First of all you should state what is the purpose of such test. In the case of asynchronous motors, the test is used to evaluate the parameters of the motor, in a similar way as the short-circuit test is carried out on power transformers. This is so, because in the induction machine, rotor currents are induced due to the flux created by stator currents, as a "secondary winding" of a power transformer (*).
This is not the case of synchronous machines. There is no induced fem in the rotor (in steady state). The flux linking the rotor winding being a DC magnitude, some parts of the magnetic circuit of the rotor (or even the whole rotor) are usually made of solid steel.
Therefore, if you perform the blocked rotor test on a synchronous machine you will find large eddy currents developping in the rotor mass, big losses, and even large rotor induced emf resulting in dangerous voltage developped at rotor terminals because its high number of turns.
So the question still remains: ¿what is the purpose of this test?
(*) the rotor frequency is reduced due to the small relative speed between the rotating air gap field and the rotor winding.
Kunal, I am not sure that this test allows you to know the current in the damper windings. What you can obtain is the global equivalent current, as seen from the stator, due to all currents flowing in the rotor (not only in damper windings, but also in the excitation winding and in every conducting parts where induced currents can be developped). I don't think you will be able to obtain the damper flux separately.
In any case you should perform the test under the same circumstances found in real operation, that is, with the excitation winding shorted, or closed across a resistor of low ohmic value, in order to avoid excessive induced voltages between rotor terminals that could damage the insulation. Should the induced voltage with the excitation winding open-circuited were small enough, you can also measure the influence of the contribution from this winding, by taking two measurements, with this winding open- and short-circuited, respectively.
I would highly recommend using low frequency supply in the stator winding. I assume that any other equipment connected to the excitation winding (static exciter, rotor protections, etc) can be properly removed/isolated during the test. Finally, I think that other alternative to blocked-rotor test is the slip test usually made to determine d- and q- stator reactances, because in both cases, the relative speed between rotor and the rotating field is small.
Locked Rotor Test is used to determine subtransient reactances. In case of salient poles machine, the rotor must be locked in a certain position and only two phases are energized.
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