How can I calculate the internal resistance of an alternator?
The source impedance is variable with load current and corrected by field current feedback to affect the mutual coupling.  Think of it as a current source controlled by voltage error.
You can measure the incremental impedance by deltaV/deltaI at different loads, but it is the battery in parallel that integrates the alternator current control to regulate voltage, with C being &gt;50kF and ESR defined by CCA(or CA at room temp)  for a 5V start drop in voltage for 30 seconds.

Since all batteries have memory (some more than others) a quick short restores the battery voltage due to many RC shunt equivalent circuits above chemical low voltage.

thus if CA=1000A @ 5V drop from 12.5V to 7.5V you get ESR=5 mOhm.

for RF additional RC or choke cap filters reduce the ESR at audio and RF frequencies.

EMI control is a separate issue.