Analytical and Simulation Study of Short Circuit Transients in Single Phase and Three Phase Synchronous Machines: Time-Domain Analysis and Rotor Angle Effects

This paper investigates the dynamic behavior of synchronous machines subjected to sudden short circuits. Initially, the case of a single-phase synchronous machine under open-circuit conditions is studied. Analytical derivations of short circuit current expressions are carried out and evaluated using numerical integration methods on a digital computer. The transient responses of both armature and field currents are analyzed, showing their dependence on rotor position and machine parameters. A SIMULINK model is developed to simulate and visualize these responses. Subsequently, the study extends to the case of a line-to-line short circuit in a three-phase synchronous machine with damper windings. The general voltage equations of the three-phase machine are derived and applied to the problem, with numerical integration and SIMULINK simulations confirming analytical insights. Results highlight the key influence of rotor angle, leakage inductance, and damper windings on the dynamics of short circuit currents.