Sequence Networks of Transmission Lines, Synchronous Generator, Synchronous Motor

Q. In an unbalanced three-phase system, phase current $I_a$ = 1$\angle (-{90}^0)$ pu, negative sequence current $I_{b2}$ = 4$\angle (-{150}^0)$ pu, zero sequence current $I_{c0}$ = 3$\angle {90}^0$pu. The magnitude of phase current $I_b$ in pu is

1. 1.00
2. 7.81
3. 11.53
4. 13.00

Q. A 3-phase transmission line is shown in figure:



Voltage drop across the transmission line is given by the following equation:

$\left[\begin{array}{c}\Delta V_a\\ \Delta V_b\\ \Delta V_c\end{array}\right]=\left[\begin{array}{ccc}{Z}_s& Z_m& Z_m\\ Z_m& Z_s& Z_m\\ Z_m& Z_m& Z_s\end{array}\right]\left[\begin{array}{c}{I}_a\\ I_b\\ I_c\end{array}\right]$

Shunt capacitance of the line can be neglected. If the line has positive sequence impedance of 15$\Omega$ and zero sequence impedance of 48$\Omega$, then the values of Z${}_s$ and Z${}_m$ will be

1. Z${}_s$ = 31.5$\Omega$; Z${}_m$ = 16.5$\Omega$
2. Z${}_s$ = 26$\Omega$; Z${}_m$ = 11$\Omega$
3. Z${}_s$ = 16.5$\Omega$; Z${}_m$ = 31.5$\Omega$
4. Z${}_s$ = 11$\Omega$; Z${}_m$ = 26$\Omega$

Q. The parameters of a transposed overhead transmission line are given as:

Self reactance $X_s$ = 0.4 $\Omega$/km and mutual reactance $X_m$ = 0.1 $\Omega$/km

The positive sequence reactance $X_1$ and zero sequence reactance $X_0$, respectively, in $\Omega$/km are

1. 0.3, 0.2
2. 0.5, 0.2
3. 0.5, 0.6
4. 0.3, 0.6

Q. The parameters of transposed overhead transmission line are, $X_s=0.8\Omega /km$ and$X_m=0.2\Omega /km$. The value of negative sequence reactance $X_2$ and zero sequence reactance $X_0$ respectively will be $\left(in\Omega /km\right)$

1. 0.3, 0.6
2. 0.6, 1.2
3. 0.6, 0.9
4. 0.3, 1.2

Q. The series impedance matrix of a short $3-\varphi$ transmission line in phase coordinates is represented by Z,

$where,Z=\left[\begin{array}{ccc}{Z}_s& Z_m& Z_m\\ Z_m& Z_s& Z_m\\ Z_m& Z_m& Z_s\end{array}\right]$

If the positive sequence impedance is $(4+j16)\Omega$ and zero sequence impedance is $(8+j32)\Omega$, then value of imaginary of $Z_m$ is ________$\Omega$

1. 5.33