Internal Resistance: DCIR and ACIR:- Let’s take a tiny step and understand how IR is measured in the first place.

How are resistances measured? A small current is injected into the component and voltage is measured across it and then resistance is calculated by R=V/I; yes! This is how a multimeter does its’ job; it’s not rocket science.

There are two different approaches followed in the battery industry to measure the internal resistance of a cell.

- DCIR (Direct Current Internal Resistance)
- ACIR (Alternating Current Internal Resistance)

### DCIR measurement

A short pulse of high current is applied to the cell; the voltages and currents are measured before and after the pulse and then ohm’s law (I = V/R) is applied to get the result. DCIR gives the sum of R_{int}, R_{1}, and R_{2} (Refer to figure 1).

The formula for DCIR measurement is,

DCIR = (V_{1} – V_{2}) / (I_{2 }– I_{1})

There are standards set by the regulatory body, which should be followed while measuring the DCIR of a cell. These standards are set for universality and apple-to-apple comparison. I will write about a few of the widely used ones.

- IEC 61960

In this standard, a discharge pulse of 0.2C is given for 10 seconds and V_{1} and I_{1} values are measured. Then, another discharge pulse of 1C is given for 1 second and V_{2} and I_{2} values are measured. Then, DCIR is calculated with the above-mentioned formula.

Then, DCIR is calculated by

DCIR = (V_{1} – V_{2}) / (I_{2} – I_{1})

- ISO 12405

In this standard; first, a discharge pulse of 1C is given for 18 seconds, then discharge at 0.75C for another 102 seconds and measure V_{1} and I_{1} values. Then, let the battery rest for 40 seconds and record V_{2} and I_{2} values.

Then, a charge pulse of 0.75C for 20 seconds is given and V_{3} and I_{3} values are recorded. Finally, rest the battery for 40 seconds and measure V_{4} and I_{4} values.

Then, DCIR is calculated by

DCIR (Discharge) = (V_{2} – V_{1}) / (I_{1})

DCIR (Charge) = (V_{3} – V_{4}) / (I_{3})

Figure 1: 2nd order Equivalent Circuit Model of a Li-ion Cell

### ACIR measurement

As the name suggests, ACIR means Alternating Current Internal Resistance. An alternating current of 100mA 1000 Hz is applied to the cell via ACIR measurement equipment. The working principle of this equipment is; applying the I_{ac} and then measuring V_{ac}. Then

Impedance Z = V_{ac} / I_{ac}

When measuring the impedance, there will be a phase shift. So, only the Real part is considered to measure the internal resistance ignoring the reactance part. ACIR gives R_{int} only (Refer to figure 1).

ACIR = Re (V_{ac} / I_{ac})

You can calculate the ACIR with the above formula. Beware, it’s complex!

Note: The Internal Resistance mentioned in the cells’ datasheet is ACIR.

### Why do all this hassle?

To sort cells and bin them to make a high-quality battery pack.

A stringent procedure has to be followed to make battery packs better and sorting cells’ IR is one of them.

Imagine a battery pack with cells randomly selected and put together. Every cell will have a different IR and hence a different current distribution which leads to different temperature distributions of the pack. This is a clear recipe for disaster and has to be avoided at any cost.

### ACIR or DCIR for sorting?

You can follow any one of the above procedures to sort cells. Since the procedure is the same for all the cells, thus sorting will be fair.

I would highly suggest going with ACIR as opposed to DCIR, as it slightly resembles real-life current excitation of a cell, especially in electric vehicles.

#### DCIR of a Cell

The DCIR of a cell is the Direct Current Internal Resistance. This is the resistance in charge and discharge to a direct current demand applied across the terminals.