Initial and sustained short-circuits in synchronous machines: Analytical and graphical treatment of general gases of armature windings displaced by arbitrary angles, with applications to one-, two- and three-phase machines

A knowledge of the instantaneous values of armature and field currents, when an alternator is short-circuited, is becoming of increasing practical importance. These currents determine the rating of protective apparatus, mechanical stresses in the machine itself, possible damage to other equipment, etc. During the first few cycles, immediately after a short-circuit, the currents are usually much larger than those on sustained short-circuit, and gradually approach the latter values over a number of cycles. It is, therefore, necessary to distinguish between the initial and sustained values of currents, and formulas are deduced in this paper for both. The novel feature of the treatment consists in starting with a generalized unsymmetrical three-phase winding, also containing an external inductance in one of the phases. The Kirchoff equations are written and solved for this general case, and it is then shown how the formulas for the usual one-, two-, and three-phase machines can be directly derived from the general expressions, without considering the magnetic linkages in detail in each case. A graphical interpretation of the equations is also given, in the form of space-vector diagrams, in which the m. m. f s. vary according to the sine law in space but not in time.