Establishing the maximum cell discharge capability is difficult without understanding the design in detail. However, you can work towards establishing this limit with a number of measurements and calculations. The aim of this post is to describe that approach, the underlying physics, some of the measurements and calculations.

First of all though we need to look at the cell specification sheet as this really should define the maximum discharge C-rate or current along with the minimum cell voltage.

It will also give a temperature range over which the cell is able to deliver that discharge rate.

The downside of specification sheets is that they only give limited data and very often are not readily available.

We need to start with the fact that the cell is not a perfect source. It has an internal resistance. Symbolically we can show a cell with the internal resistance as a resistor in series.

R_{int} is the DC internal resistance, sometimes abbreviated as DCIR.

The DCIR is not just a single number for any given cell as it varies with State of Charge, State of Health, temperature and discharge time.

Applying Ohm’s Law we see that as the current increases the voltage drop is greater. This voltage drop being relative to the Open Circuit Voltage V_{OCV} and hence as the cell discharges the OCV drops too.

What we also see on this graph is a minimum cell voltage. This will be specified by the cell manufacturer. Let’s look at a typical 5Ah 21700 cell performance.

If we have an OCV of 3.7V @ 50% SOC and an internal resistance of 0.025Ω and we draw 10A from the cell the voltage will drop 0.25V This is simply Ohms Law.

V = 3.7V – 10A x 0.025Ω = 3.45V

Hence the voltage of the cell under a 10A load will be 3.45V.

We can also calculate the maximum current we can draw taking the cell down to the minimum voltage:

2.5V = 3.7V – I x 0.025Ω

Rearranging this we can calculate the current:

I = (3.7V – 2.5V) / 0.025Ω = 48A

These numbers are quite typical of a 5Ah NMC cell. Peak discharge is around 10C.

However, there are other factors that determine the maximum discharge rate.

### Maximum Current

The cell will be designed to deliver a maximum current versus time. This will be dependent on:

- the electrode stack
- maximum current density
- thickness of the stack
- uniformity of the discharge current

- current collector thickness and material
- connection points from cell tabs to current collectors
- cross-sectional area and material used in internal connections
- joint resistance

Comparing power versus energy cells we see there are some fundamental differences. A high energy cell will have better volumetric and gravimetric energy density at the expense of the ability to deliver a high current. The power cell will have a low internal resistance and will be optimised to deliver current over energy density.

If the discharge current is too high an element of the cell is likely to degrade or fail. Hence the need to understand the cell manufacturers maximum current specification.

This post has been built based on the support and sponsorship from: **Eatron Technologies**, **About:Energy**, **AVANT Future Mobility**, **Quarto Technical Services** and **TAE Power Solutions**.

### Measurements

**Open Circuit Voltage**– in battery measurements this is normally one of the first things to establish. It takes time and patience to establish the charge and discharge versions of these curves.

2. **DCIR** – the internal resistance of cell is the other important parameter. This changes with SoC, cell temperature, pulse length and SoH [1].

The DCIR of a cell is normally measured using a defined current against time pulse. Typically the pulse duration is from 1s to 30s and most quoted values are for a 10s pulse. The resistance is the maximum voltage drop divided by the current demand.

3. **Estimating Maximum Current** – using the graph and calculation as shown above you can use the measured OCV and DCIR to estimate the discharge current at the minimum cell voltage.

As per the example given for the 5Ah cell.

*I _{max} = (V_{OCV} – V_{min}) / DCIR*

4. **Measuring Maximum Current** – having estimated the maximum current it is good practice to check this data against the actual cell. It is advisable to approach this value rather than push the cell too far and damage it.

All of these measurements are going to take time as the maxumum current is dependent on lots of parameters. This is just one thought through approach and there are other methods for establishing this that we will add.

**Note: **you will need to establish a full measurement process and safety protocols.

#### References

- Barai, A., Uddin, K., Widanage, W.D. et al. A study of the influence of measurement timescale on internal resistance characterisation methodologies for lithium-ion cells. Sci Rep 8, 21 (2018)