Internal Resistance is your enemy!

Internal resistance (IR) is a characteristic of a battery cell that is often overlooked.  It is in fact one of the most important characteristics.

Why is it important?
What is the impact of having cells with different internal resistance?

I will cover a bit of theory and translate the research results into practical impact…

The “simplified” theory

The Internal Resistance (IR) of a battery is a complex system with interrelated resistive, capacitive and inductive behaviors.  I will simplify to the extreme by representing a battery as a pure voltage source in series with a resistance.

IR varies with the cell capacity (C), the state of charge (SOC), the temperature, the cell state of health (SOH), the cell technology, and the rate of current going through the cell.

Typical IR for a 100 Ah cell is under 0.6 milliohm, and less than 0.4 milliohm for cells above 300 Ah (Winston data).  There are significant variances depending on cell technology and manufacturing process.

Special equipment is required to measure the different components of the internal resistance (ohmic, electrochemical, polarization…).  Most BMS use algorithms to estimate IR and although the measure they give is different from the manufacturer’s specification, those estimates are consistant over time and can be used to quantify cell ageing (state of health). 

Internal resistance limits the charge and discharge current

High cell internal resistance has two major impacts:

  1. more energy is dissipated when charging or discharging
  2. effective charge and discharge voltages are reduced

Here is what happens in different situations:

  • No current: the internal resistance does not dissipate energy and the voltage measured at the terminals (V) is equal to the “open circuit voltage” (Voc)
  • Charge: energy is dissipated in the internal resistance with a corresponding voltage drop (Vir) – the voltage measured at the terminals (V) is higher than the actual (effective) cell charging voltage
  • Discharge: energy is dissipated in the internal resistance with a corresponding voltage drop (Vir) – the (effective) voltage measured at the terminal (V) is lower than the actual voltage delivered by the cell

Example with a charge / discharge current of 100 A and two cells of different internal resistance:

Current = 100 AunitCell 1Cell 2
Cell internal resistancemilliohm0.40.6
Voltage drop in a cellV0.040.06
Voltage drop in a 12V packV0.160.24
Energy dissipated in cellWatt46
Energy dissipated in 12V packWatt1624

The voltage drop and the dissipated energy is directly proportional to the cell internal resistance and to the current.

So what?

  • to avoid too much heat, the continuous charge / discharge current needs to be lower for cells with higher internal resistance
  • under the same charge / discharge current, the cell with higher internal resistance will get warmer, and will age faster (which will increase it’s internal resistance even more… and go into a death spiral

the internal resistance of a cell can be estimated quite easily with two measures of discharge (or charge) current (I) and corresponding voltage measured at the terminals (V):

  1. discharge (or charge) current less than 5 A: record I1 and V1
  2. discharge (or charge) current above 25 A: record I2 and V2

Internal Resistance = (V1 – V2) / (I2 – I1)

Before each measure the current must be stable, then wait about 30 seconds for the voltage to stabilise (this will measure an aggregate internal resistance made of the pure ohmic resistance (the resistance given by the manufacturer) plus any resistance created by the electrochemical reactions and polarization).

There are different types of elementary lithium cells (cylindrical, pouch, large prismatic) and different ways to assemble them in order to produce large capacity cells or batteries… which will have different characteristics (capacity, size, weight, internal resistance, maximum continuous current…)

I do not believe that two cells of the same capacity but very different weight
can deliver the same energy over the same lifetime!

When buying lithium battery cells you should check and compare the internal resistance as well as all other characteristics specified by the manufacturers 

You can also check the maximum continuous current recommended by the manufacturer as it will be lower for cells with high internal resistance (supposing the manufacturer is reputable and provides real measured data they can reproduce consistently!)

Pack made from cells with different internal resistance

If the cells in a pack have different internal resistance, the current will have an uneven distribution between cells in parallel, and the voltage will have an uneven distribution across cells in series.  This will result in:

  • cells not charging and discharging at the same rate (therefore creating cell unbalance)
  • reduced pack capacity
  • faster ageing of some cells

This is something to watch for when you buy cells (or batteries)
assembled from 100’s of small cells

The internal resistance of a cell is not a parameter directly controlled in the manufacturing process but is the result of a number of raw material and manufacturing parameters.  It is therefore expected to see some significant internal resistance variances between cells (some research papers mention variances of 20% or more).

Reputable manufacturers who produce batteries by assembling 100’s of small capacity cells are careful to match cell internal resistance and capacity within a pack. They are usually more expensive!

It is also important to carefully inter-connect the cells in order to reduce each connection resistance. Interconnection resistance has the same effects as cell internal resistance.

“A 20% difference in cell internal resistance between two cells cycled in parallel
can lead to approximately 40% reduction in cycle life
when compared to two cells with very similar internal resistance”

“Internal resistance matching for parallel-connected lithium-ion cells and impact on battery pack cycle life”
April 2014  Journal of Power Sources 252:8-13

A single cell with an internal resistance significantly different from the other cells can drastically reduce the lifetime of the pack