Kamayani Express - Late आना है काम तुम्हारा लेकिन मैं फिर भी हूँ तुम्हारा दीवाना - Aman

HOG (Head-on generation) simply means that the electricity used for coaches (lighting, fans, A/C, pantry car cooking equipment etc) is generated by the locomotive. It is not related to electrification or OHE directly. In an electric loco, the power will come from the OHE. In a diesel loco, it will come from the diesel generator in the loco.

In an electric locomotive, since the electricity is supplied by the OHE, a locomotive having a HOG feature simply has some equipment in it which converts the power received from the OHE into something...
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suitable for powering the coaches.

In a diesel locomotive, the electricity is generated by the diesel generator (alternator). This electricity is normally used to run the traction motors and other equipment in the loco. But it is also possible to use part of this generated electricity to power the coaches. So, HOG diesel locos are the same as normal diesel locos, with just an additional option to use the electricity generated by the diesel generator for powering the coaches.