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DC battery sizing

Size the battery bank of a substation or an industrial plant from the duty cycle, with the IEEE 485 and IEEE 1115 section method and the cell's Kt factors, and estimate the number of cells and the charger current.

IEEE 485section method, lead-acidIEEE 1115section method, nickel-cadmiumIEEE 946charger current

Example cases
DC battery sizing
E1System
V
V
V

Equalize voltage: about 2.33 V for lead-acid and 1.55 V for nickel-cadmium.

E2Duty cycle
A
min
A
min
A
min
A
min
A
min
A
min

Total constant current of each period, in order; the first and last periods usually carry breaker trips and closes on top of the continuous load. The random load is added to the most demanding section. Leave unused rows empty.

E3Cell Kt factors
min
Ah/A
min
Ah/A
min
Ah/A
min
Ah/A
min
Ah/A

The preloaded values are an illustrative curve, not a real cell. Use the manufacturer's Kt values for your model, at the resulting end voltage per cell and at 25 °C. Between points the tool interpolates on a logarithmic scale.

E4Correction and cell

1.00 at 25 °C; higher in the cold.

1.25 is the usual value.

Ah

Selected cell, optional: it is compared with the required capacity.

E5Charger
h
A

1.1 for lead-acid and 1.4 for nickel-cadmium.

Use a decimal point. The calculation runs in your browser and updates as you type.

Required capacity

— Ah

Number of cells

—

End voltage per cell

— V

Charger current

— A

Uncorrected capacity

— Ah

Ah removed during the cycle

— Ah

Duty cycle
  • Duty cycle current
  • Random load
Short periods are drawn wider than their real duration so they can be seen; the duration is shown below. The random load goes at the end of the most demanding section.
Kt factor curve
  • Log-log interpolation
  • Duty cycle length
Logarithmic scales. The points are the Kt values you entered; the method does not extrapolate beyond them.

Step-by-step calculation

What it means for your battery bank

    What it is for

    To estimate the size of the battery bank and charger of the DC station service of a substation or an industrial plant, to check whether an existing bank is still enough after adding bays or equipment, and to prepare the data a manufacturer asks for to quote. It also helps to read the result of a capacity test: a bank that delivers 80 % of its capacity must still cover the duty cycle.

    How it is calculated

    IEEE 485number of cells

    N = ⌊Vmax / Vcharge per cell⌋ · Vend = Vmin / N

    It is rounded down so that the equalize charge does not exceed the maximum voltage of the equipment. The manufacturer's Kt values are read at the end voltage per cell; the tool warns if it falls outside 1.60 to 1.90 V for lead-acid or 0.90 to 1.20 V for nickel-cadmium.

    IEEE 485section methodIEEE 1115section method

    FS = ΣP=1…S (AP − AP−1) · Kt(TP)

    For each section S, made of periods 1 to S, AP is the current of period P (A0 = 0) and TP the time from the start of period P to the end of section S. Negative steps subtract. The uncorrected capacity is the largest FS plus that of the random load, AR · Kt(tR).

    IEEE 485correction factors

    Capacity = F · ktemperature · kmargin · kaging

    The temperature factor comes from the IEEE 485 table or from the manufacturer for the lowest electrolyte temperature (1.00 at 25 °C); the tool warns if a value below 1 is used, because that gives credit for a high temperature. The aging factor is 1.25 in IEEE 485 because the battery is replaced when its capacity falls to 80 %; IEEE 1115 also includes it for nickel-cadmium, with a value that depends on the cell and on the replacement criterion. The design margin covers future loads and is set by the designer. The result is in Ah at the capacity rating of the Kt curve (for example, 8 h); choose the next larger commercial cell.

    IEEE 946charger

    A = L + k · C / H

    This is the method charger manufacturers use: L is the continuous load, C the Ah removed during the duty cycle, H the recharge time in hours and k the factor that accounts for recharge efficiency: 1.1 is the usual value for lead-acid and 1.4 for nickel-cadmium, and some manufacturers use 1.15 for lead-acid.

    Limits of the calculation

    • It is a simplified form of the method, not the formal sizing. The accuracy depends entirely on the Kt values: with the illustrative curve the result is not good enough to buy a battery.
    • It assumes constant-current loads. Constant-power loads, such as inverters and converters, draw more current as the voltage drops.
    • It uses a single temperature factor for the whole cycle and adds the random load to the most demanding section, without checking that it fits at the end of that section.
    • It does not check the voltage drop in the cables or the maximum float voltage.
    • The real capacity of an installed bank is checked with a capacity test per IEEE 450 (vented lead-acid), IEEE 1188 (valve-regulated) or IEEE 1106 (nickel-cadmium).

    Frequently asked questions

    How is a substation battery bank sized?

    Build the duty cycle with every DC load and its duration: the continuous load, the breaker trips and closes at the start and at the end, and the random loads. With the IEEE 485 (lead-acid) or IEEE 1115 (nickel-cadmium) method, the required capacity is calculated with the Kt capacity factors of the chosen cell, and the temperature, design margin and aging factors are applied.

    What is the Kt factor in battery sizing?

    It is the ratio between the rated capacity of the cell in Ah and the current it can deliver for a given time down to the chosen end voltage per cell. It comes from the manufacturer's discharge curves or tables for each model, temperature and end voltage, which is why the result changes from one brand to another even with the same rated capacity.

    How many cells does a 125 V battery bank have?

    It depends on the chemistry and on the voltage limits of the system. The number is the maximum voltage the equipment accepts divided by the charge (equalize) voltage per cell; with that number, the minimum system voltage divided by the cells gives the end voltage per cell used for sizing. Lead-acid usually ends up around 60 cells, and nickel-cadmium quite a few more, because each cell has a lower voltage.

    We test and design your DC system

    We run the capacity test of your battery bank and check the charger, in Colombia, or elsewhere on request, and we design or upgrade the DC station service of substations and plants with the real duty cycle.

    Contact usSee design and studies

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