Three-Phase Short Circuit—Unloaded Synchronous Machine

The waveform amplitude decreases because magnetic flux from short-circuit armature currents initially follows high-reluctance paths, then shifts to lower-reluctance paths, increasing armature inductance. This dynamic behavior can be modeled as a time-varying series R-L circuit, causing the current to decay from its initial sub-transient peak toward a steady-state value.

The RMS sub-transient fault current at time zero is determined by the direct axis short-circuit sub-transient reactance and its associated time constant. These machine parameters, provided by manufacturers or derived from tests, are essential for calculating the instantaneous AC fault current based on the RMS line-to-neutral prefault terminal voltage.

Standard machine theory uses specific reactances—sub-transient, transient, and steady-state—to calculate instantaneous AC fault currents. These reactances, combined with time constants, enable engineers to predict how the system behaves under fault conditions, facilitating damage control strategies and maintaining system stability during power system three phase short circuits.

Each phase has a different DC offset because the peak offset depends on the initial current angle when the fault occurs. When the initial current angle equals zero, the DC offset reaches its maximum value. This phase-dependent behavior is critical for analyzing the complete fault current waveform across all three phases.

The oscillogram, with DC offset removed, shows how waveform amplitude decreases from an initially high value to steady-state level. This reveals the machine's transient response and the time-dependent shift in magnetic flux paths, providing insight into armature inductance changes and enabling accurate modeling of fault dynamics for system protection design.

Manufacturers supply machine reactances and time constants through specifications or derived from standardized tests. These parameters—including sub-transient, transient, and steady-state values—are crucial inputs for calculating fault currents and predicting machine behavior during faults, ensuring engineers can design appropriate protection and control strategies.

As magnetic flux shifts from high-reluctance to lower-reluctance paths, armature inductance increases, causing the fault current to decay toward steady-state. This increasing inductance effect is central to the time-varying R-L circuit model, explaining why the initial sub-transient current is much higher than the final steady-state fault current value.