AVR and Exciter

Then it wouldn't be self-excited and would require slip-rings to inject the AVR output directly into the field.

This already exists and it is called brush exciter and the one you mentioned is called brushless exciter.. Being a self excited synchornous generator has nothing to do with whether the excitor is brush or brushless..

if we give AVR voltage directly to the alernator field ,then how is it brushed exciter.it should be just brushed alternator because the concept of using exciter would no longer exist . why do not we just use directly AVR with brushes coz i think alternator with brushes will be more Cheap than the one with excitor+rotating diodes+varistors. is it not ?

You call it brush alternator, or brush excitation system it is the same thing and I not sure an exciter as a part of the alternator do not exist with brush type as I don't have any experience with that type of excitation system. And to answer your question maybe you are right, by using brushes it is maybe more cheap but maintenance wise it is costly and intensive compared to the brushless type as you will need to change those brushes contineously when they wear out. Therefore, brush type excitation system is much preferable. I hope I was able to answer your question.

The product (DC current) and the transport mechanism (brushed/brushless) are being are being blended in this thread.

Traditionally the term "separately-excited" refers to excitation systems where the DC source is not physically associated with the main generator; i.e., a battery bank or a totally separate DC generaotr driven by a different prime mover.

The term "self-excited" refers to excitation systems that somehow derive their power directly from the generator terminals and/or its shaft; i.e., through a combination of PTs, CTs or from a PMG.

The brushed/brushless concept simply refers to how the AVR output and/or the Excitation current gets from the stationary frame to the rotor and into the field windings; i.e., through direct physical contact (brushed), or magnetically across an air-gap (brushless).

Although economics and maintenance are considerations, nothing in the above addresses the key difference between these systems, which is how they behave during a system disturbance. If the AVR/excitaion system derives its power solely from the terminal voltage of the machine, then a close-in short-circuit or severe system undervoltage event will deprive the excitation system of power just when it needs it the most. Contrast that with the action of either a PMG, CT, or separately powered system where the DC supplying the field is independent of the mains supply, and can provide additional current (Forcing) even as the terminal voltage is dropping rapidly. It is important to note that the brushed/brushless argument has no bearing on the discussion in this paragraph.

I fully agree with you, the last key difference that you mentioned is absolutely valid. But the discussion was about why brushless is mainly used instead of a brush excitation system and it wasn't about separate or self excitation systems. Because as you mentioned at the very end of your comment, brushless and brush concepts has nothing to do with how the excitation system reacts to the disturbances in the system, they are just a mean to provide the alternator's field the output voltage of the AVR.

By this I can say that a brush type can be used in self and separate excited system, and also a brushless type can be used in self and separate excited system. So the choice between a brush or brushless will burely come to economical and maintenance considerations and not system disturbances and stability.

I hope I explained my point clearly, everything you have said is correct and actually some points you mentioned were new to me in which I am gradeful you mentioned.