## Internal Resistance is your enemy

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

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

A cell internal resistance has two major effects:

- it dissipates energy when a charge or discharge current flows through the cell
- it reduces the effective charge and discharge voltages

**No current:**the internal resistance does not dissipate energy and the voltage measured at the terminals (V) is equal to the “open circuit voltage” or “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 A | unit | Cell 1 | Cell 2 |

Cell internal resistance | milliohm | 0.4 | 0.6 |

Voltage drop in a cell | V | 0.04 | 0.06 |

Voltage drop in a 12V pack | V | 0.16 | 0.24 |

Energy dissipated in cell | Watt | 4 | 6 |

Energy dissipated in 12V pack | Watt | 16 | 24 |

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

#### So what?

- 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 spira

Cell (or battery) internal resistance can be estimated quite easily with two measures of discharge current (I) and corresponding cell (or battery) voltage (V).

Before each measure you need to have a stable current then wait about 30 seconds for the voltage to stabilise (this will measure an aggregate internal resistance made of the pure ohmic resistance – that is given by the manufacturer – with the influence of electrochemical reactions and polarization)

- with a discharge current less than 5 A: record I1 and V1
- with a discharge current at above 25 A: record I2 and V2

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

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 weightcan 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 should be lower for cells with high internal resistance (supposing the manufacturer is reputable and provides real measured data they can reproduce consistantly!)

## Pack made of 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 cylindrical or pouch 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 many cylindrical or pouch cells are careful to match cell internal resistance and capacity within a pack.

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

**“A 20% difference in cell internal resistance between two cells cycled in parallelcan lead to approximately 40% reduction in cycle lifewhen compared to two cells parallel-connected 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

*Note: other studies came to similar conclusions and although they use test conditions with current sufficient to increase cell temperature, this is something to consider when buying or assembling a battery pack for off-grid energy storage we want to last 10 or 15 years.*

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