# Usable Energy

In the simplest terms the usable energy of a battery is the Total Energy multiplied by the Usable SoC Window. The total energy is the nominal voltage multiplied by the nominal rated capacity.

However, if you have been through the Battery Basics you will have realised that the battery cell and pack do not have a linear performance and this is true for the usable energy. Factors that impact the energy you can extract from the battery pack are:

• variation in cells
• temperature
• absolute temperature
• temperature gradient within a cell
• temperature gradient across the pack
• available coolant capacity
• power demand
• state of health (SoH)
• capacity at discharge rate
• internal resistance increase
• usable window

### Statistical Variation in Cells

If the battery pack is made up of more than 1 cell there will be variation in cell capacity and internal resistance. In order to calculate the total and usable capacity of the battery pack you need to take this variation into account.

### Temperature

Fundamentally as the temperature of a battery cell decreases the chemical reactions slow down and the capacity of the cell decreases. This is very dependent on chemistry, cell design and hence different from manufacturer to manufacturer.

The curves show the voltage versus capacity for a 12V LFP battery pack being discharged at C/2.

The highest capacity is at 50°C which would be the highest operating temperature for this type of pack.

As the temperature decreases the voltage decreases due to increasing internal resistance.

The voltage and capacity of this pack show a significant decrease at -10°C.

The DC Internal Resistance of a cell is very dependent on temperature.

As the internal resistance increases the usable capacity of the cell will decrease as the voltage will drop further meaning that more current will be needed for a given power demand. There will be an upper current limit for most systems.

Also, as the resistance increases and the current increases to keep the power the same the I2R loss to heat within the cell increases. This can be useful as it will heat the cell. However, this must be managed or temperature gradients risk nonlinear ageing of the cell.

SAFT MP 176065 xtd battery [2] has a very wide operating temperature range of +85°C down to -40°C.

However, the capacity decreases significantly at temperatures below 0°C.

Also, the decrease in voltage at this quite low discharge rate of C/5 would also have to be taken into account when designing the system.

### Power Demand

If the power demand is higher the capacity of the battery will be lower. Also, the losses to heat in the complete system will be higher as the power increases and hence the current increases.

Discharge rate capability of a new SAFT MP 176065 xtd battery [2].

As you can see, at a C/8 discharge rate (purple line), the cell offers a 5.8 Ah capacity, at 1.5 C, the cell capacity goes down to 5.5 Ah (green line).

### State of Health

As the cell is cycled the capacity fades and internal resistance of the cell increases [1].

The reduced capacity and increased ageing are related to the loss of available ions to side reactions and the loss or damage of the anode and cathode structure.

This loss of capacity of the battery and hence SoH will be very closely related to the range of an electric vehicle, an SoH of 70% would be equivalent to the range dropping from 200 miles when the can is new (SoH = 100%) to 140 miles.

This loss in capacity in your phone or laptop battery would also be closely related to the number of hours of use you get before you need to recharge.

Contactors age with use, the surfaces of the contacts get pitted and oxidised hence increasing resistance. This means a bigger voltage drop and more heat generated in the contactor itself.

### Usable Window

If we want a battery cell to last a lot of cycles, extend the life in a power application or to ensure the available power is consistent then we need to set a usable SoC window that is smaller than 100%. That is we will limit the top end charge to perhaps 95% SoC and the bottom end discharge to 5% SoC.

High SoC and hence high cell voltage stresses the cell and significantly reduces the lifetime. Going over the maximum cell voltage risks safety of the cell and pack. Although this top end SoC is controlled by cell voltage, any error in SoC estimation needs to be taken into account when setting the SoC limits.

At low SoC the Open Circuit Voltage (OCV) is decreasing and the internal resistance of the cell increasing. Hence with a discharge load the cell voltage will drop even further and more rapidly approach the minimum cell voltage. This minimum cell voltage will be set by the cell manufacturer to avoid damage and extend the cell lifetime.

#### References

1. Calum Strange, Gonçalo dos Reis, Prediction of future capacity and internal resistance of Li-ion cells from one cycle of input data, Energy and AI, Volume 5, 2021
2. Lithium-ion batteries in use: 5 more tips for a longer lifespan, SAFT Batteries