Is battery charge efficiency related to its self-discharge?

Question

I've read a couple of research papers and technical user manuals concerning SOC estimation, all of which mentioned both charge efficiency and Self-discharge but did not mention whether these effects are related: charge efficiency is affected by temperature, rate of discharge, rate of charging and the current SOC of the battery, but is the self-discharge effect taken into account for determining the charge efficiency coefficient for low discharge rates?

Also, when manufacturers specify the charging efficiency coefficients in their datasheets, (not that I have seen any datasheets which do have it) do those coefficients model the self-discharge effect? in other words, will I have to subtract the self-discharge current from the charging current during current integration (coulomb counting) if I multiply the integral by the aforementioned coefficient?

Coulomb counting equation:

Equation Source: source

Answer 1

Coulombic efficiency is the ratio of charge extracted to charge inserted. It makes no assumptions about what causes the loss, and therefore incorporates self-discharge. Most battery types have very low self-discharge (< 1% per day), so at normal charge and discharge rates it is presumed to be insignificant.

However at low charge and discharge rates it does become significant. When 'trickle-charging' or 'floating' a battery, extra current is required to overcome the self-discharge. On discharge the battery may show lower capacity due to some of it being lost to self-discharge.

The 'charge efficiency' coefficient in your equation includes whatever self-discharge occurred when the value of η was measured, or if being calculated the self-discharge would be included in η(t).

Alternatively you could, as suggested, subtract the self-discharge current from I, but you would then have to change the definition of I to 'the charge/discharge current minus self-discharge current', and η to 'the coulombic efficiency without self-discharge'.

Answer 2

Self discharge good to take into account if charging current and self discharging current are comparable. In most cases with fast charging they are tens times smaller, and most impact to capacity related to temperature of the the cell and charging currents. Each cell have recommended charging current range, where efficiency of charging is good. Of course in case of bad cells, when self discharging current is significant - it must be taken into account, but it quite tricky to measure.

Answer 3

Charge losses depend on CC and CV rates for overvoltage as leakage is non-linear wrt overvoltage and charge losses are quadratic I^2ESR while power transferred is V*I(t)

So efficiency is more complex than what you show. Actual formula demands better specs on battery.

For example a Li Ion cell with CV at 4.2Vwill decay faster to 3.8V than below 3.8V and lead acid will also decay faster from 14.2 to 12.5V faster than below.

This can be estimated but unknown in question.