I had this issue on my Ford C-max 2008, always on cold
mornings and would happen on the same road going to
work. The headlights would dim, then the ESP light and ABS light would come on followed by an engine Malfunction warning. Had to stop the car, switch off the engine (the turbo would wind down slowly and the interior lights would flicker).Gave it a minute, restarted and all was good.

I brought a cigarette lighter plug that displayed the Voltage.
I started the car on a cold night and put on the lights, heating, heating fan etc everything to simulate the travel
to work on a cold morning.

The car plugin showed me (before statup) that the voltage was at 12.6V and after startup at 14.6V which is about right. After a while I saw the voltage drop and rise like a
sinusoidal wave form (constantly dropping & rising) and the headlights dimmed with the voltage drop.

I started turning things off in the car and tried different combinations, in the end I discovered it was the internal heater element that was causing the issue, if I put on maximum heat.