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Explain the concept of depth of discharge (DOD) in battery systems.
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**Depth of Discharge (DoD)** refers to the percentage of a battery’s capacity that has been used up or discharged. In simpler terms, it shows how much of the battery’s energy has been drained compared to its total capacity.

Here’s how it works:

- A battery has a total capacity, usually measured in ampere-hours (Ah) or watt-hours (Wh), which tells you how much energy it can store.
- The DoD is calculated by comparing how much of that stored energy has been used to how much was available in total.

For example, if a battery has a total capacity of 100 Ah, and 40 Ah has been used, then the DoD is:

\[
\text{DoD} = \frac{\text{Energy Used}}{\text{Total Capacity}} \times 100 = \frac{40}{100} \times 100 = 40\%
\]

So, in this case, the DoD is 40%.

### Why does DoD matter?
The DoD is important because it affects the lifespan of the battery. Generally, the deeper the discharge (higher DoD), the fewer cycles the battery will last. For instance:

- **Shallow Discharge (Low DoD)**: If you only use 10% of the battery’s capacity, it lasts longer because you’re not stressing the battery as much.
- **Deep Discharge (High DoD)**: If you use 90% or more, the battery wears out faster and may lose its ability to hold a charge properly over time.

### Practical Example:
In **electric vehicles (EVs)** or **solar power storage systems**, manufacturers often recommend keeping the DoD at around 80% to help maximize battery life. So, if you’re using a 100 kWh battery, you’d ideally only use up to 80 kWh to extend the lifespan of the battery.

In summary, the **Depth of Discharge** helps you understand how much of the battery’s capacity has been used and directly impacts how long the battery will last before it needs to be replaced or recharged.
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