To calculate the battery capacity in ampere-hours (Ah), we need to follow these steps:

Step 1: Determine the total energy required from the battery bank over the autonomy period.

• Day load: 500 Wh/day
• Night load: 1000 Wh/day

Total daily load: $\text{Total daily load} = 500 \text{ Wh} + 1000 \text{ Wh} = 1500 \text{ Wh/day}$

Total energy required over 5 days (autonomy period): $\text{Total energy required} = 1500 \text{ Wh/day} \times 5 \text{ days} = 7500 \text{ Wh}$

Step 2: Account for battery efficiency.

• Battery efficiency: 70%

The actual energy the battery needs to store, considering the efficiency, is: $\text{Energy required with efficiency} = \frac{7500 \text{ Wh}}{0.7} \approx 10714.29 \text{ Wh}$

Step 3: Adjust for the depth of discharge (DoD).

• DoD: 80% (only 80% of the battery's capacity can be used)

The required battery capacity, considering the DoD, is: $\text{Required battery capacity (Wh)} = \frac{10714.29 \text{ Wh}}{0.8} \approx 13392.86 \text{ Wh}$

Step 4: Convert the required battery capacity from Wh to Ah.

The nominal voltage of the battery bank is 24V, so the battery capacity in ampere-hours (Ah) is calculated as: $\text{Battery capacity (Ah)} = \frac{13392.86 \text{ Wh}}{24 \text{ V}} \approx 558.04 \text{ Ah}$

Final Answer

The required battery capacity is approximately 558.04 Ah.

Would you like more details on this calculation or have any other questions?

Here are 5 related questions to explore further:

1. How would the required battery capacity change if the battery efficiency was increased to 85%?
2. What is the effect of reducing the depth of discharge to 70% on the required battery capacity?
3. How would the required battery capacity change if the load demand doubled?
4. What would the battery capacity be if the nominal voltage was 48V instead of 24V?
5. How do you determine the appropriate battery bank configuration (series vs. parallel) for a given capacity?

Tip: Always ensure the battery is sized with some extra capacity to account for unforeseen loads or inefficiencies that might arise during operation.