Depth of Discharge: What It Means for Battery Life

Depth of discharge (DoD) is the percentage of a battery’s rated capacity that has been withdrawn. A battery at 80% state of charge (SoC) has a DoD of 20%. The term is central to battery design because the depth to which a battery is discharged directly influences its cycle life—the number of charge/discharge cycles it can deliver before its capacity falls below a specified threshold, typically 80% of rated capacity.

Discharging a battery deeply stresses its internal chemistry. For most chemistries, the relationship between DoD and cycle life is not linear; a battery cycled to 80% DoD will generally have far fewer cycles than one cycled to 50% DoD. This trade-off means that the usable capacity of a battery is not its rated capacity but the capacity that balances the desired cycle life against the cost of the battery. The honest figure depends on the chemistry, the manufacturer’s specifications, and the application.

The rated capacity of a battery is determined under standard test conditions, usually a 20-hour discharge at a specified temperature (often 25°C). In practice, several factors reduce the usable capacity:

• Discharge rate: Discharging faster than the rated rate (e.g., a 1-hour discharge instead of 20-hour) increases internal resistance and reduces the delivered capacity. This is known as the Peukert effect, more pronounced in lead-acid batteries.
• Temperature: Cold temperatures slow chemical reactions, reducing capacity and increasing internal resistance. A battery rated at 25°C may deliver only 70-80% of its capacity at 0°C.
• Cut-off voltage: The battery is not discharged to zero volts; the inverter or load has a minimum voltage at which it stops drawing power. This cut-off voltage is set to protect the battery from damage, and the capacity above that voltage is the usable capacity.

Thus, the depth of discharge is not a fixed number but a design parameter. The table below summarizes typical DoD limits for common chemistries, based on manufacturer recommendations for achieving a reasonable cycle life (often 3000-5000 cycles for lithium, 500-1000 for lead-acid).

Note that these are typical values; always refer to the manufacturer’s datasheet for the specific battery model. The cycle life at a given DoD is usually specified as a curve, not a single number.

Calculating Depth of Discharge

DoD is calculated as the amount of energy withdrawn from a fully charged battery divided by its rated capacity. For example, if a 10 kWh battery has 6 kWh remaining, the DoD is 40% (4 kWh used / 10 kWh rated). In practice, the state of charge (SoC) is often estimated by a battery management system (BMS) using voltage, current, and temperature measurements, but the relationship between voltage and SoC is not linear and varies with load and temperature.

To size a battery for a given daily energy need and desired cycle life, the required rated capacity is:

Rated capacity (kWh) = Daily energy use (kWh) / DoD limit (as a fraction)

For example, if a home uses 10 kWh per day and the battery is limited to 80% DoD, the rated capacity must be at least 12.5 kWh (10 / 0.8). This calculation is the starting point for battery sizing.

Chemistry and DoD

Different chemistries have different tolerances for deep discharge:

• Lead-acid: The oldest and most common chemistry. Deep discharges cause sulfation, which permanently reduces capacity. Keeping DoD to 50% or less is standard for cycling applications. Lead-acid also suffers from the Peukert effect, so high discharge rates reduce capacity.
• Lithium-ion (NMC): Common in electric vehicles and some stationary storage. They can handle deeper discharges (80-90%) without significant cycle life loss, but they degrade faster at high temperatures and high states of charge. A BMS is essential to prevent over-discharge, which can cause irreversible damage.
• Lithium iron phosphate (LFP): A subtype of lithium-ion with a flatter voltage curve and longer cycle life. LFP can be discharged to 80-90% DoD regularly and has a lower risk of thermal runaway. Many modern home storage batteries use LFP.
• Nickel-cadmium (NiCd): Rarely used in modern PV systems due to environmental concerns, but they can handle deep discharges and extreme temperatures.

The choice of chemistry affects not only the allowable DoD but also the cost, safety, and performance. For a given application, the design must select a chemistry and a DoD that meet the cycle life requirement and the energy needs.

What People Get Wrong About Depth of Discharge

The most common mistake is to treat the rated capacity as the usable capacity. A 10 kWh battery is not a 10 kWh battery if the DoD limit is 80%; it is an 8 kWh battery. This error leads to undersized systems that cannot meet the daily energy demand, or to batteries that are cycled too deeply, shortening their life.

Another frequent error is to ignore temperature effects. A battery rated at 25°C will deliver less capacity at lower temperatures, and the DoD limit may need to be reduced to avoid over-discharge. For example, on a cold morning, the voltage of a lead-acid battery at a given SoC is lower, which can cause the inverter to cut off earlier, effectively increasing the DoD. Designers must account for this by setting the cut-off voltage based on the coldest expected temperature.

A third mistake is to assume that the DoD limit is fixed for all conditions. Manufacturers specify DoD limits for a particular cycle life and temperature. If the battery is used in a warmer climate, the cycle life at a given DoD may be shorter, so a lower DoD might be needed to achieve the desired lifetime. Conversely, in a cooler climate, a slightly higher DoD may be acceptable.

Finally, some designers confuse DoD with state of charge (SoC). DoD is the inverse of SoC: DoD = 100% - SoC. A battery at 20% SoC has an 80% DoD. This confusion can lead to incorrect sizing and control settings.

Practical Considerations

When designing a battery system, the following steps are essential:

1. Determine the daily energy requirement: The average daily energy consumption in kWh that the battery must supply.
2. Select a chemistry and a DoD limit: Based on cycle life requirements and cost. For example, if the system is expected to last 10 years with daily cycling, a lithium battery with 80% DoD might be chosen.
3. Calculate the rated capacity: Divide the daily energy by the DoD limit, and add a margin for temperature and aging.
4. Set the inverter’s cut-off voltage: This must correspond to the chosen DoD, and it must be adjusted for temperature. Most inverters allow setting the cut-off voltage, but the voltage-SoC relationship is not linear, so the setting should be based on the manufacturer’s data.
5. Monitor and manage: The BMS should track SoC and prevent over-discharge. For lead-acid, a low-voltage disconnect is critical.

Example Calculation

Suppose a home needs 8 kWh per day from the battery. The design uses an LFP battery with a DoD limit of 90%. The rated capacity required is:

Rated capacity = 8 kWh / 0.9 = 8.89 kWh

So a 9 kWh battery would be the minimum. To account for temperature derating (say 10% loss at cold temperatures), the capacity should be increased by 10%:

Adjusted capacity = 8.89 kWh / 0.9 = 9.88 kWh

Thus, a 10 kWh battery would be a reasonable choice. This is a simplified example; a real design would also consider the discharge rate and the inverter’s efficiency.

Conclusion

Depth of discharge is a critical parameter in battery system design. It determines the usable capacity, the cycle life, and the overall cost. The correct DoD for a given application depends on the battery chemistry, the desired cycle life, and the operating environment. By understanding the trade-offs and calculating the required capacity with appropriate margins, a designer can avoid the common pitfalls of undersizing and premature battery failure.

For a reference, always consult the manufacturer’s datasheet for the specific battery model and the inverter’s settings for cut-off voltage. The information in this article is general and may not apply to all products.