Stationary battery calculator: sizing, autonomy and capacity test

What this calculator does

Four calculations on the same bank, in four tabs:

1. Sizing. From the load profile, the minimum capacity that has to be installed and, if the number of cells and the charger current are entered, the battery energy and the recharge time.
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 to IEEE 450-2020, IEC 60896-21:2004 or IEC 61056-1:2012, and when the next test is due.
4. Internal resistance. The resistance and short-circuit current from two current steps, to IEC 60896-21:2004 or EN 61960.

Sizing to IEEE 485-2020

The full IEEE 485-2020 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 485-2020 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 450-2020

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 450-2020 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.

Energy and recharge time

With the number of cells in series and the average discharge voltage per cell —1.9 to 2.0 V for lead-acid— the calculator gives the energy of the required battery, E = N × average V × C, which is how IEC TS 62933-3-1:2018 expresses it for energy storage systems. It uses the capacity already corrected for temperature, ageing and margin, because that specification requires rated values to hold at end of life and at the worst temperature: the same reasoning behind the 1.25 factor.

The same specification asks for the recovery time to be considered: how long the battery takes to be ready for the next duty cycle. The calculator estimates the current-limited stage as Ah discharged × recharge factor / charger current, with a factor of 1.10 to 1.15 for lead-acid. Constant-voltage absorption adds several hours, so the result is a minimum.

Testing to IEC 60896-21:2004 and IEC 61056-1:2012

In Europe, tests on stationary VRLA batteries are reported to IEC 60896-21:2004. The measured capacity, current × time, is corrected to the chosen reference temperature —20 °C or 25 °C— using the unit temperature just before the discharge, which must be between 18 °C and 27 °C:

Ca = C / [1 + λ × (θ − 20)] (or θ − 25)

In a commissioning test the discharge ends when the string reaches N × U final or when the first block reaches n × U final − 0.2 × √n, whichever comes first. For a string of eight 12 V monoblocs discharged at C3, that is 81.6 V for the string or 9.71 V for the first block. The calculator gives both values if the block voltage is entered.

Small VRLA batteries —UPS, emergency lighting, portable equipment— follow IEC 61056-1:2012. There the reference is C20: discharge at I20 = C20 / 20 to 1.75 V/cell, at 20 ± 2 °C or 25 ± 2 °C, with no temperature correction. The actual capacity is Ca = t × I20 and must reach C20; for a new battery the standard allows up to five discharges. It also requires the battery to last at least 20 minutes at 20 × I20 to 1.6 V/cell.

Expected life and next test

The life of a lead-acid battery depends above all on temperature: IEC 60896-21:2004 (note to 3.36) and the Eurobat VRLA guide halve it for every 10 °C of average temperature above 20 °C. A battery with a 10-year design life running at 30 °C lasts about 5. With the life corrected this way, the calculator applies the IEEE 450-2020 intervals:

• Below 80%: replace.
• 90% or less, a drop of more than 10 points since the previous test, or 85% of the life used: annual test (every two years if, even late in life, the battery still delivers 100%).
• Otherwise: every 25% of the expected life or every 5 years, whichever comes first. The first test within the first two years of service.

Internal resistance

The fourth tab applies the two-step current method. For lead-acid, the IEC 60896-21:2004 one, with the unit fully charged and between 20 °C and 25 °C: 4 × I10, read at 20 s and switch off before 25 s; five minutes on open circuit without recharging; 20 × I10, read at 5 s. For lithium, the EN 61960 one: 0.2 It for 10 s and, without interruption, 1.0 It for 1 s. In both cases

R = (U1 − U2) / (I2 − I1)

and extending the line to zero volts gives the short-circuit current, Isc = (U1 × I2 − U2 × I1) / (U1 − U2), the figure for sizing fuses and breakers. IEC 60896-21:2004 gives the method an accuracy of ±10%, so smaller differences from the manufacturer’s value are not significant. With the battery discharged, the short-circuit current falls to about 60%. Internal resistance is for trending a bank, not for knowing its capacity: only the discharge test tells you that.

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 485-2020 method or the manufacturer’s curves, which govern the final sizing. It does not size the charger: the recharge time is an estimate of the current-limited stage. And it says nothing about the capacity of an installed bank without a discharge test: internal resistance helps to trend it, but the test 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.