Hi all,
i also had some issues with the battery on my i20N in the cold times when it happens that i don't drive the car for some weeks. I did some research on that as i was not completly satisfied with the answer from the Hyundai Dealer that everything is ok. They were very friendly and helpful to do a check of the alternator!.
It's like this:
The i20N have not only a BMS (Battery Management System) there is also a AMS (Alternator Management System) which controls the power output from the alternator and the SOC & SOH of the battery.
Indeed the OEM Battery is a kind of AGM Type.
The AMS try to keep the Charging State of the battery between approx. 60% and 90%.
(As the AGM is designed for more cycles and is able to load and unload with a higher current compared to normal lead acid, as a prerequisite for ISG).
I've done some measerment to check the behavior of the AMS and i found out that if the battery is above approx. 70% of SOC the alternator is not generating power when you are under normal driving conditions (accelerator is engaded). When you go off the throttle and using the brake momentum from the engine the alternator came to life and delivers a high amount of charging current. If you accelerate the alternator is switched off again.
In case that the SOC will drop under approx. 60-70% the AMS provide continuously power until the SOC is back to around 90%.
If there is a high amount of current needed (as example: headlight on, window heating, etc..) the alternator will also deliver continuously the needed power and charge the battery or even will not discharge it.
As notice the ISG is also a part of the strategy and will also work only if the SOC is within these parameters.
All functions are interconnected and coherent controled by the ECU any many more parameters then i know.
I think the cause why the the car is doing so is simply to safe gasoline.
So what is my conclusion of that exercise:
It's not like older cars, if you drive 30-40km your battery isn't fully recharged!
If you want to charge your battery while driving, turn on headlight.
If the car is parked for a longer time, recharge your battery every 2 weeks, or disconnect the battery when you have a safe place as there is no central locking and burglar alarm.
Everything of this is based on my observation with my german spec. i20N.
I hope this will help you to understand the way the battery charging works on our i20N

.
Best regards
Alexander