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

Typically the lifetime of the cell is split into 2 parts:

**calendar ageing**– where the cells are held at different fixed temperatures and SoC.**cycle ageing**– where the cells are cycled through a complete charge discharge at different fixed temperatures.

Thus allowing the measurements and modelling to be broken down.

Authors: Ma’d El-Dalahmeh

This work presents a state of health (SOH) estimation of lithium-ion batteries based on advanced signal processing technique called empirical wavelet transform (EWT) and deep-learning neural network. The proposed approach first performs features extraction using WT for health degradation, and then the extracted features are used to train a deep neural network to estimate the state of health in the battery. The proposed approach is validated using NASA and Stanford University experimental datasets.

Authors: Mo’ath El-Dalahmeh

- This work has presented a novel online RUL prediction of LiBs known as SPF algorithm.
- Obtained results clearly indicated that the proposed SPF algorithm can improve the prediction accuracy compared with the classical PF algorithm. The average RUL errors and PDF width of the SPF approach are less than in PF methods, demonstrating that the suggested method is more accurate and steadier.
- RUL prediction was tested with various predicted starting points to assess whether the amount of data influenced the accuracy of the prediction. The findings clearly demonstrated that the amount of data affects the accuracy of the prediction.
- It has also been shown that the earlier the starting point of the prediction, the higher the prediction error rate relative to the higher starting point.
- The proposed approach achieves a more accurate RUL prediction than the traditional capacity-based approach. The results show that the proposed physics-based approach, which extrapolates the degradation parameters, can provide a more accurate and conservative RUL prediction when compared to extrapolating just the capacity.

#### 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.