Written by Euan McTurk, Electrochemist at Dukosi.
 

What are State of Charge and State of Health?

State of Charge (SOC) and State of Health (SOH) are commonly-encountered phrases when dealing with lithium-ion cells and battery packs, but are often misunderstood or confused with each other.  Here, we give a brief explanation of what each term means.

SOC refers to the remaining charge in a cell as a percentage of the charge contained by the cell when it is full.  We cannot accurately determine the charge remaining the cell without fully discharging it first, so the calculation for SOC is usually performed by subtracting the charge removed from the cell so far from the charge contained when it was last charged to 100% SOC:

 SOH has two common definitions, depending on the application.  For electric vehicles (EVs), the capacity of the lithium-ion cells in the battery pack is key to determining the range that can be achieved by the vehicle on one charge.  Therefore, the SOH of an EV battery pack is measured by SOHE, which refers to the change in the amount of charge that the cells can hold as they age.  Over a successive number of cycles, the capacity of a lithium-ion cell will drop due to a number of factors including loss of lithium inventory and degradation of the electrodes inside the cell.  As a result, if an aged cell is charged up to its maximum voltage and discharged to its minimum voltage, the charge obtained from the cell will be less than that of when it was new.  SOHE is an expression of this change in capacity as a percentage of its original value, thus:

Hybrid vehicles operate their battery packs over a much smaller State of Charge (SOC) window than EVs, for example between 25% and 75% SOC, and use the electric drivetrain to assist the internal combustion engine or absorb energy under regenerative braking.  As such, the total capacity of the cells is less important than the ability of the battery pack to provide power to the electric motor.  As cells age and degrade, their internal resistance increases, which results in a drop in voltage for a given load and negatively impacts on their ability to provide peak power to the electric motor.  This has led to the definition of SOHP, which quantifies the health of the cell as a function of its increasing internal resistance as it ages:

It can be seen from the above formulae that SOC is relative to the capacity of the cell in the present, whilst SOHE and SOHP are functions of the capacity and internal resistance of the cell when it was new, respectively. For example, an aged cell may have 80% of the capacity of when it was new when it is fully charged, and therefore be at 80% SOH.  Despite losing 20% of its capacity, it is still at 100% SOC when it has been charged to its maximum voltage.

SOC and SOH each present their own challenges when designing a battery management system (BMS).  As SOH decreases over successive cycles, the BMS must attempt to monitor the change in capacity of the cell, which is made more difficult by the fact that cells are rarely fully charged and fully discharged routinely in real-world applications such as electric vehicles and grid storage.  SOC determination is commonly performed using voltage sensing and coulomb counting (measuring the cumulative charge passing through the cell), so the latter method is compromised as the cell’s SOH, and therefore capacity, decreases if the BMS algorithm does not take this into account.  Additionally, as the internal resistance of the cell increases, the overpotential (i.e. the change in the voltage when the cell goes from resting to either charging or discharging) also increases, which means that the SOC algorithm of the BMS will be negatively impacted if it does not factor in changes in the voltage profile of the cell as it ages.