Question: I am studying mathematical modeling of a battery in simulink and for this it is necessary to determine some parameters. I'm stuck in the part where I need to determine an alpha parameter, which would be the relation between capacity and temperature. Not all battery manufacturers provide this parameter and would like to know with the author or how I could get to the value of it to proceed with the study of the model. Below the discussion that deals with the subject and attached the paper about it.

[![enter image description here](https://i.stack.imgur.com/hLorS.png)](https://i.stack.imgur.com/hLorS.png)

Paper: <https://drive.google.com/file/d/1u__5DWaSZtZ60xpXi2b1eJa0bVuv8yyt/view?usp=sharing>

**UPDATE**

Looking for some manufactures data I found a data sheet with some informations I think can help me. So, with this specifications what is the value of alpha ?

[![enter image description here](https://i.stack.imgur.com/OEpSm.png)](https://i.stack.imgur.com/OEpSm.png)

Answer: 
Working with Li-ion or LiPo cells, I never heard of an *alpha* parameter in datasheets. But, usually you can easily find the discharge curves at various temperatures i.e. you can estimate a correlation coefficient between temperature and total capacity.
IEC 61215 standard requires this measurement for Li-ion and I believe the manufacturer must make the results of the testing available to the public. I have found the report for some batteries in the past. All I remember is I don't want to do that again. 

You can measure it. Follow the IEC 61215 testing methods. 

See: [*Temperature Coefficients Measured pre-post Thermal Stress Testing and Comparison of Four Measurement Procedures*](https://www.nrel.gov/pv/assets/pdfs/2014_pvmrw_65_riedel.pdf) 

This may not help but it may. Li-ion batteries have a thermistor for safety. You can access and use the thermistor to measure the temperature.

> 
> If at all possible, connect the thermistor during charging and
>  discharging to protect the battery against possible overheating. Use
>  an ohmmeter to locate the internal thermistor. The most common
>  thermistors are 10 Kilo Ohm NTC, which reads 10kΩ at 20°C (68°F). NTC
>  stands for negative temperature coefficient, meaning that the
>  resistance decreases with rising temperature. In comparison, a
>  positive temperature coefficient (PTC) causes the resistance to
>  increase. Warming the battery with your hand is sufficient to detect a
>  small change in resistor value when looking for the correct terminal
>  on the battery.
> 
> 
> 

Source: [*Battery University, How to Repair a Laptop Battery*](http://batteryuniversity.com/learn/article/how_to_repair_a_laptop_battery)

See also: [*Battery University, Making Lithium-ion Safe*](http://batteryuniversity.com/learn/article/bu_304b_making_lithium_ion_safe)