Battery bank sizing: required Ah, derating factors and series-parallel arrangement

What battery bank sizing is

Sizing a battery bank is not reading an ampere-hour number off a load list: it is converting a DC load and a required autonomy into the nominal capacity to buy, after honestly accounting for everything that erodes the usable energy — the depth you are willing to discharge, the capacity lost to aging, the penalty of cold temperature and the penalty of a fast discharge. Only then does the result become an arrangement of cells: how many in series to build the bus voltage, and how many strings in parallel to reach the capacity.

The most common field failure is a bank that meets its autonomy on the day it is commissioned and falls short two winters later. The cause is almost always the same: the raw demand was bought as the nominal capacity, with no division by the depth of discharge and no derating for aging and temperature. This method exists to prevent exactly that.

The stacked-factor method (IEEE 485 / 1115)

The governing standards — IEEE 485 for lead-acid and IEEE 1115 for nickel-cadmium and lithium — build the required capacity as a chain of multiplicative factors applied to the raw demand:

C_req = (Q_demand / DoD) · AF · DM · Kt_temp · Kt_rate

Each factor answers one question:

• DoD — how deeply may the bank be discharged? Dividing by the depth of discharge converts usable energy into nominal capacity.
• AF (aging factor) — how much capacity will be lost by end of life? Stationary batteries are retired at ~80 % of rated capacity, so a factor of ~1.25 (lead-acid) sizes for that worn-out state.
• DM (design margin) — what allowance for load growth and uncertainty? Typically 1.10.
• Kt_temp (temperature correction) — how much capacity is lost in the cold? Read from the IEEE 485 table.
• Kt_rate (discharge-rate / Peukert factor) — how much usable capacity is lost because the discharge is faster than the rating?

The factors stack because they are independent and each shrinks the available energy. Their product is the honest oversizing the bank needs.

From load to current and demand

Everything starts at the load current. If the load is defined in watts behind an inverter:

I_load = P / (V_bus · η)

where η is the inverter efficiency (pure DC loads use η = 1, and the load may be entered directly in amperes). The raw ampere-hour demand is then simply:

Q_demand = I_load · t_aut

This is the gross charge the load pulls over the autonomy — the number before any derating. Buying this as the nominal capacity is the classic mistake.

The temperature correction

Battery capacity is specified at 25 °C and falls as it gets colder. IEEE 485 tabulates a multiplier that grows below 25 °C; for lead-acid it is about 1.19 at 10 °C, 1.30 at 4.4 °C and 1.40 at 0 °C. A bank installed in an unheated shelter at 10 °C must therefore carry ~19 % more nominal capacity than the same bank in a 25 °C room. Lithium (LiFePO4) is far less sensitive on discharge — but its real constraint is charging below 0 °C, which causes lithium plating and demands self-heating cells or a charge inhibit.

The method interpolates linearly between the tabulated points and clamps at the ends, never returning a factor below 1.0 (the warm side gives no capacity bonus).

The discharge-rate (Peukert) factor

A battery rated at the C10 rate (full discharge in 10 hours) delivers less usable capacity if you drain it in two hours. The Peukert relation captures this:

Kt_rate = max(0.5, (t_ref / t_aut)^(n − 1))

When the autonomy is shorter than the reference rate (t_aut < t_ref), the discharge is faster than rated and the factor rises above 1.0, derating the capacity. When it is slower, the factor falls below 1.0 (a bonus), floored at 0.5 to avoid absurd extrapolation. The exponent n is ~1.2 for lead-acid and ~1.05 for lithium. This is a conservative engineering estimate — the manufacturer’s exact Kt/Rt curves should confirm the final number.

Resolving the series-parallel arrangement

Capacity alone does not buy a bank; you must also reproduce the bus voltage. The two counts are independent:

• Series (Ns): Ns = round(V_bus / V_module). The cells in series add their voltages until the string matches the DC bus. A 48 V bus from 12 V modules needs 4 in series; the same bus from 2 V cells needs 24.
• Parallel (Np): Np = ceil(C_req / C_module). Strings in parallel add their capacities. The ceiling guarantees the installed capacity never drops below the requirement.

The installed capacity is C_inst = Np · C_module and the string voltage is V_string = Ns · V_module. A check confirms the string voltage matches the bus within a tolerance (nominal conventions such as a lithium “48 V” string at 51.2 V are accepted). When the parallel count climbs above about four, the design is flagged: current sharing between many strings degrades, and the cleaner answer is higher-capacity cells or a 2 V cell bank.

How to read the result

• Installed vs required capacity: the margin (folga) should be small and positive — a large excess means the chosen module is too big a granularity step.
• String voltage vs bus: if they diverge, the module voltage or the target bus is wrong; the series count cannot reproduce the bus.
• Parallel count: keep it at four or fewer; more strings is a signal to change cell size.
• Warnings: a DoD above 80 % on lead-acid (or above 90 % on lithium), a charging temperature below 0 °C on lithium, or a discharge faster than the rated C-rate each carry a specific caution.

Practical design considerations

• Always derate to end of life and to the coldest temperature — those two together explain most undersized banks.
• Match the chemistry to the duty: deep daily cycling favors lithium (deeper DoD, milder aging and Peukert); pure standby/emergency tolerates lead-acid at a lower cost per Ah.
• Prefer fewer, larger strings over many small parallel ones for current sharing and charger balance.
• Confirm the rate derating against the manufacturer’s Kt/Rt curves before the purchase order.
• Align standard and method: IEEE 485 governs lead-acid, IEEE 1115 nickel-cadmium and lithium, and IEC 62619 the safety of industrial lithium cells.

Following this chain — load current, raw demand, the stacked DoD/aging/temperature/rate factors and the series-parallel resolution — yields a bank that holds its autonomy not just at commissioning, but through aging, cold and fast discharge in the field.