Constant voltage charging phase of Li-ion batteries

I've read on batteryuniversity.com that the constant voltage (saturation) stage of Li-ion charging adds approximately 10% of SOC compared to charging with only the constant current (CC) charging phase. For example when charging only with CC to 4.1 volt you get approximately 80% SOC, but with full adsorption approximately 90% state of charge can be achieved. Link: https://batteryuniversity.com/learn/article/charging_lithium_ion_batteries

I have not yet been able to find a good visual representation of the saturation stage of the charging and how it is different from the constant current stage of charging. What is a good visual representation of this?

There is clearly some current flowing into the battery while in the constant voltage (CV) charging stage, meaning electrons must be flowing. Wouldn't that mean the amount of free electrons trapped in the graphite layer would increase and thus the voltage would (slightly) have to increase? Or is my assumption that during the CV charging stage electrons are moving in the same way as they do during the constant current charging stage - albeit at a much slower speed - incorrect?

If my assumption is incorrect and the amount of electrons trapped in the graphite layer does not increase during CV charging, then what happens inside the battery that causes the SOC to increase during this charging phase?

Another question (regarding C-rates and saturation time): The same page on batteryuniversity.com mentioned that faster charging (higher C-rate) of Li-ion cells results in reaching a relatively high SOC (for example, 85% SOC) quicker than when charging with lower C-rate, but mentions that, when charging with this higher C-rate, the saturation stage of charging will take longer. What is the reason behind this? Does some of the 'saturation' already occur during the CC stage of charging? And because, when charging with a higher C-rate, there is less time spent in this CC stage of charging for a full charge, so will there be less time for the 'saturation' to happen? Does this (my) theory make any sense? What is the approximate difference in 'saturation time' when charging at different C-rates (for example, when charging at 0.5c vs. at 1c vs. at 2c)?

Even though saturation takes longer with higher C-rates, I would expect the total charge time to be lower since the average power going into the battery is higher (accounting for extra losses due to charging inefficiencies being higher with higher C-rates), unless the saturation stage is very significantly slower for higher C-rates, is this assumption (higher C-rate always equals faster total charge time) correct?

Last question (regarding image from batteryuniversity.com):

The text under the image at the top of my post reads "Adding full saturation at the set voltage boosts the capacity by about 10 percent but adds stress due to high voltage"

I don't understand why this would add extra stress when according to the charging graphs the voltage during the CV charge cycle is the same as the charger cutoff voltage. If for example charging to 4.1 volt (a voltage which is well within the specs for most Li-ion cells) and charging the cell to full saturation, would this prolonged charging at 4.1 volt (until the cell is fully saturated) be harmful to the cell?

Second example: Let's say we're charging to 4.2 volt, would this prolonged charging at 4.2 volt (to reach full saturation) be any more harmful to the cell than the CC charging up to this level (4.2 volt)? If the maximum voltage for CC and CV charging is the same, why would CV charging be more harmful to the cell? Because the average charging voltage is higher? Am I missing something?

• For what it is worth, that article says it has been updated recently, but most of the text is talking about early 2000s batteries, so do not take everything you read there as applicable to modern battery cells (although the general idea won't have changed much). Things like charging currents can be much higher in modern cells for example. May 29, 2021 at 4:16

I have not yet been able to find a good visual representation of the saturation stage of the charging and how it is different from the constant current stage of charging. Does anyone have/know of a good visual representation of this?

The 'saturation' stage isn't any different as far as the cell is concerned, it's just a result of the charger having to limit its terminal voltage for safety (the battery would otherwise continue charging to higher voltage and capacity - until it blew up).

To first approximation a rechargeable battery can be imagined as a large capacitor (which stores charge) in series with a small resistance (combination of ohmic resistances and limited mobility of the ions in solution).

Now consider a circuit where this combination is charged at constant current until reaching a voltage limit, after which current changes to the usual exponential decay of a capacitor charging from fixed voltage through a resistor:-

simulate this circuit – Schematic created using CircuitLab

I1 represents the charger's constant current and D1 the constant voltage. Batt is the exterior battery terminal and int is the internal part of the battery that holds charge.

Assuming the initial 'battery' (capacitor) voltage was 2.9 V, the result looks like this:-

wouldn't that mean the amount of free electrons trapped in the graphite layer would increase and thus the voltage would (slightly) have to increase?

The battery's terminal voltage must remain constant because the charger is holding it there, but its internal voltage (which lags behind due to voltage drop across the internal resistance) continues to increase until it eventually reaches the terminal voltage. You can see this in the blue line in the graph.

In this simulation the internal battery voltage (Vint) had only reached 4.0 V when the charger switched to constant voltage mode at 4.2 V. By the time charging current dropped to 10% it had risen to 4.18 V, and as charging continued it eventually reached 4.20 V.

A real Li-ion battery is of course much more complex than just a capacitor and resistor, which is reflected in its non-linear charge and discharge curves. Apart from that though the principle is the same. In fact any resistance in the charging circuit beyond the charger's voltage measurement point will cause a similar effect, including resistance in the wires and connectors. If external resistance between the charger and battery is significant you may see voltage at the battery terminals rising slightly in CV mode.

The text under the image at the top of my post reads " Adding full saturation at the set voltage boosts the capacity by about 10 percent but adds stress due to high voltage " I don't understand why this would add extra stress when according to the charging graphs the voltage during the CV charge cycle is the same as the charger cutoff voltage.

As you can see from this simple simulation, the battery does get greater voltage stress when charged to 'saturation'. If charging is stopped earlier the battery's resting voltage will be lower, causing less stress both during charging and afterwards.

• Is a capacitance of 1 farad realistic (not a rhetorical question)? May 29, 2021 at 12:59
• It's easy to see that 1 Farad (= 1 Coulomb/Volt) would be 1/3600 Ah for a battery with 1V range between flat and charged. For a 1Ah battery, try 3600F (but the simulation will be slower, lol!)
– user16324
May 29, 2021 at 13:13