what is the relation between excitation current from A.v.r and output voltage of generator? and what is the range value of excitation current and excitation voltage from the A.V.R to exciter field
The question is similar to how long is a piece of string? It will depend entirely on the design of your generator and excitation system. If you have a manual, you might get short circuit and open circuit curves plotted there - the relationship between excitation current and stator current and voltage respectively. Alternatively, you could carry out such a test. S/C - with the machine ISOLATED, apply a 3 ph S/C across the terminals. Then spin it up, and apply excitation in steps, measuring the stator current at each step and plotting it on a graph. It should be a straight line, as you will never be able to drive the core into saturation during S/C. For O/C, obviously leave the terminals O/C and do the same thing as before, this time measuring stator voltage at each step. This graph should flatten out after a few steps as the core becomes saturated. Reading off stator voltage against excitation voltage will give you the info you need. You should also have a generator capability diagram, which will let you know the range of operating ability.