1/60) + 25×(179/60) + 80×(1/60) = 77.9 Ah
• Temperature factor at 10 °C: 1.19
• With ageing 1.25 and a 10% margin: 77.9 × 1.19 × 1.25 × 1.10 = 127 Ah

A 150 Ah cell at the 8-hour rate covers the profile comfortably; a 125 Ah one would be marginal and would have to be checked against the manufacturer’s curve before buying.

What this calculator does not do

It does not replace the section-by-section IEEE 485 method or the manufacturer’s curves, which govern the final sizing. It knows nothing about the cell type, the end-of-discharge voltage or the number of cells. And it says nothing about the condition of an installed bank: that is what the discharge test is for, and it is the one measurement no calculation can replace.

What measures it

The capacity test is run with a battery discharger able to hold the current constant and log the voltage of every cell throughout the discharge. The rest of the maintenance cycle — charging, cell testing and monitoring — is covered by the same battery maintenance and charging range.

If you would rather not pick the equipment by hand, the charger and discharger selector proposes a specific model from the bank voltage, the current and the type of test.