The State of Health (SoH) of the cell is the total available charged capacity of the cell as a percentage compared to the nominal capacity in Ah when the cell was new.

This is sometimes referred to as SoH_{C} as the state of health of the cell can be related to the internal resistance of the cell. SoH_{R} is the internal resistance (DCIR) of the cell compared to the resistance when the cell was new. As the cell ages so the resistance increases, this means that when delivering a given current the voltage of the cell will drop further. Thus the charge and discharge power capability of the cell will decrease with time.

- SOH
_{C}= ratio of the Ah capacity when fully charged to the original new Ah capacity - SOH
_{R}= this is a percentage increase in the internal resistance of the cell - SOP = ratio of the power (Watts) now of the cell compared to the original power capability of the cell
- SOH
_{E}= this is the ratio of the energy (Wh) of a fully charged cell now compared to the energy when new.

### SOH Algorithms

In simple terms the SOH of the cell in terms of capacity can be estimated by calculating the maximum capacity of the cell when fully charged and dividing this by the rated charged capacity held by the system. This maximum fully charged capacity would be best established on a slow charge when the cell is charged from an initially low SOC point to it’s maximum voltage.

The difficulty is that this needs to account for temperature, charge rate and accurate SOC estimation.

EV manufacturers like to calculate SOH using an equation of this form:

SOH = A x DOD + B x Rate + C x Environment Temperature + D x Calendar Life

This is quite complicated in terms of establishing the constants for each term.

We like to find the 50% SOC OCV, slow charge to 100% SOC, using charged capacity / 50% Initial Capacity to get the SOH.

Jerry Wan, Battery Expert at Shenzhen Mushang Electronics Co., Ltd

#### References

- A Closer Look at State of Charge (SOC) and State of Health (SOH) Estimation Techniques for Batteries, Analog Devices

#### State of Charge

State of Charge, abbreviated as SoC and defined as the amount of charge in the cell as a percentage compared to the nominal capacity of the cell in Ah.