29.1 : 串联 R-L 电路瞬态

Consider a series R-L circuit.

When the switch closes at a time equal to zero, it mimics a three-phase short circuit in an unloaded synchronous machine.

Given zero fault impedance or a bolted fault, and zero initial current, the source angle determines the initial source voltage.

This circuit's KVL equation yields the total asymmetrical fault current, and its two components.

The AC fault current, also called the symmetrical or steady-state fault current, is a sinusoid.

The DC offset current decays exponentially with a time constant as the inductance to resistance ratio.

Its magnitude varies with the source angle, peaking when the source angle equals theta plus pi over two.

The largest fault current occurs at a specific source angle.

The rms asymmetrical fault current with maximum dc offset is then calculated and simplified by substituting the time constant and time in terms of cycles and frequency.

This current equals the rms AC fault current times an asymmetry factor and the rms current decreases as tau increases.

Higher reactance to resistance ratios yields higher values of rms current.