Question

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_________$\Omega$

• A. 5.33

Answer 1

The correct option is A 5.33
For 3-$\varphi$ transmission line we can use relation,

$X_1=X_s-X_m$ ...(1)
$X_0=X_s+2X_m$ ...(2)
Also given, $X_0=32\Omega and{X}_1=16\Omega$

$\therefore$ Solving (1) and (2) simultaneously,

$X_s-X_m=16$
$X_s+2X_m=32$
(-) (-) (-)
$-3X_m=-16$

$X_m=\frac{16}{3}\underset{–}{\sim }5.33\Omega$