This is effectively an electric locomotive with a relatively small auxiliary diesel prime mover intended only for low-speed or short-distance operation (e.g. British Rail Class 73).
The Southern Region of British Railways used these locomotives to cross non-electrified gaps and to haul boat trains that used tramways at the ports of Southampton and Weymouth.
The primary function for these models is to provide a "one-seat ride" (a rail trip that does not require a transfer to a different train) between the electrified and non-electrified sections of a rail system or to allow trains to run through tunnels or other segments of track where diesel locomotives are generally prohibited due to their production of exhaust; such locomotives are used for certain trains servicing the New York City terminals of Grand Central Terminal and Penn Station, as the various rail tunnels into Manhattan have exhaust restrictions.
With modern electronics, it is much easier to construct (or adapt) an electro-diesel locomotive or multiple-unit which is equally at home running at high speeds both "under the wires" and under diesel power (e.g. British Rail Class 88, Bombardier ALP-45DP).
These will normally operate under pure electric traction where possible, and use the diesel engines to extend the journeys along non-electrified sections which would not be cost effective to electrify.
Electro-diesel locomotives whose electricity source is 25 kV 50 Hz AC overhead line include: Several, primarily diesel locomotive types and a multiple-unit have been built to operate off a 750 V DC third rail into the New York City terminals of Grand Central Terminal and Penn Station (with the third rail system being rarely used on open-air tracks).