State of Health (SOH) Estimation
The SOH of a battery can also be expressed as its lifespan. Battery lifespan can be divided into two types based on different usage conditions: storage lifespan and cycle lifespan.
Storage lifespan represents the aging phenomena and results of a battery during storage. During storage, the battery capacity irreversibly decreases, and the self-discharge rate varies greatly depending on the storage environment. Therefore, the acceleration or deceleration of the battery aging rate depends on the storage environment. Storage temperature is a major factor affecting storage lifespan and self-discharge. Compared to room temperature, higher battery storage temperatures make side reactions (such as corrosion) more likely, and the loss of metal cations is more severe; while at low temperatures, the diffusion of substances and electrochemical reactions decrease, thus reducing the battery aging rate. Another factor affecting battery storage lifespan is the SOC value during battery storage (here, SOC is defined as the ion ratio on the electrodes). At the same storage temperature but different battery storage SOCs, the battery aging path differs. At high SOCs, a large charge imbalance exists at the electrode/electrolyte interface, which promotes electrochemical reactions.

Cycle life represents the impact of battery use (charging and discharging) on the battery. Battery aging occurs continuously during both charging and discharging. The temperature and current during battery use directly affect cycle life. In addition, factors affecting battery storage life also influence cycle life, as related reactions occur regardless of whether the battery is in use or at rest. Battery use is an exothermic process; increased temperature accelerates these reactions, thus accelerating battery aging. Besides these variables, parameters related to cycle life are functions of the battery's state of charge. The amount of charge lost during a single discharge (change in state of charge) is a crucial factor with a significant impact on battery aging. This phenomenon is primarily due to the degradation of the positive electrode and the formation of the SEI film during high-current charging and discharging.
1. Definition of State of Harm (SOH) in Batteries
Different definitions of SOH can be derived from different perspectives. Currently, commonly used definitions in battery research include the internal resistance definition, the depth of discharge definition, and the remaining charge definition.
(1) Internal Resistance Definition Method
The battery's state of health deteriorates as its internal resistance gradually increases. The battery's state of health (SOH) can be defined based on this relationship:

In the formula, RNEW represents the battery's internal resistance at the time of manufacture; REOL represents the internal resistance at the end of the battery's lifespan; and R represents the battery's internal resistance in its current state.
The key to this definition is obtaining an accurate value for the battery's internal resistance. Its advantage is relatively accurate measurement results, but its disadvantage is that it does not consider the battery's rated capacity, which is significantly affected by the battery's state of health (SOH).
(2) Definition of Depth of Discharge (SOH)
The depth of discharge (SOH) of a battery refers to the ratio of the capacity discharged by the battery to its own capacity. This ratio is inversely proportional to the number of times the battery can be recharged; that is, the greater the depth of discharge, the fewer the number of times it can be recharged. Therefore, SOH can be defined from the perspective of the depth of discharge as: the percentage of the remaining number of recharges to the maximum number of recharges at a given depth of discharge.

(3) Definition of Remaining Capacity
The State of Charge (SOH) is defined from the perspective of the remaining capacity of the battery. After a period of use, the remaining capacity of the battery can be directly measured. Therefore, let Cnew be the maximum capacity of the battery when unused, and Cnorm be the maximum usable capacity of the battery. Then, SOH can be defined as...


