EngiMetric Arena / Design Challenge
What battery bank capacity does a two-day autonomy need?
Competency Design and sizing primary Systems and balances supporting Quantitative reasoning supporting
What you should take away: Size battery bank energy and amp-hour capacity from daily load, autonomy and depth of discharge, before arranging series and parallel strings.
The situation
What is happening
An off-grid load uses 4.8 kWh/day. The battery bank must provide two days of autonomy at a 48 V system voltage and an 80 % depth of discharge. The selected batteries are 100 Ah at 12 V. What bank capacity in amp-hours is required?
Given
| Quantity | Value | Unit | Note |
|---|---|---|---|
| Daily energy | 4.8 | kWh/day | Load energy per day. |
| Autonomy | 2 | days | Days without solar input. |
| System voltage | 48 | V | Nominal DC bus. |
| Depth of discharge | 80 | % | Maximum usable fraction. |
| Battery rating | 100 | Ah | Each battery is 12 V, 100 Ah. |
Assumptions this challenge makes
- The load is constant at 4.8 kWh/day.
- The depth-of-discharge limit is applied to the nameplate bank energy.
- Battery ageing, temperature and inverter efficiency are not included.
Your call
Your answer
Hints
- Convert the daily load to watt-hours, then multiply by the autonomy days.
- Divide by the depth of discharge to get the nameplate bank energy. The usable energy is only 80 % of nameplate.
- Divide the bank energy by the 48 V system voltage to get amp-hours.
Your answer Engine result
Where that comes from
Each limit, checked
Why
- Two days of load is 4 800 x 2 = 9 600 Wh.
- At 80 % DoD, the nameplate bank energy is 9 600 / 0.8 = 12 000 Wh.
- At 48 V, the bank capacity is 12 000 / 48 = 250 Ah.
- The battery arrangement is four 12 V batteries in series for 48 V, and three 100 Ah strings in parallel for 300 Ah installed. The installed capacity is above the 250 Ah requirement because whole batteries are used.
- The calculation sizes energy and amp-hours. Cable current, fuse rating, charge-controller limits and temperature derating are separate design checks.
What this challenge does not establish
- The load is treated as constant; a real load profile and inverter efficiency change the required energy.
- Temperature, ageing and Peukert losses are not modelled.
- The depth of discharge is a stated limit, not a property of every battery technology.
- The result does not size the array, charge controller, inverter or protective devices.