# How can I know the relation in time between the cicles (showed in the SoC graphic) and the SoH?

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Jorge on 10 May 2023
Answered: Gokul Nath S J on 24 May 2023
I would like to do a stimation of the cicles in wich my battery will decrease its SoH. In the output of the simulation example you obteined a graphics timed in 10 hours, however, SoH decrease in that time (6 cicles) to 60%.
I would be grateful if somebody could tell me how can i know the relation between SoC and SoH.

Gokul Nath S J on 24 May 2023
Hi Jorge,
As per my understanding it seems that you would like to know the relation between and .
To estimate the cycles in which your battery will reach a certain State of Health () level, you can create a model that relates (State of Charge) and . One of the most commonly used models for this purpose is the empirical modified Peukert's equation, which is given by:
where:
• t: time to discharge the battery (in hours)
• C: battery capacity (in Ah)
• I: discharge current (in A)
• : State of Charge (in %)
• k: Peukert constant (unitless)
This equation can be rearranged to give an expression for the number of cycles to reach a certain level. Since is a function of the number of cycles, this equation can be used to estimate the cycles in which the battery will reach a certain level.
To relate and , you can use a battery health model based on the number of cycles and the depth of discharge (), which is given by:
Where:
• : cycle life factor (unitless)
• : cycle life exponent (unitless)
• : number of cycles (unitless)
• : Depth of Discharge (in %)
• : State of Health (in %)
To estimate the cycles in which the battery will reach a certain level, you can use both equations together. First, you can calculate the time t to discharge the battery from a known level using the modified Peukert's equation. Then, you can calculate the corresponding depth of discharge using the battery capacity and the discharge current. Finally, you can use the battery health model to estimate the after cycles with that . By iterating this process for different levels, you can estimate the cycles in which the battery will reach a certain level.
Further, note that the parameters k, , and depend on the battery chemistry and can be obtained from experimental data or literature. Also, the battery health model may need to be updated periodically as the battery ages and its behavior changes.
with regards,
Gokul Nath S J

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