EngiMetric Arena / Engineering Trade-off
Choose a battery autonomy that fits the bank limit
Competency Constraints and trade-offs primary Design and sizing supporting
What you should take away: Evaluate battery autonomy against a minimum resilience requirement and a maximum bank size, recognising that a band of autonomy values can comply.
The situation
What is happening
An off-grid load uses 4.8 kWh/day at 48 V and 80 % depth of discharge. The project requires at least two days of autonomy, but the battery room limits the nameplate bank to 20 kWh. Choose an autonomy of 1, 2, 3 or 4 days.
Given
| Quantity | Value | Unit | Note |
|---|---|---|---|
| Daily energy | 4.8 | kWh/day | Load energy per day. |
| System voltage | 48 | V | Nominal DC bus. |
| Depth of discharge | 80 | % | Usable fraction of nameplate. |
| Minimum autonomy | 2 | days | Project resilience requirement. |
| Maximum bank energy | 20 | kWh | Battery room limit. |
Assumptions this challenge makes
- The load is constant at 4.8 kWh/day.
- Nameplate bank energy is daily energy times autonomy divided by depth of discharge.
- Temperature, ageing and inverter efficiency are not included.
Limits this decision must satisfy
| Limit | Requirement | If it is breached |
|---|---|---|
| Minimum autonomy | not less than 2 days | Below two days the site has less resilience than the project requires during cloudy or high-load periods. |
| Maximum bank energy | not more than 20000 Wh | Above 20 kWh the bank does not fit the available battery room and adds cost without a stated resilience need. |
Choose 1, 2, 3 or 4 days. More than one autonomy may satisfy both the resilience and bank-size limits.
Your call
Your answer
Hints
- Nameplate bank energy is daily energy times autonomy divided by 0.8.
- Check the minimum autonomy first, then the bank-energy cap.
- One candidate may meet the autonomy requirement but exceed the room limit.
Your answer Engine result
Where that comes from
Each limit, checked
Why
- At 1 day the bank is 4 800 / 0.8 = 6 000 Wh, below the two-day minimum. At 2 days it is 12 000 Wh, which passes both limits.
- At 3 days the bank is 18 000 Wh, also inside the 20 kWh cap. At 4 days it is 24 000 Wh, above the cap.
- So 2 days and 3 days are both defensible. Two days meets the requirement with the smallest bank; three days buys one extra day of resilience while still fitting the room.
- The calculation does not choose between them. The trade-off is resilience versus capital cost, space and battery replacement burden.
- The installed battery arrangement may exceed the calculated nameplate energy because whole batteries are used.
What this challenge does not establish
- The load is constant; a real load profile and inverter efficiency change the bank size.
- Temperature, ageing and Peukert losses are not modelled.
- The 20 kWh limit is a project room constraint, not a battery performance limit.
- The calculation does not size the array, charge controller or protective devices.