This is explained in most electrical engineering text books. You might try the IEEE Brown book or one of the other power system analysis references in faq238-1287.
It is actually rather difficult to calculate the time constants starting with the basic parameters = inductances and resistances. I have seen this discussed in some detail in the "EMPT Theory book" of H.W.Dommel and, more recently, in the book "Power system modelling and fault analysis" of N. Tleis.
The simplest case is that of a three phase fault at the terminals of the generator. The method is roughly the following:
Write equations for the voltages over all windings of the generator: Voltage = the time derivative of the flux linkage + the resistive voltage drop. (Some simplifying assumptions may be needed?) This gives a set of linear differential equations. Turn the crank (as my professor used to say), and out comes a set of time constants. Then just sort out, which time constant is which. It is easiest to start with a generator model with only one winding in the rotor, the field winding.
ijl, I would agree with respect to your statements on generators. I was thinking in terms of utility supplied systems. I shouldn't make such assumptions.
Can the OP provide any more information on the type of system under consideration?
