The train is a small world moving through a larger world - Niraj Kumar

I believe not. Usually the HOG systems themselves are developed concurrently for both locomotives and coaches after a standard is defined for HOG. And also there is nothing inherently HOG or non-HOG about the rake (Except probably for the option to switch between EOG and HOG). Electrically, they can always a develop a HOG system for the locomotive that is compatible with whatever connections are available in the coaches. In our case, the problem came up because of our Jugaad way of doing things. The WAP5/WAG9 design was independently developed and did not factor in any of the design specifications of the LHB coaches. So they had to come up with a way to make both of them compatible for HOG.
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And at that time IR itself had not finalized any spec for a HOG system. A simple (but ingenious I'd say) system was developed for a bunch of WAM4 and WAP1 locomotives that was soon abandoned as the focus shifted to 3 phase locos.
A better example of HOG system is visible in the west. Many trains (even those with diesel locomotives) don't run with separate power cars. The loco itself houses the entire system and just powers the coaches directly without requiring an intermediate power car. The WAM4 and WAP1 designs too did the same earlier, until they were superseded by the EOG based later design.

It is also the only train in IR to have been hauled by all WAP class locos operated so far. The WAP1 was specifically developed for this train. Later to improve the speeds, it was tested with the WAP2 locos, and later run with WAP3 locos. Subsequently, the WAP6 was developed as another high speed locomotive for the Raj. When all these experiments did not succeed, it continued operations with the WAP4 and WAP5, and now runs with a HOG WAP7.
The Howrah Raj was also the first passenger train doubled-headed by WAP class locos. In the 80's, for a while, the train was run with twin WAP1 locos. 30 years later, the experiment has now been...
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revived with the twin WAP5 hauled BCT special Raj.

rakes do need modification to go HOG
a good example of that are the EMU's in Mumbai. for years, having stayed in DC traction, we were never aware about what it meant to have neutral zones :P so once Mumbai started going under AC, areas progressively started getting the feel of lights and fans going off randomly, in middle of no where during your journey. the problem got more attention once they moved beyond Kalyan/Borivali and eventually the problem was solved by having a small pair of LED lights in coach that stayed lit even in NZ (the main lighting supply+fans go out).
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long distance trains too the lighting supply is on battery, but AC supply isn't, and that is affecting cooling
hence wanted to know if the imported rakes had such problems originally.

Ah, I wasn't thinking on those lines. I was only talking about the feasibility of using the coaches with a HOG locomotive. The nuisances with neutral zones and other issues not withstanding, the coaches themselves just operate off on the power they receive through the feeder cables. As long as the power supplied matches the specs for the coach's electrical systems, the source of the power should not matter. In that sense I mentioned that the rakes should be HOG capable.
Features like load shedding have to be added to the coaches to deal with long neutral sections, but these are just minor modifications and the bulk of the coaches electrical systems should not require any redesign....
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Also, now they are moving towards PTFE type of neutral sections. These are suitable for high speeds and the neutral section is less than 10 meters long compared to the earlier ones which were usually 41m or longer and also had some severe speed restrictions depending on the layout.