# Current Limit Estimation

There are a number of reasons to estimate the charge and discharge current limits of a battery pack in real time:

• adhere to current safety limits of the cells
• adhere to current limits of all components in the battery pack
• avoid sudden loss of power or even a need to shutdown

Hence this is a key function of the Battery Management System (BMS).

The difficulty is that the current limits are dependent on a number of factors, for the cell alone we should consider the following:

• prior state of the battery
• temperature of the battery
• age of the battery
• length of current demand
• state of charge of the battery
• cooling capability of the system

Put these factors together and this is a very non-linear function and there are several approaches to it’s estimation. Most methods use an Equivalent Circuit Model or an Adaptive Characteristic Map [4].

Instantaneously the BMS will adhere to the cell voltage limits, hence changes in SOC, temperature and internal resistance will all be accounted for in the cell chemistry. These voltage limits will have to be applied anyway, but they tend to be a hard stop. If the vehicle controller knows the current/power limits ahead of time then the battery pack can be protected and the user can be limited more gradually to avoid the sudden loss of power.

This post has been built based on the support and sponsorship of: AVANT Future MobilityQuarto Technical ServicesTAE Power Solutionsh.e.l group and The Limiting Factor.

These current limits are time dependent and constantly changing. Therefore, current limit estimation or State of Power (SoP) estimation is a continually evolving map. Typically the time window will be from 1 second to 30 seconds for an electric vehicle.

#### References

1. Sagar Bharathraj, Anshul Kaushik, Shashishekar P. Adiga, Subramanya M. Kolake, Taewon Song, Younghun Sung, Accessing the current limits in lithium ion batteries: Analysis of propensity for unexpected power loss as a function of depth of discharge, temperature and pulse duration, Journal of Power Sources, Volume 494, 2021
2. Jin, Z., Zhang, Z., Aliyev, T., Rick, A. et al., “Estimating the Power Limit of a Lithium Battery Pack by Considering Cell Variability,” SAE Technical Paper 2015-01-1181, 2015, https://doi.org/10.4271/2015-01-1181.
3. Voltage-Based Power-Limit Estimation, Lecture notes prepared by Dr. Gregory L. Plett. C
4. Alexander Farmann, Dirk Uwe Sauer, A comprehensive review of on-board State-of-Available-Power prediction techniques for lithium-ion batteries in electric vehicles, Journal of Power Sources, Volume 329, 2016