A 100-MV A, 22-kV, 50-Hz synchronous generator is operating open circuited and is excited to give rated terminal voltage. A 3-phase (symmetrical) short circuit develops at its terminals. Neglecting dc and double frequency components of current. (a) find the initial current, and (b) find the

Question

A 100-MV A, 22-kV, 50-Hz synchronous generator is operating open circuited and is excited to give rated terminal voltage. A 3-phase (symmetrical) short circuit develops at its terminals. Neglecting dc and double frequency components of current.

(a) find the initial current, and

(b) find the current at the end of two cycles and at the end of 10s.

Given:

Base 100 MV

[latex] X_{d}=1.0 pu , X_{d}^{\prime}=0.3 pu , X_{d}^{\prime \prime}=0.2 pu[/latex]

[latex] au_{d w}=0.03 s , au_{f}=1 s[/latex]

Accepted Answer

(a) Initial current, [latex] I^{\prime \prime}=\frac{E_{f}}{X_{d}^{\prime \prime}}=\frac{1}{0.2}=5 pu[/latex]

[latex] I_{ ext {Base }}=\frac{100 imes 1000}{\sqrt{3} imes 22}=2624 A[/latex]

Then [latex] I^{\prime \prime}=5 imes 2624=13120 A[/latex]

(b) [latex] I^{\prime}=\frac{E_{f}}{X_{d}^{\prime}}=\frac{1}{0.3}=3.33 pu[/latex]

[latex] I=\frac{E_{f}}{X_{d}}=\frac{1}{1}=1 pu[/latex]

[latex] I_{S C}(t)=(5-3,33) e^{-t / 0.03}+(3.33-1)^{e-t / 1}+1[/latex]

[latex] =1.07 e^{-t / 0.03}+2.33 e^{-t}+1[/latex]

[latex] t(2 ext { cycles })=1.67 e^{-0.04 / 0.03}+2.33 e^{-0.04}+1[/latex]

= 3.68 pu or 9656 A

[latex] I_{S C}(10 s )=1.67 e^{-10 / 0.03}+2.32 e^{-10}+1[/latex]

= 1.0001 pu or 2624 A (steady-state is practically reached)

Question 8.37: A 100-MV A, 22-kV, 50-Hz synchronous generator is operating ...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions