Question

The amplitude of the sinusoidal symmetrical ac component of the three-phase short-circuit current of an unloaded synchronous machine decreases from a high initial value to a lower steady-state value, going through the stages of _____ and _____ periods.

Short answer

Therefore, the amplitude of the sinusoidal symmetrical ac component of the three-phase short-circuit current of an unloaded synchronous machine decreases from a high initial value to a lower steady-state value, going through the stages ofsub transientandtransient periods.

Step-by-step solution

write the formula of fault current.

Write the formula of instantaneous ac fault current.

Here, E_g is line-to-neutral prefault behind terminal voltage, X^"_d is a sub transient reactance, X^'_d is a transient reactance, $\alpha$is phase between i (t) and e (t) , T^"_d and T^'_d is a time constant.

Determine the answer.

Write the formula of initial and final fault current.

i ($\infty$) = $\frac{E_g}{X_d}$

i ($\infty )$= $\frac{E_g}{{X_d}^{"}}$

Here, i ($\infty$) is final current and i ($\infty$) is initial current, also known as sub transient and transient current.

Therefore, the amplitude of the sinusoidal symmetrical ac component of the three-phase short-circuit current of an unloaded synchronous machine decreases from a high initial value to a lower steady-state value, going through the stages of sub transient and transient periods.